%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM689^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 3.83s 3.98s % Output : Proof 3.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : NUM689^1 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.14 % Command : duper %s % 0.14/0.36 % Computer : n001.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 08:34:38 EDT 2025 % 0.14/0.36 % CPUTime : % 3.83/3.98 SZS status Theorem for theBenchmark.p % 3.83/3.98 SZS output start Proof for theBenchmark.p % 3.83/3.98 Clause #0 (by assumption #[]): Eq (lessis x y) True % 3.83/3.98 Clause #1 (by assumption #[]): Eq (some fun Xv => diffprop u z Xv) True % 3.83/3.98 Clause #2 (by assumption #[]): Eq % 3.83/3.98 (∀ (Xx Xy Xz Xu : nat), % 3.83/3.98 moreis Xx Xy → (some fun Xu_0 => diffprop Xz Xu Xu_0) → some fun Xu_0 => diffprop (pl Xx Xz) (pl Xy Xu) Xu_0) % 3.83/3.98 True % 3.83/3.98 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy : nat), lessis Xx Xy → moreis Xy Xx) True % 3.83/3.98 Clause #4 (by assumption #[]): Eq (Not (some fun Xv => diffprop (pl y u) (pl x z) Xv)) True % 3.83/3.98 Clause #5 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy : nat), lessis a Xy → moreis Xy a) True % 3.83/3.98 Clause #6 (by clausification #[5]): ∀ (a a_1 : nat), Eq (lessis a a_1 → moreis a_1 a) True % 3.83/3.98 Clause #7 (by clausification #[6]): ∀ (a a_1 : nat), Or (Eq (lessis a a_1) False) (Eq (moreis a_1 a) True) % 3.83/3.98 Clause #8 (by superposition #[7, 0]): Or (Eq (moreis y x) True) (Eq False True) % 3.83/3.98 Clause #9 (by clausification #[8]): Eq (moreis y x) True % 3.83/3.98 Clause #10 (by betaEtaReduce #[1]): Eq (some (diffprop u z)) True % 3.83/3.98 Clause #11 (by betaEtaReduce #[4]): Eq (Not (some (diffprop (pl y u) (pl x z)))) True % 3.83/3.98 Clause #12 (by clausification #[11]): Eq (some (diffprop (pl y u) (pl x z))) False % 3.83/3.98 Clause #13 (by betaEtaReduce #[2]): Eq (∀ (Xx Xy Xz Xu : nat), moreis Xx Xy → some (diffprop Xz Xu) → some (diffprop (pl Xx Xz) (pl Xy Xu))) True % 3.83/3.98 Clause #14 (by clausification #[13]): ∀ (a : nat), Eq (∀ (Xy Xz Xu : nat), moreis a Xy → some (diffprop Xz Xu) → some (diffprop (pl a Xz) (pl Xy Xu))) True % 3.83/3.98 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Eq (∀ (Xz Xu : nat), moreis a a_1 → some (diffprop Xz Xu) → some (diffprop (pl a Xz) (pl a_1 Xu))) True % 3.83/3.98 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : nat), % 3.83/3.98 Eq (∀ (Xu : nat), moreis a a_1 → some (diffprop a_2 Xu) → some (diffprop (pl a a_2) (pl a_1 Xu))) True % 3.83/3.98 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : nat), Eq (moreis a a_1 → some (diffprop a_2 a_3) → some (diffprop (pl a a_2) (pl a_1 a_3))) True % 3.83/3.98 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : nat), % 3.83/3.98 Or (Eq (moreis a a_1) False) (Eq (some (diffprop a_2 a_3) → some (diffprop (pl a a_2) (pl a_1 a_3))) True) % 3.83/3.98 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : nat), % 3.83/3.98 Or (Eq (moreis a a_1) False) % 3.83/3.98 (Or (Eq (some (diffprop a_2 a_3)) False) (Eq (some (diffprop (pl a a_2) (pl a_1 a_3))) True)) % 3.83/3.98 Clause #20 (by superposition #[19, 9]): ∀ (a a_1 : nat), % 3.83/3.98 Or (Eq (some (diffprop a a_1)) False) (Or (Eq (some (diffprop (pl y a) (pl x a_1))) True) (Eq False True)) % 3.83/3.98 Clause #21 (by clausification #[20]): ∀ (a a_1 : nat), Or (Eq (some (diffprop a a_1)) False) (Eq (some (diffprop (pl y a) (pl x a_1))) True) % 3.83/3.98 Clause #22 (by superposition #[21, 10]): Or (Eq (some (diffprop (pl y u) (pl x z))) True) (Eq False True) % 3.83/3.98 Clause #23 (by clausification #[22]): Eq (some (diffprop (pl y u) (pl x z))) True % 3.83/3.98 Clause #24 (by superposition #[23, 12]): Eq True False % 3.83/3.98 Clause #26 (by clausification #[24]): False % 3.83/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------