%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU889^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 4.02s 4.20s % Output : Proof 4.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU889^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n021.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 05:02:08 EDT 2025 % 0.15/0.36 % CPUTime : % 4.02/4.20 SZS status Theorem for theBenchmark.p % 4.02/4.20 SZS output start Proof for theBenchmark.p % 4.02/4.20 Clause #0 (by assumption #[]): Eq % 4.02/4.20 (Not % 4.02/4.20 (∀ (Xx : a), % 4.02/4.20 (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq Xx (cF Xt))) → % 4.02/4.20 Exists fun Xt => And (cS Xt) (Eq Xx (cF (cG Xt))))) % 4.02/4.20 True % 4.02/4.20 Clause #1 (by clausification #[0]): Eq % 4.02/4.20 (∀ (Xx : a), % 4.02/4.20 (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq Xx (cF Xt))) → % 4.02/4.20 Exists fun Xt => And (cS Xt) (Eq Xx (cF (cG Xt)))) % 4.02/4.20 False % 4.02/4.20 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 4.02/4.20 Eq % 4.02/4.20 (Not % 4.02/4.20 ((Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) → % 4.02/4.20 Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt))))) % 4.02/4.20 True % 4.02/4.20 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 4.02/4.20 Eq % 4.02/4.20 ((Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) → % 4.02/4.20 Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) % 4.02/4.20 False % 4.02/4.20 Clause #4 (by clausification #[3]): ∀ (a_1 : a), Eq (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) True % 4.02/4.20 Clause #5 (by clausification #[3]): ∀ (a_1 : a), Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) False % 4.02/4.20 Clause #6 (by clausification #[4]): ∀ (a_1 : a) (a_2 : b), % 4.02/4.20 Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))) % 4.02/4.20 True % 4.02/4.20 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 % 4.02/4.20 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), Eq (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) True % 4.02/4.20 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)) % 4.02/4.20 Clause #10 (by clausification #[5]): ∀ (a_1 : c) (a_2 : a), Eq (And (cS a_1) (Eq (skS.0 0 a_2) (cF (cG a_1)))) False % 4.02/4.20 Clause #11 (by clausification #[10]): ∀ (a_1 : c) (a_2 : a), Or (Eq (cS a_1) False) (Eq (Eq (skS.0 0 a_2) (cF (cG a_1))) False) % 4.02/4.20 Clause #12 (by clausification #[11]): ∀ (a_1 : c) (a_2 : a), Or (Eq (cS a_1) False) (Ne (skS.0 0 a_2) (cF (cG a_1))) % 4.02/4.20 Clause #13 (by clausification #[8]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), % 4.02/4.20 Eq (And (cS (skS.0 2 a_1 a_2 a_3)) (Eq (skS.0 1 a_1 a_2) (cG (skS.0 2 a_1 a_2 a_3)))) True % 4.02/4.20 Clause #14 (by clausification #[13]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (Eq (skS.0 1 a_1 a_2) (cG (skS.0 2 a_1 a_2 a_3))) True % 4.02/4.20 Clause #15 (by clausification #[13]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (cS (skS.0 2 a_1 a_2 a_3)) True % 4.02/4.20 Clause #16 (by clausification #[14]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (skS.0 1 a_1 a_2) (cG (skS.0 2 a_1 a_2 a_3)) % 4.02/4.20 Clause #17 (by superposition #[15, 12]): ∀ (a_1 a_2 : a) (a_3 : b) (a_4 : c), Or (Eq True False) (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_2 a_3 a_4)))) % 4.02/4.20 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 : a) (a_3 : b) (a_4 : c), Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_2 a_3 a_4))) % 4.02/4.20 Clause #19 (by forward demodulation #[18, 16]): ∀ (a_1 a_2 : a) (a_3 : b), Ne (skS.0 0 a_1) (cF (skS.0 1 a_2 a_3)) % 4.02/4.20 Clause #20 (by forward demodulation #[19, 9]): ∀ (a_1 a_2 : a), Ne (skS.0 0 a_1) (skS.0 0 a_2) % 4.02/4.20 Clause #21 (by equality resolution #[20]): False % 4.02/4.20 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------