%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV067^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:02:48 PM UTC 2025 % Result : Theorem 3.96s 4.13s % Output : Proof 3.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEV067^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 00:55:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.96/4.13 SZS status Theorem for theBenchmark.p % 3.96/4.13 SZS output start Proof for theBenchmark.p % 3.96/4.13 Clause #0 (by assumption #[]): Eq % 3.96/4.13 (Not % 3.96/4.13 (And % 3.96/4.13 (And % 3.96/4.13 (And % 3.96/4.13 (And (And (∀ (Xx Xy Xz : a), And (cR Xx Xy) (cR Xy Xz) → cR Xx Xz) (∀ (Xx : a), cR Xx Xx)) % 3.96/4.13 (∀ (Xx Xy : a), And (cR Xx Xy) (cR Xy Xx) → Eq Xx Xy)) % 3.96/4.13 (∀ (Xx Xy : a), Or (cR Xx Xy) (cR Xy Xx))) % 3.96/4.13 (∀ (Xu Xv : a), And (cR Xu Xv) (cS Xv) → cS Xu)) % 3.96/4.13 (∀ (Xu Xv : a), And (cR Xu Xv) (cT Xv) → cT Xu) → % 3.96/4.13 Or (∀ (Xx : a), cS Xx → cT Xx) (∀ (Xx : a), cT Xx → cS Xx))) % 3.96/4.13 True % 3.96/4.13 Clause #1 (by clausification #[0]): Eq % 3.96/4.13 (And % 3.96/4.13 (And % 3.96/4.13 (And % 3.96/4.13 (And (And (∀ (Xx Xy Xz : a), And (cR Xx Xy) (cR Xy Xz) → cR Xx Xz) (∀ (Xx : a), cR Xx Xx)) % 3.96/4.13 (∀ (Xx Xy : a), And (cR Xx Xy) (cR Xy Xx) → Eq Xx Xy)) % 3.96/4.13 (∀ (Xx Xy : a), Or (cR Xx Xy) (cR Xy Xx))) % 3.96/4.13 (∀ (Xu Xv : a), And (cR Xu Xv) (cS Xv) → cS Xu)) % 3.96/4.13 (∀ (Xu Xv : a), And (cR Xu Xv) (cT Xv) → cT Xu) → % 3.96/4.13 Or (∀ (Xx : a), cS Xx → cT Xx) (∀ (Xx : a), cT Xx → cS Xx)) % 3.96/4.13 False % 3.96/4.13 Clause #2 (by clausification #[1]): Eq % 3.96/4.13 (And % 3.96/4.13 (And % 3.96/4.13 (And % 3.96/4.13 (And (And (∀ (Xx Xy Xz : a), And (cR Xx Xy) (cR Xy Xz) → cR Xx Xz) (∀ (Xx : a), cR Xx Xx)) % 3.96/4.13 (∀ (Xx Xy : a), And (cR Xx Xy) (cR Xy Xx) → Eq Xx Xy)) % 3.96/4.13 (∀ (Xx Xy : a), Or (cR Xx Xy) (cR Xy Xx))) % 3.96/4.13 (∀ (Xu Xv : a), And (cR Xu Xv) (cS Xv) → cS Xu)) % 3.96/4.13 (∀ (Xu Xv : a), And (cR Xu Xv) (cT Xv) → cT Xu)) % 3.96/4.13 True % 3.96/4.13 Clause #3 (by clausification #[1]): Eq (Or (∀ (Xx : a), cS Xx → cT Xx) (∀ (Xx : a), cT Xx → cS Xx)) False % 3.96/4.13 Clause #4 (by clausification #[2]): Eq (∀ (Xu Xv : a), And (cR Xu Xv) (cT Xv) → cT Xu) True % 3.96/4.13 Clause #5 (by clausification #[2]): Eq % 3.96/4.13 (And % 3.96/4.13 (And % 3.96/4.13 (And (And (∀ (Xx Xy Xz : a), And (cR Xx Xy) (cR Xy Xz) → cR Xx Xz) (∀ (Xx : a), cR Xx Xx)) % 3.96/4.13 (∀ (Xx Xy : a), And (cR Xx Xy) (cR Xy Xx) → Eq Xx Xy)) % 3.96/4.13 (∀ (Xx Xy : a), Or (cR Xx Xy) (cR Xy Xx))) % 3.96/4.13 (∀ (Xu Xv : a), And (cR Xu Xv) (cS Xv) → cS Xu)) % 3.96/4.13 True % 3.96/4.13 Clause #6 (by clausification #[4]): ∀ (a_1 : a), Eq (∀ (Xv : a), And (cR a_1 Xv) (cT Xv) → cT a_1) True % 3.96/4.13 Clause #7 (by clausification #[6]): ∀ (a_1 a : a), Eq (And (cR a_1 a) (cT a) → cT a_1) True % 3.96/4.13 Clause #8 (by clausification #[7]): ∀ (a_1 a : a), Or (Eq (And (cR a_1 a) (cT a)) False) (Eq (cT a_1) True) % 3.96/4.13 Clause #9 (by clausification #[8]): ∀ (a_1 a : a), Or (Eq (cT a_1) True) (Or (Eq (cR a_1 a) False) (Eq (cT a) False)) % 3.96/4.13 Clause #10 (by clausification #[3]): Eq (∀ (Xx : a), cT Xx → cS Xx) False % 3.96/4.13 Clause #11 (by clausification #[3]): Eq (∀ (Xx : a), cS Xx → cT Xx) False % 3.96/4.13 Clause #12 (by clausification #[10]): ∀ (a_1 : a), Eq (Not (cT (skS.0 0 a_1) → cS (skS.0 0 a_1))) True % 3.96/4.13 Clause #13 (by clausification #[12]): ∀ (a_1 : a), Eq (cT (skS.0 0 a_1) → cS (skS.0 0 a_1)) False % 3.96/4.13 Clause #14 (by clausification #[13]): ∀ (a_1 : a), Eq (cT (skS.0 0 a_1)) True % 3.96/4.13 Clause #15 (by clausification #[13]): ∀ (a_1 : a), Eq (cS (skS.0 0 a_1)) False % 3.96/4.13 Clause #16 (by clausification #[11]): ∀ (a_1 : a), Eq (Not (cS (skS.0 1 a_1) → cT (skS.0 1 a_1))) True % 3.96/4.13 Clause #17 (by clausification #[16]): ∀ (a_1 : a), Eq (cS (skS.0 1 a_1) → cT (skS.0 1 a_1)) False % 3.96/4.13 Clause #18 (by clausification #[17]): ∀ (a_1 : a), Eq (cS (skS.0 1 a_1)) True % 3.96/4.13 Clause #19 (by clausification #[17]): ∀ (a_1 : a), Eq (cT (skS.0 1 a_1)) False % 3.96/4.13 Clause #20 (by clausification #[5]): Eq (∀ (Xu Xv : a), And (cR Xu Xv) (cS Xv) → cS Xu) True % 3.96/4.13 Clause #21 (by clausification #[5]): Eq % 3.96/4.13 (And % 3.96/4.13 (And (And (∀ (Xx Xy Xz : a), And (cR Xx Xy) (cR Xy Xz) → cR Xx Xz) (∀ (Xx : a), cR Xx Xx)) % 3.96/4.13 (∀ (Xx Xy : a), And (cR Xx Xy) (cR Xy Xx) → Eq Xx Xy)) % 3.96/4.13 (∀ (Xx Xy : a), Or (cR Xx Xy) (cR Xy Xx))) % 3.96/4.13 True % 3.96/4.13 Clause #22 (by clausification #[20]): ∀ (a_1 : a), Eq (∀ (Xv : a), And (cR a_1 Xv) (cS Xv) → cS a_1) True % 3.96/4.13 Clause #23 (by clausification #[22]): ∀ (a_1 a : a), Eq (And (cR a_1 a) (cS a) → cS a_1) True % 3.96/4.13 Clause #24 (by clausification #[23]): ∀ (a_1 a : a), Or (Eq (And (cR a_1 a) (cS a)) False) (Eq (cS a_1) True) % 3.96/4.15 Clause #25 (by clausification #[24]): ∀ (a_1 a : a), Or (Eq (cS a_1) True) (Or (Eq (cR a_1 a) False) (Eq (cS a) False)) % 3.96/4.15 Clause #26 (by clausification #[21]): Eq (∀ (Xx Xy : a), Or (cR Xx Xy) (cR Xy Xx)) True % 3.96/4.15 Clause #28 (by clausification #[26]): ∀ (a_1 : a), Eq (∀ (Xy : a), Or (cR a_1 Xy) (cR Xy a_1)) True % 3.96/4.15 Clause #29 (by clausification #[28]): ∀ (a_1 a : a), Eq (Or (cR a_1 a) (cR a a_1)) True % 3.96/4.15 Clause #30 (by clausification #[29]): ∀ (a_1 a : a), Or (Eq (cR a_1 a) True) (Eq (cR a a_1) True) % 3.96/4.15 Clause #31 (by superposition #[30, 9]): ∀ (a_1 a : a), Or (Eq (cR a_1 a) True) (Or (Eq (cT a) True) (Or (Eq True False) (Eq (cT a_1) False))) % 3.96/4.15 Clause #53 (by clausification #[31]): ∀ (a_1 a : a), Or (Eq (cR a_1 a) True) (Or (Eq (cT a) True) (Eq (cT a_1) False)) % 3.96/4.15 Clause #54 (by superposition #[53, 14]): ∀ (a_1 a_2 : a), Or (Eq (cR (skS.0 0 a_1) a_2) True) (Or (Eq (cT a_2) True) (Eq False True)) % 3.96/4.15 Clause #74 (by clausification #[54]): ∀ (a_1 a_2 : a), Or (Eq (cR (skS.0 0 a_1) a_2) True) (Eq (cT a_2) True) % 3.96/4.15 Clause #76 (by superposition #[74, 25]): ∀ (a_1 a_2 : a), Or (Eq (cT a_1) True) (Or (Eq (cS (skS.0 0 a_2)) True) (Or (Eq True False) (Eq (cS a_1) False))) % 3.96/4.15 Clause #103 (by clausification #[76]): ∀ (a_1 a_2 : a), Or (Eq (cT a_1) True) (Or (Eq (cS (skS.0 0 a_2)) True) (Eq (cS a_1) False)) % 3.96/4.15 Clause #104 (by superposition #[103, 18]): ∀ (a_1 a_2 : a), Or (Eq (cT (skS.0 1 a_1)) True) (Or (Eq (cS (skS.0 0 a_2)) True) (Eq False True)) % 3.96/4.15 Clause #285 (by clausification #[104]): ∀ (a_1 a_2 : a), Or (Eq (cT (skS.0 1 a_1)) True) (Eq (cS (skS.0 0 a_2)) True) % 3.96/4.15 Clause #291 (by superposition #[285, 15]): ∀ (a_1 : a), Or (Eq (cT (skS.0 1 a_1)) True) (Eq True False) % 3.96/4.15 Clause #297 (by clausification #[291]): ∀ (a_1 : a), Eq (cT (skS.0 1 a_1)) True % 3.96/4.15 Clause #298 (by superposition #[297, 19]): Eq True False % 3.96/4.15 Clause #302 (by clausification #[298]): False % 3.96/4.15 SZS output end Proof for theBenchmark.p 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