%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU619^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:02:03 PM UTC 2025 % Result : Theorem 3.59s 3.75s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU619^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n031.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 04:13:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.59/3.75 SZS status Theorem for theBenchmark.p % 3.59/3.75 SZS output start Proof for theBenchmark.p % 3.59/3.75 Clause #0 (by assumption #[]): Eq % 3.59/3.75 (Eq iskpair fun A => % 3.59/3.75 Exists fun Xx => % 3.59/3.75 And (in Xx (setunion A)) % 3.59/3.75 (Exists fun Xy => % 3.59/3.75 And (in Xy (setunion A)) % 3.59/3.75 (Eq A (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.59/3.75 True % 3.59/3.75 Clause #1 (by assumption #[]): Eq % 3.59/3.75 (Eq setukpairIL % 3.59/3.75 (∀ (Xx Xy : Iota), % 3.59/3.75 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.59/3.75 True % 3.59/3.75 Clause #2 (by assumption #[]): Eq % 3.59/3.75 (Eq setukpairIR % 3.59/3.75 (∀ (Xx Xy : Iota), % 3.59/3.75 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.59/3.75 True % 3.59/3.75 Clause #3 (by assumption #[]): Eq % 3.59/3.75 (Not % 3.59/3.75 (setukpairIL → % 3.59/3.75 setukpairIR → % 3.59/3.75 ∀ (Xx Xy : Iota), % 3.59/3.75 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 True % 3.59/3.75 Clause #4 (by clausification #[3]): Eq % 3.59/3.75 (setukpairIL → % 3.59/3.75 setukpairIR → % 3.59/3.75 ∀ (Xx Xy : Iota), % 3.59/3.75 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))) % 3.59/3.75 False % 3.59/3.75 Clause #5 (by clausification #[4]): Eq setukpairIL True % 3.59/3.75 Clause #6 (by clausification #[4]): Eq % 3.59/3.75 (setukpairIR → % 3.59/3.75 ∀ (Xx Xy : Iota), % 3.59/3.75 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))) % 3.59/3.75 False % 3.59/3.75 Clause #7 (by clausification #[6]): Eq setukpairIR True % 3.59/3.75 Clause #8 (by clausification #[6]): Eq % 3.59/3.75 (∀ (Xx Xy : Iota), % 3.59/3.75 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))) % 3.59/3.75 False % 3.59/3.75 Clause #9 (by clausification #[8]): ∀ (a : Iota), % 3.59/3.75 Eq % 3.59/3.75 (Not % 3.59/3.75 (∀ (Xy : Iota), % 3.59/3.75 iskpair % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) emptyset) % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 True % 3.59/3.75 Clause #10 (by clausification #[9]): ∀ (a : Iota), % 3.59/3.75 Eq % 3.59/3.75 (∀ (Xy : Iota), % 3.59/3.75 iskpair % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) emptyset) % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) (setadjoin Xy emptyset)) emptyset))) % 3.59/3.75 False % 3.59/3.75 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 3.59/3.75 Eq % 3.59/3.75 (Not % 3.59/3.75 (iskpair % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) emptyset) % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) (setadjoin (skS.0 1 a a_1) emptyset)) emptyset)))) % 3.59/3.75 True % 3.59/3.75 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 3.59/3.75 Eq % 3.59/3.75 (iskpair % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) emptyset) % 3.59/3.75 (setadjoin (setadjoin (skS.0 0 a) (setadjoin (skS.0 1 a a_1) emptyset)) emptyset))) % 3.59/3.75 False % 3.59/3.75 Clause #13 (by clausification #[2]): Eq setukpairIR % 3.59/3.75 (∀ (Xx Xy : Iota), % 3.59/3.75 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 Clause #14 (by forward demodulation #[13, 7]): Eq True % 3.59/3.75 (∀ (Xx Xy : Iota), % 3.59/3.75 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 Clause #15 (by clausification #[14]): ∀ (a : Iota), % 3.59/3.75 Eq % 3.59/3.75 (∀ (Xy : Iota), % 3.59/3.75 in Xy (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 True % 3.59/3.75 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 3.59/3.75 Eq (in a (setunion (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a emptyset)) emptyset)))) % 3.59/3.75 True % 3.59/3.75 Clause #17 (by clausification #[1]): Eq setukpairIL % 3.59/3.75 (∀ (Xx Xy : Iota), % 3.59/3.75 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 Clause #18 (by forward demodulation #[17, 5]): Eq True % 3.59/3.75 (∀ (Xx Xy : Iota), % 3.59/3.75 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 Clause #19 (by clausification #[18]): ∀ (a : Iota), % 3.59/3.75 Eq % 3.59/3.75 (∀ (Xy : Iota), % 3.59/3.75 in a (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.75 True % 3.59/3.75 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 3.59/3.77 Eq (in a (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)))) % 3.59/3.77 True % 3.59/3.77 Clause #21 (by clausification #[0]): Eq iskpair fun A => % 3.59/3.77 Exists fun Xx => % 3.59/3.77 And (in Xx (setunion A)) % 3.59/3.77 (Exists fun Xy => % 3.59/3.77 And (in Xy (setunion A)) % 3.59/3.77 (Eq A (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.77 Clause #22 (by argument congruence #[21]): ∀ (a : Iota), % 3.59/3.77 Eq (iskpair a) % 3.59/3.77 ((fun A => % 3.59/3.77 Exists fun Xx => % 3.59/3.77 And (in Xx (setunion A)) % 3.59/3.77 (Exists fun Xy => % 3.59/3.77 And (in Xy (setunion A)) % 3.59/3.77 (Eq A (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.59/3.77 a) % 3.59/3.77 Clause #23 (by betaEtaReduce #[22]): ∀ (a : Iota), % 3.59/3.77 Eq (iskpair a) % 3.59/3.77 (Exists fun Xx => % 3.59/3.77 And (in Xx (setunion a)) % 3.59/3.77 (Exists fun Xy => % 3.59/3.77 And (in Xy (setunion a)) % 3.59/3.77 (Eq a (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.59/3.77 Clause #26 (by existsHoist #[23]): ∀ (a a_1 : Iota), % 3.59/3.77 Or (Eq (iskpair a) True) % 3.59/3.77 (Eq % 3.59/3.77 ((fun Xx => % 3.59/3.77 And (in Xx (setunion a)) % 3.59/3.77 (Exists fun Xy => % 3.59/3.77 And (in Xy (setunion a)) % 3.59/3.77 (Eq a (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.59/3.77 a_1) % 3.59/3.77 False) % 3.59/3.77 Clause #27 (by betaEtaReduce #[26]): ∀ (a a_1 : Iota), % 3.59/3.77 Or (Eq (iskpair a) True) % 3.59/3.77 (Eq % 3.59/3.77 (And (in a_1 (setunion a)) % 3.59/3.77 (Exists fun Xy => % 3.59/3.77 And (in Xy (setunion a)) % 3.59/3.77 (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin Xy emptyset)) emptyset))))) % 3.59/3.77 False) % 3.59/3.77 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), % 3.59/3.77 Or (Eq (iskpair a) True) % 3.59/3.77 (Or (Eq (in a_1 (setunion a)) False) % 3.59/3.77 (Eq % 3.59/3.77 (Exists fun Xy => % 3.59/3.77 And (in Xy (setunion a)) % 3.59/3.77 (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin Xy emptyset)) emptyset)))) % 3.59/3.77 False)) % 3.59/3.77 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 3.59/3.77 Or (Eq (iskpair a) True) % 3.59/3.77 (Or (Eq (in a_1 (setunion a)) False) % 3.59/3.77 (Eq % 3.59/3.77 (And (in a_2 (setunion a)) % 3.59/3.77 (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset)))) % 3.59/3.77 False)) % 3.59/3.77 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 3.59/3.77 Or (Eq (iskpair a) True) % 3.59/3.77 (Or (Eq (in a_1 (setunion a)) False) % 3.59/3.77 (Or (Eq (in a_2 (setunion a)) False) % 3.59/3.77 (Eq (Eq a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset))) % 3.59/3.77 False))) % 3.59/3.77 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), % 3.59/3.77 Or (Eq (iskpair a) True) % 3.59/3.77 (Or (Eq (in a_1 (setunion a)) False) % 3.59/3.77 (Or (Eq (in a_2 (setunion a)) False) % 3.59/3.77 (Ne a (setadjoin (setadjoin a_1 emptyset) (setadjoin (setadjoin a_1 (setadjoin a_2 emptyset)) emptyset))))) % 3.59/3.77 Clause #32 (by destructive equality resolution #[31]): ∀ (a a_1 : Iota), % 3.59/3.77 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True) % 3.59/3.77 (Or % 3.59/3.77 (Eq % 3.59/3.77 (in a (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)))) % 3.59/3.77 False) % 3.59/3.77 (Eq % 3.59/3.77 (in a_1 % 3.59/3.77 (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)))) % 3.59/3.77 False)) % 3.59/3.77 Clause #34 (by superposition #[32, 20]): ∀ (a a_1 : Iota), % 3.59/3.77 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True) % 3.59/3.77 (Or % 3.59/3.77 (Eq % 3.59/3.77 (in a_1 % 3.59/3.77 (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)))) % 3.59/3.77 False) % 3.59/3.77 (Eq False True)) % 3.59/3.77 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.59/3.77 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True) % 3.59/3.77 (Eq % 3.59/3.77 (in a_1 (setunion (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset)))) % 3.59/3.77 False) % 3.59/3.77 Clause #36 (by superposition #[35, 16]): ∀ (a a_1 : Iota), % 3.59/3.77 Or (Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True) % 3.59/3.77 (Eq False True) % 3.59/3.77 Clause #39 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.59/3.77 Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True % 3.59/3.77 Clause #41 (by superposition #[39, 12]): Eq True False % 3.59/3.77 Clause #42 (by clausification #[41]): False % 3.59/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------