%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE146+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 07:52:26 PM UTC 2025 % Result : Theorem 4.01s 4.23s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : KLE146+1 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.14 % Command : duper %s % 0.14/0.35 % Computer : n003.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 : Thu Oct 2 16:54:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.01/4.23 SZS status Theorem for theBenchmark.p % 4.01/4.23 SZS output start Proof for theBenchmark.p % 4.01/4.23 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (addition A B) (addition B A)) True % 4.01/4.23 Clause #1 (by assumption #[]): Eq (∀ (C B A : Iota), Eq (addition A (addition B C)) (addition (addition A B) C)) True % 4.01/4.23 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A A) A) True % 4.01/4.23 Clause #14 (by assumption #[]): Eq (∀ (A : Iota), Eq (strong_iteration A) (addition (multiplication A (strong_iteration A)) one)) True % 4.01/4.23 Clause #17 (by assumption #[]): Eq (∀ (A B : Iota), Iff (leq A B) (Eq (addition A B) B)) True % 4.01/4.23 Clause #18 (by assumption #[]): Eq (Not (∀ (X0 : Iota), leq one (strong_iteration X0))) True % 4.01/4.23 Clause #19 (by clausification #[18]): Eq (∀ (X0 : Iota), leq one (strong_iteration X0)) False % 4.01/4.23 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (leq one (strong_iteration (skS.0 0 a)))) True % 4.01/4.23 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (leq one (strong_iteration (skS.0 0 a))) False % 4.01/4.23 Clause #26 (by clausification #[3]): ∀ (a : Iota), Eq (Eq (addition a a) a) True % 4.01/4.23 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (addition a a) a % 4.01/4.23 Clause #30 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (addition a B) (addition B a)) True % 4.01/4.23 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Eq (addition a a_1) (addition a_1 a)) True % 4.01/4.23 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (addition a a_1) (addition a_1 a) % 4.01/4.23 Clause #57 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B A : Iota), Eq (addition A (addition B a)) (addition (addition A B) a)) True % 4.01/4.23 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 % 4.01/4.23 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 % 4.01/4.23 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) % 4.01/4.23 Clause #68 (by superposition #[60, 27]): ∀ (a a_1 : Iota), Eq (addition a (addition a a_1)) (addition a a_1) % 4.01/4.23 Clause #75 (by superposition #[68, 32]): ∀ (a a_1 : Iota), Eq (addition a (addition a_1 a)) (addition a_1 a) % 4.01/4.23 Clause #210 (by clausification #[14]): ∀ (a : Iota), Eq (Eq (strong_iteration a) (addition (multiplication a (strong_iteration a)) one)) True % 4.01/4.23 Clause #211 (by clausification #[210]): ∀ (a : Iota), Eq (strong_iteration a) (addition (multiplication a (strong_iteration a)) one) % 4.01/4.23 Clause #219 (by superposition #[211, 75]): ∀ (a : Iota), Eq (addition one (strong_iteration a)) (strong_iteration a) % 4.01/4.23 Clause #246 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (leq a B) (Eq (addition a B) B)) True % 4.01/4.23 Clause #247 (by clausification #[246]): ∀ (a a_1 : Iota), Eq (Iff (leq a a_1) (Eq (addition a a_1) a_1)) True % 4.01/4.23 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) % 4.01/4.23 Clause #250 (by clausification #[248]): ∀ (a a_1 : Iota), Or (Eq (leq a a_1) True) (Ne (addition a a_1) a_1) % 4.01/4.23 Clause #275 (by superposition #[219, 250]): ∀ (a : Iota), Or (Eq (leq one (strong_iteration a)) True) (Ne (strong_iteration a) (strong_iteration a)) % 4.01/4.23 Clause #381 (by eliminate resolved literals #[275]): ∀ (a : Iota), Eq (leq one (strong_iteration a)) True % 4.01/4.23 Clause #382 (by superposition #[381, 21]): Eq True False % 4.01/4.23 Clause #383 (by clausification #[382]): False % 4.01/4.23 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------