%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU629^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:02:05 PM UTC 2025 % Result : Theorem 6.27s 6.45s % Output : Proof 6.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU629^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.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 04:52:08 EDT 2025 % 0.13/0.34 % CPUTime : % 6.27/6.45 SZS status Theorem for theBenchmark.p % 6.27/6.45 SZS output start Proof for theBenchmark.p % 6.27/6.45 Clause #0 (by assumption #[]): Eq (Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 6.27/6.45 True % 6.27/6.45 Clause #1 (by assumption #[]): Eq % 6.27/6.45 (Eq ubforcartprodlem2 % 6.27/6.45 (∀ (A B Xx : Iota), % 6.27/6.45 in Xx A → % 6.27/6.45 ∀ (Xy : Iota), % 6.27/6.45 in Xy B → % 6.27/6.45 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 6.27/6.45 (powerset (powerset (binunion A B))))) % 6.27/6.45 True % 6.27/6.45 Clause #2 (by assumption #[]): Eq % 6.27/6.45 (Not % 6.27/6.45 (ubforcartprodlem2 → % 6.27/6.45 ∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → in (kpair Xx Xy) (powerset (powerset (binunion A B))))) % 6.27/6.45 True % 6.27/6.45 Clause #3 (by clausification #[2]): Eq % 6.27/6.45 (ubforcartprodlem2 → % 6.27/6.45 ∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → in (kpair Xx Xy) (powerset (powerset (binunion A B)))) % 6.27/6.45 False % 6.27/6.45 Clause #4 (by clausification #[3]): Eq ubforcartprodlem2 True % 6.27/6.45 Clause #5 (by clausification #[3]): Eq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → in (kpair Xx Xy) (powerset (powerset (binunion A B)))) False % 6.27/6.45 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 6.27/6.45 Eq % 6.27/6.45 (Not % 6.27/6.45 (∀ (B Xx : Iota), % 6.27/6.45 in Xx (skS.0 0 a) → ∀ (Xy : Iota), in Xy B → in (kpair Xx Xy) (powerset (powerset (binunion (skS.0 0 a) B))))) % 6.27/6.45 True % 6.27/6.45 Clause #7 (by clausification #[6]): ∀ (a : Iota), % 6.27/6.45 Eq % 6.27/6.45 (∀ (B Xx : Iota), % 6.27/6.45 in Xx (skS.0 0 a) → ∀ (Xy : Iota), in Xy B → in (kpair Xx Xy) (powerset (powerset (binunion (skS.0 0 a) B)))) % 6.27/6.45 False % 6.27/6.45 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 6.27/6.45 Eq % 6.27/6.45 (Not % 6.27/6.45 (∀ (Xx : Iota), % 6.27/6.45 in Xx (skS.0 0 a) → % 6.27/6.45 ∀ (Xy : Iota), % 6.27/6.45 in Xy (skS.0 1 a a_1) → in (kpair Xx Xy) (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1)))))) % 6.27/6.45 True % 6.27/6.45 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 6.27/6.45 Eq % 6.27/6.45 (∀ (Xx : Iota), % 6.27/6.45 in Xx (skS.0 0 a) → % 6.27/6.45 ∀ (Xy : Iota), % 6.27/6.45 in Xy (skS.0 1 a a_1) → in (kpair Xx Xy) (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1))))) % 6.27/6.45 False % 6.27/6.45 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 6.27/6.45 Eq % 6.27/6.45 (Not % 6.27/6.45 (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → % 6.27/6.45 ∀ (Xy : Iota), % 6.27/6.45 in Xy (skS.0 1 a a_1) → % 6.27/6.45 in (kpair (skS.0 2 a a_1 a_2) Xy) (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1)))))) % 6.27/6.45 True % 6.27/6.45 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 6.27/6.45 Eq % 6.27/6.45 (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → % 6.27/6.45 ∀ (Xy : Iota), % 6.27/6.45 in Xy (skS.0 1 a a_1) → % 6.27/6.45 in (kpair (skS.0 2 a a_1 a_2) Xy) (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1))))) % 6.27/6.45 False % 6.27/6.45 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 6.27/6.45 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 6.27/6.45 Eq % 6.27/6.45 (∀ (Xy : Iota), % 6.27/6.45 in Xy (skS.0 1 a a_1) → % 6.27/6.45 in (kpair (skS.0 2 a a_1 a_2) Xy) (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1))))) % 6.27/6.45 False % 6.27/6.45 Clause #14 (by clausification #[0]): Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset) % 6.27/6.45 Clause #15 (by argument congruence #[14]): ∀ (a : Iota), % 6.27/6.45 Eq (kpair a) % 6.27/6.45 ((fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) a) % 6.27/6.45 Clause #17 (by betaEtaReduce #[15]): ∀ (a : Iota), % 6.27/6.45 Eq (kpair a) fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset) % 6.27/6.45 Clause #18 (by argument congruence #[17]): ∀ (a a_1 : Iota), % 6.27/6.45 Eq (kpair a a_1) % 6.27/6.45 ((fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) a_1) % 6.27/6.45 Clause #21 (by clausification #[1]): Eq ubforcartprodlem2 % 6.27/6.45 (∀ (A B Xx : Iota), % 6.27/6.45 in Xx A → % 6.27/6.45 ∀ (Xy : Iota), % 6.27/6.45 in Xy B → % 6.27/6.45 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 6.27/6.45 (powerset (powerset (binunion A B)))) % 6.27/6.45 Clause #22 (by forward demodulation #[21, 4]): Eq True % 6.27/6.47 (∀ (A B Xx : Iota), % 6.27/6.47 in Xx A → % 6.27/6.47 ∀ (Xy : Iota), % 6.27/6.47 in Xy B → % 6.27/6.47 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion A B)))) % 6.27/6.47 Clause #23 (by clausification #[22]): ∀ (a : Iota), % 6.27/6.47 Eq % 6.27/6.47 (∀ (B Xx : Iota), % 6.27/6.47 in Xx a → % 6.27/6.47 ∀ (Xy : Iota), % 6.27/6.47 in Xy B → % 6.27/6.47 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion a B)))) % 6.27/6.47 True % 6.27/6.47 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), % 6.27/6.47 Eq % 6.27/6.47 (∀ (Xx : Iota), % 6.27/6.47 in Xx a → % 6.27/6.47 ∀ (Xy : Iota), % 6.27/6.47 in Xy a_1 → % 6.27/6.47 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion a a_1)))) % 6.27/6.47 True % 6.27/6.47 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 6.27/6.47 Eq % 6.27/6.47 (in a a_1 → % 6.27/6.47 ∀ (Xy : Iota), % 6.27/6.47 in Xy a_2 → % 6.27/6.47 in (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion a_1 a_2)))) % 6.27/6.47 True % 6.27/6.47 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 6.27/6.47 Or (Eq (in a a_1) False) % 6.27/6.47 (Eq % 6.27/6.47 (∀ (Xy : Iota), % 6.27/6.47 in Xy a_2 → % 6.27/6.47 in (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion a_1 a_2)))) % 6.27/6.47 True) % 6.27/6.47 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), % 6.27/6.47 Or (Eq (in a a_1) False) % 6.27/6.47 (Eq % 6.27/6.47 (in a_2 a_3 → % 6.27/6.47 in (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_2 emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion a_1 a_3)))) % 6.27/6.47 True) % 6.27/6.47 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota), % 6.27/6.47 Or (Eq (in a a_1) False) % 6.27/6.47 (Or (Eq (in a_2 a_3) False) % 6.27/6.47 (Eq % 6.27/6.47 (in (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_2 emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion a_1 a_3)))) % 6.27/6.47 True)) % 6.27/6.47 Clause #29 (by superposition #[28, 12]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.27/6.47 Or (Eq (in a a_1) False) % 6.27/6.47 (Or % 6.27/6.47 (Eq % 6.27/6.47 (in % 6.27/6.47 (setadjoin (setadjoin (skS.0 2 a_2 a_3 a_4) emptyset) % 6.27/6.47 (setadjoin (setadjoin (skS.0 2 a_2 a_3 a_4) (setadjoin a emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion (skS.0 0 a_2) a_1)))) % 6.27/6.47 True) % 6.27/6.47 (Eq False True)) % 6.27/6.47 Clause #30 (by betaEtaReduce #[18]): ∀ (a a_1 : Iota), % 6.27/6.47 Eq (kpair a a_1) (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)) % 6.27/6.47 Clause #44 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 6.27/6.47 Eq % 6.27/6.47 (Not % 6.27/6.47 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) → % 6.27/6.47 in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 6.27/6.47 (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1)))))) % 6.27/6.47 True % 6.27/6.47 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 6.27/6.47 Eq % 6.27/6.47 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) → % 6.27/6.47 in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 6.27/6.47 (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1))))) % 6.27/6.47 False % 6.27/6.47 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)) True % 6.27/6.47 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 6.27/6.47 Eq % 6.27/6.47 (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 6.27/6.47 (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a a_1))))) % 6.27/6.47 False % 6.27/6.47 Clause #80 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.27/6.47 Or (Eq (in a a_1) False) % 6.27/6.47 (Eq % 6.27/6.47 (in % 6.27/6.47 (setadjoin (setadjoin (skS.0 2 a_2 a_3 a_4) emptyset) % 6.27/6.47 (setadjoin (setadjoin (skS.0 2 a_2 a_3 a_4) (setadjoin a emptyset)) emptyset)) % 6.27/6.47 (powerset (powerset (binunion (skS.0 0 a_2) a_1)))) % 6.27/6.47 True) % 6.27/6.47 Clause #81 (by forward demodulation #[80, 30]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.27/6.47 Or (Eq (in a a_1) False) % 6.27/6.47 (Eq (in (kpair (skS.0 2 a_2 a_3 a_4) a) (powerset (powerset (binunion (skS.0 0 a_2) a_1)))) True) % 6.33/6.50 Clause #83 (by superposition #[81, 46]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.33/6.50 Or % 6.33/6.50 (Eq % 6.33/6.50 (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a_3 a_4 a_5 a_6)) % 6.33/6.50 (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a_3 a_4))))) % 6.33/6.50 True) % 6.33/6.50 (Eq False True) % 6.33/6.50 Clause #587 (by clausification #[83]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.33/6.50 Eq % 6.33/6.50 (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a_3 a_4 a_5 a_6)) % 6.33/6.50 (powerset (powerset (binunion (skS.0 0 a) (skS.0 1 a_3 a_4))))) % 6.33/6.50 True % 6.33/6.50 Clause #588 (by superposition #[587, 47]): Eq True False % 6.33/6.50 Clause #597 (by clausification #[588]): False % 6.33/6.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------