%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU511^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:01:47 PM UTC 2025 % Result : Theorem 3.59s 3.76s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU511^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.13 % Command : duper %s % 0.15/0.34 % Computer : n031.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Fri Oct 3 04:48:53 EDT 2025 % 0.15/0.34 % CPUTime : % 3.59/3.76 SZS status Theorem for theBenchmark.p % 3.59/3.76 SZS output start Proof for theBenchmark.p % 3.59/3.76 Clause #0 (by assumption #[]): Eq (Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi)) True % 3.59/3.76 Clause #1 (by assumption #[]): Eq (Eq nonempty fun Xx => Ne Xx emptyset) True % 3.59/3.76 Clause #2 (by assumption #[]): Eq (Not (emptysetE → ∀ (A : Iota), (Exists fun Xx => in Xx A) → nonempty A)) True % 3.59/3.76 Clause #3 (by clausification #[2]): Eq (emptysetE → ∀ (A : Iota), (Exists fun Xx => in Xx A) → nonempty A) False % 3.59/3.76 Clause #4 (by clausification #[3]): Eq emptysetE True % 3.59/3.76 Clause #5 (by clausification #[3]): Eq (∀ (A : Iota), (Exists fun Xx => in Xx A) → nonempty A) False % 3.59/3.76 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not ((Exists fun Xx => in Xx (skS.0 0 a)) → nonempty (skS.0 0 a))) True % 3.59/3.76 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq ((Exists fun Xx => in Xx (skS.0 0 a)) → nonempty (skS.0 0 a)) False % 3.59/3.76 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Exists fun Xx => in Xx (skS.0 0 a)) True % 3.59/3.76 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (nonempty (skS.0 0 a)) False % 3.59/3.76 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (skS.0 0 a)) True % 3.59/3.76 Clause #11 (by clausification #[0]): Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.59/3.76 Clause #12 (by forward demodulation #[11, 4]): Eq True (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.59/3.76 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (in a emptyset → ∀ (Xphi : Prop), Xphi) True % 3.59/3.76 Clause #14 (by clausification #[13]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq (∀ (Xphi : Prop), Xphi) True) % 3.59/3.76 Clause #15 (by clausification #[14]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in a emptyset) False) (Eq a_1 True) % 3.59/3.76 Clause #16 (by clausification #[1]): Eq nonempty fun Xx => Ne Xx emptyset % 3.59/3.76 Clause #17 (by argument congruence #[16]): ∀ (a : Iota), Eq (nonempty a) ((fun Xx => Ne Xx emptyset) a) % 3.59/3.76 Clause #18 (by betaEtaReduce #[17]): ∀ (a : Iota), Eq (nonempty a) (Ne a emptyset) % 3.59/3.76 Clause #21 (by neHoist #[18]): ∀ (a : Iota), Or (Eq (nonempty a) True) (Eq a emptyset) % 3.59/3.76 Clause #22 (by superposition #[21, 9]): ∀ (a : Iota), Or (Eq (skS.0 0 a) emptyset) (Eq True False) % 3.59/3.76 Clause #48 (by clausification #[22]): ∀ (a : Iota), Eq (skS.0 0 a) emptyset % 3.59/3.76 Clause #49 (by backward demodulation #[48, 10]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) emptyset) True % 3.59/3.76 Clause #60 (by superposition #[49, 15]): ∀ (a : Prop), Or (Eq True False) (Eq a True) % 3.59/3.76 Clause #67 (by clausification #[60]): ∀ (a : Prop), Eq a True % 3.59/3.76 Clause #69 (by falseElim #[67]): False % 3.59/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------