%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU652^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:02:08 PM UTC 2025 % Result : Theorem 3.77s 3.98s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU652^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.14/0.35 % Computer : n023.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 05:26:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.77/3.98 SZS status Theorem for theBenchmark.p % 3.77/3.98 SZS output start Proof for theBenchmark.p % 3.77/3.98 Clause #0 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 3.77/3.98 Clause #1 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.77/3.98 Clause #2 (by assumption #[]): Eq (Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))) True % 3.77/3.98 Clause #3 (by assumption #[]): Eq % 3.77/3.98 (Not % 3.77/3.98 (setadjoinIL → % 3.77/3.98 uniqinunit → % 3.77/3.98 secondinupair → % 3.77/3.98 ∀ (Xx Xy Xz : Iota), Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xz emptyset) → Eq Xx Xy)) % 3.77/3.98 True % 3.77/3.98 Clause #4 (by clausification #[1]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.77/3.98 Clause #18 (by clausification #[0]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.77/3.98 Clause #20 (by clausify Prop equality #[18]): Or (Eq setadjoinIL False) (Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) True) % 3.77/3.98 Clause #22 (by clausification #[2]): Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) % 3.77/3.98 Clause #24 (by clausify Prop equality #[22]): Or (Eq secondinupair False) (Eq (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) True) % 3.77/3.98 Clause #26 (by clausification #[20]): ∀ (a : Iota), Or (Eq setadjoinIL False) (Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True) % 3.77/3.98 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq setadjoinIL False) (Eq (in a (setadjoin a a_1)) True) % 3.77/3.98 Clause #36 (by clausification #[24]): ∀ (a : Iota), Or (Eq secondinupair False) (Eq (∀ (Xy : Iota), in Xy (setadjoin a (setadjoin Xy emptyset))) True) % 3.77/3.98 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq secondinupair False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True) % 3.77/3.98 Clause #38 (by clausification #[3]): Eq % 3.77/3.98 (setadjoinIL → % 3.77/3.98 uniqinunit → % 3.77/3.98 secondinupair → ∀ (Xx Xy Xz : Iota), Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xz emptyset) → Eq Xx Xy) % 3.77/3.98 False % 3.77/3.98 Clause #39 (by clausification #[38]): Eq setadjoinIL True % 3.77/3.98 Clause #40 (by clausification #[38]): Eq % 3.77/3.98 (uniqinunit → % 3.77/3.98 secondinupair → ∀ (Xx Xy Xz : Iota), Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xz emptyset) → Eq Xx Xy) % 3.77/3.98 False % 3.77/3.98 Clause #42 (by backward demodulation #[39, 27]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a a_1)) True) % 3.77/3.98 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 3.77/3.98 Clause #46 (by clausification #[40]): Eq uniqinunit True % 3.77/3.98 Clause #47 (by clausification #[40]): Eq (secondinupair → ∀ (Xx Xy Xz : Iota), Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xz emptyset) → Eq Xx Xy) % 3.77/3.98 False % 3.77/3.98 Clause #48 (by backward demodulation #[46, 4]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.77/3.98 Clause #51 (by clausification #[48]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 3.77/3.98 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 3.77/3.98 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.77/3.98 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 3.77/3.98 Clause #59 (by clausification #[47]): Eq secondinupair True % 3.77/3.98 Clause #60 (by clausification #[47]): Eq (∀ (Xx Xy Xz : Iota), Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xz emptyset) → Eq Xx Xy) False % 3.77/3.98 Clause #63 (by backward demodulation #[59, 37]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True) % 3.77/3.98 Clause #64 (by clausification #[60]): ∀ (a : Iota), % 3.77/3.98 Eq % 3.77/3.98 (Not % 3.77/3.98 (∀ (Xy Xz : Iota), % 3.77/3.98 Eq (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) (setadjoin Xz emptyset) → Eq (skS.0 6 a) Xy)) % 3.77/3.98 True % 3.77/3.98 Clause #65 (by clausification #[64]): ∀ (a : Iota), % 3.77/3.98 Eq (∀ (Xy Xz : Iota), Eq (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) (setadjoin Xz emptyset) → Eq (skS.0 6 a) Xy) % 3.77/3.98 False % 3.77/3.98 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 3.77/3.99 Eq % 3.77/3.99 (Not % 3.77/3.99 (∀ (Xz : Iota), % 3.77/3.99 Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin Xz emptyset) → % 3.77/3.99 Eq (skS.0 6 a) (skS.0 7 a a_1))) % 3.77/3.99 True % 3.77/3.99 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 3.77/3.99 Eq % 3.77/3.99 (∀ (Xz : Iota), % 3.77/3.99 Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin Xz emptyset) → % 3.77/3.99 Eq (skS.0 6 a) (skS.0 7 a a_1)) % 3.77/3.99 False % 3.77/3.99 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 3.77/3.99 Eq % 3.77/3.99 (Not % 3.77/3.99 (Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin (skS.0 8 a a_1 a_2) emptyset) → % 3.77/3.99 Eq (skS.0 6 a) (skS.0 7 a a_1))) % 3.77/3.99 True % 3.77/3.99 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 3.77/3.99 Eq % 3.77/3.99 (Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin (skS.0 8 a a_1 a_2) emptyset) → % 3.77/3.99 Eq (skS.0 6 a) (skS.0 7 a a_1)) % 3.77/3.99 False % 3.77/3.99 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 3.77/3.99 Eq (Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin (skS.0 8 a a_1 a_2) emptyset)) True % 3.77/3.99 Clause #71 (by clausification #[69]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 6 a) (skS.0 7 a a_1)) False % 3.77/3.99 Clause #72 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), % 3.77/3.99 Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 3.77/3.99 Clause #74 (by superposition #[72, 44]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a) (setadjoin (skS.0 8 a a_1 a_2) emptyset)) True % 3.77/3.99 Clause #77 (by clausification #[63]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True % 3.77/3.99 Clause #78 (by superposition #[77, 72]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1) (setadjoin (skS.0 8 a a_1 a_2) emptyset)) True % 3.77/3.99 Clause #81 (by clausification #[71]): ∀ (a a_1 : Iota), Ne (skS.0 6 a) (skS.0 7 a a_1) % 3.77/3.99 Clause #82 (by superposition #[74, 54]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 6 a) (skS.0 8 a a_1 a_2)) % 3.77/3.99 Clause #84 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 6 a) (skS.0 8 a a_1 a_2) % 3.77/3.99 Clause #87 (by forward demodulation #[78, 84]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (setadjoin (skS.0 6 a) emptyset)) True % 3.77/3.99 Clause #88 (by superposition #[87, 54]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 7 a a_1) (skS.0 6 a)) % 3.77/3.99 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (skS.0 7 a a_1) (skS.0 6 a) % 3.77/3.99 Clause #90 (by forward contextual literal cutting #[89, 81]): False % 3.77/3.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------