%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU642^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:02:07 PM UTC 2025 % Result : Theorem 3.90s 4.12s % Output : Proof 3.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU642^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n024.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 04:05:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.90/4.12 SZS status Theorem for theBenchmark.p % 3.90/4.12 SZS output start Proof for theBenchmark.p % 3.90/4.12 Clause #0 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 3.90/4.12 Clause #1 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.90/4.12 Clause #2 (by assumption #[]): Eq (Eq upairset2E (∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy))) True % 3.90/4.12 Clause #3 (by assumption #[]): Eq (Eq singletonsuniq (∀ (Xx Xy : Iota), Eq (setadjoin Xx emptyset) (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.90/4.12 Clause #4 (by assumption #[]): Eq % 3.90/4.12 (Not % 3.90/4.12 (setadjoinIL → % 3.90/4.12 uniqinunit → % 3.90/4.12 upairset2E → % 3.90/4.12 singletonsuniq → % 3.90/4.12 ∀ (Xx Xy Xz : Iota), % 3.90/4.12 in (setadjoin Xz emptyset) % 3.90/4.12 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 3.90/4.12 Eq Xx Xz)) % 3.90/4.12 True % 3.90/4.12 Clause #5 (by clausification #[3]): Eq singletonsuniq (∀ (Xx Xy : Iota), Eq (setadjoin Xx emptyset) (setadjoin Xy emptyset) → Eq Xx Xy) % 3.90/4.12 Clause #21 (by clausification #[1]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.90/4.12 Clause #25 (by clausification #[0]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.90/4.12 Clause #27 (by clausify Prop equality #[25]): Or (Eq setadjoinIL False) (Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) True) % 3.90/4.12 Clause #29 (by clausification #[27]): ∀ (a : Iota), Or (Eq setadjoinIL False) (Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True) % 3.90/4.12 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq setadjoinIL False) (Eq (in a (setadjoin a a_1)) True) % 3.90/4.12 Clause #45 (by clausification #[2]): Eq upairset2E (∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy)) % 3.90/4.12 Clause #49 (by clausification #[4]): Eq % 3.90/4.12 (setadjoinIL → % 3.90/4.12 uniqinunit → % 3.90/4.12 upairset2E → % 3.90/4.12 singletonsuniq → % 3.90/4.12 ∀ (Xx Xy Xz : Iota), % 3.90/4.12 in (setadjoin Xz emptyset) % 3.90/4.12 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 3.90/4.12 Eq Xx Xz) % 3.90/4.12 False % 3.90/4.12 Clause #50 (by clausification #[49]): Eq setadjoinIL True % 3.90/4.12 Clause #51 (by clausification #[49]): Eq % 3.90/4.12 (uniqinunit → % 3.90/4.12 upairset2E → % 3.90/4.12 singletonsuniq → % 3.90/4.12 ∀ (Xx Xy Xz : Iota), % 3.90/4.12 in (setadjoin Xz emptyset) % 3.90/4.12 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 3.90/4.12 Eq Xx Xz) % 3.90/4.12 False % 3.90/4.12 Clause #53 (by backward demodulation #[50, 30]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a a_1)) True) % 3.90/4.12 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 3.90/4.12 Clause #58 (by clausification #[51]): Eq uniqinunit True % 3.90/4.12 Clause #59 (by clausification #[51]): Eq % 3.90/4.12 (upairset2E → % 3.90/4.12 singletonsuniq → % 3.90/4.12 ∀ (Xx Xy Xz : Iota), % 3.90/4.12 in (setadjoin Xz emptyset) % 3.90/4.12 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 3.90/4.12 Eq Xx Xz) % 3.90/4.12 False % 3.90/4.12 Clause #60 (by backward demodulation #[58, 21]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.90/4.12 Clause #64 (by clausification #[60]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 3.90/4.12 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 3.90/4.12 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.90/4.12 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 3.90/4.12 Clause #71 (by clausification #[59]): Eq upairset2E True % 3.90/4.12 Clause #72 (by clausification #[59]): Eq % 3.90/4.12 (singletonsuniq → % 3.90/4.12 ∀ (Xx Xy Xz : Iota), % 3.90/4.12 in (setadjoin Xz emptyset) % 3.90/4.12 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 3.90/4.12 Eq Xx Xz) % 3.90/4.12 False % 3.90/4.12 Clause #73 (by backward demodulation #[71, 45]): Eq True (∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy)) % 3.97/4.14 Clause #74 (by clausification #[72]): Eq singletonsuniq True % 3.97/4.14 Clause #75 (by clausification #[72]): Eq % 3.97/4.14 (∀ (Xx Xy Xz : Iota), % 3.97/4.14 in (setadjoin Xz emptyset) % 3.97/4.14 (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) → % 3.97/4.14 Eq Xx Xz) % 3.97/4.14 False % 3.97/4.14 Clause #76 (by backward demodulation #[74, 5]): Eq True (∀ (Xx Xy : Iota), Eq (setadjoin Xx emptyset) (setadjoin Xy emptyset) → Eq Xx Xy) % 3.97/4.14 Clause #82 (by clausification #[76]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq (setadjoin a emptyset) (setadjoin Xy emptyset) → Eq a Xy) True % 3.97/4.14 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Eq (Eq (setadjoin a emptyset) (setadjoin a_1 emptyset) → Eq a a_1) True % 3.97/4.14 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (Eq (setadjoin a emptyset) (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.97/4.14 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Ne (setadjoin a emptyset) (setadjoin a_1 emptyset)) % 3.97/4.14 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Or (Ne (setadjoin a emptyset) (setadjoin a_1 emptyset)) (Eq a a_1) % 3.97/4.14 Clause #87 (by clausification #[75]): ∀ (a : Iota), % 3.97/4.14 Eq % 3.97/4.14 (Not % 3.97/4.14 (∀ (Xy Xz : Iota), % 3.97/4.14 in (setadjoin Xz emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) emptyset)) → % 3.97/4.14 Eq (skS.0 6 a) Xz)) % 3.97/4.14 True % 3.97/4.14 Clause #88 (by clausification #[87]): ∀ (a : Iota), % 3.97/4.14 Eq % 3.97/4.14 (∀ (Xy Xz : Iota), % 3.97/4.14 in (setadjoin Xz emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) emptyset)) → % 3.97/4.14 Eq (skS.0 6 a) Xz) % 3.97/4.14 False % 3.97/4.14 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), % 3.97/4.14 Eq % 3.97/4.14 (Not % 3.97/4.14 (∀ (Xz : Iota), % 3.97/4.14 in (setadjoin Xz emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset)) → % 3.97/4.14 Eq (skS.0 6 a) Xz)) % 3.97/4.14 True % 3.97/4.14 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), % 3.97/4.14 Eq % 3.97/4.14 (∀ (Xz : Iota), % 3.97/4.14 in (setadjoin Xz emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset)) → % 3.97/4.14 Eq (skS.0 6 a) Xz) % 3.97/4.14 False % 3.97/4.14 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), % 3.97/4.14 Eq % 3.97/4.14 (Not % 3.97/4.14 (in (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset)) → % 3.97/4.14 Eq (skS.0 6 a) (skS.0 8 a a_1 a_2))) % 3.97/4.14 True % 3.97/4.14 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), % 3.97/4.14 Eq % 3.97/4.14 (in (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset)) → % 3.97/4.14 Eq (skS.0 6 a) (skS.0 8 a a_1 a_2)) % 3.97/4.14 False % 3.97/4.14 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), % 3.97/4.14 Eq % 3.97/4.14 (in (setadjoin (skS.0 8 a a_1 a_2) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) emptyset) % 3.97/4.14 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))) % 3.97/4.14 True % 3.97/4.14 Clause #94 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 6 a) (skS.0 8 a a_1 a_2)) False % 3.97/4.14 Clause #95 (by clausification #[73]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), in Xz (setadjoin a (setadjoin Xy emptyset)) → Or (Eq Xz a) (Eq Xz Xy)) True % 3.97/4.14 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), in Xz (setadjoin a (setadjoin a_1 emptyset)) → Or (Eq Xz a) (Eq Xz a_1)) True % 3.97/4.14 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset)) → Or (Eq a a_1) (Eq a a_2)) True % 3.97/4.14 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Eq (Or (Eq a a_1) (Eq a a_2)) True) % 3.97/4.15 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), % 3.97/4.15 Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Or (Eq (Eq a a_1) True) (Eq (Eq a a_2) True)) % 3.97/4.15 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Or (Eq (Eq a a_2) True) (Eq a a_1)) % 3.97/4.15 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Or (Eq a a_1) (Eq a a_2)) % 3.97/4.15 Clause #102 (by superposition #[101, 93]): ∀ (a a_1 a_2 : Iota), % 3.97/4.15 Or (Eq (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (skS.0 6 a) emptyset)) % 3.97/4.15 (Or (Eq (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset))) % 3.97/4.15 (Eq False True)) % 3.97/4.15 Clause #122 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 6 a) (skS.0 8 a a_1 a_2) % 3.97/4.15 Clause #131 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 3.97/4.15 Or (Eq (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (skS.0 6 a) emptyset)) % 3.97/4.15 (Eq (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset))) % 3.97/4.15 Clause #147 (by superposition #[131, 55]): ∀ (a a_1 a_2 : Iota), % 3.97/4.15 Or (Eq (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (skS.0 6 a) emptyset)) % 3.97/4.15 (Eq (in (skS.0 6 a) (setadjoin (skS.0 8 a a_1 a_2) emptyset)) True) % 3.97/4.15 Clause #150 (by superposition #[147, 67]): ∀ (a a_1 a_2 : Iota), % 3.97/4.15 Or (Eq (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (skS.0 6 a) emptyset)) % 3.97/4.15 (Or (Eq True False) (Eq (skS.0 6 a) (skS.0 8 a a_1 a_2))) % 3.97/4.15 Clause #152 (by clausification #[150]): ∀ (a a_1 a_2 : Iota), % 3.97/4.15 Or (Eq (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (skS.0 6 a) emptyset)) (Eq (skS.0 6 a) (skS.0 8 a a_1 a_2)) % 3.97/4.15 Clause #153 (by forward contextual literal cutting #[152, 86]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 6 a) (skS.0 8 a a_1 a_2) % 3.97/4.15 Clause #154 (by forward contextual literal cutting #[153, 122]): False % 3.97/4.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------