%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PUZ102^5 : TPTP v9.2.0. Bugfixed v5.2.0. % 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 07:58:21 PM UTC 2025 % Result : Theorem 4.48s 4.64s % Output : Proof 4.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : PUZ102^5 : TPTP v9.2.0. Bugfixed v5.2.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.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 : Thu Oct 2 20:48:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.48/4.64 SZS status Theorem for theBenchmark.p % 4.48/4.64 SZS output start Proof for theBenchmark.p % 4.48/4.64 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 % 4.48/4.64 Clause #1 (by assumption #[]): Eq (Not (∀ (Xx : Iota), cCKB_E2 Xx (s (s Xx)))) True % 4.48/4.64 Clause #2 (by clausification #[1]): Eq (∀ (Xx : Iota), cCKB_E2 Xx (s (s Xx))) False % 4.48/4.64 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (cCKB_E2 (skS.0 0 a) (s (s (skS.0 0 a))))) True % 4.48/4.64 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (cCKB_E2 (skS.0 0 a) (s (s (skS.0 0 a)))) False % 4.48/4.64 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 % 4.48/4.64 Clause #6 (by argument congruence #[5]): ∀ (a : Iota), % 4.48/4.64 Eq (cCKB_E2 a) ((fun Xx Xy => ∀ (Xp : Iota → Prop), And (Xp Xx) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp Xy) a) % 4.48/4.64 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 % 4.48/4.64 Clause #9 (by argument congruence #[8]): ∀ (a a_1 : Iota), % 4.48/4.64 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) % 4.48/4.64 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) % 4.48/4.64 Clause #13 (by clausify Prop equality #[12]): ∀ (a a_1 : Iota), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) % 4.48/4.64 (Eq (∀ (Xp : Iota → Prop), And (Xp a) (∀ (Xu : Iota), Xp Xu → Xp (s (s Xu))) → Xp a_1) False) % 4.48/4.64 Clause #27 (by clausification #[13]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) % 4.48/4.64 (Eq % 4.48/4.64 (Not % 4.48/4.64 (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))) → % 4.48/4.64 skS.0 2 a a_1 a_2 a_1)) % 4.48/4.64 True) % 4.48/4.64 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) % 4.48/4.64 (Eq % 4.48/4.64 (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))) → % 4.48/4.64 skS.0 2 a a_1 a_2 a_1) % 4.48/4.64 False) % 4.48/4.64 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) % 4.48/4.64 (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) % 4.48/4.64 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) % 4.48/4.64 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) (Eq (∀ (Xu : Iota), skS.0 2 a a_1 a_2 Xu → skS.0 2 a a_1 a_2 (s (s Xu))) True) % 4.48/4.64 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) % 4.48/4.64 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop) (a_3 : Iota), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) (Eq (skS.0 2 a a_1 a_2 a_3 → skS.0 2 a a_1 a_2 (s (s a_3))) True) % 4.48/4.64 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop) (a_3 : Iota), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) (Or (Eq (skS.0 2 a a_1 a_2 a_3) False) (Eq (skS.0 2 a a_1 a_2 (s (s a_3))) True)) % 4.48/4.64 Clause #36 (by superposition #[32, 34]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) % 4.48/4.64 (Or (Eq (skS.0 2 a a_1 (fun x => a_2 x) (s (s a))) True) (Or (Eq (cCKB_E2 a a_1) True) (Eq False True))) % 4.48/4.64 Clause #181 (by betaEtaReduce #[36]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) % 4.48/4.64 (Or (Eq (skS.0 2 a a_1 a_2 (s (s a))) True) (Or (Eq (cCKB_E2 a a_1) True) (Eq False True))) % 4.48/4.64 Clause #182 (by clausification #[181]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.48/4.64 Or (Eq (cCKB_E2 a a_1) True) (Or (Eq (skS.0 2 a a_1 a_2 (s (s a))) True) (Eq (cCKB_E2 a a_1) True)) % 4.48/4.64 Clause #183 (by eliminate duplicate literals #[182]): ∀ (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 (s (s a))) True) % 4.48/4.66 Clause #185 (by superposition #[183, 30]): ∀ (a : Iota), Or (Eq (cCKB_E2 a (s (s a))) True) (Or (Eq (cCKB_E2 a (s (s a))) True) (Eq True False)) % 4.48/4.66 Clause #204 (by clausification #[185]): ∀ (a : Iota), Or (Eq (cCKB_E2 a (s (s a))) True) (Eq (cCKB_E2 a (s (s a))) True) % 4.48/4.66 Clause #205 (by eliminate duplicate literals #[204]): ∀ (a : Iota), Eq (cCKB_E2 a (s (s a))) True % 4.48/4.66 Clause #206 (by superposition #[205, 4]): Eq True False % 4.48/4.66 Clause #226 (by clausification #[206]): False % 4.48/4.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------