TSTP Solution File: SEU669^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU669^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n190.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 0.70s
% Output : Proof 0.70s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU669^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n190.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 11:06:41 CDT 2014
% % CPUTime : 0.70
% 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 0x2386ef0>, <kernel.DependentProduct object at 0x2368050>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2386950>, <kernel.DependentProduct object at 0x2386fc8>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x2386cf8>, <kernel.Sort object at 0x1e753f8>) 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 0x2386ef0>, <kernel.DependentProduct object at 0x23877a0>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x23867e8>, <kernel.DependentProduct object at 0x2387368>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x2386cf8>, <kernel.Sort object at 0x1e753f8>) of role type named cartprodpairmemEL_type
% Using role type
% Declaring cartprodpairmemEL:Prop
% FOF formula (((eq Prop) cartprodpairmemEL) (forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A)))) of role definition named cartprodpairmemEL
% A new definition: (((eq Prop) cartprodpairmemEL) (forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A))))
% Defined: cartprodpairmemEL:=(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0x2386cf8>, <kernel.DependentProduct object at 0x2387950>) 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->(cartprodpairmemEL->(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 Xx) A))))) of role conjecture named dpsetconstrEL1
% Conjecture to prove = (dsetconstrEL->(cartprodpairmemEL->(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 Xx) A))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(dsetconstrEL->(cartprodpairmemEL->(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 Xx) A)))))']
% 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 cartprodpairmemEL:=(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A))):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->(cartprodpairmemEL->(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 Xx) A)))))
% Found x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))
% Instantiate: Xy0:=Xy:fofType;B0:=B:fofType;Xphi0:=(fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1))))))))):(fofType->Prop)
% Found x1 as proof of ((in ((kpair Xx) Xy0)) ((dsetconstr ((cartprod A) B0)) (fun (Xy:fofType)=> (Xphi0 Xy))))
% Found (x200 x1) as proof of ((in ((kpair Xx) Xy0)) ((cartprod A) B0))
% Found ((x20 (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1) as proof of ((in ((kpair Xx) Xy0)) ((cartprod A) B0))
% Found (((fun (Xphi0:(fofType->Prop))=> ((x2 Xphi0) ((kpair Xx) Xy0))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1) as proof of ((in ((kpair Xx) Xy0)) ((cartprod A) B0))
% Found (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B0)) Xphi0) ((kpair Xx) Xy0))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1) as proof of ((in ((kpair Xx) Xy0)) ((cartprod A) B0))
% Found (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B0)) Xphi0) ((kpair Xx) Xy0))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1) as proof of ((in ((kpair Xx) Xy0)) ((cartprod A) B0))
% Found (x00000 (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B0)) Xphi0) ((kpair Xx) Xy0))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1)) as proof of ((in Xx) A)
% Found ((x0000 Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B0)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1)) as proof of ((in Xx) A)
% Found (((x000 B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1)) as proof of ((in Xx) A)
% Found ((((fun (B0:fofType)=> ((x00 B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1)) as proof of ((in Xx) A)
% Found ((((fun (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1)) as proof of ((in Xx) A)
% Found (fun (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1))) as proof of ((in Xx) A)
% Found (fun (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1))) as proof of (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xx) A))
% Found (fun (Xx:fofType) (Xy:fofType) (x1:((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))=> ((((fun (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1))) as proof of (forall (Xy:fofType), (((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))->((in Xx) A)))
% 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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) 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 Xx) A)))
% 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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) 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 Xx) A)))
% 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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) 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 Xx) A)))
% Found (fun (x0:cartprodpairmemEL) (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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) 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 Xx) A)))
% Found (fun (x:dsetconstrEL) (x0:cartprodpairmemEL) (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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1))) as proof of (cartprodpairmemEL->(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 Xx) A))))
% Found (fun (x:dsetconstrEL) (x0:cartprodpairmemEL) (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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1))) as proof of (dsetconstrEL->(cartprodpairmemEL->(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 Xx) A)))))
% Got proof (fun (x:dsetconstrEL) (x0:cartprodpairmemEL) (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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1)))
% Time elapsed = 0.365409s
% node=57 cost=2218.000000 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:cartprodpairmemEL) (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 (B0:fofType)=> (((x0 A) B0) Xx)) B) Xy) (((fun (Xphi0:(fofType->Prop))=> (((x ((cartprod A) B)) Xphi0) ((kpair Xx) Xy))) (fun (x4:fofType)=> ((ex fofType) (fun (Xx0:fofType)=> ((and ((in Xx0) A)) ((ex fofType) (fun (Xy1:fofType)=> ((and ((and ((in Xy1) B)) (((fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)) Xx0) Xy1))) (((eq fofType) x4) ((kpair Xx0) Xy1)))))))))) x1)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------