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Minlog loaded successfully
> ; ?_1: T
>
; proceed: (use-with Truth-Axiom ...)
; ok, ?_1 is proved. Proof finished.
> ; ?_1: F -> F
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: F from
; 1:F
; proceed: (use-with 1 ...)
; ok, ?_2 is proved. Proof finished.
> ; ok, predicate constant A: (arity) added
; ok, predicate constant B: (arity) added
> > ; ?_1: ((((A -> B) -> A) -> A) -> B) -> B
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: B from
; 1:(((A -> B) -> A) -> A) -> B
; proceed: (use-with 1 ...)
; ok, ?_2 can be obtained from
; ?_3: ((A -> B) -> A) -> A from
; 1:(((A -> B) -> A) -> A) -> B
; proceed: (strip)
; ok, we now have the new goal
; ?_4: A from
; 1:(((A -> B) -> A) -> A) -> B
; 2:(A -> B) -> A
; proceed: (use-with 2 ...)
; ok, ?_4 can be obtained from
; ?_5: A -> B from
; 1:(((A -> B) -> A) -> A) -> B
; 2:(A -> B) -> A
; proceed: (strip)
; ok, we now have the new goal
; ?_6: B from
; 1:(((A -> B) -> A) -> A) -> B
; 2:(A -> B) -> A
; 3:A
; proceed: (use-with 1 ...)
; ok, ?_6 can be obtained from
; ?_7: ((A -> B) -> A) -> A from
; 1:(((A -> B) -> A) -> A) -> B
; 2:(A -> B) -> A
; 3:A
; proceed: (strip)
; ok, we now have the new goal
; ?_8: A from
; 1:(((A -> B) -> A) -> A) -> B
; 2:(A -> B) -> A
; 3:A
; 4:(A -> B) -> A
; proceed: (use-with 3)
; ok, ?_8 is proved. Proof finished.
> ; ok, variable x: alpha added
; ok, variable y: alpha added
; ok, variable z: alpha added
> ; ok, predicate constant P: (arity) added
> ; ok, predicate constant Qpredconst: (arity alpha) added
> ; ok, predicate constant Rpredconst: (arity alpha alpha) added
> > > > > > ; ?_1: (all x.Q1 x -> Q2 x) -> all x Q1 x -> all x Q2 x
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: Q2 x from
; 1:all x.Q1 x -> Q2 x
; 2:all x Q1 x
; x
; proceed: (use-with 1 ...)
; ok, ?_2 can be obtained from
; ?_3: Q1 x from
; 1:all x.Q1 x -> Q2 x
; 2:all x Q1 x
; x
; proceed: (use-with 2 ...)
; ok, ?_3 is proved. Proof finished.
> > ; ?_1: (all x.Q1 x & Q2 x) -> all x Q1 x & all x Q2 x
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: all x Q1 x & all x Q2 x from
; 1:all x.Q1 x & Q2 x
; proceed: (split)
; ok, we now have the new goals
; ?_4: all x Q2 x from
; 1:all x.Q1 x & Q2 x
; ?_3: all x Q1 x from
; 1:all x.Q1 x & Q2 x
; proceed: (strip)
; ok, we now have the new goal
; ?_5: Q1 x from
; 1:all x.Q1 x & Q2 x
; x
; proceed: (use-with 1 ...)
; ok, ?_5 is proved. The active goal now is
; ?_4: all x Q2 x from
; 1:all x.Q1 x & Q2 x
; proceed: (strip)
; ok, we now have the new goal
; ?_6: Q2 x from
; 1:all x.Q1 x & Q2 x
; x
; proceed: (use-with 1 ...)
; ok, ?_6 is proved. Proof finished.
> > ; ?_1: all x Q1 x & all x Q2 x -> all x.Q1 x & Q2 x
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: Q1 x & Q2 x from
; 1:all x Q1 x & all x Q2 x
; x
; proceed: (split)
; ok, we now have the new goals
; ?_4: Q2 x from
; 1:all x Q1 x & all x Q2 x
; x
; ?_3: Q1 x from
; 1:all x Q1 x & all x Q2 x
; x
; proceed: (use-with 1 ...)
; ok, ?_3 is proved. The active goal now is
; ?_4: Q2 x from
; 1:all x Q1 x & all x Q2 x
; x
; proceed: (use-with 1 ...)
; ok, ?_4 is proved. Proof finished.
> > ; ?_1: all x Q x -> exca x Q x
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: F from
; 1:all x Q x
; 2:all x.Q x -> F
; proceed: terms required for hypothesis 2
> ; ok, Symm has been added as a new global assumption.
> ; ok, Trans has been added as a new global assumption.
> ; ?_1: all x,y.x R y -> x R x
> > ; ?_1: (all x.((Q x -> F) -> F) -> Q x) -> (all x Q x -> P) -> exca x.Q x -> P
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: F from
; 1:all x.((Q x -> F) -> F) -> Q x
; 2:all x Q x -> P
; 3:all x.(Q x -> P) -> F
; proceed: terms required for hypothesis 3
> > ; ?_1: (P -> all y Q y) -> all y.P -> Q y
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: Q y from
; 1:P -> all y Q y
; y 2:P
; proceed: (use-with 1 ...)
; ok, ?_2 can be obtained from
; ?_3: P from
; 1:P -> all y Q y
; y 2:P
; proceed: (use-with 2 ...)
; ok, ?_3 is proved. Proof finished.
> > ; ?_1: (exca x Q x -> P) -> all x.Q x -> P
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: P from
; 1:exca x Q x -> P
; x 2:Q x
; proceed: (use-with 1 ...)
; ok, ?_2 can be obtained from
; ?_3: exca x Q x from
; 1:exca x Q x -> P
; x 2:Q x
; proceed: (strip)
; ok, we now have the new goal
; ?_4: F from
; 1:exca x Q x -> P
; x 2:Q x
; 3:all x.Q x -> F
; proceed: terms required for hypothesis 3
> > ; ?_1: (all y.F -> Q y) -> (P -> exca y Q y) -> exca y.P -> Q y
>
; proceed: (strip)
; ok, we now have the new goal
; ?_2: F from
; 1:all y.F -> Q y
; 2:P -> exca y Q y
; 3:all y.(P -> Q y) -> F
; proceed: more than one usable hypothesis: 2 3
>
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