%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO143^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:08:39 PM UTC 2025 % Result : Theorem 4.51s 4.68s % Output : Proof 4.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYO143^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.13 % Command : duper %s % 0.14/0.35 % Computer : n023.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 14:16:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.51/4.68 SZS status Theorem for theBenchmark.p % 4.51/4.68 SZS output start Proof for theBenchmark.p % 4.51/4.68 Clause #0 (by assumption #[]): Eq (Not (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists fun Xz => cQ Xz) → Exists fun Xz => cQ Xz)) % 4.51/4.68 True % 4.51/4.68 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists cQ) → Exists cQ)) True % 4.51/4.68 Clause #2 (by clausification #[1]): Eq (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists cQ) → Exists cQ) False % 4.51/4.68 Clause #3 (by clausification #[2]): Eq (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists cQ)) True % 4.51/4.68 Clause #4 (by clausification #[2]): Eq (Exists cQ) False % 4.51/4.68 Clause #5 (by clausification #[3]): Or (Eq (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) True) (Eq (Exists cQ) True) % 4.51/4.68 Clause #6 (by clausification #[5]): Or (Eq (Exists cQ) True) (Eq (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx) False) % 4.51/4.68 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx) False) (Eq (cQ (skS.0 0 a)) True) % 4.51/4.68 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (∀ (Xx : Iota), cP a_1 → cP Xx) False) % 4.51/4.68 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (Not (cP a_1 → cP (skS.0 1 a_1 a_2))) True) % 4.51/4.68 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cP a_1 → cP (skS.0 1 a_1 a_2)) False) % 4.51/4.68 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cP a_1) True) % 4.51/4.68 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cP (skS.0 1 a_1 a_2)) False) % 4.51/4.68 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (cQ a) False % 4.51/4.68 Clause #14 (by superposition #[13, 11]): ∀ (a : Iota), Or (Eq False True) (Eq (cP a) True) % 4.51/4.68 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (cP a) True % 4.51/4.68 Clause #16 (by superposition #[12, 15]): ∀ (a : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq True False) % 4.51/4.68 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (cQ (skS.0 0 a)) True % 4.51/4.68 Clause #18 (by superposition #[17, 13]): Eq True False % 4.51/4.68 Clause #19 (by clausification #[18]): False % 4.51/4.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------