TSTP Solution File: SEU695^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU695^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n185.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 13:32:50 EDT 2014
% Result : Theorem 4.10s
% Output : Proof 4.10s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU695^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n185.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 11:13:46 CDT 2014
% % CPUTime : 4.10
% 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 0x1696128>, <kernel.DependentProduct object at 0x16764d0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x16965a8>, <kernel.DependentProduct object at 0x16764d0>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x18ed7e8>, <kernel.DependentProduct object at 0x1676170>) of role type named dpsetconstr_type
% Using role type
% Declaring dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType)))
% FOF formula (<kernel.Constant object at 0x16965a8>, <kernel.Sort object at 0x1379f38>) 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 0x137df80>, <kernel.DependentProduct object at 0x1676050>) of role type named func_type
% Using role type
% Declaring func:(fofType->(fofType->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1676248>, <kernel.DependentProduct object at 0x16761b8>) of role type named ap_type
% Using role type
% Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType))))
% FOF formula (<kernel.Constant object at 0x1676170>, <kernel.DependentProduct object at 0x1676488>) of role type named lam_type
% Using role type
% Declaring lam:(fofType->(fofType->((fofType->fofType)->fofType)))
% FOF formula (((eq (fofType->(fofType->((fofType->fofType)->fofType)))) lam) (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))) of role definition named lam
% A new definition: (((eq (fofType->(fofType->((fofType->fofType)->fofType)))) lam) (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))))
% Defined: lam:=(fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))
% FOF formula (<kernel.Constant object at 0x16761b8>, <kernel.Sort object at 0x1379f38>) of role type named lamp_type
% Using role type
% Declaring lamp:Prop
% FOF formula (((eq Prop) lamp) (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))) of role definition named lamp
% A new definition: (((eq Prop) lamp) (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx)))))))
% Defined: lamp:=(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))
% FOF formula (<kernel.Constant object at 0x1381680>, <kernel.Sort object at 0x1379f38>) of role type named funcGraphProp2_type
% Using role type
% Declaring funcGraphProp2:Prop
% FOF formula (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))) of role definition named funcGraphProp2
% A new definition: (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))))
% Defined: funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))
% FOF formula (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))))) of role conjecture named beta1
% Conjecture to prove = (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% 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.
% Parameter func:(fofType->(fofType->(fofType->Prop))).
% Parameter ap:(fofType->(fofType->(fofType->(fofType->fofType)))).
% Definition lam:=(fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))):(fofType->(fofType->((fofType->fofType)->fofType))).
% Definition lamp:=(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx)))))):Prop.
% Definition funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))):Prop.
% Trying to prove (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))))))
% Found x40:(P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx))
% Found (fun (x40:(P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)))=> x40) as proof of (P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx))
% Found (fun (x40:(P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)))=> x40) as proof of (P0 ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xf Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf Xx))
% Found eq_ref00:=(eq_ref0 ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)):(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx))
% Found (eq_ref0 ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b)
% Found ((eq_ref fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b)
% Found ((eq_ref fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b)
% Found ((eq_ref fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x200:=(x20 x3):((in (Xf Xx)) B)
% Found (x20 x3) as proof of ((in (Xf Xx)) B)
% Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B)
% Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B)
% Found x00000:=(x0000 x2):(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))
% Found (x0000 x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((x000 Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found (((x00 B) Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((((x0 A) B) Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((((x0 A) B) Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found eq_ref00:=(eq_ref0 (Xf Xx)):(((eq fofType) (Xf Xx)) (Xf Xx))
% Found (eq_ref0 (Xf Xx)) as proof of (((eq fofType) (Xf Xx)) (Xf Xx))
% Found ((eq_ref fofType) (Xf Xx)) as proof of (((eq fofType) (Xf Xx)) (Xf Xx))
% Found ((eq_ref fofType) (Xf Xx)) as proof of (((eq fofType) (Xf Xx)) (Xf Xx))
% Found x200:=(x20 x3):((in (Xf Xx)) B)
% Found (x20 x3) as proof of ((in (Xf Xx)) B)
% Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B)
% Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B)
% Found ((x400000 ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found (((x40000 (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((((x4000 x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found (((((x400 Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((((((x40 (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found (((((((x4 B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))
% Found ((((x100000 ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))
% Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> (((x10000 x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))
% Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> ((x1000 x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))
% Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((x100 (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))
% Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> ((((x10 B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))
% Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))
% Found (fun (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))
% Found (fun (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))
% Found (fun (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))
% Found (fun (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))
% Found (fun (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))
% Found (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))
% Found (fun (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))
% Found (fun (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))))
% Found (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))))
% Found (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))))))
% Got proof (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))))
% Time elapsed = 3.730936s
% node=517 cost=716.000000 depth=26
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------