%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM748^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 07:57:13 PM UTC 2025 % Result : Theorem 3.52s 3.70s % Output : Proof 3.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : NUM748^1 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n009.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 07:06:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.52/3.70 SZS status Theorem for theBenchmark.p % 3.52/3.70 SZS output start Proof for theBenchmark.p % 3.52/3.70 Clause #0 (by assumption #[]): Eq (∀ (Xx : frac), eq Xx Xx) True % 3.52/3.70 Clause #1 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (ts Xx Xy) (ts Xy Xx)) True % 3.52/3.70 Clause #2 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (pl Xx Xy) (pl Xy Xx)) True % 3.52/3.70 Clause #3 (by assumption #[]): Eq % 3.52/3.70 (Not % 3.52/3.70 (eq (fr (pl (ts (num x) (den y)) (ts (num y) (den x))) (ts (den x) (den y))) % 3.52/3.70 (fr (pl (ts (num y) (den x)) (ts (num x) (den y))) (ts (den y) (den x))))) % 3.52/3.70 True % 3.52/3.70 Clause #4 (by clausification #[0]): ∀ (a : frac), Eq (eq a a) True % 3.52/3.70 Clause #5 (by clausification #[1]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (ts a Xy) (ts Xy a)) True % 3.52/3.70 Clause #6 (by clausification #[5]): ∀ (a a_1 : nat), Eq (Eq (ts a a_1) (ts a_1 a)) True % 3.52/3.70 Clause #7 (by clausification #[6]): ∀ (a a_1 : nat), Eq (ts a a_1) (ts a_1 a) % 3.52/3.70 Clause #8 (by clausification #[2]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (pl a Xy) (pl Xy a)) True % 3.52/3.70 Clause #9 (by clausification #[8]): ∀ (a a_1 : nat), Eq (Eq (pl a a_1) (pl a_1 a)) True % 3.52/3.70 Clause #10 (by clausification #[9]): ∀ (a a_1 : nat), Eq (pl a a_1) (pl a_1 a) % 3.52/3.70 Clause #11 (by clausification #[3]): Eq % 3.52/3.70 (eq (fr (pl (ts (num x) (den y)) (ts (num y) (den x))) (ts (den x) (den y))) % 3.52/3.70 (fr (pl (ts (num y) (den x)) (ts (num x) (den y))) (ts (den y) (den x)))) % 3.52/3.70 False % 3.52/3.70 Clause #12 (by forward demodulation #[11, 7]): Eq % 3.52/3.70 (eq (fr (pl (ts (num x) (den y)) (ts (num y) (den x))) (ts (den x) (den y))) % 3.52/3.70 (fr (pl (ts (num y) (den x)) (ts (den y) (num x))) (ts (den y) (den x)))) % 3.52/3.70 False % 3.52/3.70 Clause #13 (by forward demodulation #[12, 10]): Eq % 3.52/3.70 (eq (fr (pl (ts (num x) (den y)) (ts (num y) (den x))) (ts (den x) (den y))) % 3.52/3.70 (fr (pl (ts (den y) (num x)) (ts (num y) (den x))) (ts (den y) (den x)))) % 3.52/3.70 False % 3.52/3.70 Clause #14 (by forward demodulation #[13, 7]): Eq % 3.52/3.70 (eq (fr (pl (ts (num x) (den y)) (ts (num y) (den x))) (ts (den x) (den y))) % 3.52/3.70 (fr (pl (ts (den y) (num x)) (ts (den x) (num y))) (ts (den y) (den x)))) % 3.52/3.70 False % 3.52/3.70 Clause #15 (by forward demodulation #[14, 7]): Eq % 3.52/3.70 (eq (fr (pl (ts (num x) (den y)) (ts (num y) (den x))) (ts (den y) (den x))) % 3.52/3.71 (fr (pl (ts (den y) (num x)) (ts (den x) (num y))) (ts (den y) (den x)))) % 3.52/3.71 False % 3.52/3.71 Clause #16 (by forward demodulation #[15, 10]): Eq % 3.52/3.71 (eq (fr (pl (ts (num y) (den x)) (ts (num x) (den y))) (ts (den y) (den x))) % 3.52/3.71 (fr (pl (ts (den y) (num x)) (ts (den x) (num y))) (ts (den y) (den x)))) % 3.52/3.71 False % 3.52/3.71 Clause #17 (by forward demodulation #[16, 7]): Eq % 3.52/3.71 (eq (fr (pl (ts (num y) (den x)) (ts (den y) (num x))) (ts (den y) (den x))) % 3.52/3.71 (fr (pl (ts (den y) (num x)) (ts (den x) (num y))) (ts (den y) (den x)))) % 3.52/3.71 False % 3.52/3.71 Clause #18 (by forward demodulation #[17, 10]): Eq % 3.52/3.71 (eq (fr (pl (ts (den y) (num x)) (ts (num y) (den x))) (ts (den y) (den x))) % 3.52/3.71 (fr (pl (ts (den y) (num x)) (ts (den x) (num y))) (ts (den y) (den x)))) % 3.52/3.71 False % 3.52/3.71 Clause #19 (by forward demodulation #[18, 7]): Eq % 3.52/3.71 (eq (fr (pl (ts (den y) (num x)) (ts (den x) (num y))) (ts (den y) (den x))) % 3.52/3.71 (fr (pl (ts (den y) (num x)) (ts (den x) (num y))) (ts (den y) (den x)))) % 3.52/3.71 False % 3.52/3.71 Clause #20 (by superposition #[19, 4]): Eq False True % 3.52/3.71 Clause #21 (by clausification #[20]): False % 3.52/3.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------