%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS095+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 07:52:37 PM UTC 2025 % Result : Unsatisfiable 3.62s 3.80s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : KRS095+1 : TPTP v9.2.0. Released v3.1.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 10:21:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.62/3.80 SZS status Theorem for theBenchmark.p % 3.62/3.80 SZS output start Proof for theBenchmark.p % 3.62/3.80 Clause #11 (by assumption #[]): Eq % 3.62/3.80 (∀ (X : Iota), % 3.62/3.80 Iff (cUnsatisfiable X) % 3.62/3.80 (And (Exists fun Y0 => Exists fun Y1 => And (And (rr X Y0) (rr X Y1)) (Ne Y0 Y1)) % 3.62/3.80 (∀ (Y0 Y1 : Iota), And (rr X Y0) (rr X Y1) → Eq Y0 Y1))) % 3.62/3.80 True % 3.62/3.80 Clause #13 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_20_14253) True % 3.62/3.80 Clause #83 (by clausification #[11]): ∀ (a : Iota), % 3.62/3.80 Eq % 3.62/3.80 (Iff (cUnsatisfiable a) % 3.62/3.80 (And (Exists fun Y0 => Exists fun Y1 => And (And (rr a Y0) (rr a Y1)) (Ne Y0 Y1)) % 3.62/3.80 (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1))) % 3.62/3.80 True % 3.62/3.80 Clause #85 (by clausification #[83]): ∀ (a : Iota), % 3.62/3.80 Or (Eq (cUnsatisfiable a) False) % 3.62/3.80 (Eq % 3.62/3.80 (And (Exists fun Y0 => Exists fun Y1 => And (And (rr a Y0) (rr a Y1)) (Ne Y0 Y1)) % 3.62/3.80 (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1)) % 3.62/3.80 True) % 3.62/3.80 Clause #100 (by clausification #[85]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) True) % 3.62/3.80 Clause #101 (by clausification #[85]): ∀ (a : Iota), % 3.62/3.80 Or (Eq (cUnsatisfiable a) False) % 3.62/3.80 (Eq (Exists fun Y0 => Exists fun Y1 => And (And (rr a Y0) (rr a Y1)) (Ne Y0 Y1)) True) % 3.62/3.80 Clause #102 (by clausification #[100]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y1 : Iota), And (rr a a_1) (rr a Y1) → Eq a_1 Y1) True) % 3.62/3.80 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a a_1) (rr a a_2) → Eq a_1 a_2) True) % 3.62/3.80 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 3.62/3.80 Or (Eq (cUnsatisfiable a) False) (Or (Eq (And (rr a a_1) (rr a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.62/3.80 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 3.62/3.80 Or (Eq (cUnsatisfiable a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rr a a_1) False) (Eq (rr a a_2) False))) % 3.62/3.80 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 3.62/3.80 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (rr a a_2) False) (Eq a_1 a_2))) % 3.62/3.80 Clause #107 (by superposition #[106, 13]): ∀ (a a_1 : Iota), % 3.62/3.80 Or (Eq (rr i2003_11_14_17_20_14253 a) False) % 3.62/3.80 (Or (Eq (rr i2003_11_14_17_20_14253 a_1) False) (Or (Eq a a_1) (Eq False True))) % 3.62/3.80 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), % 3.62/3.80 Or (Eq (rr i2003_11_14_17_20_14253 a) False) (Or (Eq (rr i2003_11_14_17_20_14253 a_1) False) (Eq a a_1)) % 3.62/3.80 Clause #109 (by clausification #[101]): ∀ (a a_1 : Iota), % 3.62/3.80 Or (Eq (cUnsatisfiable a) False) % 3.62/3.80 (Eq (Exists fun Y1 => And (And (rr a (skS.0 2 a a_1)) (rr a Y1)) (Ne (skS.0 2 a a_1) Y1)) True) % 3.62/3.80 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), % 3.62/3.80 Or (Eq (cUnsatisfiable a) False) % 3.62/3.80 (Eq (And (And (rr a (skS.0 2 a a_1)) (rr a (skS.0 3 a a_1 a_2))) (Ne (skS.0 2 a a_1) (skS.0 3 a a_1 a_2))) True) % 3.62/3.80 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Ne (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) True) % 3.62/3.80 Clause #112 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 2 a a_1)) (rr a (skS.0 3 a a_1 a_2))) True) % 3.62/3.80 Clause #113 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Ne (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) % 3.62/3.80 Clause #114 (by superposition #[113, 13]): ∀ (a a_1 : Iota), Or (Ne (skS.0 2 i2003_11_14_17_20_14253 a) (skS.0 3 i2003_11_14_17_20_14253 a a_1)) (Eq False True) % 3.62/3.80 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Ne (skS.0 2 i2003_11_14_17_20_14253 a) (skS.0 3 i2003_11_14_17_20_14253 a a_1) % 3.62/3.80 Clause #116 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 3 a a_1 a_2)) True) % 3.62/3.80 Clause #117 (by clausification #[112]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 2 a a_1)) True) % 3.62/3.80 Clause #118 (by superposition #[116, 13]): ∀ (a a_1 : Iota), Or (Eq (rr i2003_11_14_17_20_14253 (skS.0 3 i2003_11_14_17_20_14253 a a_1)) True) (Eq False True) % 3.62/3.80 Clause #120 (by superposition #[117, 13]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_14253 (skS.0 2 i2003_11_14_17_20_14253 a)) True) (Eq False True) % 3.62/3.81 Clause #121 (by clausification #[120]): ∀ (a : Iota), Eq (rr i2003_11_14_17_20_14253 (skS.0 2 i2003_11_14_17_20_14253 a)) True % 3.62/3.81 Clause #122 (by superposition #[121, 108]): ∀ (a a_1 : Iota), % 3.62/3.81 Or (Eq True False) (Or (Eq (rr i2003_11_14_17_20_14253 a) False) (Eq (skS.0 2 i2003_11_14_17_20_14253 a_1) a)) % 3.62/3.81 Clause #126 (by clausification #[118]): ∀ (a a_1 : Iota), Eq (rr i2003_11_14_17_20_14253 (skS.0 3 i2003_11_14_17_20_14253 a a_1)) True % 3.62/3.81 Clause #131 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (rr i2003_11_14_17_20_14253 a) False) (Eq (skS.0 2 i2003_11_14_17_20_14253 a_1) a) % 3.62/3.81 Clause #133 (by superposition #[131, 126]): ∀ (a a_1 a_2 : Iota), % 3.62/3.81 Or (Eq (skS.0 2 i2003_11_14_17_20_14253 a) (skS.0 3 i2003_11_14_17_20_14253 a_1 a_2)) (Eq False True) % 3.62/3.81 Clause #140 (by clausification #[133]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 i2003_11_14_17_20_14253 a) (skS.0 3 i2003_11_14_17_20_14253 a_1 a_2) % 3.62/3.81 Clause #141 (by backward contextual literal cutting #[140, 115]): False % 3.62/3.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------