TSTP Solution File: SEU937^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU937^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n098.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 13:33:24 EDT 2014
% Result : Theorem 1.82s
% Output : Proof 1.82s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU937^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.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 11:43:46 CDT 2014
% % CPUTime : 1.82
% 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 0x15d7bd8>, <kernel.Type object at 0x15d7d40>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1400ab8>, <kernel.Type object at 0x15d7c68>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1400ab8>, <kernel.Type object at 0x15d7cf8>) of role type named c_type
% Using role type
% Declaring c:Type
% FOF formula (forall (F:(b->a)) (G:(c->b)), (((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))->(forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy))))) of role conjecture named cTHM48_pme
% Conjecture to prove = (forall (F:(b->a)) (G:(c->b)), (((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))->(forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy))))):Prop
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% Parameter c_DUMMY:c.
% We need to prove ['(forall (F:(b->a)) (G:(c->b)), (((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))->(forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy)))))']
% Parameter b:Type.
% Parameter a:Type.
% Parameter c:Type.
% Trying to prove (forall (F:(b->a)) (G:(c->b)), (((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))->(forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy)))))
% Found x1000:=(x100 x0):(((eq b) (G Xx)) (G Xy))
% Found (x100 x0) as proof of (((eq b) (G Xx)) (G Xy))
% Found ((x10 (G Xy)) x0) as proof of (((eq b) (G Xx)) (G Xy))
% Found (((x1 (G Xx)) (G Xy)) x0) as proof of (((eq b) (G Xx)) (G Xy))
% Found (((x1 (G Xx)) (G Xy)) x0) as proof of (((eq b) (G Xx)) (G Xy))
% Found (x200 (((x1 (G Xx)) (G Xy)) x0)) as proof of (((eq c) Xx) Xy)
% Found ((x20 Xy) (((x1 (G Xx)) (G Xy)) x0)) as proof of (((eq c) Xx) Xy)
% Found (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0)) as proof of (((eq c) Xx) Xy)
% Found (fun (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))) as proof of (((eq c) Xx) Xy)
% Found (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))) as proof of ((forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0)))->(((eq c) Xx) Xy))
% Found (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))) as proof of ((forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))->((forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0)))->(((eq c) Xx) Xy)))
% Found (and_rect00 (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0)))) as proof of (((eq c) Xx) Xy)
% Found ((and_rect0 (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0)))) as proof of (((eq c) Xx) Xy)
% Found (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0)))) as proof of (((eq c) Xx) Xy)
% Found (fun (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))))) as proof of (((eq c) Xx) Xy)
% Found (fun (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))))) as proof of ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy))
% Found (fun (Xx:c) (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))))) as proof of (forall (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy)))
% Found (fun (x:((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))) (Xx:c) (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))))) as proof of (forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy)))
% Found (fun (G:(c->b)) (x:((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))) (Xx:c) (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))))) as proof of (((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))->(forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy))))
% Found (fun (F:(b->a)) (G:(c->b)) (x:((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))) (Xx:c) (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))))) as proof of (forall (G:(c->b)), (((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))->(forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy)))))
% Found (fun (F:(b->a)) (G:(c->b)) (x:((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))) (Xx:c) (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0))))) as proof of (forall (F:(b->a)) (G:(c->b)), (((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))->(forall (Xx:c) (Xy:c), ((((eq a) (F (G Xx))) (F (G Xy)))->(((eq c) Xx) Xy)))))
% Got proof (fun (F:(b->a)) (G:(c->b)) (x:((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))) (Xx:c) (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0)))))
% Time elapsed = 1.503277s
% node=176 cost=349.000000 depth=19
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (F:(b->a)) (G:(c->b)) (x:((and (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy))))) (Xx:c) (Xy:c) (x0:(((eq a) (F (G Xx))) (F (G Xy))))=> (((fun (P:Type) (x1:((forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))->((forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:b) (Xy:b), ((((eq a) (F Xx)) (F Xy))->(((eq b) Xx) Xy)))) (forall (Xx:c) (Xy:c), ((((eq b) (G Xx)) (G Xy))->(((eq c) Xx) Xy)))) P) x1) x)) (((eq c) Xx) Xy)) (fun (x1:(forall (Xx0:b) (Xy0:b), ((((eq a) (F Xx0)) (F Xy0))->(((eq b) Xx0) Xy0)))) (x2:(forall (Xx0:c) (Xy0:c), ((((eq b) (G Xx0)) (G Xy0))->(((eq c) Xx0) Xy0))))=> (((x2 Xx) Xy) (((x1 (G Xx)) (G Xy)) x0)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------