%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO307^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:08:53 PM UTC 2025 % Result : Theorem 3.60s 3.77s % Output : Proof 3.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYO307^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.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 : Fri Oct 3 13:18:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.60/3.77 SZS status Theorem for theBenchmark.p % 3.60/3.77 SZS output start Proof for theBenchmark.p % 3.60/3.77 Clause #0 (by assumption #[]): Eq % 3.60/3.77 (Not % 3.60/3.77 (Exists fun A => ∀ (Xx Xy Xz : Iota), Or (A Xx) (And (A Xy) (A Xz)) → Or (And (p Xx) (cR Xy)) (And (q Xx) (cT Xz)))) % 3.60/3.77 True % 3.60/3.77 Clause #1 (by clausification #[0]): Eq (Exists fun A => ∀ (Xx Xy Xz : Iota), Or (A Xx) (And (A Xy) (A Xz)) → Or (And (p Xx) (cR Xy)) (And (q Xx) (cT Xz))) % 3.60/3.77 False % 3.60/3.77 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop), % 3.60/3.77 Eq (∀ (Xx Xy Xz : Iota), Or (a Xx) (And (a Xy) (a Xz)) → Or (And (p Xx) (cR Xy)) (And (q Xx) (cT Xz))) False % 3.60/3.77 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop) (a_1 : Iota), % 3.60/3.77 Eq % 3.60/3.77 (Not % 3.60/3.77 (∀ (Xy Xz : Iota), % 3.60/3.77 Or (a (skS.0 0 a a_1)) (And (a Xy) (a Xz)) → % 3.60/3.77 Or (And (p (skS.0 0 a a_1)) (cR Xy)) (And (q (skS.0 0 a a_1)) (cT Xz)))) % 3.60/3.77 True % 3.60/3.77 Clause #4 (by clausification #[3]): ∀ (a : Iota → Prop) (a_1 : Iota), % 3.60/3.77 Eq % 3.60/3.77 (∀ (Xy Xz : Iota), % 3.60/3.77 Or (a (skS.0 0 a a_1)) (And (a Xy) (a Xz)) → % 3.60/3.77 Or (And (p (skS.0 0 a a_1)) (cR Xy)) (And (q (skS.0 0 a a_1)) (cT Xz))) % 3.60/3.77 False % 3.60/3.77 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.60/3.77 Eq % 3.60/3.77 (Not % 3.60/3.77 (∀ (Xz : Iota), % 3.60/3.77 Or (a (skS.0 0 a a_1)) (And (a (skS.0 1 a a_1 a_2)) (a Xz)) → % 3.60/3.77 Or (And (p (skS.0 0 a a_1)) (cR (skS.0 1 a a_1 a_2))) (And (q (skS.0 0 a a_1)) (cT Xz)))) % 3.60/3.77 True % 3.60/3.77 Clause #6 (by clausification #[5]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 3.60/3.77 Eq % 3.60/3.77 (∀ (Xz : Iota), % 3.60/3.77 Or (a (skS.0 0 a a_1)) (And (a (skS.0 1 a a_1 a_2)) (a Xz)) → % 3.60/3.77 Or (And (p (skS.0 0 a a_1)) (cR (skS.0 1 a a_1 a_2))) (And (q (skS.0 0 a a_1)) (cT Xz))) % 3.60/3.77 False % 3.60/3.77 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 a_2 a_3 : Iota), % 3.60/3.77 Eq % 3.60/3.77 (Not % 3.60/3.77 (Or (a (skS.0 0 a a_1)) (And (a (skS.0 1 a a_1 a_2)) (a (skS.0 2 a a_1 a_2 a_3))) → % 3.60/3.77 Or (And (p (skS.0 0 a a_1)) (cR (skS.0 1 a a_1 a_2))) (And (q (skS.0 0 a a_1)) (cT (skS.0 2 a a_1 a_2 a_3))))) % 3.60/3.77 True % 3.60/3.77 Clause #8 (by clausification #[7]): ∀ (a : Iota → Prop) (a_1 a_2 a_3 : Iota), % 3.60/3.77 Eq % 3.60/3.77 (Or (a (skS.0 0 a a_1)) (And (a (skS.0 1 a a_1 a_2)) (a (skS.0 2 a a_1 a_2 a_3))) → % 3.60/3.77 Or (And (p (skS.0 0 a a_1)) (cR (skS.0 1 a a_1 a_2))) (And (q (skS.0 0 a a_1)) (cT (skS.0 2 a a_1 a_2 a_3)))) % 3.60/3.77 False % 3.60/3.77 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 a_3 : Iota), % 3.60/3.77 Eq (Or (a (skS.0 0 a a_1)) (And (a (skS.0 1 a a_1 a_2)) (a (skS.0 2 a a_1 a_2 a_3)))) True % 3.60/3.77 Clause #11 (by clausification #[9]): ∀ (a : Iota → Prop) (a_1 a_2 a_3 : Iota), % 3.60/3.77 Or (Eq (a (skS.0 0 a a_1)) True) (Eq (And (a (skS.0 1 a a_1 a_2)) (a (skS.0 2 a a_1 a_2 a_3))) True) % 3.60/3.77 Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop) (a_1 a_2 a_3 : Iota), Or (Eq (a (skS.0 0 a a_1)) True) (Eq (a (skS.0 2 a a_1 a_2 a_3)) True) % 3.60/3.77 Clause #20 (by equality factoring #[12]): ∀ (a : Prop) (a_1 : Iota), Or (Ne True True) (Eq ((fun x => a) (skS.0 0 (fun x => a) a_1)) True) % 3.60/3.77 Clause #48 (by betaEtaReduce #[20]): ∀ (a : Prop), Or (Ne True True) (Eq a True) % 3.60/3.77 Clause #49 (by clausification #[48]): ∀ (a : Prop), Or (Eq a True) (Or (Eq True False) (Eq True False)) % 3.60/3.77 Clause #51 (by clausification #[49]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 3.60/3.77 Clause #52 (by clausification #[51]): ∀ (a : Prop), Eq a True % 3.60/3.77 Clause #53 (by falseElim #[52]): False % 3.60/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------