%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS084+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 : Fri Oct 3 07:52:35 PM UTC 2025 % Result : Unsatisfiable 4.13s 4.31s % Output : Proof 4.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : KRS084+1 : TPTP v9.2.0. Released v3.1.0. % 0.10/0.13 % Command : duper %s % 0.12/0.33 % Computer : n028.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 : Thu Oct 2 10:13:23 EDT 2025 % 0.12/0.33 % CPUTime : % 4.13/4.31 SZS status Theorem for theBenchmark.p % 4.13/4.31 SZS output start Proof for theBenchmark.p % 4.13/4.31 Clause #17 (by assumption #[]): Eq % 4.13/4.31 (∀ (X : Iota), % 4.13/4.31 Iff (cUnsatisfiable X) % 4.13/4.31 (And % 4.13/4.31 (And (Exists fun Y => And (rinvF X Y) (cd Y)) % 4.13/4.31 (∀ (Y : Iota), rinvR X Y → Exists fun Z => And (rinvF Y Z) (cd Z))) % 4.13/4.31 (Not (cc X)))) % 4.13/4.31 True % 4.13/4.31 Clause #18 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (And (Exists fun Y => And (rf X Y) (Not (cc Y))) (cc X))) True % 4.13/4.31 Clause #19 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True % 4.13/4.31 Clause #20 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True % 4.13/4.31 Clause #21 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True % 4.13/4.31 Clause #23 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_35232) True % 4.13/4.31 Clause #24 (by assumption #[]): Eq (∀ (X Y : Iota), rf X Y → rr X Y) True % 4.13/4.31 Clause #67 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf a Y → rr a Y) True % 4.13/4.31 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (rf a a_1 → rr a a_1) True % 4.13/4.31 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (rf a a_1) False) (Eq (rr a a_1) True) % 4.13/4.31 Clause #136 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True % 4.13/4.31 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 % 4.13/4.31 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 % 4.13/4.31 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) % 4.13/4.31 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)) % 4.13/4.31 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)) % 4.13/4.31 Clause #142 (by clausification #[17]): ∀ (a : Iota), % 4.13/4.31 Eq % 4.13/4.31 (Iff (cUnsatisfiable a) % 4.13/4.31 (And % 4.13/4.31 (And (Exists fun Y => And (rinvF a Y) (cd Y)) % 4.13/4.31 (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z))) % 4.13/4.31 (Not (cc a)))) % 4.13/4.31 True % 4.13/4.31 Clause #144 (by clausification #[142]): ∀ (a : Iota), % 4.13/4.31 Or (Eq (cUnsatisfiable a) False) % 4.13/4.31 (Eq % 4.13/4.31 (And % 4.13/4.31 (And (Exists fun Y => And (rinvF a Y) (cd Y)) % 4.13/4.31 (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z))) % 4.13/4.31 (Not (cc a))) % 4.13/4.31 True) % 4.13/4.31 Clause #154 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True % 4.13/4.31 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True % 4.13/4.31 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False) % 4.13/4.31 Clause #158 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True % 4.13/4.31 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True % 4.13/4.31 Clause #161 (by clausification #[159]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) False) (Eq (rf a_1 a) True) % 4.13/4.31 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 % 4.13/4.31 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) % 4.13/4.31 Clause #170 (by clausification #[144]): ∀ (a : Iota), % 4.13/4.31 Or (Eq (cUnsatisfiable a) False) % 4.13/4.31 (Eq % 4.13/4.31 (And (Exists fun Y => And (rinvF a Y) (cd Y)) (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z))) % 4.13/4.31 True) % 4.13/4.31 Clause #174 (by clausification #[164]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (cc a) True) % 4.13/4.31 Clause #175 (by clausification #[164]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists fun Y => And (rf a Y) (Not (cc Y))) True) % 4.13/4.31 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) % 4.13/4.31 Clause #177 (by clausification #[176]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (Not (cc (skS.0 1 a a_1))) True) % 4.13/4.33 Clause #178 (by clausification #[176]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (rf a (skS.0 1 a a_1)) True) % 4.13/4.33 Clause #179 (by clausification #[177]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (cc (skS.0 1 a a_1)) False) % 4.13/4.33 Clause #180 (by clausification #[170]): ∀ (a : Iota), % 4.13/4.33 Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) True) % 4.13/4.33 Clause #181 (by clausification #[170]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rinvF a Y) (cd Y)) True) % 4.13/4.33 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) % 4.13/4.33 Clause #183 (by clausification #[182]): ∀ (a a_1 : Iota), % 4.13/4.33 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (Exists fun Z => And (rinvF a_1 Z) (cd Z)) True)) % 4.13/4.33 Clause #184 (by clausification #[183]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Or (Eq (cUnsatisfiable a) False) % 4.13/4.33 (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)) % 4.13/4.33 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)) % 4.13/4.33 Clause #186 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (rinvF a_1 (skS.0 2 a_1 a_2)) True)) % 4.13/4.33 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)) % 4.13/4.33 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) % 4.13/4.33 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd (skS.0 3 a a_1)) True) % 4.13/4.33 Clause #192 (by clausification #[190]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvF a (skS.0 3 a a_1)) True) % 4.13/4.33 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) % 4.13/4.33 Clause #194 (by clausification #[193]): ∀ (a : Iota), Eq (cd (skS.0 3 i2003_11_14_17_19_35232 a)) True % 4.13/4.33 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) % 4.13/4.33 Clause #198 (by clausification #[195]): ∀ (a : Iota), Eq (cc (skS.0 3 i2003_11_14_17_19_35232 a)) True % 4.13/4.33 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) % 4.13/4.33 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 % 4.13/4.33 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) % 4.13/4.33 Clause #205 (by superposition #[186, 23]): ∀ (a a_1 : Iota), % 4.13/4.33 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)) % 4.13/4.33 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 % 4.13/4.33 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) % 4.13/4.33 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 % 4.13/4.33 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) % 4.13/4.33 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 % 4.13/4.33 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) % 4.13/4.33 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) % 4.13/4.33 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) % 4.13/4.35 Clause #221 (by superposition #[220, 213]): ∀ (a a_1 : Iota), % 4.13/4.35 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) % 4.13/4.35 (Eq False True) % 4.13/4.35 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 % 4.13/4.35 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) % 4.13/4.35 Clause #226 (by superposition #[223, 178]): ∀ (a a_1 a_2 : Iota), % 4.13/4.35 Or (Eq True False) % 4.13/4.35 (Eq % 4.13/4.35 (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) % 4.13/4.35 (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2)) % 4.13/4.35 True) % 4.13/4.35 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 % 4.13/4.35 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 % 4.13/4.35 Clause #240 (by superposition #[238, 161]): ∀ (a a_1 : Iota), % 4.13/4.35 Or (Eq True False) % 4.13/4.35 (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) % 4.13/4.35 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 % 4.13/4.35 Clause #246 (by superposition #[244, 141]): ∀ (a a_1 a_2 : Iota), % 4.13/4.35 Or (Eq True False) % 4.13/4.35 (Or (Eq (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2) False) % 4.13/4.35 (Eq (skS.0 3 i2003_11_14_17_19_35232 a) a_2)) % 4.13/4.35 Clause #256 (by clausification #[246]): ∀ (a a_1 a_2 : Iota), % 4.13/4.35 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) % 4.13/4.35 Clause #262 (by clausification #[226]): ∀ (a a_1 a_2 : Iota), % 4.13/4.35 Eq % 4.13/4.35 (rf (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) % 4.13/4.35 (skS.0 1 (skS.0 2 (skS.0 3 i2003_11_14_17_19_35232 a) a_1) a_2)) % 4.13/4.35 True % 4.13/4.35 Clause #263 (by superposition #[262, 256]): ∀ (a a_1 a_2 : Iota), % 4.13/4.35 Or (Eq True False) % 4.13/4.35 (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)) % 4.13/4.35 Clause #283 (by clausification #[263]): ∀ (a a_1 a_2 : Iota), % 4.13/4.35 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) % 4.13/4.35 Clause #284 (by backward demodulation #[283, 235]): ∀ (a : Iota), Eq (cc (skS.0 3 i2003_11_14_17_19_35232 a)) False % 4.13/4.35 Clause #285 (by superposition #[284, 198]): Eq False True % 4.13/4.35 Clause #286 (by clausification #[285]): False % 4.13/4.35 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------