%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS113+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 07:52:39 PM UTC 2025 % Result : Unsatisfiable 3.94s 4.14s % Output : Proof 3.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS113+1 : TPTP v9.2.0. Released v3.1.0. % 0.13/0.13 % Command : duper %s % 0.14/0.35 % Computer : n020.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 10:22:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.94/4.14 SZS status Theorem for theBenchmark.p % 3.94/4.14 SZS output start Proof for theBenchmark.p % 3.94/4.14 Clause #18 (by assumption #[]): Eq % 3.94/4.14 (∀ (X : Iota), % 3.94/4.14 Iff (cUnsatisfiable X) % 3.94/4.14 (And % 3.94/4.14 (And (And (∀ (Y0 Y1 : Iota), And (rr X Y0) (rr X Y1) → Eq Y0 Y1) (Exists fun Y => And (rr X Y) (ca_Vx2 Y))) % 3.94/4.14 (Exists fun Y => And (rs X Y) (cp Y))) % 3.94/4.14 (cpxcomp X))) % 3.94/4.14 True % 3.94/4.14 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.94/4.14 Clause #20 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.94/4.14 Clause #21 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx2 X) (∀ (Y : Iota), rinvS X Y → cp Y)) True % 3.94/4.14 Clause #22 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvS X Y) (rs Y X)) True % 3.94/4.14 Clause #23 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_22376) True % 3.94/4.14 Clause #24 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rr X Y) True % 3.94/4.14 Clause #73 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rr a Y) True % 3.94/4.14 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rr a a_1) True % 3.94/4.14 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rr a a_1) True) % 3.94/4.14 Clause #139 (by clausification #[18]): ∀ (a : Iota), % 3.94/4.14 Eq % 3.94/4.14 (Iff (cUnsatisfiable a) % 3.94/4.14 (And % 3.94/4.14 (And (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y))) % 3.94/4.14 (Exists fun Y => And (rs a Y) (cp Y))) % 3.94/4.14 (cpxcomp a))) % 3.94/4.14 True % 3.94/4.14 Clause #141 (by clausification #[139]): ∀ (a : Iota), % 3.94/4.14 Or (Eq (cUnsatisfiable a) False) % 3.94/4.14 (Eq % 3.94/4.14 (And % 3.94/4.14 (And (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y))) % 3.94/4.14 (Exists fun Y => And (rs a Y) (cp Y))) % 3.94/4.14 (cpxcomp a)) % 3.94/4.14 True) % 3.94/4.14 Clause #157 (by clausification #[21]): ∀ (a : Iota), Eq (Iff (ca_Vx2 a) (∀ (Y : Iota), rinvS a Y → cp Y)) True % 3.94/4.14 Clause #159 (by clausification #[157]): ∀ (a : Iota), Or (Eq (ca_Vx2 a) False) (Eq (∀ (Y : Iota), rinvS a Y → cp Y) True) % 3.94/4.14 Clause #164 (by clausification #[159]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx2 a) False) (Eq (rinvS a a_1 → cp a_1) True) % 3.94/4.14 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx2 a) False) (Or (Eq (rinvS a a_1) False) (Eq (cp a_1) True)) % 3.94/4.14 Clause #166 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvS a Y) (rs Y a)) True % 3.94/4.14 Clause #167 (by clausification #[166]): ∀ (a a_1 : Iota), Eq (Iff (rinvS a a_1) (rs a_1 a)) True % 3.94/4.14 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Or (Eq (rinvS a a_1) True) (Eq (rs a_1 a) False) % 3.94/4.14 Clause #171 (by betaEtaReduce #[20]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True % 3.94/4.14 Clause #172 (by clausification #[171]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True % 3.94/4.14 Clause #174 (by clausification #[172]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.94/4.14 Clause #176 (by betaEtaReduce #[19]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True % 3.94/4.14 Clause #177 (by clausification #[176]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True % 3.94/4.14 Clause #179 (by clausification #[177]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.94/4.14 Clause #185 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (cpxcomp a) False) (Eq (ra_Px1 a (skS.0 4 a a_1)) True) % 3.94/4.14 Clause #187 (by clausification #[179]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False) % 3.94/4.14 Clause #188 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False) % 3.94/4.14 Clause #192 (by clausification #[141]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cpxcomp a) True) % 3.94/4.14 Clause #193 (by clausification #[141]): ∀ (a : Iota), % 3.94/4.14 Or (Eq (cUnsatisfiable a) False) % 3.94/4.14 (Eq % 3.94/4.14 (And (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y))) % 3.94/4.14 (Exists fun Y => And (rs a Y) (cp Y))) % 3.94/4.14 True) % 3.94/4.14 Clause #194 (by superposition #[192, 23]): Or (Eq (cpxcomp i2003_11_14_17_21_22376) True) (Eq False True) % 3.99/4.17 Clause #195 (by clausification #[194]): Eq (cpxcomp i2003_11_14_17_21_22376) True % 3.99/4.17 Clause #197 (by superposition #[195, 185]): ∀ (a : Iota), Or (Eq True False) (Eq (ra_Px1 i2003_11_14_17_21_22376 (skS.0 4 i2003_11_14_17_21_22376 a)) True) % 3.99/4.17 Clause #198 (by clausification #[197]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_21_22376 (skS.0 4 i2003_11_14_17_21_22376 a)) True % 3.99/4.17 Clause #205 (by clausification #[193]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rs a Y) (cp Y)) True) % 3.99/4.17 Clause #206 (by clausification #[193]): ∀ (a : Iota), % 3.99/4.17 Or (Eq (cUnsatisfiable a) False) % 3.99/4.17 (Eq (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y))) True) % 3.99/4.17 Clause #207 (by clausification #[205]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rs a (skS.0 5 a a_1)) (cp (skS.0 5 a a_1))) True) % 3.99/4.17 Clause #209 (by clausification #[207]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 5 a a_1)) True) % 3.99/4.17 Clause #217 (by superposition #[209, 23]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True) (Eq False True) % 3.99/4.17 Clause #218 (by clausification #[217]): ∀ (a : Iota), Eq (rs i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True % 3.99/4.17 Clause #219 (by superposition #[218, 75]): ∀ (a : Iota), Or (Eq True False) (Eq (rr i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True) % 3.99/4.17 Clause #220 (by superposition #[218, 168]): ∀ (a : Iota), Or (Eq (rinvS (skS.0 5 i2003_11_14_17_21_22376 a) i2003_11_14_17_21_22376) True) (Eq True False) % 3.99/4.17 Clause #221 (by clausification #[220]): ∀ (a : Iota), Eq (rinvS (skS.0 5 i2003_11_14_17_21_22376 a) i2003_11_14_17_21_22376) True % 3.99/4.17 Clause #223 (by clausification #[219]): ∀ (a : Iota), Eq (rr i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True % 3.99/4.17 Clause #227 (by clausification #[206]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (ca_Vx2 Y)) True) % 3.99/4.17 Clause #228 (by clausification #[206]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) True) % 3.99/4.17 Clause #229 (by clausification #[227]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 6 a a_1)) (ca_Vx2 (skS.0 6 a a_1))) True) % 3.99/4.17 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Vx2 (skS.0 6 a a_1)) True) % 3.99/4.17 Clause #231 (by clausification #[229]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 6 a a_1)) True) % 3.99/4.17 Clause #232 (by superposition #[230, 23]): ∀ (a : Iota), Or (Eq (ca_Vx2 (skS.0 6 i2003_11_14_17_21_22376 a)) True) (Eq False True) % 3.99/4.17 Clause #233 (by clausification #[228]): ∀ (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) % 3.99/4.17 Clause #234 (by clausification #[233]): ∀ (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) % 3.99/4.17 Clause #235 (by clausification #[234]): ∀ (a a_1 a_2 : Iota), % 3.99/4.17 Or (Eq (cUnsatisfiable a) False) (Or (Eq (And (rr a a_1) (rr a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.99/4.17 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 : Iota), % 3.99/4.17 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))) % 3.99/4.17 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 : Iota), % 3.99/4.17 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (rr a a_2) False) (Eq a_1 a_2))) % 3.99/4.17 Clause #238 (by superposition #[237, 23]): ∀ (a a_1 : Iota), % 3.99/4.17 Or (Eq (rr i2003_11_14_17_21_22376 a) False) % 3.99/4.17 (Or (Eq (rr i2003_11_14_17_21_22376 a_1) False) (Or (Eq a a_1) (Eq False True))) % 3.99/4.17 Clause #239 (by clausification #[238]): ∀ (a a_1 : Iota), % 3.99/4.17 Or (Eq (rr i2003_11_14_17_21_22376 a) False) (Or (Eq (rr i2003_11_14_17_21_22376 a_1) False) (Eq a a_1)) % 3.99/4.17 Clause #241 (by clausification #[232]): ∀ (a : Iota), Eq (ca_Vx2 (skS.0 6 i2003_11_14_17_21_22376 a)) True % 3.99/4.17 Clause #242 (by superposition #[241, 165]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (rinvS (skS.0 6 i2003_11_14_17_21_22376 a) a_1) False) (Eq (cp a_1) True)) % 3.99/4.17 Clause #243 (by superposition #[231, 23]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_21_22376 (skS.0 6 i2003_11_14_17_21_22376 a)) True) (Eq False True) % 3.99/4.17 Clause #246 (by clausification #[243]): ∀ (a : Iota), Eq (rr i2003_11_14_17_21_22376 (skS.0 6 i2003_11_14_17_21_22376 a)) True % 3.99/4.17 Clause #247 (by superposition #[246, 239]): ∀ (a a_1 : Iota), % 3.99/4.17 Or (Eq True False) (Or (Eq (rr i2003_11_14_17_21_22376 a) False) (Eq (skS.0 6 i2003_11_14_17_21_22376 a_1) a)) % 3.99/4.17 Clause #251 (by clausification #[247]): ∀ (a a_1 : Iota), Or (Eq (rr i2003_11_14_17_21_22376 a) False) (Eq (skS.0 6 i2003_11_14_17_21_22376 a_1) a) % 3.99/4.17 Clause #252 (by superposition #[251, 223]): ∀ (a a_1 : Iota), Or (Eq (skS.0 6 i2003_11_14_17_21_22376 a) (skS.0 5 i2003_11_14_17_21_22376 a_1)) (Eq False True) % 3.99/4.17 Clause #254 (by clausification #[242]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 6 i2003_11_14_17_21_22376 a) a_1) False) (Eq (cp a_1) True) % 3.99/4.17 Clause #259 (by clausification #[252]): ∀ (a a_1 : Iota), Eq (skS.0 6 i2003_11_14_17_21_22376 a) (skS.0 5 i2003_11_14_17_21_22376 a_1) % 3.99/4.17 Clause #267 (by superposition #[259, 221]): ∀ (a : Iota), Eq (rinvS (skS.0 6 i2003_11_14_17_21_22376 a) i2003_11_14_17_21_22376) True % 3.99/4.17 Clause #270 (by superposition #[267, 254]): Or (Eq True False) (Eq (cp i2003_11_14_17_21_22376) True) % 3.99/4.17 Clause #272 (by clausification #[270]): Eq (cp i2003_11_14_17_21_22376) True % 3.99/4.17 Clause #273 (by superposition #[272, 188]): ∀ (a : Iota), Or (Eq True False) (Eq (ra_Px1 i2003_11_14_17_21_22376 a) False) % 3.99/4.17 Clause #277 (by clausification #[273]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_21_22376 a) False % 3.99/4.17 Clause #278 (by superposition #[277, 198]): Eq False True % 3.99/4.17 Clause #281 (by clausification #[278]): False % 3.99/4.17 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------