%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM682^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 07:57:03 PM UTC 2025 % Result : Theorem 3.71s 3.87s % Output : Proof 3.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.11 % Problem : NUM682^1 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.13 % Command : duper %s % 0.12/0.34 % Computer : n006.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 07:01:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.71/3.87 SZS status Theorem for theBenchmark.p % 3.71/3.87 SZS output start Proof for theBenchmark.p % 3.71/3.87 Clause #0 (by assumption #[]): Eq (less (pl x z) (pl y z)) True % 3.71/3.87 Clause #2 (by assumption #[]): Eq % 3.71/3.87 (∀ (Xx Xy : nat), % 3.71/3.87 Not ((Eq Xx Xy → Not (more Xx Xy)) → Not (Not ((more Xx Xy → Not (less Xx Xy)) → Not (less Xx Xy → Ne Xx Xy))))) % 3.71/3.87 True % 3.71/3.87 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), more Xx Xy → more (pl Xx Xz) (pl Xy Xz)) True % 3.71/3.87 Clause #5 (by assumption #[]): Eq (∀ (Xx Xy : nat), Ne Xx Xy → Not (more Xx Xy) → less Xx Xy) True % 3.71/3.87 Clause #6 (by assumption #[]): Eq (Not (less x y)) True % 3.71/3.87 Clause #11 (by clausification #[6]): Eq (less x y) False % 3.71/3.87 Clause #12 (by clausification #[5]): ∀ (a : nat), Eq (∀ (Xy : nat), Ne a Xy → Not (more a Xy) → less a Xy) True % 3.71/3.87 Clause #13 (by clausification #[12]): ∀ (a a_1 : nat), Eq (Ne a a_1 → Not (more a a_1) → less a a_1) True % 3.71/3.87 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), Or (Eq (Ne a a_1) False) (Eq (Not (more a a_1) → less a a_1) True) % 3.71/3.87 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Or (Eq (Not (more a a_1) → less a a_1) True) (Eq a a_1) % 3.71/3.87 Clause #16 (by clausification #[15]): ∀ (a a_1 : nat), Or (Eq a a_1) (Or (Eq (Not (more a a_1)) False) (Eq (less a a_1) True)) % 3.71/3.87 Clause #17 (by clausification #[16]): ∀ (a a_1 : nat), Or (Eq a a_1) (Or (Eq (less a a_1) True) (Eq (more a a_1) True)) % 3.71/3.87 Clause #32 (by superposition #[17, 11]): Or (Eq x y) (Or (Eq (more x y) True) (Eq True False)) % 3.71/3.87 Clause #33 (by clausification #[32]): Or (Eq x y) (Eq (more x y) True) % 3.71/3.87 Clause #38 (by clausification #[2]): ∀ (a : nat), % 3.71/3.87 Eq % 3.71/3.87 (∀ (Xy : nat), % 3.71/3.87 Not ((Eq a Xy → Not (more a Xy)) → Not (Not ((more a Xy → Not (less a Xy)) → Not (less a Xy → Ne a Xy))))) % 3.71/3.87 True % 3.71/3.87 Clause #39 (by clausification #[38]): ∀ (a a_1 : nat), % 3.71/3.87 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))))) % 3.71/3.87 True % 3.71/3.87 Clause #40 (by clausification #[39]): ∀ (a a_1 : nat), % 3.71/3.87 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 % 3.71/3.87 Clause #42 (by clausification #[40]): ∀ (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 % 3.71/3.87 Clause #47 (by clausification #[42]): ∀ (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 % 3.71/3.87 Clause #48 (by clausification #[47]): ∀ (a a_1 : nat), Eq ((more a a_1 → Not (less a a_1)) → Not (less a a_1 → Ne a a_1)) False % 3.71/3.87 Clause #49 (by clausification #[48]): ∀ (a a_1 : nat), Eq (more a a_1 → Not (less a a_1)) True % 3.71/3.87 Clause #50 (by clausification #[48]): ∀ (a a_1 : nat), Eq (Not (less a a_1 → Ne a a_1)) False % 3.71/3.87 Clause #51 (by clausification #[49]): ∀ (a a_1 : nat), Or (Eq (more a a_1) False) (Eq (Not (less a a_1)) True) % 3.71/3.87 Clause #52 (by clausification #[51]): ∀ (a a_1 : nat), Or (Eq (more a a_1) False) (Eq (less a a_1) False) % 3.71/3.87 Clause #54 (by clausification #[50]): ∀ (a a_1 : nat), Eq (less a a_1 → Ne a a_1) True % 3.71/3.87 Clause #55 (by clausification #[54]): ∀ (a a_1 : nat), Or (Eq (less a a_1) False) (Eq (Ne a a_1) True) % 3.71/3.87 Clause #56 (by clausification #[55]): ∀ (a a_1 : nat), Or (Eq (less a a_1) False) (Ne a a_1) % 3.71/3.87 Clause #57 (by destructive equality resolution #[56]): ∀ (a : nat), Eq (less a a) False % 3.71/3.87 Clause #65 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), more a Xy → more (pl a Xz) (pl Xy Xz)) True % 3.71/3.87 Clause #66 (by clausification #[65]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), more a a_1 → more (pl a Xz) (pl a_1 Xz)) True % 3.71/3.87 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : nat), Eq (more a a_1 → more (pl a a_2) (pl a_1 a_2)) True % 3.71/3.87 Clause #68 (by clausification #[67]): ∀ (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) % 3.71/3.87 Clause #69 (by superposition #[68, 33]): ∀ (a : nat), Or (Eq (more (pl x a) (pl y a)) True) (Or (Eq x y) (Eq False True)) % 3.71/3.87 Clause #70 (by clausification #[69]): ∀ (a : nat), Or (Eq (more (pl x a) (pl y a)) True) (Eq x y) % 3.71/3.87 Clause #71 (by superposition #[70, 52]): ∀ (a : nat), Or (Eq x y) (Or (Eq True False) (Eq (less (pl x a) (pl y a)) False)) % 3.71/3.87 Clause #81 (by clausification #[71]): ∀ (a : nat), Or (Eq x y) (Eq (less (pl x a) (pl y a)) False) % 3.71/3.87 Clause #82 (by superposition #[81, 0]): Or (Eq x y) (Eq False True) % 3.71/3.87 Clause #92 (by clausification #[82]): Eq x y % 3.71/3.87 Clause #94 (by backward demodulation #[92, 0]): Eq (less (pl y z) (pl y z)) True % 3.71/3.87 Clause #107 (by superposition #[94, 57]): Eq True False % 3.71/3.87 Clause #114 (by clausification #[107]): False % 3.71/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------