%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PUZ100^5 : TPTP v9.2.0. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:58:21 PM UTC 2025 % Result : Theorem 3.70s 3.87s % Output : Proof 3.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PUZ100^5 : TPTP v9.2.0. Bugfixed v5.2.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n024.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 20:50:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.70/3.87 SZS status Theorem for theBenchmark.p % 3.70/3.87 SZS output start Proof for theBenchmark.p % 3.70/3.87 Clause #0 (by assumption #[]): Eq (Eq cCKB_E2 fun Xx Xy => ∀ (Xp : Iota → Prop), And (Xp Xx) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy) True % 3.70/3.87 Clause #1 (by assumption #[]): Eq (Not (∀ (Xx : Iota), cCKB_E2 Xx Xx)) True % 3.70/3.87 Clause #2 (by clausification #[1]): Eq (∀ (Xx : Iota), cCKB_E2 Xx Xx) False % 3.70/3.87 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (cCKB_E2 (skS.0 0 a) (skS.0 0 a))) True % 3.70/3.87 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (cCKB_E2 (skS.0 0 a) (skS.0 0 a)) False % 3.70/3.87 Clause #5 (by clausification #[0]): Eq cCKB_E2 fun Xx Xy => ∀ (Xp : Iota → Prop), And (Xp Xx) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy % 3.70/3.87 Clause #6 (by argument congruence #[5]): ∀ (a : Iota), % 3.70/3.87 Eq (cCKB_E2 a) ((fun Xx Xy => ∀ (Xp : Iota → Prop), And (Xp Xx) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy) a) % 3.70/3.87 Clause #8 (by betaEtaReduce #[6]): ∀ (a : Iota), Eq (cCKB_E2 a) fun Xy => ∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy % 3.70/3.87 Clause #9 (by argument congruence #[8]): ∀ (a a_1 : Iota), % 3.70/3.87 Eq (cCKB_E2 a a_1) ((fun Xy => ∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy) a_1) % 3.70/3.87 Clause #12 (by betaEtaReduce #[9]): ∀ (a a_1 : Iota), Eq (cCKB_E2 a a_1) (∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp a_1) % 3.70/3.87 Clause #13 (by clausify Prop equality #[12]): ∀ (a a_1 : Iota), % 3.70/3.87 Or (Eq (cCKB_E2 a a_1) True) % 3.70/3.87 (Eq (∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp a_1) False) % 3.70/3.87 Clause #27 (by clausification #[13]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 3.70/3.87 Or (Eq (cCKB_E2 a a_1) True) % 3.70/3.87 (Eq % 3.70/3.87 (Not % 3.70/3.87 (And (skS.0 2 a a_1 a_2 a) (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu))) → % 3.70/3.87 skS.0 2 a a_1 a_2 a_1)) % 3.70/3.87 True) % 3.70/3.87 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 3.70/3.87 Or (Eq (cCKB_E2 a a_1) True) % 3.70/3.87 (Eq % 3.70/3.87 (And (skS.0 2 a a_1 a_2 a) (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu))) → % 3.70/3.87 skS.0 2 a a_1 a_2 a_1) % 3.70/3.87 False) % 3.70/3.87 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 3.70/3.87 Or (Eq (cCKB_E2 a a_1) True) % 3.70/3.87 (Eq (And (skS.0 2 a a_1 a_2 a) (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu)))) True) % 3.70/3.87 Clause #30 (by clausification #[28]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (cCKB_E2 a a_1) True) (Eq (skS.0 2 a a_1 a_2 a_1) False) % 3.70/3.87 Clause #32 (by clausification #[29]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (cCKB_E2 a a_1) True) (Eq (skS.0 2 a a_1 a_2 a) True) % 3.70/3.87 Clause #35 (by superposition #[32, 30]): ∀ (a : Iota), Or (Eq (cCKB_E2 a a) True) (Or (Eq (cCKB_E2 a a) True) (Eq True False)) % 3.70/3.87 Clause #45 (by clausification #[35]): ∀ (a : Iota), Or (Eq (cCKB_E2 a a) True) (Eq (cCKB_E2 a a) True) % 3.70/3.87 Clause #46 (by eliminate duplicate literals #[45]): ∀ (a : Iota), Eq (cCKB_E2 a a) True % 3.70/3.87 Clause #47 (by superposition #[46, 4]): Eq True False % 3.70/3.87 Clause #54 (by clausification #[47]): False % 3.70/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------