%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO261^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:08:49 PM UTC 2025 % Result : Theorem 4.28s 4.48s % Output : Proof 4.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.12 % Problem : SYO261^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.14/0.35 % Computer : n016.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 : Fri Oct 3 13:39:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.28/4.48 SZS status Theorem for theBenchmark.p % 4.28/4.48 SZS output start Proof for theBenchmark.p % 4.28/4.48 Clause #0 (by assumption #[]): Eq % 4.28/4.48 (Not % 4.28/4.48 (And (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO)) % 4.28/4.48 (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx)) → % 4.28/4.48 cP n)) % 4.28/4.48 True % 4.28/4.48 Clause #1 (by clausification #[0]): Eq % 4.28/4.48 (And (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO)) % 4.28/4.48 (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx)) → % 4.28/4.48 cP n) % 4.28/4.48 False % 4.28/4.48 Clause #2 (by clausification #[1]): Eq % 4.28/4.48 (And (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO)) % 4.28/4.48 (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx))) % 4.28/4.48 True % 4.28/4.48 Clause #3 (by clausification #[1]): Eq (cP n) False % 4.28/4.48 Clause #4 (by clausification #[2]): Eq (∀ (Xx : Iota), cP Xx → cP (c1_plus Xx)) True % 4.28/4.48 Clause #5 (by clausification #[2]): Eq (And (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) (cP cO)) True % 4.28/4.48 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (cP a → cP (c1_plus a)) True % 4.28/4.48 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (cP (c1_plus a)) True) % 4.28/4.48 Clause #8 (by clausification #[5]): Eq (cP cO) True % 4.28/4.48 Clause #9 (by clausification #[5]): Eq (∀ (A : Iota → Prop), And (A cO) (∀ (Xx : Iota), A Xx → A (c1_plus Xx)) → A n) True % 4.28/4.48 Clause #11 (by clausification #[9]): ∀ (a : Iota → Prop), Eq (And (a cO) (∀ (Xx : Iota), a Xx → a (c1_plus Xx)) → a n) True % 4.28/4.48 Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop), Or (Eq (And (a cO) (∀ (Xx : Iota), a Xx → a (c1_plus Xx))) False) (Eq (a n) True) % 4.28/4.48 Clause #13 (by clausification #[12]): ∀ (a : Iota → Prop), Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (∀ (Xx : Iota), a Xx → a (c1_plus Xx)) False)) % 4.28/4.48 Clause #14 (by clausification #[13]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.28/4.48 Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (Not (a (skS.0 0 a a_1) → a (c1_plus (skS.0 0 a a_1)))) True)) % 4.28/4.48 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.28/4.48 Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (a (skS.0 0 a a_1) → a (c1_plus (skS.0 0 a a_1))) False)) % 4.28/4.48 Clause #16 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (a (skS.0 0 a a_1)) True)) % 4.28/4.48 Clause #17 (by clausification #[15]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a n) True) (Or (Eq (a cO) False) (Eq (a (c1_plus (skS.0 0 a a_1))) False)) % 4.28/4.48 Clause #26 (by superposition #[16, 8]): ∀ (a : Iota), % 4.28/4.48 Or (Eq ((fun x => cP x) n) True) (Or (Eq ((fun x => cP x) (skS.0 0 (fun x => cP x) a)) True) (Eq False True)) % 4.28/4.48 Clause #39 (by fluidLoobHoist #[17]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.28/4.48 Or (Eq (a n) True) (Or (Eq (a (c1_plus (skS.0 0 a a_1))) False) (Or (Eq True False) (Eq (a cO) False))) % 4.28/4.48 Clause #111 (by clausification #[39]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a n) True) (Or (Eq (a (c1_plus (skS.0 0 a a_1))) False) (Eq (a cO) False)) % 4.28/4.48 Clause #128 (by fluidSup #[111, 8]): ∀ (a : Iota → Prop) (a_1 : Prop → Iota), % 4.28/4.48 Or (Eq (a n) True) (Or (Eq (a (c1_plus (skS.0 0 a (a_1 True)))) False) (Eq (a cO) False)) % 4.28/4.48 Clause #242 (by betaEtaReduce #[26]): ∀ (a : Iota), Or (Eq (cP n) True) (Or (Eq (cP (skS.0 0 cP a)) True) (Eq False True)) % 4.28/4.48 Clause #243 (by clausification #[242]): ∀ (a : Iota), Or (Eq (cP n) True) (Eq (cP (skS.0 0 cP a)) True) % 4.28/4.48 Clause #244 (by forward demodulation #[243, 3]): ∀ (a : Iota), Or (Eq False True) (Eq (cP (skS.0 0 cP a)) True) % 4.28/4.48 Clause #245 (by clausification #[244]): ∀ (a : Iota), Eq (cP (skS.0 0 cP a)) True % 4.28/4.48 Clause #246 (by superposition #[245, 7]): ∀ (a : Iota), Or (Eq True False) (Eq (cP (c1_plus (skS.0 0 cP a))) True) % 4.28/4.48 Clause #251 (by clausification #[246]): ∀ (a : Iota), Eq (cP (c1_plus (skS.0 0 cP a))) True % 4.28/4.48 Clause #255 (by fluidSup #[251, 128]): Or (Eq ((fun x => cP x) n) True) (Or (Eq ((fun _ => _) True) False) (Eq ((fun x => cP x) cO) False)) % 4.28/4.48 Clause #258 (by betaEtaReduce #[255]): Or (Eq (cP n) True) (Or (Eq True False) (Eq (cP cO) False)) % 4.28/4.48 Clause #259 (by clausification #[258]): Or (Eq (cP n) True) (Eq (cP cO) False) % 4.28/4.49 Clause #260 (by forward demodulation #[259, 8]): Or (Eq (cP n) True) (Eq True False) % 4.28/4.49 Clause #261 (by clausification #[260]): Eq (cP n) True % 4.28/4.49 Clause #262 (by superposition #[261, 3]): Eq True False % 4.28/4.49 Clause #276 (by clausification #[262]): False % 4.28/4.49 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------