%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE083+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 07:52:22 PM UTC 2025 % Result : Theorem 8.53s 8.73s % Output : Proof 8.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : KLE083+1 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.15 % Command : duper %s % 0.14/0.36 % Computer : n006.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 16:32:08 EDT 2025 % 0.14/0.36 % CPUTime : % 8.53/8.73 SZS status Theorem for theBenchmark.p % 8.53/8.73 SZS output start Proof for theBenchmark.p % 8.53/8.73 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A zero) A) True % 8.53/8.73 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication one A) A) True % 8.53/8.73 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), Eq (multiplication (addition A B) C) (addition (multiplication A C) (multiplication B C))) True % 8.53/8.73 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (multiplication (antidomain X0) X0) zero) True % 8.53/8.73 Clause #14 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (addition (antidomain (antidomain X0)) (antidomain X0)) one) True % 8.53/8.73 Clause #15 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (domain X0) (antidomain (antidomain X0))) True % 8.53/8.73 Clause #20 (by assumption #[]): Eq (Not (∀ (X0 : Iota), Eq X0 (multiplication (domain X0) X0))) True % 8.53/8.73 Clause #25 (by clausification #[6]): ∀ (a : Iota), Eq (Eq (multiplication one a) a) True % 8.53/8.73 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (multiplication one a) a % 8.53/8.73 Clause #29 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (addition a zero) a) True % 8.53/8.73 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (addition a zero) a % 8.53/8.73 Clause #38 (by clausification #[15]): ∀ (a : Iota), Eq (Eq (domain a) (antidomain (antidomain a))) True % 8.53/8.73 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (domain a) (antidomain (antidomain a)) % 8.53/8.73 Clause #104 (by clausification #[8]): ∀ (a : Iota), % 8.53/8.73 Eq (∀ (B C : Iota), Eq (multiplication (addition a B) C) (addition (multiplication a C) (multiplication B C))) True % 8.53/8.73 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), % 8.53/8.73 Eq (∀ (C : Iota), Eq (multiplication (addition a a_1) C) (addition (multiplication a C) (multiplication a_1 C))) True % 8.53/8.73 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 8.53/8.73 Eq (Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2))) True % 8.53/8.73 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 8.53/8.73 Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2)) % 8.53/8.73 Clause #126 (by clausification #[12]): ∀ (a : Iota), Eq (Eq (multiplication (antidomain a) a) zero) True % 8.53/8.73 Clause #127 (by clausification #[126]): ∀ (a : Iota), Eq (multiplication (antidomain a) a) zero % 8.53/8.73 Clause #132 (by superposition #[127, 107]): ∀ (a a_1 : Iota), Eq (multiplication (addition a (antidomain a_1)) a_1) (addition (multiplication a a_1) zero) % 8.53/8.73 Clause #188 (by clausification #[14]): ∀ (a : Iota), Eq (Eq (addition (antidomain (antidomain a)) (antidomain a)) one) True % 8.53/8.73 Clause #189 (by clausification #[188]): ∀ (a : Iota), Eq (addition (antidomain (antidomain a)) (antidomain a)) one % 8.53/8.73 Clause #190 (by forward demodulation #[189, 39]): ∀ (a : Iota), Eq (addition (domain a) (antidomain a)) one % 8.53/8.73 Clause #295 (by clausification #[20]): Eq (∀ (X0 : Iota), Eq X0 (multiplication (domain X0) X0)) False % 8.53/8.73 Clause #296 (by clausification #[295]): ∀ (a : Iota), Eq (Not (Eq (skS.0 0 a) (multiplication (domain (skS.0 0 a)) (skS.0 0 a)))) True % 8.53/8.73 Clause #297 (by clausification #[296]): ∀ (a : Iota), Eq (Eq (skS.0 0 a) (multiplication (domain (skS.0 0 a)) (skS.0 0 a))) False % 8.53/8.73 Clause #298 (by clausification #[297]): ∀ (a : Iota), Ne (skS.0 0 a) (multiplication (domain (skS.0 0 a)) (skS.0 0 a)) % 8.53/8.73 Clause #2197 (by forward demodulation #[132, 30]): ∀ (a a_1 : Iota), Eq (multiplication (addition a (antidomain a_1)) a_1) (multiplication a a_1) % 8.53/8.73 Clause #2240 (by superposition #[2197, 190]): ∀ (a : Iota), Eq (multiplication one a) (multiplication (domain a) a) % 8.53/8.73 Clause #2251 (by forward demodulation #[2240, 26]): ∀ (a : Iota), Eq a (multiplication (domain a) a) % 8.53/8.73 Clause #2253 (by backward contextual literal cutting #[2251, 298]): False % 8.53/8.73 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------