%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU793^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n111.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 13:33:08 EDT 2014 % Result : Theorem 7.48s % Output : Proof 7.48s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU793^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n111.star.cs.uiowa.edu % % Model : x86_64 x86_64 % % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % % Memory : 32286.75MB % % OS : Linux 2.6.32-431.20.3.el6.x86_64 % % CPULimit : 300 % % DateTime : Thu Jul 17 11:30:01 CDT 2014 % % CPUTime : 7.48 % 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 0x28a0560>, <kernel.DependentProduct object at 0x28bf878>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x2b16a28>, <kernel.DependentProduct object at 0x28bf7e8>) 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 0x25abb90>, <kernel.Sort object at 0x25a5128>) 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 (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))) of role conjecture named image1Ex % Conjecture to prove = (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))):Prop % Parameter fofType_DUMMY:fofType. % We need to prove ['(replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf 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 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. % Trying to prove (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))) % Found eq_ref00:=(eq_ref0 (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))):(((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (eq_ref0 (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b) % Found ((eq_ref (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b) % Found ((eq_ref (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b) % Found ((eq_ref (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b) % Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0)) % Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Xx:fofType), ((iff ((in Xx) x)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0)) % Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))) % Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Xx:fofType), ((iff ((in Xx) x)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found x1:((in Xx) x0) % Instantiate: x2:=Xx:fofType;x0:=A:fofType % Found x1 as proof of ((in x2) A) % Found x1:((in Xx) x0) % Instantiate: x2:=Xx:fofType;x0:=A:fofType % Found x1 as proof of ((in x2) A) % Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x))) % Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b) % Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b) % Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b) % Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b) % Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b) % Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x))) % Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x))) % Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found eq_ref00:=(eq_ref0 x2):(((eq fofType) x2) x2) % Found (eq_ref0 x2) as proof of (((eq fofType) x2) (Xf Xx)) % Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) (Xf Xx)) % Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) (Xf Xx)) % Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) (Xf Xx)) % Found eq_sym000:=(eq_sym00 (Xf Xx)):((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)) % Found (eq_sym00 (Xf Xx)) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)) % Found ((eq_sym0 Xy) (Xf Xx)) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)) % Found (((eq_sym fofType) Xy) (Xf Xx)) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)) % Found (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)) % Found (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))) as proof of (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))) % Found ((conj00 ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) % Found (((conj0 (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) % Found ((((conj (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) % Found ((((conj (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) % Found (ex_intro000 ((((conj (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy)))))) % Found ((ex_intro00 (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy)))))) % Found (((ex_intro0 (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy)))))) % Found ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy)))))) % Found ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy)))))) % Found (fun (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))) as proof of (exu (fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx)))) % Found (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))) as proof of (((in Xx) A)->(exu (fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))))) % Found (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))) as proof of (forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx)))))) % Found (x00 (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found ((x0 A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (fun (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) % Found (fun (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of (forall (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))) % Found (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of (forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))) % Found (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))) % Got proof (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) % Time elapsed = 7.109090s % node=1171 cost=2340.000000 depth=23 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------