%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU645^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:02:07 PM UTC 2025 % Result : Theorem 107.13s 107.31s % Output : Proof 108.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU645^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 04:13:08 EDT 2025 % 0.13/0.34 % CPUTime : % 107.13/107.31 SZS status Theorem for theBenchmark.p % 107.13/107.31 SZS output start Proof for theBenchmark.p % 107.13/107.31 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 107.13/107.31 True % 107.13/107.31 Clause #2 (by assumption #[]): Eq (Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 107.13/107.31 True % 107.13/107.31 Clause #3 (by assumption #[]): Eq (Eq kpairp (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy))) True % 107.13/107.31 Clause #5 (by assumption #[]): Eq % 107.13/107.31 (Eq setukpairinjL1 % 107.13/107.31 (∀ (Xx Xy Xz : Iota), % 107.13/107.31 in (setadjoin Xz emptyset) % 107.13/107.31 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 107.13/107.31 Eq Xx Xz)) % 107.13/107.31 True % 107.13/107.31 Clause #6 (by assumption #[]): Eq % 107.13/107.31 (Eq kfstsingleton % 107.13/107.31 (∀ (Xu : Iota), iskpair Xu → singleton (dsetconstr (setunion Xu) fun Xx => in (setadjoin Xx emptyset) Xu))) % 107.13/107.31 True % 107.13/107.31 Clause #7 (by assumption #[]): Eq (Eq theprop (∀ (X : Iota), singleton X → in (setunion X) X)) True % 107.13/107.31 Clause #8 (by assumption #[]): Eq (Eq kfst fun Xu => setunion (dsetconstr (setunion Xu) fun Xx => in (setadjoin Xx emptyset) Xu)) True % 107.13/107.31 Clause #9 (by assumption #[]): Eq % 107.13/107.31 (Not % 107.13/107.31 (dsetconstrER → kpairp → setukpairinjL1 → kfstsingleton → theprop → ∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx)) % 107.13/107.31 True % 107.13/107.31 Clause #10 (by clausification #[7]): Eq theprop (∀ (X : Iota), singleton X → in (setunion X) X) % 107.13/107.31 Clause #20 (by clausification #[3]): Eq kpairp (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) % 107.13/107.31 Clause #22 (by clausify Prop equality #[20]): Or (Eq kpairp False) (Eq (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) True) % 107.13/107.31 Clause #24 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 107.13/107.31 Clause #25 (by clausification #[24]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 107.13/107.31 Clause #41 (by clausification #[22]): ∀ (a : Iota), Or (Eq kpairp False) (Eq (∀ (Xy : Iota), iskpair (kpair a Xy)) True) % 107.13/107.31 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq kpairp False) (Eq (iskpair (kpair a a_1)) True) % 107.13/107.31 Clause #49 (by clausification #[5]): Eq setukpairinjL1 % 107.13/107.31 (∀ (Xx Xy Xz : Iota), % 107.13/107.31 in (setadjoin Xz emptyset) % 107.13/107.31 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 107.13/107.31 Eq Xx Xz) % 107.13/107.31 Clause #66 (by clausification #[2]): Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset) % 107.13/107.31 Clause #68 (by argument congruence #[66]): ∀ (a a_1 : Iota), % 107.13/107.31 Eq (kpair a a_1) % 107.13/107.31 ((fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) a a_1) % 107.13/107.31 Clause #69 (by clausification #[9]): Eq (dsetconstrER → kpairp → setukpairinjL1 → kfstsingleton → theprop → ∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) % 107.13/107.31 False % 107.13/107.31 Clause #70 (by clausification #[69]): Eq dsetconstrER True % 107.13/107.31 Clause #71 (by clausification #[69]): Eq (kpairp → setukpairinjL1 → kfstsingleton → theprop → ∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) False % 107.13/107.31 Clause #72 (by backward demodulation #[70, 25]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 107.13/107.31 Clause #75 (by clausification #[72]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 107.13/107.31 Clause #76 (by clausification #[75]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 107.13/107.31 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 107.13/107.31 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 107.13/107.31 Clause #97 (by clausification #[71]): Eq kpairp True % 107.13/107.31 Clause #98 (by clausification #[71]): Eq (setukpairinjL1 → kfstsingleton → theprop → ∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) False % 107.13/107.31 Clause #100 (by backward demodulation #[97, 42]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (iskpair (kpair a a_1)) True) % 107.13/107.34 Clause #104 (by clausification #[100]): ∀ (a a_1 : Iota), Eq (iskpair (kpair a a_1)) True % 107.13/107.34 Clause #108 (by clausification #[6]): Eq kfstsingleton % 107.13/107.34 (∀ (Xu : Iota), iskpair Xu → singleton (dsetconstr (setunion Xu) fun Xx => in (setadjoin Xx emptyset) Xu)) % 107.13/107.34 Clause #114 (by clausification #[98]): Eq setukpairinjL1 True % 107.13/107.34 Clause #115 (by clausification #[98]): Eq (kfstsingleton → theprop → ∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) False % 107.13/107.34 Clause #116 (by backward demodulation #[114, 49]): Eq True % 107.13/107.34 (∀ (Xx Xy Xz : Iota), % 107.13/107.34 in (setadjoin Xz emptyset) % 107.13/107.34 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 107.13/107.34 Eq Xx Xz) % 107.13/107.34 Clause #122 (by clausification #[116]): ∀ (a : Iota), % 107.13/107.34 Eq % 107.13/107.34 (∀ (Xy Xz : Iota), % 107.13/107.34 in (setadjoin Xz emptyset) % 107.13/107.34 (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) → % 107.13/107.34 Eq a Xz) % 107.13/107.34 True % 107.13/107.34 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), % 107.13/107.34 Eq % 107.13/107.34 (∀ (Xz : Iota), % 107.13/107.34 in (setadjoin Xz emptyset) % 107.13/107.34 (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)) → % 107.13/107.34 Eq a Xz) % 107.13/107.34 True % 107.13/107.34 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 107.13/107.34 Eq % 107.13/107.34 (in (setadjoin a emptyset) % 107.13/107.34 (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset)) → % 107.13/107.34 Eq a_1 a) % 107.13/107.34 True % 107.13/107.34 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), % 107.13/107.34 Or % 107.13/107.34 (Eq % 107.13/107.34 (in (setadjoin a emptyset) % 107.13/107.34 (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset))) % 107.13/107.34 False) % 107.13/107.34 (Eq (Eq a_1 a) True) % 107.13/107.34 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), % 107.13/107.34 Or % 107.13/107.34 (Eq % 107.13/107.34 (in (setadjoin a emptyset) % 107.13/107.34 (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset))) % 107.13/107.34 False) % 107.13/107.34 (Eq a_1 a) % 107.13/107.34 Clause #132 (by clausification #[8]): Eq kfst fun Xu => setunion (dsetconstr (setunion Xu) fun Xx => in (setadjoin Xx emptyset) Xu) % 107.13/107.34 Clause #133 (by argument congruence #[132]): ∀ (a : Iota), Eq (kfst a) ((fun Xu => setunion (dsetconstr (setunion Xu) fun Xx => in (setadjoin Xx emptyset) Xu)) a) % 107.13/107.34 Clause #138 (by clausification #[115]): Eq kfstsingleton True % 107.13/107.34 Clause #139 (by clausification #[115]): Eq (theprop → ∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) False % 107.13/107.34 Clause #140 (by backward demodulation #[138, 108]): Eq True (∀ (Xu : Iota), iskpair Xu → singleton (dsetconstr (setunion Xu) fun Xx => in (setadjoin Xx emptyset) Xu)) % 107.13/107.34 Clause #144 (by clausification #[139]): Eq theprop True % 107.13/107.34 Clause #145 (by clausification #[139]): Eq (∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) False % 107.13/107.34 Clause #146 (by backward demodulation #[144, 10]): Eq True (∀ (X : Iota), singleton X → in (setunion X) X) % 107.13/107.34 Clause #153 (by clausification #[146]): ∀ (a : Iota), Eq (singleton a → in (setunion a) a) True % 107.13/107.34 Clause #154 (by clausification #[153]): ∀ (a : Iota), Or (Eq (singleton a) False) (Eq (in (setunion a) a) True) % 107.13/107.34 Clause #156 (by clausification #[145]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), Eq (kfst (kpair (skS.0 9 a) Xy)) (skS.0 9 a))) True % 107.13/107.34 Clause #157 (by clausification #[156]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq (kfst (kpair (skS.0 9 a) Xy)) (skS.0 9 a)) False % 107.13/107.34 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), Eq (Not (Eq (kfst (kpair (skS.0 9 a) (skS.0 10 a a_1))) (skS.0 9 a))) True % 107.13/107.34 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), Eq (Eq (kfst (kpair (skS.0 9 a) (skS.0 10 a a_1))) (skS.0 9 a)) False % 107.13/107.34 Clause #160 (by clausification #[159]): ∀ (a a_1 : Iota), Ne (kfst (kpair (skS.0 9 a) (skS.0 10 a a_1))) (skS.0 9 a) % 107.13/107.34 Clause #162 (by clausification #[140]): ∀ (a : Iota), Eq (iskpair a → singleton (dsetconstr (setunion a) fun Xx => in (setadjoin Xx emptyset) a)) True % 107.13/107.34 Clause #163 (by clausification #[162]): ∀ (a : Iota), % 107.13/107.34 Or (Eq (iskpair a) False) (Eq (singleton (dsetconstr (setunion a) fun Xx => in (setadjoin Xx emptyset) a)) True) % 108.23/108.45 Clause #164 (by superposition #[163, 104]): ∀ (a a_1 : Iota), % 108.23/108.45 Or (Eq (singleton (dsetconstr (setunion (kpair a a_1)) fun Xx => in (setadjoin Xx emptyset) (kpair a a_1))) True) % 108.23/108.45 (Eq False True) % 108.23/108.45 Clause #176 (by betaEtaReduce #[133]): ∀ (a : Iota), Eq (kfst a) (setunion (dsetconstr (setunion a) fun Xx => in (setadjoin Xx emptyset) a)) % 108.23/108.45 Clause #255 (by betaEtaReduce #[68]): ∀ (a a_1 : Iota), % 108.23/108.45 Eq (kpair a a_1) (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)) % 108.23/108.45 Clause #256 (by backward demodulation #[255, 126]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (setadjoin a emptyset) (kpair a_1 a_2)) False) (Eq a_1 a) % 108.23/108.45 Clause #487 (by clausification #[164]): ∀ (a a_1 : Iota), % 108.23/108.45 Eq (singleton (dsetconstr (setunion (kpair a a_1)) fun Xx => in (setadjoin Xx emptyset) (kpair a a_1))) True % 108.23/108.45 Clause #488 (by superposition #[487, 154]): ∀ (a a_1 : Iota), % 108.23/108.45 Or (Eq True False) % 108.23/108.45 (Eq % 108.23/108.45 (in (setunion (dsetconstr (setunion (kpair a a_1)) fun Xx => in (setadjoin Xx emptyset) (kpair a a_1))) % 108.23/108.45 (dsetconstr (setunion (kpair a a_1)) fun Xx => in (setadjoin Xx emptyset) (kpair a a_1))) % 108.23/108.45 True) % 108.23/108.45 Clause #11258 (by clausification #[488]): ∀ (a a_1 : Iota), % 108.23/108.45 Eq % 108.23/108.45 (in (setunion (dsetconstr (setunion (kpair a a_1)) fun Xx => in (setadjoin Xx emptyset) (kpair a a_1))) % 108.23/108.45 (dsetconstr (setunion (kpair a a_1)) fun Xx => in (setadjoin Xx emptyset) (kpair a a_1))) % 108.23/108.45 True % 108.23/108.45 Clause #11259 (by forward demodulation #[11258, 176]): ∀ (a a_1 : Iota), % 108.23/108.45 Eq (in (kfst (kpair a a_1)) (dsetconstr (setunion (kpair a a_1)) fun Xx => in (setadjoin Xx emptyset) (kpair a a_1))) % 108.23/108.45 True % 108.23/108.45 Clause #11260 (by superposition #[11259, 78]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (setadjoin (kfst (kpair a a_1)) emptyset) (kpair a a_1)) True) % 108.23/108.45 Clause #11760 (by clausification #[11260]): ∀ (a a_1 : Iota), Eq (in (setadjoin (kfst (kpair a a_1)) emptyset) (kpair a a_1)) True % 108.23/108.45 Clause #11761 (by superposition #[11760, 256]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq a (kfst (kpair a a_1))) % 108.23/108.45 Clause #11816 (by clausification #[11761]): ∀ (a a_1 : Iota), Eq a (kfst (kpair a a_1)) % 108.23/108.45 Clause #11820 (by backward contextual literal cutting #[11816, 160]): False % 108.23/108.45 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------