TSTP Solution File: KRS106+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS106+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n008.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 4.22s 4.51s
% Output : Proof 4.22s
% 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 : KRS106+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 01:54:32 EDT 2023
% 0.13/0.36 % CPUTime :
% 4.22/4.51 SZS status Theorem for theBenchmark.p
% 4.22/4.51 SZS output start Proof for theBenchmark.p
% 4.22/4.51 Clause #18 (by assumption #[]): Eq
% 4.22/4.51 (∀ (X : Iota),
% 4.22/4.51 Iff (cUnsatisfiable X)
% 4.22/4.51 (And (And (Exists fun Y => And (rf3 X Y) (cp2 Y)) (Exists fun Y => And (rf1 X Y) (cp1 Y)))
% 4.22/4.51 (Exists fun Y => And (rf2 X Y) (cp1xcomp Y))))
% 4.22/4.51 True
% 4.22/4.51 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists fun Y => ra_Px1 X Y))) True
% 4.22/4.51 Clause #20 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True
% 4.22/4.51 Clause #21 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf1 X Y) (rf1 X Z) → Eq Y Z) True
% 4.22/4.51 Clause #22 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf2 X Y) (rf2 X Z) → Eq Y Z) True
% 4.22/4.51 Clause #24 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_20_57644) True
% 4.22/4.51 Clause #25 (by assumption #[]): Eq (∀ (X Y : Iota), rf3 X Y → rf1 X Y) True
% 4.22/4.51 Clause #26 (by assumption #[]): Eq (∀ (X Y : Iota), rf3 X Y → rf2 X Y) True
% 4.22/4.51 Clause #75 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf3 a Y → rf1 a Y) True
% 4.22/4.51 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (rf3 a a_1 → rf1 a a_1) True
% 4.22/4.51 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq (rf3 a a_1) False) (Eq (rf1 a a_1) True)
% 4.22/4.51 Clause #78 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf3 a Y → rf2 a Y) True
% 4.22/4.51 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Eq (rf3 a a_1 → rf2 a a_1) True
% 4.22/4.51 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Or (Eq (rf3 a a_1) False) (Eq (rf2 a a_1) True)
% 4.22/4.51 Clause #150 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf2 a Y) (rf2 a Z) → Eq Y Z) True
% 4.22/4.51 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf2 a a_1) (rf2 a Z) → Eq a_1 Z) True
% 4.22/4.51 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 : Iota), Eq (And (rf2 a a_1) (rf2 a a_2) → Eq a_1 a_2) True
% 4.22/4.51 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf2 a a_1) (rf2 a a_2)) False) (Eq (Eq a_1 a_2) True)
% 4.22/4.51 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf2 a_2 a) False) (Eq (rf2 a_2 a_1) False))
% 4.22/4.51 Clause #155 (by clausification #[154]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf2 a a_1) False) (Or (Eq (rf2 a a_2) False) (Eq a_1 a_2))
% 4.22/4.51 Clause #156 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf1 a Y) (rf1 a Z) → Eq Y Z) True
% 4.22/4.51 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf1 a a_1) (rf1 a Z) → Eq a_1 Z) True
% 4.22/4.51 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 : Iota), Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True
% 4.22/4.51 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf1 a a_1) (rf1 a a_2)) False) (Eq (Eq a_1 a_2) True)
% 4.22/4.51 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf1 a_2 a) False) (Eq (rf1 a_2 a_1) False))
% 4.22/4.51 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf1 a a_1) False) (Or (Eq (rf1 a a_2) False) (Eq a_1 a_2))
% 4.22/4.51 Clause #162 (by betaEtaReduce #[20]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists (ra_Px1 X))) True
% 4.22/4.51 Clause #163 (by clausification #[162]): ∀ (a : Iota), Eq (Iff (cp1xcomp a) (Exists (ra_Px1 a))) True
% 4.22/4.51 Clause #165 (by clausification #[163]): ∀ (a : Iota), Or (Eq (cp1xcomp a) False) (Eq (Exists (ra_Px1 a)) True)
% 4.22/4.51 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (cp1xcomp a) False) (Eq (ra_Px1 a (skS.0 0 a a_1)) True)
% 4.22/4.51 Clause #168 (by clausification #[18]): ∀ (a : Iota),
% 4.22/4.51 Eq
% 4.22/4.51 (Iff (cUnsatisfiable a)
% 4.22/4.51 (And (And (Exists fun Y => And (rf3 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y)))
% 4.22/4.51 (Exists fun Y => And (rf2 a Y) (cp1xcomp Y))))
% 4.22/4.51 True
% 4.22/4.51 Clause #170 (by clausification #[168]): ∀ (a : Iota),
% 4.22/4.51 Or (Eq (cUnsatisfiable a) False)
% 4.22/4.51 (Eq
% 4.22/4.51 (And (And (Exists fun Y => And (rf3 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y)))
% 4.22/4.51 (Exists fun Y => And (rf2 a Y) (cp1xcomp Y)))
% 4.22/4.51 True)
% 4.22/4.51 Clause #179 (by betaEtaReduce #[19]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists (ra_Px1 X)))) True
% 4.22/4.54 Clause #180 (by clausification #[179]): ∀ (a : Iota), Eq (Iff (cp1 a) (Not (Exists (ra_Px1 a)))) True
% 4.22/4.54 Clause #182 (by clausification #[180]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Not (Exists (ra_Px1 a))) True)
% 4.22/4.54 Clause #188 (by clausification #[182]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Exists (ra_Px1 a)) False)
% 4.22/4.54 Clause #189 (by clausification #[188]): ∀ (a a_1 : Iota), Or (Eq (cp1 a) False) (Eq (ra_Px1 a a_1) False)
% 4.22/4.54 Clause #191 (by clausification #[170]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf2 a Y) (cp1xcomp Y)) True)
% 4.22/4.54 Clause #192 (by clausification #[170]): ∀ (a : Iota),
% 4.22/4.54 Or (Eq (cUnsatisfiable a) False)
% 4.22/4.54 (Eq (And (Exists fun Y => And (rf3 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) True)
% 4.22/4.54 Clause #193 (by clausification #[191]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf2 a (skS.0 2 a a_1)) (cp1xcomp (skS.0 2 a a_1))) True)
% 4.22/4.54 Clause #194 (by clausification #[193]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1xcomp (skS.0 2 a a_1)) True)
% 4.22/4.54 Clause #195 (by clausification #[193]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf2 a (skS.0 2 a a_1)) True)
% 4.22/4.54 Clause #196 (by superposition #[194, 24]): ∀ (a : Iota), Or (Eq (cp1xcomp (skS.0 2 i2003_11_14_17_20_57644 a)) True) (Eq False True)
% 4.22/4.54 Clause #197 (by clausification #[192]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (cp1 Y)) True)
% 4.22/4.54 Clause #198 (by clausification #[192]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf3 a Y) (cp2 Y)) True)
% 4.22/4.54 Clause #199 (by clausification #[197]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 3 a a_1)) (cp1 (skS.0 3 a a_1))) True)
% 4.22/4.54 Clause #200 (by clausification #[199]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 3 a a_1)) True)
% 4.22/4.54 Clause #201 (by clausification #[199]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 3 a a_1)) True)
% 4.22/4.54 Clause #202 (by superposition #[200, 24]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 3 i2003_11_14_17_20_57644 a)) True) (Eq False True)
% 4.22/4.54 Clause #203 (by clausification #[202]): ∀ (a : Iota), Eq (cp1 (skS.0 3 i2003_11_14_17_20_57644 a)) True
% 4.22/4.54 Clause #204 (by superposition #[203, 189]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 3 i2003_11_14_17_20_57644 a) a_1) False)
% 4.22/4.54 Clause #205 (by clausification #[196]): ∀ (a : Iota), Eq (cp1xcomp (skS.0 2 i2003_11_14_17_20_57644 a)) True
% 4.22/4.54 Clause #206 (by superposition #[205, 167]): ∀ (a a_1 : Iota),
% 4.22/4.54 Or (Eq True False)
% 4.22/4.54 (Eq (ra_Px1 (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 0 (skS.0 2 i2003_11_14_17_20_57644 a) a_1)) True)
% 4.22/4.54 Clause #207 (by clausification #[204]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_20_57644 a) a_1) False
% 4.22/4.54 Clause #208 (by clausification #[198]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf3 a (skS.0 4 a a_1)) (cp2 (skS.0 4 a a_1))) True)
% 4.22/4.54 Clause #210 (by clausification #[208]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf3 a (skS.0 4 a a_1)) True)
% 4.22/4.54 Clause #213 (by superposition #[195, 24]): ∀ (a : Iota), Or (Eq (rf2 i2003_11_14_17_20_57644 (skS.0 2 i2003_11_14_17_20_57644 a)) True) (Eq False True)
% 4.22/4.54 Clause #214 (by clausification #[213]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_20_57644 (skS.0 2 i2003_11_14_17_20_57644 a)) True
% 4.22/4.54 Clause #215 (by superposition #[214, 155]): ∀ (a a_1 : Iota),
% 4.22/4.54 Or (Eq True False) (Or (Eq (rf2 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 2 i2003_11_14_17_20_57644 a_1) a))
% 4.22/4.54 Clause #217 (by superposition #[210, 24]): ∀ (a : Iota), Or (Eq (rf3 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True) (Eq False True)
% 4.22/4.54 Clause #218 (by clausification #[217]): ∀ (a : Iota), Eq (rf3 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True
% 4.22/4.54 Clause #219 (by superposition #[218, 77]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True)
% 4.22/4.54 Clause #220 (by superposition #[218, 80]): ∀ (a : Iota), Or (Eq True False) (Eq (rf2 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True)
% 4.22/4.55 Clause #222 (by clausification #[220]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True
% 4.22/4.55 Clause #225 (by clausification #[219]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True
% 4.22/4.55 Clause #226 (by superposition #[225, 161]): ∀ (a a_1 : Iota),
% 4.22/4.55 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 4 i2003_11_14_17_20_57644 a_1) a))
% 4.22/4.55 Clause #227 (by superposition #[201, 24]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_20_57644 (skS.0 3 i2003_11_14_17_20_57644 a)) True) (Eq False True)
% 4.22/4.55 Clause #228 (by clausification #[227]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_20_57644 (skS.0 3 i2003_11_14_17_20_57644 a)) True
% 4.22/4.55 Clause #233 (by clausification #[215]): ∀ (a a_1 : Iota), Or (Eq (rf2 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 2 i2003_11_14_17_20_57644 a_1) a)
% 4.22/4.55 Clause #235 (by superposition #[233, 222]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 4 i2003_11_14_17_20_57644 a_1)) (Eq False True)
% 4.22/4.55 Clause #239 (by clausification #[226]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 4 i2003_11_14_17_20_57644 a_1) a)
% 4.22/4.55 Clause #240 (by superposition #[239, 228]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 i2003_11_14_17_20_57644 a) (skS.0 3 i2003_11_14_17_20_57644 a_1)) (Eq False True)
% 4.22/4.55 Clause #241 (by clausification #[206]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 0 (skS.0 2 i2003_11_14_17_20_57644 a) a_1)) True
% 4.22/4.55 Clause #244 (by clausification #[240]): ∀ (a a_1 : Iota), Eq (skS.0 4 i2003_11_14_17_20_57644 a) (skS.0 3 i2003_11_14_17_20_57644 a_1)
% 4.22/4.55 Clause #250 (by superposition #[244, 207]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_20_57644 a) a_1) False
% 4.22/4.55 Clause #269 (by clausification #[235]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 4 i2003_11_14_17_20_57644 a_1)
% 4.22/4.55 Clause #277 (by superposition #[269, 250]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 2 i2003_11_14_17_20_57644 a) a_1) False
% 4.22/4.55 Clause #290 (by superposition #[277, 241]): Eq False True
% 4.22/4.55 Clause #292 (by clausification #[290]): False
% 4.22/4.55 SZS output end Proof for theBenchmark.p
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