%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS112+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 07:52:38 PM UTC 2025 % Result : Unsatisfiable 4.34s 4.50s % Output : Proof 4.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : KRS112+1 : TPTP v9.2.0. Released v3.1.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 10:17:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.34/4.50 SZS status Theorem for theBenchmark.p % 4.34/4.50 SZS output start Proof for theBenchmark.p % 4.34/4.50 Clause #25 (by assumption #[]): Eq % 4.34/4.50 (∀ (X : Iota), % 4.34/4.50 Iff (cUnsatisfiable X) (And (Exists fun Y => And (rf1 X Y) (ca_Ax2 Y)) (Exists fun Y => And (rf X Y) (cp Y)))) % 4.34/4.50 True % 4.34/4.50 Clause #26 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True % 4.34/4.50 Clause #27 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 4.34/4.50 Clause #28 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax2 X) (And (cpxcomp X) (∀ (Y : Iota), rinvF1 X Y → ca_Vx3 Y))) True % 4.34/4.50 Clause #29 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx3 X) (Exists fun Y => And (rs X Y) (cowlThing Y))) True % 4.34/4.50 Clause #30 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True % 4.34/4.50 Clause #31 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf1 X Y) (rf1 X Z) → Eq Y Z) True % 4.34/4.50 Clause #33 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF1 X Y) (rf1 Y X)) True % 4.34/4.50 Clause #36 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_19256) True % 4.34/4.50 Clause #37 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf X Y) True % 4.34/4.50 Clause #38 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf1 X Y) True % 4.34/4.50 Clause #93 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf a Y) True % 4.34/4.50 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf a a_1) True % 4.34/4.50 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf a a_1) True) % 4.34/4.50 Clause #103 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf1 a Y) True % 4.34/4.50 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf1 a a_1) True % 4.34/4.50 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf1 a a_1) True) % 4.34/4.50 Clause #205 (by clausification #[31]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf1 a Y) (rf1 a Z) → Eq Y Z) True % 4.34/4.50 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf1 a a_1) (rf1 a Z) → Eq a_1 Z) True % 4.34/4.51 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 : Iota), Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True % 4.34/4.51 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf1 a a_1) (rf1 a a_2)) False) (Eq (Eq a_1 a_2) True) % 4.34/4.51 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf1 a_2 a) False) (Eq (rf1 a_2 a_1) False)) % 4.34/4.51 Clause #210 (by clausification #[209]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf1 a a_1) False) (Or (Eq (rf1 a a_2) False) (Eq a_1 a_2)) % 4.34/4.51 Clause #211 (by clausification #[30]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True % 4.34/4.51 Clause #212 (by clausification #[211]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf a a_1) (rf a Z) → Eq a_1 Z) True % 4.34/4.51 Clause #213 (by clausification #[212]): ∀ (a a_1 a_2 : Iota), Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True % 4.34/4.51 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf a a_1) (rf a a_2)) False) (Eq (Eq a_1 a_2) True) % 4.34/4.51 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf a_2 a) False) (Eq (rf a_2 a_1) False)) % 4.34/4.51 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf a a_1) False) (Or (Eq (rf a a_2) False) (Eq a_1 a_2)) % 4.34/4.51 Clause #217 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF1 a Y) (rf1 Y a)) True % 4.34/4.51 Clause #218 (by clausification #[217]): ∀ (a a_1 : Iota), Eq (Iff (rinvF1 a a_1) (rf1 a_1 a)) True % 4.34/4.51 Clause #219 (by clausification #[218]): ∀ (a a_1 : Iota), Or (Eq (rinvF1 a a_1) True) (Eq (rf1 a_1 a) False) % 4.34/4.51 Clause #221 (by clausification #[25]): ∀ (a : Iota), % 4.34/4.51 Eq (Iff (cUnsatisfiable a) (And (Exists fun Y => And (rf1 a Y) (ca_Ax2 Y)) (Exists fun Y => And (rf a Y) (cp Y)))) % 4.34/4.51 True % 4.34/4.51 Clause #223 (by clausification #[221]): ∀ (a : Iota), % 4.34/4.51 Or (Eq (cUnsatisfiable a) False) % 4.34/4.51 (Eq (And (Exists fun Y => And (rf1 a Y) (ca_Ax2 Y)) (Exists fun Y => And (rf a Y) (cp Y))) True) % 4.34/4.51 Clause #237 (by betaEtaReduce #[27]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True % 4.37/4.53 Clause #238 (by clausification #[237]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True % 4.37/4.53 Clause #240 (by clausification #[238]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 4.37/4.53 Clause #242 (by betaEtaReduce #[26]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True % 4.37/4.53 Clause #243 (by clausification #[242]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True % 4.37/4.53 Clause #245 (by clausification #[243]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 4.37/4.53 Clause #250 (by clausification #[240]): ∀ (a a_1 : Iota), Or (Eq (cpxcomp a) False) (Eq (ra_Px1 a (skS.0 1 a a_1)) True) % 4.37/4.53 Clause #252 (by clausification #[245]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False) % 4.37/4.53 Clause #253 (by clausification #[252]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False) % 4.37/4.53 Clause #254 (by clausification #[28]): ∀ (a : Iota), Eq (Iff (ca_Ax2 a) (And (cpxcomp a) (∀ (Y : Iota), rinvF1 a Y → ca_Vx3 Y))) True % 4.37/4.53 Clause #256 (by clausification #[254]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (And (cpxcomp a) (∀ (Y : Iota), rinvF1 a Y → ca_Vx3 Y)) True) % 4.37/4.53 Clause #263 (by clausification #[256]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (∀ (Y : Iota), rinvF1 a Y → ca_Vx3 Y) True) % 4.37/4.53 Clause #264 (by clausification #[256]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (cpxcomp a) True) % 4.37/4.53 Clause #265 (by clausification #[263]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (rinvF1 a a_1 → ca_Vx3 a_1) True) % 4.37/4.53 Clause #266 (by clausification #[265]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Or (Eq (rinvF1 a a_1) False) (Eq (ca_Vx3 a_1) True)) % 4.37/4.53 Clause #267 (by clausification #[29]): ∀ (a : Iota), Eq (Iff (ca_Vx3 a) (Exists fun Y => And (rs a Y) (cowlThing Y))) True % 4.37/4.53 Clause #269 (by clausification #[267]): ∀ (a : Iota), Or (Eq (ca_Vx3 a) False) (Eq (Exists fun Y => And (rs a Y) (cowlThing Y)) True) % 4.37/4.53 Clause #274 (by clausification #[269]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (And (rs a (skS.0 3 a a_1)) (cowlThing (skS.0 3 a a_1))) True) % 4.37/4.53 Clause #276 (by clausification #[274]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (rs a (skS.0 3 a a_1)) True) % 4.37/4.53 Clause #279 (by clausification #[223]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf a Y) (cp Y)) True) % 4.37/4.53 Clause #280 (by clausification #[223]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (ca_Ax2 Y)) True) % 4.37/4.53 Clause #281 (by clausification #[279]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 4 a a_1)) (cp (skS.0 4 a a_1))) True) % 4.37/4.53 Clause #282 (by clausification #[281]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp (skS.0 4 a a_1)) True) % 4.37/4.53 Clause #283 (by clausification #[281]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 4 a a_1)) True) % 4.37/4.53 Clause #284 (by superposition #[282, 36]): ∀ (a : Iota), Or (Eq (cp (skS.0 4 i2003_11_14_17_21_19256 a)) True) (Eq False True) % 4.37/4.53 Clause #285 (by clausification #[284]): ∀ (a : Iota), Eq (cp (skS.0 4 i2003_11_14_17_21_19256 a)) True % 4.37/4.53 Clause #286 (by superposition #[285, 253]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_19256 a) a_1) False) % 4.37/4.53 Clause #287 (by clausification #[280]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 5 a a_1)) (ca_Ax2 (skS.0 5 a a_1))) True) % 4.37/4.53 Clause #288 (by clausification #[287]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax2 (skS.0 5 a a_1)) True) % 4.37/4.53 Clause #289 (by clausification #[287]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 5 a a_1)) True) % 4.37/4.53 Clause #290 (by superposition #[288, 36]): ∀ (a : Iota), Or (Eq (ca_Ax2 (skS.0 5 i2003_11_14_17_21_19256 a)) True) (Eq False True) % 4.37/4.53 Clause #291 (by clausification #[290]): ∀ (a : Iota), Eq (ca_Ax2 (skS.0 5 i2003_11_14_17_21_19256 a)) True % 4.37/4.53 Clause #292 (by superposition #[291, 266]): ∀ (a a_1 : Iota), % 4.37/4.53 Or (Eq True False) (Or (Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1) False) (Eq (ca_Vx3 a_1) True)) % 4.37/4.55 Clause #293 (by superposition #[291, 264]): ∀ (a : Iota), Or (Eq True False) (Eq (cpxcomp (skS.0 5 i2003_11_14_17_21_19256 a)) True) % 4.37/4.55 Clause #294 (by clausification #[293]): ∀ (a : Iota), Eq (cpxcomp (skS.0 5 i2003_11_14_17_21_19256 a)) True % 4.37/4.55 Clause #295 (by superposition #[294, 250]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq True False) % 4.37/4.55 (Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1)) True) % 4.37/4.55 Clause #298 (by clausification #[286]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_19256 a) a_1) False % 4.37/4.55 Clause #302 (by superposition #[289, 36]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_21_19256 (skS.0 5 i2003_11_14_17_21_19256 a)) True) (Eq False True) % 4.37/4.55 Clause #303 (by clausification #[302]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_19256 (skS.0 5 i2003_11_14_17_21_19256 a)) True % 4.37/4.55 Clause #304 (by superposition #[303, 210]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a)) % 4.37/4.55 Clause #305 (by superposition #[303, 219]): ∀ (a : Iota), Or (Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) i2003_11_14_17_21_19256) True) (Eq True False) % 4.37/4.55 Clause #307 (by clausification #[305]): ∀ (a : Iota), Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) i2003_11_14_17_21_19256) True % 4.37/4.55 Clause #310 (by superposition #[283, 36]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_21_19256 (skS.0 4 i2003_11_14_17_21_19256 a)) True) (Eq False True) % 4.37/4.55 Clause #311 (by clausification #[310]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_19256 (skS.0 4 i2003_11_14_17_21_19256 a)) True % 4.37/4.55 Clause #316 (by clausification #[304]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a) % 4.37/4.55 Clause #318 (by clausification #[292]): ∀ (a a_1 : Iota), Or (Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1) False) (Eq (ca_Vx3 a_1) True) % 4.37/4.55 Clause #319 (by superposition #[318, 307]): Or (Eq (ca_Vx3 i2003_11_14_17_21_19256) True) (Eq False True) % 4.37/4.55 Clause #321 (by clausification #[319]): Eq (ca_Vx3 i2003_11_14_17_21_19256) True % 4.37/4.55 Clause #322 (by superposition #[321, 276]): ∀ (a : Iota), Or (Eq True False) (Eq (rs i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True) % 4.37/4.55 Clause #323 (by clausification #[322]): ∀ (a : Iota), Eq (rs i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True % 4.37/4.55 Clause #324 (by superposition #[323, 95]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True) % 4.37/4.55 Clause #325 (by superposition #[323, 105]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True) % 4.37/4.55 Clause #330 (by clausification #[325]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True % 4.37/4.55 Clause #331 (by superposition #[330, 316]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 3 i2003_11_14_17_21_19256 a_1)) % 4.37/4.55 Clause #335 (by clausification #[295]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1)) True % 4.37/4.55 Clause #338 (by clausification #[324]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True % 4.37/4.55 Clause #354 (by clausification #[331]): ∀ (a a_1 : Iota), Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 3 i2003_11_14_17_21_19256 a_1) % 4.37/4.55 Clause #363 (by superposition #[354, 338]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_19256 (skS.0 5 i2003_11_14_17_21_19256 a)) True % 4.37/4.55 Clause #377 (by superposition #[363, 216]): ∀ (a a_1 : Iota), % 4.37/4.55 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a)) % 4.37/4.55 Clause #387 (by clausification #[377]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a) % 4.37/4.55 Clause #388 (by superposition #[387, 311]): ∀ (a a_1 : Iota), Or (Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 4 i2003_11_14_17_21_19256 a_1)) (Eq False True) % 4.37/4.55 Clause #393 (by clausification #[388]): ∀ (a a_1 : Iota), Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 4 i2003_11_14_17_21_19256 a_1) % 4.37/4.55 Clause #405 (by superposition #[393, 298]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1) False % 4.37/4.55 Clause #427 (by superposition #[405, 335]): Eq False True % 4.37/4.55 Clause #430 (by clausification #[427]): False % 4.37/4.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------