%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE113+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 07:52:24 PM UTC 2025 % Result : Theorem 5.52s 5.71s % Output : Proof 5.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : KLE113+1 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % 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 16:47:23 EDT 2025 % 0.13/0.35 % CPUTime : % 5.52/5.71 SZS status Theorem for theBenchmark.p % 5.52/5.71 SZS output start Proof for theBenchmark.p % 5.52/5.71 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Eq (addition A zero) A) True % 5.52/5.71 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A one) A) True % 5.52/5.71 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication A zero) zero) True % 5.52/5.71 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (multiplication (antidomain X0) X0) zero) True % 5.52/5.71 Clause #14 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (addition (antidomain (antidomain X0)) (antidomain X0)) one) True % 5.52/5.71 Clause #15 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (domain X0) (antidomain (antidomain X0))) True % 5.52/5.71 Clause #20 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (c X0) (antidomain (domain X0))) True % 5.52/5.71 Clause #22 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (forward_diamond X0 X1) (domain (multiplication X0 (domain X1)))) True % 5.52/5.71 Clause #26 (by assumption #[]): Eq (Not (∀ (X0 : Iota), Eq (forward_diamond X0 zero) zero)) True % 5.52/5.71 Clause #29 (by clausification #[9]): ∀ (a : Iota), Eq (Eq (multiplication a zero) zero) True % 5.52/5.71 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (multiplication a zero) zero % 5.52/5.71 Clause #35 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (addition a zero) a) True % 5.52/5.71 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (addition a zero) a % 5.52/5.71 Clause #42 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (multiplication a one) a) True % 5.52/5.71 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (multiplication a one) a % 5.52/5.71 Clause #44 (by clausification #[20]): ∀ (a : Iota), Eq (Eq (c a) (antidomain (domain a))) True % 5.52/5.71 Clause #45 (by clausification #[44]): ∀ (a : Iota), Eq (c a) (antidomain (domain a)) % 5.52/5.71 Clause #46 (by clausification #[15]): ∀ (a : Iota), Eq (Eq (domain a) (antidomain (antidomain a))) True % 5.52/5.71 Clause #47 (by clausification #[46]): ∀ (a : Iota), Eq (domain a) (antidomain (antidomain a)) % 5.52/5.71 Clause #48 (by superposition #[47, 47]): ∀ (a : Iota), Eq (domain (antidomain a)) (antidomain (domain a)) % 5.52/5.71 Clause #65 (by forward demodulation #[48, 45]): ∀ (a : Iota), Eq (domain (antidomain a)) (c a) % 5.52/5.71 Clause #186 (by clausification #[12]): ∀ (a : Iota), Eq (Eq (multiplication (antidomain a) a) zero) True % 5.52/5.71 Clause #187 (by clausification #[186]): ∀ (a : Iota), Eq (multiplication (antidomain a) a) zero % 5.52/5.71 Clause #188 (by superposition #[187, 43]): Eq zero (antidomain one) % 5.52/5.71 Clause #198 (by superposition #[188, 47]): Eq (domain one) (antidomain zero) % 5.52/5.71 Clause #199 (by superposition #[188, 65]): Eq (domain zero) (c one) % 5.52/5.71 Clause #205 (by superposition #[198, 45]): Eq (c one) (antidomain (antidomain zero)) % 5.52/5.71 Clause #247 (by clausification #[14]): ∀ (a : Iota), Eq (Eq (addition (antidomain (antidomain a)) (antidomain a)) one) True % 5.52/5.71 Clause #248 (by clausification #[247]): ∀ (a : Iota), Eq (addition (antidomain (antidomain a)) (antidomain a)) one % 5.52/5.71 Clause #249 (by forward demodulation #[248, 47]): ∀ (a : Iota), Eq (addition (domain a) (antidomain a)) one % 5.52/5.71 Clause #261 (by superposition #[249, 188]): Eq (addition (domain one) zero) one % 5.52/5.71 Clause #272 (by forward demodulation #[261, 198]): Eq (addition (antidomain zero) zero) one % 5.52/5.71 Clause #273 (by superposition #[272, 36]): Eq one (antidomain zero) % 5.52/5.71 Clause #282 (by backward demodulation #[273, 205]): Eq (c one) (antidomain one) % 5.52/5.71 Clause #315 (by forward demodulation #[282, 188]): Eq (c one) zero % 5.52/5.71 Clause #316 (by backward demodulation #[315, 199]): Eq (domain zero) zero % 5.52/5.71 Clause #425 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (forward_diamond a X1) (domain (multiplication a (domain X1)))) True % 5.52/5.71 Clause #426 (by clausification #[425]): ∀ (a a_1 : Iota), Eq (Eq (forward_diamond a a_1) (domain (multiplication a (domain a_1)))) True % 5.52/5.71 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Eq (forward_diamond a a_1) (domain (multiplication a (domain a_1))) % 5.52/5.71 Clause #446 (by superposition #[427, 316]): ∀ (a : Iota), Eq (forward_diamond a zero) (domain (multiplication a zero)) % 5.52/5.71 Clause #510 (by clausification #[26]): Eq (∀ (X0 : Iota), Eq (forward_diamond X0 zero) zero) False % 5.52/5.71 Clause #511 (by clausification #[510]): ∀ (a : Iota), Eq (Not (Eq (forward_diamond (skS.0 0 a) zero) zero)) True % 5.52/5.71 Clause #512 (by clausification #[511]): ∀ (a : Iota), Eq (Eq (forward_diamond (skS.0 0 a) zero) zero) False % 5.52/5.71 Clause #513 (by clausification #[512]): ∀ (a : Iota), Ne (forward_diamond (skS.0 0 a) zero) zero % 5.52/5.71 Clause #1172 (by forward demodulation #[446, 30]): ∀ (a : Iota), Eq (forward_diamond a zero) (domain zero) % 5.52/5.71 Clause #1173 (by forward demodulation #[1172, 316]): ∀ (a : Iota), Eq (forward_diamond a zero) zero % 5.52/5.71 Clause #1175 (by backward contextual literal cutting #[1173, 513]): False % 5.52/5.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------