%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU754^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 96.08s 96.23s % Output : Proof 96.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU754^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n021.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 05:51:08 EDT 2025 % 0.13/0.34 % CPUTime : % 96.08/96.23 SZS status Theorem for theBenchmark.p % 96.08/96.23 SZS output start Proof for theBenchmark.p % 96.08/96.23 Clause #0 (by assumption #[]): Eq (Eq binintersectI (∀ (A B Xx : Iota), in Xx A → in Xx B → in Xx (binintersect A B))) True % 96.08/96.23 Clause #1 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True % 96.08/96.23 Clause #2 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 96.08/96.23 Clause #3 (by assumption #[]): Eq % 96.08/96.23 (Eq binunionTILcontra % 96.08/96.23 (∀ (A X : Iota), % 96.08/96.23 in X (powerset A) → % 96.08/96.23 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X))) % 96.08/96.23 True % 96.08/96.23 Clause #4 (by assumption #[]): Eq % 96.08/96.23 (Eq binunionTIRcontra % 96.08/96.23 (∀ (A X : Iota), % 96.08/96.23 in X (powerset A) → % 96.08/96.23 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx Y))) % 96.08/96.23 True % 96.08/96.23 Clause #5 (by assumption #[]): Eq % 96.08/96.23 (Not % 96.08/96.23 (binintersectI → % 96.08/96.23 setminusI → % 96.08/96.23 setminusER → % 96.08/96.23 binunionTILcontra → % 96.08/96.23 binunionTIRcontra → % 96.08/96.23 ∀ (A X : Iota), % 96.08/96.23 in X (powerset A) → % 96.08/96.23 ∀ (Y : Iota), % 96.08/96.23 in Y (powerset A) → % 96.08/96.23 ∀ (Xx : Iota), % 96.08/96.23 in Xx A → % 96.08/96.23 in Xx (setminus A (binunion X Y)) → in Xx (binintersect (setminus A X) (setminus A Y)))) % 96.08/96.23 True % 96.08/96.23 Clause #6 (by clausification #[2]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 96.08/96.23 Clause #23 (by clausification #[1]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 96.08/96.23 Clause #27 (by clausification #[0]): Eq binintersectI (∀ (A B Xx : Iota), in Xx A → in Xx B → in Xx (binintersect A B)) % 96.08/96.23 Clause #58 (by clausification #[3]): Eq binunionTILcontra % 96.08/96.23 (∀ (A X : Iota), % 96.08/96.23 in X (powerset A) → % 96.08/96.23 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 96.08/96.23 Clause #78 (by clausification #[4]): Eq binunionTIRcontra % 96.08/96.24 (∀ (A X : Iota), % 96.08/96.24 in X (powerset A) → % 96.08/96.24 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx Y)) % 96.08/96.24 Clause #92 (by clausification #[5]): Eq % 96.08/96.24 (binintersectI → % 96.08/96.24 setminusI → % 96.08/96.24 setminusER → % 96.08/96.24 binunionTILcontra → % 96.08/96.24 binunionTIRcontra → % 96.08/96.24 ∀ (A X : Iota), % 96.08/96.24 in X (powerset A) → % 96.08/96.24 ∀ (Y : Iota), % 96.08/96.24 in Y (powerset A) → % 96.08/96.24 ∀ (Xx : Iota), % 96.08/96.24 in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (binintersect (setminus A X) (setminus A Y))) % 96.08/96.24 False % 96.08/96.24 Clause #93 (by clausification #[92]): Eq binintersectI True % 96.08/96.24 Clause #94 (by clausification #[92]): Eq % 96.08/96.24 (setminusI → % 96.08/96.24 setminusER → % 96.08/96.24 binunionTILcontra → % 96.08/96.24 binunionTIRcontra → % 96.08/96.24 ∀ (A X : Iota), % 96.08/96.24 in X (powerset A) → % 96.08/96.24 ∀ (Y : Iota), % 96.08/96.24 in Y (powerset A) → % 96.08/96.24 ∀ (Xx : Iota), % 96.08/96.24 in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (binintersect (setminus A X) (setminus A Y))) % 96.08/96.24 False % 96.08/96.24 Clause #95 (by backward demodulation #[93, 27]): Eq True (∀ (A B Xx : Iota), in Xx A → in Xx B → in Xx (binintersect A B)) % 96.08/96.24 Clause #98 (by clausification #[95]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → in Xx B → in Xx (binintersect a B)) True % 96.08/96.24 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx a_1 → in Xx (binintersect a a_1)) True % 96.08/96.24 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a a_2 → in a (binintersect a_1 a_2)) True % 96.08/96.24 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a a_2 → in a (binintersect a_1 a_2)) True) % 96.08/96.24 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a a_2) False) (Eq (in a (binintersect a_1 a_2)) True)) % 96.08/96.24 Clause #138 (by clausification #[94]): Eq setminusI True % 96.08/96.26 Clause #139 (by clausification #[94]): Eq % 96.08/96.26 (setminusER → % 96.08/96.26 binunionTILcontra → % 96.08/96.26 binunionTIRcontra → % 96.08/96.26 ∀ (A X : Iota), % 96.08/96.26 in X (powerset A) → % 96.08/96.26 ∀ (Y : Iota), % 96.08/96.26 in Y (powerset A) → % 96.08/96.26 ∀ (Xx : Iota), % 96.08/96.26 in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (binintersect (setminus A X) (setminus A Y))) % 96.08/96.26 False % 96.08/96.26 Clause #140 (by backward demodulation #[138, 23]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 96.08/96.26 Clause #143 (by clausification #[140]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True % 96.08/96.26 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True % 96.08/96.26 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True % 96.08/96.26 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a a_2) → in a (setminus a_1 a_2)) True) % 96.08/96.26 Clause #147 (by clausification #[146]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (Not (in a a_2)) False) (Eq (in a (setminus a_1 a_2)) True)) % 96.08/96.26 Clause #148 (by clausification #[147]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a (setminus a_1 a_2)) True) (Eq (in a a_2) True)) % 96.08/96.26 Clause #157 (by clausification #[139]): Eq setminusER True % 96.08/96.26 Clause #158 (by clausification #[139]): Eq % 96.08/96.26 (binunionTILcontra → % 96.08/96.26 binunionTIRcontra → % 96.08/96.26 ∀ (A X : Iota), % 96.08/96.26 in X (powerset A) → % 96.08/96.26 ∀ (Y : Iota), % 96.08/96.26 in Y (powerset A) → % 96.08/96.26 ∀ (Xx : Iota), % 96.08/96.26 in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (binintersect (setminus A X) (setminus A Y))) % 96.08/96.26 False % 96.08/96.26 Clause #159 (by backward demodulation #[157, 6]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) % 96.08/96.26 Clause #167 (by clausification #[159]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True % 96.08/96.26 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True % 96.08/96.26 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True % 96.08/96.26 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True) % 96.08/96.26 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False) % 96.08/96.26 Clause #172 (by clausification #[158]): Eq binunionTILcontra True % 96.08/96.26 Clause #173 (by clausification #[158]): Eq % 96.08/96.26 (binunionTIRcontra → % 96.08/96.26 ∀ (A X : Iota), % 96.08/96.26 in X (powerset A) → % 96.08/96.26 ∀ (Y : Iota), % 96.08/96.26 in Y (powerset A) → % 96.08/96.26 ∀ (Xx : Iota), % 96.08/96.26 in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (binintersect (setminus A X) (setminus A Y))) % 96.08/96.26 False % 96.08/96.26 Clause #174 (by backward demodulation #[172, 58]): Eq True % 96.08/96.26 (∀ (A X : Iota), % 96.08/96.26 in X (powerset A) → % 96.08/96.26 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 96.08/96.26 Clause #179 (by clausification #[174]): ∀ (a : Iota), % 96.08/96.26 Eq % 96.08/96.26 (∀ (X : Iota), % 96.08/96.26 in X (powerset a) → % 96.08/96.26 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 96.08/96.26 True % 96.08/96.26 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), % 96.08/96.26 Eq % 96.08/96.26 (in a (powerset a_1) → % 96.08/96.26 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx a)) % 96.08/96.26 True % 96.08/96.26 Clause #181 (by clausification #[180]): ∀ (a a_1 : Iota), % 96.08/96.26 Or (Eq (in a (powerset a_1)) False) % 96.08/96.26 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx a)) % 96.08/96.26 True) % 96.08/96.26 Clause #182 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 96.08/96.26 Or (Eq (in a (powerset a_1)) False) % 96.08/96.26 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a)) True) % 96.13/96.28 Clause #183 (by clausification #[182]): ∀ (a a_1 a_2 : Iota), % 96.13/96.28 Or (Eq (in a (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.28 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a)) True)) % 96.13/96.28 Clause #184 (by clausification #[183]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.28 Or (Eq (in a (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (in a_3 a_1 → Not (in a_3 (binunion a a_2)) → Not (in a_3 a)) True)) % 96.13/96.28 Clause #185 (by clausification #[184]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.28 Or (Eq (in a (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 (binunion a a_2)) → Not (in a_3 a)) True))) % 96.13/96.28 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.28 Or (Eq (in a (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 (binunion a a_2))) False) (Eq (Not (in a_3 a)) True)))) % 96.13/96.28 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.28 Or (Eq (in a (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 a)) True) (Eq (in a_3 (binunion a a_2)) True)))) % 96.13/96.28 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.28 Or (Eq (in a (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.28 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 (binunion a a_2)) True) (Eq (in a_3 a) False)))) % 96.13/96.28 Clause #191 (by clausification #[173]): Eq binunionTIRcontra True % 96.13/96.28 Clause #192 (by clausification #[173]): Eq % 96.13/96.28 (∀ (A X : Iota), % 96.13/96.28 in X (powerset A) → % 96.13/96.28 ∀ (Y : Iota), % 96.13/96.28 in Y (powerset A) → % 96.13/96.28 ∀ (Xx : Iota), % 96.13/96.28 in Xx A → in Xx (setminus A (binunion X Y)) → in Xx (binintersect (setminus A X) (setminus A Y))) % 96.13/96.28 False % 96.13/96.28 Clause #193 (by backward demodulation #[191, 78]): Eq True % 96.13/96.28 (∀ (A X : Iota), % 96.13/96.28 in X (powerset A) → % 96.13/96.28 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx Y)) % 96.13/96.29 Clause #200 (by clausification #[193]): ∀ (a : Iota), % 96.13/96.29 Eq % 96.13/96.29 (∀ (X : Iota), % 96.13/96.29 in X (powerset a) → % 96.13/96.29 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx (binunion X Y)) → Not (in Xx Y)) % 96.13/96.29 True % 96.13/96.29 Clause #201 (by clausification #[200]): ∀ (a a_1 : Iota), % 96.13/96.29 Eq % 96.13/96.29 (in a (powerset a_1) → % 96.13/96.29 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx Y)) % 96.13/96.29 True % 96.13/96.29 Clause #202 (by clausification #[201]): ∀ (a a_1 : Iota), % 96.13/96.29 Or (Eq (in a (powerset a_1)) False) % 96.13/96.29 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx Y)) % 96.13/96.29 True) % 96.13/96.29 Clause #203 (by clausification #[202]): ∀ (a a_1 a_2 : Iota), % 96.13/96.29 Or (Eq (in a (powerset a_1)) False) % 96.13/96.29 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a_2)) True) % 96.13/96.29 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota), % 96.13/96.29 Or (Eq (in a (powerset a_1)) False) % 96.13/96.29 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.29 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a_2)) True)) % 96.13/96.29 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.29 Or (Eq (in a (powerset a_1)) False) % 96.13/96.29 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (in a_3 a_1 → Not (in a_3 (binunion a a_2)) → Not (in a_3 a_2)) True)) % 96.13/96.29 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.29 Or (Eq (in a (powerset a_1)) False) % 96.13/96.29 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.29 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 (binunion a a_2)) → Not (in a_3 a_2)) True))) % 96.13/96.29 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.29 Or (Eq (in a (powerset a_1)) False) % 96.13/96.29 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.29 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 (binunion a a_2))) False) (Eq (Not (in a_3 a_2)) True)))) % 96.13/96.29 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.29 Or (Eq (in a (powerset a_1)) False) % 96.13/96.29 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.31 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 a_2)) True) (Eq (in a_3 (binunion a a_2)) True)))) % 96.13/96.31 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.31 Or (Eq (in a (powerset a_1)) False) % 96.13/96.31 (Or (Eq (in a_2 (powerset a_1)) False) % 96.13/96.31 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 (binunion a a_2)) True) (Eq (in a_3 a_2) False)))) % 96.13/96.31 Clause #210 (by clausification #[192]): ∀ (a : Iota), % 96.13/96.31 Eq % 96.13/96.31 (Not % 96.13/96.31 (∀ (X : Iota), % 96.13/96.31 in X (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Y : Iota), % 96.13/96.31 in Y (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Xx : Iota), % 96.13/96.31 in Xx (skS.0 17 a) → % 96.13/96.31 in Xx (setminus (skS.0 17 a) (binunion X Y)) → % 96.13/96.31 in Xx (binintersect (setminus (skS.0 17 a) X) (setminus (skS.0 17 a) Y)))) % 96.13/96.31 True % 96.13/96.31 Clause #211 (by clausification #[210]): ∀ (a : Iota), % 96.13/96.31 Eq % 96.13/96.31 (∀ (X : Iota), % 96.13/96.31 in X (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Y : Iota), % 96.13/96.31 in Y (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Xx : Iota), % 96.13/96.31 in Xx (skS.0 17 a) → % 96.13/96.31 in Xx (setminus (skS.0 17 a) (binunion X Y)) → % 96.13/96.31 in Xx (binintersect (setminus (skS.0 17 a) X) (setminus (skS.0 17 a) Y))) % 96.13/96.31 False % 96.13/96.31 Clause #212 (by clausification #[211]): ∀ (a a_1 : Iota), % 96.13/96.31 Eq % 96.13/96.31 (Not % 96.13/96.31 (in (skS.0 18 a a_1) (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Y : Iota), % 96.13/96.31 in Y (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Xx : Iota), % 96.13/96.31 in Xx (skS.0 17 a) → % 96.13/96.31 in Xx (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) Y)) → % 96.13/96.31 in Xx (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) Y)))) % 96.13/96.31 True % 96.13/96.31 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota), % 96.13/96.31 Eq % 96.13/96.31 (in (skS.0 18 a a_1) (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Y : Iota), % 96.13/96.31 in Y (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Xx : Iota), % 96.13/96.31 in Xx (skS.0 17 a) → % 96.13/96.31 in Xx (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) Y)) → % 96.13/96.31 in Xx (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) Y))) % 96.13/96.31 False % 96.13/96.31 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota), Eq (in (skS.0 18 a a_1) (powerset (skS.0 17 a))) True % 96.13/96.31 Clause #215 (by clausification #[213]): ∀ (a a_1 : Iota), % 96.13/96.31 Eq % 96.13/96.31 (∀ (Y : Iota), % 96.13/96.31 in Y (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Xx : Iota), % 96.13/96.31 in Xx (skS.0 17 a) → % 96.13/96.31 in Xx (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) Y)) → % 96.13/96.31 in Xx (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) Y))) % 96.13/96.31 False % 96.13/96.31 Clause #216 (by superposition #[214, 188]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.31 Or (Eq True False) % 96.13/96.31 (Or (Eq (in a (powerset (skS.0 17 a_1))) False) % 96.13/96.31 (Or (Eq (in a_2 (skS.0 17 a_1)) False) % 96.13/96.31 (Or (Eq (in a_2 (binunion (skS.0 18 a_1 a_3) a)) True) (Eq (in a_2 (skS.0 18 a_1 a_3)) False)))) % 96.13/96.31 Clause #217 (by superposition #[214, 209]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.31 Or (Eq True False) % 96.13/96.31 (Or (Eq (in a (powerset (skS.0 17 a_1))) False) % 96.13/96.31 (Or (Eq (in a_2 (skS.0 17 a_1)) False) % 96.13/96.31 (Or (Eq (in a_2 (binunion (skS.0 18 a_1 a_3) a)) True) (Eq (in a_2 a) False)))) % 96.13/96.31 Clause #248 (by clausification #[215]): ∀ (a a_1 a_2 : Iota), % 96.13/96.31 Eq % 96.13/96.31 (Not % 96.13/96.31 (in (skS.0 19 a a_1 a_2) (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Xx : Iota), % 96.13/96.31 in Xx (skS.0 17 a) → % 96.13/96.31 in Xx (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) → % 96.13/96.31 in Xx % 96.13/96.31 (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) (skS.0 19 a a_1 a_2))))) % 96.13/96.31 True % 96.13/96.31 Clause #249 (by clausification #[248]): ∀ (a a_1 a_2 : Iota), % 96.13/96.31 Eq % 96.13/96.31 (in (skS.0 19 a a_1 a_2) (powerset (skS.0 17 a)) → % 96.13/96.31 ∀ (Xx : Iota), % 96.13/96.31 in Xx (skS.0 17 a) → % 96.13/96.31 in Xx (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) → % 96.13/96.31 in Xx (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) (skS.0 19 a a_1 a_2)))) % 96.13/96.31 False % 96.13/96.31 Clause #250 (by clausification #[249]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 19 a a_1 a_2) (powerset (skS.0 17 a))) True % 96.13/96.34 Clause #251 (by clausification #[249]): ∀ (a a_1 a_2 : Iota), % 96.13/96.34 Eq % 96.13/96.34 (∀ (Xx : Iota), % 96.13/96.34 in Xx (skS.0 17 a) → % 96.13/96.34 in Xx (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) → % 96.13/96.34 in Xx (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) (skS.0 19 a a_1 a_2)))) % 96.13/96.34 False % 96.13/96.34 Clause #290 (by clausification #[217]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.34 Or (Eq (in a (powerset (skS.0 17 a_1))) False) % 96.13/96.34 (Or (Eq (in a_2 (skS.0 17 a_1)) False) % 96.13/96.34 (Or (Eq (in a_2 (binunion (skS.0 18 a_1 a_3) a)) True) (Eq (in a_2 a) False))) % 96.13/96.34 Clause #292 (by superposition #[290, 250]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.13/96.34 Or (Eq (in a (skS.0 17 a_1)) False) % 96.13/96.34 (Or (Eq (in a (binunion (skS.0 18 a_1 a_2) (skS.0 19 a_1 a_3 a_4))) True) % 96.13/96.34 (Or (Eq (in a (skS.0 19 a_1 a_3 a_4)) False) (Eq False True))) % 96.13/96.34 Clause #301 (by clausification #[251]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.34 Eq % 96.13/96.34 (Not % 96.13/96.34 (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a) → % 96.13/96.34 in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) → % 96.13/96.34 in (skS.0 20 a a_1 a_2 a_3) % 96.13/96.34 (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) (skS.0 19 a a_1 a_2))))) % 96.13/96.34 True % 96.13/96.34 Clause #302 (by clausification #[301]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.34 Eq % 96.13/96.34 (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a) → % 96.13/96.34 in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) → % 96.13/96.34 in (skS.0 20 a a_1 a_2 a_3) % 96.13/96.34 (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) (skS.0 19 a a_1 a_2)))) % 96.13/96.34 False % 96.13/96.34 Clause #303 (by clausification #[302]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a)) True % 96.13/96.34 Clause #304 (by clausification #[302]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.34 Eq % 96.13/96.34 (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) → % 96.13/96.34 in (skS.0 20 a a_1 a_2 a_3) % 96.13/96.34 (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) (skS.0 19 a a_1 a_2)))) % 96.13/96.34 False % 96.13/96.34 Clause #306 (by superposition #[303, 148]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.13/96.34 Or (Eq True False) % 96.13/96.34 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 17 a) a_4)) True) (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True)) % 96.13/96.34 Clause #307 (by clausification #[306]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.13/96.34 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 17 a) a_4)) True) (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True) % 96.13/96.34 Clause #309 (by superposition #[307, 102]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 96.13/96.34 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True) % 96.13/96.34 (Or (Eq True False) % 96.13/96.34 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) a_5) False) % 96.13/96.34 (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (setminus (skS.0 17 a) a_4) a_5)) True))) % 96.13/96.34 Clause #408 (by clausification #[216]): ∀ (a a_1 a_2 a_3 : Iota), % 96.13/96.34 Or (Eq (in a (powerset (skS.0 17 a_1))) False) % 96.13/96.34 (Or (Eq (in a_2 (skS.0 17 a_1)) False) % 96.13/96.34 (Or (Eq (in a_2 (binunion (skS.0 18 a_1 a_3) a)) True) (Eq (in a_2 (skS.0 18 a_1 a_3)) False))) % 96.13/96.34 Clause #410 (by superposition #[408, 250]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.13/96.34 Or (Eq (in a (skS.0 17 a_1)) False) % 96.13/96.34 (Or (Eq (in a (binunion (skS.0 18 a_1 a_2) (skS.0 19 a_1 a_3 a_4))) True) % 96.13/96.34 (Or (Eq (in a (skS.0 18 a_1 a_2)) False) (Eq False True))) % 96.13/96.34 Clause #413 (by clausification #[410]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.13/96.34 Or (Eq (in a (skS.0 17 a_1)) False) % 96.13/96.34 (Or (Eq (in a (binunion (skS.0 18 a_1 a_2) (skS.0 19 a_1 a_3 a_4))) True) (Eq (in a (skS.0 18 a_1 a_2)) False)) % 96.13/96.34 Clause #414 (by superposition #[413, 303]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 96.13/96.34 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_4) (skS.0 19 a a_5 a_6))) True) % 96.13/96.34 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_4)) False) (Eq False True)) % 96.13/96.34 Clause #511 (by clausification #[292]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.13/96.34 Or (Eq (in a (skS.0 17 a_1)) False) % 96.13/96.34 (Or (Eq (in a (binunion (skS.0 18 a_1 a_2) (skS.0 19 a_1 a_3 a_4))) True) (Eq (in a (skS.0 19 a_1 a_3 a_4)) False)) % 96.24/96.43 Clause #512 (by superposition #[511, 303]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_4) (skS.0 19 a a_5 a_6))) True) % 96.24/96.43 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 19 a a_5 a_6)) False) (Eq False True)) % 96.24/96.43 Clause #579 (by clausification #[304]): ∀ (a a_1 a_2 a_3 : Iota), % 96.24/96.43 Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 17 a) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2)))) True % 96.24/96.43 Clause #580 (by clausification #[304]): ∀ (a a_1 a_2 a_3 : Iota), % 96.24/96.43 Eq % 96.24/96.43 (in (skS.0 20 a a_1 a_2 a_3) % 96.24/96.43 (binintersect (setminus (skS.0 17 a) (skS.0 18 a a_1)) (setminus (skS.0 17 a) (skS.0 19 a a_1 a_2)))) % 96.24/96.43 False % 96.24/96.43 Clause #581 (by superposition #[579, 171]): ∀ (a a_1 a_2 a_3 : Iota), % 96.24/96.43 Or (Eq True False) (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) False) % 96.24/96.43 Clause #586 (by clausification #[581]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_1) (skS.0 19 a a_1 a_2))) False % 96.24/96.43 Clause #694 (by clausification #[309]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True) % 96.24/96.43 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) a_5) False) % 96.24/96.43 (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (setminus (skS.0 17 a) a_4) a_5)) True)) % 96.24/96.43 Clause #696 (by superposition #[694, 307]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True) % 96.24/96.43 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (setminus (skS.0 17 a) a_4) (setminus (skS.0 17 a) a_5))) True) % 96.24/96.43 (Or (Eq False True) (Eq (in (skS.0 20 a a_1 a_2 a_3) a_5) True))) % 96.24/96.43 Clause #2053 (by clausification #[414]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_4) (skS.0 19 a a_5 a_6))) True) % 96.24/96.43 (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_4)) False) % 96.24/96.43 Clause #2456 (by clausification #[512]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_4) (skS.0 19 a a_5 a_6))) True) % 96.24/96.43 (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 19 a a_5 a_6)) False) % 96.24/96.43 Clause #7645 (by clausification #[696]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True) % 96.24/96.43 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (setminus (skS.0 17 a) a_4) (setminus (skS.0 17 a) a_5))) True) % 96.24/96.43 (Eq (in (skS.0 20 a a_1 a_2 a_3) a_5) True)) % 96.24/96.43 Clause #7646 (by superposition #[7645, 580]): ∀ (a a_1 a_2 a_3 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_1)) True) % 96.24/96.43 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 19 a a_1 a_2)) True) (Eq True False)) % 96.24/96.43 Clause #7662 (by clausification #[7646]): ∀ (a a_1 a_2 a_3 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_1)) True) % 96.24/96.43 (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 19 a a_1 a_2)) True) % 96.24/96.43 Clause #7663 (by superposition #[7662, 2456]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_1)) True) % 96.24/96.43 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_4) (skS.0 19 a a_1 a_2))) True) (Eq True False)) % 96.24/96.43 Clause #7741 (by clausification #[7663]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_1)) True) % 96.24/96.43 (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_4) (skS.0 19 a a_1 a_2))) True) % 96.24/96.43 Clause #7742 (by superposition #[7741, 586]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_1)) True) (Eq True False) % 96.24/96.43 Clause #7758 (by clausification #[7742]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 18 a a_1)) True % 96.24/96.43 Clause #7765 (by superposition #[7758, 2053]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 96.24/96.43 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_1) (skS.0 19 a a_4 a_5))) True) (Eq True False) % 96.24/96.43 Clause #7873 (by clausification #[7765]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (binunion (skS.0 18 a a_1) (skS.0 19 a a_4 a_5))) True % 96.24/96.43 Clause #7874 (by superposition #[7873, 586]): Eq True False % 96.24/96.43 Clause #7890 (by clausification #[7874]): False % 96.24/96.43 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------