%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KLE072+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 4.10s 4.26s % Output : Proof 4.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.13 % Problem : KLE072+1 : TPTP v9.2.0. Released v4.0.0. % 0.05/0.14 % Command : duper %s % 0.14/0.35 % Computer : n031.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 16:33:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.10/4.26 SZS status Theorem for theBenchmark.p % 4.10/4.26 SZS output start Proof for theBenchmark.p % 4.10/4.26 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), Eq (multiplication (addition A B) C) (addition (multiplication A C) (multiplication B C))) True % 4.10/4.26 Clause #13 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (domain (multiplication X0 X1)) (domain (multiplication X0 (domain X1)))) True % 4.10/4.26 Clause #16 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (domain (addition X0 X1)) (addition (domain X0) (domain X1))) True % 4.10/4.26 Clause #17 (by assumption #[]): Eq % 4.10/4.26 (Not % 4.10/4.26 (∀ (X0 X1 X2 : Iota), % 4.10/4.26 Eq (domain (multiplication (addition X0 X1) (domain X2))) % 4.10/4.26 (addition (domain (multiplication X0 (domain X2))) (domain (multiplication X1 (domain X2)))))) % 4.10/4.26 True % 4.10/4.26 Clause #101 (by clausification #[8]): ∀ (a : Iota), % 4.10/4.26 Eq (∀ (B C : Iota), Eq (multiplication (addition a B) C) (addition (multiplication a C) (multiplication B C))) True % 4.10/4.26 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), % 4.10/4.26 Eq (∀ (C : Iota), Eq (multiplication (addition a a_1) C) (addition (multiplication a C) (multiplication a_1 C))) True % 4.10/4.26 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 4.10/4.26 Eq (Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2))) True % 4.10/4.26 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 4.10/4.26 Eq (multiplication (addition a a_1) a_2) (addition (multiplication a a_2) (multiplication a_1 a_2)) % 4.10/4.26 Clause #171 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (domain (multiplication a X1)) (domain (multiplication a (domain X1)))) True % 4.10/4.26 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (Eq (domain (multiplication a a_1)) (domain (multiplication a (domain a_1)))) True % 4.10/4.26 Clause #173 (by clausification #[172]): ∀ (a a_1 : Iota), Eq (domain (multiplication a a_1)) (domain (multiplication a (domain a_1))) % 4.10/4.26 Clause #189 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (domain (addition a X1)) (addition (domain a) (domain X1))) True % 4.10/4.26 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Eq (domain (addition a a_1)) (addition (domain a) (domain a_1))) True % 4.10/4.26 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (domain (addition a a_1)) (addition (domain a) (domain a_1)) % 4.10/4.26 Clause #210 (by clausification #[17]): Eq % 4.10/4.26 (∀ (X0 X1 X2 : Iota), % 4.10/4.26 Eq (domain (multiplication (addition X0 X1) (domain X2))) % 4.10/4.26 (addition (domain (multiplication X0 (domain X2))) (domain (multiplication X1 (domain X2))))) % 4.10/4.26 False % 4.10/4.26 Clause #211 (by clausification #[210]): ∀ (a : Iota), % 4.10/4.26 Eq % 4.10/4.26 (Not % 4.10/4.26 (∀ (X1 X2 : Iota), % 4.10/4.26 Eq (domain (multiplication (addition (skS.0 0 a) X1) (domain X2))) % 4.10/4.26 (addition (domain (multiplication (skS.0 0 a) (domain X2))) (domain (multiplication X1 (domain X2)))))) % 4.10/4.26 True % 4.10/4.26 Clause #212 (by clausification #[211]): ∀ (a : Iota), % 4.10/4.26 Eq % 4.10/4.26 (∀ (X1 X2 : Iota), % 4.10/4.26 Eq (domain (multiplication (addition (skS.0 0 a) X1) (domain X2))) % 4.10/4.26 (addition (domain (multiplication (skS.0 0 a) (domain X2))) (domain (multiplication X1 (domain X2))))) % 4.10/4.26 False % 4.10/4.26 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota), % 4.10/4.26 Eq % 4.10/4.26 (Not % 4.10/4.26 (∀ (X2 : Iota), % 4.10/4.26 Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain X2))) % 4.10/4.26 (addition (domain (multiplication (skS.0 0 a) (domain X2))) % 4.10/4.26 (domain (multiplication (skS.0 1 a a_1) (domain X2)))))) % 4.10/4.26 True % 4.10/4.26 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota), % 4.10/4.26 Eq % 4.10/4.26 (∀ (X2 : Iota), % 4.10/4.26 Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain X2))) % 4.10/4.26 (addition (domain (multiplication (skS.0 0 a) (domain X2))) % 4.10/4.26 (domain (multiplication (skS.0 1 a a_1) (domain X2))))) % 4.10/4.26 False % 4.10/4.26 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), % 4.10/4.26 Eq % 4.10/4.26 (Not % 4.10/4.26 (Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.26 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.26 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2))))))) % 4.10/4.26 True % 4.10/4.28 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 : Iota), % 4.10/4.28 Eq % 4.10/4.28 (Eq (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.28 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.28 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2)))))) % 4.10/4.28 False % 4.10/4.28 Clause #217 (by clausification #[216]): ∀ (a a_1 a_2 : Iota), % 4.10/4.28 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.28 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.28 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2))))) % 4.10/4.28 Clause #218 (by forward demodulation #[217, 173]): ∀ (a a_1 a_2 : Iota), % 4.10/4.28 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))) % 4.10/4.28 (addition (domain (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.28 (domain (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2))))) % 4.10/4.28 Clause #219 (by forward demodulation #[218, 191]): ∀ (a a_1 a_2 : Iota), % 4.10/4.28 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))) % 4.10/4.28 (domain % 4.10/4.28 (addition (multiplication (skS.0 0 a) (domain (skS.0 2 a a_1 a_2))) % 4.10/4.28 (multiplication (skS.0 1 a a_1) (domain (skS.0 2 a a_1 a_2))))) % 4.10/4.28 Clause #220 (by forward demodulation #[219, 104]): ∀ (a a_1 a_2 : Iota), % 4.10/4.28 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))) % 4.10/4.28 (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (domain (skS.0 2 a a_1 a_2)))) % 4.10/4.28 Clause #221 (by forward demodulation #[220, 173]): ∀ (a a_1 a_2 : Iota), % 4.10/4.28 Ne (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))) % 4.10/4.28 (domain (multiplication (addition (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2))) % 4.10/4.28 Clause #222 (by eliminate resolved literals #[221]): False % 4.10/4.28 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------