TSTP Solution File: KRS118+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS118+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 05:43:23 EDT 2023
% Result : Unsatisfiable 5.07s 5.30s
% Output : Proof 5.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KRS118+1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n031.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 : Mon Aug 28 01:35:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.07/5.30 SZS status Theorem for theBenchmark.p
% 5.07/5.30 SZS output start Proof for theBenchmark.p
% 5.07/5.30 Clause #21 (by assumption #[]): Eq
% 5.07/5.30 (∀ (X : Iota),
% 5.07/5.30 Iff (cUnsatisfiable X)
% 5.07/5.30 (And (And (∀ (Y : Iota), rinvR X Y → ca_Vx3 Y) (Exists fun Y => And (rinvF X Y) (cd Y))) (ccxcomp X)))
% 5.07/5.30 True
% 5.07/5.30 Clause #22 (by assumption #[]): Eq (∀ (X : Iota), Iff (cc X) (Not (Exists fun Y => ra_Px1 X Y))) True
% 5.07/5.30 Clause #23 (by assumption #[]): Eq (∀ (X : Iota), Iff (ccxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True
% 5.07/5.30 Clause #24 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (And (Exists fun Y => And (rf X Y) (ccxcomp Y)) (cc X))) True
% 5.07/5.30 Clause #25 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx3 X) (Exists fun Y => And (rinvF X Y) (cd Y))) True
% 5.07/5.30 Clause #26 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True
% 5.07/5.30 Clause #27 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True
% 5.07/5.30 Clause #28 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True
% 5.07/5.30 Clause #30 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_4056) True
% 5.07/5.30 Clause #31 (by assumption #[]): Eq (∀ (X Y : Iota), rf X Y → rr X Y) True
% 5.07/5.30 Clause #86 (by clausification #[31]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf a Y → rr a Y) True
% 5.07/5.30 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Eq (rf a a_1 → rr a a_1) True
% 5.07/5.30 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), Or (Eq (rf a a_1) False) (Eq (rr a a_1) True)
% 5.07/5.30 Clause #168 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True
% 5.07/5.30 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf a a_1) (rf a Z) → Eq a_1 Z) True
% 5.07/5.30 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota), Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True
% 5.07/5.30 Clause #171 (by clausification #[170]): ∀ (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)
% 5.07/5.30 Clause #172 (by clausification #[171]): ∀ (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))
% 5.07/5.30 Clause #173 (by clausification #[172]): ∀ (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))
% 5.07/5.30 Clause #174 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True
% 5.07/5.30 Clause #175 (by clausification #[174]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True
% 5.07/5.30 Clause #177 (by clausification #[175]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) False) (Eq (rf a_1 a) True)
% 5.07/5.30 Clause #178 (by clausification #[21]): ∀ (a : Iota),
% 5.07/5.30 Eq
% 5.07/5.30 (Iff (cUnsatisfiable a)
% 5.07/5.30 (And (And (∀ (Y : Iota), rinvR a Y → ca_Vx3 Y) (Exists fun Y => And (rinvF a Y) (cd Y))) (ccxcomp a)))
% 5.07/5.30 True
% 5.07/5.30 Clause #180 (by clausification #[178]): ∀ (a : Iota),
% 5.07/5.30 Or (Eq (cUnsatisfiable a) False)
% 5.07/5.30 (Eq (And (And (∀ (Y : Iota), rinvR a Y → ca_Vx3 Y) (Exists fun Y => And (rinvF a Y) (cd Y))) (ccxcomp a)) True)
% 5.07/5.30 Clause #189 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True
% 5.07/5.30 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True
% 5.07/5.30 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False)
% 5.07/5.30 Clause #193 (by betaEtaReduce #[23]): Eq (∀ (X : Iota), Iff (ccxcomp X) (Exists (ra_Px1 X))) True
% 5.07/5.30 Clause #194 (by clausification #[193]): ∀ (a : Iota), Eq (Iff (ccxcomp a) (Exists (ra_Px1 a))) True
% 5.07/5.30 Clause #196 (by clausification #[194]): ∀ (a : Iota), Or (Eq (ccxcomp a) False) (Eq (Exists (ra_Px1 a)) True)
% 5.07/5.30 Clause #198 (by clausification #[196]): ∀ (a a_1 : Iota), Or (Eq (ccxcomp a) False) (Eq (ra_Px1 a (skS.0 1 a a_1)) True)
% 5.07/5.30 Clause #199 (by betaEtaReduce #[22]): Eq (∀ (X : Iota), Iff (cc X) (Not (Exists (ra_Px1 X)))) True
% 5.07/5.30 Clause #200 (by clausification #[199]): ∀ (a : Iota), Eq (Iff (cc a) (Not (Exists (ra_Px1 a)))) True
% 5.07/5.30 Clause #202 (by clausification #[200]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (Not (Exists (ra_Px1 a))) True)
% 5.07/5.30 Clause #206 (by clausification #[24]): ∀ (a : Iota), Eq (Iff (cd a) (And (Exists fun Y => And (rf a Y) (ccxcomp Y)) (cc a))) True
% 5.07/5.32 Clause #208 (by clausification #[206]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (And (Exists fun Y => And (rf a Y) (ccxcomp Y)) (cc a)) True)
% 5.07/5.32 Clause #214 (by clausification #[202]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (Exists (ra_Px1 a)) False)
% 5.07/5.32 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota), Or (Eq (cc a) False) (Eq (ra_Px1 a a_1) False)
% 5.07/5.32 Clause #218 (by clausification #[25]): ∀ (a : Iota), Eq (Iff (ca_Vx3 a) (Exists fun Y => And (rinvF a Y) (cd Y))) True
% 5.07/5.32 Clause #220 (by clausification #[218]): ∀ (a : Iota), Or (Eq (ca_Vx3 a) False) (Eq (Exists fun Y => And (rinvF a Y) (cd Y)) True)
% 5.07/5.32 Clause #223 (by clausification #[220]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (And (rinvF a (skS.0 3 a a_1)) (cd (skS.0 3 a a_1))) True)
% 5.07/5.32 Clause #224 (by clausification #[223]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (cd (skS.0 3 a a_1)) True)
% 5.07/5.32 Clause #225 (by clausification #[223]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (rinvF a (skS.0 3 a a_1)) True)
% 5.07/5.32 Clause #227 (by clausification #[180]): ∀ (a : Iota),
% 5.07/5.32 Or (Eq (cUnsatisfiable a) False)
% 5.07/5.32 (Eq (And (∀ (Y : Iota), rinvR a Y → ca_Vx3 Y) (Exists fun Y => And (rinvF a Y) (cd Y))) True)
% 5.07/5.32 Clause #236 (by clausification #[208]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (cc a) True)
% 5.07/5.32 Clause #237 (by clausification #[208]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists fun Y => And (rf a Y) (ccxcomp Y)) True)
% 5.07/5.32 Clause #238 (by clausification #[237]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (And (rf a (skS.0 4 a a_1)) (ccxcomp (skS.0 4 a a_1))) True)
% 5.07/5.32 Clause #239 (by clausification #[238]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (ccxcomp (skS.0 4 a a_1)) True)
% 5.07/5.32 Clause #240 (by clausification #[238]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (rf a (skS.0 4 a a_1)) True)
% 5.07/5.32 Clause #241 (by clausification #[227]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rinvF a Y) (cd Y)) True)
% 5.07/5.32 Clause #242 (by clausification #[227]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rinvR a Y → ca_Vx3 Y) True)
% 5.07/5.32 Clause #243 (by clausification #[241]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rinvF a (skS.0 5 a a_1)) (cd (skS.0 5 a a_1))) True)
% 5.07/5.32 Clause #244 (by clausification #[243]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd (skS.0 5 a a_1)) True)
% 5.07/5.32 Clause #245 (by clausification #[243]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvF a (skS.0 5 a a_1)) True)
% 5.07/5.32 Clause #246 (by superposition #[244, 30]): ∀ (a : Iota), Or (Eq (cd (skS.0 5 i2003_11_14_17_21_4056 a)) True) (Eq False True)
% 5.07/5.32 Clause #247 (by clausification #[242]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvR a a_1 → ca_Vx3 a_1) True)
% 5.07/5.32 Clause #248 (by clausification #[247]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (ca_Vx3 a_1) True))
% 5.07/5.32 Clause #249 (by superposition #[248, 30]): ∀ (a : Iota), Or (Eq (rinvR i2003_11_14_17_21_4056 a) False) (Or (Eq (ca_Vx3 a) True) (Eq False True))
% 5.07/5.32 Clause #252 (by clausification #[249]): ∀ (a : Iota), Or (Eq (rinvR i2003_11_14_17_21_4056 a) False) (Eq (ca_Vx3 a) True)
% 5.07/5.32 Clause #253 (by clausification #[246]): ∀ (a : Iota), Eq (cd (skS.0 5 i2003_11_14_17_21_4056 a)) True
% 5.07/5.32 Clause #254 (by superposition #[253, 236]): ∀ (a : Iota), Or (Eq True False) (Eq (cc (skS.0 5 i2003_11_14_17_21_4056 a)) True)
% 5.07/5.32 Clause #257 (by clausification #[254]): ∀ (a : Iota), Eq (cc (skS.0 5 i2003_11_14_17_21_4056 a)) True
% 5.07/5.32 Clause #259 (by superposition #[257, 215]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) False)
% 5.07/5.32 Clause #260 (by clausification #[259]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) False
% 5.07/5.32 Clause #264 (by superposition #[245, 30]): ∀ (a : Iota), Or (Eq (rinvF i2003_11_14_17_21_4056 (skS.0 5 i2003_11_14_17_21_4056 a)) True) (Eq False True)
% 5.07/5.32 Clause #265 (by clausification #[264]): ∀ (a : Iota), Eq (rinvF i2003_11_14_17_21_4056 (skS.0 5 i2003_11_14_17_21_4056 a)) True
% 5.07/5.32 Clause #266 (by superposition #[265, 177]): ∀ (a : Iota), Or (Eq True False) (Eq (rf (skS.0 5 i2003_11_14_17_21_4056 a) i2003_11_14_17_21_4056) True)
% 5.07/5.34 Clause #268 (by clausification #[266]): ∀ (a : Iota), Eq (rf (skS.0 5 i2003_11_14_17_21_4056 a) i2003_11_14_17_21_4056) True
% 5.07/5.34 Clause #269 (by superposition #[268, 88]): ∀ (a : Iota), Or (Eq True False) (Eq (rr (skS.0 5 i2003_11_14_17_21_4056 a) i2003_11_14_17_21_4056) True)
% 5.07/5.34 Clause #273 (by clausification #[269]): ∀ (a : Iota), Eq (rr (skS.0 5 i2003_11_14_17_21_4056 a) i2003_11_14_17_21_4056) True
% 5.07/5.34 Clause #275 (by superposition #[273, 191]): ∀ (a : Iota), Or (Eq (rinvR i2003_11_14_17_21_4056 (skS.0 5 i2003_11_14_17_21_4056 a)) True) (Eq True False)
% 5.07/5.34 Clause #280 (by clausification #[275]): ∀ (a : Iota), Eq (rinvR i2003_11_14_17_21_4056 (skS.0 5 i2003_11_14_17_21_4056 a)) True
% 5.07/5.34 Clause #281 (by superposition #[280, 252]): ∀ (a : Iota), Or (Eq True False) (Eq (ca_Vx3 (skS.0 5 i2003_11_14_17_21_4056 a)) True)
% 5.07/5.34 Clause #282 (by clausification #[281]): ∀ (a : Iota), Eq (ca_Vx3 (skS.0 5 i2003_11_14_17_21_4056 a)) True
% 5.07/5.34 Clause #283 (by superposition #[282, 224]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cd (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1)) True)
% 5.07/5.34 Clause #284 (by superposition #[282, 225]): ∀ (a a_1 : Iota),
% 5.07/5.34 Or (Eq True False)
% 5.07/5.34 (Eq (rinvF (skS.0 5 i2003_11_14_17_21_4056 a) (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1)) True)
% 5.07/5.34 Clause #336 (by clausification #[283]): ∀ (a a_1 : Iota), Eq (cd (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1)) True
% 5.07/5.34 Clause #338 (by superposition #[336, 239]): ∀ (a a_1 a_2 : Iota),
% 5.07/5.34 Or (Eq True False) (Eq (ccxcomp (skS.0 4 (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2)) True)
% 5.07/5.34 Clause #339 (by superposition #[336, 240]): ∀ (a a_1 a_2 : Iota),
% 5.07/5.34 Or (Eq True False)
% 5.07/5.34 (Eq
% 5.07/5.34 (rf (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1)
% 5.07/5.34 (skS.0 4 (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2))
% 5.07/5.34 True)
% 5.07/5.34 Clause #370 (by clausification #[338]): ∀ (a a_1 a_2 : Iota), Eq (ccxcomp (skS.0 4 (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2)) True
% 5.07/5.34 Clause #390 (by clausification #[284]): ∀ (a a_1 : Iota), Eq (rinvF (skS.0 5 i2003_11_14_17_21_4056 a) (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1)) True
% 5.07/5.34 Clause #391 (by superposition #[390, 177]): ∀ (a a_1 : Iota),
% 5.07/5.34 Or (Eq True False) (Eq (rf (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) (skS.0 5 i2003_11_14_17_21_4056 a)) True)
% 5.07/5.34 Clause #393 (by clausification #[391]): ∀ (a a_1 : Iota), Eq (rf (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) (skS.0 5 i2003_11_14_17_21_4056 a)) True
% 5.07/5.34 Clause #395 (by superposition #[393, 173]): ∀ (a a_1 a_2 : Iota),
% 5.07/5.34 Or (Eq True False)
% 5.07/5.34 (Or (Eq (rf (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2) False)
% 5.07/5.34 (Eq (skS.0 5 i2003_11_14_17_21_4056 a) a_2))
% 5.07/5.34 Clause #424 (by clausification #[395]): ∀ (a a_1 a_2 : Iota),
% 5.07/5.34 Or (Eq (rf (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2) False) (Eq (skS.0 5 i2003_11_14_17_21_4056 a) a_2)
% 5.07/5.34 Clause #427 (by clausification #[339]): ∀ (a a_1 a_2 : Iota),
% 5.07/5.34 Eq
% 5.07/5.34 (rf (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) (skS.0 4 (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2))
% 5.07/5.34 True
% 5.07/5.34 Clause #428 (by superposition #[427, 424]): ∀ (a a_1 a_2 : Iota),
% 5.07/5.34 Or (Eq True False)
% 5.07/5.34 (Eq (skS.0 5 i2003_11_14_17_21_4056 a) (skS.0 4 (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2))
% 5.07/5.34 Clause #489 (by clausification #[428]): ∀ (a a_1 a_2 : Iota),
% 5.07/5.34 Eq (skS.0 5 i2003_11_14_17_21_4056 a) (skS.0 4 (skS.0 3 (skS.0 5 i2003_11_14_17_21_4056 a) a_1) a_2)
% 5.07/5.34 Clause #490 (by backward demodulation #[489, 370]): ∀ (a : Iota), Eq (ccxcomp (skS.0 5 i2003_11_14_17_21_4056 a)) True
% 5.07/5.34 Clause #492 (by superposition #[490, 198]): ∀ (a a_1 : Iota),
% 5.07/5.34 Or (Eq True False)
% 5.07/5.34 (Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_4056 a) (skS.0 1 (skS.0 5 i2003_11_14_17_21_4056 a) a_1)) True)
% 5.07/5.34 Clause #494 (by clausification #[492]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_4056 a) (skS.0 1 (skS.0 5 i2003_11_14_17_21_4056 a) a_1)) True
% 5.07/5.34 Clause #495 (by superposition #[494, 260]): Eq True False
% 5.07/5.34 Clause #497 (by clausification #[495]): False
% 5.07/5.35 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------