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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU920^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n184.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 13:33:22 EDT 2014

% Result   : Theorem 1.74s
% Output   : Proof 1.74s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU920^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n184.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 11:42:51 CDT 2014
% % CPUTime  : 1.74 
% 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 0x1b2c710>, <kernel.Type object at 0x1b2ccf8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1b2ce60>, <kernel.Type object at 0x1b0d908>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1b0d440>, <kernel.Type object at 0x1b2ccf8>) of role type named c_type
% Using role type
% Declaring c:Type
% FOF formula (forall (F:(a->b)) (G:(b->c)), ((forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))->(forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))))) of role conjecture named cFN_THM_4_pme
% Conjecture to prove = (forall (F:(a->b)) (G:(b->c)), ((forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))->(forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))))):Prop
% Parameter a_DUMMY:a.
% Parameter b_DUMMY:b.
% Parameter c_DUMMY:c.
% We need to prove ['(forall (F:(a->b)) (G:(b->c)), ((forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))->(forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y))))))']
% Parameter a:Type.
% Parameter b:Type.
% Parameter c:Type.
% Trying to prove (forall (F:(a->b)) (G:(b->c)), ((forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))->(forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:b)=> (((eq c) (G X)) Y))):(((eq (b->Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) (fun (x:b)=> (((eq c) (G x)) Y)))
% Found (eta_expansion_dep00 (fun (X:b)=> (((eq c) (G X)) Y))) as proof of (((eq (b->Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) b0)
% Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) as proof of (((eq (b->Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) b0)
% Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) as proof of (((eq (b->Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) b0)
% Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) as proof of (((eq (b->Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) b0)
% Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) as proof of (((eq (b->Prop)) (fun (X:b)=> (((eq c) (G X)) Y))) b0)
% Found x2:(((eq c) (G (F x1))) Y0)
% Instantiate: x3:=(F x1):b;Y0:=Y:c
% Found x2 as proof of (((eq c) (G x3)) Y)
% Found (ex_intro000 x2) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found ((ex_intro00 (F x1)) x2) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found (((ex_intro0 (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found (fun (x2:(((eq c) (G (F x1))) Y0))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found (fun (x1:a) (x2:(((eq c) (G (F x1))) Y0))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)) as proof of ((((eq c) (G (F x1))) Y0)->((ex b) (fun (X:b)=> (((eq c) (G X)) Y))))
% Found (fun (x1:a) (x2:(((eq c) (G (F x1))) Y0))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)) as proof of (forall (x:a), ((((eq c) (G (F x))) Y0)->((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))))
% Found (ex_ind00 (fun (x1:a) (x2:(((eq c) (G (F x1))) Y0))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2))) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found ((ex_ind0 ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y0))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2))) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found (((fun (P:Prop) (x1:(forall (x:a), ((((eq c) (G (F x))) Y0)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y0))) P) x1) x0)) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y0))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2))) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2))) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found (fun (Y:c)=> (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)))) as proof of ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))
% Found (fun (x:(forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))) (Y:c)=> (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)))) as proof of (forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y))))
% Found (fun (G:(b->c)) (x:(forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))) (Y:c)=> (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)))) as proof of ((forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))->(forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))))
% Found (fun (F:(a->b)) (G:(b->c)) (x:(forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))) (Y:c)=> (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)))) as proof of (forall (G:(b->c)), ((forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))->(forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y))))))
% Found (fun (F:(a->b)) (G:(b->c)) (x:(forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))) (Y:c)=> (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2)))) as proof of (forall (F:(a->b)) (G:(b->c)), ((forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))->(forall (Y:c), ((ex b) (fun (X:b)=> (((eq c) (G X)) Y))))))
% Got proof (fun (F:(a->b)) (G:(b->c)) (x:(forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))) (Y:c)=> (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2))))
% Time elapsed = 1.414093s
% node=239 cost=1014.000000 depth=16
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (F:(a->b)) (G:(b->c)) (x:(forall (Y:c), ((ex a) (fun (X:a)=> (((eq c) (G (F X))) Y))))) (Y:c)=> (((fun (P:Prop) (x1:(forall (x1:a), ((((eq c) (G (F x1))) Y)->P)))=> (((((ex_ind a) (fun (X:a)=> (((eq c) (G (F X))) Y))) P) x1) (x Y))) ((ex b) (fun (X:b)=> (((eq c) (G X)) Y)))) (fun (x1:a) (x2:(((eq c) (G (F x1))) Y))=> ((((ex_intro b) (fun (X:b)=> (((eq c) (G X)) Y))) (F x1)) x2))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------