TSTP Solution File: SEU779^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU779^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n188.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 13:33:06 EDT 2014
% Result : Theorem 2.81s
% Output : Proof 2.81s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU779^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n188.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 11:27:06 CDT 2014
% % CPUTime : 2.81
% 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 0x25f8050>, <kernel.DependentProduct object at 0x2599c68>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x21be830>, <kernel.DependentProduct object at 0x2599ef0>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x25f8bd8>, <kernel.DependentProduct object at 0x2599ef0>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x25f85a8>, <kernel.DependentProduct object at 0x2599ef0>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x25f8bd8>, <kernel.DependentProduct object at 0x2599ef0>) of role type named breln_type
% Using role type
% Declaring breln:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))) of role definition named breln
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))))
% Defined: breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))
% FOF formula (<kernel.Constant object at 0x25f8bd8>, <kernel.DependentProduct object at 0x2599b90>) of role type named dpsetconstr_type
% Using role type
% Declaring dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType)))
% FOF formula (<kernel.Constant object at 0x25f8bd8>, <kernel.Sort object at 0x2084bd8>) of role type named dpsetconstrI_type
% Using role type
% Declaring dpsetconstrI:Prop
% FOF formula (((eq Prop) dpsetconstrI) (forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))))))) of role definition named dpsetconstrI
% A new definition: (((eq Prop) dpsetconstrI) (forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))))))))
% Defined: dpsetconstrI:=(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))))))
% FOF formula (<kernel.Constant object at 0x2599ef0>, <kernel.DependentProduct object at 0x2599ab8>) of role type named breln1_type
% Using role type
% Declaring breln1:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) breln1) (fun (A:fofType) (R:fofType)=> (((breln A) A) R))) of role definition named breln1
% A new definition: (((eq (fofType->(fofType->Prop))) breln1) (fun (A:fofType) (R:fofType)=> (((breln A) A) R)))
% Defined: breln1:=(fun (A:fofType) (R:fofType)=> (((breln A) A) R))
% FOF formula (<kernel.Constant object at 0x2599ab8>, <kernel.DependentProduct object at 0x2599d88>) of role type named breln1compset_type
% Using role type
% Declaring breln1compset:(fofType->(fofType->(fofType->fofType)))
% FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) breln1compset) (fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))) of role definition named breln1compset
% A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) breln1compset) (fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))))
% Defined: breln1compset:=(fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)))))))
% FOF formula (dpsetconstrI->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))))))) of role conjecture named breln1compI
% Conjecture to prove = (dpsetconstrI->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(dpsetconstrI->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter subset:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))):(fofType->(fofType->(fofType->Prop))).
% Parameter dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType))).
% Definition dpsetconstrI:=(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))))))):Prop.
% Definition breln1:=(fun (A:fofType) (R:fofType)=> (((breln A) A) R)):(fofType->(fofType->Prop)).
% Definition breln1compset:=(fun (A:fofType) (R:fofType) (S:fofType)=> (((dpsetconstr A) A) (fun (Xx:fofType) (Xy:fofType)=> ((ex fofType) (fun (Xz:fofType)=> ((and ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S))))))):(fofType->(fofType->(fofType->fofType))).
% Trying to prove (dpsetconstrI->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))))))))
% Found x3:((in Xy) A)
% Found x3 as proof of ((in Xy) A)
% Found x3:((in Xy) A)
% Found x3 as proof of ((in Xy) A)
% Found x3:((in Xy) A)
% Found x3 as proof of ((in Xy) A)
% Found x3:((in Xy) A)
% Found x3 as proof of ((in Xy) A)
% Found x2:((in Xx) A)
% Found x2 as proof of ((in Xx) A)
% Found x3:((in Xy) A)
% Found x3 as proof of ((in Xy) A)
% Found x3:((in Xy) A)
% Found x3 as proof of ((in Xy) A)
% Found x2:((in Xx) A)
% Found x2 as proof of ((in Xx) A)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found x6:((in ((kpair Xz) Xy)) S)
% Instantiate: x8:=Xz:fofType
% Found x6 as proof of ((in ((kpair x8) Xy)) S)
% Found conj1000:=(conj100 x5):((and ((in x8) A)) ((in ((kpair Xx) x8)) R))
% Found (conj100 x5) as proof of ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))
% Found ((conj10 ((in ((kpair Xx) x8)) R)) x5) as proof of ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))
% Found (((fun (B:Prop)=> ((conj1 B) x4)) ((in ((kpair Xx) x8)) R)) x5) as proof of ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))
% Found (((fun (B:Prop)=> (((conj ((in x8) A)) B) x4)) ((in ((kpair Xx) x8)) R)) x5) as proof of ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))
% Found (((fun (B:Prop)=> (((conj ((in x8) A)) B) x4)) ((in ((kpair Xx) x8)) R)) x5) as proof of ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))
% Found ((conj00 (((fun (B:Prop)=> (((conj ((in x8) A)) B) x4)) ((in ((kpair Xx) x8)) R)) x5)) x6) as proof of ((and ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))) ((in ((kpair x8) Xy)) S))
% Found (((conj0 ((in ((kpair x8) Xy)) S)) (((fun (B:Prop)=> (((conj ((in x8) A)) B) x4)) ((in ((kpair Xx) x8)) R)) x5)) x6) as proof of ((and ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))) ((in ((kpair x8) Xy)) S))
% Found ((((conj ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))) ((in ((kpair x8) Xy)) S)) (((fun (B:Prop)=> (((conj ((in x8) A)) B) x4)) ((in ((kpair Xx) x8)) R)) x5)) x6) as proof of ((and ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))) ((in ((kpair x8) Xy)) S))
% Found ((((conj ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))) ((in ((kpair x8) Xy)) S)) (((fun (B:Prop)=> (((conj ((in x8) A)) B) x4)) ((in ((kpair Xx) x8)) R)) x5)) x6) as proof of ((and ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))) ((in ((kpair x8) Xy)) S))
% Found (ex_intro000 ((((conj ((and ((in x8) A)) ((in ((kpair Xx) x8)) R))) ((in ((kpair x8) Xy)) S)) (((fun (B:Prop)=> (((conj ((in x8) A)) B) x4)) ((in ((kpair Xx) x8)) R)) x5)) x6)) as proof of ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S))))
% Found ((ex_intro00 Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)) as proof of ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S))))
% Found (((ex_intro0 (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)) as proof of ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S))))
% Found ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)) as proof of ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S))))
% Found ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)) as proof of ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S))))
% Found ((x700000 x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found (((x70000 Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found ((((x7000 x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found (((((x700 Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found ((((((x70 (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found (((((((x7 A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found (fun (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of ((in ((kpair Xx) Xy)) (((breln1compset A) R) S))
% Found (fun (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))
% Found (fun (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))
% Found (fun (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))
% Found (fun (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))
% Found (fun (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))
% Found (fun (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))
% Found (fun (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))
% Found (fun (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))
% Found (fun (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))))
% Found (fun (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))))
% Found (fun (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))))))
% Found (fun (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (forall (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))))))
% Found (fun (x:dpsetconstrI) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S))))))))))))))
% Found (fun (x:dpsetconstrI) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6)))) as proof of (dpsetconstrI->(forall (A:fofType) (R:fofType), (((breln1 A) R)->(forall (S:fofType), (((breln1 A) S)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(forall (Xz:fofType), (((in Xz) A)->(((in ((kpair Xx) Xz)) R)->(((in ((kpair Xz) Xy)) S)->((in ((kpair Xx) Xy)) (((breln1compset A) R) S)))))))))))))))
% Got proof (fun (x:dpsetconstrI) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))))
% Time elapsed = 2.436490s
% node=300 cost=1152.000000 depth=35
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:dpsetconstrI) (A:fofType) (R:fofType) (x0:((breln1 A) R)) (S:fofType) (x1:((breln1 A) S)) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (Xz:fofType) (x4:((in Xz) A)) (x5:((in ((kpair Xx) Xz)) R)) (x6:((in ((kpair Xz) Xy)) S))=> ((((((((x A) A) (fun (x14:fofType) (x130:fofType)=> ((ex fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair x14) Xz0)) R))) ((in ((kpair Xz0) x130)) S)))))) Xx) x2) Xy) x3) ((((ex_intro fofType) (fun (Xz0:fofType)=> ((and ((and ((in Xz0) A)) ((in ((kpair Xx) Xz0)) R))) ((in ((kpair Xz0) Xy)) S)))) Xz) ((((conj ((and ((in Xz) A)) ((in ((kpair Xx) Xz)) R))) ((in ((kpair Xz) Xy)) S)) (((fun (B:Prop)=> (((conj ((in Xz) A)) B) x4)) ((in ((kpair Xx) Xz)) R)) x5)) x6))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------