%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU843^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:02:32 PM UTC 2025 % Result : Theorem 3.76s 3.95s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU843^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.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 05:43:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.76/3.95 SZS status Theorem for theBenchmark.p % 3.76/3.95 SZS output start Proof for theBenchmark.p % 3.76/3.95 Clause #0 (by assumption #[]): Eq (Not (∀ (S T : a → Prop), Eq (fun Xz => Or (S Xz) (T Xz)) S → ∀ (Xx : a), T Xx → S Xx)) True % 3.76/3.95 Clause #1 (by clausification #[0]): Eq (∀ (S T : a → Prop), Eq (fun Xz => Or (S Xz) (T Xz)) S → ∀ (Xx : a), T Xx → S Xx) False % 3.76/3.95 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.76/3.95 Eq % 3.76/3.95 (Not % 3.76/3.95 (∀ (T : a → Prop), Eq (fun Xz => Or (skS.0 0 a_1 Xz) (T Xz)) (skS.0 0 a_1) → ∀ (Xx : a), T Xx → skS.0 0 a_1 Xx)) % 3.76/3.95 True % 3.76/3.95 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.76/3.95 Eq (∀ (T : a → Prop), Eq (fun Xz => Or (skS.0 0 a_1 Xz) (T Xz)) (skS.0 0 a_1) → ∀ (Xx : a), T Xx → skS.0 0 a_1 Xx) % 3.76/3.95 False % 3.76/3.95 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.76/3.95 Eq % 3.76/3.95 (Not % 3.76/3.95 (Eq (fun Xz => Or (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (skS.0 0 a_1) → % 3.76/3.95 ∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 0 a_1 Xx)) % 3.76/3.95 True % 3.76/3.95 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.76/3.95 Eq % 3.76/3.95 (Eq (fun Xz => Or (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (skS.0 0 a_1) → % 3.76/3.95 ∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 0 a_1 Xx) % 3.76/3.95 False % 3.76/3.95 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : a → Prop), Eq (Eq (fun Xz => Or (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (skS.0 0 a_1)) True % 3.76/3.95 Clause #7 (by clausification #[5]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 0 a_1 Xx) False % 3.76/3.95 Clause #8 (by clausification #[6]): ∀ (a_1 a_2 : a → Prop), Eq (fun Xz => Or (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (skS.0 0 a_1) % 3.76/3.95 Clause #9 (by argument congruence #[8]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq ((fun Xz => Or (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) a_3) (skS.0 0 a_1 a_3) % 3.76/3.95 Clause #10 (by clausification #[7]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.76/3.95 Eq (Not (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3) → skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) True % 3.76/3.95 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3) → skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) False % 3.76/3.95 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 (skS.0 2 a_1 a_2 a_3)) True % 3.76/3.95 Clause #13 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) False % 3.76/3.95 Clause #16 (by betaEtaReduce #[9]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Eq (Or (skS.0 0 a_1 a_2) (skS.0 1 a_1 a_3 a_2)) (skS.0 0 a_1 a_2) % 3.76/3.95 Clause #17 (by identity loobHoist #[16]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), % 3.76/3.95 Or (Eq (Or (skS.0 0 a_1 a_2) True) (skS.0 0 a_1 a_2)) (Eq (skS.0 1 a_1 a_3 a_2) False) % 3.76/3.95 Clause #19 (by bool simp #[17]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Or (Eq True (skS.0 0 a_1 a_2)) (Eq (skS.0 1 a_1 a_3 a_2) False) % 3.76/3.95 Clause #20 (by superposition #[19, 12]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Eq True (skS.0 0 (fun x => a_1 x) (skS.0 2 a_1 a_2 a_3))) (Eq False True) % 3.76/3.95 Clause #22 (by betaEtaReduce #[20]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Eq True (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3))) (Eq False True) % 3.76/3.95 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq True (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3)) % 3.76/3.95 Clause #26 (by superposition #[23, 13]): Eq True False % 3.76/3.95 Clause #28 (by clausification #[26]): False % 3.76/3.95 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------