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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  : SEU670^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n101.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 13:32:46 EDT 2014

% Result   : Theorem 0.73s
% Output   : Proof 0.73s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU670^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n101.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 11:06:51 CDT 2014
% % CPUTime  : 0.73 
% 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 0x1c09998>, <kernel.DependentProduct object at 0x1c091b8>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1c07710>, <kernel.DependentProduct object at 0x1c09a28>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x1c097e8>, <kernel.Sort object at 0x18fb638>) of role type named dsetconstrEL_type
% Using role type
% Declaring dsetconstrEL:Prop
% FOF formula (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))) of role definition named dsetconstrEL
% A new definition: (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))))
% Defined: dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0x1c09998>, <kernel.DependentProduct object at 0x1c08ef0>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1c093f8>, <kernel.DependentProduct object at 0x1c086c8>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1c097e8>, <kernel.Sort object at 0x18fb638>) of role type named cartprodpairmemER_type
% Using role type
% Declaring cartprodpairmemER:Prop
% FOF formula (((eq Prop) cartprodpairmemER) (forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xy) B)))) of role definition named cartprodpairmemER
% A new definition: (((eq Prop) cartprodpairmemER) (forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xy) B))))
% Defined: cartprodpairmemER:=(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xy) B)))
% FOF formula (<kernel.Constant object at 0x1c097e8>, <kernel.DependentProduct object at 0x1c083b0>) of role type named dpsetconstr_type
% Using role type
% Declaring dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType)))
% FOF formula (((eq (fofType->(fofType->((fofType->(fofType->Prop))->fofType)))) dpsetconstr) (fun (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop)))=> ((dsetconstr ((cartprod A) B)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((in Xy) B)) ((Xphi Xx) Xy))) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))))) of role definition named dpsetconstr
% A new definition: (((eq (fofType->(fofType->((fofType->(fofType->Prop))->fofType)))) dpsetconstr) (fun (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop)))=> ((dsetconstr ((cartprod A) B)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((in Xy) B)) ((Xphi Xx) Xy))) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))))
% Defined: dpsetconstr:=(fun (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop)))=> ((dsetconstr ((cartprod A) B)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((in Xy) B)) ((Xphi Xx) Xy))) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))))
% FOF formula (dsetconstrEL->(cartprodpairmemER->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B))))) of role conjecture named dpsetconstrEL2
% Conjecture to prove = (dsetconstrEL->(cartprodpairmemER->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(dsetconstrEL->(cartprodpairmemER->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))):Prop.
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition cartprodpairmemER:=(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xy) B))):Prop.
% Definition dpsetconstr:=(fun (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop)))=> ((dsetconstr ((cartprod A) B)) (fun (Xu:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((and ((in Xy) B)) ((Xphi Xx) Xy))) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))):(fofType->(fofType->((fofType->(fofType->Prop))->fofType))).
% Trying to prove (dsetconstrEL->(cartprodpairmemER->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))))
% Found x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))
% Instantiate: A0:=A:fofType;Xx0:=Xx:fofType;Xphi0:=(fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0))))))))):(fofType->Prop)
% Found x1 as proof of ((in ((kpair Xx0) Xy)) ((dsetconstr ((cartprod A0) B)) (fun (Xy0:fofType)=> (Xphi0 Xy0))))
% Found (x200 x1) as proof of ((in ((kpair Xx0) Xy)) ((cartprod A0) B))
% Found ((x20 (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1) as proof of ((in ((kpair Xx0) Xy)) ((cartprod A0) B))
% Found (((fun (Xphi0:(fofType->Prop))=> ((x2 Xphi0) ((kpair Xx0) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1) as proof of ((in ((kpair Xx0) Xy)) ((cartprod A0) B))
% Found (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A0) B)) Xphi0) ((kpair Xx0) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1) as proof of ((in ((kpair Xx0) Xy)) ((cartprod A0) B))
% Found (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A0) B)) Xphi0) ((kpair Xx0) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1) as proof of ((in ((kpair Xx0) Xy)) ((cartprod A0) B))
% Found (x00000 (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A0) B)) Xphi0) ((kpair Xx0) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1)) as proof of ((in Xy) B)
% Found ((x0000 Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A0) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1)) as proof of ((in Xy) B)
% Found (((x000 A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1)) as proof of ((in Xy) B)
% Found ((((fun (A0:fofType) (Xx0:fofType)=> (((x00 A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1)) as proof of ((in Xy) B)
% Found ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1)) as proof of ((in Xy) B)
% Found (fun (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of ((in Xy) B)
% Found (fun (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B))
% Found (fun (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (forall (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))
% Found (fun (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (forall (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))
% Found (fun (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (forall (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))
% Found (fun (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (forall (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))
% Found (fun (x0:cartprodpairmemER) (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))
% Found (fun (x:dsetconstrEL) (x0:cartprodpairmemER) (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (cartprodpairmemER->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B))))
% Found (fun (x:dsetconstrEL) (x0:cartprodpairmemER) (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1))) as proof of (dsetconstrEL->(cartprodpairmemER->(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xy) B)))))
% Got proof (fun (x:dsetconstrEL) (x0:cartprodpairmemER) (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1)))
% Time elapsed = 0.398109s
% node=63 cost=2298.000000 depth=19
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:dsetconstrEL) (x0:cartprodpairmemER) (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (A0:fofType) (Xx0:fofType)=> ((((fun (A0:fofType)=> ((x0 A0) B)) A0) Xx0) Xy)) A) Xx) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx1:fofType)=> ((and ((in Xx1) A)) ((ex fofType) (fun (Xy0:fofType)=> ((and ((and ((in Xy0) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx1) Xy0))) (((eq fofType) x4) ((kpair Xx1) Xy0)))))))))) x1)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------