%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU808^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 3.49s 3.70s % Output : Proof 3.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU808^2 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.14 % Command : duper %s % 0.14/0.35 % Computer : n017.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 05:37:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.49/3.70 SZS status Theorem for theBenchmark.p % 3.49/3.70 SZS output start Proof for theBenchmark.p % 3.49/3.70 Clause #0 (by assumption #[]): Eq (Eq omegaSAx (∀ (Xx : Iota), in Xx omega → in (setadjoin Xx Xx) omega)) True % 3.49/3.70 Clause #1 (by assumption #[]): Eq (Eq omegaS fun Xx => setadjoin Xx Xx) True % 3.49/3.70 Clause #2 (by assumption #[]): Eq (Not (omegaSAx → ∀ (Xx : Iota), in Xx omega → in (omegaS Xx) omega)) True % 3.49/3.70 Clause #3 (by clausification #[2]): Eq (omegaSAx → ∀ (Xx : Iota), in Xx omega → in (omegaS Xx) omega) False % 3.49/3.70 Clause #4 (by clausification #[3]): Eq omegaSAx True % 3.49/3.70 Clause #5 (by clausification #[3]): Eq (∀ (Xx : Iota), in Xx omega → in (omegaS Xx) omega) False % 3.49/3.70 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (in (skS.0 0 a) omega → in (omegaS (skS.0 0 a)) omega)) True % 3.49/3.70 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (in (skS.0 0 a) omega → in (omegaS (skS.0 0 a)) omega) False % 3.49/3.70 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (in (skS.0 0 a) omega) True % 3.49/3.70 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (in (omegaS (skS.0 0 a)) omega) False % 3.49/3.70 Clause #10 (by clausification #[1]): Eq omegaS fun Xx => setadjoin Xx Xx % 3.49/3.70 Clause #11 (by argument congruence #[10]): ∀ (a : Iota), Eq (omegaS a) ((fun Xx => setadjoin Xx Xx) a) % 3.49/3.70 Clause #12 (by betaEtaReduce #[11]): ∀ (a : Iota), Eq (omegaS a) (setadjoin a a) % 3.49/3.70 Clause #13 (by clausification #[0]): Eq omegaSAx (∀ (Xx : Iota), in Xx omega → in (setadjoin Xx Xx) omega) % 3.49/3.70 Clause #14 (by forward demodulation #[13, 4]): Eq True (∀ (Xx : Iota), in Xx omega → in (setadjoin Xx Xx) omega) % 3.49/3.70 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (in a omega → in (setadjoin a a) omega) True % 3.49/3.70 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (in a omega) False) (Eq (in (setadjoin a a) omega) True) % 3.49/3.70 Clause #17 (by forward demodulation #[16, 12]): ∀ (a : Iota), Or (Eq (in a omega) False) (Eq (in (omegaS a) omega) True) % 3.49/3.70 Clause #18 (by superposition #[17, 8]): ∀ (a : Iota), Or (Eq (in (omegaS (skS.0 0 a)) omega) True) (Eq False True) % 3.49/3.70 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (in (omegaS (skS.0 0 a)) omega) True % 3.49/3.70 Clause #20 (by superposition #[19, 9]): Eq True False % 3.49/3.70 Clause #22 (by clausification #[20]): False % 3.49/3.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------