%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU526^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:01:49 PM UTC 2025 % Result : Theorem 4.54s 4.75s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.09 % Problem : SEU526^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.10 % Command : duper %s % 0.09/0.31 % Computer : n010.cluster.edu % 0.09/0.31 % Model : x86_64 x86_64 % 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.31 % Memory : 8042.1875MB % 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.31 % CPULimit : 300 % 0.09/0.31 % WCLimit : 300 % 0.09/0.31 % DateTime : Fri Oct 3 06:29:08 EDT 2025 % 0.09/0.31 % CPUTime : % 4.54/4.75 SZS status Theorem for theBenchmark.p % 4.54/4.75 SZS output start Proof for theBenchmark.p % 4.54/4.75 Clause #0 (by assumption #[]): Eq (Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi)) True % 4.54/4.75 Clause #1 (by assumption #[]): Eq (Eq setext (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B)) True % 4.54/4.75 Clause #2 (by assumption #[]): Eq (Eq nonempty fun Xx => Ne Xx emptyset) True % 4.54/4.75 Clause #3 (by assumption #[]): Eq (Not (emptysetE → setext → ∀ (A : Iota), nonempty A → Exists fun Xx => And (in Xx A) True)) True % 4.54/4.75 Clause #4 (by clausification #[0]): Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 4.54/4.75 Clause #19 (by clausification #[1]): Eq setext (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) % 4.54/4.75 Clause #23 (by clausification #[2]): Eq nonempty fun Xx => Ne Xx emptyset % 4.54/4.75 Clause #24 (by argument congruence #[23]): ∀ (a : Iota), Eq (nonempty a) ((fun Xx => Ne Xx emptyset) a) % 4.54/4.75 Clause #25 (by betaEtaReduce #[24]): ∀ (a : Iota), Eq (nonempty a) (Ne a emptyset) % 4.54/4.75 Clause #27 (by clausify Prop equality #[25]): ∀ (a : Iota), Or (Eq (nonempty a) False) (Eq (Ne a emptyset) True) % 4.54/4.75 Clause #32 (by clausification #[27]): ∀ (a : Iota), Or (Eq (nonempty a) False) (Ne a emptyset) % 4.54/4.75 Clause #33 (by destructive equality resolution #[32]): Eq (nonempty emptyset) False % 4.54/4.75 Clause #35 (by clausification #[3]): Eq (emptysetE → setext → ∀ (A : Iota), nonempty A → Exists fun Xx => And (in Xx A) True) False % 4.54/4.75 Clause #36 (by clausification #[35]): Eq emptysetE True % 4.54/4.75 Clause #37 (by clausification #[35]): Eq (setext → ∀ (A : Iota), nonempty A → Exists fun Xx => And (in Xx A) True) False % 4.54/4.75 Clause #38 (by backward demodulation #[36, 4]): Eq True (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 4.54/4.75 Clause #42 (by clausification #[38]): ∀ (a : Iota), Eq (in a emptyset → ∀ (Xphi : Prop), Xphi) True % 4.54/4.75 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq (∀ (Xphi : Prop), Xphi) True) % 4.54/4.75 Clause #44 (by clausification #[43]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in a emptyset) False) (Eq a_1 True) % 4.54/4.75 Clause #91 (by clausification #[37]): Eq setext True % 4.54/4.75 Clause #92 (by clausification #[37]): Eq (∀ (A : Iota), nonempty A → Exists fun Xx => And (in Xx A) True) False % 4.54/4.75 Clause #93 (by backward demodulation #[91, 19]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) % 4.54/4.75 Clause #96 (by clausification #[93]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx a) → Eq a B) True % 4.54/4.75 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a) → Eq a a_1) True % 4.54/4.75 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), % 4.54/4.75 Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq ((∀ (Xx : Iota), in Xx a_1 → in Xx a) → Eq a a_1) True) % 4.54/4.75 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), % 4.54/4.75 Or (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → Eq a_1 a) True) % 4.54/4.75 (Eq (Not (in (skS.0 6 a_1 a a_2) a_1 → in (skS.0 6 a_1 a a_2) a)) True) % 4.54/4.75 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), % 4.54/4.75 Or (Eq (Not (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1)) True) % 4.54/4.75 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a) False) (Eq (Eq a a_1) True)) % 4.54/4.75 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 4.54/4.75 Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) % 4.54/4.75 (Or (Eq (Eq a_1 a) True) (Eq (in (skS.0 6 a_1 a a_2) a_1 → in (skS.0 6 a_1 a a_2) a) False)) % 4.54/4.75 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota), % 4.54/4.75 Or (Eq (Eq a a_1) True) % 4.54/4.75 (Or (Eq (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1) False) % 4.54/4.75 (Eq (Not (in (skS.0 7 a_1 a a_3) a_1 → in (skS.0 7 a_1 a a_3) a)) True)) % 4.54/4.75 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 a_3 : Iota), % 4.54/4.75 Or (Eq (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1) False) % 4.54/4.76 (Or (Eq (Not (in (skS.0 7 a_1 a a_3) a_1 → in (skS.0 7 a_1 a a_3) a)) True) (Eq a a_1)) % 4.54/4.76 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 4.54/4.76 Or (Eq (Not (in (skS.0 7 a a_1 a_2) a → in (skS.0 7 a a_1 a_2) a_1)) True) % 4.54/4.76 (Or (Eq a_1 a) (Eq (in (skS.0 6 a_1 a a_3) a_1) True)) % 4.54/4.76 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), % 4.54/4.76 Or (Eq a a_1) % 4.54/4.76 (Or (Eq (in (skS.0 6 a a_1 a_2) a) True) (Eq (in (skS.0 7 a_1 a a_3) a_1 → in (skS.0 7 a_1 a a_3) a) False)) % 4.54/4.76 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a a_1) (Or (Eq (in (skS.0 6 a a_1 a_2) a) True) (Eq (in (skS.0 7 a_1 a a_3) a_1) True)) % 4.54/4.76 Clause #123 (by superposition #[107, 44]): ∀ (a a_1 : Iota) (a_2 : Prop), % 4.54/4.76 Or (Eq a emptyset) (Or (Eq (in (skS.0 6 a emptyset a_1) a) True) (Or (Eq True False) (Eq a_2 True))) % 4.54/4.76 Clause #129 (by clausification #[92]): ∀ (a : Iota), Eq (Not (nonempty (skS.0 8 a) → Exists fun Xx => And (in Xx (skS.0 8 a)) True)) True % 4.54/4.76 Clause #130 (by clausification #[129]): ∀ (a : Iota), Eq (nonempty (skS.0 8 a) → Exists fun Xx => And (in Xx (skS.0 8 a)) True) False % 4.54/4.76 Clause #131 (by clausification #[130]): ∀ (a : Iota), Eq (nonempty (skS.0 8 a)) True % 4.54/4.76 Clause #132 (by clausification #[130]): ∀ (a : Iota), Eq (Exists fun Xx => And (in Xx (skS.0 8 a)) True) False % 4.54/4.76 Clause #141 (by clausification #[132]): ∀ (a a_1 : Iota), Eq (And (in a (skS.0 8 a_1)) True) False % 4.54/4.76 Clause #142 (by clausification #[141]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 8 a_1)) False) (Eq True False) % 4.54/4.76 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota), Eq (in a (skS.0 8 a_1)) False % 4.54/4.76 Clause #157 (by clausification #[123]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq a emptyset) (Or (Eq (in (skS.0 6 a emptyset a_1) a) True) (Eq a_2 True)) % 4.54/4.76 Clause #164 (by superposition #[157, 143]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (skS.0 8 a) emptyset) (Or (Eq a_1 True) (Eq True False)) % 4.54/4.76 Clause #180 (by clausification #[164]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (skS.0 8 a) emptyset) (Eq a_1 True) % 4.54/4.76 Clause #181 (by superposition #[180, 131]): ∀ (a : Prop), Or (Eq a True) (Eq (nonempty emptyset) True) % 4.54/4.76 Clause #190 (by superposition #[181, 33]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 4.54/4.76 Clause #199 (by clausification #[190]): ∀ (a : Prop), Eq a True % 4.54/4.76 Clause #201 (by falseElim #[199]): False % 4.54/4.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------