TSTP Solution File: SYN382^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYN382^5 : 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 13:38:18 EDT 2014
% Result : Theorem 2.13s
% Output : Proof 2.13s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SYN382^5 : 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 09:32:56 CDT 2014
% % CPUTime: 2.13
% 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 0x25ba248>, <kernel.DependentProduct object at 0x2635d88>) of role type named cQ
% Using role type
% Declaring cQ:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x20cbc20>, <kernel.DependentProduct object at 0x2635e60>) of role type named cP
% Using role type
% Declaring cP:(fofType->(fofType->Prop))
% FOF formula ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))) of role conjecture named cX2134
% Conjecture to prove = ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))))']
% Parameter fofType:Type.
% Parameter cQ:(fofType->(fofType->Prop)).
% Parameter cP:(fofType->(fofType->Prop)).
% Trying to prove ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))))
% Found or_intror00:=(or_intror0 ((cQ x1) Xz)):(((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x1) Xz)))
% Found (or_intror0 ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy)))
% Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy)))
% Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy)))
% Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy)))
% Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy)))
% Found or_intror00:=(or_intror0 ((cQ x2) Xz)):(((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x2) Xz)))
% Found (or_intror0 ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy)))
% Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy)))
% Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy)))
% Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy)))
% Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy)))
% Found x40:=(x4 Xy):((cP x1) Xy)
% Found (x4 Xy) as proof of ((cP x3) Xy)
% Found (x4 Xy) as proof of ((cP x3) Xy)
% Found (or_introl00 (x4 Xy)) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found ((or_introl0 ((cQ x3) Xy)) (x4 Xy)) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy))) as proof of ((forall (Xy0:fofType), ((cP x1) Xy0))->((or ((cP x3) Xy)) ((cQ x3) Xy)))
% Found ((or_ind00 (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found (((or_ind0 ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy))
% Found (ex_intro000 ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found ((ex_intro00 x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found (((ex_intro0 (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found (fun (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz))))) as proof of (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz))->((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))
% Found (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz))))) as proof of (forall (x:fofType), (((or (forall (Xy0:fofType), ((cP x) Xy0))) ((cQ x) Xz))->((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))))
% Found (ex_ind00 (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found ((ex_ind0 ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found (((fun (P:Prop) (x1:(forall (x:fofType), (((or (forall (Xy:fofType), ((cP x) Xy))) ((cQ x) Xz))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found (fun (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))
% Found (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) as proof of (forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))
% Found (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) as proof of ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))))
% Got proof (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy)))))))
% Time elapsed = 1.794600s
% node=356 cost=1246.000000 depth=24
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------