%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU893^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:02:36 PM UTC 2025 % Result : Theorem 3.73s 3.88s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU893^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.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 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 06:36:08 EDT 2025 % 0.14/0.36 % CPUTime : % 3.73/3.88 SZS status Theorem for theBenchmark.p % 3.73/3.88 SZS output start Proof for theBenchmark.p % 3.73/3.88 Clause #0 (by assumption #[]): Eq % 3.73/3.88 (Not % 3.73/3.88 (∀ (Xx : a), % 3.73/3.88 (Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq Xx (cF Xt))) → % 3.73/3.88 Or (Exists fun Xt => And (cR Xt) (Eq Xx (cF Xt))) (Exists fun Xt => And (cS Xt) (Eq Xx (cF Xt))))) % 3.73/3.88 True % 3.73/3.88 Clause #1 (by clausification #[0]): Eq % 3.73/3.88 (∀ (Xx : a), % 3.73/3.88 (Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq Xx (cF Xt))) → % 3.73/3.88 Or (Exists fun Xt => And (cR Xt) (Eq Xx (cF Xt))) (Exists fun Xt => And (cS Xt) (Eq Xx (cF Xt)))) % 3.73/3.88 False % 3.73/3.88 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 3.73/3.88 Eq % 3.73/3.88 (Not % 3.73/3.88 ((Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq (skS.0 0 a_1) (cF Xt))) → % 3.73/3.88 Or (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) % 3.73/3.88 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt))))) % 3.73/3.88 True % 3.73/3.88 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 3.73/3.88 Eq % 3.73/3.88 ((Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq (skS.0 0 a_1) (cF Xt))) → % 3.73/3.88 Or (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) % 3.73/3.88 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt)))) % 3.73/3.88 False % 3.73/3.88 Clause #4 (by clausification #[3]): ∀ (a_1 : a), Eq (Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq (skS.0 0 a_1) (cF Xt))) True % 3.73/3.88 Clause #5 (by clausification #[3]): ∀ (a_1 : a), % 3.73/3.88 Eq % 3.73/3.88 (Or (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) % 3.73/3.88 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt)))) % 3.73/3.88 False % 3.73/3.88 Clause #6 (by clausification #[4]): ∀ (a_1 : a) (a_2 : b), % 3.73/3.88 Eq (And (Or (cR (skS.0 1 a_1 a_2)) (cS (skS.0 1 a_1 a_2))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))) True % 3.73/3.88 Clause #7 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) True % 3.73/3.88 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), Eq (Or (cR (skS.0 1 a_1 a_2)) (cS (skS.0 1 a_1 a_2))) True % 3.73/3.88 Clause #9 (by clausification #[7]): ∀ (a_1 : a) (a_2 : b), Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)) % 3.73/3.88 Clause #10 (by clausification #[8]): ∀ (a_1 : a) (a_2 : b), Or (Eq (cR (skS.0 1 a_1 a_2)) True) (Eq (cS (skS.0 1 a_1 a_2)) True) % 3.73/3.88 Clause #11 (by clausification #[5]): ∀ (a_1 : a), Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt))) False % 3.73/3.88 Clause #12 (by clausification #[5]): ∀ (a_1 : a), Eq (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) False % 3.73/3.88 Clause #13 (by clausification #[11]): ∀ (a_1 : b) (a_2 : a), Eq (And (cS a_1) (Eq (skS.0 0 a_2) (cF a_1))) False % 3.73/3.88 Clause #14 (by clausification #[13]): ∀ (a_1 : b) (a_2 : a), Or (Eq (cS a_1) False) (Eq (Eq (skS.0 0 a_2) (cF a_1)) False) % 3.73/3.88 Clause #15 (by clausification #[14]): ∀ (a_1 : b) (a_2 : a), Or (Eq (cS a_1) False) (Ne (skS.0 0 a_2) (cF a_1)) % 3.73/3.88 Clause #16 (by superposition #[15, 10]): ∀ (a_1 a_2 : a) (a_3 : b), % 3.73/3.88 Or (Ne (skS.0 0 a_1) (cF (skS.0 1 a_2 a_3))) (Or (Eq (cR (skS.0 1 a_2 a_3)) True) (Eq False True)) % 3.73/3.88 Clause #17 (by clausification #[12]): ∀ (a_1 : b) (a_2 : a), Eq (And (cR a_1) (Eq (skS.0 0 a_2) (cF a_1))) False % 3.73/3.88 Clause #18 (by clausification #[17]): ∀ (a_1 : b) (a_2 : a), Or (Eq (cR a_1) False) (Eq (Eq (skS.0 0 a_2) (cF a_1)) False) % 3.73/3.88 Clause #19 (by clausification #[18]): ∀ (a_1 : b) (a_2 : a), Or (Eq (cR a_1) False) (Ne (skS.0 0 a_2) (cF a_1)) % 3.73/3.88 Clause #20 (by clausification #[16]): ∀ (a_1 a_2 : a) (a_3 : b), Or (Ne (skS.0 0 a_1) (cF (skS.0 1 a_2 a_3))) (Eq (cR (skS.0 1 a_2 a_3)) True) % 3.73/3.88 Clause #21 (by forward demodulation #[20, 9]): ∀ (a_1 a_2 : a) (a_3 : b), Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Eq (cR (skS.0 1 a_2 a_3)) True) % 3.73/3.88 Clause #22 (by equality resolution #[21]): ∀ (a_1 : a) (a_2 : b), Eq (cR (skS.0 1 a_1 a_2)) True % 3.73/3.88 Clause #24 (by superposition #[22, 19]): ∀ (a_1 a_2 : a) (a_3 : b), Or (Eq True False) (Ne (skS.0 0 a_1) (cF (skS.0 1 a_2 a_3))) % 3.73/3.88 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 : a) (a_3 : b), Ne (skS.0 0 a_1) (cF (skS.0 1 a_2 a_3)) % 3.73/3.88 Clause #26 (by forward demodulation #[25, 9]): ∀ (a_1 a_2 : a), Ne (skS.0 0 a_1) (skS.0 0 a_2) % 3.73/3.88 Clause #27 (by equality resolution #[26]): False % 3.73/3.88 SZS output end Proof for theBenchmark.p 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