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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU707^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n103.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 13:32:52 EDT 2014

% Result   : Theorem 2.46s
% Output   : Proof 2.46s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU707^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n103.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 11:15:51 CDT 2014
% % CPUTime  : 2.46 
% 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 0x17da098>, <kernel.DependentProduct object at 0x1581e18>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x17da098>, <kernel.DependentProduct object at 0x1581b00>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x17e1b90>, <kernel.DependentProduct object at 0x1581d88>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x17e1b90>, <kernel.DependentProduct object at 0x1581ef0>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1581ea8>, <kernel.Sort object at 0x1273c20>) of role type named iftrueProp1_type
% Using role type
% Declaring iftrueProp1:Prop
% FOF formula (((eq Prop) iftrueProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))) of role definition named iftrueProp1
% A new definition: (((eq Prop) iftrueProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))))
% Defined: iftrueProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))
% FOF formula (<kernel.Constant object at 0x1271758>, <kernel.Sort object at 0x1273c20>) of role type named ifSingleton_type
% Using role type
% Declaring ifSingleton:Prop
% FOF formula (((eq Prop) ifSingleton) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))) of role definition named ifSingleton
% A new definition: (((eq Prop) ifSingleton) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))
% Defined: ifSingleton:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))
% FOF formula (<kernel.Constant object at 0x1274908>, <kernel.DependentProduct object at 0x1581638>) of role type named if_type
% Using role type
% Declaring if:(fofType->(Prop->(fofType->(fofType->fofType))))
% FOF formula (((eq (fofType->(Prop->(fofType->(fofType->fofType))))) if) (fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))) of role definition named if
% A new definition: (((eq (fofType->(Prop->(fofType->(fofType->fofType))))) if) (fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))
% Defined: if:=(fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% FOF formula (<kernel.Constant object at 0x1274830>, <kernel.Sort object at 0x1273c20>) of role type named theeq_type
% Using role type
% Declaring theeq:Prop
% FOF formula (((eq Prop) theeq) (forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx)))))) of role definition named theeq
% A new definition: (((eq Prop) theeq) (forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx))))))
% Defined: theeq:=(forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx)))))
% FOF formula (iftrueProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))))))))) of role conjecture named iftrue
% Conjecture to prove = (iftrueProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(iftrueProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter setunion:(fofType->fofType).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Parameter singleton:(fofType->Prop).
% Definition iftrueProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))):Prop.
% Definition ifSingleton:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))):Prop.
% Definition if:=(fun (A:fofType) (Xphi:Prop) (Xx:fofType) (Xy:fofType)=> (setunion ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))):(fofType->(Prop->(fofType->(fofType->fofType)))).
% Definition theeq:=(forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx))))):Prop.
% Trying to prove (iftrueProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)))))))))
% Found eq_ref00:=(eq_ref0 ((((if A) Xphi) Xx) Xy)):(((eq fofType) ((((if A) Xphi) Xx) Xy)) ((((if A) Xphi) Xx) Xy))
% Found (eq_ref0 ((((if A) Xphi) Xx) Xy)) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) b)
% Found ((eq_ref fofType) ((((if A) Xphi) Xx) Xy)) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) b)
% Found ((eq_ref fofType) ((((if A) Xphi) Xx) Xy)) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) b)
% Found ((eq_ref fofType) ((((if A) Xphi) Xx) Xy)) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x0000000:=(x000000 x3):(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (x000000 x3) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((x00000 Xy) x3) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((x0000 x2) Xy) x3) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((((x000 Xx) x2) Xy) x3) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((((x00 Xphi) Xx) x2) Xy) x3) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((((((x0 A) Xphi) Xx) x2) Xy) x3) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((((((x0 A) Xphi) Xx) x2) Xy) x3) as proof of (singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x5000000:=(x500000 x3):((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (x500000 x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((x50000 Xy) x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((x5000 x2) Xy) x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((((x500 Xx) x2) Xy) x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((x50 Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> ((((((x5 Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3) as proof of ((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((x100 ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3)) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)
% Found (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> ((x10 x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3)) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)
% Found (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3)) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)
% Found (fun (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)
% Found (fun (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))
% Found (fun (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)))
% Found (fun (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))))
% Found (fun (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)))))
% Found (fun (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))))))
% Found (fun (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (forall (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))))))
% Found (fun (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))))))
% Found (fun (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)))))))
% Found (fun (x:iftrueProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx))))))))
% Found (fun (x:iftrueProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3))) as proof of (iftrueProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xx)))))))))
% Got proof (fun (x:iftrueProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3)))
% Time elapsed = 2.114951s
% node=323 cost=457.000000 depth=21
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:iftrueProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:Xphi)=> (((fun (x5:(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))=> (((x1 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) x5) Xx)) ((((((x0 A) Xphi) Xx) x2) Xy) x3)) (((((fun (Xx0:fofType) (x6:((in Xx0) A)) (Xy0:fofType) (x7:((in Xy0) A))=> (((((((x A) Xphi) Xx0) x6) Xy0) x7) x4)) Xx) x2) Xy) x3)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------