%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN375^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:07:32 PM UTC 2025 % Result : Theorem 3.63s 3.80s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SYN375^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.12 % Command : duper %s % 0.13/0.33 % Computer : n021.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Oct 2 15:07:08 EDT 2025 % 0.13/0.33 % CPUTime : % 3.63/3.80 SZS status Theorem for theBenchmark.p % 3.63/3.80 SZS output start Proof for theBenchmark.p % 3.63/3.80 Clause #0 (by assumption #[]): Eq % 3.63/3.80 (Not % 3.63/3.80 (And ((∀ (Xx : Iota), cP Xx) → Exists fun Xy => cP Xy) ((Exists fun Xy => cP Xy) → ∀ (Xx : Iota), cP Xx) → % 3.63/3.80 Iff (Exists fun Xy => cP Xy) (∀ (Xx : Iota), cP Xx))) % 3.63/3.80 True % 3.63/3.80 Clause #1 (by betaEtaReduce #[0]): Eq % 3.63/3.80 (Not % 3.63/3.80 (And ((∀ (Xx : Iota), cP Xx) → Exists cP) (Exists cP → ∀ (Xx : Iota), cP Xx) → % 3.63/3.80 Iff (Exists cP) (∀ (Xx : Iota), cP Xx))) % 3.63/3.80 True % 3.63/3.80 Clause #2 (by clausification #[1]): Eq % 3.63/3.80 (And ((∀ (Xx : Iota), cP Xx) → Exists cP) (Exists cP → ∀ (Xx : Iota), cP Xx) → Iff (Exists cP) (∀ (Xx : Iota), cP Xx)) % 3.63/3.80 False % 3.63/3.80 Clause #3 (by clausification #[2]): Eq (And ((∀ (Xx : Iota), cP Xx) → Exists cP) (Exists cP → ∀ (Xx : Iota), cP Xx)) True % 3.63/3.80 Clause #4 (by clausification #[2]): Eq (Iff (Exists cP) (∀ (Xx : Iota), cP Xx)) False % 3.63/3.80 Clause #5 (by clausification #[3]): Eq (Exists cP → ∀ (Xx : Iota), cP Xx) True % 3.63/3.80 Clause #7 (by clausification #[5]): Or (Eq (Exists cP) False) (Eq (∀ (Xx : Iota), cP Xx) True) % 3.63/3.80 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cP Xx) True) (Eq (cP a) False) % 3.63/3.80 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cP a_1) True) % 3.63/3.80 Clause #14 (by clausification #[4]): Or (Eq (Exists cP) False) (Eq (∀ (Xx : Iota), cP Xx) False) % 3.63/3.80 Clause #15 (by clausification #[4]): Or (Eq (Exists cP) True) (Eq (∀ (Xx : Iota), cP Xx) True) % 3.63/3.80 Clause #16 (by clausification #[14]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cP Xx) False) (Eq (cP a) False) % 3.63/3.80 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (Not (cP (skS.0 2 a_1))) True) % 3.63/3.80 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cP (skS.0 2 a_1)) False) % 3.63/3.80 Clause #19 (by clausification #[15]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cP Xx) True) (Eq (cP (skS.0 3 a)) True) % 3.63/3.80 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 3 a)) True) (Eq (cP a_1) True) % 3.63/3.80 Clause #21 (by superposition #[20, 9]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq True False) (Eq (cP a_1) True)) % 3.63/3.80 Clause #26 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cP a_1) True) % 3.63/3.80 Clause #27 (by equality factoring #[26]): ∀ (a : Iota), Or (Ne True True) (Eq (cP a) True) % 3.63/3.80 Clause #29 (by clausification #[27]): ∀ (a : Iota), Or (Eq (cP a) True) (Or (Eq True False) (Eq True False)) % 3.63/3.80 Clause #31 (by clausification #[29]): ∀ (a : Iota), Or (Eq (cP a) True) (Eq True False) % 3.63/3.80 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (cP a) True % 3.63/3.80 Clause #33 (by superposition #[32, 18]): ∀ (a : Iota), Or (Eq True False) (Eq (cP (skS.0 2 a)) False) % 3.63/3.80 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (cP (skS.0 2 a)) False % 3.63/3.80 Clause #35 (by superposition #[34, 32]): Eq False True % 3.63/3.80 Clause #36 (by clausification #[35]): False % 3.63/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------