%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE001+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 07:52:14 PM UTC 2025 % Result : Theorem 10.01s 10.19s % Output : Proof 10.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : KLE001+1 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : duper %s % 0.15/0.35 % Computer : n022.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Thu Oct 2 16:51:38 EDT 2025 % 0.15/0.35 % CPUTime : % 10.01/10.19 SZS status Theorem for theBenchmark.p % 10.01/10.19 SZS output start Proof for theBenchmark.p % 10.01/10.19 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A A) A) True % 10.01/10.19 Clause #11 (by assumption #[]): Eq (∀ (A B : Iota), Iff (leq A B) (Eq (addition A B) B)) True % 10.01/10.19 Clause #12 (by assumption #[]): Eq (Not (∀ (X0 X1 X2 : Iota), leq X0 X1 → leq (addition X0 X2) (addition X0 X2))) True % 10.01/10.19 Clause #19 (by clausification #[3]): ∀ (a : Iota), Eq (Eq (addition a a) a) True % 10.01/10.19 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (addition a a) a % 10.01/10.19 Clause #30 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (leq a B) (Eq (addition a B) B)) True % 10.01/10.19 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Iff (leq a a_1) (Eq (addition a a_1) a_1)) True % 10.01/10.19 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (leq a a_1) True) (Eq (Eq (addition a a_1) a_1) False) % 10.01/10.19 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (leq a a_1) True) (Ne (addition a a_1) a_1) % 10.01/10.19 Clause #37 (by superposition #[34, 20]): ∀ (a : Iota), Or (Eq (leq a a) True) (Ne a a) % 10.01/10.19 Clause #39 (by eliminate resolved literals #[37]): ∀ (a : Iota), Eq (leq a a) True % 10.01/10.19 Clause #156 (by clausification #[12]): Eq (∀ (X0 X1 X2 : Iota), leq X0 X1 → leq (addition X0 X2) (addition X0 X2)) False % 10.01/10.19 Clause #157 (by clausification #[156]): ∀ (a : Iota), % 10.01/10.19 Eq (Not (∀ (X1 X2 : Iota), leq (skS.0 0 a) X1 → leq (addition (skS.0 0 a) X2) (addition (skS.0 0 a) X2))) True % 10.01/10.19 Clause #158 (by clausification #[157]): ∀ (a : Iota), Eq (∀ (X1 X2 : Iota), leq (skS.0 0 a) X1 → leq (addition (skS.0 0 a) X2) (addition (skS.0 0 a) X2)) False % 10.01/10.19 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), % 10.01/10.19 Eq (Not (∀ (X2 : Iota), leq (skS.0 0 a) (skS.0 1 a a_1) → leq (addition (skS.0 0 a) X2) (addition (skS.0 0 a) X2))) % 10.01/10.19 True % 10.01/10.19 Clause #160 (by clausification #[159]): ∀ (a a_1 : Iota), % 10.01/10.19 Eq (∀ (X2 : Iota), leq (skS.0 0 a) (skS.0 1 a a_1) → leq (addition (skS.0 0 a) X2) (addition (skS.0 0 a) X2)) False % 10.01/10.19 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 : Iota), % 10.01/10.19 Eq % 10.01/10.19 (Not % 10.01/10.19 (leq (skS.0 0 a) (skS.0 1 a a_1) → % 10.01/10.19 leq (addition (skS.0 0 a) (skS.0 2 a a_1 a_2)) (addition (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 10.01/10.19 True % 10.01/10.19 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 : Iota), % 10.01/10.19 Eq % 10.01/10.19 (leq (skS.0 0 a) (skS.0 1 a a_1) → % 10.01/10.19 leq (addition (skS.0 0 a) (skS.0 2 a a_1 a_2)) (addition (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 10.01/10.19 False % 10.01/10.19 Clause #164 (by clausification #[162]): ∀ (a a_1 a_2 : Iota), % 10.01/10.19 Eq (leq (addition (skS.0 0 a) (skS.0 2 a a_1 a_2)) (addition (skS.0 0 a) (skS.0 2 a a_1 a_2))) False % 10.01/10.19 Clause #4988 (by superposition #[164, 39]): Eq False True % 10.01/10.19 Clause #4989 (by clausification #[4988]): False % 10.01/10.19 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------