TSTP Solution File: SEU534^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU534^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n117.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 13:32:24 EDT 2014
% Result : Theorem 4.68s
% Output : Proof 4.68s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU534^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n117.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 10:32:51 CDT 2014
% % CPUTime : 4.68
% 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 0xf0fa70>, <kernel.DependentProduct object at 0xf0f950>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x12cc098>, <kernel.Single object at 0xf0f908>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0xf0f950>, <kernel.DependentProduct object at 0xf0fbd8>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0xf0fb90>, <kernel.Sort object at 0xdd5518>) of role type named dsetconstrI_type
% Using role type
% Declaring dsetconstrI:Prop
% FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI
% A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0xf0f998>, <kernel.Sort object at 0xdd5518>) of role type named emptysetE_type
% Using role type
% Declaring emptysetE:Prop
% FOF formula (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))) of role definition named emptysetE
% A new definition: (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))))
% Defined: emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))
% FOF formula (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))) of role conjecture named emptyE1
% Conjecture to prove = (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))):Prop
% We need to prove ['(dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop.
% Definition emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))):Prop.
% Trying to prove (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))))
% Found x500:=(x50 x3):(((in x3) A)->((Xphi x3)->((in x3) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))
% Found (x50 x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))))
% Found ((x5 Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))))
% Found (((x A) Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))))
% Found (((x A) Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))))
% Found (((x A) Xphi) x3) as proof of (((in x3) A)->((Xphi x3)->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))))
% Found (x20 (((x A) Xphi) x3)) as proof of (((in x3) A)->((Xphi x3)->((in Xx) emptyset)))
% Found ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)) as proof of (((in x3) A)->((Xphi x3)->((in Xx) emptyset)))
% Found ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)) as proof of (((in x3) A)->((Xphi x3)->((in Xx) emptyset)))
% Found (and_rect00 ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset)
% Found ((and_rect0 ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset)
% Found (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset)
% Found (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3))) as proof of ((in Xx) emptyset)
% Found (x000 (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)))) as proof of False
% Found (x000 (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)))) as proof of False
% Found ((fun (x5:((in Xx) emptyset))=> ((x00 x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in Xx) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in Xx) x6))))) (((x A) Xphi) x3)))) as proof of False
% Found ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))) as proof of False
% Found (fun (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))) as proof of False
% Found (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))) as proof of (((and ((in x3) A)) (Xphi x3))->False)
% Found (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))) as proof of (forall (x:fofType), (((and ((in x) A)) (Xphi x))->False))
% Found (ex_ind00 (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))) as proof of False
% Found ((ex_ind0 False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))) as proof of False
% Found (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))) as proof of False
% Found (fun (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of False
% Found (fun (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of ((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)
% Found (fun (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))
% Found (fun (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))
% Found (fun (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))
% Found (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))
% Found (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3))))))) as proof of (dsetconstrI->(emptysetE->(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))))
% Got proof (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))))
% Time elapsed = 4.322874s
% node=675 cost=968.000000 depth=28
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:dsetconstrI) (x0:emptysetE) (A:fofType) (Xphi:(fofType->Prop)) (x1:((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))) (x2:(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))=> (((fun (P:Prop) (x3:(forall (x:fofType), (((and ((in x) A)) (Xphi x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P) x3) x1)) False) (fun (x3:fofType) (x4:((and ((in x3) A)) (Xphi x3)))=> ((fun (x5:((in x3) emptyset))=> (((x0 x3) x5) False)) (((fun (P:Type) (x5:(((in x3) A)->((Xphi x3)->P)))=> (((((and_rect ((in x3) A)) (Xphi x3)) P) x5) x4)) ((in x3) emptyset)) ((x2 (fun (x6:fofType)=> (((in x3) A)->((Xphi x3)->((in x3) x6))))) (((x A) Xphi) x3)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------