TSTP Solution File: KRS109+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS109+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 05:43:21 EDT 2023
% Result : Unsatisfiable 4.10s 4.40s
% Output : Proof 4.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KRS109+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 02:05:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.10/4.40 SZS status Theorem for theBenchmark.p
% 4.10/4.40 SZS output start Proof for theBenchmark.p
% 4.10/4.40 Clause #25 (by assumption #[]): Eq (∀ (X : Iota), Iff (cUnsatisfiable X) (And (cpxcomp X) (Exists fun Y => And (rf X Y) (ca_Ax2 Y)))) True
% 4.10/4.40 Clause #26 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True
% 4.10/4.40 Clause #27 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True
% 4.10/4.40 Clause #28 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax2 X) (And (∀ (Y : Iota), rinvS X Y → cp Y) (∀ (Y : Iota), rinvF X Y → ca_Vx3 Y))) True
% 4.10/4.40 Clause #29 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx3 X) (Exists fun Y => And (rs X Y) (cp Y))) True
% 4.10/4.40 Clause #30 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True
% 4.10/4.40 Clause #32 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True
% 4.10/4.40 Clause #34 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvS X Y) (rs Y X)) True
% 4.10/4.40 Clause #36 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_08508) True
% 4.10/4.40 Clause #37 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf X Y) True
% 4.10/4.40 Clause #93 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf a Y) True
% 4.10/4.40 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf a a_1) True
% 4.10/4.40 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf a a_1) True)
% 4.10/4.40 Clause #211 (by clausification #[30]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True
% 4.10/4.40 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
% 4.10/4.40 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
% 4.10/4.40 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)
% 4.10/4.40 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))
% 4.10/4.40 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))
% 4.10/4.40 Clause #221 (by clausification #[25]): ∀ (a : Iota), Eq (Iff (cUnsatisfiable a) (And (cpxcomp a) (Exists fun Y => And (rf a Y) (ca_Ax2 Y)))) True
% 4.10/4.40 Clause #223 (by clausification #[221]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (cpxcomp a) (Exists fun Y => And (rf a Y) (ca_Ax2 Y))) True)
% 4.10/4.40 Clause #227 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvS a Y) (rs Y a)) True
% 4.10/4.40 Clause #228 (by clausification #[227]): ∀ (a a_1 : Iota), Eq (Iff (rinvS a a_1) (rs a_1 a)) True
% 4.10/4.40 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Or (Eq (rinvS a a_1) True) (Eq (rs a_1 a) False)
% 4.10/4.40 Clause #231 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True
% 4.10/4.40 Clause #232 (by clausification #[231]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True
% 4.10/4.40 Clause #233 (by clausification #[232]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) True) (Eq (rf a_1 a) False)
% 4.10/4.40 Clause #235 (by betaEtaReduce #[27]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True
% 4.10/4.40 Clause #236 (by clausification #[235]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True
% 4.10/4.40 Clause #238 (by clausification #[236]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True)
% 4.10/4.40 Clause #240 (by betaEtaReduce #[26]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True
% 4.10/4.40 Clause #241 (by clausification #[240]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True
% 4.10/4.40 Clause #243 (by clausification #[241]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True)
% 4.10/4.40 Clause #249 (by clausification #[238]): ∀ (a a_1 : Iota), Or (Eq (cpxcomp a) False) (Eq (ra_Px1 a (skS.0 1 a a_1)) True)
% 4.10/4.40 Clause #251 (by clausification #[243]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False)
% 4.10/4.40 Clause #252 (by clausification #[251]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False)
% 4.10/4.40 Clause #253 (by clausification #[29]): ∀ (a : Iota), Eq (Iff (ca_Vx3 a) (Exists fun Y => And (rs a Y) (cp Y))) True
% 4.10/4.42 Clause #255 (by clausification #[253]): ∀ (a : Iota), Or (Eq (ca_Vx3 a) False) (Eq (Exists fun Y => And (rs a Y) (cp Y)) True)
% 4.10/4.42 Clause #258 (by clausification #[255]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (And (rs a (skS.0 2 a a_1)) (cp (skS.0 2 a a_1))) True)
% 4.10/4.42 Clause #260 (by clausification #[258]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (rs a (skS.0 2 a a_1)) True)
% 4.10/4.42 Clause #261 (by clausification #[28]): ∀ (a : Iota), Eq (Iff (ca_Ax2 a) (And (∀ (Y : Iota), rinvS a Y → cp Y) (∀ (Y : Iota), rinvF a Y → ca_Vx3 Y))) True
% 4.10/4.42 Clause #263 (by clausification #[261]): ∀ (a : Iota),
% 4.10/4.42 Or (Eq (ca_Ax2 a) False) (Eq (And (∀ (Y : Iota), rinvS a Y → cp Y) (∀ (Y : Iota), rinvF a Y → ca_Vx3 Y)) True)
% 4.10/4.42 Clause #275 (by clausification #[263]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (∀ (Y : Iota), rinvF a Y → ca_Vx3 Y) True)
% 4.10/4.42 Clause #276 (by clausification #[263]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (∀ (Y : Iota), rinvS a Y → cp Y) True)
% 4.10/4.42 Clause #277 (by clausification #[275]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (rinvF a a_1 → ca_Vx3 a_1) True)
% 4.10/4.42 Clause #278 (by clausification #[277]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Or (Eq (rinvF a a_1) False) (Eq (ca_Vx3 a_1) True))
% 4.10/4.42 Clause #279 (by clausification #[276]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (rinvS a a_1 → cp a_1) True)
% 4.10/4.42 Clause #280 (by clausification #[279]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Or (Eq (rinvS a a_1) False) (Eq (cp a_1) True))
% 4.10/4.42 Clause #283 (by clausification #[223]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf a Y) (ca_Ax2 Y)) True)
% 4.10/4.42 Clause #284 (by clausification #[223]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cpxcomp a) True)
% 4.10/4.42 Clause #285 (by clausification #[283]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 5 a a_1)) (ca_Ax2 (skS.0 5 a a_1))) True)
% 4.10/4.42 Clause #286 (by clausification #[285]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax2 (skS.0 5 a a_1)) True)
% 4.10/4.42 Clause #287 (by clausification #[285]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 5 a a_1)) True)
% 4.10/4.42 Clause #288 (by superposition #[286, 36]): ∀ (a : Iota), Or (Eq (ca_Ax2 (skS.0 5 i2003_11_14_17_21_08508 a)) True) (Eq False True)
% 4.10/4.42 Clause #289 (by superposition #[284, 36]): Or (Eq (cpxcomp i2003_11_14_17_21_08508) True) (Eq False True)
% 4.10/4.42 Clause #290 (by clausification #[289]): Eq (cpxcomp i2003_11_14_17_21_08508) True
% 4.10/4.42 Clause #292 (by superposition #[290, 249]): ∀ (a : Iota), Or (Eq True False) (Eq (ra_Px1 i2003_11_14_17_21_08508 (skS.0 1 i2003_11_14_17_21_08508 a)) True)
% 4.10/4.42 Clause #293 (by clausification #[288]): ∀ (a : Iota), Eq (ca_Ax2 (skS.0 5 i2003_11_14_17_21_08508 a)) True
% 4.10/4.42 Clause #294 (by superposition #[293, 278]): ∀ (a a_1 : Iota),
% 4.10/4.42 Or (Eq True False) (Or (Eq (rinvF (skS.0 5 i2003_11_14_17_21_08508 a) a_1) False) (Eq (ca_Vx3 a_1) True))
% 4.10/4.42 Clause #295 (by superposition #[293, 280]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (rinvS (skS.0 5 i2003_11_14_17_21_08508 a) a_1) False) (Eq (cp a_1) True))
% 4.10/4.42 Clause #298 (by clausification #[292]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_21_08508 (skS.0 1 i2003_11_14_17_21_08508 a)) True
% 4.10/4.42 Clause #302 (by superposition #[287, 36]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_21_08508 (skS.0 5 i2003_11_14_17_21_08508 a)) True) (Eq False True)
% 4.10/4.42 Clause #303 (by clausification #[302]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_08508 (skS.0 5 i2003_11_14_17_21_08508 a)) True
% 4.10/4.42 Clause #304 (by superposition #[303, 216]): ∀ (a a_1 : Iota),
% 4.10/4.42 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_21_08508 a) False) (Eq (skS.0 5 i2003_11_14_17_21_08508 a_1) a))
% 4.10/4.42 Clause #305 (by superposition #[303, 233]): ∀ (a : Iota), Or (Eq (rinvF (skS.0 5 i2003_11_14_17_21_08508 a) i2003_11_14_17_21_08508) True) (Eq True False)
% 4.10/4.42 Clause #307 (by clausification #[305]): ∀ (a : Iota), Eq (rinvF (skS.0 5 i2003_11_14_17_21_08508 a) i2003_11_14_17_21_08508) True
% 4.10/4.42 Clause #309 (by clausification #[304]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_21_08508 a) False) (Eq (skS.0 5 i2003_11_14_17_21_08508 a_1) a)
% 4.10/4.43 Clause #311 (by clausification #[295]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 5 i2003_11_14_17_21_08508 a) a_1) False) (Eq (cp a_1) True)
% 4.10/4.43 Clause #313 (by clausification #[294]): ∀ (a a_1 : Iota), Or (Eq (rinvF (skS.0 5 i2003_11_14_17_21_08508 a) a_1) False) (Eq (ca_Vx3 a_1) True)
% 4.10/4.43 Clause #314 (by superposition #[313, 307]): Or (Eq (ca_Vx3 i2003_11_14_17_21_08508) True) (Eq False True)
% 4.10/4.43 Clause #316 (by clausification #[314]): Eq (ca_Vx3 i2003_11_14_17_21_08508) True
% 4.10/4.43 Clause #318 (by superposition #[316, 260]): ∀ (a : Iota), Or (Eq True False) (Eq (rs i2003_11_14_17_21_08508 (skS.0 2 i2003_11_14_17_21_08508 a)) True)
% 4.10/4.43 Clause #329 (by clausification #[318]): ∀ (a : Iota), Eq (rs i2003_11_14_17_21_08508 (skS.0 2 i2003_11_14_17_21_08508 a)) True
% 4.10/4.43 Clause #330 (by superposition #[329, 95]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_21_08508 (skS.0 2 i2003_11_14_17_21_08508 a)) True)
% 4.10/4.43 Clause #333 (by superposition #[329, 229]): ∀ (a : Iota), Or (Eq (rinvS (skS.0 2 i2003_11_14_17_21_08508 a) i2003_11_14_17_21_08508) True) (Eq True False)
% 4.10/4.43 Clause #335 (by clausification #[333]): ∀ (a : Iota), Eq (rinvS (skS.0 2 i2003_11_14_17_21_08508 a) i2003_11_14_17_21_08508) True
% 4.10/4.43 Clause #340 (by clausification #[330]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_08508 (skS.0 2 i2003_11_14_17_21_08508 a)) True
% 4.10/4.43 Clause #341 (by superposition #[340, 309]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 5 i2003_11_14_17_21_08508 a) (skS.0 2 i2003_11_14_17_21_08508 a_1))
% 4.10/4.43 Clause #363 (by clausification #[341]): ∀ (a a_1 : Iota), Eq (skS.0 5 i2003_11_14_17_21_08508 a) (skS.0 2 i2003_11_14_17_21_08508 a_1)
% 4.10/4.43 Clause #369 (by superposition #[363, 335]): ∀ (a : Iota), Eq (rinvS (skS.0 5 i2003_11_14_17_21_08508 a) i2003_11_14_17_21_08508) True
% 4.10/4.43 Clause #381 (by superposition #[369, 311]): Or (Eq True False) (Eq (cp i2003_11_14_17_21_08508) True)
% 4.10/4.43 Clause #383 (by clausification #[381]): Eq (cp i2003_11_14_17_21_08508) True
% 4.10/4.43 Clause #384 (by superposition #[383, 252]): ∀ (a : Iota), Or (Eq True False) (Eq (ra_Px1 i2003_11_14_17_21_08508 a) False)
% 4.10/4.43 Clause #385 (by clausification #[384]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_21_08508 a) False
% 4.10/4.43 Clause #386 (by superposition #[385, 298]): Eq False True
% 4.10/4.43 Clause #389 (by clausification #[386]): False
% 4.10/4.43 SZS output end Proof for theBenchmark.p
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