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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  : SEV049^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.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 13:33:39 EDT 2014

% Result   : Theorem 0.86s
% Output   : Proof 0.86s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV049^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.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 07:44:06 CDT 2014
% % CPUTime  : 0.86 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz)))))) of role conjecture named cTHM120A_pme
% Conjecture to prove = ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz))))))']
% Parameter fofType:Type.
% Trying to prove ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz))))))
% Found x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))
% Found x0 as proof of False
% Found (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0) as proof of False
% Found (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0) as proof of (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)
% Found x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))
% Found x0 as proof of False
% Found (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0) as proof of False
% Found (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0) as proof of (not ((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))
% Found x01:((x Xy) Xz)
% Found (fun (x01:((x Xy) Xz))=> x01) as proof of ((x Xx) Xz)
% Found (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01) as proof of (((x Xy) Xz)->((x Xx) Xz))
% Found (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01) as proof of (((x Xx) Xy)->(((x Xy) Xz)->((x Xx) Xz)))
% Found (and_rect00 (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01)) as proof of ((x Xx) Xz)
% Found ((and_rect0 ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01)) as proof of ((x Xx) Xz)
% Found (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01)) as proof of ((x Xx) Xz)
% Found (fun (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01))) as proof of ((x Xx) Xz)
% Found (fun (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01))) as proof of (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz))
% Found (fun (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01))) as proof of (forall (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz)))
% Found (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01))) as proof of (forall (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz)))
% Found (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01))) as proof of (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz)))
% Found ((conj00 (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01)))) as proof of ((and (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz))))
% Found (((conj0 (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz)))) (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01)))) as proof of ((and (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz))))
% Found ((((conj (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz)))) (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01)))) as proof of ((and (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz))))
% Found ((((conj (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz)))) (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01)))) as proof of ((and (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz))))
% Found (ex_intro000 ((((conj (((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((x Xx) Xy)) ((x Xy) Xz))->((x Xx) Xz)))) (fun (x0:((x (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and ((x Xx) Xy)) ((x Xy) Xz)))=> (((fun (P:Type) (x1:(((x Xx) Xy)->(((x Xy) Xz)->P)))=> (((((and_rect ((x Xx) Xy)) ((x Xy) Xz)) P) x1) x0)) ((x Xx) Xz)) (fun (x00:((x Xx) Xy)) (x01:((x Xy) Xz))=> x01))))) as proof of ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz))))))
% Found ((ex_intro00 (fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False)) ((((conj ((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))->(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)))) (fun (x0:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)))=> (((fun (P:Type) (x1:((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)->((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)->P)))=> (((((and_rect (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)) P) x1) x0)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)) (fun (x00:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (x01:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))=> x01))))) as proof of ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz))))))
% Found (((ex_intro0 (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz)))))) (fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False)) ((((conj ((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))->(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)))) (fun (x0:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)))=> (((fun (P:Type) (x1:((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)->((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)->P)))=> (((((and_rect (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)) P) x1) x0)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)) (fun (x00:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (x01:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))=> x01))))) as proof of ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz))))))
% Found ((((ex_intro ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz)))))) (fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False)) ((((conj ((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))->(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)))) (fun (x0:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)))=> (((fun (P:Type) (x1:((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)->((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)->P)))=> (((((and_rect (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)) P) x1) x0)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)) (fun (x00:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (x01:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))=> x01))))) as proof of ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz))))))
% Found ((((ex_intro ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz)))))) (fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False)) ((((conj ((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))->(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)))) (fun (x0:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)))=> (((fun (P:Type) (x1:((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)->((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)->P)))=> (((((and_rect (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)) P) x1) x0)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)) (fun (x00:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (x01:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))=> x01))))) as proof of ((ex ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz))))))
% Got proof ((((ex_intro ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz)))))) (fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False)) ((((conj ((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))->(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)))) (fun (x0:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)))=> (((fun (P:Type) (x1:((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)->((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)->P)))=> (((((and_rect (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)) P) x1) x0)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)) (fun (x00:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (x01:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))=> x01)))))
% Time elapsed = 0.545525s
% node=50 cost=527.000000 depth=19
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% ((((ex_intro ((fofType->Prop)->((fofType->Prop)->Prop))) (fun (R:((fofType->Prop)->((fofType->Prop)->Prop)))=> ((and (((R (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and ((R Xx) Xy)) ((R Xy) Xz))->((R Xx) Xz)))))) (fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False)) ((((conj ((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False))->False)) (forall (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)), (((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))->(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)))) (fun (x0:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) (fun (Xx:fofType)=> True)) (fun (Xx:fofType)=> False)))=> x0)) (fun (Xx:(fofType->Prop)) (Xy:(fofType->Prop)) (Xz:(fofType->Prop)) (x0:((and (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)))=> (((fun (P:Type) (x1:((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)->((((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)->P)))=> (((((and_rect (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz)) P) x1) x0)) (((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xz)) (fun (x00:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xx) Xy)) (x01:(((fun (a0:(fofType->Prop)) (a1:(fofType->Prop))=> False) Xy) Xz))=> x01)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------