%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU500^1 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n098.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 13:32:18 EDT 2014 % Result : Theorem 0.89s % Output : Proof 0.89s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU500^1 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n098.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 10:24:26 CDT 2014 % % CPUTime : 0.89 % 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 0x25a05a8>, <kernel.DependentProduct object at 0x25a03f8>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x29d8638>, <kernel.DependentProduct object at 0x25a0518>) 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 0x25a0518>, <kernel.Sort object at 0x246be18>) of role type named setextAx_type % Using role type % Declaring setextAx:Prop % FOF formula (((eq Prop) setextAx) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B)))) of role definition named setextAx % A new definition: (((eq Prop) setextAx) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B)))) % Defined: setextAx:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B))) % FOF formula (<kernel.Constant object at 0x25a09e0>, <kernel.Single object at 0x25a03f8>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x25a0a70>, <kernel.Sort object at 0x246be18>) of role type named emptysetAx_type % Using role type % Declaring emptysetAx:Prop % FOF formula (((eq Prop) emptysetAx) (forall (Xx:fofType), (((in Xx) emptyset)->False))) of role definition named emptysetAx % A new definition: (((eq Prop) emptysetAx) (forall (Xx:fofType), (((in Xx) emptyset)->False))) % Defined: emptysetAx:=(forall (Xx:fofType), (((in Xx) emptyset)->False)) % FOF formula (<kernel.Constant object at 0x25a0a28>, <kernel.DependentProduct object at 0x25a0950>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x25a0998>, <kernel.Sort object at 0x246be18>) of role type named setadjoinAx_type % Using role type % Declaring setadjoinAx:Prop % FOF formula (((eq Prop) setadjoinAx) (forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A))))) of role definition named setadjoinAx % A new definition: (((eq Prop) setadjoinAx) (forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A))))) % Defined: setadjoinAx:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A)))) % FOF formula (<kernel.Constant object at 0x29da488>, <kernel.DependentProduct object at 0x25a07e8>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x25a09e0>, <kernel.Sort object at 0x246be18>) of role type named powersetAx_type % Using role type % Declaring powersetAx:Prop % FOF formula (((eq Prop) powersetAx) (forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))))) of role definition named powersetAx % A new definition: (((eq Prop) powersetAx) (forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))))) % Defined: powersetAx:=(forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A))))) % FOF formula (<kernel.Constant object at 0x25a0950>, <kernel.DependentProduct object at 0x25a0518>) of role type named setunion_type % Using role type % Declaring setunion:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x25a0758>, <kernel.Sort object at 0x246be18>) of role type named setunionAx_type % Using role type % Declaring setunionAx:Prop % FOF formula (((eq Prop) setunionAx) (forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A))))))) of role definition named setunionAx % A new definition: (((eq Prop) setunionAx) (forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A))))))) % Defined: setunionAx:=(forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A)))))) % FOF formula (<kernel.Constant object at 0x25a09e0>, <kernel.Single object at 0x25a0758>) of role type named omega_type % Using role type % Declaring omega:fofType % FOF formula (<kernel.Constant object at 0x25a0cb0>, <kernel.Sort object at 0x246be18>) of role type named omega0Ax_type % Using role type % Declaring omega0Ax:Prop % FOF formula (((eq Prop) omega0Ax) ((in emptyset) omega)) of role definition named omega0Ax % A new definition: (((eq Prop) omega0Ax) ((in emptyset) omega)) % Defined: omega0Ax:=((in emptyset) omega) % FOF formula (<kernel.Constant object at 0x25a0cf8>, <kernel.Sort object at 0x246be18>) of role type named omegaSAx_type % Using role type % Declaring omegaSAx:Prop % FOF formula (((eq Prop) omegaSAx) (forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega)))) of role definition named omegaSAx % A new definition: (((eq Prop) omegaSAx) (forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega)))) % Defined: omegaSAx:=(forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega))) % FOF formula (<kernel.Constant object at 0x25a0fc8>, <kernel.Sort object at 0x246be18>) of role type named omegaIndAx_type % Using role type % Declaring omegaIndAx:Prop % FOF formula (((eq Prop) omegaIndAx) (forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A)))))) of role definition named omegaIndAx % A new definition: (((eq Prop) omegaIndAx) (forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A)))))) % Defined: omegaIndAx:=(forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A))))) % FOF formula (<kernel.Constant object at 0x25a05f0>, <kernel.Sort object at 0x246be18>) of role type named replAx_type % Using role type % Declaring replAx:Prop % FOF formula (((eq Prop) replAx) (forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx))))))))))) of role definition named replAx % A new definition: (((eq Prop) replAx) (forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx))))))))))) % Defined: replAx:=(forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx)))))))))) % FOF formula (<kernel.Constant object at 0x25a0d88>, <kernel.Sort object at 0x246be18>) of role type named foundationAx_type % Using role type % Declaring foundationAx:Prop % FOF formula (((eq Prop) foundationAx) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False))))))) of role definition named foundationAx % A new definition: (((eq Prop) foundationAx) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False))))))) % Defined: foundationAx:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False)))))) % FOF formula (<kernel.Constant object at 0x25a0f80>, <kernel.Sort object at 0x246be18>) of role type named wellorderingAx_type % Using role type % Declaring wellorderingAx:Prop % FOF formula (((eq Prop) wellorderingAx) (forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E)))))))))))))))) of role definition named wellorderingAx % A new definition: (((eq Prop) wellorderingAx) (forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E)))))))))))))))) % Defined: wellorderingAx:=(forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E))))))))))))))) % FOF formula (<kernel.Constant object at 0x25a0b48>, <kernel.DependentProduct object at 0x246ec20>) of role type named descr_type % Using role type % Declaring descr:((fofType->Prop)->fofType) % FOF formula (<kernel.Constant object at 0x246ecb0>, <kernel.Sort object at 0x246be18>) of role type named descrp_type % Using role type % Declaring descrp:Prop % FOF formula (((eq Prop) descrp) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx))))))) of role definition named descrp % A new definition: (((eq Prop) descrp) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx))))))) % Defined: descrp:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx)))))) % FOF formula (<kernel.Constant object at 0x25a09e0>, <kernel.DependentProduct object at 0x2794fc8>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x25a0f80>, <kernel.Sort object at 0x246be18>) 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 0x25a0a28>, <kernel.Sort object at 0x246be18>) of role type named dsetconstrEL_type % Using role type % Declaring dsetconstrEL:Prop % FOF formula (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))) of role definition named dsetconstrEL % A new definition: (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))) % Defined: dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))) % FOF formula (<kernel.Constant object at 0x25a0a28>, <kernel.Sort object at 0x246be18>) 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 0x25a0d88>, <kernel.Sort object at 0x246be18>) 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 (<kernel.Constant object at 0x2794b90>, <kernel.DependentProduct object at 0x27948c0>) of role type named prop2set_type % Using role type % Declaring prop2set:(Prop->fofType) % FOF formula (((eq (Prop->fofType)) prop2set) (fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi)))) of role definition named prop2set % A new definition: (((eq (Prop->fofType)) prop2set) (fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi)))) % Defined: prop2set:=(fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi))) % FOF formula (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))))))))))) of role conjecture named prop2setE % Conjecture to prove = (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))))))))))):Prop % We need to prove ['(setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))))))))))))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % 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 setextAx:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B))):Prop. % Parameter emptyset:fofType. % Definition emptysetAx:=(forall (Xx:fofType), (((in Xx) emptyset)->False)):Prop. % Parameter setadjoin:(fofType->(fofType->fofType)). % Definition setadjoinAx:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A)))):Prop. % Parameter powerset:(fofType->fofType). % Definition powersetAx:=(forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A))))):Prop. % Parameter setunion:(fofType->fofType). % Definition setunionAx:=(forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A)))))):Prop. % Parameter omega:fofType. % Definition omega0Ax:=((in emptyset) omega):Prop. % Definition omegaSAx:=(forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega))):Prop. % Definition omegaIndAx:=(forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A))))):Prop. % Definition replAx:=(forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx)))))))))):Prop. % Definition foundationAx:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False)))))):Prop. % Definition wellorderingAx:=(forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E))))))))))))))):Prop. % Parameter descr:((fofType->Prop)->fofType). % Definition descrp:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx)))))):Prop. % 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 dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))):Prop. % Definition dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))):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. % Definition prop2set:=(fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi))):(Prop->fofType). % Trying to prove (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))))))))))) % Found x1300:=(x130 (fun (x17:fofType)=> Xphi)):(forall (Xx:fofType), (((in Xx) ((dsetconstr (powerset emptyset)) (fun (Xy:fofType)=> Xphi)))->Xphi)) % Found (x130 (fun (x17:fofType)=> Xphi)) as proof of (forall (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)) % Found ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi)) as proof of (forall (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)) % Found (fun (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (forall (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)) % Found (fun (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)) % Found (fun (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))) % Found (fun (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))) % Found (fun (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))) % Found (fun (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))) % Found (fun (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))))) % Found (fun (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))) % Found (fun (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))))))) % Found (fun (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))) % Found (fun (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))))))))) % Found (fun (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))))) % Found (fun (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))))))))))) % Found (fun (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))))))) % Found (fun (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))))))))))))) % Found (fun (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))))))))) % Found (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))))))))))))))))) % Found (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) as proof of (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))))))))))))))))) % Got proof (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) % Time elapsed = 0.500178s % node=51 cost=16.000000 depth=19 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (Xphi:Prop)=> ((x13 (powerset emptyset)) (fun (x17:fofType)=> Xphi))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------