%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE137+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 07:52:25 PM UTC 2025 % Result : Theorem 48.86s 49.03s % Output : Proof 48.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : KLE137+1 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.14 % Command : duper %s % 0.13/0.35 % Computer : n006.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 : Thu Oct 2 16:36:38 EDT 2025 % 0.20/0.35 % CPUTime : % 48.86/49.03 SZS status Theorem for theBenchmark.p % 48.86/49.03 SZS output start Proof for theBenchmark.p % 48.86/49.03 Clause #1 (by assumption #[]): Eq (∀ (C B A : Iota), Eq (addition A (addition B C)) (addition (addition A B) C)) True % 48.86/49.03 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A A) A) True % 48.86/49.03 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A one) A) True % 48.86/49.03 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication one A) A) True % 48.86/49.03 Clause #15 (by assumption #[]): Eq (∀ (A B C : Iota), leq C (addition (multiplication A C) B) → leq C (multiplication (strong_iteration A) B)) True % 48.86/49.03 Clause #17 (by assumption #[]): Eq (∀ (A B : Iota), Iff (leq A B) (Eq (addition A B) B)) True % 48.86/49.03 Clause #18 (by assumption #[]): Eq (Not (∀ (X0 : Iota), leq X0 (strong_iteration one))) True % 48.86/49.03 Clause #19 (by clausification #[18]): Eq (∀ (X0 : Iota), leq X0 (strong_iteration one)) False % 48.86/49.03 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (leq (skS.0 0 a) (strong_iteration one))) True % 48.86/49.03 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (leq (skS.0 0 a) (strong_iteration one)) False % 48.86/49.03 Clause #24 (by clausification #[6]): ∀ (a : Iota), Eq (Eq (multiplication one a) a) True % 48.86/49.03 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (multiplication one a) a % 48.86/49.03 Clause #26 (by clausification #[3]): ∀ (a : Iota), Eq (Eq (addition a a) a) True % 48.86/49.03 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (addition a a) a % 48.86/49.03 Clause #35 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (multiplication a one) a) True % 48.86/49.03 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (multiplication a one) a % 48.86/49.03 Clause #37 (by clausification #[15]): ∀ (a : Iota), % 48.86/49.03 Eq (∀ (B C : Iota), leq C (addition (multiplication a C) B) → leq C (multiplication (strong_iteration a) B)) True % 48.86/49.03 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 48.86/49.03 Eq (∀ (C : Iota), leq C (addition (multiplication a C) a_1) → leq C (multiplication (strong_iteration a) a_1)) True % 48.86/49.03 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 48.86/49.03 Eq (leq a (addition (multiplication a_1 a) a_2) → leq a (multiplication (strong_iteration a_1) a_2)) True % 48.86/49.03 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 48.86/49.03 Or (Eq (leq a (addition (multiplication a_1 a) a_2)) False) % 48.86/49.03 (Eq (leq a (multiplication (strong_iteration a_1) a_2)) True) % 48.86/49.03 Clause #46 (by superposition #[40, 25]): ∀ (a a_1 : Iota), Or (Eq (leq a (addition a a_1)) False) (Eq (leq a (multiplication (strong_iteration one) a_1)) True) % 48.86/49.03 Clause #57 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B A : Iota), Eq (addition A (addition B a)) (addition (addition A B) a)) True % 48.86/49.03 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (∀ (A : Iota), Eq (addition A (addition a a_1)) (addition (addition A a) a_1)) True % 48.86/49.03 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Eq (Eq (addition a (addition a_1 a_2)) (addition (addition a a_1) a_2)) True % 48.86/49.03 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Eq (addition a (addition a_1 a_2)) (addition (addition a a_1) a_2) % 48.86/49.03 Clause #68 (by superposition #[60, 27]): ∀ (a a_1 : Iota), Eq (addition a (addition a a_1)) (addition a a_1) % 48.86/49.03 Clause #246 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (leq a B) (Eq (addition a B) B)) True % 48.86/49.03 Clause #247 (by clausification #[246]): ∀ (a a_1 : Iota), Eq (Iff (leq a a_1) (Eq (addition a a_1) a_1)) True % 48.86/49.03 Clause #248 (by clausification #[247]): ∀ (a a_1 : Iota), Or (Eq (leq a a_1) True) (Eq (Eq (addition a a_1) a_1) False) % 48.86/49.03 Clause #250 (by clausification #[248]): ∀ (a a_1 : Iota), Or (Eq (leq a a_1) True) (Ne (addition a a_1) a_1) % 48.86/49.03 Clause #262 (by superposition #[250, 68]): ∀ (a a_1 : Iota), Or (Eq (leq a (addition a a_1)) True) (Ne (addition a a_1) (addition a a_1)) % 48.86/49.03 Clause #9159 (by eliminate resolved literals #[262]): ∀ (a a_1 : Iota), Eq (leq a (addition a a_1)) True % 48.86/49.03 Clause #9162 (by superposition #[9159, 46]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (leq a (multiplication (strong_iteration one) a_1)) True) % 48.86/49.03 Clause #16687 (by clausification #[9162]): ∀ (a a_1 : Iota), Eq (leq a (multiplication (strong_iteration one) a_1)) True % 48.95/49.12 Clause #16714 (by superposition #[16687, 36]): ∀ (a : Iota), Eq (leq a (strong_iteration one)) True % 48.95/49.12 Clause #16775 (by superposition #[16714, 21]): Eq True False % 48.95/49.12 Clause #16797 (by clausification #[16775]): False % 48.95/49.12 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------