%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS114+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 3.93s 4.16s % Output : Proof 4.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : KRS114+1 : TPTP v9.2.0. Released v3.1.0. % 0.08/0.14 % Command : duper %s % 0.14/0.35 % Computer : n013.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 10:21:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.93/4.16 SZS status Theorem for theBenchmark.p % 3.93/4.16 SZS output start Proof for theBenchmark.p % 3.93/4.16 Clause #24 (by assumption #[]): Eq % 3.93/4.16 (∀ (X : Iota), % 3.93/4.16 Iff (cUnsatisfiable X) (And (Exists fun Y => And (rr X Y) (ca_Ax4 Y)) (Exists fun Y => And (rs X Y) (ca_Ax3 Y)))) % 3.93/4.16 True % 3.93/4.16 Clause #25 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.93/4.16 Clause #26 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.93/4.16 Clause #29 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax3 X) (And (cqxcomp X) (cpxcomp X))) True % 3.93/4.16 Clause #30 (by assumption #[]): Eq % 3.93/4.16 (∀ (X : Iota), % 3.93/4.16 Iff (ca_Ax4 X) % 3.93/4.16 (And (∀ (Y0 Y1 : Iota), And (rinvR X Y0) (rinvR X Y1) → Eq Y0 Y1) (Exists fun Y => And (rinvR X Y) (ca_Vx5 Y)))) % 3.93/4.16 True % 3.93/4.16 Clause #31 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx5 X) (∀ (Y : Iota), rs X Y → cp Y)) True % 3.93/4.16 Clause #32 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True % 3.93/4.16 Clause #33 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_262) True % 3.93/4.16 Clause #180 (by clausification #[31]): ∀ (a : Iota), Eq (Iff (ca_Vx5 a) (∀ (Y : Iota), rs a Y → cp Y)) True % 3.93/4.16 Clause #182 (by clausification #[180]): ∀ (a : Iota), Or (Eq (ca_Vx5 a) False) (Eq (∀ (Y : Iota), rs a Y → cp Y) True) % 3.93/4.16 Clause #187 (by clausification #[182]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx5 a) False) (Eq (rs a a_1 → cp a_1) True) % 3.93/4.16 Clause #188 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx5 a) False) (Or (Eq (rs a a_1) False) (Eq (cp a_1) True)) % 3.93/4.16 Clause #189 (by clausification #[24]): ∀ (a : Iota), % 3.93/4.16 Eq (Iff (cUnsatisfiable a) (And (Exists fun Y => And (rr a Y) (ca_Ax4 Y)) (Exists fun Y => And (rs a Y) (ca_Ax3 Y)))) % 3.93/4.16 True % 3.93/4.16 Clause #191 (by clausification #[189]): ∀ (a : Iota), % 3.93/4.16 Or (Eq (cUnsatisfiable a) False) % 3.93/4.16 (Eq (And (Exists fun Y => And (rr a Y) (ca_Ax4 Y)) (Exists fun Y => And (rs a Y) (ca_Ax3 Y))) True) % 3.93/4.16 Clause #197 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True % 3.93/4.16 Clause #198 (by clausification #[197]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True % 3.93/4.16 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False) % 3.93/4.16 Clause #201 (by clausification #[29]): ∀ (a : Iota), Eq (Iff (ca_Ax3 a) (And (cqxcomp a) (cpxcomp a))) True % 3.93/4.16 Clause #203 (by clausification #[201]): ∀ (a : Iota), Or (Eq (ca_Ax3 a) False) (Eq (And (cqxcomp a) (cpxcomp a)) True) % 3.93/4.16 Clause #205 (by clausification #[203]): ∀ (a : Iota), Or (Eq (ca_Ax3 a) False) (Eq (cpxcomp a) True) % 3.93/4.16 Clause #207 (by betaEtaReduce #[25]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True % 3.93/4.16 Clause #208 (by clausification #[207]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True % 3.93/4.16 Clause #210 (by clausification #[208]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.93/4.16 Clause #213 (by clausification #[210]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False) % 3.93/4.16 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False) % 3.93/4.16 Clause #221 (by betaEtaReduce #[26]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True % 3.93/4.16 Clause #222 (by clausification #[221]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True % 3.93/4.16 Clause #224 (by clausification #[222]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.93/4.16 Clause #237 (by clausification #[224]): ∀ (a a_1 : Iota), Or (Eq (cpxcomp a) False) (Eq (ra_Px1 a (skS.0 4 a a_1)) True) % 3.93/4.16 Clause #243 (by clausification #[30]): ∀ (a : Iota), % 3.93/4.16 Eq % 3.93/4.16 (Iff (ca_Ax4 a) % 3.93/4.16 (And (∀ (Y0 Y1 : Iota), And (rinvR a Y0) (rinvR a Y1) → Eq Y0 Y1) (Exists fun Y => And (rinvR a Y) (ca_Vx5 Y)))) % 3.93/4.16 True % 3.93/4.16 Clause #245 (by clausification #[243]): ∀ (a : Iota), % 3.93/4.16 Or (Eq (ca_Ax4 a) False) % 3.93/4.16 (Eq (And (∀ (Y0 Y1 : Iota), And (rinvR a Y0) (rinvR a Y1) → Eq Y0 Y1) (Exists fun Y => And (rinvR a Y) (ca_Vx5 Y))) % 3.93/4.16 True) % 3.93/4.16 Clause #259 (by clausification #[245]): ∀ (a : Iota), Or (Eq (ca_Ax4 a) False) (Eq (Exists fun Y => And (rinvR a Y) (ca_Vx5 Y)) True) % 3.93/4.16 Clause #260 (by clausification #[245]): ∀ (a : Iota), Or (Eq (ca_Ax4 a) False) (Eq (∀ (Y0 Y1 : Iota), And (rinvR a Y0) (rinvR a Y1) → Eq Y0 Y1) True) % 4.00/4.19 Clause #261 (by clausification #[259]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax4 a) False) (Eq (And (rinvR a (skS.0 7 a a_1)) (ca_Vx5 (skS.0 7 a a_1))) True) % 4.00/4.19 Clause #262 (by clausification #[261]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax4 a) False) (Eq (ca_Vx5 (skS.0 7 a a_1)) True) % 4.00/4.19 Clause #263 (by clausification #[261]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax4 a) False) (Eq (rinvR a (skS.0 7 a a_1)) True) % 4.00/4.19 Clause #264 (by clausification #[260]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax4 a) False) (Eq (∀ (Y1 : Iota), And (rinvR a a_1) (rinvR a Y1) → Eq a_1 Y1) True) % 4.00/4.19 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 : Iota), Or (Eq (ca_Ax4 a) False) (Eq (And (rinvR a a_1) (rinvR a a_2) → Eq a_1 a_2) True) % 4.00/4.19 Clause #266 (by clausification #[265]): ∀ (a a_1 a_2 : Iota), Or (Eq (ca_Ax4 a) False) (Or (Eq (And (rinvR a a_1) (rinvR a a_2)) False) (Eq (Eq a_1 a_2) True)) % 4.00/4.19 Clause #267 (by clausification #[266]): ∀ (a a_1 a_2 : Iota), % 4.00/4.19 Or (Eq (ca_Ax4 a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rinvR a a_1) False) (Eq (rinvR a a_2) False))) % 4.00/4.19 Clause #268 (by clausification #[267]): ∀ (a a_1 a_2 : Iota), Or (Eq (ca_Ax4 a) False) (Or (Eq (rinvR a a_1) False) (Or (Eq (rinvR a a_2) False) (Eq a_1 a_2))) % 4.00/4.19 Clause #269 (by clausification #[191]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rs a Y) (ca_Ax3 Y)) True) % 4.00/4.19 Clause #270 (by clausification #[191]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (ca_Ax4 Y)) True) % 4.00/4.19 Clause #271 (by clausification #[269]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rs a (skS.0 8 a a_1)) (ca_Ax3 (skS.0 8 a a_1))) True) % 4.00/4.19 Clause #272 (by clausification #[271]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax3 (skS.0 8 a a_1)) True) % 4.00/4.19 Clause #273 (by clausification #[271]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 8 a a_1)) True) % 4.00/4.19 Clause #274 (by superposition #[272, 33]): ∀ (a : Iota), Or (Eq (ca_Ax3 (skS.0 8 i2003_11_14_17_21_262 a)) True) (Eq False True) % 4.00/4.19 Clause #275 (by clausification #[274]): ∀ (a : Iota), Eq (ca_Ax3 (skS.0 8 i2003_11_14_17_21_262 a)) True % 4.00/4.19 Clause #276 (by superposition #[275, 205]): ∀ (a : Iota), Or (Eq True False) (Eq (cpxcomp (skS.0 8 i2003_11_14_17_21_262 a)) True) % 4.00/4.19 Clause #281 (by clausification #[276]): ∀ (a : Iota), Eq (cpxcomp (skS.0 8 i2003_11_14_17_21_262 a)) True % 4.00/4.19 Clause #282 (by superposition #[281, 237]): ∀ (a a_1 : Iota), % 4.00/4.19 Or (Eq True False) % 4.00/4.19 (Eq (ra_Px1 (skS.0 8 i2003_11_14_17_21_262 a) (skS.0 4 (skS.0 8 i2003_11_14_17_21_262 a) a_1)) True) % 4.00/4.19 Clause #286 (by clausification #[270]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 9 a a_1)) (ca_Ax4 (skS.0 9 a a_1))) True) % 4.00/4.19 Clause #287 (by clausification #[286]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax4 (skS.0 9 a a_1)) True) % 4.00/4.19 Clause #288 (by clausification #[286]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 9 a a_1)) True) % 4.00/4.19 Clause #289 (by superposition #[287, 33]): ∀ (a : Iota), Or (Eq (ca_Ax4 (skS.0 9 i2003_11_14_17_21_262 a)) True) (Eq False True) % 4.00/4.19 Clause #290 (by clausification #[289]): ∀ (a : Iota), Eq (ca_Ax4 (skS.0 9 i2003_11_14_17_21_262 a)) True % 4.00/4.19 Clause #291 (by superposition #[290, 262]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ca_Vx5 (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1)) True) % 4.00/4.19 Clause #292 (by superposition #[290, 268]): ∀ (a a_1 a_2 : Iota), % 4.00/4.19 Or (Eq True False) % 4.00/4.19 (Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_1) False) % 4.00/4.19 (Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_2) False) (Eq a_1 a_2))) % 4.00/4.19 Clause #293 (by superposition #[290, 263]): ∀ (a a_1 : Iota), % 4.00/4.19 Or (Eq True False) (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1)) True) % 4.00/4.19 Clause #294 (by superposition #[288, 33]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_21_262 (skS.0 9 i2003_11_14_17_21_262 a)) True) (Eq False True) % 4.00/4.19 Clause #295 (by clausification #[294]): ∀ (a : Iota), Eq (rr i2003_11_14_17_21_262 (skS.0 9 i2003_11_14_17_21_262 a)) True % 4.00/4.20 Clause #297 (by superposition #[295, 199]): ∀ (a : Iota), Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) i2003_11_14_17_21_262) True) (Eq True False) % 4.00/4.20 Clause #298 (by clausification #[297]): ∀ (a : Iota), Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) i2003_11_14_17_21_262) True % 4.00/4.20 Clause #303 (by superposition #[273, 33]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_21_262 (skS.0 8 i2003_11_14_17_21_262 a)) True) (Eq False True) % 4.00/4.20 Clause #304 (by clausification #[303]): ∀ (a : Iota), Eq (rs i2003_11_14_17_21_262 (skS.0 8 i2003_11_14_17_21_262 a)) True % 4.00/4.20 Clause #305 (by clausification #[291]): ∀ (a a_1 : Iota), Eq (ca_Vx5 (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1)) True % 4.00/4.20 Clause #306 (by superposition #[305, 188]): ∀ (a a_1 a_2 : Iota), % 4.00/4.20 Or (Eq True False) (Or (Eq (rs (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1) a_2) False) (Eq (cp a_2) True)) % 4.00/4.20 Clause #309 (by clausification #[282]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 8 i2003_11_14_17_21_262 a) (skS.0 4 (skS.0 8 i2003_11_14_17_21_262 a) a_1)) True % 4.00/4.20 Clause #313 (by clausification #[306]): ∀ (a a_1 a_2 : Iota), Or (Eq (rs (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1) a_2) False) (Eq (cp a_2) True) % 4.00/4.20 Clause #315 (by clausification #[292]): ∀ (a a_1 a_2 : Iota), % 4.00/4.20 Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_1) False) % 4.00/4.20 (Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_2) False) (Eq a_1 a_2)) % 4.00/4.20 Clause #316 (by superposition #[315, 298]): ∀ (a a_1 : Iota), % 4.00/4.20 Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_1) False) (Or (Eq i2003_11_14_17_21_262 a_1) (Eq False True)) % 4.00/4.20 Clause #317 (by clausification #[316]): ∀ (a a_1 : Iota), Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_1) False) (Eq i2003_11_14_17_21_262 a_1) % 4.00/4.20 Clause #319 (by clausification #[293]): ∀ (a a_1 : Iota), Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1)) True % 4.00/4.20 Clause #321 (by superposition #[319, 317]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq i2003_11_14_17_21_262 (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1)) % 4.00/4.20 Clause #327 (by clausification #[321]): ∀ (a a_1 : Iota), Eq i2003_11_14_17_21_262 (skS.0 7 (skS.0 9 i2003_11_14_17_21_262 a) a_1) % 4.00/4.20 Clause #329 (by backward demodulation #[327, 313]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_21_262 a) False) (Eq (cp a) True) % 4.00/4.20 Clause #331 (by superposition #[329, 304]): ∀ (a : Iota), Or (Eq (cp (skS.0 8 i2003_11_14_17_21_262 a)) True) (Eq False True) % 4.00/4.20 Clause #335 (by clausification #[331]): ∀ (a : Iota), Eq (cp (skS.0 8 i2003_11_14_17_21_262 a)) True % 4.00/4.20 Clause #336 (by superposition #[335, 214]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 8 i2003_11_14_17_21_262 a) a_1) False) % 4.00/4.20 Clause #337 (by clausification #[336]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 8 i2003_11_14_17_21_262 a) a_1) False % 4.00/4.20 Clause #338 (by superposition #[337, 309]): Eq False True % 4.00/4.20 Clause #340 (by clausification #[338]): False % 4.00/4.20 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------