%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 : Tue May 5 06:59:10 PM UTC 2026 % Result : Theorem 4.75s 4.90s % Output : Proof 4.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : duper %s % 0.17/0.34 % Computer : n005.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue May 5 11:28:30 EDT 2026 % 0.17/0.35 % CPUTime : % 4.75/4.90 SZS status Theorem for theBenchmark.p % 4.75/4.90 SZS output start Proof for theBenchmark.p % 4.75/4.90 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), Eq (proj1S (s X)) X) True % 4.75/4.90 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Ne z (s X)) True % 4.75/4.90 Clause #2 (by assumption #[]): Eq (∀ (Y : Iota), Eq (x2 z Y) Y) True % 4.75/4.90 Clause #3 (by assumption #[]): Eq (∀ (Y N : Iota), Eq (x2 (s N) Y) (s (x2 N Y))) True % 4.75/4.90 Clause #4 (by assumption #[]): Eq (∀ (Y : Iota), Eq (x22 z Y) z) True % 4.75/4.90 Clause #5 (by assumption #[]): Eq (∀ (Y N : Iota), Eq (x22 (s N) Y) (x2 Y (x22 N Y))) True % 4.75/4.90 Clause #6 (by assumption #[]): Eq (Not (Exists fun X => Ne (x22 X X) X)) True % 4.75/4.90 Clause #7 (by clausification #[1]): ∀ (a : Iota), Eq (Ne z (s a)) True % 4.75/4.90 Clause #8 (by clausification #[7]): ∀ (a : Iota), Ne z (s a) % 4.75/4.90 Clause #9 (by clausification #[0]): ∀ (a : Iota), Eq (Eq (proj1S (s a)) a) True % 4.75/4.90 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (proj1S (s a)) a % 4.75/4.90 Clause #11 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (x2 z a) a) True % 4.75/4.90 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (x2 z a) a % 4.75/4.90 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (x22 z a) z) True % 4.75/4.90 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (x22 z a) z % 4.75/4.90 Clause #15 (by clausification #[6]): Eq (Exists fun X => Ne (x22 X X) X) False % 4.75/4.90 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (Ne (x22 a a) a) False % 4.75/4.90 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (x22 a a) a % 4.75/4.90 Clause #18 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (N : Iota), Eq (x2 (s N) a) (s (x2 N a))) True % 4.75/4.90 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Eq (x2 (s a) a_1) (s (x2 a a_1))) True % 4.75/4.90 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (x2 (s a) a_1) (s (x2 a a_1)) % 4.75/4.90 Clause #22 (by superposition #[20, 10]): ∀ (a a_1 : Iota), Eq (proj1S (x2 (s a) a_1)) (x2 a a_1) % 4.75/4.90 Clause #23 (by superposition #[20, 12]): ∀ (a : Iota), Eq (x2 (s z) a) (s a) % 4.75/4.90 Clause #25 (by superposition #[23, 20]): ∀ (a : Iota), Eq (x2 (s (s z)) a) (s (s a)) % 4.75/4.90 Clause #30 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (N : Iota), Eq (x22 (s N) a) (x2 a (x22 N a))) True % 4.75/4.90 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Eq (x22 (s a) a_1) (x2 a_1 (x22 a a_1))) True % 4.75/4.90 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (x22 (s a) a_1) (x2 a_1 (x22 a a_1)) % 4.75/4.90 Clause #38 (by superposition #[32, 22]): ∀ (a a_1 : Iota), Eq (proj1S (x22 (s a) (s a_1))) (x2 a_1 (x22 a (s a_1))) % 4.75/4.90 Clause #53 (by superposition #[25, 32]): ∀ (a : Iota), Eq (x22 (s a) (s (s z))) (s (s (x22 a (s (s z))))) % 4.75/4.90 Clause #108 (by superposition #[38, 23]): ∀ (a : Iota), Eq (proj1S (x22 (s a) (s (s z)))) (s (x22 a (s (s z)))) % 4.75/4.90 Clause #245 (by superposition #[53, 14]): Eq (x22 (s z) (s (s z))) (s (s z)) % 4.75/4.90 Clause #809 (by superposition #[108, 17]): Eq (proj1S (s (s z))) (s (x22 (s z) (s (s z)))) % 4.75/4.90 Clause #814 (by forward demodulation #[809, 10]): Eq (s z) (s (x22 (s z) (s (s z)))) % 4.75/4.90 Clause #815 (by forward demodulation #[814, 245]): Eq (s z) (s (s (s z))) % 4.75/4.90 Clause #822 (by superposition #[815, 10]): Eq (proj1S (s z)) (s (s z)) % 4.75/4.90 Clause #956 (by forward demodulation #[822, 10]): Eq z (s (s z)) % 4.75/4.90 Clause #957 (by forward contextual literal cutting #[956, 8]): False % 4.75/4.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------