%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM705^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 07:57:08 PM UTC 2025 % Result : Theorem 7.91s 8.07s % Output : Proof 7.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM705^1 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.14/0.34 % Computer : n020.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 08:10:38 EDT 2025 % 0.14/0.35 % CPUTime : % 7.91/8.07 SZS status Theorem for theBenchmark.p % 7.91/8.07 SZS output start Proof for theBenchmark.p % 7.91/8.07 Clause #0 (by assumption #[]): Eq (some p) True % 7.91/8.07 Clause #1 (by assumption #[]): Eq (∀ (Xx Xy : nat), lessis Xx Xy → Not (more Xy Xx) → Eq Xy Xx) True % 7.91/8.07 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy : nat), lessis Xx Xy → Not (more Xx Xy)) True % 7.91/8.07 Clause #4 (by assumption #[]): Eq (∀ (Xp : nat → Prop), some Xp → some fun Xx => Not ((∀ (Xx_0 : nat), Xp Xx_0 → lessis Xx Xx_0) → Not (Xp Xx))) True % 7.91/8.07 Clause #5 (by assumption #[]): Eq % 7.91/8.07 (Not % 7.91/8.07 (Not % 7.91/8.07 ((∀ (Xx Xy : nat), % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)) → % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xy Xx_0) → Not (p Xy)) → Eq Xx Xy) → % 7.91/8.07 Not (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)))))) % 7.91/8.07 True % 7.91/8.07 Clause #10 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy : nat), lessis a Xy → Not (more a Xy)) True % 7.91/8.07 Clause #11 (by clausification #[10]): ∀ (a a_1 : nat), Eq (lessis a a_1 → Not (more a a_1)) True % 7.91/8.07 Clause #12 (by clausification #[11]): ∀ (a a_1 : nat), Or (Eq (lessis a a_1) False) (Eq (Not (more a a_1)) True) % 7.91/8.07 Clause #13 (by clausification #[12]): ∀ (a a_1 : nat), Or (Eq (lessis a a_1) False) (Eq (more a a_1) False) % 7.91/8.07 Clause #14 (by clausification #[1]): ∀ (a : nat), Eq (∀ (Xy : nat), lessis a Xy → Not (more Xy a) → Eq Xy a) True % 7.91/8.07 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Eq (lessis a a_1 → Not (more a_1 a) → Eq a_1 a) True % 7.91/8.07 Clause #16 (by clausification #[15]): ∀ (a a_1 : nat), Or (Eq (lessis a a_1) False) (Eq (Not (more a_1 a) → Eq a_1 a) True) % 7.91/8.07 Clause #17 (by clausification #[16]): ∀ (a a_1 : nat), Or (Eq (lessis a a_1) False) (Or (Eq (Not (more a_1 a)) False) (Eq (Eq a_1 a) True)) % 7.91/8.07 Clause #18 (by clausification #[17]): ∀ (a a_1 : nat), Or (Eq (lessis a a_1) False) (Or (Eq (Eq a_1 a) True) (Eq (more a_1 a) True)) % 7.91/8.07 Clause #19 (by clausification #[18]): ∀ (a a_1 : nat), Or (Eq (lessis a a_1) False) (Or (Eq (more a_1 a) True) (Eq a_1 a)) % 7.91/8.07 Clause #20 (by clausification #[4]): ∀ (a : nat → Prop), Eq (some a → some fun Xx => Not ((∀ (Xx_0 : nat), a Xx_0 → lessis Xx Xx_0) → Not (a Xx))) True % 7.91/8.07 Clause #21 (by clausification #[20]): ∀ (a : nat → Prop), % 7.91/8.07 Or (Eq (some a) False) (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), a Xx_0 → lessis Xx Xx_0) → Not (a Xx))) True) % 7.91/8.07 Clause #22 (by superposition #[21, 0]): Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), (fun x => p x) Xx_0 → lessis Xx Xx_0) → Not ((fun x => p x) Xx))) True) % 7.91/8.07 (Eq False True) % 7.91/8.07 Clause #24 (by clausification #[5]): Eq % 7.91/8.07 (Not % 7.91/8.07 ((∀ (Xx Xy : nat), % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)) → % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xy Xx_0) → Not (p Xy)) → Eq Xx Xy) → % 7.91/8.07 Not (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))))) % 7.91/8.07 False % 7.91/8.07 Clause #25 (by clausification #[24]): Eq % 7.91/8.07 ((∀ (Xx Xy : nat), % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)) → % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xy Xx_0) → Not (p Xy)) → Eq Xx Xy) → % 7.91/8.07 Not (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)))) % 7.91/8.07 True % 7.91/8.07 Clause #26 (by clausification #[25]): Or % 7.91/8.07 (Eq % 7.91/8.07 (∀ (Xx Xy : nat), % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)) → % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xy Xx_0) → Not (p Xy)) → Eq Xx Xy) % 7.91/8.07 False) % 7.91/8.07 (Eq (Not (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)))) True) % 7.91/8.07 Clause #27 (by clausification #[26]): ∀ (a : nat), % 7.91/8.07 Or (Eq (Not (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx)))) True) % 7.91/8.07 (Eq % 7.91/8.07 (Not % 7.91/8.07 (∀ (Xy : nat), % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) → Not (p (skS.0 0 a))) → % 7.91/8.07 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xy Xx_0) → Not (p Xy)) → Eq (skS.0 0 a) Xy)) % 7.91/8.07 True) % 7.91/8.07 Clause #28 (by clausification #[27]): ∀ (a : nat), % 7.91/8.07 Or % 7.91/8.07 (Eq % 7.91/8.10 (Not % 7.91/8.10 (∀ (Xy : nat), % 7.91/8.10 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) → Not (p (skS.0 0 a))) → % 7.91/8.10 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xy Xx_0) → Not (p Xy)) → Eq (skS.0 0 a) Xy)) % 7.91/8.10 True) % 7.91/8.10 (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 Clause #29 (by clausification #[28]): ∀ (a : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq % 7.91/8.10 (∀ (Xy : nat), % 7.91/8.10 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) → Not (p (skS.0 0 a))) → % 7.91/8.10 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xy Xx_0) → Not (p Xy)) → Eq (skS.0 0 a) Xy) % 7.91/8.10 False) % 7.91/8.10 Clause #30 (by clausification #[29]): ∀ (a a_1 : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq % 7.91/8.10 (Not % 7.91/8.10 (Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) → Not (p (skS.0 0 a))) → % 7.91/8.10 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 1 a a_1) Xx_0) → Not (p (skS.0 1 a a_1))) → % 7.91/8.10 Eq (skS.0 0 a) (skS.0 1 a a_1))) % 7.91/8.10 True) % 7.91/8.10 Clause #31 (by clausification #[30]): ∀ (a a_1 : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq % 7.91/8.10 (Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) → Not (p (skS.0 0 a))) → % 7.91/8.10 Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 1 a a_1) Xx_0) → Not (p (skS.0 1 a a_1))) → % 7.91/8.10 Eq (skS.0 0 a) (skS.0 1 a a_1)) % 7.91/8.10 False) % 7.91/8.10 Clause #32 (by clausification #[31]): ∀ (a : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq (Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) → Not (p (skS.0 0 a)))) True) % 7.91/8.10 Clause #33 (by clausification #[31]): ∀ (a a_1 : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq % 7.91/8.10 (Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 1 a a_1) Xx_0) → Not (p (skS.0 1 a a_1))) → % 7.91/8.10 Eq (skS.0 0 a) (skS.0 1 a a_1)) % 7.91/8.10 False) % 7.91/8.10 Clause #34 (by clausification #[32]): ∀ (a : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) → Not (p (skS.0 0 a))) False) % 7.91/8.10 Clause #35 (by clausification #[34]): ∀ (a : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq (∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 0 a) Xx_0) True) % 7.91/8.10 Clause #36 (by clausification #[34]): ∀ (a : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq (Not (p (skS.0 0 a))) False) % 7.91/8.10 Clause #37 (by clausification #[35]): ∀ (a a_1 : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq (p a → lessis (skS.0 0 a_1) a) True) % 7.91/8.10 Clause #38 (by clausification #[37]): ∀ (a a_1 : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Or (Eq (p a) False) (Eq (lessis (skS.0 0 a_1) a) True)) % 7.91/8.10 Clause #39 (by betaEtaReduce #[22]): Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) True) (Eq False True) % 7.91/8.10 Clause #40 (by clausification #[39]): Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) True % 7.91/8.10 Clause #41 (by superposition #[40, 38]): ∀ (a a_1 : nat), Or (Eq True False) (Or (Eq (p a) False) (Eq (lessis (skS.0 0 a_1) a) True)) % 7.91/8.10 Clause #47 (by clausification #[41]): ∀ (a a_1 : nat), Or (Eq (p a) False) (Eq (lessis (skS.0 0 a_1) a) True) % 7.91/8.10 Clause #56 (by clausification #[33]): ∀ (a a_1 : nat), % 7.91/8.10 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.10 (Eq (Not ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 1 a a_1) Xx_0) → Not (p (skS.0 1 a a_1)))) True) % 7.91/8.10 Clause #57 (by clausification #[33]): ∀ (a a_1 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) False) % 7.91/8.15 Clause #58 (by clausification #[56]): ∀ (a a_1 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Eq ((∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 1 a a_1) Xx_0) → Not (p (skS.0 1 a a_1))) False) % 7.91/8.15 Clause #59 (by clausification #[58]): ∀ (a a_1 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Eq (∀ (Xx_0 : nat), p Xx_0 → lessis (skS.0 1 a a_1) Xx_0) True) % 7.91/8.15 Clause #60 (by clausification #[58]): ∀ (a a_1 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Eq (Not (p (skS.0 1 a a_1))) False) % 7.91/8.15 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Eq (p a → lessis (skS.0 1 a_1 a_2) a) True) % 7.91/8.15 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Or (Eq (p a) False) (Eq (lessis (skS.0 1 a_1 a_2) a) True)) % 7.91/8.15 Clause #63 (by superposition #[62, 40]): ∀ (a a_1 a_2 : nat), Or (Eq (p a) False) (Or (Eq (lessis (skS.0 1 a_1 a_2) a) True) (Eq False True)) % 7.91/8.15 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : nat), Or (Eq (p a) False) (Eq (lessis (skS.0 1 a_1 a_2) a) True) % 7.91/8.15 Clause #65 (by clausification #[36]): ∀ (a : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) (Eq (p (skS.0 0 a)) True) % 7.91/8.15 Clause #66 (by superposition #[65, 40]): ∀ (a : nat), Or (Eq (p (skS.0 0 a)) True) (Eq False True) % 7.91/8.15 Clause #67 (by clausification #[66]): ∀ (a : nat), Eq (p (skS.0 0 a)) True % 7.91/8.15 Clause #69 (by superposition #[67, 64]): ∀ (a a_1 a_2 : nat), Or (Eq True False) (Eq (lessis (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 7.91/8.15 Clause #95 (by clausification #[69]): ∀ (a a_1 a_2 : nat), Eq (lessis (skS.0 1 a a_1) (skS.0 0 a_2)) True % 7.91/8.15 Clause #97 (by superposition #[95, 19]): ∀ (a a_1 a_2 : nat), % 7.91/8.15 Or (Eq True False) (Or (Eq (more (skS.0 0 a) (skS.0 1 a_1 a_2)) True) (Eq (skS.0 0 a) (skS.0 1 a_1 a_2))) % 7.91/8.15 Clause #103 (by clausification #[60]): ∀ (a a_1 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Eq (p (skS.0 1 a a_1)) True) % 7.91/8.15 Clause #104 (by superposition #[103, 40]): ∀ (a a_1 : nat), Or (Eq (p (skS.0 1 a a_1)) True) (Eq False True) % 7.91/8.15 Clause #105 (by clausification #[104]): ∀ (a a_1 : nat), Eq (p (skS.0 1 a a_1)) True % 7.91/8.15 Clause #106 (by superposition #[105, 47]): ∀ (a a_1 a_2 : nat), Or (Eq True False) (Eq (lessis (skS.0 0 a) (skS.0 1 a_1 a_2)) True) % 7.91/8.15 Clause #109 (by clausification #[106]): ∀ (a a_1 a_2 : nat), Eq (lessis (skS.0 0 a) (skS.0 1 a_1 a_2)) True % 7.91/8.15 Clause #110 (by superposition #[109, 13]): ∀ (a a_1 a_2 : nat), Or (Eq True False) (Eq (more (skS.0 0 a) (skS.0 1 a_1 a_2)) False) % 7.91/8.15 Clause #113 (by clausification #[110]): ∀ (a a_1 a_2 : nat), Eq (more (skS.0 0 a) (skS.0 1 a_1 a_2)) False % 7.91/8.15 Clause #129 (by clausification #[57]): ∀ (a a_1 : nat), % 7.91/8.15 Or (Eq (some fun Xx => Not ((∀ (Xx_0 : nat), p Xx_0 → lessis Xx Xx_0) → Not (p Xx))) False) % 7.91/8.15 (Ne (skS.0 0 a) (skS.0 1 a a_1)) % 7.91/8.15 Clause #130 (by superposition #[129, 40]): ∀ (a a_1 : nat), Or (Ne (skS.0 0 a) (skS.0 1 a a_1)) (Eq False True) % 7.91/8.15 Clause #132 (by clausification #[130]): ∀ (a a_1 : nat), Ne (skS.0 0 a) (skS.0 1 a a_1) % 7.91/8.15 Clause #201 (by clausification #[97]): ∀ (a a_1 a_2 : nat), Or (Eq (more (skS.0 0 a) (skS.0 1 a_1 a_2)) True) (Eq (skS.0 0 a) (skS.0 1 a_1 a_2)) % 7.91/8.15 Clause #202 (by superposition #[201, 113]): ∀ (a a_1 a_2 : nat), Or (Eq (skS.0 0 a) (skS.0 1 a_1 a_2)) (Eq True False) % 7.91/8.15 Clause #218 (by clausification #[202]): ∀ (a a_1 a_2 : nat), Eq (skS.0 0 a) (skS.0 1 a_1 a_2) % 7.91/8.15 Clause #219 (by backward contextual literal cutting #[218, 132]): False % 7.91/8.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------