%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU756^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:02:22 PM UTC 2025 % Result : Theorem 4.37s 4.56s % Output : Proof 4.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU756^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n008.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 06:27:53 EDT 2025 % 0.15/0.35 % CPUTime : % 4.37/4.56 SZS status Theorem for theBenchmark.p % 4.37/4.56 SZS output start Proof for theBenchmark.p % 4.37/4.56 Clause #0 (by assumption #[]): Eq (Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)) True % 4.37/4.56 Clause #1 (by assumption #[]): Eq (Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B)) True % 4.37/4.56 Clause #2 (by assumption #[]): Eq % 4.37/4.56 (Eq demorgan2b2 % 4.37/4.56 (∀ (A X : Iota), % 4.37/4.56 in X (powerset A) → % 4.37/4.56 ∀ (Y : Iota), % 4.37/4.56 in Y (powerset A) → % 4.37/4.56 ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y)))) % 4.37/4.56 True % 4.37/4.56 Clause #3 (by assumption #[]): Eq % 4.37/4.56 (Not % 4.37/4.56 (binintersectEL → % 4.37/4.56 binintersectER → % 4.37/4.56 demorgan2b2 → % 4.37/4.56 ∀ (A X : Iota), % 4.37/4.56 in X (powerset A) → % 4.37/4.56 ∀ (Y : Iota), % 4.37/4.56 in Y (powerset A) → % 4.37/4.56 ∀ (Xx : Iota), % 4.37/4.56 in Xx A → in Xx (binintersect (setminus A X) (setminus A Y)) → in Xx (setminus A (binunion X Y)))) % 4.37/4.56 True % 4.37/4.56 Clause #4 (by clausification #[1]): Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 4.37/4.56 Clause #20 (by clausification #[0]): Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 4.37/4.56 Clause #24 (by clausification #[2]): Eq demorgan2b2 % 4.37/4.56 (∀ (A X : Iota), % 4.37/4.56 in X (powerset A) → % 4.37/4.56 ∀ (Y : Iota), % 4.37/4.56 in Y (powerset A) → % 4.37/4.56 ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y))) % 4.37/4.56 Clause #55 (by clausification #[3]): Eq % 4.37/4.56 (binintersectEL → % 4.37/4.56 binintersectER → % 4.37/4.56 demorgan2b2 → % 4.37/4.56 ∀ (A X : Iota), % 4.37/4.56 in X (powerset A) → % 4.37/4.56 ∀ (Y : Iota), % 4.37/4.56 in Y (powerset A) → % 4.37/4.56 ∀ (Xx : Iota), % 4.37/4.56 in Xx A → in Xx (binintersect (setminus A X) (setminus A Y)) → in Xx (setminus A (binunion X Y))) % 4.37/4.56 False % 4.37/4.56 Clause #56 (by clausification #[55]): Eq binintersectEL True % 4.37/4.56 Clause #57 (by clausification #[55]): Eq % 4.37/4.56 (binintersectER → % 4.37/4.56 demorgan2b2 → % 4.37/4.56 ∀ (A X : Iota), % 4.37/4.56 in X (powerset A) → % 4.37/4.56 ∀ (Y : Iota), % 4.37/4.56 in Y (powerset A) → % 4.37/4.56 ∀ (Xx : Iota), % 4.37/4.56 in Xx A → in Xx (binintersect (setminus A X) (setminus A Y)) → in Xx (setminus A (binunion X Y))) % 4.37/4.56 False % 4.37/4.56 Clause #58 (by backward demodulation #[56, 20]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 4.37/4.56 Clause #61 (by clausification #[58]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx a) True % 4.37/4.56 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a) True % 4.37/4.56 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_1) True % 4.37/4.56 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_1) True) % 4.37/4.56 Clause #66 (by clausification #[57]): Eq binintersectER True % 4.37/4.56 Clause #67 (by clausification #[57]): Eq % 4.37/4.56 (demorgan2b2 → % 4.37/4.56 ∀ (A X : Iota), % 4.37/4.56 in X (powerset A) → % 4.37/4.56 ∀ (Y : Iota), % 4.37/4.56 in Y (powerset A) → % 4.37/4.56 ∀ (Xx : Iota), % 4.37/4.56 in Xx A → in Xx (binintersect (setminus A X) (setminus A Y)) → in Xx (setminus A (binunion X Y))) % 4.37/4.56 False % 4.37/4.56 Clause #68 (by backward demodulation #[66, 4]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 4.37/4.56 Clause #71 (by clausification #[68]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx B) True % 4.37/4.56 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a_1) True % 4.37/4.56 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_2) True % 4.37/4.56 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_2) True) % 4.37/4.56 Clause #76 (by clausification #[67]): Eq demorgan2b2 True % 4.37/4.56 Clause #77 (by clausification #[67]): Eq % 4.37/4.56 (∀ (A X : Iota), % 4.37/4.56 in X (powerset A) → % 4.37/4.56 ∀ (Y : Iota), % 4.37/4.56 in Y (powerset A) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx A → in Xx (binintersect (setminus A X) (setminus A Y)) → in Xx (setminus A (binunion X Y))) % 4.44/4.59 False % 4.44/4.59 Clause #78 (by backward demodulation #[76, 24]): Eq True % 4.44/4.59 (∀ (A X : Iota), % 4.44/4.59 in X (powerset A) → % 4.44/4.59 ∀ (Y : Iota), % 4.44/4.59 in Y (powerset A) → % 4.44/4.59 ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y))) % 4.44/4.59 Clause #81 (by clausification #[77]): ∀ (a : Iota), % 4.44/4.59 Eq % 4.44/4.59 (Not % 4.44/4.59 (∀ (X : Iota), % 4.44/4.59 in X (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Y : Iota), % 4.44/4.59 in Y (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx (skS.0 8 a) → % 4.44/4.59 in Xx (binintersect (setminus (skS.0 8 a) X) (setminus (skS.0 8 a) Y)) → % 4.44/4.59 in Xx (setminus (skS.0 8 a) (binunion X Y)))) % 4.44/4.59 True % 4.44/4.59 Clause #82 (by clausification #[81]): ∀ (a : Iota), % 4.44/4.59 Eq % 4.44/4.59 (∀ (X : Iota), % 4.44/4.59 in X (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Y : Iota), % 4.44/4.59 in Y (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx (skS.0 8 a) → % 4.44/4.59 in Xx (binintersect (setminus (skS.0 8 a) X) (setminus (skS.0 8 a) Y)) → % 4.44/4.59 in Xx (setminus (skS.0 8 a) (binunion X Y))) % 4.44/4.59 False % 4.44/4.59 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), % 4.44/4.59 Eq % 4.44/4.59 (Not % 4.44/4.59 (in (skS.0 9 a a_1) (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Y : Iota), % 4.44/4.59 in Y (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx (skS.0 8 a) → % 4.44/4.59 in Xx (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) Y)) → % 4.44/4.59 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) Y)))) % 4.44/4.59 True % 4.44/4.59 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), % 4.44/4.59 Eq % 4.44/4.59 (in (skS.0 9 a a_1) (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Y : Iota), % 4.44/4.59 in Y (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx (skS.0 8 a) → % 4.44/4.59 in Xx (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) Y)) → % 4.44/4.59 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) Y))) % 4.44/4.59 False % 4.44/4.59 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), Eq (in (skS.0 9 a a_1) (powerset (skS.0 8 a))) True % 4.44/4.59 Clause #86 (by clausification #[84]): ∀ (a a_1 : Iota), % 4.44/4.59 Eq % 4.44/4.59 (∀ (Y : Iota), % 4.44/4.59 in Y (powerset (skS.0 8 a)) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx (skS.0 8 a) → % 4.44/4.59 in Xx (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) Y)) → % 4.44/4.59 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) Y))) % 4.44/4.59 False % 4.44/4.59 Clause #87 (by clausification #[78]): ∀ (a : Iota), % 4.44/4.59 Eq % 4.44/4.59 (∀ (X : Iota), % 4.44/4.59 in X (powerset a) → % 4.44/4.59 ∀ (Y : Iota), % 4.44/4.59 in Y (powerset a) → % 4.44/4.59 ∀ (Xx : Iota), in Xx a → in Xx (setminus a X) → in Xx (setminus a Y) → in Xx (setminus a (binunion X Y))) % 4.44/4.59 True % 4.44/4.59 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), % 4.44/4.59 Eq % 4.44/4.59 (in a (powerset a_1) → % 4.44/4.59 ∀ (Y : Iota), % 4.44/4.59 in Y (powerset a_1) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx a_1 → in Xx (setminus a_1 a) → in Xx (setminus a_1 Y) → in Xx (setminus a_1 (binunion a Y))) % 4.44/4.59 True % 4.44/4.59 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), % 4.44/4.59 Or (Eq (in a (powerset a_1)) False) % 4.44/4.59 (Eq % 4.44/4.59 (∀ (Y : Iota), % 4.44/4.59 in Y (powerset a_1) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx a_1 → in Xx (setminus a_1 a) → in Xx (setminus a_1 Y) → in Xx (setminus a_1 (binunion a Y))) % 4.44/4.59 True) % 4.44/4.59 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), % 4.44/4.59 Or (Eq (in a (powerset a_1)) False) % 4.44/4.59 (Eq % 4.44/4.59 (in a_2 (powerset a_1) → % 4.44/4.59 ∀ (Xx : Iota), % 4.44/4.59 in Xx a_1 → in Xx (setminus a_1 a) → in Xx (setminus a_1 a_2) → in Xx (setminus a_1 (binunion a a_2))) % 4.44/4.59 True) % 4.44/4.59 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), % 4.44/4.59 Or (Eq (in a (powerset a_1)) False) % 4.44/4.59 (Or (Eq (in a_2 (powerset a_1)) False) % 4.44/4.59 (Eq % 4.44/4.59 (∀ (Xx : Iota), % 4.44/4.59 in Xx a_1 → in Xx (setminus a_1 a) → in Xx (setminus a_1 a_2) → in Xx (setminus a_1 (binunion a a_2))) % 4.44/4.61 True)) % 4.44/4.61 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Or (Eq (in a (powerset a_1)) False) % 4.44/4.61 (Or (Eq (in a_2 (powerset a_1)) False) % 4.44/4.61 (Eq (in a_3 a_1 → in a_3 (setminus a_1 a) → in a_3 (setminus a_1 a_2) → in a_3 (setminus a_1 (binunion a a_2))) % 4.44/4.61 True)) % 4.44/4.61 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Or (Eq (in a (powerset a_1)) False) % 4.44/4.61 (Or (Eq (in a_2 (powerset a_1)) False) % 4.44/4.61 (Or (Eq (in a_3 a_1) False) % 4.44/4.61 (Eq (in a_3 (setminus a_1 a) → in a_3 (setminus a_1 a_2) → in a_3 (setminus a_1 (binunion a a_2))) True))) % 4.44/4.61 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Or (Eq (in a (powerset a_1)) False) % 4.44/4.61 (Or (Eq (in a_2 (powerset a_1)) False) % 4.44/4.61 (Or (Eq (in a_3 a_1) False) % 4.44/4.61 (Or (Eq (in a_3 (setminus a_1 a)) False) % 4.44/4.61 (Eq (in a_3 (setminus a_1 a_2) → in a_3 (setminus a_1 (binunion a a_2))) True)))) % 4.44/4.61 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Or (Eq (in a (powerset a_1)) False) % 4.44/4.61 (Or (Eq (in a_2 (powerset a_1)) False) % 4.44/4.61 (Or (Eq (in a_3 a_1) False) % 4.44/4.61 (Or (Eq (in a_3 (setminus a_1 a)) False) % 4.44/4.61 (Or (Eq (in a_3 (setminus a_1 a_2)) False) (Eq (in a_3 (setminus a_1 (binunion a a_2))) True))))) % 4.44/4.61 Clause #96 (by superposition #[95, 85]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Or (Eq (in a (powerset (skS.0 8 a_1))) False) % 4.44/4.61 (Or (Eq (in a_2 (skS.0 8 a_1)) False) % 4.44/4.61 (Or (Eq (in a_2 (setminus (skS.0 8 a_1) (skS.0 9 a_1 a_3))) False) % 4.44/4.61 (Or (Eq (in a_2 (setminus (skS.0 8 a_1) a)) False) % 4.44/4.61 (Or (Eq (in a_2 (setminus (skS.0 8 a_1) (binunion (skS.0 9 a_1 a_3) a))) True) (Eq False True))))) % 4.44/4.61 Clause #100 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 4.44/4.61 Eq % 4.44/4.61 (Not % 4.44/4.61 (in (skS.0 10 a a_1 a_2) (powerset (skS.0 8 a)) → % 4.44/4.61 ∀ (Xx : Iota), % 4.44/4.61 in Xx (skS.0 8 a) → % 4.44/4.61 in Xx (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) → % 4.44/4.61 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2))))) % 4.44/4.61 True % 4.44/4.61 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 4.44/4.61 Eq % 4.44/4.61 (in (skS.0 10 a a_1 a_2) (powerset (skS.0 8 a)) → % 4.44/4.61 ∀ (Xx : Iota), % 4.44/4.61 in Xx (skS.0 8 a) → % 4.44/4.61 in Xx (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) → % 4.44/4.61 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2)))) % 4.44/4.61 False % 4.44/4.61 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 10 a a_1 a_2) (powerset (skS.0 8 a))) True % 4.44/4.61 Clause #103 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 4.44/4.61 Eq % 4.44/4.61 (∀ (Xx : Iota), % 4.44/4.61 in Xx (skS.0 8 a) → % 4.44/4.61 in Xx (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) → % 4.44/4.61 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2)))) % 4.44/4.61 False % 4.44/4.61 Clause #110 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Eq % 4.44/4.61 (Not % 4.44/4.61 (in (skS.0 12 a a_1 a_2 a_3) (skS.0 8 a) → % 4.44/4.61 in (skS.0 12 a a_1 a_2 a_3) % 4.44/4.61 (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) → % 4.44/4.61 in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2))))) % 4.44/4.61 True % 4.44/4.61 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Eq % 4.44/4.61 (in (skS.0 12 a a_1 a_2 a_3) (skS.0 8 a) → % 4.44/4.61 in (skS.0 12 a a_1 a_2 a_3) % 4.44/4.61 (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) → % 4.44/4.61 in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2)))) % 4.44/4.61 False % 4.44/4.61 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 12 a a_1 a_2 a_3) (skS.0 8 a)) True % 4.44/4.61 Clause #113 (by clausification #[111]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.61 Eq % 4.44/4.61 (in (skS.0 12 a a_1 a_2 a_3) % 4.44/4.61 (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) → % 4.44/4.64 in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2)))) % 4.44/4.64 False % 4.44/4.64 Clause #119 (by clausification #[113]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.64 Eq % 4.44/4.64 (in (skS.0 12 a a_1 a_2 a_3) % 4.44/4.64 (binintersect (setminus (skS.0 8 a) (skS.0 9 a a_1)) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2)))) % 4.44/4.64 True % 4.44/4.64 Clause #120 (by clausification #[113]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.64 Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2)))) False % 4.44/4.64 Clause #121 (by superposition #[119, 64]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.64 Or (Eq True False) (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_1))) True) % 4.44/4.64 Clause #122 (by superposition #[119, 74]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.64 Or (Eq True False) (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) True) % 4.44/4.64 Clause #123 (by clausification #[121]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_1))) True % 4.44/4.64 Clause #124 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 10 a a_1 a_2))) True % 4.44/4.64 Clause #125 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.64 Or (Eq (in a (powerset (skS.0 8 a_1))) False) % 4.44/4.64 (Or (Eq (in a_2 (skS.0 8 a_1)) False) % 4.44/4.64 (Or (Eq (in a_2 (setminus (skS.0 8 a_1) (skS.0 9 a_1 a_3))) False) % 4.44/4.64 (Or (Eq (in a_2 (setminus (skS.0 8 a_1) a)) False) % 4.44/4.64 (Eq (in a_2 (setminus (skS.0 8 a_1) (binunion (skS.0 9 a_1 a_3) a))) True)))) % 4.44/4.64 Clause #127 (by superposition #[125, 102]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.44/4.64 Or (Eq (in a (skS.0 8 a_1)) False) % 4.44/4.64 (Or (Eq (in a (setminus (skS.0 8 a_1) (skS.0 9 a_1 a_2))) False) % 4.44/4.64 (Or (Eq (in a (setminus (skS.0 8 a_1) (skS.0 10 a_1 a_3 a_4))) False) % 4.44/4.64 (Or (Eq (in a (setminus (skS.0 8 a_1) (binunion (skS.0 9 a_1 a_2) (skS.0 10 a_1 a_3 a_4)))) True) % 4.44/4.64 (Eq False True)))) % 4.44/4.64 Clause #140 (by clausification #[127]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.44/4.64 Or (Eq (in a (skS.0 8 a_1)) False) % 4.44/4.64 (Or (Eq (in a (setminus (skS.0 8 a_1) (skS.0 9 a_1 a_2))) False) % 4.44/4.64 (Or (Eq (in a (setminus (skS.0 8 a_1) (skS.0 10 a_1 a_3 a_4))) False) % 4.44/4.64 (Eq (in a (setminus (skS.0 8 a_1) (binunion (skS.0 9 a_1 a_2) (skS.0 10 a_1 a_3 a_4)))) True))) % 4.44/4.64 Clause #141 (by superposition #[140, 112]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.44/4.64 Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_4))) False) % 4.44/4.64 (Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 10 a a_5 a_6))) False) % 4.44/4.64 (Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_4) (skS.0 10 a a_5 a_6)))) True) % 4.44/4.64 (Eq False True))) % 4.44/4.64 Clause #150 (by clausification #[141]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 4.44/4.64 Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_4))) False) % 4.44/4.64 (Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 10 a a_5 a_6))) False) % 4.44/4.64 (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_4) (skS.0 10 a a_5 a_6)))) True)) % 4.44/4.64 Clause #151 (by superposition #[150, 123]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.44/4.64 Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 10 a a_4 a_5))) False) % 4.44/4.64 (Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_4 a_5)))) True) % 4.44/4.64 (Eq False True)) % 4.44/4.64 Clause #153 (by clausification #[151]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.44/4.64 Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 10 a a_4 a_5))) False) % 4.44/4.64 (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_4 a_5)))) True) % 4.44/4.64 Clause #154 (by superposition #[153, 124]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.64 Or (Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2)))) True) % 4.44/4.64 (Eq False True) % 4.44/4.64 Clause #155 (by clausification #[154]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.64 Eq (in (skS.0 12 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 10 a a_1 a_2)))) True % 4.44/4.64 Clause #156 (by superposition #[155, 120]): Eq True False % 4.44/4.64 Clause #157 (by clausification #[156]): False % 4.44/4.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------