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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  : SET633^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n116.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 13:30:54 EDT 2014

% Result   : Theorem 0.77s
% Output   : Proof 0.77s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET633^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n116.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 10:27:56 CDT 2014
% % CPUTime  : 0.77 
% 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 0x16f6d40>, <kernel.Type object at 0x16f6bd8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx))))) of role conjecture named cBOOL_PROP_115_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx)))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx)))))
% Found x20:=(x2 Xx):(((and (Y Xx)) ((X Xx)->False))->(Z Xx))
% Found (x2 Xx) as proof of (((and (Y Xx)) ((X Xx)->False))->(Z Xx))
% Found (x2 Xx) as proof of (((and (Y Xx)) ((X Xx)->False))->(Z Xx))
% Found x10:=(x1 Xx):(((and (X Xx)) ((Y Xx)->False))->(Z Xx))
% Found (x1 Xx) as proof of (((and (X Xx)) ((Y Xx)->False))->(Z Xx))
% Found (x1 Xx) as proof of (((and (X Xx)) ((Y Xx)->False))->(Z Xx))
% Found ((or_ind00 (x1 Xx)) (x2 Xx)) as proof of (Z Xx)
% Found (((or_ind0 (Z Xx)) (x1 Xx)) (x2 Xx)) as proof of (Z Xx)
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)) as proof of (Z Xx)
% Found (fun (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))) as proof of (Z Xx)
% Found (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))) as proof of ((forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0)))->(Z Xx))
% Found (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))) as proof of ((forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))->((forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0)))->(Z Xx)))
% Found (and_rect00 (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))) as proof of (Z Xx)
% Found ((and_rect0 (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))) as proof of (Z Xx)
% Found (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))) as proof of (Z Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (Z Xx)
% Found (fun (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx))
% Found (fun (x:((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))) (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx)))
% Found (fun (Z:(a->Prop)) (x:((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))) (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx))))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))) (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (Z:(a->Prop)), (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx)))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))) (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx)))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))) (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))->(forall (Xx:a), (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(Z Xx)))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))) (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))))
% Time elapsed = 0.455721s
% node=94 cost=203.000000 depth=17
% ::::::::::::::::::::::
% % 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)) (x:((and (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx))))) (Xx:a) (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> (((fun (P:Type) (x1:((forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))->((forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))->P)))=> (((((and_rect (forall (Xx:a), (((and (X Xx)) ((Y Xx)->False))->(Z Xx)))) (forall (Xx:a), (((and (Y Xx)) ((X Xx)->False))->(Z Xx)))) P) x1) x)) (Z Xx)) (fun (x1:(forall (Xx0:a), (((and (X Xx0)) ((Y Xx0)->False))->(Z Xx0)))) (x2:(forall (Xx0:a), (((and (Y Xx0)) ((X Xx0)->False))->(Z Xx0))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x0)) (Z Xx)) (x1 Xx)) (x2 Xx)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------