%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS073+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 07:52:34 PM UTC 2025 % Result : Unsatisfiable 3.85s 4.04s % Output : Proof 3.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS073+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 10:12:38 EDT 2025 % 0.12/0.34 % CPUTime : % 3.85/4.04 SZS status Theorem for theBenchmark.p % 3.85/4.04 SZS output start Proof for theBenchmark.p % 3.85/4.04 Clause #20 (by assumption #[]): Eq % 3.85/4.04 (∀ (X : Iota), % 3.85/4.04 Iff (cUnsatisfiable X) % 3.85/4.04 (And % 3.85/4.04 (Exists fun Y => % 3.85/4.04 And (And (rf X Y) (∀ (Z : Iota), rinvS Y Z → cp Z)) % 3.85/4.04 (∀ (Z : Iota), rinvF Y Z → Exists fun W => And (rs Z W) (cp W))) % 3.85/4.04 (Not (cp X)))) % 3.85/4.04 True % 3.85/4.04 Clause #21 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True % 3.85/4.04 Clause #23 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True % 3.85/4.04 Clause #25 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvS X Y) (rs Y X)) True % 3.85/4.04 Clause #27 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_18_54369) True % 3.85/4.04 Clause #29 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf X Y) True % 3.85/4.04 Clause #66 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf a Y) True % 3.85/4.04 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf a a_1) True % 3.85/4.04 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf a a_1) True) % 3.85/4.04 Clause #173 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True % 3.85/4.04 Clause #174 (by clausification #[173]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf a a_1) (rf a Z) → Eq a_1 Z) True % 3.85/4.04 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 : Iota), Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True % 3.85/4.04 Clause #176 (by clausification #[175]): ∀ (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) % 3.85/4.04 Clause #177 (by clausification #[176]): ∀ (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)) % 3.85/4.04 Clause #178 (by clausification #[177]): ∀ (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)) % 3.85/4.04 Clause #179 (by clausification #[20]): ∀ (a : Iota), % 3.85/4.04 Eq % 3.85/4.04 (Iff (cUnsatisfiable a) % 3.85/4.04 (And % 3.85/4.04 (Exists fun Y => % 3.85/4.04 And (And (rf a Y) (∀ (Z : Iota), rinvS Y Z → cp Z)) % 3.85/4.04 (∀ (Z : Iota), rinvF Y Z → Exists fun W => And (rs Z W) (cp W))) % 3.85/4.04 (Not (cp a)))) % 3.85/4.04 True % 3.85/4.04 Clause #181 (by clausification #[179]): ∀ (a : Iota), % 3.85/4.04 Or (Eq (cUnsatisfiable a) False) % 3.85/4.04 (Eq % 3.85/4.04 (And % 3.85/4.04 (Exists fun Y => % 3.85/4.04 And (And (rf a Y) (∀ (Z : Iota), rinvS Y Z → cp Z)) % 3.85/4.04 (∀ (Z : Iota), rinvF Y Z → Exists fun W => And (rs Z W) (cp W))) % 3.85/4.04 (Not (cp a))) % 3.85/4.04 True) % 3.85/4.04 Clause #195 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvS a Y) (rs Y a)) True % 3.85/4.04 Clause #196 (by clausification #[195]): ∀ (a a_1 : Iota), Eq (Iff (rinvS a a_1) (rs a_1 a)) True % 3.85/4.04 Clause #197 (by clausification #[196]): ∀ (a a_1 : Iota), Or (Eq (rinvS a a_1) True) (Eq (rs a_1 a) False) % 3.85/4.04 Clause #203 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True % 3.85/4.04 Clause #204 (by clausification #[203]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True % 3.85/4.04 Clause #205 (by clausification #[204]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) True) (Eq (rf a_1 a) False) % 3.85/4.04 Clause #207 (by clausification #[181]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (cp a)) True) % 3.85/4.04 Clause #208 (by clausification #[181]): ∀ (a : Iota), % 3.85/4.04 Or (Eq (cUnsatisfiable a) False) % 3.85/4.04 (Eq % 3.85/4.04 (Exists fun Y => % 3.85/4.04 And (And (rf a Y) (∀ (Z : Iota), rinvS Y Z → cp Z)) % 3.85/4.04 (∀ (Z : Iota), rinvF Y Z → Exists fun W => And (rs Z W) (cp W))) % 3.85/4.04 True) % 3.85/4.04 Clause #209 (by clausification #[207]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp a) False) % 3.85/4.04 Clause #210 (by superposition #[209, 27]): Or (Eq (cp i2003_11_14_17_18_54369) False) (Eq False True) % 3.85/4.04 Clause #211 (by clausification #[210]): Eq (cp i2003_11_14_17_18_54369) False % 3.85/4.04 Clause #212 (by clausification #[208]): ∀ (a a_1 : Iota), % 3.85/4.04 Or (Eq (cUnsatisfiable a) False) % 3.85/4.04 (Eq % 3.85/4.04 (And (And (rf a (skS.0 2 a a_1)) (∀ (Z : Iota), rinvS (skS.0 2 a a_1) Z → cp Z)) % 3.85/4.04 (∀ (Z : Iota), rinvF (skS.0 2 a a_1) Z → Exists fun W => And (rs Z W) (cp W))) % 3.85/4.04 True) % 3.85/4.04 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota), % 3.85/4.06 Or (Eq (cUnsatisfiable a) False) % 3.85/4.06 (Eq (∀ (Z : Iota), rinvF (skS.0 2 a a_1) Z → Exists fun W => And (rs Z W) (cp W)) True) % 3.85/4.06 Clause #214 (by clausification #[212]): ∀ (a a_1 : Iota), % 3.85/4.06 Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 2 a a_1)) (∀ (Z : Iota), rinvS (skS.0 2 a a_1) Z → cp Z)) True) % 3.85/4.06 Clause #215 (by clausification #[213]): ∀ (a a_1 a_2 : Iota), % 3.85/4.06 Or (Eq (cUnsatisfiable a) False) (Eq (rinvF (skS.0 2 a a_1) a_2 → Exists fun W => And (rs a_2 W) (cp W)) True) % 3.85/4.06 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 : Iota), % 3.85/4.06 Or (Eq (cUnsatisfiable a) False) % 3.85/4.06 (Or (Eq (rinvF (skS.0 2 a a_1) a_2) False) (Eq (Exists fun W => And (rs a_2 W) (cp W)) True)) % 3.85/4.06 Clause #217 (by clausification #[216]): ∀ (a a_1 a_2 a_3 : Iota), % 3.85/4.06 Or (Eq (cUnsatisfiable a) False) % 3.85/4.06 (Or (Eq (rinvF (skS.0 2 a a_1) a_2) False) (Eq (And (rs a_2 (skS.0 3 a_2 a_3)) (cp (skS.0 3 a_2 a_3))) True)) % 3.85/4.06 Clause #219 (by clausification #[217]): ∀ (a a_1 a_2 a_3 : Iota), % 3.85/4.06 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvF (skS.0 2 a a_1) a_2) False) (Eq (rs a_2 (skS.0 3 a_2 a_3)) True)) % 3.85/4.06 Clause #221 (by clausification #[214]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Z : Iota), rinvS (skS.0 2 a a_1) Z → cp Z) True) % 3.85/4.06 Clause #222 (by clausification #[214]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 2 a a_1)) True) % 3.85/4.06 Clause #223 (by clausification #[221]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvS (skS.0 2 a a_1) a_2 → cp a_2) True) % 3.85/4.06 Clause #224 (by clausification #[223]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvS (skS.0 2 a a_1) a_2) False) (Eq (cp a_2) True)) % 3.85/4.06 Clause #225 (by superposition #[224, 27]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 2 i2003_11_14_17_18_54369 a) a_1) False) (Or (Eq (cp a_1) True) (Eq False True)) % 3.85/4.06 Clause #226 (by superposition #[222, 27]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_18_54369 (skS.0 2 i2003_11_14_17_18_54369 a)) True) (Eq False True) % 3.85/4.06 Clause #231 (by clausification #[226]): ∀ (a : Iota), Eq (rf i2003_11_14_17_18_54369 (skS.0 2 i2003_11_14_17_18_54369 a)) True % 3.85/4.06 Clause #232 (by superposition #[231, 178]): ∀ (a a_1 : Iota), % 3.85/4.06 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_18_54369 a) False) (Eq (skS.0 2 i2003_11_14_17_18_54369 a_1) a)) % 3.85/4.06 Clause #234 (by superposition #[231, 205]): ∀ (a : Iota), Or (Eq (rinvF (skS.0 2 i2003_11_14_17_18_54369 a) i2003_11_14_17_18_54369) True) (Eq True False) % 3.85/4.06 Clause #236 (by clausification #[234]): ∀ (a : Iota), Eq (rinvF (skS.0 2 i2003_11_14_17_18_54369 a) i2003_11_14_17_18_54369) True % 3.85/4.06 Clause #238 (by clausification #[232]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_18_54369 a) False) (Eq (skS.0 2 i2003_11_14_17_18_54369 a_1) a) % 3.85/4.06 Clause #240 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 2 i2003_11_14_17_18_54369 a) a_1) False) (Eq (cp a_1) True) % 3.85/4.06 Clause #246 (by superposition #[219, 27]): ∀ (a a_1 a_2 : Iota), % 3.85/4.06 Or (Eq (rinvF (skS.0 2 i2003_11_14_17_18_54369 a) a_1) False) % 3.85/4.06 (Or (Eq (rs a_1 (skS.0 3 a_1 a_2)) True) (Eq False True)) % 3.85/4.06 Clause #247 (by clausification #[246]): ∀ (a a_1 a_2 : Iota), Or (Eq (rinvF (skS.0 2 i2003_11_14_17_18_54369 a) a_1) False) (Eq (rs a_1 (skS.0 3 a_1 a_2)) True) % 3.85/4.06 Clause #248 (by superposition #[247, 236]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_18_54369 (skS.0 3 i2003_11_14_17_18_54369 a)) True) (Eq False True) % 3.85/4.06 Clause #252 (by clausification #[248]): ∀ (a : Iota), Eq (rs i2003_11_14_17_18_54369 (skS.0 3 i2003_11_14_17_18_54369 a)) True % 3.85/4.06 Clause #253 (by superposition #[252, 68]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_18_54369 (skS.0 3 i2003_11_14_17_18_54369 a)) True) % 3.85/4.06 Clause #256 (by superposition #[252, 197]): ∀ (a : Iota), Or (Eq (rinvS (skS.0 3 i2003_11_14_17_18_54369 a) i2003_11_14_17_18_54369) True) (Eq True False) % 3.85/4.06 Clause #257 (by clausification #[256]): ∀ (a : Iota), Eq (rinvS (skS.0 3 i2003_11_14_17_18_54369 a) i2003_11_14_17_18_54369) True % 3.85/4.06 Clause #265 (by clausification #[253]): ∀ (a : Iota), Eq (rf i2003_11_14_17_18_54369 (skS.0 3 i2003_11_14_17_18_54369 a)) True % 3.90/4.07 Clause #266 (by superposition #[265, 238]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 i2003_11_14_17_18_54369 a) (skS.0 3 i2003_11_14_17_18_54369 a_1)) % 3.90/4.07 Clause #281 (by clausification #[266]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_18_54369 a) (skS.0 3 i2003_11_14_17_18_54369 a_1) % 3.90/4.07 Clause #289 (by superposition #[281, 257]): ∀ (a : Iota), Eq (rinvS (skS.0 2 i2003_11_14_17_18_54369 a) i2003_11_14_17_18_54369) True % 3.90/4.07 Clause #295 (by superposition #[289, 240]): Or (Eq True False) (Eq (cp i2003_11_14_17_18_54369) True) % 3.90/4.07 Clause #297 (by clausification #[295]): Eq (cp i2003_11_14_17_18_54369) True % 3.90/4.07 Clause #298 (by superposition #[297, 211]): Eq True False % 3.90/4.07 Clause #301 (by clausification #[298]): False % 3.90/4.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------