TSTP Solution File: KRS113+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS113+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n006.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 4.07s 4.39s
% Output : Proof 4.20s
% 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 : KRS113+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.36 % Computer : n006.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Aug 28 01:30:52 EDT 2023
% 0.21/0.36 % CPUTime :
% 4.07/4.39 SZS status Theorem for theBenchmark.p
% 4.07/4.39 SZS output start Proof for theBenchmark.p
% 4.07/4.39 Clause #18 (by assumption #[]): Eq
% 4.07/4.39 (∀ (X : Iota),
% 4.07/4.39 Iff (cUnsatisfiable X)
% 4.07/4.39 (And
% 4.07/4.39 (And (And (∀ (Y0 Y1 : Iota), And (rr X Y0) (rr X Y1) → Eq Y0 Y1) (Exists fun Y => And (rr X Y) (ca_Vx2 Y)))
% 4.07/4.39 (Exists fun Y => And (rs X Y) (cp Y)))
% 4.07/4.39 (cpxcomp X)))
% 4.07/4.39 True
% 4.07/4.39 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True
% 4.07/4.39 Clause #20 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True
% 4.07/4.39 Clause #21 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx2 X) (∀ (Y : Iota), rinvS X Y → cp Y)) True
% 4.07/4.39 Clause #22 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvS X Y) (rs Y X)) True
% 4.07/4.39 Clause #23 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_22376) True
% 4.07/4.39 Clause #24 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rr X Y) True
% 4.07/4.39 Clause #73 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rr a Y) True
% 4.07/4.39 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rr a a_1) True
% 4.07/4.39 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rr a a_1) True)
% 4.07/4.39 Clause #139 (by clausification #[18]): ∀ (a : Iota),
% 4.07/4.39 Eq
% 4.07/4.39 (Iff (cUnsatisfiable a)
% 4.07/4.39 (And
% 4.07/4.39 (And (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y)))
% 4.07/4.39 (Exists fun Y => And (rs a Y) (cp Y)))
% 4.07/4.39 (cpxcomp a)))
% 4.07/4.39 True
% 4.07/4.39 Clause #141 (by clausification #[139]): ∀ (a : Iota),
% 4.07/4.39 Or (Eq (cUnsatisfiable a) False)
% 4.07/4.39 (Eq
% 4.07/4.39 (And
% 4.07/4.39 (And (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y)))
% 4.07/4.39 (Exists fun Y => And (rs a Y) (cp Y)))
% 4.07/4.39 (cpxcomp a))
% 4.07/4.39 True)
% 4.07/4.39 Clause #157 (by clausification #[21]): ∀ (a : Iota), Eq (Iff (ca_Vx2 a) (∀ (Y : Iota), rinvS a Y → cp Y)) True
% 4.07/4.39 Clause #159 (by clausification #[157]): ∀ (a : Iota), Or (Eq (ca_Vx2 a) False) (Eq (∀ (Y : Iota), rinvS a Y → cp Y) True)
% 4.07/4.39 Clause #164 (by clausification #[159]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx2 a) False) (Eq (rinvS a a_1 → cp a_1) True)
% 4.07/4.39 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx2 a) False) (Or (Eq (rinvS a a_1) False) (Eq (cp a_1) True))
% 4.07/4.39 Clause #166 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvS a Y) (rs Y a)) True
% 4.07/4.39 Clause #167 (by clausification #[166]): ∀ (a a_1 : Iota), Eq (Iff (rinvS a a_1) (rs a_1 a)) True
% 4.07/4.39 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Or (Eq (rinvS a a_1) True) (Eq (rs a_1 a) False)
% 4.07/4.39 Clause #171 (by betaEtaReduce #[20]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True
% 4.07/4.39 Clause #172 (by clausification #[171]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True
% 4.07/4.39 Clause #174 (by clausification #[172]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True)
% 4.07/4.39 Clause #176 (by betaEtaReduce #[19]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True
% 4.07/4.39 Clause #177 (by clausification #[176]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True
% 4.07/4.39 Clause #179 (by clausification #[177]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True)
% 4.07/4.39 Clause #185 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (cpxcomp a) False) (Eq (ra_Px1 a (skS.0 4 a a_1)) True)
% 4.07/4.39 Clause #187 (by clausification #[179]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False)
% 4.07/4.39 Clause #188 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False)
% 4.07/4.39 Clause #192 (by clausification #[141]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cpxcomp a) True)
% 4.07/4.39 Clause #193 (by clausification #[141]): ∀ (a : Iota),
% 4.07/4.39 Or (Eq (cUnsatisfiable a) False)
% 4.07/4.39 (Eq
% 4.07/4.39 (And (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y)))
% 4.07/4.39 (Exists fun Y => And (rs a Y) (cp Y)))
% 4.07/4.39 True)
% 4.07/4.39 Clause #194 (by superposition #[192, 23]): Or (Eq (cpxcomp i2003_11_14_17_21_22376) True) (Eq False True)
% 4.20/4.41 Clause #195 (by clausification #[194]): Eq (cpxcomp i2003_11_14_17_21_22376) True
% 4.20/4.41 Clause #197 (by superposition #[195, 185]): ∀ (a : Iota), Or (Eq True False) (Eq (ra_Px1 i2003_11_14_17_21_22376 (skS.0 4 i2003_11_14_17_21_22376 a)) True)
% 4.20/4.41 Clause #198 (by clausification #[197]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_21_22376 (skS.0 4 i2003_11_14_17_21_22376 a)) True
% 4.20/4.41 Clause #205 (by clausification #[193]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rs a Y) (cp Y)) True)
% 4.20/4.41 Clause #206 (by clausification #[193]): ∀ (a : Iota),
% 4.20/4.41 Or (Eq (cUnsatisfiable a) False)
% 4.20/4.41 (Eq (And (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) (Exists fun Y => And (rr a Y) (ca_Vx2 Y))) True)
% 4.20/4.41 Clause #207 (by clausification #[205]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rs a (skS.0 5 a a_1)) (cp (skS.0 5 a a_1))) True)
% 4.20/4.41 Clause #209 (by clausification #[207]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 5 a a_1)) True)
% 4.20/4.41 Clause #217 (by superposition #[209, 23]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True) (Eq False True)
% 4.20/4.41 Clause #218 (by clausification #[217]): ∀ (a : Iota), Eq (rs i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True
% 4.20/4.41 Clause #219 (by superposition #[218, 75]): ∀ (a : Iota), Or (Eq True False) (Eq (rr i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True)
% 4.20/4.41 Clause #220 (by superposition #[218, 168]): ∀ (a : Iota), Or (Eq (rinvS (skS.0 5 i2003_11_14_17_21_22376 a) i2003_11_14_17_21_22376) True) (Eq True False)
% 4.20/4.41 Clause #221 (by clausification #[220]): ∀ (a : Iota), Eq (rinvS (skS.0 5 i2003_11_14_17_21_22376 a) i2003_11_14_17_21_22376) True
% 4.20/4.41 Clause #223 (by clausification #[219]): ∀ (a : Iota), Eq (rr i2003_11_14_17_21_22376 (skS.0 5 i2003_11_14_17_21_22376 a)) True
% 4.20/4.41 Clause #227 (by clausification #[206]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (ca_Vx2 Y)) True)
% 4.20/4.41 Clause #228 (by clausification #[206]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) True)
% 4.20/4.41 Clause #229 (by clausification #[227]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 6 a a_1)) (ca_Vx2 (skS.0 6 a a_1))) True)
% 4.20/4.41 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Vx2 (skS.0 6 a a_1)) True)
% 4.20/4.41 Clause #231 (by clausification #[229]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 6 a a_1)) True)
% 4.20/4.41 Clause #232 (by superposition #[230, 23]): ∀ (a : Iota), Or (Eq (ca_Vx2 (skS.0 6 i2003_11_14_17_21_22376 a)) True) (Eq False True)
% 4.20/4.41 Clause #233 (by clausification #[228]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y1 : Iota), And (rr a a_1) (rr a Y1) → Eq a_1 Y1) True)
% 4.20/4.41 Clause #234 (by clausification #[233]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a a_1) (rr a a_2) → Eq a_1 a_2) True)
% 4.20/4.41 Clause #235 (by clausification #[234]): ∀ (a a_1 a_2 : Iota),
% 4.20/4.41 Or (Eq (cUnsatisfiable a) False) (Or (Eq (And (rr a a_1) (rr a a_2)) False) (Eq (Eq a_1 a_2) True))
% 4.20/4.41 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 : Iota),
% 4.20/4.41 Or (Eq (cUnsatisfiable a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rr a a_1) False) (Eq (rr a a_2) False)))
% 4.20/4.41 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 : Iota),
% 4.20/4.41 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (rr a a_2) False) (Eq a_1 a_2)))
% 4.20/4.41 Clause #238 (by superposition #[237, 23]): ∀ (a a_1 : Iota),
% 4.20/4.41 Or (Eq (rr i2003_11_14_17_21_22376 a) False)
% 4.20/4.41 (Or (Eq (rr i2003_11_14_17_21_22376 a_1) False) (Or (Eq a a_1) (Eq False True)))
% 4.20/4.41 Clause #239 (by clausification #[238]): ∀ (a a_1 : Iota),
% 4.20/4.41 Or (Eq (rr i2003_11_14_17_21_22376 a) False) (Or (Eq (rr i2003_11_14_17_21_22376 a_1) False) (Eq a a_1))
% 4.20/4.41 Clause #241 (by clausification #[232]): ∀ (a : Iota), Eq (ca_Vx2 (skS.0 6 i2003_11_14_17_21_22376 a)) True
% 4.20/4.41 Clause #242 (by superposition #[241, 165]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (rinvS (skS.0 6 i2003_11_14_17_21_22376 a) a_1) False) (Eq (cp a_1) True))
% 4.20/4.42 Clause #243 (by superposition #[231, 23]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_21_22376 (skS.0 6 i2003_11_14_17_21_22376 a)) True) (Eq False True)
% 4.20/4.42 Clause #246 (by clausification #[243]): ∀ (a : Iota), Eq (rr i2003_11_14_17_21_22376 (skS.0 6 i2003_11_14_17_21_22376 a)) True
% 4.20/4.42 Clause #247 (by superposition #[246, 239]): ∀ (a a_1 : Iota),
% 4.20/4.42 Or (Eq True False) (Or (Eq (rr i2003_11_14_17_21_22376 a) False) (Eq (skS.0 6 i2003_11_14_17_21_22376 a_1) a))
% 4.20/4.42 Clause #251 (by clausification #[247]): ∀ (a a_1 : Iota), Or (Eq (rr i2003_11_14_17_21_22376 a) False) (Eq (skS.0 6 i2003_11_14_17_21_22376 a_1) a)
% 4.20/4.42 Clause #252 (by superposition #[251, 223]): ∀ (a a_1 : Iota), Or (Eq (skS.0 6 i2003_11_14_17_21_22376 a) (skS.0 5 i2003_11_14_17_21_22376 a_1)) (Eq False True)
% 4.20/4.42 Clause #254 (by clausification #[242]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 6 i2003_11_14_17_21_22376 a) a_1) False) (Eq (cp a_1) True)
% 4.20/4.42 Clause #259 (by clausification #[252]): ∀ (a a_1 : Iota), Eq (skS.0 6 i2003_11_14_17_21_22376 a) (skS.0 5 i2003_11_14_17_21_22376 a_1)
% 4.20/4.42 Clause #267 (by superposition #[259, 221]): ∀ (a : Iota), Eq (rinvS (skS.0 6 i2003_11_14_17_21_22376 a) i2003_11_14_17_21_22376) True
% 4.20/4.42 Clause #270 (by superposition #[267, 254]): Or (Eq True False) (Eq (cp i2003_11_14_17_21_22376) True)
% 4.20/4.42 Clause #272 (by clausification #[270]): Eq (cp i2003_11_14_17_21_22376) True
% 4.20/4.42 Clause #273 (by superposition #[272, 188]): ∀ (a : Iota), Or (Eq True False) (Eq (ra_Px1 i2003_11_14_17_21_22376 a) False)
% 4.20/4.42 Clause #277 (by clausification #[273]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_21_22376 a) False
% 4.20/4.42 Clause #278 (by superposition #[277, 198]): Eq False True
% 4.20/4.42 Clause #281 (by clausification #[278]): False
% 4.20/4.42 SZS output end Proof for theBenchmark.p
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