%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV054^5 : TPTP v9.2.0. Released v4.0.0. % 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 08:02:47 PM UTC 2025 % Result : Theorem 3.77s 4.00s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEV054^5 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.14 % Command : duper %s % 0.13/0.35 % Computer : n024.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 01:49:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.77/4.00 SZS status Theorem for theBenchmark.p % 3.77/4.00 SZS output start Proof for theBenchmark.p % 3.77/4.00 Clause #0 (by assumption #[]): Eq % 3.77/4.00 (Not % 3.77/4.00 (∀ (R : a → a → Prop) (U : (a → Prop) → a), % 3.77/4.00 And (∀ (Xx Xy Xz : a), And (R Xx Xy) (R Xy Xz) → R Xx Xz) % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → R Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → R Xk Xj) → R (U Xs) Xj)) → % 3.77/4.00 ∀ (Xf : a → a), (∀ (Xx Xy : a), R Xx Xy → R (Xf Xx) (Xf Xy)) → Exists fun Xw => R (Xf Xw) Xw)) % 3.77/4.00 True % 3.77/4.00 Clause #1 (by clausification #[0]): Eq % 3.77/4.00 (∀ (R : a → a → Prop) (U : (a → Prop) → a), % 3.77/4.00 And (∀ (Xx Xy Xz : a), And (R Xx Xy) (R Xy Xz) → R Xx Xz) % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → R Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → R Xk Xj) → R (U Xs) Xj)) → % 3.77/4.00 ∀ (Xf : a → a), (∀ (Xx Xy : a), R Xx Xy → R (Xf Xx) (Xf Xy)) → Exists fun Xw => R (Xf Xw) Xw) % 3.77/4.00 False % 3.77/4.00 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 3.77/4.00 Eq % 3.77/4.00 (Not % 3.77/4.00 (∀ (U : (a → Prop) → a), % 3.77/4.00 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) % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs)) % 3.77/4.00 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) → % 3.77/4.00 ∀ (Xf : a → a), % 3.77/4.00 (∀ (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 (Xf Xw) Xw)) % 3.77/4.00 True % 3.77/4.00 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 3.77/4.00 Eq % 3.77/4.00 (∀ (U : (a → Prop) → a), % 3.77/4.00 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) % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs)) % 3.77/4.00 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) → % 3.77/4.00 ∀ (Xf : a → a), % 3.77/4.00 (∀ (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 (Xf Xw) Xw) % 3.77/4.00 False % 3.77/4.00 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 3.77/4.00 Eq % 3.77/4.00 (Not % 3.77/4.00 (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) % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 3.77/4.00 (∀ (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)) → % 3.77/4.00 ∀ (Xf : a → a), % 3.77/4.00 (∀ (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 (Xf Xw) Xw)) % 3.77/4.00 True % 3.77/4.00 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 3.77/4.00 Eq % 3.77/4.00 (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) % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 3.77/4.00 (∀ (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)) → % 3.77/4.00 ∀ (Xf : a → a), % 3.77/4.00 (∀ (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 (Xf Xw) Xw) % 3.77/4.00 False % 3.77/4.00 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 3.77/4.00 Eq % 3.77/4.00 (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) % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 3.77/4.00 (∀ (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))) % 3.77/4.00 True % 3.77/4.00 Clause #7 (by clausification #[5]): ∀ (a_1 : a → a → Prop), % 3.77/4.00 Eq % 3.77/4.00 (∀ (Xf : a → a), % 3.77/4.00 (∀ (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 (Xf Xw) Xw) % 3.77/4.00 False % 3.77/4.00 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 3.77/4.00 Eq % 3.77/4.00 (∀ (Xs : a → Prop), % 3.77/4.00 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 3.77/4.02 (∀ (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)) % 3.77/4.02 True % 3.77/4.02 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a), % 3.77/4.02 Eq % 3.77/4.02 (And (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1)) % 3.77/4.02 (∀ (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)) % 3.77/4.02 True % 3.77/4.02 Clause #12 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a), % 3.77/4.02 Eq (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1)) True % 3.77/4.02 Clause #51 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a → a), % 3.77/4.02 Eq % 3.77/4.02 (Not % 3.77/4.02 ((∀ (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)) → % 3.77/4.02 Exists fun Xw => skS.0 0 a_1 (skS.0 3 a_1 a_2 Xw) Xw)) % 3.77/4.02 True % 3.77/4.02 Clause #52 (by clausification #[51]): ∀ (a_1 : a → a → Prop) (a_2 : a → a), % 3.77/4.02 Eq % 3.77/4.02 ((∀ (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)) → % 3.77/4.02 Exists fun Xw => skS.0 0 a_1 (skS.0 3 a_1 a_2 Xw) Xw) % 3.77/4.02 False % 3.77/4.02 Clause #54 (by clausification #[52]): ∀ (a_1 : a → a → Prop) (a_2 : a → a), Eq (Exists fun Xw => skS.0 0 a_1 (skS.0 3 a_1 a_2 Xw) Xw) False % 3.77/4.02 Clause #60 (by clausification #[12]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : (a → Prop) → a), % 3.77/4.02 Eq (a_1 a_2 → skS.0 0 a_3 a_2 (skS.0 1 a_3 a_4 a_1)) True % 3.77/4.02 Clause #61 (by clausification #[60]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : (a → Prop) → a), % 3.77/4.02 Or (Eq (a_1 a_2) False) (Eq (skS.0 0 a_3 a_2 (skS.0 1 a_3 a_4 a_1)) True) % 3.77/4.02 Clause #73 (by clausification #[54]): ∀ (a_1 : a → a → Prop) (a_2 : a → a) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) a_3) False % 3.77/4.02 Clause #75 (by fluidSup #[73, 61]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 3.77/4.02 Or (Eq ((fun _ => a_1) False) False) (Eq (skS.0 0 a_2 a_3 (skS.0 1 a_2 a_4 fun x => a_1)) True) % 3.77/4.02 Clause #83 (by betaEtaReduce #[75]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 3.77/4.02 Or (Eq a_1 False) (Eq (skS.0 0 a_2 a_3 (skS.0 1 a_2 a_4 fun x => a_1)) True) % 3.77/4.02 Clause #85 (by falseElim #[83]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : (a → Prop) → a), Eq (skS.0 0 a_1 a_2 (skS.0 1 a_1 a_3 fun x => True)) True % 3.77/4.02 Clause #93 (by superposition #[85, 73]): Eq True False % 3.77/4.02 Clause #110 (by clausification #[93]): False % 3.77/4.02 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------