%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS077+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 07:52:35 PM UTC 2025 % Result : Unsatisfiable 3.72s 4.06s % Output : Proof 3.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.24 % Problem : KRS077+1 : TPTP v9.2.0. Released v3.1.0. % 0.13/0.25 % Command : duper %s % 0.18/0.53 % Computer : n009.cluster.edu % 0.18/0.53 % Model : x86_64 x86_64 % 0.18/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.53 % Memory : 8042.1875MB % 0.18/0.53 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.53 % CPULimit : 300 % 0.18/0.53 % WCLimit : 300 % 0.18/0.53 % DateTime : Thu Oct 2 10:24:38 EDT 2025 % 0.18/0.53 % CPUTime : % 3.72/4.06 SZS status Theorem for theBenchmark.p % 3.72/4.06 SZS output start Proof for theBenchmark.p % 3.72/4.06 Clause #14 (by assumption #[]): Eq % 3.72/4.06 (∀ (X : Iota), % 3.72/4.06 Iff (cUnsatisfiable X) % 3.72/4.06 (And % 3.72/4.06 (And % 3.72/4.06 (And (∀ (Y0 Y1 : Iota), And (rr X Y0) (rr X Y1) → Eq Y0 Y1) % 3.72/4.06 (Exists fun Y => And (rr X Y) (∀ (Z : Iota), rinvS Y Z → cp Z))) % 3.72/4.06 (Not (cp X))) % 3.72/4.06 (Exists fun Y => And (rs X Y) (cp Y)))) % 3.72/4.06 True % 3.72/4.06 Clause #15 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvS X Y) (rs Y X)) True % 3.72/4.06 Clause #16 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_09372) True % 3.72/4.06 Clause #17 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rr X Y) True % 3.72/4.06 Clause #54 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rr a Y) True % 3.72/4.06 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rr a a_1) True % 3.72/4.06 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rr a a_1) True) % 3.72/4.06 Clause #105 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvS a Y) (rs Y a)) True % 3.72/4.06 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (Iff (rinvS a a_1) (rs a_1 a)) True % 3.72/4.06 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Or (Eq (rinvS a a_1) True) (Eq (rs a_1 a) False) % 3.72/4.06 Clause #109 (by clausification #[14]): ∀ (a : Iota), % 3.72/4.06 Eq % 3.72/4.06 (Iff (cUnsatisfiable a) % 3.72/4.06 (And % 3.72/4.06 (And % 3.72/4.06 (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) % 3.72/4.06 (Exists fun Y => And (rr a Y) (∀ (Z : Iota), rinvS Y Z → cp Z))) % 3.72/4.06 (Not (cp a))) % 3.72/4.06 (Exists fun Y => And (rs a Y) (cp Y)))) % 3.72/4.06 True % 3.72/4.06 Clause #111 (by clausification #[109]): ∀ (a : Iota), % 3.72/4.06 Or (Eq (cUnsatisfiable a) False) % 3.72/4.06 (Eq % 3.72/4.06 (And % 3.72/4.06 (And % 3.72/4.06 (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) % 3.72/4.06 (Exists fun Y => And (rr a Y) (∀ (Z : Iota), rinvS Y Z → cp Z))) % 3.72/4.06 (Not (cp a))) % 3.72/4.06 (Exists fun Y => And (rs a Y) (cp Y))) % 3.72/4.06 True) % 3.72/4.06 Clause #132 (by clausification #[111]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rs a Y) (cp Y)) True) % 3.72/4.06 Clause #133 (by clausification #[111]): ∀ (a : Iota), % 3.72/4.06 Or (Eq (cUnsatisfiable a) False) % 3.72/4.06 (Eq % 3.72/4.06 (And % 3.72/4.06 (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) % 3.72/4.06 (Exists fun Y => And (rr a Y) (∀ (Z : Iota), rinvS Y Z → cp Z))) % 3.72/4.06 (Not (cp a))) % 3.72/4.06 True) % 3.72/4.06 Clause #134 (by clausification #[132]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rs a (skS.0 3 a a_1)) (cp (skS.0 3 a a_1))) True) % 3.72/4.06 Clause #136 (by clausification #[134]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 3 a a_1)) True) % 3.72/4.06 Clause #142 (by superposition #[136, 16]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_19_09372 (skS.0 3 i2003_11_14_17_19_09372 a)) True) (Eq False True) % 3.72/4.06 Clause #143 (by clausification #[142]): ∀ (a : Iota), Eq (rs i2003_11_14_17_19_09372 (skS.0 3 i2003_11_14_17_19_09372 a)) True % 3.72/4.06 Clause #144 (by superposition #[143, 56]): ∀ (a : Iota), Or (Eq True False) (Eq (rr i2003_11_14_17_19_09372 (skS.0 3 i2003_11_14_17_19_09372 a)) True) % 3.72/4.06 Clause #145 (by superposition #[143, 107]): ∀ (a : Iota), Or (Eq (rinvS (skS.0 3 i2003_11_14_17_19_09372 a) i2003_11_14_17_19_09372) True) (Eq True False) % 3.72/4.06 Clause #148 (by clausification #[145]): ∀ (a : Iota), Eq (rinvS (skS.0 3 i2003_11_14_17_19_09372 a) i2003_11_14_17_19_09372) True % 3.72/4.06 Clause #150 (by clausification #[144]): ∀ (a : Iota), Eq (rr i2003_11_14_17_19_09372 (skS.0 3 i2003_11_14_17_19_09372 a)) True % 3.72/4.06 Clause #154 (by clausification #[133]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (cp a)) True) % 3.72/4.06 Clause #155 (by clausification #[133]): ∀ (a : Iota), % 3.72/4.06 Or (Eq (cUnsatisfiable a) False) % 3.72/4.06 (Eq % 3.72/4.06 (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) % 3.72/4.06 (Exists fun Y => And (rr a Y) (∀ (Z : Iota), rinvS Y Z → cp Z))) % 3.72/4.06 True) % 3.72/4.06 Clause #156 (by clausification #[154]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp a) False) % 3.72/4.06 Clause #157 (by superposition #[156, 16]): Or (Eq (cp i2003_11_14_17_19_09372) False) (Eq False True) % 3.72/4.08 Clause #158 (by clausification #[157]): Eq (cp i2003_11_14_17_19_09372) False % 3.72/4.08 Clause #159 (by clausification #[155]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (∀ (Z : Iota), rinvS Y Z → cp Z)) True) % 3.72/4.08 Clause #160 (by clausification #[155]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) True) % 3.72/4.08 Clause #161 (by clausification #[159]): ∀ (a a_1 : Iota), % 3.72/4.08 Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 4 a a_1)) (∀ (Z : Iota), rinvS (skS.0 4 a a_1) Z → cp Z)) True) % 3.72/4.08 Clause #162 (by clausification #[161]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Z : Iota), rinvS (skS.0 4 a a_1) Z → cp Z) True) % 3.72/4.08 Clause #163 (by clausification #[161]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 4 a a_1)) True) % 3.72/4.08 Clause #164 (by clausification #[162]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvS (skS.0 4 a a_1) a_2 → cp a_2) True) % 3.72/4.08 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvS (skS.0 4 a a_1) a_2) False) (Eq (cp a_2) True)) % 3.72/4.08 Clause #166 (by superposition #[165, 16]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 4 i2003_11_14_17_19_09372 a) a_1) False) (Or (Eq (cp a_1) True) (Eq False True)) % 3.72/4.08 Clause #167 (by clausification #[160]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y1 : Iota), And (rr a a_1) (rr a Y1) → Eq a_1 Y1) True) % 3.72/4.08 Clause #168 (by clausification #[167]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a a_1) (rr a a_2) → Eq a_1 a_2) True) % 3.72/4.08 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 : Iota), % 3.72/4.08 Or (Eq (cUnsatisfiable a) False) (Or (Eq (And (rr a a_1) (rr a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.72/4.08 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota), % 3.72/4.08 Or (Eq (cUnsatisfiable a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rr a a_1) False) (Eq (rr a a_2) False))) % 3.72/4.08 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 : Iota), % 3.72/4.08 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (rr a a_2) False) (Eq a_1 a_2))) % 3.72/4.08 Clause #172 (by superposition #[171, 16]): ∀ (a a_1 : Iota), % 3.72/4.08 Or (Eq (rr i2003_11_14_17_19_09372 a) False) % 3.72/4.08 (Or (Eq (rr i2003_11_14_17_19_09372 a_1) False) (Or (Eq a a_1) (Eq False True))) % 3.72/4.08 Clause #173 (by clausification #[172]): ∀ (a a_1 : Iota), % 3.72/4.08 Or (Eq (rr i2003_11_14_17_19_09372 a) False) (Or (Eq (rr i2003_11_14_17_19_09372 a_1) False) (Eq a a_1)) % 3.72/4.08 Clause #174 (by superposition #[173, 150]): ∀ (a a_1 : Iota), % 3.72/4.08 Or (Eq (rr i2003_11_14_17_19_09372 a) False) (Or (Eq (skS.0 3 i2003_11_14_17_19_09372 a_1) a) (Eq False True)) % 3.72/4.08 Clause #176 (by superposition #[163, 16]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_19_09372 (skS.0 4 i2003_11_14_17_19_09372 a)) True) (Eq False True) % 3.72/4.08 Clause #177 (by clausification #[176]): ∀ (a : Iota), Eq (rr i2003_11_14_17_19_09372 (skS.0 4 i2003_11_14_17_19_09372 a)) True % 3.72/4.08 Clause #179 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (rr i2003_11_14_17_19_09372 a) False) (Eq (skS.0 3 i2003_11_14_17_19_09372 a_1) a) % 3.72/4.08 Clause #181 (by superposition #[179, 177]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 i2003_11_14_17_19_09372 a) (skS.0 4 i2003_11_14_17_19_09372 a_1)) (Eq False True) % 3.72/4.08 Clause #185 (by clausification #[166]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 4 i2003_11_14_17_19_09372 a) a_1) False) (Eq (cp a_1) True) % 3.72/4.08 Clause #188 (by clausification #[181]): ∀ (a a_1 : Iota), Eq (skS.0 3 i2003_11_14_17_19_09372 a) (skS.0 4 i2003_11_14_17_19_09372 a_1) % 3.72/4.08 Clause #191 (by superposition #[188, 148]): ∀ (a : Iota), Eq (rinvS (skS.0 4 i2003_11_14_17_19_09372 a) i2003_11_14_17_19_09372) True % 3.72/4.08 Clause #202 (by superposition #[191, 185]): Or (Eq True False) (Eq (cp i2003_11_14_17_19_09372) True) % 3.72/4.08 Clause #204 (by clausification #[202]): Eq (cp i2003_11_14_17_19_09372) True % 3.72/4.08 Clause #205 (by superposition #[204, 158]): Eq True False % 3.72/4.08 Clause #208 (by clausification #[205]): False % 3.72/4.08 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------