%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU746^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:02:21 PM UTC 2025 % Result : Theorem 5.66s 5.88s % Output : Proof 5.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU746^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n007.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 05:43:53 EDT 2025 % 0.13/0.35 % CPUTime : % 5.66/5.88 SZS status Theorem for theBenchmark.p % 5.66/5.88 SZS output start Proof for theBenchmark.p % 5.66/5.88 Clause #0 (by assumption #[]): Eq (Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))) True % 5.66/5.88 Clause #1 (by assumption #[]): Eq % 5.66/5.88 (Not % 5.66/5.88 (binunionE → % 5.66/5.88 ∀ (A X : Iota), % 5.66/5.88 in X (powerset A) → % 5.66/5.88 ∀ (Y : Iota), % 5.66/5.88 in Y (powerset A) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), in Xx A → in Xx (binunion X Y) → (in Xx X → Xphi) → (in Xx Y → Xphi) → Xphi)) % 5.66/5.88 True % 5.66/5.88 Clause #2 (by clausification #[1]): Eq % 5.66/5.88 (binunionE → % 5.66/5.88 ∀ (A X : Iota), % 5.66/5.88 in X (powerset A) → % 5.66/5.88 ∀ (Y : Iota), % 5.66/5.88 in Y (powerset A) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), in Xx A → in Xx (binunion X Y) → (in Xx X → Xphi) → (in Xx Y → Xphi) → Xphi) % 5.66/5.88 False % 5.66/5.88 Clause #3 (by clausification #[2]): Eq binunionE True % 5.66/5.88 Clause #4 (by clausification #[2]): Eq % 5.66/5.88 (∀ (A X : Iota), % 5.66/5.88 in X (powerset A) → % 5.66/5.88 ∀ (Y : Iota), % 5.66/5.88 in Y (powerset A) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), in Xx A → in Xx (binunion X Y) → (in Xx X → Xphi) → (in Xx Y → Xphi) → Xphi) % 5.66/5.88 False % 5.66/5.88 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 5.66/5.88 Eq % 5.66/5.88 (Not % 5.66/5.88 (∀ (X : Iota), % 5.66/5.88 in X (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Y : Iota), % 5.66/5.88 in Y (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → in Xx (binunion X Y) → (in Xx X → Xphi) → (in Xx Y → Xphi) → Xphi)) % 5.66/5.88 True % 5.66/5.88 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 5.66/5.88 Eq % 5.66/5.88 (∀ (X : Iota), % 5.66/5.88 in X (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Y : Iota), % 5.66/5.88 in Y (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → in Xx (binunion X Y) → (in Xx X → Xphi) → (in Xx Y → Xphi) → Xphi) % 5.66/5.88 False % 5.66/5.88 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 5.66/5.88 Eq % 5.66/5.88 (Not % 5.66/5.88 (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Y : Iota), % 5.66/5.88 in Y (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → % 5.66/5.88 in Xx (binunion (skS.0 1 a a_1) Y) → (in Xx (skS.0 1 a a_1) → Xphi) → (in Xx Y → Xphi) → Xphi)) % 5.66/5.88 True % 5.66/5.88 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 5.66/5.88 Eq % 5.66/5.88 (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Y : Iota), % 5.66/5.88 in Y (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → % 5.66/5.88 in Xx (binunion (skS.0 1 a a_1) Y) → (in Xx (skS.0 1 a a_1) → Xphi) → (in Xx Y → Xphi) → Xphi) % 5.66/5.88 False % 5.66/5.88 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), % 5.66/5.88 Eq % 5.66/5.88 (∀ (Y : Iota), % 5.66/5.88 in Y (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → % 5.66/5.88 in Xx (binunion (skS.0 1 a a_1) Y) → (in Xx (skS.0 1 a a_1) → Xphi) → (in Xx Y → Xphi) → Xphi) % 5.66/5.88 False % 5.66/5.88 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 5.66/5.88 Eq % 5.66/5.88 (Not % 5.66/5.88 (in (skS.0 2 a a_1 a_2) (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → % 5.66/5.88 in Xx (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.66/5.88 (in Xx (skS.0 1 a a_1) → Xphi) → (in Xx (skS.0 2 a a_1 a_2) → Xphi) → Xphi)) % 5.66/5.88 True % 5.66/5.88 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 5.66/5.88 Eq % 5.66/5.88 (in (skS.0 2 a a_1 a_2) (powerset (skS.0 0 a)) → % 5.66/5.88 ∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → % 5.66/5.88 in Xx (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.66/5.88 (in Xx (skS.0 1 a a_1) → Xphi) → (in Xx (skS.0 2 a a_1 a_2) → Xphi) → Xphi) % 5.66/5.88 False % 5.66/5.88 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 5.66/5.88 Eq % 5.66/5.88 (∀ (Xphi : Prop) (Xx : Iota), % 5.66/5.88 in Xx (skS.0 0 a) → % 5.66/5.88 in Xx (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.66/5.88 (in Xx (skS.0 1 a a_1) → Xphi) → (in Xx (skS.0 2 a a_1 a_2) → Xphi) → Xphi) % 5.66/5.88 False % 5.66/5.88 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 5.66/5.88 Eq % 5.66/5.88 (Not % 5.75/5.94 (∀ (Xx : Iota), % 5.75/5.94 in Xx (skS.0 0 a) → % 5.75/5.94 in Xx (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.75/5.94 (in Xx (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → % 5.75/5.94 (in Xx (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3)) % 5.75/5.94 True % 5.75/5.94 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 5.75/5.94 Eq % 5.75/5.94 (∀ (Xx : Iota), % 5.75/5.94 in Xx (skS.0 0 a) → % 5.75/5.94 in Xx (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.75/5.94 (in Xx (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → % 5.75/5.94 (in Xx (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) % 5.75/5.94 False % 5.75/5.94 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.94 Eq % 5.75/5.94 (Not % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) → % 5.75/5.94 in (skS.0 4 a a_1 a_2 a_3 a_4) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3)) % 5.75/5.94 True % 5.75/5.94 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.94 Eq % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 0 a) → % 5.75/5.94 in (skS.0 4 a a_1 a_2 a_3 a_4) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) % 5.75/5.94 False % 5.75/5.94 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.94 Eq % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) % 5.75/5.94 False % 5.75/5.94 Clause #25 (by clausification #[0]): Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) % 5.75/5.94 Clause #26 (by forward demodulation #[25, 3]): Eq True (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) % 5.75/5.94 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binunion a B) → Or (in Xx a) (in Xx B)) True % 5.75/5.94 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binunion a a_1) → Or (in Xx a) (in Xx a_1)) True % 5.75/5.94 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a (binunion a_1 a_2) → Or (in a a_1) (in a a_2)) True % 5.75/5.94 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Eq (Or (in a a_1) (in a a_2)) True) % 5.75/5.94 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1) True) (Eq (in a a_2) True)) % 5.75/5.94 Clause #32 (by clausification #[20]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.94 Eq (in (skS.0 4 a a_1 a_2 a_3 a_4) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 5.75/5.94 Clause #33 (by clausification #[20]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.94 Eq % 5.75/5.94 ((in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → % 5.75/5.94 (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) % 5.75/5.94 False % 5.75/5.94 Clause #34 (by identity loobHoist #[32]): ∀ (a a_1 a_2 a_3 : Iota) (a_4 : Prop), % 5.75/5.94 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True) (Eq a_4 False) % 5.75/5.94 Clause #37 (by falseElim #[34]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 4 a a_1 a_2 True a_3) (binunion (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 5.75/5.94 Clause #38 (by clausification #[33]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.94 Eq (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) True % 5.75/5.94 Clause #39 (by clausification #[33]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.94 Eq ((in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) False % 5.75/5.94 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1)) False) (Eq (skS.0 3 a a_1 a_2 a_3) True) % 5.75/5.99 Clause #41 (by identity loobHoist #[40]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.99 Or (Eq (skS.0 3 a a_1 a_2 a_3) True) (Or (Eq (in (skS.0 4 a a_1 a_2 True a_4) (skS.0 1 a a_1)) False) (Eq a_3 False)) % 5.75/5.99 Clause #43 (by identity loobHoist #[41]): ∀ (a a_1 a_2 a_3 : Iota) (a_4 : Prop), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 1 a a_1)) False) % 5.75/5.99 (Or (Eq a_4 False) (Or (Eq (skS.0 3 a a_1 a_2 True) True) (Eq a_4 False))) % 5.75/5.99 Clause #45 (by eliminate duplicate literals #[43]): ∀ (a a_1 a_2 a_3 : Iota) (a_4 : Prop), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 1 a a_1)) False) (Or (Eq a_4 False) (Eq (skS.0 3 a a_1 a_2 True) True)) % 5.75/5.99 Clause #46 (by clausification #[39]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.99 Eq (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2) → skS.0 3 a a_1 a_2 a_3) True % 5.75/5.99 Clause #47 (by clausification #[39]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (skS.0 3 a a_1 a_2 a_3) False % 5.75/5.99 Clause #48 (by clausification #[46]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2)) False) (Eq (skS.0 3 a a_1 a_2 a_3) True) % 5.75/5.99 Clause #49 (by identity loobHoist #[48]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop) (a_4 : Iota), % 5.75/5.99 Or (Eq (skS.0 3 a a_1 a_2 a_3) True) % 5.75/5.99 (Or (Eq (in (skS.0 4 a a_1 a_2 True a_4) (skS.0 2 a a_1 a_2)) False) (Eq a_3 False)) % 5.75/5.99 Clause #51 (by identity loobHoist #[49]): ∀ (a a_1 a_2 a_3 : Iota) (a_4 : Prop), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 2 a a_1 a_2)) False) % 5.75/5.99 (Or (Eq a_4 False) (Or (Eq (skS.0 3 a a_1 a_2 True) True) (Eq a_4 False))) % 5.75/5.99 Clause #53 (by eliminate duplicate literals #[51]): ∀ (a a_1 a_2 a_3 : Iota) (a_4 : Prop), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 2 a a_1 a_2)) False) % 5.75/5.99 (Or (Eq a_4 False) (Eq (skS.0 3 a a_1 a_2 True) True)) % 5.75/5.99 Clause #54 (by identity loobHoist #[47]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 True) False) (Eq a_3 False) % 5.75/5.99 Clause #62 (by superposition #[37, 31]): ∀ (a a_1 a_2 a_3 : Iota), % 5.75/5.99 Or (Eq True False) % 5.75/5.99 (Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 1 a a_1)) True) % 5.75/5.99 (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 2 a a_1 a_2)) True)) % 5.75/5.99 Clause #81 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 1 a a_1)) True) % 5.75/5.99 (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 2 a a_1 a_2)) True) % 5.75/5.99 Clause #82 (by superposition #[81, 53]): ∀ (a a_1 a_2 a_3 : Iota) (a_4 : Prop), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 1 a a_1)) True) % 5.75/5.99 (Or (Eq True False) (Or (Eq a_4 False) (Eq (skS.0 3 a a_1 a_2 True) True))) % 5.75/5.99 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota) (a_4 : Prop), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 1 a a_1)) True) (Or (Eq a_4 False) (Eq (skS.0 3 a a_1 a_2 True) True)) % 5.75/5.99 Clause #86 (by falseElim #[83]): ∀ (a a_1 a_2 a_3 : Iota), % 5.75/5.99 Or (Eq (in (skS.0 4 a a_1 a_2 True a_3) (skS.0 1 a a_1)) True) (Eq (skS.0 3 a a_1 a_2 True) True) % 5.75/5.99 Clause #87 (by superposition #[86, 45]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 5.75/5.99 Or (Eq (skS.0 3 a a_1 a_2 True) True) (Or (Eq True False) (Or (Eq a_3 False) (Eq (skS.0 3 a a_1 a_2 True) True))) % 5.75/5.99 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 5.75/5.99 Or (Eq (skS.0 3 a a_1 a_2 True) True) (Or (Eq a_3 False) (Eq (skS.0 3 a a_1 a_2 True) True)) % 5.75/5.99 Clause #89 (by eliminate duplicate literals #[88]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 True) True) (Eq a_3 False) % 5.75/5.99 Clause #93 (by falseElim #[89]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 3 a a_1 a_2 True) True % 5.75/5.99 Clause #95 (by superposition #[93, 54]): ∀ (a : Prop), Or (Eq True False) (Eq a False) % 5.75/5.99 Clause #96 (by clausification #[95]): ∀ (a : Prop), Eq a False % 5.75/5.99 Clause #99 (by falseElim #[96]): False % 5.75/5.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------