%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU515^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:01:48 PM UTC 2025 % Result : Theorem 4.62s 4.78s % Output : Proof 4.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU515^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 05:23:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.62/4.78 SZS status Theorem for theBenchmark.p % 4.62/4.78 SZS output start Proof for theBenchmark.p % 4.62/4.78 Clause #0 (by assumption #[]): Eq (Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A)))) True % 4.62/4.78 Clause #1 (by assumption #[]): Eq % 4.62/4.78 (Not % 4.62/4.78 (setadjoinAx → % 4.62/4.78 ∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi)) % 4.62/4.78 True % 4.62/4.78 Clause #2 (by clausification #[1]): Eq % 4.62/4.78 (setadjoinAx → % 4.62/4.78 ∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) % 4.62/4.78 False % 4.62/4.78 Clause #3 (by clausification #[2]): Eq setadjoinAx True % 4.62/4.78 Clause #4 (by clausification #[2]): Eq (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) False % 4.62/4.78 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 4.62/4.78 Eq % 4.62/4.78 (Not % 4.62/4.78 (∀ (A Xy : Iota), % 4.62/4.78 in Xy (setadjoin (skS.0 0 a) A) → ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy A → Xphi) → Xphi)) % 4.62/4.78 True % 4.62/4.78 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 4.62/4.78 Eq % 4.62/4.78 (∀ (A Xy : Iota), % 4.62/4.78 in Xy (setadjoin (skS.0 0 a) A) → ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy A → Xphi) → Xphi) % 4.62/4.78 False % 4.62/4.78 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.62/4.78 Eq % 4.62/4.78 (Not % 4.62/4.78 (∀ (Xy : Iota), % 4.62/4.78 in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → % 4.62/4.78 ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy (skS.0 1 a a_1) → Xphi) → Xphi)) % 4.62/4.78 True % 4.62/4.78 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.62/4.78 Eq % 4.62/4.78 (∀ (Xy : Iota), % 4.62/4.78 in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → % 4.62/4.78 ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy (skS.0 1 a a_1) → Xphi) → Xphi) % 4.62/4.78 False % 4.62/4.78 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.62/4.78 Eq % 4.62/4.78 (Not % 4.62/4.78 (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → % 4.62/4.78 ∀ (Xphi : Prop), % 4.62/4.78 (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → Xphi) → (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → Xphi) → Xphi)) % 4.62/4.78 True % 4.62/4.78 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.62/4.78 Eq % 4.62/4.78 (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → % 4.62/4.78 ∀ (Xphi : Prop), % 4.62/4.78 (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → Xphi) → (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → Xphi) → Xphi) % 4.62/4.78 False % 4.62/4.78 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1))) True % 4.62/4.78 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.62/4.78 Eq % 4.62/4.78 (∀ (Xphi : Prop), % 4.62/4.78 (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → Xphi) → (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → Xphi) → Xphi) % 4.62/4.78 False % 4.62/4.78 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.62/4.78 Eq % 4.62/4.78 (Not % 4.62/4.78 ((Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → skS.0 3 a a_1 a_2 a_3) → % 4.62/4.78 (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3)) % 4.62/4.78 True % 4.62/4.78 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.62/4.78 Eq % 4.62/4.78 ((Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → skS.0 3 a a_1 a_2 a_3) → % 4.62/4.78 (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) % 4.62/4.78 False % 4.62/4.78 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → skS.0 3 a a_1 a_2 a_3) True % 4.62/4.78 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.62/4.78 Eq ((in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) False % 4.62/4.78 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) False) (Eq (skS.0 3 a a_1 a_2 a_3) True) % 4.62/4.78 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 a_3) True) (Ne (skS.0 2 a a_1 a_2) (skS.0 0 a)) % 4.62/4.78 Clause #20 (by identity boolHoist #[18]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.62/4.78 Or (Ne (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True)) % 4.62/4.78 Clause #21 (by clausification #[16]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) True % 4.63/4.80 Clause #22 (by clausification #[16]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (skS.0 3 a a_1 a_2 a_3) False % 4.63/4.80 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.63/4.80 Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False) (Eq (skS.0 3 a a_1 a_2 a_3) True) % 4.63/4.80 Clause #25 (by identity boolHoist #[23]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.63/4.80 Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True)) % 4.63/4.80 Clause #27 (by identity boolHoist #[22]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 False) False) (Eq a_3 True) % 4.63/4.80 Clause #28 (by clausification #[0]): Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A))) % 4.63/4.80 Clause #29 (by forward demodulation #[28, 3]): Eq True (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A))) % 4.63/4.80 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), Iff (in Xy (setadjoin a A)) (Or (Eq Xy a) (in Xy A))) True % 4.63/4.80 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), Iff (in Xy (setadjoin a a_1)) (Or (Eq Xy a) (in Xy a_1))) True % 4.63/4.80 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (Iff (in a (setadjoin a_1 a_2)) (Or (Eq a a_1) (in a a_2))) True % 4.63/4.80 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq (Or (Eq a a_1) (in a a_2)) True) % 4.63/4.80 Clause #47 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1) True) (Eq (in a a_2) True)) % 4.63/4.80 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (in a a_2) True) (Eq a a_1)) % 4.63/4.80 Clause #49 (by superposition #[48, 11]): ∀ (a a_1 a_2 : Iota), % 4.63/4.80 Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Eq False True)) % 4.63/4.80 Clause #81 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) % 4.63/4.80 Clause #83 (by superposition #[81, 25]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.63/4.80 Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Or (Eq True False) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True))) % 4.63/4.80 Clause #102 (by clausification #[83]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 4.63/4.80 Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True)) % 4.63/4.80 Clause #103 (by forward contextual literal cutting #[102, 20]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True) % 4.63/4.80 Clause #104 (by superposition #[103, 27]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq True False) (Eq a_1 True)) % 4.63/4.80 Clause #112 (by clausification #[104]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True) % 4.63/4.80 Clause #121 (by falseElim #[112]): ∀ (a : Prop), Eq a True % 4.63/4.80 Clause #126 (by falseElim #[121]): False % 4.63/4.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------