%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU523^2 : 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 08:01:49 PM UTC 2025 % Result : Theorem 3.77s 3.94s % Output : Proof 3.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU523^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % Command : duper %s % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 05:07:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.77/3.94 SZS status Theorem for theBenchmark.p % 3.77/3.94 SZS output start Proof for theBenchmark.p % 3.77/3.94 Clause #0 (by assumption #[]): Eq (Eq setunionAx (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A)))) True % 3.77/3.94 Clause #1 (by assumption #[]): Eq % 3.77/3.94 (Not % 3.77/3.94 (setunionAx → % 3.77/3.94 ∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi)) % 3.77/3.94 True % 3.77/3.94 Clause #2 (by clausification #[1]): Eq (setunionAx → ∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi) % 3.77/3.94 False % 3.77/3.94 Clause #3 (by clausification #[2]): Eq setunionAx True % 3.77/3.94 Clause #4 (by clausification #[2]): Eq (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi) False % 3.77/3.94 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 3.77/3.94 Eq % 3.77/3.94 (Not % 3.77/3.94 (∀ (Xx : Iota), % 3.77/3.94 in Xx (setunion (skS.0 0 a)) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B (skS.0 0 a) → Xphi) → Xphi)) % 3.77/3.94 True % 3.77/3.94 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 3.77/3.94 Eq % 3.77/3.94 (∀ (Xx : Iota), % 3.77/3.94 in Xx (setunion (skS.0 0 a)) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B (skS.0 0 a) → Xphi) → Xphi) % 3.77/3.94 False % 3.77/3.94 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.77/3.94 Eq % 3.77/3.94 (Not % 3.77/3.94 (in (skS.0 1 a a_1) (setunion (skS.0 0 a)) → % 3.77/3.94 ∀ (Xphi : Prop), (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → Xphi) → Xphi)) % 3.77/3.94 True % 3.77/3.94 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 3.77/3.94 Eq % 3.77/3.94 (in (skS.0 1 a a_1) (setunion (skS.0 0 a)) → % 3.77/3.94 ∀ (Xphi : Prop), (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → Xphi) → Xphi) % 3.77/3.94 False % 3.77/3.94 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (setunion (skS.0 0 a))) True % 3.77/3.94 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (∀ (Xphi : Prop), (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → Xphi) → Xphi) False % 3.77/3.94 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota) (a_2 : Prop), % 3.77/3.94 Eq (Not ((∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → skS.0 2 a a_1 a_2) → skS.0 2 a a_1 a_2)) True % 3.77/3.94 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota) (a_2 : Prop), % 3.77/3.94 Eq ((∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → skS.0 2 a a_1 a_2) → skS.0 2 a a_1 a_2) False % 3.77/3.94 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota) (a_2 : Prop), Eq (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → skS.0 2 a a_1 a_2) True % 3.77/3.94 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota) (a_2 : Prop), Eq (skS.0 2 a a_1 a_2) False % 3.77/3.94 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (in (skS.0 1 a a_1) a_2 → in a_2 (skS.0 0 a) → skS.0 2 a a_1 a_3) True % 3.77/3.94 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.77/3.94 Or (Eq (in (skS.0 1 a a_1) a_2) False) (Eq (in a_2 (skS.0 0 a) → skS.0 2 a a_1 a_3) True) % 3.77/3.94 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.77/3.94 Or (Eq (in (skS.0 1 a a_1) a_2) False) (Or (Eq (in a_2 (skS.0 0 a)) False) (Eq (skS.0 2 a a_1 a_3) True)) % 3.77/3.94 Clause #18 (by identity loobHoist #[17]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.77/3.94 Or (Eq (in (skS.0 1 a a_1) a_2) False) % 3.77/3.94 (Or (Eq (in a_2 (skS.0 0 a)) False) (Or (Eq (skS.0 2 a a_1 True) True) (Eq a_3 False))) % 3.77/3.94 Clause #21 (by identity loobHoist #[14]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (skS.0 2 a a_1 True) False) (Eq a_2 False) % 3.77/3.94 Clause #23 (by clausification #[0]): Eq setunionAx (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A))) % 3.77/3.94 Clause #24 (by forward demodulation #[23, 3]): Eq True (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A))) % 3.77/3.94 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Xx : Iota), Iff (in Xx (setunion a)) (Exists fun B => And (in Xx B) (in B a))) True % 3.77/3.94 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Iff (in a (setunion a_1)) (Exists fun B => And (in a B) (in B a_1))) True % 3.77/3.94 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (Exists fun B => And (in a B) (in B a_1)) True) % 3.80/3.96 Clause #32 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 3.80/3.96 Or (Eq (in a (setunion a_1)) False) (Eq (And (in a (skS.0 3 a a_1 a_2)) (in (skS.0 3 a a_1 a_2) a_1)) True) % 3.80/3.96 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (in (skS.0 3 a a_1 a_2) a_1) True) % 3.80/3.96 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (in a (skS.0 3 a a_1 a_2)) True) % 3.80/3.96 Clause #35 (by superposition #[33, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) (Eq False True) % 3.80/3.96 Clause #36 (by superposition #[34, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True) (Eq False True) % 3.80/3.96 Clause #39 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True % 3.80/3.96 Clause #43 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True % 3.80/3.96 Clause #44 (by superposition #[43, 18]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.80/3.96 Or (Eq True False) % 3.80/3.96 (Or (Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False) % 3.80/3.96 (Or (Eq (skS.0 2 a a_1 True) True) (Eq a_3 False))) % 3.80/3.96 Clause #50 (by clausification #[44]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.80/3.96 Or (Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False) % 3.80/3.96 (Or (Eq (skS.0 2 a a_1 True) True) (Eq a_3 False)) % 3.80/3.96 Clause #51 (by superposition #[50, 39]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (skS.0 2 a a_1 True) True) (Or (Eq a_2 False) (Eq False True)) % 3.80/3.96 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (skS.0 2 a a_1 True) True) (Eq a_2 False) % 3.80/3.96 Clause #54 (by falseElim #[52]): ∀ (a a_1 : Iota), Eq (skS.0 2 a a_1 True) True % 3.80/3.96 Clause #55 (by superposition #[54, 21]): ∀ (a : Prop), Or (Eq True False) (Eq a False) % 3.80/3.96 Clause #56 (by clausification #[55]): ∀ (a : Prop), Eq a False % 3.80/3.96 Clause #58 (by falseElim #[56]): False % 3.80/3.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------