%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV076^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:02:49 PM UTC 2025 % Result : Theorem 4.23s 4.39s % Output : Proof 4.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV076^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 01:21:53 EDT 2025 % 0.14/0.34 % CPUTime : % 4.23/4.39 SZS status Theorem for theBenchmark.p % 4.23/4.39 SZS output start Proof for theBenchmark.p % 4.23/4.39 Clause #0 (by assumption #[]): Eq % 4.23/4.39 (Not % 4.23/4.39 (∀ (RRR : a → a → Prop) (U : (a → Prop) → a), % 4.23/4.39 And (∀ (Xx Xy Xz : a), And (RRR Xx Xy) (RRR Xy Xz) → RRR Xx Xz) % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → RRR Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → RRR Xk Xj) → RRR (U Xs) Xj)) → % 4.23/4.39 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → RRR Xz Xb)) % 4.23/4.39 True % 4.23/4.39 Clause #1 (by clausification #[0]): Eq % 4.23/4.39 (∀ (RRR : a → a → Prop) (U : (a → Prop) → a), % 4.23/4.39 And (∀ (Xx Xy Xz : a), And (RRR Xx Xy) (RRR Xy Xz) → RRR Xx Xz) % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → RRR Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → RRR Xk Xj) → RRR (U Xs) Xj)) → % 4.23/4.39 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → RRR Xz Xb) % 4.23/4.39 False % 4.23/4.39 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 4.23/4.39 Eq % 4.23/4.39 (Not % 4.23/4.39 (∀ (U : (a → Prop) → a), % 4.23/4.39 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) % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs)) % 4.23/4.39 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) → % 4.23/4.39 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb)) % 4.23/4.39 True % 4.23/4.39 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 4.23/4.39 Eq % 4.23/4.39 (∀ (U : (a → Prop) → a), % 4.23/4.39 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) % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs)) % 4.23/4.39 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) → % 4.23/4.39 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb) % 4.23/4.39 False % 4.23/4.39 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 4.23/4.39 Eq % 4.23/4.39 (Not % 4.23/4.39 (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) % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 4.23/4.39 (∀ (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)) → % 4.23/4.39 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb)) % 4.23/4.39 True % 4.23/4.39 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 4.23/4.39 Eq % 4.23/4.39 (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) % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 4.23/4.39 (∀ (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)) → % 4.23/4.39 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb) % 4.23/4.39 False % 4.23/4.39 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 4.23/4.39 Eq % 4.23/4.39 (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) % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 4.23/4.39 (∀ (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))) % 4.23/4.39 True % 4.23/4.39 Clause #7 (by clausification #[5]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb) False % 4.23/4.39 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a), % 4.23/4.39 Eq % 4.23/4.39 (∀ (Xs : a → Prop), % 4.23/4.39 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs)) % 4.23/4.39 (∀ (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)) % 4.23/4.39 True % 4.23/4.39 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a), % 4.23/4.39 Eq % 4.23/4.39 (And (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1)) % 4.23/4.41 (∀ (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)) % 4.23/4.41 True % 4.23/4.41 Clause #11 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a), % 4.23/4.41 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 % 4.23/4.41 Clause #12 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a), % 4.23/4.41 Eq (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1)) True % 4.23/4.41 Clause #13 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 4.23/4.41 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 % 4.23/4.41 Clause #14 (by clausification #[13]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 4.23/4.41 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) % 4.23/4.41 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a), % 4.23/4.41 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True) % 4.23/4.41 (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) % 4.23/4.41 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a), % 4.23/4.41 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True) % 4.23/4.41 (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) % 4.23/4.41 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a), % 4.23/4.41 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) % 4.23/4.41 Clause #51 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop), % 4.23/4.41 Eq (Not (Exists fun Xb => ∀ (Xz : a), skS.0 3 a_1 a_2 Xz → skS.0 0 a_1 Xz Xb)) True % 4.23/4.41 Clause #52 (by clausification #[51]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop), Eq (Exists fun Xb => ∀ (Xz : a), skS.0 3 a_1 a_2 Xz → skS.0 0 a_1 Xz Xb) False % 4.23/4.41 Clause #53 (by clausification #[52]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 : a), Eq (∀ (Xz : a), skS.0 3 a_1 a_2 Xz → skS.0 0 a_1 Xz a_3) False % 4.23/4.41 Clause #54 (by clausification #[53]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 a_4 : a), % 4.23/4.41 Eq (Not (skS.0 3 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4) a_3)) True % 4.23/4.41 Clause #55 (by clausification #[54]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 a_4 : a), % 4.23/4.41 Eq (skS.0 3 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4) a_3) False % 4.23/4.41 Clause #57 (by clausification #[55]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4) a_3) False % 4.23/4.41 Clause #67 (by fluidSup #[57, 17]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a), % 4.23/4.41 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) % 4.23/4.41 Clause #68 (by clausification #[12]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : (a → Prop) → a), % 4.23/4.41 Eq (a_1 a_2 → skS.0 0 a_3 a_2 (skS.0 1 a_3 a_4 a_1)) True % 4.23/4.41 Clause #69 (by clausification #[68]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : (a → Prop) → a), % 4.23/4.41 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) % 4.23/4.41 Clause #83 (by betaEtaReduce #[67]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a), % 4.23/4.41 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) % 4.23/4.41 Clause #118 (by fluidBoolHoist #[83]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a) (a_4 : a), % 4.23/4.41 Or (Eq a_1 True) (Or (Eq (skS.0 0 a_2 (skS.0 1 a_2 a_3 fun x => False) a_4) True) (Eq a_1 True)) % 4.23/4.41 Clause #121 (by eliminate duplicate literals #[118]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a) (a_4 : a), % 4.23/4.41 Or (Eq a_1 True) (Eq (skS.0 0 a_2 (skS.0 1 a_2 a_3 fun x => False) a_4) True) % 4.23/4.41 Clause #122 (by superposition #[121, 57]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a), % 4.23/4.42 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => False) a_3) True) (Eq True False) % 4.23/4.42 Clause #153 (by clausification #[122]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => False) a_3) True % 4.23/4.42 Clause #162 (by fluidSup #[153, 69]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 4.23/4.42 Or (Eq ((fun _ => a_1) True) False) (Eq (skS.0 0 a_2 a_3 (skS.0 1 a_2 a_4 fun x => a_1)) True) % 4.23/4.42 Clause #168 (by betaEtaReduce #[162]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a), % 4.23/4.42 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) % 4.23/4.42 Clause #173 (by falseElim #[168]): ∀ (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 % 4.23/4.42 Clause #180 (by superposition #[173, 57]): Eq True False % 4.23/4.42 Clause #194 (by clausification #[180]): False % 4.23/4.42 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------