%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS101+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 4.18s 4.36s % Output : Proof 4.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : KRS101+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.14 % Command : duper %s % 0.14/0.36 % Computer : n010.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 10:21:53 EDT 2025 % 0.14/0.36 % CPUTime : % 4.18/4.36 SZS status Theorem for theBenchmark.p % 4.18/4.36 SZS output start Proof for theBenchmark.p % 4.18/4.36 Clause #13 (by assumption #[]): Eq % 4.18/4.36 (∀ (X : Iota), % 4.18/4.36 Iff (cUnsatisfiable X) % 4.18/4.36 (And % 4.18/4.36 (And (∀ (Y : Iota), rr X Y → cd Y) % 4.18/4.36 (∀ (Y : Iota), % 4.18/4.36 rr X Y → Or (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs Y Z0) (rs Y Z1)) (Ne Z0 Z1))) (cc Y))) % 4.18/4.36 (Exists fun Y => And (rr X Y) (Not (∀ (Z0 Z1 : Iota), And (rs Y Z0) (rs Y Z1) → Eq Z0 Z1))))) % 4.18/4.36 True % 4.18/4.36 Clause #14 (by assumption #[]): Eq (∀ (X : Iota), cc X → Not (cd X)) True % 4.18/4.36 Clause #15 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_20_36582) True % 4.18/4.36 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (cc a → Not (cd a)) True % 4.18/4.36 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (Not (cd a)) True) % 4.18/4.36 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (cd a) False) % 4.18/4.36 Clause #96 (by clausification #[13]): ∀ (a : Iota), % 4.18/4.36 Eq % 4.18/4.36 (Iff (cUnsatisfiable a) % 4.18/4.36 (And % 4.18/4.36 (And (∀ (Y : Iota), rr a Y → cd Y) % 4.18/4.36 (∀ (Y : Iota), % 4.18/4.36 rr a Y → Or (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs Y Z0) (rs Y Z1)) (Ne Z0 Z1))) (cc Y))) % 4.18/4.36 (Exists fun Y => And (rr a Y) (Not (∀ (Z0 Z1 : Iota), And (rs Y Z0) (rs Y Z1) → Eq Z0 Z1))))) % 4.18/4.36 True % 4.18/4.36 Clause #98 (by clausification #[96]): ∀ (a : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq % 4.18/4.36 (And % 4.18/4.36 (And (∀ (Y : Iota), rr a Y → cd Y) % 4.18/4.36 (∀ (Y : Iota), % 4.18/4.36 rr a Y → Or (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs Y Z0) (rs Y Z1)) (Ne Z0 Z1))) (cc Y))) % 4.18/4.36 (Exists fun Y => And (rr a Y) (Not (∀ (Z0 Z1 : Iota), And (rs Y Z0) (rs Y Z1) → Eq Z0 Z1)))) % 4.18/4.36 True) % 4.18/4.36 Clause #117 (by clausification #[98]): ∀ (a : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq (Exists fun Y => And (rr a Y) (Not (∀ (Z0 Z1 : Iota), And (rs Y Z0) (rs Y Z1) → Eq Z0 Z1))) True) % 4.18/4.36 Clause #118 (by clausification #[98]): ∀ (a : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq % 4.18/4.36 (And (∀ (Y : Iota), rr a Y → cd Y) % 4.18/4.36 (∀ (Y : Iota), % 4.18/4.36 rr a Y → Or (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs Y Z0) (rs Y Z1)) (Ne Z0 Z1))) (cc Y))) % 4.18/4.36 True) % 4.18/4.36 Clause #119 (by clausification #[117]): ∀ (a a_1 : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq % 4.18/4.36 (And (rr a (skS.0 2 a a_1)) % 4.18/4.36 (Not (∀ (Z0 Z1 : Iota), And (rs (skS.0 2 a a_1) Z0) (rs (skS.0 2 a a_1) Z1) → Eq Z0 Z1))) % 4.18/4.36 True) % 4.18/4.36 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq (Not (∀ (Z0 Z1 : Iota), And (rs (skS.0 2 a a_1) Z0) (rs (skS.0 2 a a_1) Z1) → Eq Z0 Z1)) True) % 4.18/4.36 Clause #121 (by clausification #[119]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 2 a a_1)) True) % 4.18/4.36 Clause #122 (by clausification #[120]): ∀ (a a_1 : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq (∀ (Z0 Z1 : Iota), And (rs (skS.0 2 a a_1) Z0) (rs (skS.0 2 a a_1) Z1) → Eq Z0 Z1) False) % 4.18/4.36 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq % 4.18/4.36 (Not % 4.18/4.36 (∀ (Z1 : Iota), % 4.18/4.36 And (rs (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) (rs (skS.0 2 a a_1) Z1) → Eq (skS.0 3 a a_1 a_2) Z1)) % 4.18/4.36 True) % 4.18/4.36 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq % 4.18/4.36 (∀ (Z1 : Iota), And (rs (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) (rs (skS.0 2 a a_1) Z1) → Eq (skS.0 3 a a_1 a_2) Z1) % 4.18/4.36 False) % 4.18/4.36 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq % 4.18/4.36 (Not % 4.18/4.36 (And (rs (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) (rs (skS.0 2 a a_1) (skS.0 4 a a_1 a_2 a_3)) → % 4.18/4.36 Eq (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3))) % 4.18/4.36 True) % 4.18/4.36 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.36 Or (Eq (cUnsatisfiable a) False) % 4.18/4.36 (Eq % 4.18/4.36 (And (rs (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) (rs (skS.0 2 a a_1) (skS.0 4 a a_1 a_2 a_3)) → % 4.18/4.36 Eq (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) % 4.18/4.36 False) % 4.18/4.36 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Eq (And (rs (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) (rs (skS.0 2 a a_1) (skS.0 4 a a_1 a_2 a_3))) True) % 4.18/4.38 Clause #128 (by clausification #[126]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Eq (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) False) % 4.18/4.38 Clause #129 (by clausification #[127]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs (skS.0 2 a a_1) (skS.0 4 a a_1 a_2 a_3)) True) % 4.18/4.38 Clause #130 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) True) % 4.18/4.38 Clause #131 (by superposition #[129, 15]): ∀ (a a_1 a_2 : Iota), % 4.18/4.38 Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) (skS.0 4 i2003_11_14_17_20_36582 a a_1 a_2)) True) (Eq False True) % 4.18/4.38 Clause #132 (by superposition #[121, 15]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_36582 (skS.0 2 i2003_11_14_17_20_36582 a)) True) (Eq False True) % 4.18/4.38 Clause #133 (by clausification #[132]): ∀ (a : Iota), Eq (rr i2003_11_14_17_20_36582 (skS.0 2 i2003_11_14_17_20_36582 a)) True % 4.18/4.38 Clause #135 (by superposition #[130, 15]): ∀ (a a_1 : Iota), % 4.18/4.38 Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) (skS.0 3 i2003_11_14_17_20_36582 a a_1)) True) (Eq False True) % 4.18/4.38 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) (skS.0 3 i2003_11_14_17_20_36582 a a_1)) True % 4.18/4.38 Clause #145 (by clausification #[131]): ∀ (a a_1 a_2 : Iota), Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) (skS.0 4 i2003_11_14_17_20_36582 a a_1 a_2)) True % 4.18/4.38 Clause #146 (by clausification #[128]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cUnsatisfiable a) False) (Ne (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) % 4.18/4.38 Clause #147 (by superposition #[146, 15]): ∀ (a a_1 a_2 : Iota), % 4.18/4.38 Or (Ne (skS.0 3 i2003_11_14_17_20_36582 a a_1) (skS.0 4 i2003_11_14_17_20_36582 a a_1 a_2)) (Eq False True) % 4.18/4.38 Clause #148 (by clausification #[147]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 3 i2003_11_14_17_20_36582 a a_1) (skS.0 4 i2003_11_14_17_20_36582 a a_1 a_2) % 4.18/4.38 Clause #149 (by clausification #[118]): ∀ (a : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Eq % 4.18/4.38 (∀ (Y : Iota), % 4.18/4.38 rr a Y → Or (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs Y Z0) (rs Y Z1)) (Ne Z0 Z1))) (cc Y)) % 4.18/4.38 True) % 4.18/4.38 Clause #150 (by clausification #[118]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rr a Y → cd Y) True) % 4.18/4.38 Clause #151 (by clausification #[149]): ∀ (a a_1 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Eq (rr a a_1 → Or (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs a_1 Z0) (rs a_1 Z1)) (Ne Z0 Z1))) (cc a_1)) % 4.18/4.38 True) % 4.18/4.38 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Or (Eq (rr a a_1) False) % 4.18/4.38 (Eq (Or (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs a_1 Z0) (rs a_1 Z1)) (Ne Z0 Z1))) (cc a_1)) True)) % 4.18/4.38 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Or (Eq (rr a a_1) False) % 4.18/4.38 (Or (Eq (Not (Exists fun Z0 => Exists fun Z1 => And (And (rs a_1 Z0) (rs a_1 Z1)) (Ne Z0 Z1))) True) % 4.18/4.38 (Eq (cc a_1) True))) % 4.18/4.38 Clause #154 (by clausification #[153]): ∀ (a a_1 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Or (Eq (rr a a_1) False) % 4.18/4.38 (Or (Eq (cc a_1) True) % 4.18/4.38 (Eq (Exists fun Z0 => Exists fun Z1 => And (And (rs a_1 Z0) (rs a_1 Z1)) (Ne Z0 Z1)) False))) % 4.18/4.38 Clause #155 (by clausification #[154]): ∀ (a a_1 a_2 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Or (Eq (rr a a_1) False) % 4.18/4.38 (Or (Eq (cc a_1) True) (Eq (Exists fun Z1 => And (And (rs a_1 a_2) (rs a_1 Z1)) (Ne a_2 Z1)) False))) % 4.18/4.38 Clause #156 (by clausification #[155]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Or (Eq (rr a a_1) False) (Or (Eq (cc a_1) True) (Eq (And (And (rs a_1 a_2) (rs a_1 a_3)) (Ne a_2 a_3)) False))) % 4.18/4.38 Clause #157 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.38 Or (Eq (cUnsatisfiable a) False) % 4.18/4.38 (Or (Eq (rr a a_1) False) % 4.18/4.38 (Or (Eq (cc a_1) True) (Or (Eq (And (rs a_1 a_2) (rs a_1 a_3)) False) (Eq (Ne a_2 a_3) False)))) % 4.18/4.41 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.41 Or (Eq (cUnsatisfiable a) False) % 4.18/4.41 (Or (Eq (rr a a_1) False) % 4.18/4.41 (Or (Eq (cc a_1) True) (Or (Eq (Ne a_2 a_3) False) (Or (Eq (rs a_1 a_2) False) (Eq (rs a_1 a_3) False))))) % 4.18/4.41 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.41 Or (Eq (cUnsatisfiable a) False) % 4.18/4.41 (Or (Eq (rr a a_1) False) % 4.18/4.41 (Or (Eq (cc a_1) True) (Or (Eq (rs a_1 a_2) False) (Or (Eq (rs a_1 a_3) False) (Eq a_2 a_3))))) % 4.18/4.41 Clause #160 (by superposition #[159, 15]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (rr i2003_11_14_17_20_36582 a) False) % 4.18/4.41 (Or (Eq (cc a) True) (Or (Eq (rs a a_1) False) (Or (Eq (rs a a_2) False) (Or (Eq a_1 a_2) (Eq False True))))) % 4.18/4.41 Clause #161 (by clausification #[150]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a a_1 → cd a_1) True) % 4.18/4.41 Clause #162 (by clausification #[161]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Eq (cd a_1) True)) % 4.18/4.41 Clause #163 (by superposition #[162, 15]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_36582 a) False) (Or (Eq (cd a) True) (Eq False True)) % 4.18/4.41 Clause #172 (by clausification #[163]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_36582 a) False) (Eq (cd a) True) % 4.18/4.41 Clause #173 (by superposition #[172, 133]): ∀ (a : Iota), Or (Eq (cd (skS.0 2 i2003_11_14_17_20_36582 a)) True) (Eq False True) % 4.18/4.41 Clause #174 (by clausification #[173]): ∀ (a : Iota), Eq (cd (skS.0 2 i2003_11_14_17_20_36582 a)) True % 4.18/4.41 Clause #175 (by clausification #[160]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (rr i2003_11_14_17_20_36582 a) False) % 4.18/4.41 (Or (Eq (cc a) True) (Or (Eq (rs a a_1) False) (Or (Eq (rs a a_2) False) (Eq a_1 a_2)))) % 4.18/4.41 Clause #176 (by superposition #[175, 133]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) a_1) False) % 4.18/4.41 (Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) a_2) False) (Or (Eq a_1 a_2) (Eq False True)))) % 4.18/4.41 Clause #177 (by clausification #[176]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) a_1) False) % 4.18/4.41 (Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) a_2) False) (Eq a_1 a_2))) % 4.18/4.41 Clause #178 (by superposition #[177, 136]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) a_1) False) % 4.18/4.41 (Or (Eq (skS.0 3 i2003_11_14_17_20_36582 a a_2) a_1) (Eq False True))) % 4.18/4.41 Clause #180 (by clausification #[178]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Or (Eq (rs (skS.0 2 i2003_11_14_17_20_36582 a) a_1) False) (Eq (skS.0 3 i2003_11_14_17_20_36582 a a_2) a_1)) % 4.18/4.41 Clause #181 (by superposition #[180, 136]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Or (Eq (skS.0 3 i2003_11_14_17_20_36582 a a_1) (skS.0 3 i2003_11_14_17_20_36582 a a_2)) (Eq False True)) % 4.18/4.41 Clause #182 (by superposition #[180, 145]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Or (Eq (skS.0 3 i2003_11_14_17_20_36582 a a_1) (skS.0 4 i2003_11_14_17_20_36582 a a_2 a_3)) (Eq False True)) % 4.18/4.41 Clause #185 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Eq (skS.0 3 i2003_11_14_17_20_36582 a a_1) (skS.0 3 i2003_11_14_17_20_36582 a a_2)) % 4.18/4.41 Clause #188 (by clausification #[182]): ∀ (a a_1 a_2 a_3 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Eq (skS.0 3 i2003_11_14_17_20_36582 a a_1) (skS.0 4 i2003_11_14_17_20_36582 a a_2 a_3)) % 4.18/4.41 Clause #193 (by superposition #[188, 148]): ∀ (a a_1 a_2 : Iota), % 4.18/4.41 Or (Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True) % 4.18/4.41 (Ne (skS.0 3 i2003_11_14_17_20_36582 a a_1) (skS.0 3 i2003_11_14_17_20_36582 a a_2)) % 4.18/4.41 Clause #194 (by forward contextual literal cutting #[193, 185]): ∀ (a : Iota), Eq (cc (skS.0 2 i2003_11_14_17_20_36582 a)) True % 4.18/4.41 Clause #199 (by superposition #[194, 18]): ∀ (a : Iota), Or (Eq True False) (Eq (cd (skS.0 2 i2003_11_14_17_20_36582 a)) False) % 4.18/4.41 Clause #200 (by clausification #[199]): ∀ (a : Iota), Eq (cd (skS.0 2 i2003_11_14_17_20_36582 a)) False % 4.18/4.41 Clause #201 (by superposition #[200, 174]): Eq False True % 4.18/4.41 Clause #210 (by clausification #[201]): False % 4.18/4.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------