%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM688^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 07:57:04 PM UTC 2025 % Result : Theorem 3.53s 3.75s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM688^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n029.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 07:01:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.53/3.75 SZS status Theorem for theBenchmark.p % 3.53/3.75 SZS output start Proof for theBenchmark.p % 3.53/3.75 Clause #0 (by assumption #[]): Eq (more x y) True % 3.53/3.75 Clause #1 (by assumption #[]): Eq (Not (more z u) → Eq z u) True % 3.53/3.75 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : nat), Eq Xx Xy → more Xz Xu → more (pl Xz Xx) (pl Xu Xy)) True % 3.53/3.75 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : nat), more Xx Xy → more Xz Xu → more (pl Xx Xz) (pl Xy Xu)) True % 3.53/3.75 Clause #5 (by assumption #[]): Eq (Not (more (pl x z) (pl y u))) True % 3.53/3.75 Clause #10 (by clausification #[1]): Or (Eq (Not (more z u)) False) (Eq (Eq z u) True) % 3.53/3.75 Clause #11 (by clausification #[10]): Or (Eq (Eq z u) True) (Eq (more z u) True) % 3.53/3.75 Clause #12 (by clausification #[11]): Or (Eq (more z u) True) (Eq z u) % 3.53/3.75 Clause #13 (by clausification #[5]): Eq (more (pl x z) (pl y u)) False % 3.53/3.75 Clause #14 (by clausification #[4]): ∀ (a : nat), Eq (∀ (Xy Xz Xu : nat), more a Xy → more Xz Xu → more (pl a Xz) (pl Xy Xu)) True % 3.53/3.75 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Eq (∀ (Xz Xu : nat), more a a_1 → more Xz Xu → more (pl a Xz) (pl a_1 Xu)) True % 3.53/3.75 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : nat), Eq (∀ (Xu : nat), more a a_1 → more a_2 Xu → more (pl a a_2) (pl a_1 Xu)) True % 3.53/3.75 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : nat), Eq (more a a_1 → more a_2 a_3 → more (pl a a_2) (pl a_1 a_3)) True % 3.53/3.75 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : nat), Or (Eq (more a a_1) False) (Eq (more a_2 a_3 → more (pl a a_2) (pl a_1 a_3)) True) % 3.53/3.75 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : nat), % 3.53/3.75 Or (Eq (more a a_1) False) (Or (Eq (more a_2 a_3) False) (Eq (more (pl a a_2) (pl a_1 a_3)) True)) % 3.53/3.75 Clause #20 (by superposition #[19, 0]): ∀ (a a_1 : nat), Or (Eq (more a a_1) False) (Or (Eq (more (pl x a) (pl y a_1)) True) (Eq False True)) % 3.53/3.75 Clause #22 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz Xu : nat), Eq a Xy → more Xz Xu → more (pl Xz a) (pl Xu Xy)) True % 3.53/3.75 Clause #23 (by clausification #[22]): ∀ (a a_1 : nat), Eq (∀ (Xz Xu : nat), Eq a a_1 → more Xz Xu → more (pl Xz a) (pl Xu a_1)) True % 3.53/3.75 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : nat), Eq (∀ (Xu : nat), Eq a a_1 → more a_2 Xu → more (pl a_2 a) (pl Xu a_1)) True % 3.53/3.75 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : nat), Eq (Eq a a_1 → more a_2 a_3 → more (pl a_2 a) (pl a_3 a_1)) True % 3.53/3.75 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : nat), Or (Eq (Eq a a_1) False) (Eq (more a_2 a_3 → more (pl a_2 a) (pl a_3 a_1)) True) % 3.53/3.75 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : nat), Or (Eq (more a a_1 → more (pl a a_2) (pl a_1 a_3)) True) (Ne a_2 a_3) % 3.53/3.75 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : nat), Or (Ne a a_1) (Or (Eq (more a_2 a_3) False) (Eq (more (pl a_2 a) (pl a_3 a_1)) True)) % 3.53/3.75 Clause #29 (by destructive equality resolution #[28]): ∀ (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) % 3.53/3.75 Clause #30 (by superposition #[29, 0]): ∀ (a : nat), Or (Eq (more (pl x a) (pl y a)) True) (Eq False True) % 3.53/3.75 Clause #32 (by clausification #[30]): ∀ (a : nat), Eq (more (pl x a) (pl y a)) True % 3.53/3.75 Clause #38 (by clausification #[20]): ∀ (a a_1 : nat), Or (Eq (more a a_1) False) (Eq (more (pl x a) (pl y a_1)) True) % 3.53/3.75 Clause #40 (by superposition #[38, 12]): Or (Eq (more (pl x z) (pl y u)) True) (Or (Eq False True) (Eq z u)) % 3.53/3.75 Clause #47 (by clausification #[40]): Or (Eq (more (pl x z) (pl y u)) True) (Eq z u) % 3.53/3.75 Clause #48 (by superposition #[47, 13]): Or (Eq z u) (Eq True False) % 3.53/3.75 Clause #59 (by clausification #[48]): Eq z u % 3.53/3.75 Clause #61 (by backward demodulation #[59, 13]): Eq (more (pl x u) (pl y u)) False % 3.53/3.75 Clause #66 (by superposition #[61, 32]): Eq False True % 3.53/3.75 Clause #67 (by clausification #[66]): False % 3.53/3.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------