%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM656^1 : 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 07:56:57 PM UTC 2025 % Result : Theorem 3.50s 3.68s % Output : Proof 3.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUM656^1 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.13 % 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 07:11:08 EDT 2025 % 0.14/0.34 % CPUTime : % 3.50/3.68 SZS status Theorem for theBenchmark.p % 3.50/3.68 SZS output start Proof for theBenchmark.p % 3.50/3.68 Clause #0 (by assumption #[]): Eq (more x y) True % 3.50/3.68 Clause #2 (by assumption #[]): Eq % 3.50/3.68 (∀ (Xx Xy : nat), % 3.50/3.68 Not ((Eq Xx Xy → Not (more Xx Xy)) → Not (Not ((more Xx Xy → Not (less Xx Xy)) → Not (less Xx Xy → Ne Xx Xy))))) % 3.50/3.68 True % 3.50/3.68 Clause #3 (by assumption #[]): Eq (Not (Not (Not (less x y) → Eq x y))) True % 3.50/3.68 Clause #8 (by clausification #[3]): Eq (Not (Not (less x y) → Eq x y)) False % 3.50/3.68 Clause #9 (by clausification #[8]): Eq (Not (less x y) → Eq x y) True % 3.50/3.68 Clause #10 (by clausification #[9]): Or (Eq (Not (less x y)) False) (Eq (Eq x y) True) % 3.50/3.68 Clause #11 (by clausification #[10]): Or (Eq (Eq x y) True) (Eq (less x y) True) % 3.50/3.68 Clause #12 (by clausification #[11]): Or (Eq (less x y) True) (Eq x y) % 3.50/3.68 Clause #13 (by clausification #[2]): ∀ (a : nat), % 3.50/3.68 Eq % 3.50/3.68 (∀ (Xy : nat), % 3.50/3.68 Not ((Eq a Xy → Not (more a Xy)) → Not (Not ((more a Xy → Not (less a Xy)) → Not (less a Xy → Ne a Xy))))) % 3.50/3.68 True % 3.50/3.68 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), % 3.50/3.68 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))))) % 3.50/3.68 True % 3.50/3.68 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), % 3.50/3.68 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 % 3.50/3.68 Clause #16 (by clausification #[15]): ∀ (a a_1 : nat), Eq (Eq a a_1 → Not (more a a_1)) True % 3.50/3.68 Clause #17 (by clausification #[15]): ∀ (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 % 3.50/3.68 Clause #18 (by clausification #[16]): ∀ (a a_1 : nat), Or (Eq (Eq a a_1) False) (Eq (Not (more a a_1)) True) % 3.50/3.68 Clause #19 (by clausification #[18]): ∀ (a a_1 : nat), Or (Eq (Not (more a a_1)) True) (Ne a a_1) % 3.50/3.68 Clause #20 (by clausification #[19]): ∀ (a a_1 : nat), Or (Ne a a_1) (Eq (more a a_1) False) % 3.50/3.68 Clause #21 (by destructive equality resolution #[20]): ∀ (a : nat), Eq (more a a) False % 3.50/3.68 Clause #22 (by clausification #[17]): ∀ (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 % 3.50/3.68 Clause #23 (by clausification #[22]): ∀ (a a_1 : nat), Eq ((more a a_1 → Not (less a a_1)) → Not (less a a_1 → Ne a a_1)) False % 3.50/3.68 Clause #24 (by clausification #[23]): ∀ (a a_1 : nat), Eq (more a a_1 → Not (less a a_1)) True % 3.50/3.68 Clause #26 (by clausification #[24]): ∀ (a a_1 : nat), Or (Eq (more a a_1) False) (Eq (Not (less a a_1)) True) % 3.50/3.68 Clause #27 (by clausification #[26]): ∀ (a a_1 : nat), Or (Eq (more a a_1) False) (Eq (less a a_1) False) % 3.50/3.68 Clause #28 (by superposition #[27, 0]): Or (Eq (less x y) False) (Eq False True) % 3.50/3.68 Clause #33 (by clausification #[28]): Eq (less x y) False % 3.50/3.68 Clause #34 (by superposition #[33, 12]): Or (Eq False True) (Eq x y) % 3.50/3.68 Clause #35 (by clausification #[34]): Eq x y % 3.50/3.68 Clause #36 (by backward demodulation #[35, 0]): Eq (more y y) True % 3.50/3.68 Clause #39 (by superposition #[36, 21]): Eq True False % 3.50/3.68 Clause #41 (by clausification #[39]): False % 3.50/3.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------