%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS096+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 3.69s 3.90s % Output : Proof 3.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.13 % Problem : KRS096+1 : TPTP v9.2.0. Released v3.1.0. % 0.10/0.15 % Command : duper %s % 0.12/0.37 % Computer : n017.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8042.1875MB % 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Thu Oct 2 10:19:38 EDT 2025 % 0.12/0.37 % CPUTime : % 3.69/3.90 SZS status Theorem for theBenchmark.p % 3.69/3.90 SZS output start Proof for theBenchmark.p % 3.69/3.90 Clause #11 (by assumption #[]): Eq % 3.69/3.90 (∀ (X : Iota), % 3.69/3.90 Iff (cUnsatisfiable X) % 3.69/3.90 (And (And (Exists fun Y => And (rr X Y) (cc Y)) (Exists fun Y => And (rr X Y) (cd Y))) % 3.69/3.90 (∀ (Y0 Y1 : Iota), And (rr X Y0) (rr X Y1) → Eq Y0 Y1))) % 3.69/3.90 True % 3.69/3.90 Clause #12 (by assumption #[]): Eq (∀ (X : Iota), cc X → Not (cd X)) True % 3.69/3.90 Clause #13 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_20_18265) True % 3.69/3.90 Clause #14 (by clausification #[12]): ∀ (a : Iota), Eq (cc a → Not (cd a)) True % 3.69/3.90 Clause #15 (by clausification #[14]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (Not (cd a)) True) % 3.69/3.90 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (cd a) False) % 3.69/3.90 Clause #81 (by clausification #[11]): ∀ (a : Iota), % 3.69/3.90 Eq % 3.69/3.90 (Iff (cUnsatisfiable a) % 3.69/3.90 (And (And (Exists fun Y => And (rr a Y) (cc Y)) (Exists fun Y => And (rr a Y) (cd Y))) % 3.69/3.90 (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1))) % 3.69/3.90 True % 3.69/3.90 Clause #83 (by clausification #[81]): ∀ (a : Iota), % 3.69/3.90 Or (Eq (cUnsatisfiable a) False) % 3.69/3.90 (Eq % 3.69/3.90 (And (And (Exists fun Y => And (rr a Y) (cc Y)) (Exists fun Y => And (rr a Y) (cd Y))) % 3.69/3.90 (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1)) % 3.69/3.90 True) % 3.69/3.90 Clause #98 (by clausification #[83]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y0 Y1 : Iota), And (rr a Y0) (rr a Y1) → Eq Y0 Y1) True) % 3.69/3.90 Clause #99 (by clausification #[83]): ∀ (a : Iota), % 3.69/3.90 Or (Eq (cUnsatisfiable a) False) % 3.69/3.90 (Eq (And (Exists fun Y => And (rr a Y) (cc Y)) (Exists fun Y => And (rr a Y) (cd Y))) True) % 3.69/3.90 Clause #100 (by clausification #[98]): ∀ (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) % 3.69/3.90 Clause #101 (by clausification #[100]): ∀ (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) % 3.69/3.90 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 3.69/3.90 Or (Eq (cUnsatisfiable a) False) (Or (Eq (And (rr a a_1) (rr a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.69/3.90 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 3.69/3.90 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))) % 3.69/3.90 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 3.69/3.90 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (rr a a_2) False) (Eq a_1 a_2))) % 3.69/3.90 Clause #105 (by superposition #[104, 13]): ∀ (a a_1 : Iota), % 3.69/3.90 Or (Eq (rr i2003_11_14_17_20_18265 a) False) % 3.69/3.90 (Or (Eq (rr i2003_11_14_17_20_18265 a_1) False) (Or (Eq a a_1) (Eq False True))) % 3.69/3.90 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), % 3.69/3.90 Or (Eq (rr i2003_11_14_17_20_18265 a) False) (Or (Eq (rr i2003_11_14_17_20_18265 a_1) False) (Eq a a_1)) % 3.69/3.90 Clause #107 (by clausification #[99]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cd Y)) True) % 3.69/3.90 Clause #108 (by clausification #[99]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cc Y)) True) % 3.69/3.90 Clause #109 (by clausification #[107]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 2 a a_1)) (cd (skS.0 2 a a_1))) True) % 3.69/3.90 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd (skS.0 2 a a_1)) True) % 3.69/3.90 Clause #111 (by clausification #[109]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 2 a a_1)) True) % 3.69/3.90 Clause #112 (by superposition #[110, 13]): ∀ (a : Iota), Or (Eq (cd (skS.0 2 i2003_11_14_17_20_18265 a)) True) (Eq False True) % 3.69/3.90 Clause #113 (by clausification #[112]): ∀ (a : Iota), Eq (cd (skS.0 2 i2003_11_14_17_20_18265 a)) True % 3.69/3.90 Clause #114 (by clausification #[108]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 3 a a_1)) (cc (skS.0 3 a a_1))) True) % 3.69/3.90 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cc (skS.0 3 a a_1)) True) % 3.69/3.90 Clause #116 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 3 a a_1)) True) % 3.69/3.91 Clause #117 (by superposition #[115, 13]): ∀ (a : Iota), Or (Eq (cc (skS.0 3 i2003_11_14_17_20_18265 a)) True) (Eq False True) % 3.69/3.91 Clause #118 (by clausification #[117]): ∀ (a : Iota), Eq (cc (skS.0 3 i2003_11_14_17_20_18265 a)) True % 3.69/3.91 Clause #119 (by superposition #[118, 16]): ∀ (a : Iota), Or (Eq True False) (Eq (cd (skS.0 3 i2003_11_14_17_20_18265 a)) False) % 3.69/3.91 Clause #121 (by clausification #[119]): ∀ (a : Iota), Eq (cd (skS.0 3 i2003_11_14_17_20_18265 a)) False % 3.69/3.91 Clause #122 (by superposition #[116, 13]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_18265 (skS.0 3 i2003_11_14_17_20_18265 a)) True) (Eq False True) % 3.69/3.91 Clause #123 (by clausification #[122]): ∀ (a : Iota), Eq (rr i2003_11_14_17_20_18265 (skS.0 3 i2003_11_14_17_20_18265 a)) True % 3.69/3.91 Clause #128 (by superposition #[111, 13]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_18265 (skS.0 2 i2003_11_14_17_20_18265 a)) True) (Eq False True) % 3.69/3.91 Clause #129 (by clausification #[128]): ∀ (a : Iota), Eq (rr i2003_11_14_17_20_18265 (skS.0 2 i2003_11_14_17_20_18265 a)) True % 3.69/3.91 Clause #130 (by superposition #[129, 106]): ∀ (a a_1 : Iota), % 3.69/3.91 Or (Eq True False) (Or (Eq (rr i2003_11_14_17_20_18265 a) False) (Eq (skS.0 2 i2003_11_14_17_20_18265 a_1) a)) % 3.69/3.91 Clause #137 (by clausification #[130]): ∀ (a a_1 : Iota), Or (Eq (rr i2003_11_14_17_20_18265 a) False) (Eq (skS.0 2 i2003_11_14_17_20_18265 a_1) a) % 3.69/3.91 Clause #138 (by superposition #[137, 123]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 i2003_11_14_17_20_18265 a) (skS.0 3 i2003_11_14_17_20_18265 a_1)) (Eq False True) % 3.69/3.91 Clause #141 (by clausification #[138]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_20_18265 a) (skS.0 3 i2003_11_14_17_20_18265 a_1) % 3.69/3.91 Clause #144 (by superposition #[141, 121]): ∀ (a : Iota), Eq (cd (skS.0 2 i2003_11_14_17_20_18265 a)) False % 3.69/3.91 Clause #147 (by superposition #[144, 113]): Eq False True % 3.69/3.91 Clause #148 (by clausification #[147]): False % 3.69/3.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------