%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS111+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 07:52:38 PM UTC 2025 % Result : Unsatisfiable 4.22s 4.42s % Output : Proof 4.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.14 % Problem : KRS111+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.15 % Command : duper %s % 0.13/0.37 % Computer : n013.cluster.edu % 0.13/0.37 % Model : x86_64 x86_64 % 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.37 % Memory : 8042.1875MB % 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.37 % CPULimit : 300 % 0.13/0.37 % WCLimit : 300 % 0.13/0.37 % DateTime : Thu Oct 2 10:19:38 EDT 2025 % 0.13/0.37 % CPUTime : % 4.22/4.42 SZS status Theorem for theBenchmark.p % 4.22/4.42 SZS output start Proof for theBenchmark.p % 4.22/4.42 Clause #23 (by assumption #[]): Eq % 4.22/4.42 (∀ (X : Iota), % 4.22/4.42 Iff (cUnsatisfiable X) % 4.22/4.42 (And (And (Exists fun Y => And (rf1 X Y) (cpxcomp Y)) (Exists fun Y => And (rs X Y) (cowlThing Y))) % 4.22/4.42 (Exists fun Y => And (rf X Y) (cp Y)))) % 4.22/4.42 True % 4.22/4.42 Clause #24 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True % 4.22/4.42 Clause #25 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 4.22/4.42 Clause #26 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True % 4.22/4.42 Clause #27 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf1 X Y) (rf1 X Z) → Eq Y Z) True % 4.22/4.42 Clause #32 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_15425) True % 4.22/4.42 Clause #33 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf X Y) True % 4.22/4.42 Clause #34 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf1 X Y) True % 4.22/4.42 Clause #77 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf a Y) True % 4.22/4.42 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf a a_1) True % 4.22/4.42 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf a a_1) True) % 4.22/4.42 Clause #80 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf1 a Y) True % 4.22/4.42 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf1 a a_1) True % 4.22/4.42 Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf1 a a_1) True) % 4.22/4.42 Clause #189 (by clausification #[23]): ∀ (a : Iota), % 4.22/4.42 Eq % 4.22/4.42 (Iff (cUnsatisfiable a) % 4.22/4.42 (And (And (Exists fun Y => And (rf1 a Y) (cpxcomp Y)) (Exists fun Y => And (rs a Y) (cowlThing Y))) % 4.22/4.42 (Exists fun Y => And (rf a Y) (cp Y)))) % 4.22/4.42 True % 4.22/4.42 Clause #191 (by clausification #[189]): ∀ (a : Iota), % 4.22/4.42 Or (Eq (cUnsatisfiable a) False) % 4.22/4.42 (Eq % 4.22/4.42 (And (And (Exists fun Y => And (rf1 a Y) (cpxcomp Y)) (Exists fun Y => And (rs a Y) (cowlThing Y))) % 4.22/4.42 (Exists fun Y => And (rf a Y) (cp Y))) % 4.22/4.42 True) % 4.22/4.42 Clause #202 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf1 a Y) (rf1 a Z) → Eq Y Z) True % 4.22/4.42 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf1 a a_1) (rf1 a Z) → Eq a_1 Z) True % 4.22/4.42 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota), Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True % 4.22/4.42 Clause #205 (by clausification #[204]): ∀ (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) % 4.22/4.42 Clause #206 (by clausification #[205]): ∀ (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)) % 4.22/4.42 Clause #207 (by clausification #[206]): ∀ (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)) % 4.22/4.42 Clause #208 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True % 4.22/4.42 Clause #209 (by clausification #[208]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf a a_1) (rf a Z) → Eq a_1 Z) True % 4.22/4.42 Clause #210 (by clausification #[209]): ∀ (a a_1 a_2 : Iota), Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True % 4.22/4.42 Clause #211 (by clausification #[210]): ∀ (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) % 4.22/4.42 Clause #212 (by clausification #[211]): ∀ (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)) % 4.22/4.42 Clause #213 (by clausification #[212]): ∀ (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)) % 4.22/4.42 Clause #222 (by betaEtaReduce #[24]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True % 4.22/4.42 Clause #223 (by clausification #[222]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True % 4.22/4.42 Clause #225 (by clausification #[223]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 4.22/4.42 Clause #228 (by clausification #[225]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False) % 4.22/4.42 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False) % 4.22/4.45 Clause #234 (by betaEtaReduce #[25]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True % 4.22/4.45 Clause #235 (by clausification #[234]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True % 4.22/4.45 Clause #237 (by clausification #[235]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 4.22/4.45 Clause #240 (by clausification #[191]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf a Y) (cp Y)) True) % 4.22/4.45 Clause #241 (by clausification #[191]): ∀ (a : Iota), % 4.22/4.45 Or (Eq (cUnsatisfiable a) False) % 4.22/4.45 (Eq (And (Exists fun Y => And (rf1 a Y) (cpxcomp Y)) (Exists fun Y => And (rs a Y) (cowlThing Y))) True) % 4.22/4.45 Clause #242 (by clausification #[240]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 1 a a_1)) (cp (skS.0 1 a a_1))) True) % 4.22/4.45 Clause #243 (by clausification #[242]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp (skS.0 1 a a_1)) True) % 4.22/4.45 Clause #244 (by clausification #[242]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 1 a a_1)) True) % 4.22/4.45 Clause #245 (by superposition #[243, 32]): ∀ (a : Iota), Or (Eq (cp (skS.0 1 i2003_11_14_17_21_15425 a)) True) (Eq False True) % 4.22/4.45 Clause #247 (by clausification #[237]): ∀ (a a_1 : Iota), Or (Eq (cpxcomp a) False) (Eq (ra_Px1 a (skS.0 2 a a_1)) True) % 4.22/4.45 Clause #249 (by clausification #[245]): ∀ (a : Iota), Eq (cp (skS.0 1 i2003_11_14_17_21_15425 a)) True % 4.22/4.45 Clause #250 (by superposition #[249, 229]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 1 i2003_11_14_17_21_15425 a) a_1) False) % 4.22/4.45 Clause #251 (by clausification #[250]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 1 i2003_11_14_17_21_15425 a) a_1) False % 4.22/4.45 Clause #252 (by superposition #[244, 32]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_21_15425 (skS.0 1 i2003_11_14_17_21_15425 a)) True) (Eq False True) % 4.22/4.45 Clause #253 (by clausification #[241]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rs a Y) (cowlThing Y)) True) % 4.22/4.45 Clause #254 (by clausification #[241]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (cpxcomp Y)) True) % 4.22/4.45 Clause #255 (by clausification #[253]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rs a (skS.0 3 a a_1)) (cowlThing (skS.0 3 a a_1))) True) % 4.22/4.45 Clause #257 (by clausification #[255]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 3 a a_1)) True) % 4.22/4.45 Clause #258 (by clausification #[254]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 4 a a_1)) (cpxcomp (skS.0 4 a a_1))) True) % 4.22/4.45 Clause #259 (by clausification #[258]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cpxcomp (skS.0 4 a a_1)) True) % 4.22/4.45 Clause #260 (by clausification #[258]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 4 a a_1)) True) % 4.22/4.45 Clause #261 (by superposition #[259, 32]): ∀ (a : Iota), Or (Eq (cpxcomp (skS.0 4 i2003_11_14_17_21_15425 a)) True) (Eq False True) % 4.22/4.45 Clause #262 (by clausification #[261]): ∀ (a : Iota), Eq (cpxcomp (skS.0 4 i2003_11_14_17_21_15425 a)) True % 4.22/4.45 Clause #263 (by superposition #[262, 247]): ∀ (a a_1 : Iota), % 4.22/4.45 Or (Eq True False) % 4.22/4.45 (Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_15425 a) (skS.0 2 (skS.0 4 i2003_11_14_17_21_15425 a) a_1)) True) % 4.22/4.45 Clause #264 (by clausification #[252]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_15425 (skS.0 1 i2003_11_14_17_21_15425 a)) True % 4.22/4.45 Clause #266 (by superposition #[264, 213]): ∀ (a a_1 : Iota), % 4.22/4.45 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_21_15425 a) False) (Eq (skS.0 1 i2003_11_14_17_21_15425 a_1) a)) % 4.22/4.45 Clause #274 (by superposition #[260, 32]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_21_15425 (skS.0 4 i2003_11_14_17_21_15425 a)) True) (Eq False True) % 4.22/4.45 Clause #275 (by clausification #[274]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_15425 (skS.0 4 i2003_11_14_17_21_15425 a)) True % 4.22/4.45 Clause #276 (by superposition #[275, 207]): ∀ (a a_1 : Iota), % 4.22/4.45 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_21_15425 a) False) (Eq (skS.0 4 i2003_11_14_17_21_15425 a_1) a)) % 4.22/4.45 Clause #280 (by superposition #[257, 32]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_21_15425 (skS.0 3 i2003_11_14_17_21_15425 a)) True) (Eq False True) % 4.22/4.46 Clause #281 (by clausification #[280]): ∀ (a : Iota), Eq (rs i2003_11_14_17_21_15425 (skS.0 3 i2003_11_14_17_21_15425 a)) True % 4.22/4.46 Clause #282 (by superposition #[281, 79]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_21_15425 (skS.0 3 i2003_11_14_17_21_15425 a)) True) % 4.22/4.46 Clause #283 (by superposition #[281, 82]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_21_15425 (skS.0 3 i2003_11_14_17_21_15425 a)) True) % 4.22/4.46 Clause #288 (by clausification #[283]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_15425 (skS.0 3 i2003_11_14_17_21_15425 a)) True % 4.22/4.46 Clause #292 (by clausification #[263]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_15425 a) (skS.0 2 (skS.0 4 i2003_11_14_17_21_15425 a) a_1)) True % 4.22/4.46 Clause #294 (by clausification #[282]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_15425 (skS.0 3 i2003_11_14_17_21_15425 a)) True % 4.22/4.46 Clause #299 (by clausification #[276]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_21_15425 a) False) (Eq (skS.0 4 i2003_11_14_17_21_15425 a_1) a) % 4.22/4.46 Clause #301 (by superposition #[299, 288]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 i2003_11_14_17_21_15425 a) (skS.0 3 i2003_11_14_17_21_15425 a_1)) (Eq False True) % 4.22/4.46 Clause #304 (by clausification #[266]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_21_15425 a) False) (Eq (skS.0 1 i2003_11_14_17_21_15425 a_1) a) % 4.22/4.46 Clause #306 (by superposition #[304, 294]): ∀ (a a_1 : Iota), Or (Eq (skS.0 1 i2003_11_14_17_21_15425 a) (skS.0 3 i2003_11_14_17_21_15425 a_1)) (Eq False True) % 4.22/4.46 Clause #313 (by clausification #[306]): ∀ (a a_1 : Iota), Eq (skS.0 1 i2003_11_14_17_21_15425 a) (skS.0 3 i2003_11_14_17_21_15425 a_1) % 4.22/4.46 Clause #315 (by superposition #[313, 251]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_15425 a) a_1) False % 4.22/4.46 Clause #336 (by clausification #[301]): ∀ (a a_1 : Iota), Eq (skS.0 4 i2003_11_14_17_21_15425 a) (skS.0 3 i2003_11_14_17_21_15425 a_1) % 4.22/4.46 Clause #346 (by superposition #[336, 315]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_15425 a) a_1) False % 4.22/4.46 Clause #356 (by superposition #[346, 292]): Eq False True % 4.22/4.46 Clause #359 (by clausification #[356]): False % 4.22/4.46 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------