TSTP Solution File: KRS114+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS114+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n024.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 : Thu Aug 31 05:43:22 EDT 2023
% Result : Unsatisfiable 4.06s 4.22s
% Output : Proof 4.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS114+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n024.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 : Mon Aug 28 01:13:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.06/4.22 SZS status Theorem for theBenchmark.p
% 4.06/4.22 SZS output start Proof for theBenchmark.p
% 4.06/4.22 Clause #24 (by assumption #[]): Eq
% 4.06/4.22 (∀ (X : Iota),
% 4.06/4.22 Iff (cUnsatisfiable X) (And (Exists fun Y => And (rr X Y) (ca_Ax4 Y)) (Exists fun Y => And (rs X Y) (ca_Ax3 Y))))
% 4.06/4.22 True
% 4.06/4.22 Clause #25 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True
% 4.06/4.22 Clause #26 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True
% 4.06/4.22 Clause #29 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax3 X) (And (cqxcomp X) (cpxcomp X))) True
% 4.06/4.22 Clause #30 (by assumption #[]): Eq
% 4.06/4.22 (∀ (X : Iota),
% 4.06/4.22 Iff (ca_Ax4 X)
% 4.06/4.22 (And (∀ (Y0 Y1 : Iota), And (rinvR X Y0) (rinvR X Y1) → Eq Y0 Y1) (Exists fun Y => And (rinvR X Y) (ca_Vx5 Y))))
% 4.06/4.22 True
% 4.06/4.22 Clause #31 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx5 X) (∀ (Y : Iota), rs X Y → cp Y)) True
% 4.06/4.22 Clause #32 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True
% 4.06/4.22 Clause #33 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_262) True
% 4.06/4.22 Clause #180 (by clausification #[31]): ∀ (a : Iota), Eq (Iff (ca_Vx5 a) (∀ (Y : Iota), rs a Y → cp Y)) True
% 4.06/4.22 Clause #182 (by clausification #[180]): ∀ (a : Iota), Or (Eq (ca_Vx5 a) False) (Eq (∀ (Y : Iota), rs a Y → cp Y) True)
% 4.06/4.22 Clause #187 (by clausification #[182]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx5 a) False) (Eq (rs a a_1 → cp a_1) True)
% 4.06/4.22 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))
% 4.06/4.22 Clause #189 (by clausification #[24]): ∀ (a : Iota),
% 4.06/4.22 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))))
% 4.06/4.22 True
% 4.06/4.22 Clause #191 (by clausification #[189]): ∀ (a : Iota),
% 4.06/4.22 Or (Eq (cUnsatisfiable a) False)
% 4.06/4.22 (Eq (And (Exists fun Y => And (rr a Y) (ca_Ax4 Y)) (Exists fun Y => And (rs a Y) (ca_Ax3 Y))) True)
% 4.06/4.22 Clause #197 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True
% 4.06/4.22 Clause #198 (by clausification #[197]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True
% 4.06/4.22 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False)
% 4.06/4.22 Clause #201 (by clausification #[29]): ∀ (a : Iota), Eq (Iff (ca_Ax3 a) (And (cqxcomp a) (cpxcomp a))) True
% 4.06/4.22 Clause #203 (by clausification #[201]): ∀ (a : Iota), Or (Eq (ca_Ax3 a) False) (Eq (And (cqxcomp a) (cpxcomp a)) True)
% 4.06/4.22 Clause #205 (by clausification #[203]): ∀ (a : Iota), Or (Eq (ca_Ax3 a) False) (Eq (cpxcomp a) True)
% 4.06/4.22 Clause #207 (by betaEtaReduce #[25]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True
% 4.06/4.22 Clause #208 (by clausification #[207]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True
% 4.06/4.22 Clause #210 (by clausification #[208]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True)
% 4.06/4.22 Clause #213 (by clausification #[210]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False)
% 4.06/4.22 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False)
% 4.06/4.22 Clause #221 (by betaEtaReduce #[26]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True
% 4.06/4.22 Clause #222 (by clausification #[221]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True
% 4.06/4.22 Clause #224 (by clausification #[222]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True)
% 4.06/4.22 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)
% 4.06/4.22 Clause #243 (by clausification #[30]): ∀ (a : Iota),
% 4.06/4.22 Eq
% 4.06/4.22 (Iff (ca_Ax4 a)
% 4.06/4.22 (And (∀ (Y0 Y1 : Iota), And (rinvR a Y0) (rinvR a Y1) → Eq Y0 Y1) (Exists fun Y => And (rinvR a Y) (ca_Vx5 Y))))
% 4.06/4.22 True
% 4.06/4.22 Clause #245 (by clausification #[243]): ∀ (a : Iota),
% 4.06/4.22 Or (Eq (ca_Ax4 a) False)
% 4.06/4.22 (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)))
% 4.06/4.22 True)
% 4.06/4.22 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)
% 4.06/4.22 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)
% 4.06/4.24 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)
% 4.06/4.24 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)
% 4.06/4.24 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)
% 4.06/4.24 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)
% 4.06/4.24 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)
% 4.06/4.24 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))
% 4.06/4.24 Clause #267 (by clausification #[266]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.24 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)))
% 4.06/4.24 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)))
% 4.06/4.24 Clause #269 (by clausification #[191]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rs a Y) (ca_Ax3 Y)) True)
% 4.06/4.24 Clause #270 (by clausification #[191]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (ca_Ax4 Y)) True)
% 4.06/4.24 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)
% 4.06/4.24 Clause #272 (by clausification #[271]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax3 (skS.0 8 a a_1)) True)
% 4.06/4.24 Clause #273 (by clausification #[271]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 8 a a_1)) True)
% 4.06/4.24 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)
% 4.06/4.24 Clause #275 (by clausification #[274]): ∀ (a : Iota), Eq (ca_Ax3 (skS.0 8 i2003_11_14_17_21_262 a)) True
% 4.06/4.24 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)
% 4.06/4.24 Clause #281 (by clausification #[276]): ∀ (a : Iota), Eq (cpxcomp (skS.0 8 i2003_11_14_17_21_262 a)) True
% 4.06/4.24 Clause #282 (by superposition #[281, 237]): ∀ (a a_1 : Iota),
% 4.06/4.24 Or (Eq True False)
% 4.06/4.24 (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)
% 4.06/4.24 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)
% 4.06/4.24 Clause #287 (by clausification #[286]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax4 (skS.0 9 a a_1)) True)
% 4.06/4.24 Clause #288 (by clausification #[286]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 9 a a_1)) True)
% 4.06/4.24 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)
% 4.06/4.24 Clause #290 (by clausification #[289]): ∀ (a : Iota), Eq (ca_Ax4 (skS.0 9 i2003_11_14_17_21_262 a)) True
% 4.06/4.24 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)
% 4.06/4.24 Clause #292 (by superposition #[290, 268]): ∀ (a a_1 a_2 : Iota),
% 4.06/4.24 Or (Eq True False)
% 4.06/4.24 (Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_1) False)
% 4.06/4.24 (Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_2) False) (Eq a_1 a_2)))
% 4.06/4.24 Clause #293 (by superposition #[290, 263]): ∀ (a a_1 : Iota),
% 4.06/4.24 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)
% 4.06/4.24 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)
% 4.06/4.24 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
% 4.10/4.26 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)
% 4.10/4.26 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
% 4.10/4.26 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)
% 4.10/4.26 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
% 4.10/4.26 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
% 4.10/4.26 Clause #306 (by superposition #[305, 188]): ∀ (a a_1 a_2 : Iota),
% 4.10/4.26 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))
% 4.10/4.26 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
% 4.10/4.26 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)
% 4.10/4.26 Clause #315 (by clausification #[292]): ∀ (a a_1 a_2 : Iota),
% 4.10/4.26 Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_1) False)
% 4.10/4.26 (Or (Eq (rinvR (skS.0 9 i2003_11_14_17_21_262 a) a_2) False) (Eq a_1 a_2))
% 4.10/4.26 Clause #316 (by superposition #[315, 298]): ∀ (a a_1 : Iota),
% 4.10/4.26 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))
% 4.10/4.26 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)
% 4.10/4.26 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
% 4.10/4.26 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))
% 4.10/4.26 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)
% 4.10/4.26 Clause #329 (by backward demodulation #[327, 313]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_21_262 a) False) (Eq (cp a) True)
% 4.10/4.26 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)
% 4.10/4.26 Clause #335 (by clausification #[331]): ∀ (a : Iota), Eq (cp (skS.0 8 i2003_11_14_17_21_262 a)) True
% 4.10/4.26 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)
% 4.10/4.26 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
% 4.10/4.26 Clause #338 (by superposition #[337, 309]): Eq False True
% 4.10/4.26 Clause #340 (by clausification #[338]): False
% 4.10/4.26 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------