TSTP Solution File: SEU504^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU504^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n110.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 13:32:19 EDT 2014
% Result : Theorem 1.48s
% Output : Proof 1.48s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU504^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n110.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 10:25:36 CDT 2014
% % CPUTime : 1.48
% 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 0x27c1b90>, <kernel.DependentProduct object at 0x27c1a70>) of role type named exu_type
% Using role type
% Declaring exu:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))) of role definition named exu
% A new definition: (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))
% Defined: exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))
% FOF formula (<kernel.Constant object at 0x27c1b90>, <kernel.Sort object at 0x2687758>) of role type named exuE1_type
% Using role type
% Declaring exuE1:Prop
% FOF formula (((eq Prop) exuE1) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))) of role definition named exuE1
% A new definition: (((eq Prop) exuE1) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))))
% Defined: exuE1:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))
% FOF formula (exuE1->(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))) of role conjecture named exuE3e
% Conjecture to prove = (exuE1->(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(exuE1->(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))))']
% Parameter fofType:Type.
% Definition exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))):((fofType->Prop)->Prop).
% Definition exuE1:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))):Prop.
% Trying to prove (exuE1->(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found x4:(Xphi x2)
% Instantiate: x1:=x2:fofType
% Found (fun (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy))))=> x4) as proof of (Xphi x1)
% Found (fun (x4:(Xphi x2)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy))))=> x4) as proof of ((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy)))->(Xphi x1))
% Found (fun (x4:(Xphi x2)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy))))=> x4) as proof of ((Xphi x2)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy)))->(Xphi x1)))
% Found (and_rect00 (fun (x4:(Xphi x2)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy))))=> x4)) as proof of (Xphi x1)
% Found ((and_rect0 (Xphi x1)) (fun (x4:(Xphi x2)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy))))=> x4)) as proof of (Xphi x1)
% Found (((fun (P:Type) (x4:((Xphi x2)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy)))->P)))=> (((((and_rect (Xphi x2)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy)))) P) x4) x3)) (Xphi x1)) (fun (x4:(Xphi x2)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy))))=> x4)) as proof of (Xphi x1)
% Found (fun (x3:((and (Xphi x2)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy)))))=> (((fun (P:Type) (x4:((Xphi x2)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy)))->P)))=> (((((and_rect (Xphi x2)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy)))) P) x4) x3)) (Xphi x1)) (fun (x4:(Xphi x2)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x2) Xy))))=> x4))) as proof of (Xphi x1)
% Found x4:(Xphi x1)
% Instantiate: x3:=x1:fofType
% Found (fun (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4) as proof of (Xphi x3)
% Found (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4) as proof of ((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->(Xphi x3))
% Found (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4) as proof of ((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->(Xphi x3)))
% Found (and_rect00 (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)) as proof of (Xphi x3)
% Found ((and_rect0 (Xphi x3)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)) as proof of (Xphi x3)
% Found (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x3)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)) as proof of (Xphi x3)
% Found (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x3)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)) as proof of (Xphi x3)
% Found (ex_intro000 (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x3)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((ex_intro00 x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (fun (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)))) as proof of (((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)))) as proof of (forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (ex_ind00 (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((ex_ind0 ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((fun (P:Prop) (x1:(forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (fun (x0:(exu (fun (Xx:fofType)=> (Xphi Xx))))=> (((fun (P:Prop) (x1:(forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (fun (Xphi:(fofType->Prop)) (x0:(exu (fun (Xx:fofType)=> (Xphi Xx))))=> (((fun (P:Prop) (x1:(forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)))))) as proof of ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x:exuE1) (Xphi:(fofType->Prop)) (x0:(exu (fun (Xx:fofType)=> (Xphi Xx))))=> (((fun (P:Prop) (x1:(forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)))))) as proof of (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (fun (x:exuE1) (Xphi:(fofType->Prop)) (x0:(exu (fun (Xx:fofType)=> (Xphi Xx))))=> (((fun (P:Prop) (x1:(forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4)))))) as proof of (exuE1->(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))))
% Got proof (fun (x:exuE1) (Xphi:(fofType->Prop)) (x0:(exu (fun (Xx:fofType)=> (Xphi Xx))))=> (((fun (P:Prop) (x1:(forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))))))
% Time elapsed = 1.161039s
% node=226 cost=526.000000 depth=20
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:exuE1) (Xphi:(fofType->Prop)) (x0:(exu (fun (Xx:fofType)=> (Xphi Xx))))=> (((fun (P:Prop) (x1:(forall (x:fofType), (((and (Xphi x)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x) Xy))))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (x1:fofType) (x2:((and (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (Xphi Xx))) x1) (((fun (P:Type) (x4:((Xphi x1)->((forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))->P)))=> (((((and_rect (Xphi x1)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy)))) P) x4) x2)) (Xphi x1)) (fun (x4:(Xphi x1)) (x5:(forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) x1) Xy))))=> x4))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------