%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU891^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 4.51s 4.69s % Output : Proof 4.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU891^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 04:54:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.51/4.69 SZS status Theorem for theBenchmark.p % 4.51/4.69 SZS output start Proof for theBenchmark.p % 4.51/4.69 Clause #0 (by assumption #[]): Eq % 4.51/4.69 (Not % 4.51/4.69 (∀ (Xx : a), % 4.51/4.69 Or (Exists fun Xt => And (cR Xt) (Eq Xx (cF Xt))) (Exists fun Xt => And (cS Xt) (Eq Xx (cF Xt))) → % 4.51/4.69 Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq Xx (cF Xt)))) % 4.51/4.69 True % 4.51/4.69 Clause #1 (by clausification #[0]): Eq % 4.51/4.69 (∀ (Xx : a), % 4.51/4.69 Or (Exists fun Xt => And (cR Xt) (Eq Xx (cF Xt))) (Exists fun Xt => And (cS Xt) (Eq Xx (cF Xt))) → % 4.51/4.69 Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq Xx (cF Xt))) % 4.51/4.69 False % 4.51/4.69 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 4.51/4.69 Eq % 4.51/4.69 (Not % 4.51/4.69 (Or (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) % 4.51/4.69 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt))) → % 4.51/4.69 Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq (skS.0 0 a_1) (cF Xt)))) % 4.51/4.69 True % 4.51/4.69 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 4.51/4.69 Eq % 4.51/4.69 (Or (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) % 4.51/4.69 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt))) → % 4.51/4.69 Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq (skS.0 0 a_1) (cF Xt))) % 4.51/4.69 False % 4.51/4.69 Clause #4 (by clausification #[3]): ∀ (a_1 : a), % 4.51/4.69 Eq % 4.51/4.69 (Or (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) % 4.51/4.69 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt)))) % 4.51/4.69 True % 4.51/4.69 Clause #5 (by clausification #[3]): ∀ (a_1 : a), Eq (Exists fun Xt => And (Or (cR Xt) (cS Xt)) (Eq (skS.0 0 a_1) (cF Xt))) False % 4.51/4.69 Clause #6 (by clausification #[4]): ∀ (a_1 : a), % 4.51/4.69 Or (Eq (Exists fun Xt => And (cR Xt) (Eq (skS.0 0 a_1) (cF Xt))) True) % 4.51/4.69 (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt))) True) % 4.51/4.69 Clause #7 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), % 4.51/4.69 Or (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF Xt))) True) % 4.51/4.69 (Eq (And (cR (skS.0 1 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))) True) % 4.51/4.69 Clause #8 (by clausification #[7]): ∀ (a_1 : a) (a_2 a_3 : b), % 4.51/4.69 Or (Eq (And (cR (skS.0 1 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))) True) % 4.51/4.69 (Eq (And (cS (skS.0 2 a_1 a_3)) (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_3)))) True) % 4.51/4.69 Clause #9 (by clausification #[8]): ∀ (a_1 : a) (a_2 a_3 : b), % 4.51/4.69 Or (Eq (And (cS (skS.0 2 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_2)))) True) % 4.51/4.69 (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) True) % 4.51/4.69 Clause #10 (by clausification #[8]): ∀ (a_1 : a) (a_2 a_3 : b), % 4.51/4.69 Or (Eq (And (cS (skS.0 2 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_2)))) True) (Eq (cR (skS.0 1 a_1 a_3)) True) % 4.51/4.69 Clause #11 (by clausification #[9]): ∀ (a_1 : a) (a_2 a_3 : b), % 4.51/4.69 Or (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) True) (Eq (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_3))) True) % 4.51/4.69 Clause #12 (by clausification #[9]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) True) (Eq (cS (skS.0 2 a_1 a_3)) True) % 4.51/4.69 Clause #13 (by clausification #[11]): ∀ (a_1 : a) (a_2 a_3 : b), % 4.51/4.69 Or (Eq (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_2))) True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 4.51/4.69 Clause #14 (by clausification #[13]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_3))) % 4.51/4.69 Clause #15 (by clausification #[5]): ∀ (a_1 : b) (a_2 : a), Eq (And (Or (cR a_1) (cS a_1)) (Eq (skS.0 0 a_2) (cF a_1))) False % 4.51/4.69 Clause #16 (by clausification #[15]): ∀ (a_1 : b) (a_2 : a), Or (Eq (Or (cR a_1) (cS a_1)) False) (Eq (Eq (skS.0 0 a_2) (cF a_1)) False) % 4.51/4.69 Clause #17 (by clausification #[16]): ∀ (a_1 : a) (a_2 : b), Or (Eq (Eq (skS.0 0 a_1) (cF a_2)) False) (Eq (cS a_2) False) % 4.51/4.69 Clause #18 (by clausification #[16]): ∀ (a_1 : a) (a_2 : b), Or (Eq (Eq (skS.0 0 a_1) (cF a_2)) False) (Eq (cR a_2) False) % 4.51/4.69 Clause #19 (by clausification #[17]): ∀ (a_1 : b) (a_2 : a), Or (Eq (cS a_1) False) (Ne (skS.0 0 a_2) (cF a_1)) % 4.51/4.69 Clause #20 (by clausification #[18]): ∀ (a_1 : b) (a_2 : a), Or (Eq (cR a_1) False) (Ne (skS.0 0 a_2) (cF a_1)) % 4.51/4.69 Clause #21 (by clausification #[12]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 4.51/4.69 Clause #22 (by superposition #[21, 19]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b), % 4.51/4.71 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) (Or (Eq True False) (Ne (skS.0 0 a_3) (cF (skS.0 2 a_1 a_4)))) % 4.51/4.71 Clause #23 (by clausification #[22]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b), % 4.51/4.71 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) (Ne (skS.0 0 a_3) (cF (skS.0 2 a_1 a_4))) % 4.51/4.71 Clause #24 (by backward contextual literal cutting #[23, 14]): ∀ (a_1 : a) (a_2 : b), Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)) % 4.51/4.71 Clause #25 (by clausification #[10]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (cR (skS.0 1 a_1 a_2)) True) (Eq (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_3))) True) % 4.51/4.71 Clause #26 (by clausification #[10]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (cR (skS.0 1 a_1 a_2)) True) (Eq (cS (skS.0 2 a_1 a_3)) True) % 4.51/4.71 Clause #27 (by clausification #[25]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (cR (skS.0 1 a_1 a_2)) True) (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_3))) % 4.51/4.71 Clause #28 (by superposition #[27, 20]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b), % 4.51/4.71 Or (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_2))) (Or (Eq True False) (Ne (skS.0 0 a_3) (cF (skS.0 1 a_1 a_4)))) % 4.51/4.71 Clause #30 (by superposition #[26, 20]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b), % 4.51/4.71 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq True False) (Ne (skS.0 0 a_3) (cF (skS.0 1 a_1 a_4)))) % 4.51/4.71 Clause #32 (by clausification #[30]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Ne (skS.0 0 a_3) (cF (skS.0 1 a_1 a_4))) % 4.51/4.71 Clause #33 (by forward demodulation #[32, 24]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Ne (skS.0 0 a_3) (skS.0 0 a_1)) % 4.51/4.71 Clause #34 (by equality resolution #[33]): ∀ (a_1 : a) (a_2 : b), Eq (cS (skS.0 2 a_1 a_2)) True % 4.51/4.71 Clause #35 (by superposition #[34, 19]): ∀ (a_1 a_2 : a) (a_3 : b), Or (Eq True False) (Ne (skS.0 0 a_1) (cF (skS.0 2 a_2 a_3))) % 4.51/4.71 Clause #36 (by clausification #[35]): ∀ (a_1 a_2 : a) (a_3 : b), Ne (skS.0 0 a_1) (cF (skS.0 2 a_2 a_3)) % 4.51/4.71 Clause #38 (by clausification #[28]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b), % 4.51/4.71 Or (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_2))) (Ne (skS.0 0 a_3) (cF (skS.0 1 a_1 a_4))) % 4.51/4.71 Clause #39 (by forward demodulation #[38, 24]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), Or (Eq (skS.0 0 a_1) (cF (skS.0 2 a_1 a_2))) (Ne (skS.0 0 a_3) (skS.0 0 a_1)) % 4.51/4.71 Clause #40 (by forward contextual literal cutting #[39, 36]): ∀ (a_1 a_2 : a), Ne (skS.0 0 a_1) (skS.0 0 a_2) % 4.51/4.71 Clause #41 (by equality resolution #[40]): False % 4.51/4.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------