%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE119+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 07:52:24 PM UTC 2025 % Result : Theorem 4.31s 4.55s % Output : Proof 4.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KLE119+1 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n007.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 16:57:38 EDT 2025 % 0.14/0.35 % CPUTime : % 4.31/4.55 SZS status Theorem for theBenchmark.p % 4.31/4.55 SZS output start Proof for theBenchmark.p % 4.31/4.55 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (addition A B) (addition B A)) True % 4.31/4.55 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A zero) A) True % 4.31/4.55 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication one A) A) True % 4.31/4.55 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A zero) zero) True % 4.31/4.55 Clause #16 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (multiplication X0 (coantidomain X0)) zero) True % 4.31/4.55 Clause #18 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (addition (coantidomain (coantidomain X0)) (coantidomain X0)) one) True % 4.31/4.55 Clause #19 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (codomain X0) (coantidomain (coantidomain X0))) True % 4.31/4.55 Clause #23 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (backward_diamond X0 X1) (codomain (multiplication (codomain X1) X0))) True % 4.31/4.55 Clause #26 (by assumption #[]): Eq (Not (∀ (X0 X1 : Iota), Eq (addition (backward_diamond zero (domain X0)) (domain X1)) (domain X1))) True % 4.31/4.55 Clause #29 (by clausification #[9]): ∀ (a : Iota), Eq (Eq (multiplication a zero) zero) True % 4.31/4.55 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (multiplication a zero) zero % 4.31/4.55 Clause #31 (by clausification #[6]): ∀ (a : Iota), Eq (Eq (multiplication one a) a) True % 4.31/4.55 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (multiplication one a) a % 4.31/4.55 Clause #35 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (addition a zero) a) True % 4.31/4.55 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (addition a zero) a % 4.31/4.55 Clause #37 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (addition a B) (addition B a)) True % 4.31/4.55 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Eq (addition a a_1) (addition a_1 a)) True % 4.31/4.55 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (addition a a_1) (addition a_1 a) % 4.31/4.55 Clause #40 (by superposition #[39, 36]): ∀ (a : Iota), Eq (addition zero a) a % 4.31/4.55 Clause #271 (by clausification #[16]): ∀ (a : Iota), Eq (Eq (multiplication a (coantidomain a)) zero) True % 4.31/4.55 Clause #272 (by clausification #[271]): ∀ (a : Iota), Eq (multiplication a (coantidomain a)) zero % 4.31/4.55 Clause #273 (by superposition #[272, 32]): Eq zero (coantidomain one) % 4.31/4.55 Clause #313 (by clausification #[18]): ∀ (a : Iota), Eq (Eq (addition (coantidomain (coantidomain a)) (coantidomain a)) one) True % 4.31/4.55 Clause #314 (by clausification #[313]): ∀ (a : Iota), Eq (addition (coantidomain (coantidomain a)) (coantidomain a)) one % 4.31/4.55 Clause #322 (by superposition #[314, 273]): Eq (addition (coantidomain zero) zero) one % 4.31/4.55 Clause #323 (by superposition #[322, 36]): Eq one (coantidomain zero) % 4.31/4.55 Clause #339 (by clausification #[19]): ∀ (a : Iota), Eq (Eq (codomain a) (coantidomain (coantidomain a))) True % 4.31/4.55 Clause #340 (by clausification #[339]): ∀ (a : Iota), Eq (codomain a) (coantidomain (coantidomain a)) % 4.31/4.55 Clause #348 (by superposition #[340, 323]): Eq (codomain zero) (coantidomain one) % 4.31/4.55 Clause #349 (by forward demodulation #[348, 273]): Eq (codomain zero) zero % 4.31/4.55 Clause #396 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (backward_diamond a X1) (codomain (multiplication (codomain X1) a))) True % 4.31/4.55 Clause #397 (by clausification #[396]): ∀ (a a_1 : Iota), Eq (Eq (backward_diamond a a_1) (codomain (multiplication (codomain a_1) a))) True % 4.31/4.55 Clause #398 (by clausification #[397]): ∀ (a a_1 : Iota), Eq (backward_diamond a a_1) (codomain (multiplication (codomain a_1) a)) % 4.31/4.55 Clause #402 (by superposition #[398, 30]): ∀ (a : Iota), Eq (backward_diamond zero a) (codomain zero) % 4.31/4.55 Clause #407 (by forward demodulation #[402, 349]): ∀ (a : Iota), Eq (backward_diamond zero a) zero % 4.31/4.55 Clause #460 (by clausification #[26]): Eq (∀ (X0 X1 : Iota), Eq (addition (backward_diamond zero (domain X0)) (domain X1)) (domain X1)) False % 4.31/4.55 Clause #461 (by clausification #[460]): ∀ (a : Iota), % 4.31/4.55 Eq (Not (∀ (X1 : Iota), Eq (addition (backward_diamond zero (domain (skS.0 0 a))) (domain X1)) (domain X1))) True % 4.31/4.55 Clause #462 (by clausification #[461]): ∀ (a : Iota), % 4.31/4.55 Eq (∀ (X1 : Iota), Eq (addition (backward_diamond zero (domain (skS.0 0 a))) (domain X1)) (domain X1)) False % 4.40/4.57 Clause #463 (by clausification #[462]): ∀ (a a_1 : Iota), % 4.40/4.57 Eq % 4.40/4.57 (Not (Eq (addition (backward_diamond zero (domain (skS.0 0 a))) (domain (skS.0 1 a a_1))) (domain (skS.0 1 a a_1)))) % 4.40/4.57 True % 4.40/4.57 Clause #464 (by clausification #[463]): ∀ (a a_1 : Iota), % 4.40/4.57 Eq (Eq (addition (backward_diamond zero (domain (skS.0 0 a))) (domain (skS.0 1 a a_1))) (domain (skS.0 1 a a_1))) % 4.40/4.57 False % 4.40/4.57 Clause #465 (by clausification #[464]): ∀ (a a_1 : Iota), % 4.40/4.57 Ne (addition (backward_diamond zero (domain (skS.0 0 a))) (domain (skS.0 1 a a_1))) (domain (skS.0 1 a a_1)) % 4.40/4.57 Clause #466 (by forward demodulation #[465, 407]): ∀ (a a_1 : Iota), Ne (addition zero (domain (skS.0 1 a a_1))) (domain (skS.0 1 a a_1)) % 4.40/4.57 Clause #467 (by forward demodulation #[466, 40]): ∀ (a a_1 : Iota), Ne (domain (skS.0 1 a a_1)) (domain (skS.0 1 a a_1)) % 4.40/4.57 Clause #468 (by eliminate resolved literals #[467]): False % 4.40/4.57 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------