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cocATP---0.2.0.THM-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SET589^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n112.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 13:30:46 EDT 2014

% Result   : Theorem 1.55s
% Output   : Proof 1.55s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET589^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n112.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 10:13:01 CDT 2014
% % CPUTime  : 1.55 
% 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 0x15a8320>, <kernel.Type object at 0x15a83f8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False)))))) of role conjecture named cBOOL_PROP_48_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False))))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False))))))
% Found x100:=(x10 x3):(Y Xx)
% Found (x10 x3) as proof of (Y Xx)
% Found ((x1 Xx) x3) as proof of (Y Xx)
% Found ((x1 Xx) x3) as proof of (Y Xx)
% Found x200:=(x20 x5):(V Xx)
% Found (x20 x5) as proof of (V Xx)
% Found ((x2 Xx) x5) as proof of (V Xx)
% Found ((x2 Xx) x5) as proof of (V Xx)
% Found (x4 ((x2 Xx) x5)) as proof of False
% Found (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))) as proof of False
% Found (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))) as proof of ((Z Xx)->False)
% Found ((conj00 ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (((conj0 ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (fun (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))) as proof of (((V Xx)->False)->((and (Y Xx)) ((Z Xx)->False)))
% Found (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))) as proof of ((X Xx)->(((V Xx)->False)->((and (Y Xx)) ((Z Xx)->False))))
% Found (and_rect10 (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found ((and_rect1 ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (fun (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))) as proof of ((forall (Xx0:a), ((Z Xx0)->(V Xx0)))->((and (Y Xx)) ((Z Xx)->False)))
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))) as proof of ((forall (Xx0:a), ((X Xx0)->(Y Xx0)))->((forall (Xx0:a), ((Z Xx0)->(V Xx0)))->((and (Y Xx)) ((Z Xx)->False))))
% Found (and_rect00 (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found ((and_rect0 ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (fun (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of ((and (Y Xx)) ((Z Xx)->False))
% Found (fun (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False)))
% Found (fun (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False))))
% Found (fun (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False)))))
% Found (fun (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False))))))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((and (X Xx)) ((V Xx)->False))->((and (Y Xx)) ((Z Xx)->False))))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))))))
% Time elapsed = 1.220017s
% node=311 cost=683.000000 depth=28
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((and (X Xx)) ((V Xx)->False)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> (((fun (P:Type) (x3:((X Xx)->(((V Xx)->False)->P)))=> (((((and_rect (X Xx)) ((V Xx)->False)) P) x3) x0)) ((and (Y Xx)) ((Z Xx)->False))) (fun (x3:(X Xx)) (x4:((V Xx)->False))=> ((((conj (Y Xx)) ((Z Xx)->False)) ((x1 Xx) x3)) (fun (x5:(Z Xx))=> (x4 ((x2 Xx) x5)))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------