%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM696^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:57:06 PM UTC 2025 % Result : Theorem 3.68s 3.91s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM696^1 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.14 % Command : duper %s % 0.13/0.35 % Computer : n024.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 08:26:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.68/3.91 SZS status Theorem for theBenchmark.p % 3.68/3.91 SZS output start Proof for theBenchmark.p % 3.68/3.91 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True % 3.68/3.91 Clause #2 (by assumption #[]): Eq (∀ (Xx : nat), Not (Not (∀ (Xx_0 : nat), Ne Xx (pl n_1 Xx_0))) → Eq Xx n_1) True % 3.68/3.91 Clause #3 (by assumption #[]): Eq % 3.68/3.91 (∀ (Xx Xy Xz : nat), % 3.68/3.91 Not (∀ (Xx_0 : nat), Ne Xx (pl Xy Xx_0)) → Not (∀ (Xx_0 : nat), Ne (pl Xx Xz) (pl (pl Xy Xz) Xx_0))) % 3.68/3.91 True % 3.68/3.91 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (pl Xx Xy) (pl Xy Xx)) True % 3.68/3.91 Clause #5 (by assumption #[]): Eq (Not (Not (Not (∀ (Xx_0 : nat), Ne y (pl (pl x n_1) Xx_0))) → Eq y (pl x n_1))) True % 3.68/3.91 Clause #10 (by clausification #[2]): ∀ (a : nat), Eq (Not (Not (∀ (Xx_0 : nat), Ne a (pl n_1 Xx_0))) → Eq a n_1) True % 3.68/3.91 Clause #11 (by clausification #[10]): ∀ (a : nat), Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne a (pl n_1 Xx_0)))) False) (Eq (Eq a n_1) True) % 3.68/3.91 Clause #12 (by clausification #[11]): ∀ (a : nat), Or (Eq (Eq a n_1) True) (Eq (Not (∀ (Xx_0 : nat), Ne a (pl n_1 Xx_0))) True) % 3.68/3.91 Clause #13 (by clausification #[12]): ∀ (a : nat), Or (Eq (Not (∀ (Xx_0 : nat), Ne a (pl n_1 Xx_0))) True) (Eq a n_1) % 3.68/3.91 Clause #14 (by clausification #[13]): ∀ (a : nat), Or (Eq a n_1) (Eq (∀ (Xx_0 : nat), Ne a (pl n_1 Xx_0)) False) % 3.68/3.91 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Or (Eq a n_1) (Eq (Not (Ne a (pl n_1 (skS.0 0 a a_1)))) True) % 3.68/3.91 Clause #16 (by clausification #[15]): ∀ (a a_1 : nat), Or (Eq a n_1) (Eq (Ne a (pl n_1 (skS.0 0 a a_1))) False) % 3.68/3.91 Clause #17 (by clausification #[16]): ∀ (a a_1 : nat), Or (Eq a n_1) (Eq a (pl n_1 (skS.0 0 a a_1))) % 3.68/3.91 Clause #20 (by clausification #[5]): Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl (pl x n_1) Xx_0))) → Eq y (pl x n_1)) False % 3.68/3.91 Clause #21 (by clausification #[20]): Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl (pl x n_1) Xx_0)))) True % 3.68/3.91 Clause #22 (by clausification #[20]): Eq (Eq y (pl x n_1)) False % 3.68/3.91 Clause #23 (by clausification #[21]): Eq (Not (∀ (Xx_0 : nat), Ne y (pl (pl x n_1) Xx_0))) False % 3.68/3.91 Clause #24 (by clausification #[23]): Eq (∀ (Xx_0 : nat), Ne y (pl (pl x n_1) Xx_0)) True % 3.68/3.91 Clause #25 (by clausification #[24]): ∀ (a : nat), Eq (Ne y (pl (pl x n_1) a)) True % 3.68/3.91 Clause #26 (by clausification #[25]): ∀ (a : nat), Ne y (pl (pl x n_1) a) % 3.68/3.91 Clause #28 (by clausification #[22]): Ne y (pl x n_1) % 3.68/3.91 Clause #30 (by clausification #[0]): Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False % 3.68/3.91 Clause #31 (by clausification #[30]): ∀ (a : nat), Eq (Not (Ne y (pl x (skS.0 1 a)))) True % 3.68/3.91 Clause #32 (by clausification #[31]): ∀ (a : nat), Eq (Ne y (pl x (skS.0 1 a))) False % 3.68/3.91 Clause #33 (by clausification #[32]): ∀ (a : nat), Eq y (pl x (skS.0 1 a)) % 3.68/3.91 Clause #34 (by clausification #[3]): ∀ (a : nat), % 3.68/3.91 Eq % 3.68/3.91 (∀ (Xy Xz : nat), Not (∀ (Xx_0 : nat), Ne a (pl Xy Xx_0)) → Not (∀ (Xx_0 : nat), Ne (pl a Xz) (pl (pl Xy Xz) Xx_0))) % 3.68/3.91 True % 3.68/3.91 Clause #35 (by clausification #[34]): ∀ (a a_1 : nat), % 3.68/3.91 Eq (∀ (Xz : nat), Not (∀ (Xx_0 : nat), Ne a (pl a_1 Xx_0)) → Not (∀ (Xx_0 : nat), Ne (pl a Xz) (pl (pl a_1 Xz) Xx_0))) % 3.68/3.91 True % 3.68/3.91 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : nat), % 3.68/3.91 Eq (Not (∀ (Xx_0 : nat), Ne a (pl a_1 Xx_0)) → Not (∀ (Xx_0 : nat), Ne (pl a a_2) (pl (pl a_1 a_2) Xx_0))) True % 3.68/3.91 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : nat), % 3.68/3.91 Or (Eq (Not (∀ (Xx_0 : nat), Ne a (pl a_1 Xx_0))) False) % 3.68/3.91 (Eq (Not (∀ (Xx_0 : nat), Ne (pl a a_2) (pl (pl a_1 a_2) Xx_0))) True) % 3.68/3.91 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : nat), % 3.68/3.91 Or (Eq (Not (∀ (Xx_0 : nat), Ne (pl a a_1) (pl (pl a_2 a_1) Xx_0))) True) % 3.68/3.91 (Eq (∀ (Xx_0 : nat), Ne a (pl a_2 Xx_0)) True) % 3.68/3.91 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : nat), % 3.68/3.91 Or (Eq (∀ (Xx_0 : nat), Ne a (pl a_1 Xx_0)) True) (Eq (∀ (Xx_0 : nat), Ne (pl a a_2) (pl (pl a_1 a_2) Xx_0)) False) % 3.68/3.91 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : nat), % 3.68/3.91 Or (Eq (∀ (Xx_0 : nat), Ne (pl a a_1) (pl (pl a_2 a_1) Xx_0)) False) (Eq (Ne a (pl a_2 a_3)) True) % 3.68/3.91 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 a_4 : nat), % 3.68/3.91 Or (Eq (Ne a (pl a_1 a_2)) True) (Eq (Not (Ne (pl a a_3) (pl (pl a_1 a_3) (skS.0 2 a a_3 a_1 a_4)))) True) % 3.68/3.92 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : nat), % 3.68/3.92 Or (Eq (Not (Ne (pl a a_1) (pl (pl a_2 a_1) (skS.0 2 a a_1 a_2 a_3)))) True) (Ne a (pl a_2 a_4)) % 3.68/3.92 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : nat), Or (Ne a (pl a_1 a_2)) (Eq (Ne (pl a a_3) (pl (pl a_1 a_3) (skS.0 2 a a_3 a_1 a_4))) False) % 3.68/3.92 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : nat), Or (Ne a (pl a_1 a_2)) (Eq (pl a a_3) (pl (pl a_1 a_3) (skS.0 2 a a_3 a_1 a_4))) % 3.68/3.92 Clause #45 (by destructive equality resolution #[44]): ∀ (a a_1 a_2 a_3 : nat), Eq (pl (pl a a_1) a_2) (pl (pl a a_2) (skS.0 2 (pl a a_1) a_2 a a_3)) % 3.68/3.92 Clause #56 (by clausification #[4]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (pl a Xy) (pl Xy a)) True % 3.68/3.92 Clause #57 (by clausification #[56]): ∀ (a a_1 : nat), Eq (Eq (pl a a_1) (pl a_1 a)) True % 3.68/3.92 Clause #58 (by clausification #[57]): ∀ (a a_1 : nat), Eq (pl a a_1) (pl a_1 a) % 3.68/3.92 Clause #59 (by superposition #[58, 26]): ∀ (a : nat), Ne y (pl (pl n_1 x) a) % 3.68/3.92 Clause #146 (by superposition #[59, 45]): ∀ (a : nat), Ne y (pl (pl n_1 a) x) % 3.68/3.92 Clause #167 (by forward demodulation #[146, 58]): ∀ (a : nat), Ne y (pl x (pl n_1 a)) % 3.68/3.92 Clause #170 (by superposition #[167, 17]): ∀ (a : nat), Or (Eq a n_1) (Ne y (pl x a)) % 3.68/3.92 Clause #190 (by superposition #[170, 33]): ∀ (a : nat), Or (Eq (skS.0 1 a) n_1) (Ne y y) % 3.68/3.92 Clause #237 (by eliminate resolved literals #[190]): ∀ (a : nat), Eq (skS.0 1 a) n_1 % 3.68/3.92 Clause #238 (by backward demodulation #[237, 33]): Eq y (pl x n_1) % 3.68/3.92 Clause #239 (by forward contextual literal cutting #[238, 28]): False % 3.68/3.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------