%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU811^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:02:29 PM UTC 2025 % Result : Theorem 4.26s 4.46s % Output : Proof 4.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SEU811^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.15 % Command : duper %s % 0.15/0.37 % Computer : n015.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Fri Oct 3 05:06:08 EDT 2025 % 0.15/0.37 % CPUTime : % 4.26/4.46 SZS status Theorem for theBenchmark.p % 4.26/4.46 SZS output start Proof for theBenchmark.p % 4.26/4.46 Clause #0 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 4.26/4.46 Clause #1 (by assumption #[]): Eq % 4.26/4.46 (Eq setadjoinE % 4.26/4.46 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi)) % 4.26/4.46 True % 4.26/4.46 Clause #3 (by assumption #[]): Eq (Eq notinself2 (∀ (A B : Iota), in A B → Not (in B A))) True % 4.26/4.46 Clause #4 (by assumption #[]): Eq (Eq omegaS fun Xx => setadjoin Xx Xx) True % 4.26/4.46 Clause #5 (by assumption #[]): Eq % 4.26/4.46 (Not % 4.26/4.46 (setadjoinIL → % 4.26/4.46 setadjoinE → % 4.26/4.46 in__Cong → % 4.26/4.46 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy)) % 4.26/4.46 True % 4.26/4.46 Clause #6 (by clausification #[4]): Eq omegaS fun Xx => setadjoin Xx Xx % 4.26/4.46 Clause #7 (by argument congruence #[6]): ∀ (a : Iota), Eq (omegaS a) ((fun Xx => setadjoin Xx Xx) a) % 4.26/4.46 Clause #8 (by betaEtaReduce #[7]): ∀ (a : Iota), Eq (omegaS a) (setadjoin a a) % 4.26/4.46 Clause #9 (by clausification #[3]): Eq notinself2 (∀ (A B : Iota), in A B → Not (in B A)) % 4.26/4.46 Clause #23 (by clausification #[0]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 4.26/4.46 Clause #25 (by clausify Prop equality #[23]): Or (Eq setadjoinIL False) (Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) True) % 4.26/4.46 Clause #27 (by clausification #[25]): ∀ (a : Iota), Or (Eq setadjoinIL False) (Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True) % 4.26/4.46 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq setadjoinIL False) (Eq (in a (setadjoin a a_1)) True) % 4.26/4.46 Clause #33 (by clausification #[1]): Eq setadjoinE % 4.26/4.46 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) % 4.26/4.46 Clause #72 (by clausification #[5]): Eq % 4.26/4.46 (setadjoinIL → % 4.26/4.46 setadjoinE → % 4.26/4.46 in__Cong → % 4.26/4.46 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy) % 4.26/4.46 False % 4.26/4.46 Clause #73 (by clausification #[72]): Eq setadjoinIL True % 4.26/4.46 Clause #74 (by clausification #[72]): Eq % 4.26/4.46 (setadjoinE → % 4.26/4.46 in__Cong → % 4.26/4.46 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy) % 4.26/4.46 False % 4.26/4.46 Clause #76 (by backward demodulation #[73, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a a_1)) True) % 4.26/4.46 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 4.26/4.46 Clause #79 (by superposition #[78, 8]): ∀ (a : Iota), Eq (in a (omegaS a)) True % 4.26/4.46 Clause #81 (by clausification #[74]): Eq setadjoinE True % 4.26/4.46 Clause #82 (by clausification #[74]): Eq % 4.26/4.46 (in__Cong → % 4.26/4.46 notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy) % 4.26/4.46 False % 4.26/4.46 Clause #83 (by backward demodulation #[81, 33]): Eq True (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) % 4.26/4.46 Clause #87 (by clausification #[83]): ∀ (a : Iota), % 4.26/4.46 Eq (∀ (A Xy : Iota), in Xy (setadjoin a A) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy A → Xphi) → Xphi) True % 4.26/4.46 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), % 4.26/4.46 Eq (∀ (Xy : Iota), in Xy (setadjoin a a_1) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy a_1 → Xphi) → Xphi) True % 4.26/4.46 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 a_2) → ∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True % 4.26/4.46 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), % 4.26/4.46 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq (∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True) % 4.26/4.46 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.26/4.46 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq ((Eq a a_1 → a_3) → (in a a_2 → a_3) → a_3) True) % 4.26/4.46 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.26/4.46 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1 → a_3) False) (Eq ((in a a_2 → a_3) → a_3) True)) % 4.30/4.48 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.30/4.48 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq ((in a a_2 → a_3) → a_3) True) (Eq (Eq a a_1) True)) % 4.30/4.48 Clause #95 (by clausification #[93]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.30/4.48 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1) True) (Or (Eq (in a a_2 → a_3) False) (Eq a_3 True))) % 4.30/4.48 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.30/4.48 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (in a a_2 → a_3) False) (Or (Eq a_3 True) (Eq a a_1))) % 4.30/4.48 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.30/4.48 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq a_3 True) (Or (Eq a a_1) (Eq (in a a_2) True))) % 4.30/4.48 Clause #100 (by superposition #[97, 8]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (in a (omegaS a_1)) False) (Or (Eq a_2 True) (Or (Eq a a_1) (Eq (in a a_1) True))) % 4.30/4.48 Clause #107 (by clausification #[82]): Eq (notinself2 → ∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy) False % 4.30/4.48 Clause #117 (by clausification #[107]): Eq notinself2 True % 4.30/4.48 Clause #118 (by clausification #[107]): Eq (∀ (Xx : Iota), in Xx omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS Xx) (omegaS Xy) → Eq Xx Xy) False % 4.30/4.48 Clause #119 (by backward demodulation #[117, 9]): Eq True (∀ (A B : Iota), in A B → Not (in B A)) % 4.30/4.48 Clause #123 (by clausification #[119]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Not (in B a)) True % 4.30/4.48 Clause #124 (by clausification #[123]): ∀ (a a_1 : Iota), Eq (in a a_1 → Not (in a_1 a)) True % 4.30/4.48 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a_1 a)) True) % 4.30/4.48 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a) False) % 4.30/4.48 Clause #143 (by clausification #[118]): ∀ (a : Iota), % 4.30/4.48 Eq % 4.30/4.48 (Not % 4.30/4.48 (in (skS.0 10 a) omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS (skS.0 10 a)) (omegaS Xy) → Eq (skS.0 10 a) Xy)) % 4.30/4.48 True % 4.30/4.48 Clause #144 (by clausification #[143]): ∀ (a : Iota), % 4.30/4.48 Eq (in (skS.0 10 a) omega → ∀ (Xy : Iota), in Xy omega → Eq (omegaS (skS.0 10 a)) (omegaS Xy) → Eq (skS.0 10 a) Xy) % 4.30/4.48 False % 4.30/4.48 Clause #145 (by clausification #[144]): ∀ (a : Iota), Eq (in (skS.0 10 a) omega) True % 4.30/4.48 Clause #146 (by clausification #[144]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in Xy omega → Eq (omegaS (skS.0 10 a)) (omegaS Xy) → Eq (skS.0 10 a) Xy) False % 4.30/4.48 Clause #147 (by superposition #[145, 126]): ∀ (a : Iota), Or (Eq True False) (Eq (in omega (skS.0 10 a)) False) % 4.30/4.48 Clause #148 (by clausification #[147]): ∀ (a : Iota), Eq (in omega (skS.0 10 a)) False % 4.30/4.48 Clause #151 (by clausification #[146]): ∀ (a a_1 : Iota), % 4.30/4.48 Eq % 4.30/4.48 (Not % 4.30/4.48 (in (skS.0 11 a a_1) omega → % 4.30/4.48 Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1)) → Eq (skS.0 10 a) (skS.0 11 a a_1))) % 4.30/4.48 True % 4.30/4.48 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota), % 4.30/4.48 Eq (in (skS.0 11 a a_1) omega → Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1)) → Eq (skS.0 10 a) (skS.0 11 a a_1)) % 4.30/4.48 False % 4.30/4.48 Clause #154 (by clausification #[152]): ∀ (a a_1 : Iota), Eq (Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1)) → Eq (skS.0 10 a) (skS.0 11 a a_1)) False % 4.30/4.48 Clause #178 (by clausification #[154]): ∀ (a a_1 : Iota), Eq (Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1))) True % 4.30/4.48 Clause #179 (by clausification #[154]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 10 a) (skS.0 11 a a_1)) False % 4.30/4.48 Clause #180 (by clausification #[178]): ∀ (a a_1 : Iota), Eq (omegaS (skS.0 10 a)) (omegaS (skS.0 11 a a_1)) % 4.30/4.48 Clause #181 (by superposition #[180, 79]): ∀ (a a_1 : Iota), Eq (in (skS.0 11 a a_1) (omegaS (skS.0 10 a))) True % 4.30/4.48 Clause #183 (by superposition #[180, 100]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 4.30/4.48 Or (Eq (in a (omegaS (skS.0 10 a_1))) False) % 4.30/4.48 (Or (Eq a_2 True) (Or (Eq a (skS.0 11 a_1 a_3)) (Eq (in a (skS.0 11 a_1 a_3)) True))) % 4.30/4.48 Clause #185 (by superposition #[181, 100]): ∀ (a : Prop) (a_1 a_2 : Iota), % 4.30/4.48 Or (Eq True False) % 4.30/4.48 (Or (Eq a True) (Or (Eq (skS.0 11 a_1 a_2) (skS.0 10 a_1)) (Eq (in (skS.0 11 a_1 a_2) (skS.0 10 a_1)) True))) % 4.30/4.49 Clause #187 (by clausification #[179]): ∀ (a a_1 : Iota), Ne (skS.0 10 a) (skS.0 11 a a_1) % 4.30/4.49 Clause #197 (by superposition #[183, 79]): ∀ (a : Prop) (a_1 a_2 : Iota), % 4.30/4.49 Or (Eq a True) % 4.30/4.49 (Or (Eq (skS.0 10 a_1) (skS.0 11 a_1 a_2)) (Or (Eq (in (skS.0 10 a_1) (skS.0 11 a_1 a_2)) True) (Eq False True))) % 4.30/4.49 Clause #198 (by clausification #[185]): ∀ (a : Prop) (a_1 a_2 : Iota), % 4.30/4.49 Or (Eq a True) (Or (Eq (skS.0 11 a_1 a_2) (skS.0 10 a_1)) (Eq (in (skS.0 11 a_1 a_2) (skS.0 10 a_1)) True)) % 4.30/4.49 Clause #199 (by forward contextual literal cutting #[198, 187]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (in (skS.0 11 a_1 a_2) (skS.0 10 a_1)) True) % 4.30/4.49 Clause #200 (by superposition #[199, 148]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 11 a a_1) (skS.0 10 a)) True) (Eq True False) % 4.30/4.49 Clause #213 (by clausification #[200]): ∀ (a a_1 : Iota), Eq (in (skS.0 11 a a_1) (skS.0 10 a)) True % 4.30/4.49 Clause #214 (by superposition #[213, 126]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (skS.0 10 a) (skS.0 11 a a_1)) False) % 4.30/4.49 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota), Eq (in (skS.0 10 a) (skS.0 11 a a_1)) False % 4.30/4.49 Clause #232 (by clausification #[197]): ∀ (a : Prop) (a_1 a_2 : Iota), % 4.30/4.49 Or (Eq a True) (Or (Eq (skS.0 10 a_1) (skS.0 11 a_1 a_2)) (Eq (in (skS.0 10 a_1) (skS.0 11 a_1 a_2)) True)) % 4.30/4.49 Clause #233 (by forward contextual literal cutting #[232, 187]): ∀ (a : Prop) (a_1 a_2 : Iota), Or (Eq a True) (Eq (in (skS.0 10 a_1) (skS.0 11 a_1 a_2)) True) % 4.30/4.49 Clause #239 (by superposition #[233, 215]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 4.30/4.49 Clause #244 (by clausification #[239]): ∀ (a : Prop), Eq a True % 4.30/4.49 Clause #247 (by falseElim #[244]): False % 4.30/4.49 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------