%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU557^2 : TPTP v9.2.0. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:01:54 PM UTC 2025 % Result : Theorem 11.30s 11.49s % Output : Proof 11.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU557^2 : TPTP v9.2.0. Bugfixed v5.2.0. % 0.13/0.13 % Command : duper %s % 0.14/0.35 % Computer : n005.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 05:12:38 EDT 2025 % 0.21/0.35 % CPUTime : % 11.30/11.49 SZS status Theorem for theBenchmark.p % 11.30/11.49 SZS output start Proof for theBenchmark.p % 11.30/11.49 Clause #1 (by assumption #[]): Eq (Eq exuEu (∀ (Xphi : Iota → Prop), (exu fun Xx => Xphi Xx) → ∀ (Xx Xy : Iota), Xphi Xx → Xphi Xy → Eq Xx Xy)) True % 11.30/11.49 Clause #2 (by assumption #[]): Eq (Eq descrp (∀ (Xphi : Iota → Prop), (exu fun Xx => Xphi Xx) → Xphi (descr fun Xx => Xphi Xx))) True % 11.30/11.49 Clause #3 (by assumption #[]): Eq % 11.30/11.49 (Not % 11.30/11.49 (descrp → % 11.30/11.49 exuEu → % 11.30/11.49 ∀ (Xphi Xpsi : Iota → Prop), % 11.30/11.49 (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (Xphi Xx) (Xpsi Xy)) → % 11.30/11.49 (exu fun Xx => Xphi Xx) → (exu fun Xx => Xpsi Xx) → Eq (descr fun Xx => Xphi Xx) (descr fun Xx => Xpsi Xx))) % 11.30/11.49 True % 11.30/11.49 Clause #4 (by betaEtaReduce #[2]): Eq (Eq descrp (∀ (Xphi : Iota → Prop), exu Xphi → Xphi (descr Xphi))) True % 11.30/11.49 Clause #5 (by clausification #[4]): Eq descrp (∀ (Xphi : Iota → Prop), exu Xphi → Xphi (descr Xphi)) % 11.30/11.49 Clause #15 (by betaEtaReduce #[1]): Eq (Eq exuEu (∀ (Xphi : Iota → Prop), exu Xphi → ∀ (Xx Xy : Iota), Xphi Xx → Xphi Xy → Eq Xx Xy)) True % 11.30/11.49 Clause #16 (by clausification #[15]): Eq exuEu (∀ (Xphi : Iota → Prop), exu Xphi → ∀ (Xx Xy : Iota), Xphi Xx → Xphi Xy → Eq Xx Xy) % 11.30/11.49 Clause #48 (by betaEtaReduce #[3]): Eq % 11.30/11.49 (Not % 11.30/11.49 (descrp → % 11.30/11.49 exuEu → % 11.30/11.49 ∀ (Xphi Xpsi : Iota → Prop), % 11.30/11.49 (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (Xphi Xx) (Xpsi Xy)) → exu Xphi → exu Xpsi → Eq (descr Xphi) (descr Xpsi))) % 11.30/11.49 True % 11.30/11.49 Clause #49 (by clausification #[48]): Eq % 11.30/11.49 (descrp → % 11.30/11.49 exuEu → % 11.30/11.49 ∀ (Xphi Xpsi : Iota → Prop), % 11.30/11.49 (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (Xphi Xx) (Xpsi Xy)) → exu Xphi → exu Xpsi → Eq (descr Xphi) (descr Xpsi)) % 11.30/11.49 False % 11.30/11.49 Clause #50 (by clausification #[49]): Eq descrp True % 11.30/11.49 Clause #51 (by clausification #[49]): Eq % 11.30/11.49 (exuEu → % 11.30/11.49 ∀ (Xphi Xpsi : Iota → Prop), % 11.30/11.49 (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (Xphi Xx) (Xpsi Xy)) → exu Xphi → exu Xpsi → Eq (descr Xphi) (descr Xpsi)) % 11.30/11.49 False % 11.30/11.49 Clause #52 (by backward demodulation #[50, 5]): Eq True (∀ (Xphi : Iota → Prop), exu Xphi → Xphi (descr Xphi)) % 11.30/11.49 Clause #56 (by clausification #[52]): ∀ (a : Iota → Prop), Eq (exu a → a (descr a)) True % 11.30/11.49 Clause #57 (by clausification #[56]): ∀ (a : Iota → Prop), Or (Eq (exu a) False) (Eq (a (descr a)) True) % 11.30/11.49 Clause #65 (by clausification #[51]): Eq exuEu True % 11.30/11.49 Clause #66 (by clausification #[51]): Eq % 11.30/11.49 (∀ (Xphi Xpsi : Iota → Prop), % 11.30/11.49 (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (Xphi Xx) (Xpsi Xy)) → exu Xphi → exu Xpsi → Eq (descr Xphi) (descr Xpsi)) % 11.30/11.49 False % 11.30/11.49 Clause #67 (by backward demodulation #[65, 16]): Eq True (∀ (Xphi : Iota → Prop), exu Xphi → ∀ (Xx Xy : Iota), Xphi Xx → Xphi Xy → Eq Xx Xy) % 11.30/11.49 Clause #74 (by clausification #[67]): ∀ (a : Iota → Prop), Eq (exu a → ∀ (Xx Xy : Iota), a Xx → a Xy → Eq Xx Xy) True % 11.30/11.49 Clause #75 (by clausification #[74]): ∀ (a : Iota → Prop), Or (Eq (exu a) False) (Eq (∀ (Xx Xy : Iota), a Xx → a Xy → Eq Xx Xy) True) % 11.30/11.49 Clause #76 (by clausification #[75]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (exu a) False) (Eq (∀ (Xy : Iota), a a_1 → a Xy → Eq a_1 Xy) True) % 11.30/11.49 Clause #77 (by clausification #[76]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (exu a) False) (Eq (a a_1 → a a_2 → Eq a_1 a_2) True) % 11.30/11.49 Clause #78 (by clausification #[77]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (exu a) False) (Or (Eq (a a_1) False) (Eq (a a_2 → Eq a_1 a_2) True)) % 11.30/11.49 Clause #79 (by clausification #[78]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 11.30/11.49 Or (Eq (exu a) False) (Or (Eq (a a_1) False) (Or (Eq (a a_2) False) (Eq (Eq a_1 a_2) True))) % 11.30/11.49 Clause #80 (by clausification #[79]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (exu a) False) (Or (Eq (a a_1) False) (Or (Eq (a a_2) False) (Eq a_1 a_2))) % 11.30/11.49 Clause #82 (by clausification #[66]): ∀ (a : Iota → Prop), % 11.30/11.49 Eq % 11.30/11.49 (Not % 11.30/11.49 (∀ (Xpsi : Iota → Prop), % 11.30/11.49 (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (skS.0 4 a Xx) (Xpsi Xy)) → % 11.30/11.49 exu (skS.0 4 a) → exu Xpsi → Eq (descr (skS.0 4 a)) (descr Xpsi))) % 11.30/11.49 True % 11.30/11.49 Clause #83 (by clausification #[82]): ∀ (a : Iota → Prop), % 11.30/11.52 Eq % 11.30/11.52 (∀ (Xpsi : Iota → Prop), % 11.30/11.52 (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (skS.0 4 a Xx) (Xpsi Xy)) → % 11.30/11.52 exu (skS.0 4 a) → exu Xpsi → Eq (descr (skS.0 4 a)) (descr Xpsi)) % 11.30/11.52 False % 11.30/11.52 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota → Prop), % 11.30/11.52 Eq % 11.30/11.52 (Not % 11.30/11.52 ((∀ (Xx Xy : Iota), Eq Xx Xy → Iff (skS.0 4 a Xx) (skS.0 5 a a_1 Xy)) → % 11.30/11.52 exu (skS.0 4 a) → exu (skS.0 5 a a_1) → Eq (descr (skS.0 4 a)) (descr (skS.0 5 a a_1)))) % 11.30/11.52 True % 11.30/11.52 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota → Prop), % 11.30/11.52 Eq % 11.30/11.52 ((∀ (Xx Xy : Iota), Eq Xx Xy → Iff (skS.0 4 a Xx) (skS.0 5 a a_1 Xy)) → % 11.30/11.52 exu (skS.0 4 a) → exu (skS.0 5 a a_1) → Eq (descr (skS.0 4 a)) (descr (skS.0 5 a a_1))) % 11.30/11.52 False % 11.30/11.52 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota → Prop), Eq (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (skS.0 4 a Xx) (skS.0 5 a a_1 Xy)) True % 11.30/11.52 Clause #87 (by clausification #[85]): ∀ (a a_1 : Iota → Prop), % 11.30/11.52 Eq (exu (skS.0 4 a) → exu (skS.0 5 a a_1) → Eq (descr (skS.0 4 a)) (descr (skS.0 5 a a_1))) False % 11.30/11.52 Clause #88 (by clausification #[86]): ∀ (a : Iota) (a_1 a_2 : Iota → Prop), Eq (∀ (Xy : Iota), Eq a Xy → Iff (skS.0 4 a_1 a) (skS.0 5 a_1 a_2 Xy)) True % 11.30/11.52 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota) (a_2 a_3 : Iota → Prop), Eq (Eq a a_1 → Iff (skS.0 4 a_2 a) (skS.0 5 a_2 a_3 a_1)) True % 11.30/11.52 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota) (a_2 a_3 : Iota → Prop), Or (Eq (Eq a a_1) False) (Eq (Iff (skS.0 4 a_2 a) (skS.0 5 a_2 a_3 a_1)) True) % 11.30/11.52 Clause #91 (by clausification #[90]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop) (a_3 : Iota), % 11.30/11.52 Or (Eq (Iff (skS.0 4 a a_1) (skS.0 5 a a_2 a_3)) True) (Ne a_1 a_3) % 11.30/11.52 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota) (a_2 a_3 : Iota → Prop), Or (Ne a a_1) (Or (Eq (skS.0 4 a_2 a) True) (Eq (skS.0 5 a_2 a_3 a_1) False)) % 11.30/11.52 Clause #94 (by destructive equality resolution #[92]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (skS.0 4 a a_1) True) (Eq (skS.0 5 a a_2 a_1) False) % 11.30/11.52 Clause #775 (by clausification #[87]): ∀ (a : Iota → Prop), Eq (exu (skS.0 4 a)) True % 11.30/11.52 Clause #776 (by clausification #[87]): ∀ (a a_1 : Iota → Prop), Eq (exu (skS.0 5 a a_1) → Eq (descr (skS.0 4 a)) (descr (skS.0 5 a a_1))) False % 11.30/11.52 Clause #777 (by superposition #[775, 57]): ∀ (a : Iota → Prop), Or (Eq True False) (Eq (skS.0 4 a (descr (skS.0 4 a))) True) % 11.30/11.52 Clause #778 (by superposition #[775, 80]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 11.30/11.52 Or (Eq True False) (Or (Eq (skS.0 4 a a_1) False) (Or (Eq (skS.0 4 a a_2) False) (Eq a_1 a_2))) % 11.30/11.52 Clause #810 (by clausification #[777]): ∀ (a : Iota → Prop), Eq (skS.0 4 a (descr (skS.0 4 a))) True % 11.30/11.52 Clause #1172 (by clausification #[776]): ∀ (a a_1 : Iota → Prop), Eq (exu (skS.0 5 a a_1)) True % 11.30/11.52 Clause #1173 (by clausification #[776]): ∀ (a a_1 : Iota → Prop), Eq (Eq (descr (skS.0 4 a)) (descr (skS.0 5 a a_1))) False % 11.30/11.52 Clause #1174 (by superposition #[1172, 57]): ∀ (a a_1 : Iota → Prop), Or (Eq True False) (Eq (skS.0 5 a a_1 (descr (skS.0 5 a a_1))) True) % 11.30/11.52 Clause #1212 (by clausification #[1173]): ∀ (a a_1 : Iota → Prop), Ne (descr (skS.0 4 a)) (descr (skS.0 5 a a_1)) % 11.30/11.52 Clause #1214 (by clausification #[1174]): ∀ (a a_1 : Iota → Prop), Eq (skS.0 5 a a_1 (descr (skS.0 5 a a_1))) True % 11.30/11.52 Clause #1215 (by superposition #[1214, 94]): ∀ (a a_1 : Iota → Prop), Or (Eq (skS.0 4 a (descr (skS.0 5 a a_1))) True) (Eq True False) % 11.30/11.52 Clause #1245 (by clausification #[1215]): ∀ (a a_1 : Iota → Prop), Eq (skS.0 4 a (descr (skS.0 5 a a_1))) True % 11.30/11.52 Clause #1421 (by clausification #[778]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (skS.0 4 a a_1) False) (Or (Eq (skS.0 4 a a_2) False) (Eq a_1 a_2)) % 11.30/11.52 Clause #1422 (by superposition #[1421, 810]): ∀ (a : Iota → Prop) (a_1 : Iota), % 11.30/11.52 Or (Eq (skS.0 4 (fun x => a x) a_1) False) (Or (Eq (descr (skS.0 4 a)) a_1) (Eq False True)) % 11.30/11.52 Clause #1499 (by betaEtaReduce #[1422]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 4 a a_1) False) (Or (Eq (descr (skS.0 4 a)) a_1) (Eq False True)) % 11.44/11.61 Clause #1500 (by clausification #[1499]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 4 a a_1) False) (Eq (descr (skS.0 4 a)) a_1) % 11.44/11.61 Clause #1502 (by superposition #[1500, 1245]): ∀ (a a_1 : Iota → Prop), Or (Eq (descr (skS.0 4 fun x => a x)) (descr (skS.0 5 a a_1))) (Eq False True) % 11.44/11.61 Clause #1533 (by betaEtaReduce #[1502]): ∀ (a a_1 : Iota → Prop), Or (Eq (descr (skS.0 4 a)) (descr (skS.0 5 a a_1))) (Eq False True) % 11.44/11.61 Clause #1534 (by clausification #[1533]): ∀ (a a_1 : Iota → Prop), Eq (descr (skS.0 4 a)) (descr (skS.0 5 a a_1)) % 11.44/11.61 Clause #1535 (by forward contextual literal cutting #[1534, 1212]): False % 11.44/11.61 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------