%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU564^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:01:55 PM UTC 2025 % Result : Theorem 11.91s 12.11s % Output : Proof 11.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU564^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 06:21:23 EDT 2025 % 0.13/0.35 % CPUTime : % 11.91/12.11 SZS status Theorem for theBenchmark.p % 11.91/12.11 SZS output start Proof for theBenchmark.p % 11.91/12.11 Clause #0 (by assumption #[]): Eq (Eq subset fun A B => ∀ (Xx : Iota), in Xx A → in Xx B) True % 11.91/12.11 Clause #1 (by assumption #[]): Eq (Not (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 11.91/12.11 Clause #2 (by clausification #[1]): Eq (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) False % 11.91/12.11 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), subset (skS.0 0 a) B → in Xx (skS.0 0 a) → in Xx B)) True % 11.91/12.11 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset (skS.0 0 a) B → in Xx (skS.0 0 a) → in Xx B) False % 11.91/12.11 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 11.91/12.11 Eq (Not (∀ (Xx : Iota), subset (skS.0 0 a) (skS.0 1 a a_1) → in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1))) True % 11.91/12.11 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), % 11.91/12.11 Eq (∀ (Xx : Iota), subset (skS.0 0 a) (skS.0 1 a a_1) → in Xx (skS.0 0 a) → in Xx (skS.0 1 a a_1)) False % 11.91/12.11 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 11.91/12.11 Eq % 11.91/12.11 (Not % 11.91/12.11 (subset (skS.0 0 a) (skS.0 1 a a_1) → % 11.91/12.11 in (skS.0 2 a a_1 a_2) (skS.0 0 a) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) % 11.91/12.11 True % 11.91/12.11 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 11.91/12.11 Eq (subset (skS.0 0 a) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (skS.0 0 a) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) % 11.91/12.11 False % 11.91/12.11 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 11.91/12.11 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 11.91/12.11 Clause #11 (by clausification #[0]): Eq subset fun A B => ∀ (Xx : Iota), in Xx A → in Xx B % 11.91/12.11 Clause #12 (by argument congruence #[11]): ∀ (a : Iota), Eq (subset a) ((fun A B => ∀ (Xx : Iota), in Xx A → in Xx B) a) % 11.91/12.11 Clause #14 (by betaEtaReduce #[12]): ∀ (a : Iota), Eq (subset a) fun B => ∀ (Xx : Iota), in Xx a → in Xx B % 11.91/12.11 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) % 11.91/12.11 Clause #18 (by betaEtaReduce #[15]): ∀ (a a_1 : Iota), Eq (subset a a_1) (∀ (Xx : Iota), in Xx a → in Xx a_1) % 11.91/12.11 Clause #20 (by clausify Prop equality #[18]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) True) % 11.91/12.11 Clause #22 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 11.91/12.11 Clause #23 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 11.91/12.11 Clause #25 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 11.91/12.11 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 11.91/12.11 Clause #27 (by superposition #[26, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Or (Eq (in a (skS.0 1 a_1 a_2)) True) (Eq False True)) % 11.91/12.11 Clause #105 (by clausification #[27]): ∀ (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) % 11.91/12.11 Clause #106 (by superposition #[105, 22]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True) (Eq False True) % 11.91/12.11 Clause #2089 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True % 11.91/12.11 Clause #2090 (by superposition #[2089, 23]): Eq True False % 11.91/12.11 Clause #2100 (by clausification #[2090]): False % 11.91/12.11 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------