%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU559^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:01:54 PM UTC 2025 % Result : Theorem 13.84s 14.03s % Output : Proof 13.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU559^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n013.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 06:33:08 EDT 2025 % 0.13/0.35 % CPUTime : % 13.84/14.03 SZS status Theorem for theBenchmark.p % 13.84/14.03 SZS output start Proof for theBenchmark.p % 13.84/14.03 Clause #0 (by assumption #[]): Eq (Eq subset fun A B => ∀ (Xx : Iota), in Xx A → in Xx B) True % 13.84/14.03 Clause #1 (by assumption #[]): Eq (Not (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 13.84/14.03 Clause #2 (by clausification #[1]): Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) False % 13.84/14.03 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx B) → subset (skS.0 0 a) B)) True % 13.84/14.03 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx B) → subset (skS.0 0 a) B) False % 13.84/14.03 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 13.84/14.03 Eq (Not ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) → subset (skS.0 0 a) (skS.0 1 a a_1))) True % 13.84/14.03 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), % 13.84/14.03 Eq ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) → subset (skS.0 0 a) (skS.0 1 a a_1)) False % 13.84/14.03 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) True % 13.84/14.03 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) False % 13.84/14.03 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (in a (skS.0 0 a_1) → in a (skS.0 1 a_1 a_2)) True % 13.84/14.03 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (in a (skS.0 1 a_1 a_2)) True) % 13.84/14.03 Clause #11 (by clausification #[0]): Eq subset fun A B => ∀ (Xx : Iota), in Xx A → in Xx B % 13.84/14.03 Clause #12 (by argument congruence #[11]): ∀ (a : Iota), Eq (subset a) ((fun A B => ∀ (Xx : Iota), in Xx A → in Xx B) a) % 13.84/14.03 Clause #14 (by betaEtaReduce #[12]): ∀ (a : Iota), Eq (subset a) fun B => ∀ (Xx : Iota), in Xx a → in Xx B % 13.84/14.03 Clause #15 (by argument congruence #[14]): ∀ (a a_1 : Iota), Eq (subset a a_1) ((fun B => ∀ (Xx : Iota), in Xx a → in Xx B) a_1) % 13.84/14.03 Clause #18 (by betaEtaReduce #[15]): ∀ (a a_1 : Iota), Eq (subset a a_1) (∀ (Xx : Iota), in Xx a → in Xx a_1) % 13.84/14.03 Clause #19 (by clausify Prop equality #[18]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) % 13.84/14.03 Clause #25 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 13.84/14.03 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True) % 13.84/14.03 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 13.84/14.03 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a) True) % 13.84/14.03 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) False) % 13.84/14.03 Clause #29 (by superposition #[27, 10]): ∀ (a a_1 a_2 a_3 : Iota), % 13.84/14.03 Or (Eq (subset (skS.0 0 a) a_1) True) % 13.84/14.03 (Or (Eq True False) (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True)) % 13.84/14.03 Clause #119 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), % 13.84/14.03 Or (Eq (subset (skS.0 0 a) a_1) True) (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) % 13.84/14.03 Clause #120 (by superposition #[119, 28]): ∀ (a a_1 : Iota), % 13.84/14.03 Or (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Or (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)) % 13.84/14.03 Clause #2771 (by clausification #[120]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True) % 13.84/14.03 Clause #2772 (by eliminate duplicate literals #[2771]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 13.84/14.03 Clause #2773 (by superposition #[2772, 8]): Eq True False % 13.84/14.03 Clause #2784 (by clausification #[2773]): False % 13.84/14.03 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------