TSTP Solution File: SEU696^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU696^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n116.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 8.68s
% Output : Proof 8.68s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU696^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n116.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 11:14:01 CDT 2014
% % CPUTime : 8.68
% 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 0x1a73e60>, <kernel.DependentProduct object at 0x1a74e60>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1a73b00>, <kernel.DependentProduct object at 0x1a74e60>) of role type named dpsetconstr_type
% Using role type
% Declaring dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType)))
% FOF formula (<kernel.Constant object at 0x1a73c68>, <kernel.DependentProduct object at 0x1a74e60>) of role type named func_type
% Using role type
% Declaring func:(fofType->(fofType->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0x1a73b00>, <kernel.DependentProduct object at 0x1a74e60>) of role type named ap_type
% Using role type
% Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType))))
% FOF formula (<kernel.Constant object at 0x1a73e60>, <kernel.Sort object at 0x155d3f8>) of role type named app_type
% Using role type
% Declaring app:Prop
% FOF formula (((eq Prop) app) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))))) of role definition named app
% A new definition: (((eq Prop) app) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))))
% Defined: app:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))))
% FOF formula (<kernel.Constant object at 0x1a73b00>, <kernel.DependentProduct object at 0x1a741b8>) 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 0x1a741b8>, <kernel.Sort object at 0x155d3f8>) 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 0x1a74c68>, <kernel.Sort object at 0x155d3f8>) of role type named funcext_type
% Using role type
% Declaring funcext:Prop
% FOF formula (((eq Prop) funcext) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))) of role definition named funcext
% A new definition: (((eq Prop) funcext) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))))
% Defined: funcext:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))
% FOF formula (<kernel.Constant object at 0x1a74560>, <kernel.Sort object at 0x155d3f8>) of role type named beta1_type
% Using role type
% Declaring beta1:Prop
% FOF formula (((eq Prop) beta1) (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 definition named beta1
% A new definition: (((eq Prop) beta1) (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)))))))
% Defined: beta1:=(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))))))
% FOF formula (app->(lamp->(funcext->(beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf))))))) of role conjecture named eta1
% Conjecture to prove = (app->(lamp->(funcext->(beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(app->(lamp->(funcext->(beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType))).
% Parameter func:(fofType->(fofType->(fofType->Prop))).
% Parameter ap:(fofType->(fofType->(fofType->(fofType->fofType)))).
% Definition app:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B))))):Prop.
% 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 funcext:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))):Prop.
% Definition beta1:=(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.
% Trying to prove (app->(lamp->(funcext->(beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)))))))
% Found eq_ref00:=(eq_ref0 (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))):(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found (eq_ref0 (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) b)
% Found ((eq_ref fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) b)
% Found ((eq_ref fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) b)
% Found ((eq_ref fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xf)
% Found x3:(((func A) B) Xf)
% Found x3 as proof of (((func A) B) Xf)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found x3:(((func A) B) Xf)
% Found x3 as proof of (((func A) B) Xf)
% Found x4:(P (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Instantiate: b:=(((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found x3:(((func A) B) Xf)
% Found x3 as proof of (((func A) B) Xf)
% Found x4000:=(x400 x3):(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found (x400 x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found ((x40 Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found (((x4 B) Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found ((((x A) B) Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found ((((x A) B) Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found (x2000 ((((x A) B) Xf) x3)) as proof of (forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xx)) ((((ap A) B) Xf) Xx))))
% Found ((x200 (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xx)) ((((ap A) B) Xf) Xx))))
% Found (((x20 B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xx)) ((((ap A) B) Xf) Xx))))
% Found ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xx)) ((((ap A) B) Xf) Xx))))
% Found ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xx)) ((((ap A) B) Xf) Xx))))
% Found x4000:=(x400 x3):(forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found (x400 x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found ((x40 Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found (((x4 B) Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found ((((x A) B) Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found ((((x A) B) Xf) x3) as proof of (forall (Xx:fofType), (((in Xx) A)->((in ((((ap A) B) Xf) Xx)) B)))
% Found (x0000 ((((x A) B) Xf) x3)) as proof of (((func A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found ((x000 (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (((func A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found (((x00 B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (((func A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (((func A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)) as proof of (((func A) B) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))
% Found (((x1000 ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)
% Found (((((x100 A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)
% Found ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> ((((x10 A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)
% Found ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)
% Found (fun (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)
% Found (fun (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf))
% Found (fun (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (forall (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)))
% Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (forall (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)))
% Found (fun (x2:beta1) (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)))
% Found (fun (x1:funcext) (x2:beta1) (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf))))
% Found (fun (x0:lamp) (x1:funcext) (x2:beta1) (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (funcext->(beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)))))
% Found (fun (x:app) (x0:lamp) (x1:funcext) (x2:beta1) (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (lamp->(funcext->(beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf))))))
% Found (fun (x:app) (x0:lamp) (x1:funcext) (x2:beta1) (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3)))) as proof of (app->(lamp->(funcext->(beta1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(((eq fofType) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))) Xf)))))))
% Got proof (fun (x:app) (x0:lamp) (x1:funcext) (x2:beta1) (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))))
% Time elapsed = 8.295929s
% node=815 cost=806.000000 depth=22
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:app) (x0:lamp) (x1:funcext) (x2:beta1) (A:fofType) (B:fofType) (Xf:fofType) (x3:(((func A) B) Xf))=> ((((((fun (A0:fofType) (B0:fofType) (x4:(((func A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx)))))=> (((((fun (A0:fofType) (B0:fofType)=> (((x1 A0) B0) (((lam A) B) (fun (Xx:fofType)=> ((((ap A) B) Xf) Xx))))) A0) B0) x4) Xf)) A) B) ((((x0 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))) x3) ((((x2 A) B) (((ap A) B) Xf)) ((((x A) B) Xf) x3))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------