%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS128+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 07:52:40 PM UTC 2025 % Result : Unsatisfiable 3.83s 3.99s % Output : Proof 3.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.12 % Problem : KRS128+1 : TPTP v9.2.0. Released v3.1.0. % 0.09/0.13 % Command : duper %s % 0.13/0.34 % Computer : n001.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 10:10:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.83/3.99 SZS status Theorem for theBenchmark.p % 3.83/3.99 SZS output start Proof for theBenchmark.p % 3.83/3.99 Clause #2 (by assumption #[]): Eq % 3.83/3.99 (∀ (X : Iota), % 3.83/3.99 Iff (cUnsatisfiable X) % 3.83/3.99 (And (And (Exists fun Y => And (rr X Y) (cexcomp Y)) (∀ (Y : Iota), rr X Y → cd Y)) % 3.83/3.99 (∀ (Y : Iota), rr X Y → ca_Cx4 Y))) % 3.83/3.99 True % 3.83/3.99 Clause #8 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Cx4 X) (Exists fun Y0 => ra_Px4 X Y0)) True % 3.83/3.99 Clause #9 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Cx4xcomp X) (Not (Exists fun Y => ra_Px4 X Y))) True % 3.83/3.99 Clause #10 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Cx4xcomp X) (And (cd X) (cexcomp X))) True % 3.83/3.99 Clause #11 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_22_31584) True % 3.83/3.99 Clause #25 (by clausification #[10]): ∀ (a : Iota), Eq (Iff (ca_Cx4xcomp a) (And (cd a) (cexcomp a))) True % 3.83/3.99 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (ca_Cx4xcomp a) True) (Eq (And (cd a) (cexcomp a)) False) % 3.83/3.99 Clause #28 (by clausification #[26]): ∀ (a : Iota), Or (Eq (ca_Cx4xcomp a) True) (Or (Eq (cd a) False) (Eq (cexcomp a) False)) % 3.83/3.99 Clause #31 (by betaEtaReduce #[8]): Eq (∀ (X : Iota), Iff (ca_Cx4 X) (Exists (ra_Px4 X))) True % 3.83/3.99 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (Iff (ca_Cx4 a) (Exists (ra_Px4 a))) True % 3.83/3.99 Clause #34 (by clausification #[32]): ∀ (a : Iota), Or (Eq (ca_Cx4 a) False) (Eq (Exists (ra_Px4 a)) True) % 3.83/3.99 Clause #36 (by clausification #[2]): ∀ (a : Iota), % 3.83/3.99 Eq % 3.83/3.99 (Iff (cUnsatisfiable a) % 3.83/3.99 (And (And (Exists fun Y => And (rr a Y) (cexcomp Y)) (∀ (Y : Iota), rr a Y → cd Y)) % 3.83/3.99 (∀ (Y : Iota), rr a Y → ca_Cx4 Y))) % 3.83/3.99 True % 3.83/3.99 Clause #38 (by clausification #[36]): ∀ (a : Iota), % 3.83/3.99 Or (Eq (cUnsatisfiable a) False) % 3.83/3.99 (Eq % 3.83/3.99 (And (And (Exists fun Y => And (rr a Y) (cexcomp Y)) (∀ (Y : Iota), rr a Y → cd Y)) % 3.83/3.99 (∀ (Y : Iota), rr a Y → ca_Cx4 Y)) % 3.83/3.99 True) % 3.83/3.99 Clause #51 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (ca_Cx4 a) False) (Eq (ra_Px4 a (skS.0 2 a a_1)) True) % 3.83/3.99 Clause #76 (by betaEtaReduce #[9]): Eq (∀ (X : Iota), Iff (ca_Cx4xcomp X) (Not (Exists (ra_Px4 X)))) True % 3.83/3.99 Clause #77 (by clausification #[76]): ∀ (a : Iota), Eq (Iff (ca_Cx4xcomp a) (Not (Exists (ra_Px4 a)))) True % 3.83/3.99 Clause #79 (by clausification #[77]): ∀ (a : Iota), Or (Eq (ca_Cx4xcomp a) False) (Eq (Not (Exists (ra_Px4 a))) True) % 3.83/3.99 Clause #98 (by clausification #[79]): ∀ (a : Iota), Or (Eq (ca_Cx4xcomp a) False) (Eq (Exists (ra_Px4 a)) False) % 3.83/3.99 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), Or (Eq (ca_Cx4xcomp a) False) (Eq (ra_Px4 a a_1) False) % 3.83/3.99 Clause #102 (by clausification #[38]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rr a Y → ca_Cx4 Y) True) % 3.83/3.99 Clause #103 (by clausification #[38]): ∀ (a : Iota), % 3.83/3.99 Or (Eq (cUnsatisfiable a) False) % 3.83/3.99 (Eq (And (Exists fun Y => And (rr a Y) (cexcomp Y)) (∀ (Y : Iota), rr a Y → cd Y)) True) % 3.83/3.99 Clause #104 (by clausification #[102]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a a_1 → ca_Cx4 a_1) True) % 3.83/3.99 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Eq (ca_Cx4 a_1) True)) % 3.83/3.99 Clause #106 (by superposition #[105, 11]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_31584 a) False) (Or (Eq (ca_Cx4 a) True) (Eq False True)) % 3.83/3.99 Clause #107 (by clausification #[106]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_31584 a) False) (Eq (ca_Cx4 a) True) % 3.83/3.99 Clause #120 (by clausification #[103]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rr a Y → cd Y) True) % 3.83/3.99 Clause #121 (by clausification #[103]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cexcomp Y)) True) % 3.83/3.99 Clause #122 (by clausification #[120]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a a_1 → cd a_1) True) % 3.83/3.99 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Eq (cd a_1) True)) % 3.83/3.99 Clause #124 (by superposition #[123, 11]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_31584 a) False) (Or (Eq (cd a) True) (Eq False True)) % 3.83/3.99 Clause #125 (by clausification #[124]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_31584 a) False) (Eq (cd a) True) % 3.83/4.01 Clause #126 (by clausification #[121]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 8 a a_1)) (cexcomp (skS.0 8 a a_1))) True) % 3.83/4.01 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cexcomp (skS.0 8 a a_1)) True) % 3.83/4.01 Clause #128 (by clausification #[126]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 8 a a_1)) True) % 3.83/4.01 Clause #129 (by superposition #[127, 11]): ∀ (a : Iota), Or (Eq (cexcomp (skS.0 8 i2003_11_14_17_22_31584 a)) True) (Eq False True) % 3.83/4.01 Clause #130 (by clausification #[129]): ∀ (a : Iota), Eq (cexcomp (skS.0 8 i2003_11_14_17_22_31584 a)) True % 3.83/4.01 Clause #132 (by superposition #[128, 11]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_31584 (skS.0 8 i2003_11_14_17_22_31584 a)) True) (Eq False True) % 3.83/4.01 Clause #133 (by clausification #[132]): ∀ (a : Iota), Eq (rr i2003_11_14_17_22_31584 (skS.0 8 i2003_11_14_17_22_31584 a)) True % 3.83/4.01 Clause #134 (by superposition #[133, 107]): ∀ (a : Iota), Or (Eq True False) (Eq (ca_Cx4 (skS.0 8 i2003_11_14_17_22_31584 a)) True) % 3.83/4.01 Clause #135 (by superposition #[133, 125]): ∀ (a : Iota), Or (Eq True False) (Eq (cd (skS.0 8 i2003_11_14_17_22_31584 a)) True) % 3.83/4.01 Clause #139 (by clausification #[135]): ∀ (a : Iota), Eq (cd (skS.0 8 i2003_11_14_17_22_31584 a)) True % 3.83/4.01 Clause #140 (by superposition #[139, 28]): ∀ (a : Iota), % 3.83/4.01 Or (Eq (ca_Cx4xcomp (skS.0 8 i2003_11_14_17_22_31584 a)) True) % 3.83/4.01 (Or (Eq True False) (Eq (cexcomp (skS.0 8 i2003_11_14_17_22_31584 a)) False)) % 3.83/4.01 Clause #142 (by clausification #[134]): ∀ (a : Iota), Eq (ca_Cx4 (skS.0 8 i2003_11_14_17_22_31584 a)) True % 3.83/4.01 Clause #143 (by superposition #[142, 51]): ∀ (a a_1 : Iota), % 3.83/4.01 Or (Eq True False) % 3.83/4.01 (Eq (ra_Px4 (skS.0 8 i2003_11_14_17_22_31584 a) (skS.0 2 (skS.0 8 i2003_11_14_17_22_31584 a) a_1)) True) % 3.83/4.01 Clause #145 (by clausification #[140]): ∀ (a : Iota), % 3.83/4.01 Or (Eq (ca_Cx4xcomp (skS.0 8 i2003_11_14_17_22_31584 a)) True) % 3.83/4.01 (Eq (cexcomp (skS.0 8 i2003_11_14_17_22_31584 a)) False) % 3.83/4.01 Clause #146 (by forward demodulation #[145, 130]): ∀ (a : Iota), Or (Eq (ca_Cx4xcomp (skS.0 8 i2003_11_14_17_22_31584 a)) True) (Eq True False) % 3.83/4.01 Clause #147 (by clausification #[146]): ∀ (a : Iota), Eq (ca_Cx4xcomp (skS.0 8 i2003_11_14_17_22_31584 a)) True % 3.83/4.01 Clause #149 (by superposition #[147, 99]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px4 (skS.0 8 i2003_11_14_17_22_31584 a) a_1) False) % 3.83/4.01 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (ra_Px4 (skS.0 8 i2003_11_14_17_22_31584 a) a_1) False % 3.83/4.01 Clause #155 (by clausification #[143]): ∀ (a a_1 : Iota), Eq (ra_Px4 (skS.0 8 i2003_11_14_17_22_31584 a) (skS.0 2 (skS.0 8 i2003_11_14_17_22_31584 a) a_1)) True % 3.83/4.01 Clause #156 (by superposition #[155, 150]): Eq True False % 3.83/4.01 Clause #158 (by clausification #[156]): False % 3.83/4.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------