TSTP Solution File: SEU708^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU708^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n112.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 13:32:53 EDT 2014
% Result : Theorem 2.64s
% Output : Proof 2.64s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU708^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n112.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 11:16:06 CDT 2014
% % CPUTime : 2.64
% 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 0x16d5ab8>, <kernel.DependentProduct object at 0x16baf38>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1b10f80>, <kernel.DependentProduct object at 0x16bad88>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1b10f80>, <kernel.DependentProduct object at 0x16bafc8>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x16d5a28>, <kernel.DependentProduct object at 0x16bacf8>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x16d5ab8>, <kernel.Sort object at 0x159aab8>) of role type named iffalseProp1_type
% Using role type
% Declaring iffalseProp1:Prop
% FOF formula (((eq Prop) iffalseProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))) of role definition named iffalseProp1
% A new definition: (((eq Prop) iffalseProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))))
% Defined: iffalseProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((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 0x16d5a28>, <kernel.Sort object at 0x159aab8>) 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 0x16bab48>, <kernel.DependentProduct object at 0x16bacb0>) 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 0x16bacb0>, <kernel.Sort object at 0x159aab8>) 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 (iffalseProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))))))))) of role conjecture named iffalse
% Conjecture to prove = (iffalseProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(iffalseProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter setunion:(fofType->fofType).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Parameter singleton:(fofType->Prop).
% Definition iffalseProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((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 (iffalseProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy)))))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% 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 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 Xy) ((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 Xy) ((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 Xy) ((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 Xy) ((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 Xy) ((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 Xy) ((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 Xy) ((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 Xy) ((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 Xy) ((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)) Xy)
% 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) Xy)) ((((((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)) Xy)
% 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) Xy)) ((((((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)) Xy)
% Found (fun (x4:(Xphi->False))=> (((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) Xy)) ((((((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)) Xy)
% Found (fun (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))
% Found (fun (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy)))
% Found (fun (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))))
% Found (fun (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy)))))
% Found (fun (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))))))
% Found (fun (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))))))
% Found (fun (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))))))
% Found (fun (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy)))))))
% Found (fun (x:iffalseProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy))))))))
% Found (fun (x:iffalseProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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 (iffalseProp1->(ifSingleton->(theeq->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((((if A) Xphi) Xx) Xy)) Xy)))))))))
% Got proof (fun (x:iffalseProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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 = 2.278742s
% node=358 cost=458.000000 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:iffalseProp1) (x0:ifSingleton) (x1:theeq) (A:fofType) (Xphi:Prop) (Xx:fofType) (x2:((in Xx) A)) (Xy:fofType) (x3:((in Xy) A)) (x4:(Xphi->False))=> (((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) Xy)) ((((((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
%------------------------------------------------------------------------------