%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU884^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:02:35 PM UTC 2025 % Result : Theorem 3.73s 3.92s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU884^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n013.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 05:09:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.73/3.92 SZS status Theorem for theBenchmark.p % 3.73/3.92 SZS output start Proof for theBenchmark.p % 3.73/3.92 Clause #0 (by assumption #[]): Eq % 3.73/3.92 (Not % 3.73/3.92 ((∀ (Xx : a), (Exists fun Xt => And (cR Xt) (Eq Xx Xt)) → Exists fun Xt => And (cS Xt) (Eq Xx Xt)) → % 3.73/3.92 ∀ (Xx : a), cR Xx → cS Xx)) % 3.73/3.92 True % 3.73/3.92 Clause #1 (by clausification #[0]): Eq % 3.73/3.92 ((∀ (Xx : a), (Exists fun Xt => And (cR Xt) (Eq Xx Xt)) → Exists fun Xt => And (cS Xt) (Eq Xx Xt)) → % 3.73/3.92 ∀ (Xx : a), cR Xx → cS Xx) % 3.73/3.92 False % 3.73/3.92 Clause #2 (by clausification #[1]): Eq (∀ (Xx : a), (Exists fun Xt => And (cR Xt) (Eq Xx Xt)) → Exists fun Xt => And (cS Xt) (Eq Xx Xt)) True % 3.73/3.92 Clause #3 (by clausification #[1]): Eq (∀ (Xx : a), cR Xx → cS Xx) False % 3.73/3.92 Clause #4 (by clausification #[2]): ∀ (a_1 : a), Eq ((Exists fun Xt => And (cR Xt) (Eq a_1 Xt)) → Exists fun Xt => And (cS Xt) (Eq a_1 Xt)) True % 3.73/3.92 Clause #5 (by clausification #[4]): ∀ (a_1 : a), % 3.73/3.92 Or (Eq (Exists fun Xt => And (cR Xt) (Eq a_1 Xt)) False) (Eq (Exists fun Xt => And (cS Xt) (Eq a_1 Xt)) True) % 3.73/3.92 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : a), Or (Eq (Exists fun Xt => And (cS Xt) (Eq a_1 Xt)) True) (Eq (And (cR a_2) (Eq a_1 a_2)) False) % 3.73/3.92 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a), % 3.73/3.92 Or (Eq (And (cR a_1) (Eq a_2 a_1)) False) (Eq (And (cS (skS.0 0 a_2 a_3)) (Eq a_2 (skS.0 0 a_2 a_3))) True) % 3.73/3.92 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a), % 3.73/3.92 Or (Eq (And (cS (skS.0 0 a_1 a_2)) (Eq a_1 (skS.0 0 a_1 a_2))) True) (Or (Eq (cR a_3) False) (Eq (Eq a_1 a_3) False)) % 3.73/3.92 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cR a_1) False) (Or (Eq (Eq a_2 a_1) False) (Eq (Eq a_2 (skS.0 0 a_2 a_3)) True)) % 3.73/3.92 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cR a_1) False) (Or (Eq (Eq a_2 a_1) False) (Eq (cS (skS.0 0 a_2 a_3)) True)) % 3.73/3.92 Clause #11 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cR a_1) False) (Or (Eq (Eq a_2 (skS.0 0 a_2 a_3)) True) (Ne a_2 a_1)) % 3.73/3.92 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cR a_1) False) (Or (Ne a_2 a_1) (Eq a_2 (skS.0 0 a_2 a_3))) % 3.73/3.92 Clause #13 (by destructive equality resolution #[12]): ∀ (a_1 a_2 : a), Or (Eq (cR a_1) False) (Eq a_1 (skS.0 0 a_1 a_2)) % 3.73/3.92 Clause #14 (by clausification #[3]): ∀ (a_1 : a), Eq (Not (cR (skS.0 1 a_1) → cS (skS.0 1 a_1))) True % 3.73/3.92 Clause #15 (by clausification #[14]): ∀ (a_1 : a), Eq (cR (skS.0 1 a_1) → cS (skS.0 1 a_1)) False % 3.73/3.92 Clause #16 (by clausification #[15]): ∀ (a_1 : a), Eq (cR (skS.0 1 a_1)) True % 3.73/3.92 Clause #17 (by clausification #[15]): ∀ (a_1 : a), Eq (cS (skS.0 1 a_1)) False % 3.73/3.92 Clause #18 (by superposition #[16, 13]): ∀ (a_1 a_2 : a), Or (Eq True False) (Eq (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) % 3.73/3.92 Clause #19 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cR a_1) False) (Or (Eq (cS (skS.0 0 a_2 a_3)) True) (Ne a_2 a_1)) % 3.73/3.92 Clause #20 (by destructive equality resolution #[19]): ∀ (a_1 a_2 : a), Or (Eq (cR a_1) False) (Eq (cS (skS.0 0 a_1 a_2)) True) % 3.73/3.92 Clause #21 (by superposition #[20, 16]): ∀ (a_1 a_2 : a), Or (Eq (cS (skS.0 0 (skS.0 1 a_1) a_2)) True) (Eq False True) % 3.73/3.92 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 : a), Eq (cS (skS.0 0 (skS.0 1 a_1) a_2)) True % 3.73/3.92 Clause #23 (by clausification #[18]): ∀ (a_1 a_2 : a), Eq (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2) % 3.73/3.92 Clause #24 (by backward demodulation #[23, 22]): ∀ (a_1 : a), Eq (cS (skS.0 1 a_1)) True % 3.73/3.92 Clause #25 (by superposition #[24, 17]): Eq True False % 3.73/3.92 Clause #26 (by clausification #[25]): False % 3.73/3.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------