%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO161^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:08:40 PM UTC 2025 % Result : Theorem 3.62s 3.85s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO161^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 13:09:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.62/3.85 SZS status Theorem for theBenchmark.p % 3.62/3.85 SZS output start Proof for theBenchmark.p % 3.62/3.85 Clause #0 (by assumption #[]): Eq % 3.62/3.85 (Not % 3.62/3.85 ((Exists fun Xx => ∀ (Xy : Iota), And (cP Xx → cP Xy) (cP Xy → cP Xx)) → % 3.62/3.85 And ((Exists fun Xx => cP Xx) → ∀ (Xy : Iota), cP Xy) ((∀ (Xy : Iota), cP Xy) → Exists fun Xx => cP Xx))) % 3.62/3.85 True % 3.62/3.85 Clause #1 (by betaEtaReduce #[0]): Eq % 3.62/3.85 (Not % 3.62/3.85 ((Exists fun Xx => ∀ (Xy : Iota), And (cP Xx → cP Xy) (cP Xy → cP Xx)) → % 3.62/3.85 And (Exists cP → ∀ (Xy : Iota), cP Xy) ((∀ (Xy : Iota), cP Xy) → Exists cP))) % 3.62/3.85 True % 3.62/3.85 Clause #2 (by clausification #[1]): Eq % 3.62/3.85 ((Exists fun Xx => ∀ (Xy : Iota), And (cP Xx → cP Xy) (cP Xy → cP Xx)) → % 3.62/3.85 And (Exists cP → ∀ (Xy : Iota), cP Xy) ((∀ (Xy : Iota), cP Xy) → Exists cP)) % 3.62/3.85 False % 3.62/3.85 Clause #3 (by clausification #[2]): Eq (Exists fun Xx => ∀ (Xy : Iota), And (cP Xx → cP Xy) (cP Xy → cP Xx)) True % 3.62/3.85 Clause #4 (by clausification #[2]): Eq (And (Exists cP → ∀ (Xy : Iota), cP Xy) ((∀ (Xy : Iota), cP Xy) → Exists cP)) False % 3.62/3.85 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Xy : Iota), And (cP (skS.0 0 a) → cP Xy) (cP Xy → cP (skS.0 0 a))) True % 3.62/3.85 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (And (cP (skS.0 0 a) → cP a_1) (cP a_1 → cP (skS.0 0 a))) True % 3.62/3.85 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (cP a → cP (skS.0 0 a_1)) True % 3.62/3.85 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (cP (skS.0 0 a) → cP a_1) True % 3.62/3.85 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cP (skS.0 0 a_1)) True) % 3.62/3.85 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 0 a)) False) (Eq (cP a_1) True) % 3.62/3.85 Clause #11 (by clausification #[4]): Or (Eq (Exists cP → ∀ (Xy : Iota), cP Xy) False) (Eq ((∀ (Xy : Iota), cP Xy) → Exists cP) False) % 3.62/3.85 Clause #12 (by clausification #[11]): Or (Eq ((∀ (Xy : Iota), cP Xy) → Exists cP) False) (Eq (Exists cP) True) % 3.62/3.85 Clause #13 (by clausification #[11]): Or (Eq ((∀ (Xy : Iota), cP Xy) → Exists cP) False) (Eq (∀ (Xy : Iota), cP Xy) False) % 3.62/3.85 Clause #14 (by clausification #[12]): Or (Eq (Exists cP) True) (Eq (∀ (Xy : Iota), cP Xy) True) % 3.62/3.85 Clause #16 (by clausification #[14]): ∀ (a : Iota), Or (Eq (∀ (Xy : Iota), cP Xy) True) (Eq (cP (skS.0 1 a)) True) % 3.62/3.85 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 a)) True) (Eq (cP a_1) True) % 3.62/3.85 Clause #18 (by superposition #[17, 9]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq True False) (Eq (cP (skS.0 0 a_1)) True)) % 3.62/3.85 Clause #27 (by clausification #[13]): Or (Eq (∀ (Xy : Iota), cP Xy) False) (Eq (Exists cP) False) % 3.62/3.85 Clause #32 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cP (skS.0 0 a_1)) True) % 3.62/3.85 Clause #37 (by superposition #[32, 10]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq True False) (Eq (cP a_1) True)) % 3.62/3.85 Clause #40 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cP a_1) True) % 3.62/3.85 Clause #42 (by equality factoring #[40]): ∀ (a : Iota), Or (Ne True True) (Eq (cP a) True) % 3.62/3.85 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (cP a) True) (Or (Eq True False) (Eq True False)) % 3.62/3.85 Clause #45 (by clausification #[43]): ∀ (a : Iota), Or (Eq (cP a) True) (Eq True False) % 3.62/3.85 Clause #46 (by clausification #[45]): ∀ (a : Iota), Eq (cP a) True % 3.62/3.85 Clause #47 (by clausification #[27]): ∀ (a : Iota), Or (Eq (Exists cP) False) (Eq (Not (cP (skS.0 4 a))) True) % 3.62/3.85 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (Not (cP (skS.0 4 a))) True) (Eq (cP a_1) False) % 3.62/3.85 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cP (skS.0 4 a_1)) False) % 3.62/3.85 Clause #50 (by superposition #[49, 46]): ∀ (a : Iota), Or (Eq (cP (skS.0 4 a)) False) (Eq False True) % 3.62/3.85 Clause #59 (by clausification #[50]): ∀ (a : Iota), Eq (cP (skS.0 4 a)) False % 3.62/3.85 Clause #60 (by superposition #[59, 46]): Eq False True % 3.62/3.85 Clause #61 (by clausification #[60]): False % 3.62/3.85 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------