%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE067+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 07:52:21 PM UTC 2025 % Result : Theorem 3.76s 3.96s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KLE067+1 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 16:34:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.76/3.96 SZS status Theorem for theBenchmark.p % 3.76/3.96 SZS output start Proof for theBenchmark.p % 3.76/3.96 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Eq (multiplication one A) A) True % 3.76/3.96 Clause #13 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (domain (multiplication X0 X1)) (domain (multiplication X0 (domain X1)))) True % 3.76/3.96 Clause #16 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (domain (addition X0 X1)) (addition (domain X0) (domain X1))) True % 3.76/3.96 Clause #17 (by assumption #[]): Eq (Not (∀ (X0 X1 : Iota), Eq (domain (addition (domain X0) (domain X1))) (addition (domain X0) (domain X1)))) True % 3.76/3.96 Clause #19 (by clausification #[6]): ∀ (a : Iota), Eq (Eq (multiplication one a) a) True % 3.76/3.96 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (multiplication one a) a % 3.76/3.96 Clause #171 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (domain (multiplication a X1)) (domain (multiplication a (domain X1)))) True % 3.76/3.96 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (Eq (domain (multiplication a a_1)) (domain (multiplication a (domain a_1)))) True % 3.76/3.96 Clause #173 (by clausification #[172]): ∀ (a a_1 : Iota), Eq (domain (multiplication a a_1)) (domain (multiplication a (domain a_1))) % 3.76/3.96 Clause #180 (by superposition #[173, 20]): ∀ (a : Iota), Eq (domain (multiplication one a)) (domain (domain a)) % 3.76/3.96 Clause #184 (by forward demodulation #[180, 20]): ∀ (a : Iota), Eq (domain a) (domain (domain a)) % 3.76/3.96 Clause #189 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (domain (addition a X1)) (addition (domain a) (domain X1))) True % 3.76/3.96 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Eq (domain (addition a a_1)) (addition (domain a) (domain a_1))) True % 3.76/3.96 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (domain (addition a a_1)) (addition (domain a) (domain a_1)) % 3.76/3.96 Clause #210 (by clausification #[17]): Eq (∀ (X0 X1 : Iota), Eq (domain (addition (domain X0) (domain X1))) (addition (domain X0) (domain X1))) False % 3.76/3.96 Clause #211 (by clausification #[210]): ∀ (a : Iota), % 3.76/3.96 Eq % 3.76/3.96 (Not % 3.76/3.96 (∀ (X1 : Iota), % 3.76/3.96 Eq (domain (addition (domain (skS.0 0 a)) (domain X1))) (addition (domain (skS.0 0 a)) (domain X1)))) % 3.76/3.96 True % 3.76/3.96 Clause #212 (by clausification #[211]): ∀ (a : Iota), % 3.76/3.96 Eq % 3.76/3.96 (∀ (X1 : Iota), Eq (domain (addition (domain (skS.0 0 a)) (domain X1))) (addition (domain (skS.0 0 a)) (domain X1))) % 3.76/3.96 False % 3.76/3.96 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota), % 3.76/3.96 Eq % 3.76/3.96 (Not % 3.76/3.96 (Eq (domain (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1)))) % 3.76/3.96 (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1))))) % 3.76/3.96 True % 3.76/3.96 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota), % 3.76/3.96 Eq % 3.76/3.96 (Eq (domain (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1)))) % 3.76/3.96 (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1)))) % 3.76/3.96 False % 3.76/3.96 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota), % 3.76/3.96 Ne (domain (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1)))) % 3.76/3.96 (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1))) % 3.76/3.96 Clause #216 (by forward demodulation #[215, 191]): ∀ (a a_1 : Iota), % 3.76/3.96 Ne (domain (domain (addition (skS.0 0 a) (skS.0 1 a a_1)))) (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1))) % 3.76/3.96 Clause #217 (by forward demodulation #[216, 184]): ∀ (a a_1 : Iota), % 3.76/3.96 Ne (domain (addition (skS.0 0 a) (skS.0 1 a a_1))) (addition (domain (skS.0 0 a)) (domain (skS.0 1 a a_1))) % 3.76/3.96 Clause #218 (by forward demodulation #[217, 191]): ∀ (a a_1 : Iota), Ne (domain (addition (skS.0 0 a) (skS.0 1 a a_1))) (domain (addition (skS.0 0 a) (skS.0 1 a a_1))) % 3.76/3.96 Clause #219 (by eliminate resolved literals #[218]): False % 3.76/3.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------