%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS075+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 3.85s 4.01s % Output : Proof 3.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.10 % Problem : KRS075+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.11 % Command : duper %s % 0.11/0.32 % Computer : n027.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Thu Oct 2 10:15:53 EDT 2025 % 0.11/0.32 % CPUTime : % 3.85/4.01 SZS status Theorem for theBenchmark.p % 3.85/4.01 SZS output start Proof for theBenchmark.p % 3.85/4.01 Clause #20 (by assumption #[]): Eq % 3.85/4.01 (∀ (X : Iota), % 3.85/4.01 Iff (cUnsatisfiable X) % 3.85/4.01 (And (And (Exists fun Y => And (rf1 X Y) (Not (cp Y))) (Exists fun Y => And (rs X Y) (cowlThing Y))) % 3.85/4.01 (Exists fun Y => And (rf X Y) (cp Y)))) % 3.85/4.01 True % 3.85/4.01 Clause #21 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True % 3.85/4.01 Clause #22 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf1 X Y) (rf1 X Z) → Eq Y Z) True % 3.85/4.01 Clause #27 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_02584) True % 3.85/4.01 Clause #28 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf1 X Y) True % 3.85/4.01 Clause #29 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf X Y) True % 3.85/4.01 Clause #66 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf a Y) True % 3.85/4.01 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf a a_1) True % 3.85/4.01 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf a a_1) True) % 3.85/4.01 Clause #69 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf1 a Y) True % 3.85/4.01 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf1 a a_1) True % 3.85/4.01 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf1 a a_1) True) % 3.85/4.01 Clause #167 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf1 a Y) (rf1 a Z) → Eq Y Z) True % 3.85/4.01 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf1 a a_1) (rf1 a Z) → Eq a_1 Z) True % 3.85/4.01 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 : Iota), Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True % 3.85/4.01 Clause #170 (by clausification #[169]): ∀ (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) % 3.85/4.01 Clause #171 (by clausification #[170]): ∀ (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)) % 3.85/4.01 Clause #172 (by clausification #[171]): ∀ (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)) % 3.85/4.01 Clause #173 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True % 3.85/4.01 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 % 3.85/4.01 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 % 3.85/4.01 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) % 3.85/4.01 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)) % 3.85/4.01 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)) % 3.85/4.01 Clause #179 (by clausification #[20]): ∀ (a : Iota), % 3.85/4.01 Eq % 3.85/4.01 (Iff (cUnsatisfiable a) % 3.85/4.01 (And (And (Exists fun Y => And (rf1 a Y) (Not (cp Y))) (Exists fun Y => And (rs a Y) (cowlThing Y))) % 3.85/4.01 (Exists fun Y => And (rf a Y) (cp Y)))) % 3.85/4.01 True % 3.85/4.01 Clause #181 (by clausification #[179]): ∀ (a : Iota), % 3.85/4.01 Or (Eq (cUnsatisfiable a) False) % 3.85/4.01 (Eq % 3.85/4.01 (And (And (Exists fun Y => And (rf1 a Y) (Not (cp Y))) (Exists fun Y => And (rs a Y) (cowlThing Y))) % 3.85/4.01 (Exists fun Y => And (rf a Y) (cp Y))) % 3.85/4.01 True) % 3.85/4.01 Clause #205 (by clausification #[181]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf a Y) (cp Y)) True) % 3.85/4.01 Clause #206 (by clausification #[181]): ∀ (a : Iota), % 3.85/4.01 Or (Eq (cUnsatisfiable a) False) % 3.85/4.01 (Eq (And (Exists fun Y => And (rf1 a Y) (Not (cp Y))) (Exists fun Y => And (rs a Y) (cowlThing Y))) True) % 3.85/4.01 Clause #207 (by clausification #[205]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 0 a a_1)) (cp (skS.0 0 a a_1))) True) % 3.85/4.01 Clause #208 (by clausification #[207]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp (skS.0 0 a a_1)) True) % 3.85/4.01 Clause #209 (by clausification #[207]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 0 a a_1)) True) % 3.85/4.03 Clause #210 (by superposition #[208, 27]): ∀ (a : Iota), Or (Eq (cp (skS.0 0 i2003_11_14_17_19_02584 a)) True) (Eq False True) % 3.85/4.03 Clause #211 (by clausification #[210]): ∀ (a : Iota), Eq (cp (skS.0 0 i2003_11_14_17_19_02584 a)) True % 3.85/4.03 Clause #212 (by superposition #[209, 27]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_19_02584 (skS.0 0 i2003_11_14_17_19_02584 a)) True) (Eq False True) % 3.85/4.03 Clause #213 (by clausification #[212]): ∀ (a : Iota), Eq (rf i2003_11_14_17_19_02584 (skS.0 0 i2003_11_14_17_19_02584 a)) True % 3.85/4.03 Clause #214 (by superposition #[213, 178]): ∀ (a a_1 : Iota), % 3.85/4.03 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_19_02584 a) False) (Eq (skS.0 0 i2003_11_14_17_19_02584 a_1) a)) % 3.85/4.03 Clause #219 (by clausification #[206]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rs a Y) (cowlThing Y)) True) % 3.85/4.03 Clause #220 (by clausification #[206]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (Not (cp Y))) True) % 3.85/4.03 Clause #221 (by clausification #[219]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rs a (skS.0 1 a a_1)) (cowlThing (skS.0 1 a a_1))) True) % 3.85/4.03 Clause #223 (by clausification #[221]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 1 a a_1)) True) % 3.85/4.03 Clause #224 (by clausification #[220]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 2 a a_1)) (Not (cp (skS.0 2 a a_1)))) True) % 3.85/4.03 Clause #225 (by clausification #[224]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (cp (skS.0 2 a a_1))) True) % 3.85/4.03 Clause #226 (by clausification #[224]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 2 a a_1)) True) % 3.85/4.03 Clause #227 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp (skS.0 2 a a_1)) False) % 3.85/4.03 Clause #228 (by superposition #[227, 27]): ∀ (a : Iota), Or (Eq (cp (skS.0 2 i2003_11_14_17_19_02584 a)) False) (Eq False True) % 3.85/4.03 Clause #229 (by clausification #[228]): ∀ (a : Iota), Eq (cp (skS.0 2 i2003_11_14_17_19_02584 a)) False % 3.85/4.03 Clause #230 (by superposition #[226, 27]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_19_02584 (skS.0 2 i2003_11_14_17_19_02584 a)) True) (Eq False True) % 3.85/4.03 Clause #231 (by clausification #[230]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_19_02584 (skS.0 2 i2003_11_14_17_19_02584 a)) True % 3.85/4.03 Clause #232 (by superposition #[231, 172]): ∀ (a a_1 : Iota), % 3.85/4.03 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_19_02584 a) False) (Eq (skS.0 2 i2003_11_14_17_19_02584 a_1) a)) % 3.85/4.03 Clause #234 (by clausification #[214]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_19_02584 a) False) (Eq (skS.0 0 i2003_11_14_17_19_02584 a_1) a) % 3.85/4.03 Clause #238 (by superposition #[223, 27]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_19_02584 (skS.0 1 i2003_11_14_17_19_02584 a)) True) (Eq False True) % 3.85/4.03 Clause #239 (by clausification #[238]): ∀ (a : Iota), Eq (rs i2003_11_14_17_19_02584 (skS.0 1 i2003_11_14_17_19_02584 a)) True % 3.85/4.03 Clause #240 (by superposition #[239, 68]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_19_02584 (skS.0 1 i2003_11_14_17_19_02584 a)) True) % 3.85/4.03 Clause #241 (by superposition #[239, 71]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_19_02584 (skS.0 1 i2003_11_14_17_19_02584 a)) True) % 3.85/4.03 Clause #248 (by clausification #[241]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_19_02584 (skS.0 1 i2003_11_14_17_19_02584 a)) True % 3.85/4.03 Clause #252 (by clausification #[240]): ∀ (a : Iota), Eq (rf i2003_11_14_17_19_02584 (skS.0 1 i2003_11_14_17_19_02584 a)) True % 3.85/4.03 Clause #253 (by superposition #[252, 234]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 0 i2003_11_14_17_19_02584 a) (skS.0 1 i2003_11_14_17_19_02584 a_1)) % 3.85/4.03 Clause #258 (by clausification #[232]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_19_02584 a) False) (Eq (skS.0 2 i2003_11_14_17_19_02584 a_1) a) % 3.85/4.03 Clause #260 (by superposition #[258, 248]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 i2003_11_14_17_19_02584 a) (skS.0 1 i2003_11_14_17_19_02584 a_1)) (Eq False True) % 3.85/4.03 Clause #267 (by clausification #[260]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_19_02584 a) (skS.0 1 i2003_11_14_17_19_02584 a_1) % 3.85/4.04 Clause #268 (by superposition #[267, 229]): ∀ (a : Iota), Eq (cp (skS.0 1 i2003_11_14_17_19_02584 a)) False % 3.85/4.04 Clause #285 (by clausification #[253]): ∀ (a a_1 : Iota), Eq (skS.0 0 i2003_11_14_17_19_02584 a) (skS.0 1 i2003_11_14_17_19_02584 a_1) % 3.85/4.04 Clause #293 (by superposition #[285, 268]): ∀ (a : Iota), Eq (cp (skS.0 0 i2003_11_14_17_19_02584 a)) False % 3.85/4.04 Clause #294 (by superposition #[293, 211]): Eq False True % 3.85/4.04 Clause #295 (by clausification #[294]): False % 3.85/4.04 SZS output end Proof for theBenchmark.p 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