%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO038^1.003.003 : TPTP v9.2.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:08:27 PM UTC 2025 % Result : Theorem 5.45s 5.68s % Output : Proof 5.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.14 % Problem : SYO038^1.003.003 : TPTP v9.2.0. Released v5.3.0. % 0.13/0.15 % Command : duper %s % 0.15/0.37 % Computer : n010.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Fri Oct 3 13:19:53 EDT 2025 % 0.15/0.37 % CPUTime : % 5.45/5.68 SZS status Theorem for theBenchmark.p % 5.45/5.68 SZS output start Proof for theBenchmark.p % 5.45/5.68 Clause #0 (by assumption #[]): Eq (∀ (N : Iota), Eq (f N one) (s one)) True % 5.45/5.68 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Eq (f one (s X)) (s (s (f one X)))) True % 5.45/5.68 Clause #2 (by assumption #[]): Eq (∀ (N X : Iota), Eq (f (s N) (s X)) (f N (f (s N) X))) True % 5.45/5.68 Clause #3 (by assumption #[]): Eq (d one) True % 5.45/5.68 Clause #4 (by assumption #[]): Eq (∀ (X : Iota), d X → d (s X)) True % 5.45/5.68 Clause #5 (by assumption #[]): Eq (Not (d (f (s (s one)) (s (s one))))) True % 5.45/5.68 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (d a → d (s a)) True % 5.45/5.68 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (d a) False) (Eq (d (s a)) True) % 5.45/5.68 Clause #8 (by superposition #[7, 3]): Or (Eq (d (s one)) True) (Eq False True) % 5.45/5.68 Clause #9 (by clausification #[8]): Eq (d (s one)) True % 5.45/5.68 Clause #10 (by superposition #[9, 7]): Or (Eq True False) (Eq (d (s (s one))) True) % 5.45/5.68 Clause #11 (by clausification #[10]): Eq (d (s (s one))) True % 5.45/5.68 Clause #12 (by superposition #[11, 7]): Or (Eq True False) (Eq (d (s (s (s one)))) True) % 5.45/5.68 Clause #13 (by clausification #[12]): Eq (d (s (s (s one)))) True % 5.45/5.68 Clause #14 (by superposition #[13, 7]): Or (Eq True False) (Eq (d (s (s (s (s one))))) True) % 5.45/5.68 Clause #15 (by clausification #[0]): ∀ (a : Iota), Eq (Eq (f a one) (s one)) True % 5.45/5.68 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (f a one) (s one) % 5.45/5.68 Clause #17 (by clausification #[14]): Eq (d (s (s (s (s one))))) True % 5.45/5.68 Clause #18 (by superposition #[17, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s one)))))) True) % 5.45/5.68 Clause #19 (by clausification #[5]): Eq (d (f (s (s one)) (s (s one)))) False % 5.45/5.68 Clause #20 (by clausification #[18]): Eq (d (s (s (s (s (s one)))))) True % 5.45/5.68 Clause #21 (by superposition #[20, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s (s one))))))) True) % 5.45/5.68 Clause #22 (by clausification #[21]): Eq (d (s (s (s (s (s (s one))))))) True % 5.45/5.68 Clause #23 (by superposition #[22, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s (s (s one)))))))) True) % 5.45/5.68 Clause #24 (by clausification #[23]): Eq (d (s (s (s (s (s (s (s one)))))))) True % 5.45/5.68 Clause #25 (by superposition #[24, 7]): Or (Eq True False) (Eq (d (s (s (s (s (s (s (s (s one))))))))) True) % 5.45/5.68 Clause #26 (by clausification #[1]): ∀ (a : Iota), Eq (Eq (f one (s a)) (s (s (f one a)))) True % 5.45/5.68 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (f one (s a)) (s (s (f one a))) % 5.45/5.68 Clause #28 (by superposition #[27, 16]): Eq (f one (s one)) (s (s (s one))) % 5.45/5.68 Clause #38 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (X : Iota), Eq (f (s a) (s X)) (f a (f (s a) X))) True % 5.45/5.68 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (f (s a) (s a_1)) (f a (f (s a) a_1))) True % 5.45/5.68 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (f (s a) (s a_1)) (f a (f (s a) a_1)) % 5.45/5.68 Clause #43 (by superposition #[40, 16]): ∀ (a : Iota), Eq (f (s a) (s one)) (f a (s one)) % 5.45/5.68 Clause #46 (by superposition #[43, 40]): ∀ (a : Iota), Eq (f (s a) (s (s one))) (f a (f a (s one))) % 5.45/5.68 Clause #55 (by clausification #[25]): Eq (d (s (s (s (s (s (s (s (s one))))))))) True % 5.45/5.68 Clause #56 (by forward demodulation #[55, 28]): Eq (d (s (s (s (s (s (f one (s one)))))))) True % 5.45/5.68 Clause #57 (by forward demodulation #[56, 27]): Eq (d (s (s (s (f one (s (s one))))))) True % 5.45/5.68 Clause #58 (by forward demodulation #[57, 27]): Eq (d (s (f one (s (s (s one)))))) True % 5.45/5.68 Clause #59 (by forward demodulation #[58, 28]): Eq (d (s (f one (f one (s one))))) True % 5.45/5.68 Clause #60 (by superposition #[59, 7]): Or (Eq True False) (Eq (d (s (s (f one (f one (s one)))))) True) % 5.45/5.68 Clause #61 (by clausification #[60]): Eq (d (s (s (f one (f one (s one)))))) True % 5.45/5.68 Clause #62 (by forward demodulation #[61, 27]): Eq (d (f one (s (f one (s one))))) True % 5.45/5.68 Clause #63 (by superposition #[62, 7]): Or (Eq True False) (Eq (d (s (f one (s (f one (s one)))))) True) % 5.45/5.68 Clause #64 (by clausification #[63]): Eq (d (s (f one (s (f one (s one)))))) True % 5.45/5.68 Clause #65 (by superposition #[64, 7]): Or (Eq True False) (Eq (d (s (s (f one (s (f one (s one))))))) True) % 5.45/5.68 Clause #66 (by superposition #[46, 40]): ∀ (a : Iota), Eq (f (s a) (s (s (s one)))) (f a (f a (f a (s one)))) % 5.52/5.70 Clause #68 (by superposition #[46, 43]): ∀ (a : Iota), Eq (f (s (s a)) (s (s one))) (f (s a) (f a (s one))) % 5.52/5.70 Clause #80 (by clausification #[65]): Eq (d (s (s (f one (s (f one (s one))))))) True % 5.52/5.70 Clause #81 (by forward demodulation #[80, 27]): Eq (d (f one (s (s (f one (s one)))))) True % 5.52/5.70 Clause #82 (by forward demodulation #[81, 27]): Eq (d (f one (f one (s (s one))))) True % 5.52/5.70 Clause #83 (by superposition #[82, 7]): Or (Eq True False) (Eq (d (s (f one (f one (s (s one)))))) True) % 5.52/5.70 Clause #84 (by clausification #[83]): Eq (d (s (f one (f one (s (s one)))))) True % 5.52/5.70 Clause #85 (by superposition #[84, 7]): Or (Eq True False) (Eq (d (s (s (f one (f one (s (s one))))))) True) % 5.52/5.70 Clause #86 (by clausification #[85]): Eq (d (s (s (f one (f one (s (s one))))))) True % 5.52/5.70 Clause #87 (by forward demodulation #[86, 27]): Eq (d (f one (s (f one (s (s one)))))) True % 5.52/5.70 Clause #88 (by superposition #[87, 7]): Or (Eq True False) (Eq (d (s (f one (s (f one (s (s one))))))) True) % 5.52/5.70 Clause #101 (by clausification #[88]): Eq (d (s (f one (s (f one (s (s one))))))) True % 5.52/5.70 Clause #102 (by superposition #[101, 7]): Or (Eq True False) (Eq (d (s (s (f one (s (f one (s (s one)))))))) True) % 5.52/5.70 Clause #104 (by superposition #[68, 19]): Eq (d (f (s one) (f one (s one)))) False % 5.52/5.70 Clause #114 (by clausification #[102]): Eq (d (s (s (f one (s (f one (s (s one)))))))) True % 5.52/5.70 Clause #115 (by forward demodulation #[114, 27]): Eq (d (f one (s (s (f one (s (s one))))))) True % 5.52/5.70 Clause #116 (by forward demodulation #[115, 27]): Eq (d (f one (f one (s (s (s one)))))) True % 5.52/5.70 Clause #117 (by forward demodulation #[116, 28]): Eq (d (f one (f one (f one (s one))))) True % 5.52/5.70 Clause #157 (by forward demodulation #[66, 28]): ∀ (a : Iota), Eq (f (s a) (f one (s one))) (f a (f a (f a (s one)))) % 5.52/5.70 Clause #158 (by backward demodulation #[157, 117]): Eq (d (f (s one) (f one (s one)))) True % 5.52/5.70 Clause #170 (by superposition #[158, 104]): Eq True False % 5.52/5.70 Clause #172 (by clausification #[170]): False % 5.52/5.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------