%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU510^1 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n186.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 13:32:20 EDT 2014 % Result : Theorem 260.23s % Output : Proof 260.23s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU510^1 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n186.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 10:27:06 CDT 2014 % % CPUTime : 260.23 % 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 0xe6d170>, <kernel.DependentProduct object at 0xe6d050>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0xb74cb0>, <kernel.DependentProduct object at 0xe6d320>) 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 0xe6d320>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6d440>, <kernel.Single object at 0xe6d320>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0xe6d488>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6d440>, <kernel.DependentProduct object at 0xe8b320>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0xe6d488>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6d488>, <kernel.DependentProduct object at 0xe8b0e0>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0xe6d488>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8ba70>, <kernel.DependentProduct object at 0x10e2908>) of role type named setunion_type % Using role type % Declaring setunion:(fofType->fofType) % FOF formula (<kernel.Constant object at 0xe8b170>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8b830>, <kernel.Single object at 0xe8b170>) of role type named omega_type % Using role type % Declaring omega:fofType % FOF formula (<kernel.Constant object at 0xe8ba70>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8ba70>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8b710>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6ad40>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2320>, <kernel.Sort object at 0xb6ffc8>) 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 0xcaab90>, <kernel.Sort object at 0xb6ffc8>) 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 0xcaab90>, <kernel.DependentProduct object at 0x10e28c0>) of role type named descr_type % Using role type % Declaring descr:((fofType->Prop)->fofType) % FOF formula (<kernel.Constant object at 0xcaaef0>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2950>, <kernel.DependentProduct object at 0x10e2830>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x10e2a70>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2bd8>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2710>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2dd0>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2c68>, <kernel.DependentProduct object at 0x10e22d8>) 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 (<kernel.Constant object at 0x10e2488>, <kernel.Sort object at 0xb6ffc8>) of role type named prop2setE_type % Using role type % Declaring prop2setE:Prop % FOF formula (((eq Prop) prop2setE) (forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))) of role definition named prop2setE % A new definition: (((eq Prop) prop2setE) (forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))) % Defined: prop2setE:=(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)) % FOF formula (<kernel.Constant object at 0x10e25f0>, <kernel.Sort object at 0xb6ffc8>) 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 (<kernel.Constant object at 0x10e22d8>, <kernel.Sort object at 0xb6ffc8>) of role type named emptysetimpfalse_type % Using role type % Declaring emptysetimpfalse:Prop % FOF formula (((eq Prop) emptysetimpfalse) (forall (Xx:fofType), (((in Xx) emptyset)->False))) of role definition named emptysetimpfalse % A new definition: (((eq Prop) emptysetimpfalse) (forall (Xx:fofType), (((in Xx) emptyset)->False))) % Defined: emptysetimpfalse:=(forall (Xx:fofType), (((in Xx) emptyset)->False)) % FOF formula (<kernel.Constant object at 0x10e22d8>, <kernel.Sort object at 0xb6ffc8>) of role type named notinemptyset_type % Using role type % Declaring notinemptyset:Prop % FOF formula (((eq Prop) notinemptyset) (forall (Xx:fofType), (((in Xx) emptyset)->False))) of role definition named notinemptyset % A new definition: (((eq Prop) notinemptyset) (forall (Xx:fofType), (((in Xx) emptyset)->False))) % Defined: notinemptyset:=(forall (Xx:fofType), (((in Xx) emptyset)->False)) % FOF formula (<kernel.Constant object at 0x10e22d8>, <kernel.Sort object at 0xb6ffc8>) of role type named exuE3e_type % Using role type % Declaring exuE3e:Prop % FOF formula (((eq Prop) exuE3e) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named exuE3e % A new definition: (((eq Prop) exuE3e) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))) % Defined: exuE3e:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))) % FOF formula (<kernel.Constant object at 0xe8c488>, <kernel.Sort object at 0xb6ffc8>) of role type named setext_type % Using role type % Declaring setext:Prop % FOF formula (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))) of role definition named setext % A new definition: (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))) % Defined: setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))) % FOF formula (<kernel.Constant object at 0xe8c638>, <kernel.Sort object at 0xb6ffc8>) of role type named emptyI_type % Using role type % Declaring emptyI:Prop % FOF formula (((eq Prop) emptyI) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))) of role definition named emptyI % A new definition: (((eq Prop) emptyI) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))) % Defined: emptyI:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))) % FOF formula (<kernel.Constant object at 0xe8c2d8>, <kernel.Sort object at 0xb6ffc8>) of role type named noeltsimpempty_type % Using role type % Declaring noeltsimpempty:Prop % FOF formula (((eq Prop) noeltsimpempty) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))) of role definition named noeltsimpempty % A new definition: (((eq Prop) noeltsimpempty) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))) % Defined: noeltsimpempty:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))) % FOF formula (<kernel.Constant object at 0xe8c950>, <kernel.Sort object at 0xb6ffc8>) of role type named setbeta_type % Using role type % Declaring setbeta:Prop % FOF formula (((eq Prop) setbeta) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx))))) of role definition named setbeta % A new definition: (((eq Prop) setbeta) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx))))) % Defined: setbeta:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx)))) % FOF formula (<kernel.Constant object at 0xe8c128>, <kernel.DependentProduct object at 0xe8cc20>) of role type named nonempty_type % Using role type % Declaring nonempty:(fofType->Prop) % FOF formula (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))) of role definition named nonempty % A new definition: (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))) % Defined: nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))) % FOF formula (<kernel.Constant object at 0xe8cc20>, <kernel.Sort object at 0xb6ffc8>) of role type named nonemptyE1_type % Using role type % Declaring nonemptyE1:Prop % FOF formula (((eq Prop) nonemptyE1) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))))) of role definition named nonemptyE1 % A new definition: (((eq Prop) nonemptyE1) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))))) % Defined: nonemptyE1:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A))))) % FOF formula (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))))) of role conjecture named nonemptyI % Conjecture to prove = (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))))):Prop % We need to prove ['(setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))))))'] % 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). % Definition prop2setE:=(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)):Prop. % Definition emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))):Prop. % Definition emptysetimpfalse:=(forall (Xx:fofType), (((in Xx) emptyset)->False)):Prop. % Definition notinemptyset:=(forall (Xx:fofType), (((in Xx) emptyset)->False)):Prop. % Definition exuE3e:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))):Prop. % Definition setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))):Prop. % Definition emptyI:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))):Prop. % Definition noeltsimpempty:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))):Prop. % Definition setbeta:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx)))):Prop. % Definition nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))):(fofType->Prop). % Definition nonemptyE1:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A))))):Prop. % Trying to prove (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))))) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx:=emptyset:fofType % Found x4 as proof of ((in Xx) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x4:omega0Ax % Instantiate: Xx0:=emptyset:fofType % Found x4 as proof of ((in Xx0) omega) % Found x25:((in Xx) A) % Instantiate: Xx0:=Xx:fofType % Found x25 as proof of ((in Xx0) A) % Found x26:(Xphi Xx) % Instantiate: Xx0:=Xx:fofType % Found x26 as proof of (Xphi Xx0) % Found ((x11000 x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) % Found (((x1100 Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) % Found ((((x110 Xphi) Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) % Found (((((x11 A) Xphi) Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) % Found (((((x11 A) Xphi) Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) % Found (x270 (((((x11 A) Xphi) Xx0) x25) x26)) as proof of ((in Xx0) emptyset) % Found ((x27 (in Xx0)) (((((x11 A) Xphi) Xx0) x25) x26)) as proof of ((in Xx0) emptyset) % Found ((x27 (in Xx0)) (((((x11 A) Xphi) Xx0) x25) x26)) as proof of ((in Xx0) emptyset) % Found (x00 ((x27 (in Xx0)) (((((x11 A) Xphi) Xx0) x25) x26))) as proof of False % Found ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26))) as proof of False % Found (fun (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of False % Found (fun (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) % Found (fun (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of ((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) % Found (fun (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))) % Found (fun (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))) % Found (fun (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (forall (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))) % Found (fun (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))) % Found (fun (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) % Found (fun (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))) % Found (fun (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))) % Found (fun (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))) % Found (fun (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))) % Found (fun (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))) % Found (fun (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))) % Found (fun (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))) % Found (fun (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))) % Found (fun (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))) % Found (fun (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))) % Found (fun (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))) % Found (fun (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))) % Found (fun (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))) % Found (fun (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))) % Found (fun (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))) % Found (fun (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))) % Found (fun (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))) % Found (fun (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))) % Found (fun (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))) % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))) % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))) % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))) % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))) % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))))) % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))))) % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) % Time elapsed = 258.731538s % node=15512 cost=1240.000000 depth=43 % :::::::::::::::::::::: % % 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) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------