%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV051^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:02:47 PM UTC 2025 % Result : Theorem 3.68s 3.85s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV051^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n004.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 : Fri Oct 3 00:58:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.68/3.85 SZS status Theorem for theBenchmark.p % 3.68/3.85 SZS output start Proof for theBenchmark.p % 3.68/3.85 Clause #0 (by assumption #[]): Eq (Not (And (∀ (Xx : a), Eq Xx Xx) (∀ (Xu Xv Xw : a), And (Eq Xu Xw) (Eq Xv Xw) → Eq Xu Xv))) True % 3.68/3.85 Clause #1 (by clausification #[0]): Eq (And (∀ (Xx : a), Eq Xx Xx) (∀ (Xu Xv Xw : a), And (Eq Xu Xw) (Eq Xv Xw) → Eq Xu Xv)) False % 3.68/3.85 Clause #2 (by clausification #[1]): Or (Eq (∀ (Xx : a), Eq Xx Xx) False) (Eq (∀ (Xu Xv Xw : a), And (Eq Xu Xw) (Eq Xv Xw) → Eq Xu Xv) False) % 3.68/3.85 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 3.68/3.85 Or (Eq (∀ (Xu Xv Xw : a), And (Eq Xu Xw) (Eq Xv Xw) → Eq Xu Xv) False) % 3.68/3.85 (Eq (Not (Eq (skS.0 0 a_1) (skS.0 0 a_1))) True) % 3.68/3.85 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a), % 3.68/3.85 Or (Eq (Not (Eq (skS.0 0 a_1) (skS.0 0 a_1))) True) % 3.68/3.85 (Eq (Not (∀ (Xv Xw : a), And (Eq (skS.0 1 a_2) Xw) (Eq Xv Xw) → Eq (skS.0 1 a_2) Xv)) True) % 3.68/3.85 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a), % 3.68/3.85 Or (Eq (Not (∀ (Xv Xw : a), And (Eq (skS.0 1 a_1) Xw) (Eq Xv Xw) → Eq (skS.0 1 a_1) Xv)) True) % 3.68/3.85 (Eq (Eq (skS.0 0 a_2) (skS.0 0 a_2)) False) % 3.68/3.85 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : a), % 3.68/3.85 Or (Eq (Eq (skS.0 0 a_1) (skS.0 0 a_1)) False) % 3.68/3.85 (Eq (∀ (Xv Xw : a), And (Eq (skS.0 1 a_2) Xw) (Eq Xv Xw) → Eq (skS.0 1 a_2) Xv) False) % 3.68/3.85 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 : a), % 3.68/3.85 Or (Eq (∀ (Xv Xw : a), And (Eq (skS.0 1 a_1) Xw) (Eq Xv Xw) → Eq (skS.0 1 a_1) Xv) False) % 3.68/3.85 (Ne (skS.0 0 a_2) (skS.0 0 a_2)) % 3.68/3.85 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a), % 3.68/3.85 Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) % 3.68/3.85 (Eq (Not (∀ (Xw : a), And (Eq (skS.0 1 a_2) Xw) (Eq (skS.0 2 a_2 a_3) Xw) → Eq (skS.0 1 a_2) (skS.0 2 a_2 a_3))) % 3.68/3.85 True) % 3.68/3.85 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a), % 3.68/3.85 Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) % 3.68/3.85 (Eq (∀ (Xw : a), And (Eq (skS.0 1 a_2) Xw) (Eq (skS.0 2 a_2 a_3) Xw) → Eq (skS.0 1 a_2) (skS.0 2 a_2 a_3)) False) % 3.68/3.85 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.68/3.85 Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) % 3.68/3.85 (Eq % 3.68/3.85 (Not % 3.68/3.85 (And (Eq (skS.0 1 a_2) (skS.0 3 a_2 a_3 a_4)) (Eq (skS.0 2 a_2 a_3) (skS.0 3 a_2 a_3 a_4)) → % 3.68/3.85 Eq (skS.0 1 a_2) (skS.0 2 a_2 a_3))) % 3.68/3.85 True) % 3.68/3.85 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.68/3.85 Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) % 3.68/3.85 (Eq % 3.68/3.85 (And (Eq (skS.0 1 a_2) (skS.0 3 a_2 a_3 a_4)) (Eq (skS.0 2 a_2 a_3) (skS.0 3 a_2 a_3 a_4)) → % 3.68/3.85 Eq (skS.0 1 a_2) (skS.0 2 a_2 a_3)) % 3.68/3.85 False) % 3.68/3.85 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.68/3.85 Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) % 3.68/3.85 (Eq (And (Eq (skS.0 1 a_2) (skS.0 3 a_2 a_3 a_4)) (Eq (skS.0 2 a_2 a_3) (skS.0 3 a_2 a_3 a_4))) True) % 3.68/3.85 Clause #13 (by clausification #[11]): ∀ (a_1 a_2 a_3 : a), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (Eq (skS.0 1 a_2) (skS.0 2 a_2 a_3)) False) % 3.68/3.85 Clause #14 (by clausification #[12]): ∀ (a_1 a_2 a_3 a_4 : a), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (Eq (skS.0 2 a_2 a_3) (skS.0 3 a_2 a_3 a_4)) True) % 3.68/3.85 Clause #15 (by clausification #[12]): ∀ (a_1 a_2 a_3 a_4 : a), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (Eq (skS.0 1 a_2) (skS.0 3 a_2 a_3 a_4)) True) % 3.68/3.85 Clause #16 (by clausification #[14]): ∀ (a_1 a_2 a_3 a_4 : a), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 2 a_2 a_3) (skS.0 3 a_2 a_3 a_4)) % 3.68/3.85 Clause #17 (by eliminate resolved literals #[16]): ∀ (a_1 a_2 a_3 : a), Eq (skS.0 2 a_1 a_2) (skS.0 3 a_1 a_2 a_3) % 3.68/3.85 Clause #18 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Ne (skS.0 1 a_2) (skS.0 2 a_2 a_3)) % 3.68/3.85 Clause #19 (by eliminate resolved literals #[18]): ∀ (a_1 a_2 : a), Ne (skS.0 1 a_1) (skS.0 2 a_1 a_2) % 3.68/3.85 Clause #20 (by clausification #[15]): ∀ (a_1 a_2 a_3 a_4 : a), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 1 a_2) (skS.0 3 a_2 a_3 a_4)) % 3.68/3.85 Clause #21 (by eliminate resolved literals #[20]): ∀ (a_1 a_2 a_3 : a), Eq (skS.0 1 a_1) (skS.0 3 a_1 a_2 a_3) % 3.68/3.85 Clause #22 (by superposition #[21, 17]): ∀ (a_1 a_2 : a), Eq (skS.0 2 a_1 a_2) (skS.0 1 a_1) % 3.68/3.85 Clause #23 (by forward contextual literal cutting #[22, 19]): False % 3.68/3.85 SZS output end Proof for theBenchmark.p 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