%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM691^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 07:57:05 PM UTC 2025 % Result : Theorem 5.89s 6.06s % Output : Proof 5.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM691^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 08:24:23 EDT 2025 % 0.13/0.34 % CPUTime : % 5.89/6.06 SZS status Theorem for theBenchmark.p % 5.89/6.06 SZS output start Proof for theBenchmark.p % 5.89/6.06 Clause #0 (by assumption #[]): Eq (Not (more x y) → Eq x y) True % 5.89/6.06 Clause #1 (by assumption #[]): Eq (Not (more z u) → Eq z u) True % 5.89/6.06 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : nat), (Not (more Xx Xy) → Eq Xx Xy) → more Xz Xu → more (pl Xx Xz) (pl Xy Xu)) True % 5.89/6.06 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : nat), more Xx Xy → (Not (more Xz Xu) → Eq Xz Xu) → more (pl Xx Xz) (pl Xy Xu)) True % 5.89/6.06 Clause #5 (by assumption #[]): Eq (Not (Not (more (pl x z) (pl y u)) → Eq (pl x z) (pl y u))) True % 5.89/6.06 Clause #10 (by clausification #[1]): Or (Eq (Not (more z u)) False) (Eq (Eq z u) True) % 5.89/6.06 Clause #11 (by clausification #[10]): Or (Eq (Eq z u) True) (Eq (more z u) True) % 5.89/6.06 Clause #12 (by clausification #[11]): Or (Eq (more z u) True) (Eq z u) % 5.89/6.06 Clause #13 (by clausification #[0]): Or (Eq (Not (more x y)) False) (Eq (Eq x y) True) % 5.89/6.06 Clause #14 (by clausification #[13]): Or (Eq (Eq x y) True) (Eq (more x y) True) % 5.89/6.06 Clause #15 (by clausification #[14]): Or (Eq (more x y) True) (Eq x y) % 5.89/6.06 Clause #16 (by clausification #[5]): Eq (Not (more (pl x z) (pl y u)) → Eq (pl x z) (pl y u)) False % 5.89/6.06 Clause #17 (by clausification #[16]): Eq (Not (more (pl x z) (pl y u))) True % 5.89/6.06 Clause #18 (by clausification #[16]): Eq (Eq (pl x z) (pl y u)) False % 5.89/6.06 Clause #19 (by clausification #[17]): Eq (more (pl x z) (pl y u)) False % 5.89/6.06 Clause #20 (by clausification #[18]): Ne (pl x z) (pl y u) % 5.89/6.06 Clause #21 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz Xu : nat), (Not (more a Xy) → Eq a Xy) → more Xz Xu → more (pl a Xz) (pl Xy Xu)) True % 5.89/6.06 Clause #22 (by clausification #[21]): ∀ (a a_1 : nat), Eq (∀ (Xz Xu : nat), (Not (more a a_1) → Eq a a_1) → more Xz Xu → more (pl a Xz) (pl a_1 Xu)) True % 5.89/6.06 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : nat), Eq (∀ (Xu : nat), (Not (more a a_1) → Eq a a_1) → more a_2 Xu → more (pl a a_2) (pl a_1 Xu)) True % 5.89/6.06 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : nat), Eq ((Not (more a a_1) → Eq a a_1) → more a_2 a_3 → more (pl a a_2) (pl a_1 a_3)) True % 5.89/6.06 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : nat), % 5.89/6.06 Or (Eq (Not (more a a_1) → Eq a a_1) False) (Eq (more a_2 a_3 → more (pl a a_2) (pl a_1 a_3)) True) % 5.89/6.06 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : nat), Or (Eq (more a a_1 → more (pl a_2 a) (pl a_3 a_1)) True) (Eq (Not (more a_2 a_3)) True) % 5.89/6.06 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : nat), Or (Eq (more a a_1 → more (pl a_2 a) (pl a_3 a_1)) True) (Eq (Eq a_2 a_3) False) % 5.89/6.06 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : nat), % 5.89/6.06 Or (Eq (Not (more a a_1)) True) (Or (Eq (more a_2 a_3) False) (Eq (more (pl a a_2) (pl a_1 a_3)) True)) % 5.89/6.06 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : nat), % 5.89/6.06 Or (Eq (more a a_1) False) (Or (Eq (more (pl a_2 a) (pl a_3 a_1)) True) (Eq (more a_2 a_3) False)) % 5.89/6.06 Clause #30 (by superposition #[29, 12]): ∀ (a a_1 : nat), Or (Eq (more (pl a z) (pl a_1 u)) True) (Or (Eq (more a a_1) False) (Or (Eq False True) (Eq z u))) % 5.89/6.06 Clause #32 (by clausification #[4]): ∀ (a : nat), Eq (∀ (Xy Xz Xu : nat), more a Xy → (Not (more Xz Xu) → Eq Xz Xu) → more (pl a Xz) (pl Xy Xu)) True % 5.89/6.06 Clause #33 (by clausification #[32]): ∀ (a a_1 : nat), Eq (∀ (Xz Xu : nat), more a a_1 → (Not (more Xz Xu) → Eq Xz Xu) → more (pl a Xz) (pl a_1 Xu)) True % 5.89/6.06 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : nat), Eq (∀ (Xu : nat), more a a_1 → (Not (more a_2 Xu) → Eq a_2 Xu) → more (pl a a_2) (pl a_1 Xu)) True % 5.89/6.06 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : nat), Eq (more a a_1 → (Not (more a_2 a_3) → Eq a_2 a_3) → more (pl a a_2) (pl a_1 a_3)) True % 5.89/6.06 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : nat), % 5.89/6.06 Or (Eq (more a a_1) False) (Eq ((Not (more a_2 a_3) → Eq a_2 a_3) → more (pl a a_2) (pl a_1 a_3)) True) % 5.89/6.06 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : nat), % 5.89/6.06 Or (Eq (more a a_1) False) (Or (Eq (Not (more a_2 a_3) → Eq a_2 a_3) False) (Eq (more (pl a a_2) (pl a_1 a_3)) True)) % 5.89/6.06 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : nat), % 5.89/6.09 Or (Eq (more a a_1) False) (Or (Eq (more (pl a a_2) (pl a_1 a_3)) True) (Eq (Eq a_2 a_3) False)) % 5.89/6.09 Clause #43 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : nat), % 5.89/6.09 Or (Eq (Eq a a_1) False) (Or (Eq (more a_2 a_3) False) (Eq (more (pl a a_2) (pl a_1 a_3)) True)) % 5.89/6.09 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : nat), Or (Eq (more a a_1) False) (Or (Eq (more (pl a_2 a) (pl a_3 a_1)) True) (Ne a_2 a_3)) % 5.89/6.09 Clause #45 (by destructive equality resolution #[44]): ∀ (a a_1 a_2 : nat), Or (Eq (more a a_1) False) (Eq (more (pl a_2 a) (pl a_2 a_1)) True) % 5.89/6.09 Clause #46 (by superposition #[45, 12]): ∀ (a : nat), Or (Eq (more (pl a z) (pl a u)) True) (Or (Eq False True) (Eq z u)) % 5.89/6.09 Clause #52 (by clausification #[46]): ∀ (a : nat), Or (Eq (more (pl a z) (pl a u)) True) (Eq z u) % 5.89/6.09 Clause #61 (by clausification #[30]): ∀ (a a_1 : nat), Or (Eq (more (pl a z) (pl a_1 u)) True) (Or (Eq (more a a_1) False) (Eq z u)) % 5.89/6.09 Clause #63 (by superposition #[61, 15]): Or (Eq (more (pl x z) (pl y u)) True) (Or (Eq z u) (Or (Eq False True) (Eq x y))) % 5.89/6.09 Clause #66 (by clausification #[63]): Or (Eq (more (pl x z) (pl y u)) True) (Or (Eq z u) (Eq x y)) % 5.89/6.09 Clause #67 (by superposition #[66, 19]): Or (Eq z u) (Or (Eq x y) (Eq True False)) % 5.89/6.09 Clause #73 (by clausification #[67]): Or (Eq z u) (Eq x y) % 5.89/6.09 Clause #74 (by superposition #[73, 19]): Or (Eq z u) (Eq (more (pl y z) (pl y u)) False) % 5.89/6.09 Clause #76 (by superposition #[74, 52]): Or (Eq z u) (Or (Eq False True) (Eq z u)) % 5.89/6.09 Clause #77 (by clausification #[76]): Or (Eq z u) (Eq z u) % 5.89/6.09 Clause #78 (by eliminate duplicate literals #[77]): Eq z u % 5.89/6.09 Clause #80 (by backward demodulation #[78, 19]): Eq (more (pl x u) (pl y u)) False % 5.89/6.09 Clause #81 (by backward demodulation #[78, 20]): Ne (pl x u) (pl y u) % 5.89/6.09 Clause #87 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : nat), Or (Eq (more a a_1) False) (Or (Eq (more (pl a a_2) (pl a_1 a_3)) True) (Ne a_2 a_3)) % 5.89/6.09 Clause #88 (by destructive equality resolution #[87]): ∀ (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) % 5.89/6.09 Clause #89 (by superposition #[88, 15]): ∀ (a : nat), Or (Eq (more (pl x a) (pl y a)) True) (Or (Eq False True) (Eq x y)) % 5.89/6.09 Clause #96 (by clausification #[89]): ∀ (a : nat), Or (Eq (more (pl x a) (pl y a)) True) (Eq x y) % 5.89/6.09 Clause #97 (by superposition #[96, 80]): Or (Eq x y) (Eq True False) % 5.89/6.09 Clause #103 (by clausification #[97]): Eq x y % 5.89/6.09 Clause #110 (by backward positive simplify reflect #[103, 81]): False % 5.89/6.09 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------