TSTP Solution File: KRS084+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS084+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 05:43:16 EDT 2023
% Result : Unsatisfiable 3.86s 4.22s
% Output : Proof 3.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KRS084+1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n006.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 01:11:06 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.86/4.22 SZS status Theorem for theBenchmark.p
% 3.86/4.22 SZS output start Proof for theBenchmark.p
% 3.86/4.22 Clause #17 (by assumption #[]): Eq
% 3.86/4.22 (∀ (X : Iota),
% 3.86/4.22 Iff (cUnsatisfiable X)
% 3.86/4.22 (And
% 3.86/4.22 (And (Exists fun Y => And (rinvF X Y) (cd Y))
% 3.86/4.22 (∀ (Y : Iota), rinvR X Y → Exists fun Z => And (rinvF Y Z) (cd Z)))
% 3.86/4.22 (Not (cc X))))
% 3.86/4.22 True
% 3.86/4.22 Clause #18 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (And (Exists fun Y => And (rf X Y) (Not (cc Y))) (cc X))) True
% 3.86/4.22 Clause #19 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True
% 3.86/4.22 Clause #20 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True
% 3.86/4.22 Clause #21 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True
% 3.86/4.22 Clause #23 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_35232) True
% 3.86/4.22 Clause #24 (by assumption #[]): Eq (∀ (X Y : Iota), rf X Y → rr X Y) True
% 3.86/4.22 Clause #67 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf a Y → rr a Y) True
% 3.86/4.22 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (rf a a_1 → rr a a_1) True
% 3.86/4.22 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (rf a a_1) False) (Eq (rr a a_1) True)
% 3.86/4.22 Clause #136 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True
% 3.86/4.22 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf a a_1) (rf a Z) → Eq a_1 Z) True
% 3.86/4.22 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 : Iota), Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True
% 3.86/4.22 Clause #139 (by clausification #[138]): ∀ (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)
% 3.86/4.22 Clause #140 (by clausification #[139]): ∀ (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))
% 3.86/4.22 Clause #141 (by clausification #[140]): ∀ (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))
% 3.86/4.22 Clause #142 (by clausification #[17]): ∀ (a : Iota),
% 3.86/4.22 Eq
% 3.86/4.22 (Iff (cUnsatisfiable a)
% 3.86/4.22 (And
% 3.86/4.22 (And (Exists fun Y => And (rinvF a Y) (cd Y))
% 3.86/4.22 (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)))
% 3.86/4.22 (Not (cc a))))
% 3.86/4.22 True
% 3.86/4.22 Clause #144 (by clausification #[142]): ∀ (a : Iota),
% 3.86/4.22 Or (Eq (cUnsatisfiable a) False)
% 3.86/4.22 (Eq
% 3.86/4.22 (And
% 3.86/4.22 (And (Exists fun Y => And (rinvF a Y) (cd Y))
% 3.86/4.22 (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)))
% 3.86/4.22 (Not (cc a)))
% 3.86/4.22 True)
% 3.86/4.22 Clause #154 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True
% 3.86/4.22 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True
% 3.86/4.22 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False)
% 3.86/4.22 Clause #158 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True
% 3.86/4.22 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True
% 3.86/4.22 Clause #161 (by clausification #[159]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) False) (Eq (rf a_1 a) True)
% 3.86/4.22 Clause #162 (by clausification #[18]): ∀ (a : Iota), Eq (Iff (cd a) (And (Exists fun Y => And (rf a Y) (Not (cc Y))) (cc a))) True
% 3.86/4.22 Clause #164 (by clausification #[162]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (And (Exists fun Y => And (rf a Y) (Not (cc Y))) (cc a)) True)
% 3.86/4.22 Clause #170 (by clausification #[144]): ∀ (a : Iota),
% 3.86/4.22 Or (Eq (cUnsatisfiable a) False)
% 3.86/4.22 (Eq
% 3.86/4.22 (And (Exists fun Y => And (rinvF a Y) (cd Y)) (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)))
% 3.86/4.22 True)
% 3.86/4.22 Clause #174 (by clausification #[164]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (cc a) True)
% 3.86/4.22 Clause #175 (by clausification #[164]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists fun Y => And (rf a Y) (Not (cc Y))) True)
% 3.86/4.22 Clause #176 (by clausification #[175]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (And (rf a (skS.0 1 a a_1)) (Not (cc (skS.0 1 a a_1)))) True)
% 3.86/4.22 Clause #177 (by clausification #[176]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (Not (cc (skS.0 1 a a_1))) True)
% 3.86/4.24 Clause #178 (by clausification #[176]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (rf a (skS.0 1 a a_1)) True)
% 3.86/4.24 Clause #179 (by clausification #[177]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (cc (skS.0 1 a a_1)) False)
% 3.86/4.24 Clause #180 (by clausification #[170]): ∀ (a : Iota),
% 3.86/4.24 Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) True)
% 3.86/4.24 Clause #181 (by clausification #[170]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rinvF a Y) (cd Y)) True)
% 3.86/4.24 Clause #182 (by clausification #[180]): ∀ (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)
% 3.86/4.24 Clause #183 (by clausification #[182]): ∀ (a a_1 : Iota),
% 3.86/4.24 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (Exists fun Z => And (rinvF a_1 Z) (cd Z)) True))
% 3.86/4.24 Clause #184 (by clausification #[183]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.24 Or (Eq (cUnsatisfiable a) False)
% 3.86/4.24 (Or (Eq (rinvR a a_1) False) (Eq (And (rinvF a_1 (skS.0 2 a_1 a_2)) (cd (skS.0 2 a_1 a_2))) True))
% 3.86/4.25 Clause #185 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (cd (skS.0 2 a_1 a_2)) True))
% 3.86/4.25 Clause #186 (by clausification #[184]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.25 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (rinvF a_1 (skS.0 2 a_1 a_2)) True))
% 3.86/4.25 Clause #187 (by superposition #[185, 23]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_35232 a) False) (Or (Eq (cd (skS.0 2 a a_1)) True) (Eq False True))
% 3.86/4.25 Clause #190 (by clausification #[181]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rinvF a (skS.0 3 a a_1)) (cd (skS.0 3 a a_1))) True)
% 3.86/4.25 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd (skS.0 3 a a_1)) True)
% 3.86/4.25 Clause #192 (by clausification #[190]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvF a (skS.0 3 a a_1)) True)
% 3.86/4.25 Clause #193 (by superposition #[191, 23]): ∀ (a : Iota), Or (Eq (cd (skS.0 3 i2003_11_14_17_19_35232 a)) True) (Eq False True)
% 3.86/4.25 Clause #194 (by clausification #[193]): ∀ (a : Iota), Eq (cd (skS.0 3 i2003_11_14_17_19_35232 a)) True
% 3.86/4.25 Clause #195 (by superposition #[194, 174]): ∀ (a : Iota), Or (Eq True False) (Eq (cc (skS.0 3 i2003_11_14_17_19_35232 a)) True)
% 3.86/4.25 Clause #198 (by clausification #[195]): ∀ (a : Iota), Eq (cc (skS.0 3 i2003_11_14_17_19_35232 a)) True
% 3.86/4.25 Clause #200 (by superposition #[192, 23]): ∀ (a : Iota), Or (Eq (rinvF i2003_11_14_17_19_35232 (skS.0 3 i2003_11_14_17_19_35232 a)) True) (Eq False True)
% 3.86/4.25 Clause #201 (by clausification #[200]): ∀ (a : Iota), Eq (rinvF i2003_11_14_17_19_35232 (skS.0 3 i2003_11_14_17_19_35232 a)) True
% 3.86/4.25 Clause #203 (by superposition #[201, 161]): ∀ (a : Iota), Or (Eq True False) (Eq (rf (skS.0 3 i2003_11_14_17_19_35232 a) i2003_11_14_17_19_35232) True)
% 3.86/4.25 Clause #205 (by superposition #[186, 23]): ∀ (a a_1 : Iota),
% 3.86/4.25 Or (Eq (rinvR i2003_11_14_17_19_35232 a) False) (Or (Eq (rinvF a (skS.0 2 a a_1)) True) (Eq False True))
% 3.86/4.25 Clause #206 (by clausification #[203]): ∀ (a : Iota), Eq (rf (skS.0 3 i2003_11_14_17_19_35232 a) i2003_11_14_17_19_35232) True
% 3.86/4.25 Clause #207 (by superposition #[206, 69]): ∀ (a : Iota), Or (Eq True False) (Eq (rr (skS.0 3 i2003_11_14_17_19_35232 a) i2003_11_14_17_19_35232) True)
% 3.86/4.25 Clause #210 (by clausification #[207]): ∀ (a : Iota), Eq (rr (skS.0 3 i2003_11_14_17_19_35232 a) i2003_11_14_17_19_35232) True
% 3.86/4.25 Clause #212 (by superposition #[210, 156]): ∀ (a : Iota), Or (Eq (rinvR i2003_11_14_17_19_35232 (skS.0 3 i2003_11_14_17_19_35232 a)) True) (Eq True False)
% 3.86/4.25 Clause #213 (by clausification #[212]): ∀ (a : Iota), Eq (rinvR i2003_11_14_17_19_35232 (skS.0 3 i2003_11_14_17_19_35232 a)) True
% 3.86/4.25 Clause #216 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_35232 a) False) (Eq (cd (skS.0 2 a a_1)) True)
% 3.86/4.25 Clause #217 (by superposition #[216, 213]): ∀ (a a_1 : Iota), Or (Eq (cd (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1)) True) (Eq False True)
% 3.86/4.25 Clause #220 (by clausification #[205]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_35232 a) False) (Eq (rinvF a (skS.0 2 a a_1)) True)
% 3.86/4.26 Clause #221 (by superposition #[220, 213]): ∀ (a a_1 : Iota),
% 3.86/4.26 Or (Eq (rinvF (skS.0 3 i2003_11_14_17_19_35232 a) (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1)) True)
% 3.86/4.26 (Eq False True)
% 3.86/4.26 Clause #223 (by clausification #[217]): ∀ (a a_1 : Iota), Eq (cd (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1)) True
% 3.86/4.26 Clause #225 (by superposition #[223, 179]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (cc (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2)) False)
% 3.86/4.26 Clause #226 (by superposition #[223, 178]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.26 Or (Eq True False)
% 3.86/4.26 (Eq
% 3.86/4.26 (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1)
% 3.86/4.26 (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2))
% 3.86/4.26 True)
% 3.86/4.26 Clause #235 (by clausification #[225]): ∀ (a a_1 a_2 : Iota), Eq (cc (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2)) False
% 3.86/4.26 Clause #238 (by clausification #[221]): ∀ (a a_1 : Iota), Eq (rinvF (skS.0 3 i2003_11_14_17_19_35232 a) (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1)) True
% 3.86/4.26 Clause #240 (by superposition #[238, 161]): ∀ (a a_1 : Iota),
% 3.86/4.26 Or (Eq True False)
% 3.86/4.26 (Eq (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) (skS.0 3 i2003_11_14_17_19_35232 a)) True)
% 3.86/4.26 Clause #244 (by clausification #[240]): ∀ (a a_1 : Iota), Eq (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) (skS.0 3 i2003_11_14_17_19_35232 a)) True
% 3.86/4.26 Clause #246 (by superposition #[244, 141]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.26 Or (Eq True False)
% 3.86/4.26 (Or (Eq (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2) False)
% 3.86/4.26 (Eq (skS.0 3 i2003_11_14_17_19_35232 a) a_2))
% 3.86/4.26 Clause #256 (by clausification #[246]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.26 Or (Eq (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2) False) (Eq (skS.0 3 i2003_11_14_17_19_35232 a) a_2)
% 3.86/4.26 Clause #262 (by clausification #[226]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.26 Eq
% 3.86/4.26 (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1)
% 3.86/4.26 (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2))
% 3.86/4.26 True
% 3.86/4.26 Clause #263 (by superposition #[262, 256]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.26 Or (Eq True False)
% 3.86/4.26 (Eq (skS.0 3 i2003_11_14_17_19_35232 a) (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2))
% 3.86/4.26 Clause #283 (by clausification #[263]): ∀ (a a_1 a_2 : Iota),
% 3.86/4.26 Eq (skS.0 3 i2003_11_14_17_19_35232 a) (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2)
% 3.86/4.26 Clause #284 (by backward demodulation #[283, 235]): ∀ (a : Iota), Eq (cc (skS.0 3 i2003_11_14_17_19_35232 a)) False
% 3.86/4.26 Clause #285 (by superposition #[284, 198]): Eq False True
% 3.86/4.26 Clause #286 (by clausification #[285]): False
% 3.86/4.26 SZS output end Proof for theBenchmark.p
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