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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYO263^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Tue Mar 29 00:51:01 EDT 2022

% Result   : Theorem 1.15s 1.37s
% Output   : Proof 1.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SYO263^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.12  % Command    : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33  % Computer   : n015.cluster.edu
% 0.12/0.33  % Model      : x86_64 x86_64
% 0.12/0.33  % CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % RAMPerCPU  : 8042.1875MB
% 0.12/0.33  % OS         : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % DateTime   : Fri Mar 11 23:04:33 EST 2022
% 0.12/0.33  % CPUTime    : 
% 0.12/0.34  ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34  Python 2.7.5
% 1.15/1.35  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.15/1.35  FOF formula (forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))))) of role conjecture named cTHM125D
% 1.15/1.35  Conjecture to prove = (forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))))):Prop
% 1.15/1.35  Parameter fofType_DUMMY:fofType.
% 1.15/1.35  We need to prove ['(forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))))']
% 1.15/1.35  Parameter fofType:Type.
% 1.15/1.35  Trying to prove (forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))))
% 1.15/1.35  Found classic0:=(classic (x Xc)):((or (x Xc)) (not (x Xc)))
% 1.15/1.35  Found (classic (x Xc)) as proof of ((or (x Xc)) ((P Xc)->False))
% 1.15/1.35  Found (classic (x Xc)) as proof of ((or (x Xc)) ((P Xc)->False))
% 1.15/1.35  Found (classic (x Xc)) as proof of ((or (x Xc)) ((P Xc)->False))
% 1.15/1.35  Found x1:(x0 Xx)
% 1.15/1.35  Found x1 as proof of ((P Xx)->False)
% 1.15/1.35  Found (fun (x1:(x0 Xx))=> x1) as proof of ((P Xx)->False)
% 1.15/1.35  Found (fun (x1:(x0 Xx))=> x1) as proof of ((x0 Xx)->((P Xx)->False))
% 1.15/1.35  Found x1:((P Xx)->False)
% 1.15/1.35  Found (fun (x1:((P Xx)->False))=> x1) as proof of (x0 Xx)
% 1.15/1.35  Found (fun (x1:((P Xx)->False))=> x1) as proof of (((P Xx)->False)->(x0 Xx))
% 1.15/1.35  Found ((conj10 (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)) as proof of ((and ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx)))
% 1.15/1.35  Found (((conj1 (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)) as proof of ((and ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx)))
% 1.15/1.35  Found ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)) as proof of ((and ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx)))
% 1.15/1.35  Found ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)) as proof of ((and ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx)))
% 1.15/1.35  Found (fun (Xx:fofType)=> ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))) as proof of ((iff (x0 Xx)) ((P Xx)->False))
% 1.15/1.35  Found (fun (Xx:fofType)=> ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))) as proof of (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False)))
% 1.15/1.35  Found classic0:=(classic (x Xc)):((or (x Xc)) (not (x Xc)))
% 1.15/1.35  Found (classic (x Xc)) as proof of ((or (x Xc)) ((P Xc)->False))
% 1.15/1.35  Found (classic (x Xc)) as proof of ((or (x Xc)) ((P Xc)->False))
% 1.15/1.35  Found (classic (x Xc)) as proof of ((or (x Xc)) ((P Xc)->False))
% 1.15/1.35  Found classic0:=(classic (P Xb)):((or (P Xb)) (not (P Xb)))
% 1.15/1.35  Found (classic (P Xb)) as proof of ((or (P Xb)) (x0 Xb))
% 1.15/1.35  Found (classic (P Xb)) as proof of ((or (P Xb)) (x0 Xb))
% 1.15/1.35  Found classic0:=(classic (P Xb)):((or (P Xb)) (not (P Xb)))
% 1.15/1.35  Found (classic (P Xb)) as proof of ((or (P Xb)) (x0 Xb))
% 1.15/1.35  Found (classic (P Xb)) as proof of ((or (P Xb)) (x0 Xb))
% 1.15/1.35  Found classic0:=(classic (x Xa)):((or (x Xa)) (not (x Xa)))
% 1.15/1.35  Found (classic (x Xa)) as proof of ((or (x Xa)) (x0 Xa))
% 1.15/1.35  Found (classic (x Xa)) as proof of ((or (x Xa)) (x0 Xa))
% 1.15/1.35  Found (or_comm_i00 (classic (x Xa))) as proof of ((or (x0 Xa)) (x Xa))
% 1.15/1.35  Found ((or_comm_i0 (x0 Xa)) (classic (x Xa))) as proof of ((or (x0 Xa)) (x Xa))
% 1.15/1.35  Found (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa))) as proof of ((or (x0 Xa)) (x Xa))
% 1.15/1.35  Found (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa))) as proof of ((or (x0 Xa)) (x Xa))
% 1.15/1.35  Found ((conj20 (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb))) as proof of ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))
% 1.15/1.35  Found (((conj2 ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb))) as proof of ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))
% 1.15/1.35  Found ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb))) as proof of ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))
% 1.15/1.35  Found ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb))) as proof of ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))
% 1.15/1.35  Found ((conj10 ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc))) as proof of ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))
% 1.15/1.35  Found (((conj1 ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc))) as proof of ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))
% 1.15/1.35  Found ((((conj ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc))) as proof of ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))
% 1.15/1.35  Found ((((conj ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc))) as proof of ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))
% 1.15/1.35  Found ((conj00 ((((conj ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))) as proof of ((and ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False))))
% 1.15/1.35  Found (((conj0 (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False)))) ((((conj ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))) as proof of ((and ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False))))
% 1.15/1.35  Found ((((conj ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False)))) ((((conj ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))) as proof of ((and ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False))))
% 1.15/1.35  Found ((((conj ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False)))) ((((conj ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))) as proof of ((and ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False))))
% 1.15/1.35  Found (ex_intro010 ((((conj ((and ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (x0 Xx)) ((P Xx)->False)))) ((((conj ((and ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or (x0 Xa)) (x Xa))) ((or (P Xb)) (x0 Xb))) (((or_comm_i (x Xa)) (x0 Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj ((x0 Xx)->((P Xx)->False))) (((P Xx)->False)->(x0 Xx))) (fun (x1:(x0 Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))) as proof of ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (x Xa))) ((or (P Xb)) (Xn Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))
% 1.15/1.35  Found ((ex_intro01 (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (x Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))) as proof of ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (x Xa))) ((or (P Xb)) (Xn Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))
% 1.15/1.35  Found (((ex_intro0 (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (x Xa))) ((or (P Xb)) (Xn Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (x Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))) as proof of ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (x Xa))) ((or (P Xb)) (Xn Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))
% 1.15/1.36  Found (((ex_intro0 (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (x Xa))) ((or (P Xb)) (Xn Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (x Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))) as proof of ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (x Xa))) ((or (P Xb)) (Xn Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))
% 1.15/1.36  Found (ex_intro000 (((ex_intro0 (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (x Xa))) ((or (P Xb)) (Xn Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (x Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (x Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (x Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (x Xa)))) (classic (P Xb)))) (classic (x Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))))) as proof of ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))))
% 1.15/1.36  Found ((ex_intro00 P) (((ex_intro0 (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))))) as proof of ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))))
% 1.15/1.36  Found (((ex_intro0 (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) (((ex_intro0 (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))))) as proof of ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))))
% 1.15/1.36  Found ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))))) as proof of ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))))
% 1.15/1.36  Found (fun (P:(fofType->Prop))=> ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))))) as proof of ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False))))))))
% 1.15/1.36  Found (fun (Xc:fofType) (P:(fofType->Prop))=> ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))))) as proof of (forall (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))))
% 1.15/1.36  Found (fun (Xb:fofType) (Xc:fofType) (P:(fofType->Prop))=> ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))))) as proof of (forall (Xc:fofType) (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))))
% 1.15/1.36  Found (fun (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop))=> ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))))) as proof of (forall (Xb:fofType) (Xc:fofType) (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))))
% 1.15/1.36  Found (fun (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop))=> ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1))))))) as proof of (forall (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop)), ((ex (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))))
% 1.15/1.37  Got proof (fun (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop))=> ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))))))
% 1.15/1.37  Time elapsed = 0.751605s
% 1.15/1.37  node=235 cost=1646.000000 depth=30
% 1.15/1.37  ::::::::::::::::::::::
% 1.15/1.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.37  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.37  (fun (Xa:fofType) (Xb:fofType) (Xc:fofType) (P:(fofType->Prop))=> ((((ex_intro (fofType->Prop)) (fun (Xm:(fofType->Prop))=> ((ex (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (Xm Xa))) ((or (P Xb)) (Xn Xb)))) ((or (Xm Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))))) P) ((((ex_intro (fofType->Prop)) (fun (Xn:(fofType->Prop))=> ((and ((and ((and ((or (Xn Xa)) (P Xa))) ((or (P Xb)) (Xn Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff (Xn Xx)) ((P Xx)->False)))))) (fun (a0:fofType)=> ((P a0)->False))) ((((conj ((and ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False)))) (forall (Xx:fofType), ((iff ((fun (a0:fofType)=> ((P a0)->False)) Xx)) ((P Xx)->False)))) ((((conj ((and ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb)))) ((or (P Xc)) ((P Xc)->False))) ((((conj ((or ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (P Xa))) ((or (P Xb)) ((fun (a0:fofType)=> ((P a0)->False)) Xb))) (((or_comm_i (P Xa)) ((fun (a0:fofType)=> ((P a0)->False)) Xa)) (classic (P Xa)))) (classic (P Xb)))) (classic (P Xc)))) (fun (Xx:fofType)=> ((((conj (((fun (a0:fofType)=> ((P a0)->False)) Xx)->((P Xx)->False))) (((P Xx)->False)->((fun (a0:fofType)=> ((P a0)->False)) Xx))) (fun (x1:((fun (a0:fofType)=> ((P a0)->False)) Xx))=> x1)) (fun (x1:((P Xx)->False))=> x1)))))))
% 1.15/1.37  % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------