TSTP Solution File: SEU675^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU675^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n115.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 13:32:47 EDT 2014
% Result : Theorem 0.47s
% Output : Proof 0.47s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU675^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.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 11:08:11 CDT 2014
% % CPUTime : 0.47
% 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 0x9b1d40>, <kernel.DependentProduct object at 0xb92c20>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xdd0d88>, <kernel.Single object at 0x9b15f0>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0xdd0d88>, <kernel.DependentProduct object at 0xb92758>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x9b15f0>, <kernel.DependentProduct object at 0xb92b00>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x9b1d40>, <kernel.DependentProduct object at 0xb92878>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x9b15f0>, <kernel.Sort object at 0x8791b8>) of role type named dsetconstrER_type
% Using role type
% Declaring dsetconstrER:Prop
% FOF formula (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))) of role definition named dsetconstrER
% A new definition: (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))))
% Defined: dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))
% FOF formula (<kernel.Constant object at 0xb92c20>, <kernel.DependentProduct object at 0xb92758>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xb929e0>, <kernel.DependentProduct object at 0xb92b00>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xb92b90>, <kernel.DependentProduct object at 0xb92c20>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xb92710>, <kernel.DependentProduct object at 0xb92ab8>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton
% A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))))
% Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))
% FOF formula (<kernel.Constant object at 0xb92ab8>, <kernel.DependentProduct object at 0xb92a28>) of role type named ex1_type
% Using role type
% Declaring ex1:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named ex1
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (<kernel.Constant object at 0xb92a28>, <kernel.DependentProduct object at 0xb923f8>) of role type named breln_type
% Using role type
% Declaring breln:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))) of role definition named breln
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))))
% Defined: breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))
% FOF formula (<kernel.Constant object at 0xb923f8>, <kernel.DependentProduct object at 0xb92b48>) of role type named func_type
% Using role type
% Declaring func:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))) of role definition named func
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))))
% Defined: func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))
% FOF formula (<kernel.Constant object at 0xb92b48>, <kernel.DependentProduct object at 0xb92b00>) of role type named funcSet_type
% Using role type
% Declaring funcSet:(fofType->(fofType->fofType))
% FOF formula (((eq (fofType->(fofType->fofType))) funcSet) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf))))) of role definition named funcSet
% A new definition: (((eq (fofType->(fofType->fofType))) funcSet) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf)))))
% Defined: funcSet:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf))))
% FOF formula (dsetconstrER->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))) of role conjecture named infuncsetfunc
% Conjecture to prove = (dsetconstrER->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))):Prop
% We need to prove ['(dsetconstrER->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter powerset:(fofType->fofType).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))):Prop.
% Parameter subset:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Definition ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))):(fofType->((fofType->Prop)->Prop)).
% Definition breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))):(fofType->(fofType->(fofType->Prop))).
% Definition func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))):(fofType->(fofType->(fofType->Prop))).
% Definition funcSet:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf)))):(fofType->(fofType->fofType)).
% Trying to prove (dsetconstrER->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))))
% Found x00:=(x0 ((func A) B)):(forall (Xx:fofType), (((in Xx) ((dsetconstr (powerset ((cartprod A) B))) (fun (Xy:fofType)=> (((func A) B) Xy))))->(((func A) B) Xx)))
% Found (x0 ((func A) B)) as proof of (forall (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))
% Found ((x (powerset ((cartprod A) B))) ((func A) B)) as proof of (forall (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))
% Found (fun (B:fofType)=> ((x (powerset ((cartprod A) B))) ((func A) B))) as proof of (forall (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))
% Found (fun (A:fofType) (B:fofType)=> ((x (powerset ((cartprod A) B))) ((func A) B))) as proof of (forall (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))
% Found (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset ((cartprod A) B))) ((func A) B))) as proof of (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))
% Found (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset ((cartprod A) B))) ((func A) B))) as proof of (dsetconstrER->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))))
% Got proof (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset ((cartprod A) B))) ((func A) B)))
% Time elapsed = 0.119725s
% node=6 cost=-179.000000 depth=5
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:dsetconstrER) (A:fofType) (B:fofType)=> ((x (powerset ((cartprod A) B))) ((func A) B)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------