%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS070+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 07:52:34 PM UTC 2025 % Result : Unsatisfiable 3.70s 3.91s % Output : Proof 3.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS070+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 10:12:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.70/3.91 SZS status Theorem for theBenchmark.p % 3.70/3.91 SZS output start Proof for theBenchmark.p % 3.70/3.91 Clause #29 (by assumption #[]): Eq % 3.70/3.91 (∀ (X : Iota), % 3.70/3.91 Iff (cUnsatisfiable X) % 3.70/3.91 (And (And (Exists fun Y => And (rrx4 X Y) (cc2 Y)) (Not (Exists fun Y => And (And (rrx3 X Y) (cc2 Y)) (cc1 Y)))) % 3.70/3.91 (Exists fun Y => And (rrx3 X Y) (cc1 Y)))) % 3.70/3.91 True % 3.70/3.91 Clause #30 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rrx X Y) (rrx X Z) → Eq Y Z) True % 3.70/3.91 Clause #35 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_18_32242) True % 3.70/3.91 Clause #36 (by assumption #[]): Eq (∀ (X Y : Iota), rrx3 X Y → rrx X Y) True % 3.70/3.91 Clause #43 (by assumption #[]): Eq (∀ (X Y : Iota), rrx4 X Y → rrx X Y) True % 3.70/3.91 Clause #102 (by clausification #[36]): ∀ (a : Iota), Eq (∀ (Y : Iota), rrx3 a Y → rrx a Y) True % 3.70/3.91 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), Eq (rrx3 a a_1 → rrx a a_1) True % 3.70/3.91 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota), Or (Eq (rrx3 a a_1) False) (Eq (rrx a a_1) True) % 3.70/3.91 Clause #105 (by clausification #[43]): ∀ (a : Iota), Eq (∀ (Y : Iota), rrx4 a Y → rrx a Y) True % 3.70/3.91 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (rrx4 a a_1 → rrx a a_1) True % 3.70/3.91 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Or (Eq (rrx4 a a_1) False) (Eq (rrx a a_1) True) % 3.70/3.91 Clause #255 (by clausification #[29]): ∀ (a : Iota), % 3.70/3.91 Eq % 3.70/3.91 (Iff (cUnsatisfiable a) % 3.70/3.91 (And (And (Exists fun Y => And (rrx4 a Y) (cc2 Y)) (Not (Exists fun Y => And (And (rrx3 a Y) (cc2 Y)) (cc1 Y)))) % 3.70/3.91 (Exists fun Y => And (rrx3 a Y) (cc1 Y)))) % 3.70/3.91 True % 3.70/3.91 Clause #257 (by clausification #[255]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (cUnsatisfiable a) False) % 3.70/3.91 (Eq % 3.70/3.91 (And (And (Exists fun Y => And (rrx4 a Y) (cc2 Y)) (Not (Exists fun Y => And (And (rrx3 a Y) (cc2 Y)) (cc1 Y)))) % 3.70/3.91 (Exists fun Y => And (rrx3 a Y) (cc1 Y))) % 3.70/3.91 True) % 3.70/3.91 Clause #286 (by clausification #[30]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rrx a Y) (rrx a Z) → Eq Y Z) True % 3.70/3.91 Clause #287 (by clausification #[286]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rrx a a_1) (rrx a Z) → Eq a_1 Z) True % 3.70/3.91 Clause #288 (by clausification #[287]): ∀ (a a_1 a_2 : Iota), Eq (And (rrx a a_1) (rrx a a_2) → Eq a_1 a_2) True % 3.70/3.91 Clause #289 (by clausification #[288]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rrx a a_1) (rrx a a_2)) False) (Eq (Eq a_1 a_2) True) % 3.70/3.91 Clause #290 (by clausification #[289]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rrx a_2 a) False) (Eq (rrx a_2 a_1) False)) % 3.70/3.91 Clause #291 (by clausification #[290]): ∀ (a a_1 a_2 : Iota), Or (Eq (rrx a a_1) False) (Or (Eq (rrx a a_2) False) (Eq a_1 a_2)) % 3.70/3.91 Clause #292 (by clausification #[257]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rrx3 a Y) (cc1 Y)) True) % 3.70/3.91 Clause #293 (by clausification #[257]): ∀ (a : Iota), % 3.70/3.91 Or (Eq (cUnsatisfiable a) False) % 3.70/3.91 (Eq (And (Exists fun Y => And (rrx4 a Y) (cc2 Y)) (Not (Exists fun Y => And (And (rrx3 a Y) (cc2 Y)) (cc1 Y)))) % 3.70/3.91 True) % 3.70/3.91 Clause #294 (by clausification #[292]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rrx3 a (skS.0 1 a a_1)) (cc1 (skS.0 1 a a_1))) True) % 3.70/3.91 Clause #295 (by clausification #[294]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cc1 (skS.0 1 a a_1)) True) % 3.70/3.91 Clause #296 (by clausification #[294]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rrx3 a (skS.0 1 a a_1)) True) % 3.70/3.91 Clause #297 (by superposition #[295, 35]): ∀ (a : Iota), Or (Eq (cc1 (skS.0 1 i2003_11_14_17_18_32242 a)) True) (Eq False True) % 3.70/3.91 Clause #300 (by clausification #[297]): ∀ (a : Iota), Eq (cc1 (skS.0 1 i2003_11_14_17_18_32242 a)) True % 3.70/3.91 Clause #301 (by superposition #[296, 35]): ∀ (a : Iota), Or (Eq (rrx3 i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) True) (Eq False True) % 3.70/3.91 Clause #302 (by clausification #[301]): ∀ (a : Iota), Eq (rrx3 i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) True % 3.70/3.91 Clause #303 (by superposition #[302, 104]): ∀ (a : Iota), Or (Eq True False) (Eq (rrx i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) True) % 3.70/3.91 Clause #309 (by clausification #[303]): ∀ (a : Iota), Eq (rrx i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) True % 3.78/3.93 Clause #310 (by superposition #[309, 291]): ∀ (a a_1 : Iota), % 3.78/3.93 Or (Eq True False) (Or (Eq (rrx i2003_11_14_17_18_32242 a) False) (Eq (skS.0 1 i2003_11_14_17_18_32242 a_1) a)) % 3.78/3.93 Clause #311 (by clausification #[293]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (Exists fun Y => And (And (rrx3 a Y) (cc2 Y)) (cc1 Y))) True) % 3.78/3.93 Clause #312 (by clausification #[293]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rrx4 a Y) (cc2 Y)) True) % 3.78/3.93 Clause #313 (by clausification #[311]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (And (rrx3 a Y) (cc2 Y)) (cc1 Y)) False) % 3.78/3.93 Clause #314 (by clausification #[313]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (And (rrx3 a a_1) (cc2 a_1)) (cc1 a_1)) False) % 3.78/3.93 Clause #315 (by clausification #[314]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (And (rrx3 a a_1) (cc2 a_1)) False) (Eq (cc1 a_1) False)) % 3.78/3.93 Clause #316 (by clausification #[315]): ∀ (a a_1 : Iota), % 3.78/3.93 Or (Eq (cUnsatisfiable a) False) (Or (Eq (cc1 a_1) False) (Or (Eq (rrx3 a a_1) False) (Eq (cc2 a_1) False))) % 3.78/3.93 Clause #317 (by superposition #[316, 35]): ∀ (a : Iota), % 3.78/3.93 Or (Eq (cc1 a) False) (Or (Eq (rrx3 i2003_11_14_17_18_32242 a) False) (Or (Eq (cc2 a) False) (Eq False True))) % 3.78/3.93 Clause #318 (by clausification #[317]): ∀ (a : Iota), Or (Eq (cc1 a) False) (Or (Eq (rrx3 i2003_11_14_17_18_32242 a) False) (Eq (cc2 a) False)) % 3.78/3.93 Clause #319 (by superposition #[318, 300]): ∀ (a : Iota), % 3.78/3.93 Or (Eq (rrx3 i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) False) % 3.78/3.93 (Or (Eq (cc2 (skS.0 1 i2003_11_14_17_18_32242 a)) False) (Eq False True)) % 3.78/3.93 Clause #320 (by clausification #[312]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rrx4 a (skS.0 2 a a_1)) (cc2 (skS.0 2 a a_1))) True) % 3.78/3.93 Clause #321 (by clausification #[320]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cc2 (skS.0 2 a a_1)) True) % 3.78/3.93 Clause #322 (by clausification #[320]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rrx4 a (skS.0 2 a a_1)) True) % 3.78/3.93 Clause #323 (by superposition #[321, 35]): ∀ (a : Iota), Or (Eq (cc2 (skS.0 2 i2003_11_14_17_18_32242 a)) True) (Eq False True) % 3.78/3.93 Clause #324 (by clausification #[323]): ∀ (a : Iota), Eq (cc2 (skS.0 2 i2003_11_14_17_18_32242 a)) True % 3.78/3.93 Clause #325 (by superposition #[322, 35]): ∀ (a : Iota), Or (Eq (rrx4 i2003_11_14_17_18_32242 (skS.0 2 i2003_11_14_17_18_32242 a)) True) (Eq False True) % 3.78/3.93 Clause #326 (by clausification #[325]): ∀ (a : Iota), Eq (rrx4 i2003_11_14_17_18_32242 (skS.0 2 i2003_11_14_17_18_32242 a)) True % 3.78/3.93 Clause #328 (by superposition #[326, 107]): ∀ (a : Iota), Or (Eq True False) (Eq (rrx i2003_11_14_17_18_32242 (skS.0 2 i2003_11_14_17_18_32242 a)) True) % 3.78/3.93 Clause #331 (by clausification #[328]): ∀ (a : Iota), Eq (rrx i2003_11_14_17_18_32242 (skS.0 2 i2003_11_14_17_18_32242 a)) True % 3.78/3.93 Clause #338 (by clausification #[310]): ∀ (a a_1 : Iota), Or (Eq (rrx i2003_11_14_17_18_32242 a) False) (Eq (skS.0 1 i2003_11_14_17_18_32242 a_1) a) % 3.78/3.93 Clause #340 (by superposition #[338, 331]): ∀ (a a_1 : Iota), Or (Eq (skS.0 1 i2003_11_14_17_18_32242 a) (skS.0 2 i2003_11_14_17_18_32242 a_1)) (Eq False True) % 3.78/3.93 Clause #345 (by clausification #[340]): ∀ (a a_1 : Iota), Eq (skS.0 1 i2003_11_14_17_18_32242 a) (skS.0 2 i2003_11_14_17_18_32242 a_1) % 3.78/3.93 Clause #351 (by superposition #[345, 324]): ∀ (a : Iota), Eq (cc2 (skS.0 1 i2003_11_14_17_18_32242 a)) True % 3.78/3.93 Clause #366 (by clausification #[319]): ∀ (a : Iota), % 3.78/3.93 Or (Eq (rrx3 i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) False) % 3.78/3.93 (Eq (cc2 (skS.0 1 i2003_11_14_17_18_32242 a)) False) % 3.78/3.93 Clause #367 (by forward demodulation #[366, 351]): ∀ (a : Iota), Or (Eq (rrx3 i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) False) (Eq True False) % 3.78/3.93 Clause #368 (by clausification #[367]): ∀ (a : Iota), Eq (rrx3 i2003_11_14_17_18_32242 (skS.0 1 i2003_11_14_17_18_32242 a)) False % 3.78/3.93 Clause #369 (by superposition #[368, 302]): Eq False True % 3.78/3.93 Clause #370 (by clausification #[369]): False % 3.78/3.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------