TSTP Solution File: KRS083+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS083+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 05:43:16 EDT 2023
% Result : Unsatisfiable 4.15s 4.34s
% Output : Proof 4.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS083+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.13 % Command : duper %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 01:59:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 4.15/4.34 SZS status Theorem for theBenchmark.p
% 4.15/4.34 SZS output start Proof for theBenchmark.p
% 4.15/4.34 Clause #15 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True
% 4.15/4.34 Clause #17 (by assumption #[]): Eq
% 4.15/4.34 (∀ (X : Iota),
% 4.15/4.34 Iff (cUnsatisfiable X)
% 4.15/4.34 (And (And (∀ (Y : Iota), rinvR X Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc X)))
% 4.15/4.34 (Exists fun Y => And (rinvF X Y) (cd Y))))
% 4.15/4.34 True
% 4.15/4.34 Clause #18 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (And (Exists fun Y => And (rf X Y) (Not (cc Y))) (cc X))) True
% 4.15/4.34 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf X Y0) (rf X Y1) → Eq Y0 Y1) True
% 4.15/4.34 Clause #20 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True
% 4.15/4.34 Clause #21 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True
% 4.15/4.34 Clause #23 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_32337) True
% 4.15/4.34 Clause #24 (by assumption #[]): Eq (∀ (X Y : Iota), rf X Y → rr X Y) True
% 4.15/4.34 Clause #67 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf a Y → rr a Y) True
% 4.15/4.34 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (rf a a_1 → rr a a_1) True
% 4.15/4.34 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (rf a a_1) False) (Eq (rr a a_1) True)
% 4.15/4.34 Clause #122 (by clausification #[15]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True
% 4.15/4.34 Clause #124 (by clausification #[122]): ∀ (a : Iota), Eq (cowlThing a) True
% 4.15/4.34 Clause #136 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True
% 4.15/4.34 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True
% 4.15/4.34 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False)
% 4.15/4.34 Clause #140 (by clausification #[17]): ∀ (a : Iota),
% 4.15/4.34 Eq
% 4.15/4.34 (Iff (cUnsatisfiable a)
% 4.15/4.34 (And (And (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc a)))
% 4.15/4.34 (Exists fun Y => And (rinvF a Y) (cd Y))))
% 4.15/4.34 True
% 4.15/4.34 Clause #142 (by clausification #[140]): ∀ (a : Iota),
% 4.15/4.34 Or (Eq (cUnsatisfiable a) False)
% 4.15/4.34 (Eq
% 4.15/4.34 (And (And (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc a)))
% 4.15/4.34 (Exists fun Y => And (rinvF a Y) (cd Y)))
% 4.15/4.34 True)
% 4.15/4.34 Clause #152 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True
% 4.15/4.34 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True
% 4.15/4.34 Clause #155 (by clausification #[153]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) False) (Eq (rf a_1 a) True)
% 4.15/4.34 Clause #156 (by clausification #[19]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True
% 4.15/4.34 Clause #157 (by clausification #[156]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True)
% 4.15/4.34 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y1 : Iota), And (rf a a_1) (rf a Y1) → Eq a_1 Y1) True)
% 4.15/4.34 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True)
% 4.15/4.34 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (And (rf a a_1) (rf a a_2)) False) (Eq (Eq a_1 a_2) True))
% 4.15/4.34 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 : Iota),
% 4.15/4.34 Or (Eq (cowlThing a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rf a a_1) False) (Eq (rf a a_2) False)))
% 4.15/4.34 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (rf a a_1) False) (Or (Eq (rf a a_2) False) (Eq a_1 a_2)))
% 4.15/4.34 Clause #163 (by forward demodulation #[162, 124]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (rf a a_1) False) (Or (Eq (rf a a_2) False) (Eq a_1 a_2)))
% 4.15/4.34 Clause #164 (by clausification #[163]): ∀ (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))
% 4.15/4.34 Clause #165 (by clausification #[18]): ∀ (a : Iota), Eq (Iff (cd a) (And (Exists fun Y => And (rf a Y) (Not (cc Y))) (cc a))) True
% 4.15/4.36 Clause #167 (by clausification #[165]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (And (Exists fun Y => And (rf a Y) (Not (cc Y))) (cc a)) True)
% 4.15/4.36 Clause #172 (by clausification #[142]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rinvF a Y) (cd Y)) True)
% 4.15/4.36 Clause #173 (by clausification #[142]): ∀ (a : Iota),
% 4.15/4.36 Or (Eq (cUnsatisfiable a) False)
% 4.15/4.36 (Eq (And (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc a))) True)
% 4.15/4.36 Clause #174 (by clausification #[172]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rinvF a (skS.0 1 a a_1)) (cd (skS.0 1 a a_1))) True)
% 4.15/4.36 Clause #175 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd (skS.0 1 a a_1)) True)
% 4.15/4.36 Clause #176 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvF a (skS.0 1 a a_1)) True)
% 4.15/4.36 Clause #177 (by superposition #[175, 23]): ∀ (a : Iota), Or (Eq (cd (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq False True)
% 4.15/4.36 Clause #178 (by clausification #[177]): ∀ (a : Iota), Eq (cd (skS.0 1 i2003_11_14_17_19_32337 a)) True
% 4.15/4.36 Clause #179 (by superposition #[176, 23]): ∀ (a : Iota), Or (Eq (rinvF i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq False True)
% 4.15/4.36 Clause #180 (by clausification #[179]): ∀ (a : Iota), Eq (rinvF i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True
% 4.15/4.36 Clause #182 (by superposition #[180, 155]): ∀ (a : Iota), Or (Eq True False) (Eq (rf (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True)
% 4.15/4.36 Clause #183 (by clausification #[182]): ∀ (a : Iota), Eq (rf (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True
% 4.15/4.36 Clause #184 (by superposition #[183, 69]): ∀ (a : Iota), Or (Eq True False) (Eq (rr (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True)
% 4.15/4.36 Clause #190 (by clausification #[184]): ∀ (a : Iota), Eq (rr (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True
% 4.15/4.36 Clause #192 (by superposition #[190, 138]): ∀ (a : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq True False)
% 4.15/4.36 Clause #193 (by clausification #[192]): ∀ (a : Iota), Eq (rinvR i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True
% 4.15/4.36 Clause #198 (by clausification #[167]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (cc a) True)
% 4.15/4.36 Clause #199 (by clausification #[167]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists fun Y => And (rf a Y) (Not (cc Y))) True)
% 4.15/4.36 Clause #200 (by superposition #[198, 178]): ∀ (a : Iota), Or (Eq (cc (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq False True)
% 4.15/4.36 Clause #201 (by clausification #[200]): ∀ (a : Iota), Eq (cc (skS.0 1 i2003_11_14_17_19_32337 a)) True
% 4.15/4.36 Clause #203 (by clausification #[199]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (And (rf a (skS.0 2 a a_1)) (Not (cc (skS.0 2 a a_1)))) True)
% 4.15/4.36 Clause #204 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (Not (cc (skS.0 2 a a_1))) True)
% 4.15/4.36 Clause #205 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (rf a (skS.0 2 a a_1)) True)
% 4.15/4.36 Clause #206 (by clausification #[204]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (cc (skS.0 2 a a_1)) False)
% 4.15/4.36 Clause #211 (by clausification #[173]): ∀ (a : Iota),
% 4.15/4.36 Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) True)
% 4.15/4.36 Clause #217 (by clausification #[211]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvR a a_1 → Exists fun Z => And (rinvF a_1 Z) (cd Z)) True)
% 4.15/4.36 Clause #218 (by clausification #[217]): ∀ (a a_1 : Iota),
% 4.15/4.36 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (Exists fun Z => And (rinvF a_1 Z) (cd Z)) True))
% 4.15/4.36 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 : Iota),
% 4.15/4.36 Or (Eq (cUnsatisfiable a) False)
% 4.15/4.36 (Or (Eq (rinvR a a_1) False) (Eq (And (rinvF a_1 (skS.0 3 a_1 a_2)) (cd (skS.0 3 a_1 a_2))) True))
% 4.15/4.36 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (cd (skS.0 3 a_1 a_2)) True))
% 4.23/4.38 Clause #221 (by clausification #[219]): ∀ (a a_1 a_2 : Iota),
% 4.23/4.38 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (rinvF a_1 (skS.0 3 a_1 a_2)) True))
% 4.23/4.38 Clause #222 (by superposition #[220, 23]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Or (Eq (cd (skS.0 3 a a_1)) True) (Eq False True))
% 4.23/4.38 Clause #223 (by clausification #[222]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Eq (cd (skS.0 3 a a_1)) True)
% 4.23/4.38 Clause #224 (by superposition #[223, 193]): ∀ (a a_1 : Iota), Or (Eq (cd (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True) (Eq False True)
% 4.23/4.38 Clause #225 (by superposition #[221, 23]): ∀ (a a_1 : Iota),
% 4.23/4.38 Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Or (Eq (rinvF a (skS.0 3 a a_1)) True) (Eq False True))
% 4.23/4.38 Clause #226 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Eq (rinvF a (skS.0 3 a a_1)) True)
% 4.23/4.38 Clause #227 (by superposition #[226, 193]): ∀ (a a_1 : Iota),
% 4.23/4.38 Or (Eq (rinvF (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True)
% 4.23/4.38 (Eq False True)
% 4.23/4.38 Clause #230 (by clausification #[224]): ∀ (a a_1 : Iota), Eq (cd (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True
% 4.23/4.38 Clause #232 (by superposition #[230, 206]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (cc (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)) False)
% 4.23/4.38 Clause #233 (by superposition #[230, 205]): ∀ (a a_1 a_2 : Iota),
% 4.23/4.38 Or (Eq True False)
% 4.23/4.38 (Eq
% 4.23/4.38 (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)
% 4.23/4.38 (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2))
% 4.23/4.38 True)
% 4.23/4.38 Clause #238 (by clausification #[232]): ∀ (a a_1 a_2 : Iota), Eq (cc (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)) False
% 4.23/4.38 Clause #239 (by clausification #[227]): ∀ (a a_1 : Iota), Eq (rinvF (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True
% 4.23/4.38 Clause #241 (by superposition #[239, 155]): ∀ (a a_1 : Iota),
% 4.23/4.38 Or (Eq True False)
% 4.23/4.38 (Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) (skS.0 1 i2003_11_14_17_19_32337 a)) True)
% 4.23/4.38 Clause #251 (by clausification #[241]): ∀ (a a_1 : Iota), Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) (skS.0 1 i2003_11_14_17_19_32337 a)) True
% 4.23/4.38 Clause #254 (by superposition #[251, 164]): ∀ (a a_1 a_2 : Iota),
% 4.23/4.38 Or (Eq True False)
% 4.23/4.38 (Or (Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2) False)
% 4.23/4.38 (Eq (skS.0 1 i2003_11_14_17_19_32337 a) a_2))
% 4.23/4.38 Clause #255 (by clausification #[233]): ∀ (a a_1 a_2 : Iota),
% 4.23/4.38 Eq
% 4.23/4.38 (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)
% 4.23/4.38 (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2))
% 4.23/4.38 True
% 4.23/4.38 Clause #264 (by clausification #[254]): ∀ (a a_1 a_2 : Iota),
% 4.23/4.38 Or (Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2) False) (Eq (skS.0 1 i2003_11_14_17_19_32337 a) a_2)
% 4.23/4.38 Clause #266 (by superposition #[264, 255]): ∀ (a a_1 a_2 : Iota),
% 4.23/4.38 Or (Eq (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2))
% 4.23/4.38 (Eq False True)
% 4.23/4.38 Clause #288 (by clausification #[266]): ∀ (a a_1 a_2 : Iota),
% 4.23/4.38 Eq (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)
% 4.23/4.38 Clause #289 (by backward demodulation #[288, 238]): ∀ (a : Iota), Eq (cc (skS.0 1 i2003_11_14_17_19_32337 a)) False
% 4.23/4.38 Clause #290 (by superposition #[289, 201]): Eq False True
% 4.23/4.38 Clause #291 (by clausification #[290]): False
% 4.23/4.38 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------