%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS120+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:52:39 PM UTC 2025 % Result : Unsatisfiable 4.67s 4.86s % Output : Proof 4.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS120+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n014.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 10:14:53 EDT 2025 % 0.14/0.35 % CPUTime : % 4.67/4.86 SZS status Theorem for theBenchmark.p % 4.67/4.86 SZS output start Proof for theBenchmark.p % 4.67/4.86 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 4.67/4.86 Clause #21 (by assumption #[]): Eq (∀ (X : Iota), Iff (cUnsatisfiable X) (Exists fun Y => And (rf X Y) (ca_Ax2 Y))) True % 4.67/4.86 Clause #22 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists fun Y => ra_Px1 X Y))) True % 4.67/4.86 Clause #23 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 4.67/4.86 Clause #24 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax2 X) (And (Exists fun Y => And (rinvF X Y) (ca_Vx3 Y)) (cp1 X))) True % 4.67/4.86 Clause #25 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx3 X) (Exists fun Y => And (rf X Y) (cp1xcomp Y))) True % 4.67/4.86 Clause #26 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf X Y0) (rf X Y1) → Eq Y0 Y1) True % 4.67/4.86 Clause #27 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True % 4.67/4.86 Clause #30 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_48796) True % 4.67/4.86 Clause #110 (by clausification #[19]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 4.67/4.86 Clause #112 (by clausification #[110]): ∀ (a : Iota), Eq (cowlThing a) True % 4.67/4.86 Clause #164 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True % 4.67/4.86 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True % 4.67/4.86 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) False) (Eq (rf a_1 a) True) % 4.67/4.86 Clause #168 (by clausification #[26]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True % 4.67/4.86 Clause #169 (by clausification #[168]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True) % 4.67/4.86 Clause #170 (by clausification #[169]): ∀ (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) % 4.67/4.86 Clause #171 (by clausification #[170]): ∀ (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) % 4.67/4.86 Clause #172 (by clausification #[171]): ∀ (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)) % 4.67/4.86 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 : Iota), % 4.67/4.86 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))) % 4.67/4.86 Clause #174 (by clausification #[173]): ∀ (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))) % 4.67/4.86 Clause #175 (by forward demodulation #[174, 112]): ∀ (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))) % 4.67/4.86 Clause #176 (by clausification #[175]): ∀ (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)) % 4.67/4.86 Clause #181 (by clausification #[21]): ∀ (a : Iota), Eq (Iff (cUnsatisfiable a) (Exists fun Y => And (rf a Y) (ca_Ax2 Y))) True % 4.67/4.86 Clause #183 (by clausification #[181]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf a Y) (ca_Ax2 Y)) True) % 4.67/4.86 Clause #186 (by betaEtaReduce #[23]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists (ra_Px1 X))) True % 4.67/4.86 Clause #187 (by clausification #[186]): ∀ (a : Iota), Eq (Iff (cp1xcomp a) (Exists (ra_Px1 a))) True % 4.67/4.86 Clause #189 (by clausification #[187]): ∀ (a : Iota), Or (Eq (cp1xcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 4.67/4.86 Clause #191 (by clausification #[189]): ∀ (a a_1 : Iota), Or (Eq (cp1xcomp a) False) (Eq (ra_Px1 a (skS.0 0 a a_1)) True) % 4.67/4.86 Clause #192 (by betaEtaReduce #[22]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists (ra_Px1 X)))) True % 4.67/4.86 Clause #193 (by clausification #[192]): ∀ (a : Iota), Eq (Iff (cp1 a) (Not (Exists (ra_Px1 a)))) True % 4.67/4.86 Clause #195 (by clausification #[193]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 4.67/4.86 Clause #201 (by clausification #[24]): ∀ (a : Iota), Eq (Iff (ca_Ax2 a) (And (Exists fun Y => And (rinvF a Y) (ca_Vx3 Y)) (cp1 a))) True % 4.70/4.88 Clause #203 (by clausification #[201]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (And (Exists fun Y => And (rinvF a Y) (ca_Vx3 Y)) (cp1 a)) True) % 4.70/4.88 Clause #207 (by clausification #[195]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Exists (ra_Px1 a)) False) % 4.70/4.88 Clause #208 (by clausification #[207]): ∀ (a a_1 : Iota), Or (Eq (cp1 a) False) (Eq (ra_Px1 a a_1) False) % 4.70/4.88 Clause #209 (by clausification #[183]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 2 a a_1)) (ca_Ax2 (skS.0 2 a a_1))) True) % 4.70/4.88 Clause #210 (by clausification #[209]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax2 (skS.0 2 a a_1)) True) % 4.70/4.88 Clause #211 (by clausification #[209]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 2 a a_1)) True) % 4.70/4.88 Clause #212 (by superposition #[210, 30]): ∀ (a : Iota), Or (Eq (ca_Ax2 (skS.0 2 i2003_11_14_17_21_48796 a)) True) (Eq False True) % 4.70/4.88 Clause #213 (by clausification #[212]): ∀ (a : Iota), Eq (ca_Ax2 (skS.0 2 i2003_11_14_17_21_48796 a)) True % 4.70/4.88 Clause #214 (by superposition #[211, 30]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_21_48796 (skS.0 2 i2003_11_14_17_21_48796 a)) True) (Eq False True) % 4.70/4.88 Clause #215 (by clausification #[214]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_48796 (skS.0 2 i2003_11_14_17_21_48796 a)) True % 4.70/4.88 Clause #217 (by superposition #[215, 176]): ∀ (a a_1 : Iota), % 4.70/4.88 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_21_48796 a) False) (Eq (skS.0 2 i2003_11_14_17_21_48796 a_1) a)) % 4.70/4.88 Clause #219 (by clausification #[25]): ∀ (a : Iota), Eq (Iff (ca_Vx3 a) (Exists fun Y => And (rf a Y) (cp1xcomp Y))) True % 4.70/4.88 Clause #220 (by clausification #[219]): ∀ (a : Iota), Or (Eq (ca_Vx3 a) True) (Eq (Exists fun Y => And (rf a Y) (cp1xcomp Y)) False) % 4.70/4.88 Clause #221 (by clausification #[219]): ∀ (a : Iota), Or (Eq (ca_Vx3 a) False) (Eq (Exists fun Y => And (rf a Y) (cp1xcomp Y)) True) % 4.70/4.88 Clause #222 (by clausification #[220]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) True) (Eq (And (rf a a_1) (cp1xcomp a_1)) False) % 4.70/4.88 Clause #223 (by clausification #[222]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) True) (Or (Eq (rf a a_1) False) (Eq (cp1xcomp a_1) False)) % 4.70/4.88 Clause #224 (by superposition #[223, 215]): ∀ (a : Iota), % 4.70/4.88 Or (Eq (ca_Vx3 i2003_11_14_17_21_48796) True) % 4.70/4.88 (Or (Eq (cp1xcomp (skS.0 2 i2003_11_14_17_21_48796 a)) False) (Eq False True)) % 4.70/4.88 Clause #225 (by clausification #[221]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (And (rf a (skS.0 3 a a_1)) (cp1xcomp (skS.0 3 a a_1))) True) % 4.70/4.88 Clause #226 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (cp1xcomp (skS.0 3 a a_1)) True) % 4.70/4.88 Clause #227 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (rf a (skS.0 3 a a_1)) True) % 4.70/4.88 Clause #230 (by clausification #[224]): ∀ (a : Iota), Or (Eq (ca_Vx3 i2003_11_14_17_21_48796) True) (Eq (cp1xcomp (skS.0 2 i2003_11_14_17_21_48796 a)) False) % 4.70/4.88 Clause #236 (by clausification #[217]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_21_48796 a) False) (Eq (skS.0 2 i2003_11_14_17_21_48796 a_1) a) % 4.70/4.88 Clause #240 (by clausification #[203]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (cp1 a) True) % 4.70/4.88 Clause #241 (by clausification #[203]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (Exists fun Y => And (rinvF a Y) (ca_Vx3 Y)) True) % 4.70/4.88 Clause #242 (by superposition #[240, 213]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 2 i2003_11_14_17_21_48796 a)) True) (Eq False True) % 4.70/4.88 Clause #243 (by clausification #[242]): ∀ (a : Iota), Eq (cp1 (skS.0 2 i2003_11_14_17_21_48796 a)) True % 4.70/4.88 Clause #245 (by superposition #[243, 208]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) False) % 4.70/4.88 Clause #248 (by clausification #[241]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (And (rinvF a (skS.0 4 a a_1)) (ca_Vx3 (skS.0 4 a a_1))) True) % 4.70/4.88 Clause #249 (by clausification #[248]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (ca_Vx3 (skS.0 4 a a_1)) True) % 4.70/4.88 Clause #250 (by clausification #[248]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (rinvF a (skS.0 4 a a_1)) True) % 4.70/4.88 Clause #251 (by superposition #[249, 213]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1)) True) (Eq False True) % 4.70/4.90 Clause #252 (by clausification #[245]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) False % 4.70/4.90 Clause #253 (by superposition #[250, 213]): ∀ (a a_1 : Iota), % 4.70/4.90 Or (Eq (rinvF (skS.0 2 i2003_11_14_17_21_48796 a) (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1)) True) % 4.70/4.90 (Eq False True) % 4.70/4.90 Clause #258 (by clausification #[251]): ∀ (a a_1 : Iota), Eq (ca_Vx3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1)) True % 4.70/4.90 Clause #259 (by superposition #[258, 226]): ∀ (a a_1 a_2 : Iota), % 4.70/4.90 Or (Eq True False) (Eq (cp1xcomp (skS.0 3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2)) True) % 4.70/4.90 Clause #260 (by superposition #[258, 227]): ∀ (a a_1 a_2 : Iota), % 4.70/4.90 Or (Eq True False) % 4.70/4.90 (Eq % 4.70/4.90 (rf (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) % 4.70/4.90 (skS.0 3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2)) % 4.70/4.90 True) % 4.70/4.90 Clause #261 (by clausification #[259]): ∀ (a a_1 a_2 : Iota), Eq (cp1xcomp (skS.0 3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2)) True % 4.70/4.90 Clause #263 (by clausification #[253]): ∀ (a a_1 : Iota), Eq (rinvF (skS.0 2 i2003_11_14_17_21_48796 a) (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1)) True % 4.70/4.90 Clause #264 (by superposition #[263, 167]): ∀ (a a_1 : Iota), % 4.70/4.90 Or (Eq True False) % 4.70/4.90 (Eq (rf (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) (skS.0 2 i2003_11_14_17_21_48796 a)) True) % 4.70/4.90 Clause #265 (by clausification #[264]): ∀ (a a_1 : Iota), Eq (rf (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) (skS.0 2 i2003_11_14_17_21_48796 a)) True % 4.70/4.90 Clause #267 (by superposition #[265, 176]): ∀ (a a_1 a_2 : Iota), % 4.70/4.90 Or (Eq True False) % 4.70/4.90 (Or (Eq (rf (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2) False) % 4.70/4.90 (Eq (skS.0 2 i2003_11_14_17_21_48796 a) a_2)) % 4.70/4.90 Clause #270 (by clausification #[260]): ∀ (a a_1 a_2 : Iota), % 4.70/4.90 Eq % 4.70/4.90 (rf (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) % 4.70/4.90 (skS.0 3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2)) % 4.70/4.90 True % 4.70/4.90 Clause #292 (by clausification #[267]): ∀ (a a_1 a_2 : Iota), % 4.70/4.90 Or (Eq (rf (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2) False) (Eq (skS.0 2 i2003_11_14_17_21_48796 a) a_2) % 4.70/4.90 Clause #294 (by superposition #[292, 270]): ∀ (a a_1 a_2 : Iota), % 4.70/4.90 Or (Eq (skS.0 2 i2003_11_14_17_21_48796 a) (skS.0 3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2)) % 4.70/4.90 (Eq False True) % 4.70/4.90 Clause #296 (by clausification #[294]): ∀ (a a_1 a_2 : Iota), % 4.70/4.90 Eq (skS.0 2 i2003_11_14_17_21_48796 a) (skS.0 3 (skS.0 4 (skS.0 2 i2003_11_14_17_21_48796 a) a_1) a_2) % 4.70/4.90 Clause #297 (by backward demodulation #[296, 261]): ∀ (a : Iota), Eq (cp1xcomp (skS.0 2 i2003_11_14_17_21_48796 a)) True % 4.70/4.90 Clause #300 (by superposition #[297, 230]): Or (Eq (ca_Vx3 i2003_11_14_17_21_48796) True) (Eq True False) % 4.70/4.90 Clause #302 (by clausification #[300]): Eq (ca_Vx3 i2003_11_14_17_21_48796) True % 4.70/4.90 Clause #304 (by superposition #[302, 226]): ∀ (a : Iota), Or (Eq True False) (Eq (cp1xcomp (skS.0 3 i2003_11_14_17_21_48796 a)) True) % 4.70/4.90 Clause #305 (by superposition #[302, 227]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_21_48796 (skS.0 3 i2003_11_14_17_21_48796 a)) True) % 4.70/4.90 Clause #306 (by clausification #[304]): ∀ (a : Iota), Eq (cp1xcomp (skS.0 3 i2003_11_14_17_21_48796 a)) True % 4.70/4.90 Clause #307 (by superposition #[306, 191]): ∀ (a a_1 : Iota), % 4.70/4.90 Or (Eq True False) % 4.70/4.90 (Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_48796 a) (skS.0 0 (skS.0 3 i2003_11_14_17_21_48796 a) a_1)) True) % 4.70/4.90 Clause #308 (by clausification #[305]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_48796 (skS.0 3 i2003_11_14_17_21_48796 a)) True % 4.70/4.90 Clause #309 (by superposition #[308, 236]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 i2003_11_14_17_21_48796 a) (skS.0 3 i2003_11_14_17_21_48796 a_1)) % 4.70/4.90 Clause #323 (by clausification #[309]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_21_48796 a) (skS.0 3 i2003_11_14_17_21_48796 a_1) % 4.70/4.90 Clause #326 (by superposition #[323, 252]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_48796 a) a_1) False % 4.70/4.90 Clause #382 (by clausification #[307]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_48796 a) (skS.0 0 (skS.0 3 i2003_11_14_17_21_48796 a) a_1)) True % 4.70/4.91 Clause #383 (by superposition #[382, 326]): Eq True False % 4.70/4.91 Clause #385 (by clausification #[383]): False % 4.70/4.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------