%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS122+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 07:52:40 PM UTC 2025 % Result : Unsatisfiable 3.93s 4.15s % Output : Proof 3.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS122+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n015.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 10:09:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.93/4.15 SZS status Theorem for theBenchmark.p % 3.93/4.15 SZS output start Proof for theBenchmark.p % 3.93/4.15 Clause #21 (by assumption #[]): Eq (∀ (X : Iota), Iff (cUnsatisfiable X) (Exists fun Y => And (rf X Y) (ca_Ax2 Y))) True % 3.93/4.15 Clause #22 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.93/4.15 Clause #23 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.93/4.15 Clause #24 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax2 X) (And (cp1 X) (∀ (Y : Iota), rinvF X Y → ca_Vx3 Y))) True % 3.93/4.15 Clause #25 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx3 X) (Exists fun Y => And (rf X Y) (cp1xcomp Y))) True % 3.93/4.15 Clause #26 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True % 3.93/4.15 Clause #27 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True % 3.93/4.15 Clause #30 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_55116) True % 3.93/4.15 Clause #164 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True % 3.93/4.15 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf a a_1) (rf a Z) → Eq a_1 Z) True % 3.93/4.15 Clause #166 (by clausification #[165]): ∀ (a a_1 a_2 : Iota), Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True % 3.93/4.15 Clause #167 (by clausification #[166]): ∀ (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) % 3.93/4.15 Clause #168 (by clausification #[167]): ∀ (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)) % 3.93/4.15 Clause #169 (by clausification #[168]): ∀ (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)) % 3.93/4.15 Clause #170 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True % 3.93/4.15 Clause #171 (by clausification #[170]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True % 3.93/4.15 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) True) (Eq (rf a_1 a) False) % 3.93/4.15 Clause #178 (by clausification #[21]): ∀ (a : Iota), Eq (Iff (cUnsatisfiable a) (Exists fun Y => And (rf a Y) (ca_Ax2 Y))) True % 3.93/4.15 Clause #180 (by clausification #[178]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf a Y) (ca_Ax2 Y)) True) % 3.93/4.15 Clause #183 (by betaEtaReduce #[23]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists (ra_Px1 X))) True % 3.93/4.15 Clause #184 (by clausification #[183]): ∀ (a : Iota), Eq (Iff (cp1xcomp a) (Exists (ra_Px1 a))) True % 3.93/4.15 Clause #186 (by clausification #[184]): ∀ (a : Iota), Or (Eq (cp1xcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.93/4.15 Clause #188 (by clausification #[186]): ∀ (a a_1 : Iota), Or (Eq (cp1xcomp a) False) (Eq (ra_Px1 a (skS.0 0 a a_1)) True) % 3.93/4.15 Clause #189 (by betaEtaReduce #[22]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists (ra_Px1 X)))) True % 3.93/4.15 Clause #190 (by clausification #[189]): ∀ (a : Iota), Eq (Iff (cp1 a) (Not (Exists (ra_Px1 a)))) True % 3.93/4.15 Clause #192 (by clausification #[190]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.93/4.15 Clause #198 (by clausification #[24]): ∀ (a : Iota), Eq (Iff (ca_Ax2 a) (And (cp1 a) (∀ (Y : Iota), rinvF a Y → ca_Vx3 Y))) True % 3.93/4.15 Clause #200 (by clausification #[198]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (And (cp1 a) (∀ (Y : Iota), rinvF a Y → ca_Vx3 Y)) True) % 3.93/4.15 Clause #206 (by clausification #[192]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Exists (ra_Px1 a)) False) % 3.93/4.15 Clause #207 (by clausification #[206]): ∀ (a a_1 : Iota), Or (Eq (cp1 a) False) (Eq (ra_Px1 a a_1) False) % 3.93/4.15 Clause #208 (by clausification #[200]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (∀ (Y : Iota), rinvF a Y → ca_Vx3 Y) True) % 3.93/4.15 Clause #209 (by clausification #[200]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (cp1 a) True) % 3.93/4.15 Clause #210 (by clausification #[208]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (rinvF a a_1 → ca_Vx3 a_1) True) % 3.93/4.15 Clause #211 (by clausification #[210]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Or (Eq (rinvF a a_1) False) (Eq (ca_Vx3 a_1) True)) % 3.93/4.15 Clause #212 (by clausification #[180]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 3 a a_1)) (ca_Ax2 (skS.0 3 a a_1))) True) % 3.93/4.17 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax2 (skS.0 3 a a_1)) True) % 3.93/4.17 Clause #214 (by clausification #[212]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 3 a a_1)) True) % 3.93/4.17 Clause #215 (by superposition #[213, 30]): ∀ (a : Iota), Or (Eq (ca_Ax2 (skS.0 3 i2003_11_14_17_21_55116 a)) True) (Eq False True) % 3.93/4.17 Clause #216 (by clausification #[215]): ∀ (a : Iota), Eq (ca_Ax2 (skS.0 3 i2003_11_14_17_21_55116 a)) True % 3.93/4.17 Clause #217 (by superposition #[216, 211]): ∀ (a a_1 : Iota), % 3.93/4.17 Or (Eq True False) (Or (Eq (rinvF (skS.0 3 i2003_11_14_17_21_55116 a) a_1) False) (Eq (ca_Vx3 a_1) True)) % 3.93/4.17 Clause #218 (by superposition #[216, 209]): ∀ (a : Iota), Or (Eq True False) (Eq (cp1 (skS.0 3 i2003_11_14_17_21_55116 a)) True) % 3.93/4.17 Clause #219 (by clausification #[25]): ∀ (a : Iota), Eq (Iff (ca_Vx3 a) (Exists fun Y => And (rf a Y) (cp1xcomp Y))) True % 3.93/4.17 Clause #221 (by clausification #[219]): ∀ (a : Iota), Or (Eq (ca_Vx3 a) False) (Eq (Exists fun Y => And (rf a Y) (cp1xcomp Y)) True) % 3.93/4.17 Clause #224 (by clausification #[218]): ∀ (a : Iota), Eq (cp1 (skS.0 3 i2003_11_14_17_21_55116 a)) True % 3.93/4.17 Clause #226 (by superposition #[224, 207]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_55116 a) a_1) False) % 3.93/4.17 Clause #227 (by clausification #[221]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (And (rf a (skS.0 4 a a_1)) (cp1xcomp (skS.0 4 a a_1))) True) % 3.93/4.17 Clause #228 (by clausification #[227]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (cp1xcomp (skS.0 4 a a_1)) True) % 3.93/4.17 Clause #229 (by clausification #[227]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (rf a (skS.0 4 a a_1)) True) % 3.93/4.17 Clause #230 (by clausification #[226]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_55116 a) a_1) False % 3.93/4.17 Clause #234 (by superposition #[214, 30]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_21_55116 (skS.0 3 i2003_11_14_17_21_55116 a)) True) (Eq False True) % 3.93/4.17 Clause #235 (by clausification #[234]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_55116 (skS.0 3 i2003_11_14_17_21_55116 a)) True % 3.93/4.17 Clause #237 (by superposition #[235, 172]): ∀ (a : Iota), Or (Eq (rinvF (skS.0 3 i2003_11_14_17_21_55116 a) i2003_11_14_17_21_55116) True) (Eq True False) % 3.93/4.17 Clause #240 (by clausification #[237]): ∀ (a : Iota), Eq (rinvF (skS.0 3 i2003_11_14_17_21_55116 a) i2003_11_14_17_21_55116) True % 3.93/4.17 Clause #250 (by clausification #[217]): ∀ (a a_1 : Iota), Or (Eq (rinvF (skS.0 3 i2003_11_14_17_21_55116 a) a_1) False) (Eq (ca_Vx3 a_1) True) % 3.93/4.17 Clause #251 (by superposition #[250, 240]): Or (Eq (ca_Vx3 i2003_11_14_17_21_55116) True) (Eq False True) % 3.93/4.17 Clause #254 (by clausification #[251]): Eq (ca_Vx3 i2003_11_14_17_21_55116) True % 3.93/4.17 Clause #256 (by superposition #[254, 228]): ∀ (a : Iota), Or (Eq True False) (Eq (cp1xcomp (skS.0 4 i2003_11_14_17_21_55116 a)) True) % 3.93/4.17 Clause #257 (by superposition #[254, 229]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_21_55116 (skS.0 4 i2003_11_14_17_21_55116 a)) True) % 3.93/4.17 Clause #258 (by clausification #[256]): ∀ (a : Iota), Eq (cp1xcomp (skS.0 4 i2003_11_14_17_21_55116 a)) True % 3.93/4.17 Clause #259 (by superposition #[258, 188]): ∀ (a a_1 : Iota), % 3.93/4.17 Or (Eq True False) % 3.93/4.17 (Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_55116 a) (skS.0 0 (skS.0 4 i2003_11_14_17_21_55116 a) a_1)) True) % 3.93/4.17 Clause #260 (by clausification #[257]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_55116 (skS.0 4 i2003_11_14_17_21_55116 a)) True % 3.93/4.17 Clause #262 (by superposition #[260, 169]): ∀ (a a_1 : Iota), % 3.93/4.17 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_21_55116 a) False) (Eq (skS.0 4 i2003_11_14_17_21_55116 a_1) a)) % 3.93/4.17 Clause #269 (by clausification #[262]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_21_55116 a) False) (Eq (skS.0 4 i2003_11_14_17_21_55116 a_1) a) % 3.93/4.17 Clause #270 (by superposition #[269, 235]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 i2003_11_14_17_21_55116 a) (skS.0 3 i2003_11_14_17_21_55116 a_1)) (Eq False True) % 3.93/4.17 Clause #277 (by clausification #[270]): ∀ (a a_1 : Iota), Eq (skS.0 4 i2003_11_14_17_21_55116 a) (skS.0 3 i2003_11_14_17_21_55116 a_1) % 3.93/4.17 Clause #281 (by superposition #[277, 230]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_55116 a) a_1) False % 3.93/4.17 Clause #285 (by clausification #[259]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_55116 a) (skS.0 0 (skS.0 4 i2003_11_14_17_21_55116 a) a_1)) True % 3.93/4.17 Clause #294 (by superposition #[281, 285]): Eq True False % 3.93/4.17 Clause #295 (by clausification #[294]): False % 3.93/4.17 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------