%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM681^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 07:57:02 PM UTC 2025 % Result : Theorem 3.73s 3.88s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM681^1 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n016.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 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 07:20:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.73/3.88 SZS status Theorem for theBenchmark.p % 3.73/3.88 SZS output start Proof for theBenchmark.p % 3.73/3.88 Clause #0 (by assumption #[]): Eq (Eq (pl x z) (pl y z)) True % 3.73/3.88 Clause #2 (by assumption #[]): Eq % 3.73/3.88 (∀ (Xx Xy : nat), % 3.73/3.88 Not ((Eq Xx Xy → Not (more Xx Xy)) → Not (Not ((more Xx Xy → Not (less Xx Xy)) → Not (less Xx Xy → Ne Xx Xy))))) % 3.73/3.88 True % 3.73/3.88 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), less Xx Xy → less (pl Xx Xz) (pl Xy Xz)) True % 3.73/3.88 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy : nat), Ne Xx Xy → Not (more Xx Xy) → less Xx Xy) True % 3.73/3.88 Clause #5 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), more Xx Xy → more (pl Xx Xz) (pl Xy Xz)) True % 3.73/3.88 Clause #6 (by assumption #[]): Eq (Not (Eq x y)) True % 3.73/3.88 Clause #11 (by clausification #[6]): Eq (Eq x y) False % 3.73/3.88 Clause #12 (by clausification #[11]): Ne x y % 3.73/3.88 Clause #13 (by clausification #[4]): ∀ (a : nat), Eq (∀ (Xy : nat), Ne a Xy → Not (more a Xy) → less a Xy) True % 3.73/3.88 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), Eq (Ne a a_1 → Not (more a a_1) → less a a_1) True % 3.73/3.88 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Or (Eq (Ne a a_1) False) (Eq (Not (more a a_1) → less a a_1) True) % 3.73/3.88 Clause #16 (by clausification #[15]): ∀ (a a_1 : nat), Or (Eq (Not (more a a_1) → less a a_1) True) (Eq a a_1) % 3.73/3.88 Clause #17 (by clausification #[16]): ∀ (a a_1 : nat), Or (Eq a a_1) (Or (Eq (Not (more a a_1)) False) (Eq (less a a_1) True)) % 3.73/3.88 Clause #18 (by clausification #[17]): ∀ (a a_1 : nat), Or (Eq a a_1) (Or (Eq (less a a_1) True) (Eq (more a a_1) True)) % 3.73/3.88 Clause #20 (by superposition #[18, 12]): ∀ (a : nat), Or (Eq (less a x) True) (Or (Eq (more a x) True) (Ne a y)) % 3.73/3.88 Clause #21 (by clausification #[0]): Eq (pl x z) (pl y z) % 3.73/3.88 Clause #31 (by clausification #[2]): ∀ (a : nat), % 3.73/3.88 Eq % 3.73/3.88 (∀ (Xy : nat), % 3.73/3.88 Not ((Eq a Xy → Not (more a Xy)) → Not (Not ((more a Xy → Not (less a Xy)) → Not (less a Xy → Ne a Xy))))) % 3.73/3.88 True % 3.73/3.88 Clause #32 (by clausification #[31]): ∀ (a a_1 : nat), % 3.73/3.88 Eq (Not ((Eq a a_1 → Not (more a a_1)) → Not (Not ((more a a_1 → Not (less a a_1)) → Not (less a a_1 → Ne a a_1))))) % 3.73/3.88 True % 3.73/3.88 Clause #33 (by clausification #[32]): ∀ (a a_1 : nat), % 3.73/3.88 Eq ((Eq a a_1 → Not (more a a_1)) → Not (Not ((more a a_1 → Not (less a a_1)) → Not (less a a_1 → Ne a a_1)))) False % 3.73/3.88 Clause #34 (by clausification #[33]): ∀ (a a_1 : nat), Eq (Eq a a_1 → Not (more a a_1)) True % 3.73/3.88 Clause #35 (by clausification #[33]): ∀ (a a_1 : nat), Eq (Not (Not ((more a a_1 → Not (less a a_1)) → Not (less a a_1 → Ne a a_1)))) False % 3.73/3.88 Clause #36 (by clausification #[34]): ∀ (a a_1 : nat), Or (Eq (Eq a a_1) False) (Eq (Not (more a a_1)) True) % 3.73/3.88 Clause #37 (by clausification #[36]): ∀ (a a_1 : nat), Or (Eq (Not (more a a_1)) True) (Ne a a_1) % 3.73/3.88 Clause #38 (by clausification #[37]): ∀ (a a_1 : nat), Or (Ne a a_1) (Eq (more a a_1) False) % 3.73/3.88 Clause #39 (by destructive equality resolution #[38]): ∀ (a : nat), Eq (more a a) False % 3.73/3.88 Clause #40 (by clausification #[35]): ∀ (a a_1 : nat), Eq (Not ((more a a_1 → Not (less a a_1)) → Not (less a a_1 → Ne a a_1))) True % 3.73/3.88 Clause #41 (by clausification #[40]): ∀ (a a_1 : nat), Eq ((more a a_1 → Not (less a a_1)) → Not (less a a_1 → Ne a a_1)) False % 3.73/3.88 Clause #43 (by clausification #[41]): ∀ (a a_1 : nat), Eq (Not (less a a_1 → Ne a a_1)) False % 3.73/3.88 Clause #46 (by clausification #[43]): ∀ (a a_1 : nat), Eq (less a a_1 → Ne a a_1) True % 3.73/3.88 Clause #47 (by clausification #[46]): ∀ (a a_1 : nat), Or (Eq (less a a_1) False) (Eq (Ne a a_1) True) % 3.73/3.88 Clause #48 (by clausification #[47]): ∀ (a a_1 : nat), Or (Eq (less a a_1) False) (Ne a a_1) % 3.73/3.88 Clause #49 (by destructive equality resolution #[48]): ∀ (a : nat), Eq (less a a) False % 3.73/3.88 Clause #50 (by destructive equality resolution #[20]): Or (Eq (less y x) True) (Eq (more y x) True) % 3.73/3.88 Clause #55 (by clausification #[5]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), more a Xy → more (pl a Xz) (pl Xy Xz)) True % 3.73/3.88 Clause #56 (by clausification #[55]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), more a a_1 → more (pl a Xz) (pl a_1 Xz)) True % 3.73/3.88 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : nat), Eq (more a a_1 → more (pl a a_2) (pl a_1 a_2)) True % 3.73/3.89 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : nat), Or (Eq (more a a_1) False) (Eq (more (pl a a_2) (pl a_1 a_2)) True) % 3.73/3.89 Clause #59 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), less a Xy → less (pl a Xz) (pl Xy Xz)) True % 3.73/3.89 Clause #60 (by clausification #[59]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), less a a_1 → less (pl a Xz) (pl a_1 Xz)) True % 3.73/3.89 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : nat), Eq (less a a_1 → less (pl a a_2) (pl a_1 a_2)) True % 3.73/3.89 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : nat), Or (Eq (less a a_1) False) (Eq (less (pl a a_2) (pl a_1 a_2)) True) % 3.73/3.89 Clause #64 (by superposition #[62, 50]): ∀ (a : nat), Or (Eq (less (pl y a) (pl x a)) True) (Or (Eq False True) (Eq (more y x) True)) % 3.73/3.89 Clause #81 (by clausification #[64]): ∀ (a : nat), Or (Eq (less (pl y a) (pl x a)) True) (Eq (more y x) True) % 3.73/3.89 Clause #83 (by superposition #[81, 21]): Or (Eq (less (pl y z) (pl y z)) True) (Eq (more y x) True) % 3.73/3.89 Clause #95 (by superposition #[83, 49]): Or (Eq (more y x) True) (Eq True False) % 3.73/3.89 Clause #103 (by clausification #[95]): Eq (more y x) True % 3.73/3.89 Clause #108 (by superposition #[103, 58]): ∀ (a : nat), Or (Eq True False) (Eq (more (pl y a) (pl x a)) True) % 3.73/3.89 Clause #124 (by clausification #[108]): ∀ (a : nat), Eq (more (pl y a) (pl x a)) True % 3.73/3.89 Clause #127 (by superposition #[124, 21]): Eq (more (pl y z) (pl y z)) True % 3.73/3.89 Clause #136 (by superposition #[127, 39]): Eq True False % 3.73/3.89 Clause #145 (by clausification #[136]): False % 3.73/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------