%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM651^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 07:56:56 PM UTC 2025 % Result : Theorem 4.91s 5.08s % Output : Proof 4.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM651^1 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n028.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 08:18:38 EDT 2025 % 0.14/0.34 % CPUTime : % 4.91/5.08 SZS status Theorem for theBenchmark.p % 4.91/5.08 SZS output start Proof for theBenchmark.p % 4.91/5.08 Clause #0 (by assumption #[]): Eq (∀ (Xx Xy : nat), Ne Xy (pl Xx Xy)) True % 4.91/5.08 Clause #1 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (pl Xx Xy) (pl Xy Xx)) True % 4.91/5.08 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), Eq (pl (pl Xx Xy) Xz) (pl Xx (pl Xy Xz))) True % 4.91/5.08 Clause #4 (by assumption #[]): Eq % 4.91/5.08 (Not % 4.91/5.08 (Not % 4.91/5.08 ((Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) → % 4.91/5.08 Not % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))))) % 4.91/5.08 True % 4.91/5.08 Clause #9 (by clausification #[0]): ∀ (a : nat), Eq (∀ (Xy : nat), Ne Xy (pl a Xy)) True % 4.91/5.08 Clause #10 (by clausification #[9]): ∀ (a a_1 : nat), Eq (Ne a (pl a_1 a)) True % 4.91/5.08 Clause #11 (by clausification #[10]): ∀ (a a_1 : nat), Ne a (pl a_1 a) % 4.91/5.08 Clause #12 (by clausification #[1]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (pl a Xy) (pl Xy a)) True % 4.91/5.08 Clause #13 (by clausification #[12]): ∀ (a a_1 : nat), Eq (Eq (pl a a_1) (pl a_1 a)) True % 4.91/5.08 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), Eq (pl a a_1) (pl a_1 a) % 4.91/5.08 Clause #15 (by superposition #[14, 11]): ∀ (a a_1 : nat), Ne a (pl a a_1) % 4.91/5.08 Clause #16 (by clausification #[4]): Eq % 4.91/5.08 (Not % 4.91/5.08 ((Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) → % 4.91/5.08 Not % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))))) % 4.91/5.08 False % 4.91/5.08 Clause #17 (by clausification #[16]): Eq % 4.91/5.08 ((Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) → % 4.91/5.08 Not % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))) % 4.91/5.08 True % 4.91/5.08 Clause #18 (by clausification #[17]): Or (Eq (Eq x y → Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) False) % 4.91/5.08 (Eq % 4.91/5.08 (Not % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))) % 4.91/5.08 True) % 4.91/5.08 Clause #19 (by clausification #[18]): Or % 4.91/5.08 (Eq % 4.91/5.08 (Not % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))) % 4.91/5.08 True) % 4.91/5.08 (Eq (Eq x y) True) % 4.91/5.08 Clause #20 (by clausification #[18]): Or % 4.91/5.08 (Eq % 4.91/5.08 (Not % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)))) % 4.91/5.08 True) % 4.91/5.08 (Eq (Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) False) % 4.91/5.08 Clause #21 (by clausification #[19]): Or (Eq (Eq x y) True) % 4.91/5.08 (Eq % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))) % 4.91/5.08 False) % 4.91/5.08 Clause #22 (by clausification #[21]): Or % 4.91/5.08 (Eq % 4.91/5.08 (Not % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))) % 4.91/5.08 False) % 4.91/5.08 (Eq x y) % 4.91/5.08 Clause #23 (by clausification #[22]): Or (Eq x y) % 4.91/5.08 (Eq % 4.91/5.08 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.08 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) % 4.91/5.08 True) % 4.91/5.08 Clause #24 (by clausification #[23]): Or (Eq x y) % 4.91/5.08 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False) % 4.91/5.08 (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True)) % 4.91/5.08 Clause #25 (by clausification #[24]): Or (Eq x y) % 4.91/5.08 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True) % 4.91/5.08 (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True)) % 4.91/5.08 Clause #26 (by clausification #[24]): Or (Eq x y) % 4.91/5.08 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True) % 4.91/5.10 (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False)) % 4.91/5.10 Clause #27 (by clausification #[25]): Or (Eq x y) % 4.91/5.10 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False)) % 4.91/5.10 Clause #28 (by clausification #[27]): Or (Eq x y) % 4.91/5.10 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False) (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False)) % 4.91/5.10 Clause #30 (by clausification #[28]): Or (Eq x y) (Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False) (Eq (Ne x y) False)) % 4.91/5.10 Clause #42 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), Eq (pl (pl a Xy) Xz) (pl a (pl Xy Xz))) True % 4.91/5.10 Clause #43 (by clausification #[42]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), Eq (pl (pl a a_1) Xz) (pl a (pl a_1 Xz))) True % 4.91/5.10 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : nat), Eq (Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2))) True % 4.91/5.10 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : nat), Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2)) % 4.91/5.10 Clause #46 (by superposition #[45, 11]): ∀ (a a_1 a_2 : nat), Ne a (pl a_1 (pl a_2 a)) % 4.91/5.10 Clause #49 (by superposition #[45, 15]): ∀ (a a_1 a_2 : nat), Ne (pl a a_1) (pl a (pl a_1 a_2)) % 4.91/5.10 Clause #58 (by superposition #[46, 14]): ∀ (a a_1 a_2 : nat), Ne a (pl a_1 (pl a a_2)) % 4.91/5.10 Clause #70 (by superposition #[49, 14]): ∀ (a a_1 a_2 : nat), Ne (pl a a_1) (pl a (pl a_2 a_1)) % 4.91/5.10 Clause #71 (by clausification #[20]): Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)))) False) % 4.91/5.10 (Eq % 4.91/5.10 (Not % 4.91/5.10 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.10 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))) % 4.91/5.10 False) % 4.91/5.10 Clause #72 (by clausification #[71]): Or % 4.91/5.10 (Eq % 4.91/5.10 (Not % 4.91/5.10 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.10 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y))) % 4.91/5.10 False) % 4.91/5.10 (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True) % 4.91/5.10 Clause #73 (by clausification #[72]): Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True) % 4.91/5.10 (Eq % 4.91/5.10 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.10 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) % 4.91/5.10 True) % 4.91/5.10 Clause #74 (by clausification #[73]): Or % 4.91/5.10 (Eq % 4.91/5.10 ((Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) → % 4.91/5.10 Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) % 4.91/5.10 True) % 4.91/5.10 (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False) % 4.91/5.10 Clause #75 (by clausification #[74]): Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False) % 4.91/5.10 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False) % 4.91/5.10 (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True)) % 4.91/5.10 Clause #76 (by clausification #[75]): ∀ (a : nat), % 4.91/5.10 Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) → Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False) % 4.91/5.10 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True) (Eq (Not (Ne x (pl y (skS.0 2 a)))) True)) % 4.91/5.10 Clause #77 (by clausification #[76]): ∀ (a : nat), % 4.91/5.10 Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y)) True) % 4.91/5.10 (Or (Eq (Not (Ne x (pl y (skS.0 2 a)))) True) (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True)) % 4.91/5.10 Clause #79 (by clausification #[77]): ∀ (a : nat), % 4.91/5.10 Or (Eq (Not (Ne x (pl y (skS.0 2 a)))) True) % 4.91/5.10 (Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False)) % 4.91/5.10 Clause #80 (by clausification #[79]): ∀ (a : nat), % 4.91/5.10 Or (Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True) % 4.91/5.10 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False) (Eq (Ne x (pl y (skS.0 2 a))) False)) % 4.91/5.10 Clause #81 (by clausification #[80]): ∀ (a : nat), % 4.91/5.10 Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False) % 4.91/5.10 (Or (Eq (Ne x (pl y (skS.0 2 a))) False) (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False)) % 4.91/5.10 Clause #82 (by clausification #[81]): ∀ (a : nat), % 4.91/5.10 Or (Eq (Ne x (pl y (skS.0 2 a))) False) % 4.96/5.13 (Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True)) % 4.96/5.13 Clause #84 (by clausification #[82]): ∀ (a : nat), % 4.96/5.13 Or (Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False) % 4.96/5.13 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True) (Eq x (pl y (skS.0 2 a)))) % 4.96/5.13 Clause #85 (by clausification #[84]): ∀ (a a_1 : nat), % 4.96/5.13 Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True) % 4.96/5.13 (Or (Eq x (pl y (skS.0 2 a))) (Eq (Not (Ne x (pl y (skS.0 3 a_1)))) True)) % 4.96/5.13 Clause #86 (by clausification #[85]): ∀ (a a_1 : nat), % 4.96/5.13 Or (Eq x (pl y (skS.0 2 a))) % 4.96/5.13 (Or (Eq (Not (Ne x (pl y (skS.0 3 a_1)))) True) (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False)) % 4.96/5.13 Clause #87 (by clausification #[86]): ∀ (a a_1 : nat), % 4.96/5.13 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False) (Eq (Ne x (pl y (skS.0 3 a_1))) False)) % 4.96/5.13 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : nat), % 4.96/5.13 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq (Ne x (pl y (skS.0 3 a_1))) False) (Eq (Not (Ne y (pl x (skS.0 4 a_2)))) True)) % 4.96/5.13 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : nat), % 4.96/5.13 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq (Not (Ne y (pl x (skS.0 4 a_1)))) True) (Eq x (pl y (skS.0 3 a_2)))) % 4.96/5.13 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : nat), % 4.96/5.13 Or (Eq x (pl y (skS.0 2 a))) (Or (Eq x (pl y (skS.0 3 a_1))) (Eq (Ne y (pl x (skS.0 4 a_2))) False)) % 4.96/5.13 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : nat), Or (Eq x (pl y (skS.0 2 a))) (Or (Eq x (pl y (skS.0 3 a_1))) (Eq y (pl x (skS.0 4 a_2)))) % 4.96/5.13 Clause #94 (by superposition #[91, 45]): ∀ (a a_1 a_2 a_3 : nat), % 4.96/5.13 Or (Eq x (pl y (skS.0 3 a))) (Or (Eq y (pl x (skS.0 4 a_1))) (Eq (pl x a_2) (pl y (pl (skS.0 2 a_3) a_2)))) % 4.96/5.13 Clause #146 (by clausification #[26]): Or (Eq x y) % 4.96/5.13 (Or (Eq (Not (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)))) False) % 4.96/5.13 (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False)) % 4.96/5.13 Clause #147 (by clausification #[146]): Or (Eq x y) % 4.96/5.13 (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) → Ne x y) False) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True)) % 4.96/5.13 Clause #148 (by clausification #[147]): Or (Eq x y) (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True) (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True)) % 4.96/5.13 Clause #150 (by clausification #[148]): Or (Eq x y) (Or (Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True) (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False)) % 4.96/5.13 Clause #151 (by clausification #[150]): Or (Eq x y) (Or (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False) (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False)) % 4.96/5.13 Clause #152 (by clausification #[151]): ∀ (a : nat), Or (Eq x y) (Or (Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False) (Eq (Not (Ne y (pl x (skS.0 5 a)))) True)) % 4.96/5.13 Clause #153 (by clausification #[152]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Not (Ne y (pl x (skS.0 5 a)))) True) (Eq (Not (Ne y (pl x (skS.0 6 a_1)))) True)) % 4.96/5.13 Clause #154 (by clausification #[153]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Not (Ne y (pl x (skS.0 6 a)))) True) (Eq (Ne y (pl x (skS.0 5 a_1))) False)) % 4.96/5.13 Clause #155 (by clausification #[154]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Ne y (pl x (skS.0 5 a))) False) (Eq (Ne y (pl x (skS.0 6 a_1))) False)) % 4.96/5.13 Clause #156 (by clausification #[155]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq (Ne y (pl x (skS.0 6 a))) False) (Eq y (pl x (skS.0 5 a_1)))) % 4.96/5.13 Clause #157 (by clausification #[156]): ∀ (a a_1 : nat), Or (Eq x y) (Or (Eq y (pl x (skS.0 5 a))) (Eq y (pl x (skS.0 6 a_1)))) % 4.96/5.13 Clause #200 (by clausification #[30]): ∀ (a : nat), Or (Eq x y) (Or (Eq (Ne x y) False) (Eq (Not (Ne x (pl y (skS.0 7 a)))) True)) % 4.96/5.13 Clause #201 (by clausification #[200]): ∀ (a : nat), Or (Eq x y) (Or (Eq (Not (Ne x (pl y (skS.0 7 a)))) True) (Eq x y)) % 4.96/5.13 Clause #202 (by clausification #[201]): ∀ (a : nat), Or (Eq x y) (Or (Eq x y) (Eq (Ne x (pl y (skS.0 7 a))) False)) % 4.96/5.13 Clause #203 (by clausification #[202]): ∀ (a : nat), Or (Eq x y) (Or (Eq x y) (Eq x (pl y (skS.0 7 a)))) % 4.96/5.13 Clause #204 (by eliminate duplicate literals #[203]): ∀ (a : nat), Or (Eq x y) (Eq x (pl y (skS.0 7 a))) % 4.96/5.13 Clause #209 (by superposition #[204, 58]): ∀ (a : nat), Or (Eq x y) (Ne y (pl a x)) % 4.96/5.14 Clause #217 (by superposition #[209, 14]): ∀ (a : nat), Or (Eq x y) (Ne y (pl x a)) % 4.96/5.14 Clause #219 (by backward contextual literal cutting #[217, 157]): ∀ (a : nat), Or (Eq x y) (Eq y (pl x (skS.0 6 a))) % 4.96/5.14 Clause #1155 (by forward contextual literal cutting #[219, 217]): Eq x y % 4.96/5.14 Clause #1194 (by forward demodulation #[94, 1155]): ∀ (a a_1 a_2 a_3 : nat), % 4.96/5.14 Or (Eq y (pl y (skS.0 3 a))) (Or (Eq y (pl x (skS.0 4 a_1))) (Eq (pl x a_2) (pl y (pl (skS.0 2 a_3) a_2)))) % 4.96/5.14 Clause #1195 (by forward demodulation #[1194, 1155]): ∀ (a a_1 a_2 a_3 : nat), % 4.96/5.14 Or (Eq y (pl y (skS.0 3 a))) (Or (Eq y (pl y (skS.0 4 a_1))) (Eq (pl x a_2) (pl y (pl (skS.0 2 a_3) a_2)))) % 4.96/5.14 Clause #1196 (by forward demodulation #[1195, 1155]): ∀ (a a_1 a_2 a_3 : nat), % 4.96/5.14 Or (Eq y (pl y (skS.0 3 a))) (Or (Eq y (pl y (skS.0 4 a_1))) (Eq (pl y a_2) (pl y (pl (skS.0 2 a_3) a_2)))) % 4.96/5.14 Clause #1197 (by forward contextual literal cutting #[1196, 15]): ∀ (a a_1 a_2 : nat), Or (Eq y (pl y (skS.0 4 a))) (Eq (pl y a_1) (pl y (pl (skS.0 2 a_2) a_1))) % 4.96/5.14 Clause #1198 (by forward contextual literal cutting #[1197, 15]): ∀ (a a_1 : nat), Eq (pl y a) (pl y (pl (skS.0 2 a_1) a)) % 4.96/5.14 Clause #1199 (by forward contextual literal cutting #[1198, 70]): False % 4.96/5.14 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------