%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV049^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:02:47 PM UTC 2025 % Result : Theorem 5.73s 5.98s % Output : Proof 5.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEV049^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.12 % Command : duper %s % 0.11/0.33 % Computer : n006.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Fri Oct 3 01:21:53 EDT 2025 % 0.11/0.33 % CPUTime : % 5.73/5.98 SZS status Theorem for theBenchmark.p % 5.73/5.98 SZS output start Proof for theBenchmark.p % 5.73/5.98 Clause #0 (by assumption #[]): Eq % 5.73/5.98 (Not % 5.73/5.98 (Exists fun R => % 5.73/5.98 And (Not (R (fun Xx => True) fun Xx => False)) (∀ (Xx Xy Xz : Iota → Prop), And (R Xx Xy) (R Xy Xz) → R Xx Xz))) % 5.73/5.98 True % 5.73/5.98 Clause #1 (by clausification #[0]): Eq % 5.73/5.98 (Exists fun R => % 5.73/5.98 And (Not (R (fun Xx => True) fun Xx => False)) (∀ (Xx Xy Xz : Iota → Prop), And (R Xx Xy) (R Xy Xz) → R Xx Xz)) % 5.73/5.98 False % 5.73/5.98 Clause #2 (by clausification #[1]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop), % 5.73/5.98 Eq (And (Not (a (fun Xx => True) fun Xx => False)) (∀ (Xx Xy Xz : Iota → Prop), And (a Xx Xy) (a Xy Xz) → a Xx Xz)) % 5.73/5.98 False % 5.73/5.98 Clause #3 (by clausification #[2]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop), % 5.73/5.98 Or (Eq (Not (a (fun Xx => True) fun Xx => False)) False) % 5.73/5.98 (Eq (∀ (Xx Xy Xz : Iota → Prop), And (a Xx Xy) (a Xy Xz) → a Xx Xz) False) % 5.73/5.98 Clause #4 (by clausification #[3]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop), % 5.73/5.98 Or (Eq (∀ (Xx Xy Xz : Iota → Prop), And (a Xx Xy) (a Xy Xz) → a Xx Xz) False) % 5.73/5.98 (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 Clause #5 (by clausification #[4]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 (Eq (Not (∀ (Xy Xz : Iota → Prop), And (a (skS.0 0 a a_1) Xy) (a Xy Xz) → a (skS.0 0 a a_1) Xz)) True) % 5.73/5.98 Clause #6 (by clausification #[5]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 (Eq (∀ (Xy Xz : Iota → Prop), And (a (skS.0 0 a a_1) Xy) (a Xy Xz) → a (skS.0 0 a a_1) Xz) False) % 5.73/5.98 Clause #7 (by clausification #[6]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 (Eq % 5.73/5.98 (Not % 5.73/5.98 (∀ (Xz : Iota → Prop), % 5.73/5.98 And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) Xz) → a (skS.0 0 a a_1) Xz)) % 5.73/5.98 True) % 5.73/5.98 Clause #8 (by clausification #[7]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 (Eq % 5.73/5.98 (∀ (Xz : Iota → Prop), % 5.73/5.98 And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) Xz) → a (skS.0 0 a a_1) Xz) % 5.73/5.98 False) % 5.73/5.98 Clause #9 (by clausification #[8]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 a_3 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 (Eq % 5.73/5.98 (Not % 5.73/5.98 (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3)) → % 5.73/5.98 a (skS.0 0 a a_1) (skS.0 2 a a_1 a_2 a_3))) % 5.73/5.98 True) % 5.73/5.98 Clause #10 (by clausification #[9]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 a_3 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 (Eq % 5.73/5.98 (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3)) → % 5.73/5.98 a (skS.0 0 a a_1) (skS.0 2 a a_1 a_2 a_3)) % 5.73/5.98 False) % 5.73/5.98 Clause #11 (by clausification #[10]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 a_3 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) % 5.73/5.98 (Eq (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3))) True) % 5.73/5.98 Clause #13 (by clausification #[11]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 a_3 : Iota → Prop), % 5.73/5.98 Or (Eq (a (fun Xx => True) fun Xx => False) True) (Eq (a (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3)) True) % 5.73/5.98 Clause #21 (by equality factoring #[13]): ∀ (a : Prop), Or (Ne True True) (Eq ((fun x x => a) (fun Xx => True) fun Xx => False) True) % 5.73/5.98 Clause #47 (by betaEtaReduce #[21]): ∀ (a : Prop), Or (Ne True True) (Eq a True) % 5.73/5.98 Clause #48 (by clausification #[47]): ∀ (a : Prop), Or (Eq a True) (Or (Eq True False) (Eq True False)) % 5.73/5.98 Clause #50 (by clausification #[48]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 5.73/5.98 Clause #51 (by clausification #[50]): ∀ (a : Prop), Eq a True % 5.73/5.98 Clause #52 (by falseElim #[51]): False % 5.73/5.98 SZS output end Proof for theBenchmark.p 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