%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN056^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:07:04 PM UTC 2025 % Result : Theorem 4.62s 4.80s % Output : Proof 4.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SYN056^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.11 % Command : duper %s % 0.12/0.31 % Computer : n028.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 300 % 0.12/0.31 % DateTime : Thu Oct 2 15:36:53 EDT 2025 % 0.12/0.31 % CPUTime : % 4.62/4.80 SZS status Theorem for theBenchmark.p % 4.62/4.80 SZS output start Proof for theBenchmark.p % 4.62/4.80 Clause #0 (by assumption #[]): Eq % 4.62/4.80 (Not % 4.62/4.80 (And (And ((Exists fun Xx => cP Xx) → Exists fun Xx => cQ Xx) ((Exists fun Xx => cQ Xx) → Exists fun Xx => cP Xx)) % 4.62/4.80 (∀ (Xx Xy : Iota), And (cP Xx) (cQ Xy) → And (cR Xx → cS Xy) (cS Xy → cR Xx)) → % 4.62/4.80 And ((∀ (Xx : Iota), cP Xx → cR Xx) → ∀ (Xx : Iota), cQ Xx → cS Xx) % 4.62/4.80 ((∀ (Xx : Iota), cQ Xx → cS Xx) → ∀ (Xx : Iota), cP Xx → cR Xx))) % 4.62/4.80 True % 4.62/4.80 Clause #1 (by betaEtaReduce #[0]): Eq % 4.62/4.80 (Not % 4.62/4.80 (And (And (Exists cP → Exists cQ) (Exists cQ → Exists cP)) % 4.62/4.80 (∀ (Xx Xy : Iota), And (cP Xx) (cQ Xy) → And (cR Xx → cS Xy) (cS Xy → cR Xx)) → % 4.62/4.80 And ((∀ (Xx : Iota), cP Xx → cR Xx) → ∀ (Xx : Iota), cQ Xx → cS Xx) % 4.62/4.80 ((∀ (Xx : Iota), cQ Xx → cS Xx) → ∀ (Xx : Iota), cP Xx → cR Xx))) % 4.62/4.80 True % 4.62/4.80 Clause #2 (by clausification #[1]): Eq % 4.62/4.80 (And (And (Exists cP → Exists cQ) (Exists cQ → Exists cP)) % 4.62/4.80 (∀ (Xx Xy : Iota), And (cP Xx) (cQ Xy) → And (cR Xx → cS Xy) (cS Xy → cR Xx)) → % 4.62/4.80 And ((∀ (Xx : Iota), cP Xx → cR Xx) → ∀ (Xx : Iota), cQ Xx → cS Xx) % 4.62/4.80 ((∀ (Xx : Iota), cQ Xx → cS Xx) → ∀ (Xx : Iota), cP Xx → cR Xx)) % 4.62/4.80 False % 4.62/4.80 Clause #3 (by clausification #[2]): Eq % 4.62/4.80 (And (And (Exists cP → Exists cQ) (Exists cQ → Exists cP)) % 4.62/4.80 (∀ (Xx Xy : Iota), And (cP Xx) (cQ Xy) → And (cR Xx → cS Xy) (cS Xy → cR Xx))) % 4.62/4.80 True % 4.62/4.80 Clause #4 (by clausification #[2]): Eq % 4.62/4.80 (And ((∀ (Xx : Iota), cP Xx → cR Xx) → ∀ (Xx : Iota), cQ Xx → cS Xx) % 4.62/4.80 ((∀ (Xx : Iota), cQ Xx → cS Xx) → ∀ (Xx : Iota), cP Xx → cR Xx)) % 4.62/4.80 False % 4.62/4.80 Clause #5 (by clausification #[3]): Eq (∀ (Xx Xy : Iota), And (cP Xx) (cQ Xy) → And (cR Xx → cS Xy) (cS Xy → cR Xx)) True % 4.62/4.80 Clause #6 (by clausification #[3]): Eq (And (Exists cP → Exists cQ) (Exists cQ → Exists cP)) True % 4.62/4.80 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Xy : Iota), And (cP a) (cQ Xy) → And (cR a → cS Xy) (cS Xy → cR a)) True % 4.62/4.80 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (And (cP a) (cQ a_1) → And (cR a → cS a_1) (cS a_1 → cR a)) True % 4.62/4.80 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (And (cP a) (cQ a_1)) False) (Eq (And (cR a → cS a_1) (cS a_1 → cR a)) True) % 4.62/4.80 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (And (cR a → cS a_1) (cS a_1 → cR a)) True) (Or (Eq (cP a) False) (Eq (cQ a_1) False)) % 4.62/4.80 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Or (Eq (cQ a_1) False) (Eq (cS a_1 → cR a) True)) % 4.62/4.80 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Or (Eq (cQ a_1) False) (Eq (cR a → cS a_1) True)) % 4.62/4.80 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Or (Eq (cQ a_1) False) (Or (Eq (cS a_1) False) (Eq (cR a) True))) % 4.62/4.80 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Or (Eq (cQ a_1) False) (Or (Eq (cR a) False) (Eq (cS a_1) True))) % 4.62/4.80 Clause #15 (by clausification #[6]): Eq (Exists cQ → Exists cP) True % 4.62/4.80 Clause #16 (by clausification #[6]): Eq (Exists cP → Exists cQ) True % 4.62/4.80 Clause #17 (by clausification #[15]): Or (Eq (Exists cQ) False) (Eq (Exists cP) True) % 4.62/4.80 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (Exists cP) True) (Eq (cQ a) False) % 4.62/4.80 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (cQ a) False) (Eq (cP (skS.0 0 a_1)) True) % 4.62/4.80 Clause #20 (by clausification #[16]): Or (Eq (Exists cP) False) (Eq (Exists cQ) True) % 4.62/4.80 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (Exists cQ) True) (Eq (cP a) False) % 4.62/4.80 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cQ (skS.0 1 a_1)) True) % 4.62/4.80 Clause #23 (by clausification #[4]): Or (Eq ((∀ (Xx : Iota), cP Xx → cR Xx) → ∀ (Xx : Iota), cQ Xx → cS Xx) False) % 4.62/4.80 (Eq ((∀ (Xx : Iota), cQ Xx → cS Xx) → ∀ (Xx : Iota), cP Xx → cR Xx) False) % 4.62/4.80 Clause #24 (by clausification #[23]): Or (Eq ((∀ (Xx : Iota), cQ Xx → cS Xx) → ∀ (Xx : Iota), cP Xx → cR Xx) False) (Eq (∀ (Xx : Iota), cP Xx → cR Xx) True) % 4.62/4.82 Clause #25 (by clausification #[23]): Or (Eq ((∀ (Xx : Iota), cQ Xx → cS Xx) → ∀ (Xx : Iota), cP Xx → cR Xx) False) (Eq (∀ (Xx : Iota), cQ Xx → cS Xx) False) % 4.62/4.82 Clause #26 (by clausification #[24]): Or (Eq (∀ (Xx : Iota), cP Xx → cR Xx) True) (Eq (∀ (Xx : Iota), cQ Xx → cS Xx) True) % 4.62/4.82 Clause #28 (by clausification #[26]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cQ Xx → cS Xx) True) (Eq (cP a → cR a) True) % 4.62/4.82 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (cP a → cR a) True) (Eq (cQ a_1 → cS a_1) True) % 4.62/4.82 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (cQ a → cS a) True) (Or (Eq (cP a_1) False) (Eq (cR a_1) True)) % 4.62/4.82 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Or (Eq (cR a) True) (Or (Eq (cQ a_1) False) (Eq (cS a_1) True))) % 4.62/4.82 Clause #32 (by clausification #[25]): Or (Eq (∀ (Xx : Iota), cQ Xx → cS Xx) False) (Eq (∀ (Xx : Iota), cQ Xx → cS Xx) True) % 4.62/4.82 Clause #33 (by clausification #[25]): Or (Eq (∀ (Xx : Iota), cQ Xx → cS Xx) False) (Eq (∀ (Xx : Iota), cP Xx → cR Xx) False) % 4.62/4.82 Clause #34 (by clausification #[32]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cQ Xx → cS Xx) True) (Eq (Not (cQ (skS.0 2 a) → cS (skS.0 2 a))) True) % 4.62/4.82 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Not (cQ (skS.0 2 a) → cS (skS.0 2 a))) True) (Eq (cQ a_1 → cS a_1) True) % 4.62/4.82 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (cQ a → cS a) True) (Eq (cQ (skS.0 2 a_1) → cS (skS.0 2 a_1)) False) % 4.62/4.82 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a) → cS (skS.0 2 a)) False) (Or (Eq (cQ a_1) False) (Eq (cS a_1) True)) % 4.62/4.82 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (cQ a) False) (Or (Eq (cS a) True) (Eq (cQ (skS.0 2 a_1)) True)) % 4.62/4.82 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (cQ a) False) (Or (Eq (cS a) True) (Eq (cS (skS.0 2 a_1)) False)) % 4.62/4.82 Clause #40 (by clausification #[33]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cP Xx → cR Xx) False) (Eq (Not (cQ (skS.0 3 a) → cS (skS.0 3 a))) True) % 4.62/4.82 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 4.62/4.82 Or (Eq (Not (cQ (skS.0 3 a) → cS (skS.0 3 a))) True) (Eq (Not (cP (skS.0 4 a_1) → cR (skS.0 4 a_1))) True) % 4.62/4.82 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (Not (cP (skS.0 4 a) → cR (skS.0 4 a))) True) (Eq (cQ (skS.0 3 a_1) → cS (skS.0 3 a_1)) False) % 4.62/4.82 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 3 a) → cS (skS.0 3 a)) False) (Eq (cP (skS.0 4 a_1) → cR (skS.0 4 a_1)) False) % 4.62/4.82 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a) → cR (skS.0 4 a)) False) (Eq (cQ (skS.0 3 a_1)) True) % 4.62/4.82 Clause #45 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a) → cR (skS.0 4 a)) False) (Eq (cS (skS.0 3 a_1)) False) % 4.62/4.82 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 3 a)) True) (Eq (cP (skS.0 4 a_1)) True) % 4.62/4.82 Clause #47 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 3 a)) True) (Eq (cR (skS.0 4 a_1)) False) % 4.62/4.82 Clause #48 (by superposition #[46, 19]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq True False) (Eq (cP (skS.0 0 a_1)) True)) % 4.62/4.82 Clause #49 (by superposition #[46, 38]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 4 a)) True) (Or (Eq True False) (Or (Eq (cS (skS.0 3 a_1)) True) (Eq (cQ (skS.0 2 a_2)) True))) % 4.62/4.82 Clause #62 (by superposition #[39, 46]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 4 a)) True) (Or (Eq True False) (Or (Eq (cS (skS.0 3 a_1)) True) (Eq (cS (skS.0 2 a_2)) False))) % 4.62/4.82 Clause #63 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 3 a)) False) (Eq (cP (skS.0 4 a_1)) True) % 4.62/4.82 Clause #64 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 3 a)) False) (Eq (cR (skS.0 4 a_1)) False) % 4.62/4.82 Clause #65 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Eq (cP (skS.0 0 a_1)) True) % 4.62/4.82 Clause #74 (by superposition #[65, 22]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq True False) (Eq (cQ (skS.0 1 a_1)) True)) % 4.62/4.85 Clause #78 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Eq (cQ (skS.0 1 a_1)) True) % 4.62/4.85 Clause #81 (by superposition #[78, 22]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 1 a)) True) (Or (Eq True False) (Eq (cQ (skS.0 1 a_1)) True)) % 4.62/4.85 Clause #87 (by clausification #[81]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 1 a)) True) (Eq (cQ (skS.0 1 a_1)) True) % 4.62/4.85 Clause #91 (by equality factoring #[87]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 1 a)) True) % 4.62/4.85 Clause #92 (by clausification #[91]): ∀ (a : Iota), Or (Eq (cQ (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 4.62/4.85 Clause #94 (by clausification #[92]): ∀ (a : Iota), Or (Eq (cQ (skS.0 1 a)) True) (Eq True False) % 4.62/4.85 Clause #95 (by clausification #[94]): ∀ (a : Iota), Eq (cQ (skS.0 1 a)) True % 4.62/4.85 Clause #96 (by superposition #[95, 19]): ∀ (a : Iota), Or (Eq True False) (Eq (cP (skS.0 0 a)) True) % 4.62/4.85 Clause #99 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq (cS (skS.0 3 a_1)) True) (Eq (cQ (skS.0 2 a_2)) True)) % 4.62/4.85 Clause #105 (by superposition #[99, 63]): ∀ (a a_1 a_2 : Iota), % 4.62/4.85 Or (Eq (cP (skS.0 4 a)) True) (Or (Eq (cQ (skS.0 2 a_1)) True) (Or (Eq True False) (Eq (cP (skS.0 4 a_2)) True))) % 4.62/4.85 Clause #110 (by clausification #[96]): ∀ (a : Iota), Eq (cP (skS.0 0 a)) True % 4.62/4.85 Clause #111 (by superposition #[110, 13]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cQ a) False) (Or (Eq (cS a) False) (Eq (cR (skS.0 0 a_1)) True))) % 4.62/4.85 Clause #112 (by superposition #[110, 14]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cQ a) False) (Or (Eq (cR (skS.0 0 a_1)) False) (Eq (cS a) True))) % 4.62/4.85 Clause #113 (by superposition #[110, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cR (skS.0 0 a)) True) (Or (Eq (cQ a_1) False) (Eq (cS a_1) True))) % 4.62/4.85 Clause #116 (by clausification #[111]): ∀ (a a_1 : Iota), Or (Eq (cQ a) False) (Or (Eq (cS a) False) (Eq (cR (skS.0 0 a_1)) True)) % 4.62/4.85 Clause #118 (by superposition #[116, 95]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 1 a)) False) (Or (Eq (cR (skS.0 0 a_1)) True) (Eq False True)) % 4.62/4.85 Clause #120 (by clausification #[113]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a)) True) (Or (Eq (cQ a_1) False) (Eq (cS a_1) True)) % 4.62/4.85 Clause #122 (by superposition #[120, 95]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a)) True) (Or (Eq (cS (skS.0 1 a_1)) True) (Eq False True)) % 4.62/4.85 Clause #124 (by clausification #[112]): ∀ (a a_1 : Iota), Or (Eq (cQ a) False) (Or (Eq (cR (skS.0 0 a_1)) False) (Eq (cS a) True)) % 4.62/4.85 Clause #126 (by superposition #[124, 95]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a)) False) (Or (Eq (cS (skS.0 1 a_1)) True) (Eq False True)) % 4.62/4.85 Clause #139 (by clausification #[126]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a)) False) (Eq (cS (skS.0 1 a_1)) True) % 4.62/4.85 Clause #149 (by clausification #[118]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 1 a)) False) (Eq (cR (skS.0 0 a_1)) True) % 4.62/4.85 Clause #153 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a)) True) (Eq (cS (skS.0 1 a_1)) True) % 4.62/4.85 Clause #155 (by superposition #[153, 149]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a)) True) (Or (Eq True False) (Eq (cR (skS.0 0 a_1)) True)) % 4.62/4.85 Clause #160 (by clausification #[155]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a)) True) (Eq (cR (skS.0 0 a_1)) True) % 4.62/4.85 Clause #162 (by equality factoring #[160]): ∀ (a : Iota), Or (Ne True True) (Eq (cR (skS.0 0 a)) True) % 4.62/4.85 Clause #163 (by clausification #[162]): ∀ (a : Iota), Or (Eq (cR (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 4.62/4.85 Clause #165 (by clausification #[163]): ∀ (a : Iota), Or (Eq (cR (skS.0 0 a)) True) (Eq True False) % 4.62/4.85 Clause #166 (by clausification #[165]): ∀ (a : Iota), Eq (cR (skS.0 0 a)) True % 4.62/4.85 Clause #167 (by superposition #[166, 139]): ∀ (a : Iota), Or (Eq True False) (Eq (cS (skS.0 1 a)) True) % 4.62/4.85 Clause #168 (by clausification #[167]): ∀ (a : Iota), Eq (cS (skS.0 1 a)) True % 4.62/4.85 Clause #192 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq (cS (skS.0 3 a_1)) True) (Eq (cS (skS.0 2 a_2)) False)) % 4.62/4.85 Clause #216 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq (cQ (skS.0 2 a_1)) True) (Eq (cP (skS.0 4 a_2)) True)) % 4.72/4.88 Clause #232 (by equality factoring #[216]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a)) True) (Or (Ne True True) (Eq (cP (skS.0 4 a_1)) True)) % 4.72/4.88 Clause #234 (by clausification #[232]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a)) True) (Or (Eq (cP (skS.0 4 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.72/4.88 Clause #236 (by clausification #[234]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a)) True) (Or (Eq (cP (skS.0 4 a_1)) True) (Eq True False)) % 4.72/4.88 Clause #237 (by clausification #[236]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a)) True) (Eq (cP (skS.0 4 a_1)) True) % 4.72/4.88 Clause #243 (by superposition #[237, 13]): ∀ (a a_1 a_2 : Iota), % 4.72/4.88 Or (Eq (cQ (skS.0 2 a)) True) % 4.72/4.88 (Or (Eq True False) (Or (Eq (cQ a_1) False) (Or (Eq (cS a_1) False) (Eq (cR (skS.0 4 a_2)) True)))) % 4.72/4.88 Clause #250 (by clausification #[243]): ∀ (a a_1 a_2 : Iota), % 4.72/4.88 Or (Eq (cQ (skS.0 2 a)) True) (Or (Eq (cQ a_1) False) (Or (Eq (cS a_1) False) (Eq (cR (skS.0 4 a_2)) True))) % 4.72/4.88 Clause #252 (by superposition #[250, 95]): ∀ (a a_1 a_2 : Iota), % 4.72/4.88 Or (Eq (cQ (skS.0 2 a)) True) (Or (Eq (cS (skS.0 1 a_1)) False) (Or (Eq (cR (skS.0 4 a_2)) True) (Eq False True))) % 4.72/4.88 Clause #256 (by clausification #[252]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 2 a)) True) (Or (Eq (cS (skS.0 1 a_1)) False) (Eq (cR (skS.0 4 a_2)) True)) % 4.72/4.88 Clause #257 (by superposition #[256, 168]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a)) True) (Or (Eq (cR (skS.0 4 a_1)) True) (Eq False True)) % 4.72/4.88 Clause #258 (by clausification #[257]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a)) True) (Eq (cR (skS.0 4 a_1)) True) % 4.72/4.88 Clause #261 (by superposition #[258, 124]): ∀ (a a_1 a_2 : Iota), % 4.72/4.88 Or (Eq (cR (skS.0 4 a)) True) (Or (Eq True False) (Or (Eq (cR (skS.0 0 a_1)) False) (Eq (cS (skS.0 2 a_2)) True))) % 4.72/4.88 Clause #279 (by clausification #[261]): ∀ (a a_1 a_2 : Iota), Or (Eq (cR (skS.0 4 a)) True) (Or (Eq (cR (skS.0 0 a_1)) False) (Eq (cS (skS.0 2 a_2)) True)) % 4.72/4.88 Clause #280 (by superposition #[279, 166]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 4 a)) True) (Or (Eq (cS (skS.0 2 a_1)) True) (Eq False True)) % 4.72/4.88 Clause #281 (by clausification #[280]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 4 a)) True) (Eq (cS (skS.0 2 a_1)) True) % 4.72/4.88 Clause #282 (by superposition #[281, 47]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Or (Eq (cQ (skS.0 3 a_1)) True) (Eq True False)) % 4.72/4.88 Clause #284 (by clausification #[282]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq (cQ (skS.0 3 a_1)) True) % 4.72/4.88 Clause #288 (by superposition #[284, 124]): ∀ (a a_1 a_2 : Iota), % 4.72/4.88 Or (Eq (cS (skS.0 2 a)) True) (Or (Eq True False) (Or (Eq (cR (skS.0 0 a_1)) False) (Eq (cS (skS.0 3 a_2)) True))) % 4.72/4.88 Clause #291 (by clausification #[288]): ∀ (a a_1 a_2 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Or (Eq (cR (skS.0 0 a_1)) False) (Eq (cS (skS.0 3 a_2)) True)) % 4.72/4.88 Clause #292 (by superposition #[291, 166]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Or (Eq (cS (skS.0 3 a_1)) True) (Eq False True)) % 4.72/4.88 Clause #293 (by clausification #[292]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq (cS (skS.0 3 a_1)) True) % 4.72/4.88 Clause #296 (by superposition #[293, 64]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Or (Eq True False) (Eq (cR (skS.0 4 a_1)) False)) % 4.72/4.88 Clause #298 (by clausification #[296]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq (cR (skS.0 4 a_1)) False) % 4.72/4.88 Clause #301 (by superposition #[298, 281]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Or (Eq False True) (Eq (cS (skS.0 2 a_1)) True)) % 4.72/4.88 Clause #302 (by clausification #[301]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq (cS (skS.0 2 a_1)) True) % 4.72/4.88 Clause #304 (by equality factoring #[302]): ∀ (a : Iota), Or (Ne True True) (Eq (cS (skS.0 2 a)) True) % 4.72/4.88 Clause #305 (by clausification #[304]): ∀ (a : Iota), Or (Eq (cS (skS.0 2 a)) True) (Or (Eq True False) (Eq True False)) % 4.72/4.88 Clause #307 (by clausification #[305]): ∀ (a : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq True False) % 4.72/4.88 Clause #308 (by clausification #[307]): ∀ (a : Iota), Eq (cS (skS.0 2 a)) True % 4.72/4.88 Clause #309 (by superposition #[308, 192]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq (cS (skS.0 3 a_1)) True) (Eq True False)) % 4.75/4.90 Clause #313 (by clausification #[309]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Eq (cS (skS.0 3 a_1)) True) % 4.75/4.90 Clause #319 (by superposition #[313, 63]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq True False) (Eq (cP (skS.0 4 a_1)) True)) % 4.75/4.90 Clause #325 (by clausification #[319]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 4 a)) True) (Eq (cP (skS.0 4 a_1)) True) % 4.75/4.90 Clause #331 (by equality factoring #[325]): ∀ (a : Iota), Or (Ne True True) (Eq (cP (skS.0 4 a)) True) % 4.75/4.90 Clause #333 (by clausification #[331]): ∀ (a : Iota), Or (Eq (cP (skS.0 4 a)) True) (Or (Eq True False) (Eq True False)) % 4.75/4.90 Clause #335 (by clausification #[333]): ∀ (a : Iota), Or (Eq (cP (skS.0 4 a)) True) (Eq True False) % 4.75/4.90 Clause #336 (by clausification #[335]): ∀ (a : Iota), Eq (cP (skS.0 4 a)) True % 4.75/4.90 Clause #337 (by superposition #[336, 13]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cQ a) False) (Or (Eq (cS a) False) (Eq (cR (skS.0 4 a_1)) True))) % 4.75/4.90 Clause #348 (by clausification #[337]): ∀ (a a_1 : Iota), Or (Eq (cQ a) False) (Or (Eq (cS a) False) (Eq (cR (skS.0 4 a_1)) True)) % 4.75/4.90 Clause #349 (by superposition #[348, 95]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 1 a)) False) (Or (Eq (cR (skS.0 4 a_1)) True) (Eq False True)) % 4.75/4.90 Clause #381 (by clausification #[349]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 1 a)) False) (Eq (cR (skS.0 4 a_1)) True) % 4.75/4.90 Clause #382 (by superposition #[381, 168]): ∀ (a : Iota), Or (Eq (cR (skS.0 4 a)) True) (Eq False True) % 4.75/4.90 Clause #383 (by clausification #[382]): ∀ (a : Iota), Eq (cR (skS.0 4 a)) True % 4.75/4.90 Clause #384 (by superposition #[383, 47]): ∀ (a : Iota), Or (Eq (cQ (skS.0 3 a)) True) (Eq True False) % 4.75/4.90 Clause #386 (by clausification #[384]): ∀ (a : Iota), Eq (cQ (skS.0 3 a)) True % 4.75/4.90 Clause #388 (by superposition #[386, 39]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cS (skS.0 3 a)) True) (Eq (cS (skS.0 2 a_1)) False)) % 4.75/4.90 Clause #393 (by clausification #[388]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 3 a)) True) (Eq (cS (skS.0 2 a_1)) False) % 4.75/4.90 Clause #394 (by superposition #[393, 308]): ∀ (a : Iota), Or (Eq (cS (skS.0 3 a)) True) (Eq False True) % 4.75/4.90 Clause #395 (by clausification #[394]): ∀ (a : Iota), Eq (cS (skS.0 3 a)) True % 4.75/4.90 Clause #396 (by superposition #[395, 64]): ∀ (a : Iota), Or (Eq True False) (Eq (cR (skS.0 4 a)) False) % 4.75/4.90 Clause #398 (by clausification #[396]): ∀ (a : Iota), Eq (cR (skS.0 4 a)) False % 4.75/4.90 Clause #399 (by superposition #[398, 383]): Eq False True % 4.75/4.90 Clause #400 (by clausification #[399]): False % 4.75/4.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------