TSTP Solution File: ALG001^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ALG001^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n100.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:17:42 EDT 2014
% Result : Theorem 1.64s
% Output : Proof 1.64s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG001^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n100.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:23:51 CDT 2014
% % CPUTime : 1.64
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x170cab8>, <kernel.Type object at 0x152ac68>) of role type named g_type
% Using role type
% Declaring g:Type
% FOF formula (<kernel.Constant object at 0x13f8dd0>, <kernel.Type object at 0x152a758>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x170cab8>, <kernel.Type object at 0x152ad40>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))) of role conjecture named cTHM133_pme
% Conjecture to prove = (forall (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))):Prop
% Parameter g_DUMMY:g.
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))']
% Parameter g:Type.
% Parameter b:Type.
% Parameter a:Type.
% Trying to prove (forall (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% Found x0000:=(x000 (fun (x2:b)=> (P (Xh2 x2)))):((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 ((Xf2 (Xh1 Xx)) (Xh1 Xy)))))
% Found (x000 (fun (x2:b)=> (P (Xh2 x2)))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 ((Xf2 (Xh1 Xx)) (Xh1 Xy)))))
% Found ((x00 Xy) (fun (x2:b)=> (P (Xh2 x2)))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 ((Xf2 (Xh1 Xx)) (Xh1 Xy)))))
% Found (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 ((Xf2 (Xh1 Xx)) (Xh1 Xy)))))
% Found (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P (Xh2 ((Xf2 (Xh1 Xx)) (Xh1 Xy)))))
% Found (x1000 (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found ((x100 (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found (((x10 (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found (fun (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))) as proof of ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found (fun (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% Found (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))) as proof of ((forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))) as proof of ((forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))->((forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))->(((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))
% Found (and_rect00 (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% Found ((and_rect0 (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% Found (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% Found (fun (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))
% Found (fun (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (forall (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found (fun (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))
% Found (fun (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))))
% Found (fun (Xf2:(b->(b->b))) (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (forall (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% Found (fun (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (forall (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% Found (fun (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (forall (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% Found (fun (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (forall (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% Found (fun (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2)))))))) as proof of (forall (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))), (((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))->(forall (Xx:g) (Xy:g), (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy)))))))
% Got proof (fun (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))))))
% Time elapsed = 1.300448s
% node=165 cost=114.000000 depth=23
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (Xh1:(g->b)) (Xh2:(b->a)) (Xf1:(g->(g->g))) (Xf2:(b->(b->b))) (Xf3:(a->(a->a))) (x:((and (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy)))))) (Xx:g) (Xy:g)=> (((fun (P:Type) (x0:((forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))->((forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))->P)))=> (((((and_rect (forall (Xx:g) (Xy:g), (((eq b) (Xh1 ((Xf1 Xx) Xy))) ((Xf2 (Xh1 Xx)) (Xh1 Xy))))) (forall (Xx:b) (Xy:b), (((eq a) (Xh2 ((Xf2 Xx) Xy))) ((Xf3 (Xh2 Xx)) (Xh2 Xy))))) P) x0) x)) (((eq a) (Xh2 (Xh1 ((Xf1 Xx) Xy)))) ((Xf3 (Xh2 (Xh1 Xx))) (Xh2 (Xh1 Xy))))) (fun (x0:(forall (Xx0:g) (Xy0:g), (((eq b) (Xh1 ((Xf1 Xx0) Xy0))) ((Xf2 (Xh1 Xx0)) (Xh1 Xy0))))) (x1:(forall (Xx0:b) (Xy0:b), (((eq a) (Xh2 ((Xf2 Xx0) Xy0))) ((Xf3 (Xh2 Xx0)) (Xh2 Xy0))))) (P:(a->Prop))=> ((((x1 (Xh1 Xx)) (Xh1 Xy)) (fun (x3:a)=> ((P (Xh2 (Xh1 ((Xf1 Xx) Xy))))->(P x3)))) (((x0 Xx) Xy) (fun (x2:b)=> (P (Xh2 x2))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------