%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV055^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:02:47 PM UTC 2025 % Result : Theorem 5.90s 6.08s % Output : Proof 5.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV055^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.33 % Computer : n006.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Fri Oct 3 01:36:53 EDT 2025 % 0.13/0.34 % CPUTime : % 5.90/6.08 SZS status Theorem for theBenchmark.p % 5.90/6.08 SZS output start Proof for theBenchmark.p % 5.90/6.08 Clause #0 (by assumption #[]): Eq % 5.90/6.08 (Not % 5.90/6.08 (∀ (R : a → a → Prop) (U : (a → Prop) → a), % 5.90/6.08 And (∀ (Xx Xy Xz : a), And (R Xx Xy) (R Xy Xz) → R Xx Xz) % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → R Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → R Xk Xj) → R (U Xs) Xj)) → % 5.90/6.08 ∀ (Xf : a → a), (∀ (Xx Xy : a), R Xx Xy → R (Xf Xx) (Xf Xy)) → Exists fun Xw => R Xw (Xf Xw))) % 5.90/6.08 True % 5.90/6.08 Clause #1 (by clausification #[0]): Eq % 5.90/6.08 (∀ (R : a → a → Prop) (U : (a → Prop) → a), % 5.90/6.08 And (∀ (Xx Xy Xz : a), And (R Xx Xy) (R Xy Xz) → R Xx Xz) % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → R Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → R Xk Xj) → R (U Xs) Xj)) → % 5.90/6.08 ∀ (Xf : a → a), (∀ (Xx Xy : a), R Xx Xy → R (Xf Xx) (Xf Xy)) → Exists fun Xw => R Xw (Xf Xw)) % 5.90/6.08 False % 5.90/6.08 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 5.90/6.08 Eq % 5.90/6.08 (Not % 5.90/6.08 (∀ (U : (a → Prop) → a), % 5.90/6.08 And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz) % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs)) % 5.90/6.08 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) → % 5.90/6.08 ∀ (Xf : a → a), % 5.90/6.08 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw))) % 5.90/6.08 True % 5.90/6.08 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 5.90/6.08 Eq % 5.90/6.08 (∀ (U : (a → Prop) → a), % 5.90/6.08 And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz) % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs)) % 5.90/6.08 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) → % 5.90/6.08 ∀ (Xf : a → a), % 5.90/6.08 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw)) % 5.90/6.08 False % 5.90/6.08 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 5.90/6.08 Eq % 5.90/6.08 (Not % 5.90/6.08 (And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz) % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 5.90/6.08 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj)) → % 5.90/6.08 ∀ (Xf : a → a), % 5.90/6.08 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw))) % 5.90/6.08 True % 5.90/6.08 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 5.90/6.08 Eq % 5.90/6.08 (And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz) % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 5.90/6.08 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj)) → % 5.90/6.08 ∀ (Xf : a → a), % 5.90/6.08 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw)) % 5.90/6.08 False % 5.90/6.08 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 5.90/6.08 Eq % 5.90/6.08 (And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz) % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 5.90/6.08 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj))) % 5.90/6.08 True % 5.90/6.08 Clause #7 (by clausification #[5]): ∀ (a_1 : a → a → Prop), % 5.90/6.08 Eq % 5.90/6.08 (∀ (Xf : a → a), % 5.90/6.08 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw)) % 5.90/6.08 False % 5.90/6.08 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 5.90/6.08 Eq % 5.90/6.08 (∀ (Xs : a → Prop), % 5.90/6.08 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 5.95/6.13 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj)) % 5.95/6.13 True % 5.95/6.13 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a), % 5.95/6.13 Eq % 5.95/6.13 (And (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1)) % 5.95/6.13 (∀ (Xj : a), (∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk Xj) → skS.0 0 a_2 (skS.0 1 a_2 a_3 a_1) Xj)) % 5.95/6.13 True % 5.95/6.13 Clause #11 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a), % 5.95/6.13 Eq (∀ (Xj : a), (∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk Xj) → skS.0 0 a_2 (skS.0 1 a_2 a_3 a_1) Xj) True % 5.95/6.13 Clause #13 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 5.95/6.13 Eq ((∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk a_3) → skS.0 0 a_2 (skS.0 1 a_2 a_4 a_1) a_3) True % 5.95/6.13 Clause #14 (by clausification #[13]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 5.95/6.13 Or (Eq (∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk a_3) False) (Eq (skS.0 0 a_2 (skS.0 1 a_2 a_4 a_1) a_3) True) % 5.95/6.13 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a), % 5.95/6.13 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True) % 5.95/6.13 (Eq (Not (a_3 (skS.0 2 a_3 a_1 a_4 a_5) → skS.0 0 a_1 (skS.0 2 a_3 a_1 a_4 a_5) a_4)) True) % 5.95/6.13 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a), % 5.95/6.13 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True) % 5.95/6.13 (Eq (a_3 (skS.0 2 a_3 a_1 a_4 a_5) → skS.0 0 a_1 (skS.0 2 a_3 a_1 a_4 a_5) a_4) False) % 5.95/6.13 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a), % 5.95/6.13 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True) (Eq (a_3 (skS.0 2 a_3 a_1 a_4 a_5)) True) % 5.95/6.13 Clause #51 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a → a), % 5.95/6.13 Eq % 5.95/6.13 (Not % 5.95/6.13 ((∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (skS.0 3 a_1 a_2 Xx) (skS.0 3 a_1 a_2 Xy)) → % 5.95/6.13 Exists fun Xw => skS.0 0 a_1 Xw (skS.0 3 a_1 a_2 Xw))) % 5.95/6.13 True % 5.95/6.13 Clause #52 (by clausification #[51]): ∀ (a_1 : a → a → Prop) (a_2 : a → a), % 5.95/6.13 Eq % 5.95/6.13 ((∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (skS.0 3 a_1 a_2 Xx) (skS.0 3 a_1 a_2 Xy)) → % 5.95/6.13 Exists fun Xw => skS.0 0 a_1 Xw (skS.0 3 a_1 a_2 Xw)) % 5.95/6.13 False % 5.95/6.13 Clause #54 (by clausification #[52]): ∀ (a_1 : a → a → Prop) (a_2 : a → a), Eq (Exists fun Xw => skS.0 0 a_1 Xw (skS.0 3 a_1 a_2 Xw)) False % 5.95/6.13 Clause #73 (by clausification #[54]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → a), Eq (skS.0 0 a_1 a_2 (skS.0 3 a_1 a_3 a_2)) False % 5.95/6.13 Clause #75 (by fluidSup #[73, 17]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a), % 5.95/6.13 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => a_3) a_4) True) (Eq ((fun _ => a_3) False) True) % 5.95/6.13 Clause #84 (by betaEtaReduce #[75]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a), % 5.95/6.13 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => a_3) a_4) True) (Eq a_3 True) % 5.95/6.13 Clause #85 (by superposition #[84, 73]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 5.95/6.13 Clause #124 (by clausification #[85]): ∀ (a : Prop), Eq a True % 5.95/6.13 Clause #126 (by falseElim #[124]): False % 5.95/6.13 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------