%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS124+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 3.71s 3.90s % Output : Proof 3.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS124+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 10:10:23 EDT 2025 % 0.14/0.34 % CPUTime : % 3.71/3.90 SZS status Theorem for theBenchmark.p % 3.71/3.90 SZS output start Proof for theBenchmark.p % 3.71/3.90 Clause #2 (by assumption #[]): Eq % 3.71/3.90 (∀ (X : Iota), % 3.71/3.90 Iff (cUnsatisfiable X) (And (Exists fun Y => And (rr X Y) (cowlThing Y)) (∀ (Y : Iota), rr X Y → ca_Ax3 Y))) % 3.71/3.90 True % 3.71/3.90 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), cc X → cdxcomp X) True % 3.71/3.90 Clause #6 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.71/3.90 Clause #7 (by assumption #[]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.71/3.90 Clause #12 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax3 X) (And (cd X) (cc X))) True % 3.71/3.90 Clause #13 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_22_10903) True % 3.71/3.90 Clause #26 (by clausification #[3]): ∀ (a : Iota), Eq (cc a → cdxcomp a) True % 3.71/3.90 Clause #27 (by clausification #[26]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (cdxcomp a) True) % 3.71/3.90 Clause #35 (by clausification #[2]): ∀ (a : Iota), % 3.71/3.90 Eq (Iff (cUnsatisfiable a) (And (Exists fun Y => And (rr a Y) (cowlThing Y)) (∀ (Y : Iota), rr a Y → ca_Ax3 Y))) True % 3.71/3.90 Clause #37 (by clausification #[35]): ∀ (a : Iota), % 3.71/3.90 Or (Eq (cUnsatisfiable a) False) % 3.71/3.90 (Eq (And (Exists fun Y => And (rr a Y) (cowlThing Y)) (∀ (Y : Iota), rr a Y → ca_Ax3 Y)) True) % 3.71/3.90 Clause #47 (by clausification #[12]): ∀ (a : Iota), Eq (Iff (ca_Ax3 a) (And (cd a) (cc a))) True % 3.71/3.90 Clause #49 (by clausification #[47]): ∀ (a : Iota), Or (Eq (ca_Ax3 a) False) (Eq (And (cd a) (cc a)) True) % 3.71/3.90 Clause #51 (by clausification #[49]): ∀ (a : Iota), Or (Eq (ca_Ax3 a) False) (Eq (cc a) True) % 3.71/3.90 Clause #52 (by clausification #[49]): ∀ (a : Iota), Or (Eq (ca_Ax3 a) False) (Eq (cd a) True) % 3.71/3.90 Clause #53 (by betaEtaReduce #[7]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists (ra_Px1 X))) True % 3.71/3.90 Clause #54 (by clausification #[53]): ∀ (a : Iota), Eq (Iff (cdxcomp a) (Exists (ra_Px1 a))) True % 3.71/3.90 Clause #56 (by clausification #[54]): ∀ (a : Iota), Or (Eq (cdxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.71/3.90 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (cdxcomp a) False) (Eq (ra_Px1 a (skS.0 1 a a_1)) True) % 3.71/3.90 Clause #59 (by betaEtaReduce #[6]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists (ra_Px1 X)))) True % 3.71/3.90 Clause #60 (by clausification #[59]): ∀ (a : Iota), Eq (Iff (cd a) (Not (Exists (ra_Px1 a)))) True % 3.71/3.90 Clause #62 (by clausification #[60]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.71/3.90 Clause #68 (by clausification #[62]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists (ra_Px1 a)) False) % 3.71/3.90 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (ra_Px1 a a_1) False) % 3.71/3.90 Clause #83 (by clausification #[37]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rr a Y → ca_Ax3 Y) True) % 3.71/3.90 Clause #84 (by clausification #[37]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cowlThing Y)) True) % 3.71/3.90 Clause #85 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a a_1 → ca_Ax3 a_1) True) % 3.71/3.90 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Eq (ca_Ax3 a_1) True)) % 3.71/3.90 Clause #87 (by superposition #[86, 13]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_10903 a) False) (Or (Eq (ca_Ax3 a) True) (Eq False True)) % 3.71/3.90 Clause #93 (by clausification #[87]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_10903 a) False) (Eq (ca_Ax3 a) True) % 3.71/3.90 Clause #94 (by clausification #[84]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 5 a a_1)) (cowlThing (skS.0 5 a a_1))) True) % 3.71/3.90 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 5 a a_1)) True) % 3.71/3.90 Clause #99 (by superposition #[96, 13]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_22_10903 (skS.0 5 i2003_11_14_17_22_10903 a)) True) (Eq False True) % 3.71/3.90 Clause #100 (by clausification #[99]): ∀ (a : Iota), Eq (rr i2003_11_14_17_22_10903 (skS.0 5 i2003_11_14_17_22_10903 a)) True % 3.71/3.90 Clause #101 (by superposition #[100, 93]): ∀ (a : Iota), Or (Eq True False) (Eq (ca_Ax3 (skS.0 5 i2003_11_14_17_22_10903 a)) True) % 3.71/3.90 Clause #104 (by clausification #[101]): ∀ (a : Iota), Eq (ca_Ax3 (skS.0 5 i2003_11_14_17_22_10903 a)) True % 3.71/3.90 Clause #105 (by superposition #[104, 51]): ∀ (a : Iota), Or (Eq True False) (Eq (cc (skS.0 5 i2003_11_14_17_22_10903 a)) True) % 3.71/3.90 Clause #106 (by superposition #[104, 52]): ∀ (a : Iota), Or (Eq True False) (Eq (cd (skS.0 5 i2003_11_14_17_22_10903 a)) True) % 3.71/3.90 Clause #107 (by clausification #[106]): ∀ (a : Iota), Eq (cd (skS.0 5 i2003_11_14_17_22_10903 a)) True % 3.71/3.90 Clause #109 (by superposition #[107, 69]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 5 i2003_11_14_17_22_10903 a) a_1) False) % 3.71/3.90 Clause #110 (by clausification #[105]): ∀ (a : Iota), Eq (cc (skS.0 5 i2003_11_14_17_22_10903 a)) True % 3.71/3.90 Clause #111 (by superposition #[110, 27]): ∀ (a : Iota), Or (Eq True False) (Eq (cdxcomp (skS.0 5 i2003_11_14_17_22_10903 a)) True) % 3.71/3.90 Clause #113 (by clausification #[111]): ∀ (a : Iota), Eq (cdxcomp (skS.0 5 i2003_11_14_17_22_10903 a)) True % 3.71/3.90 Clause #114 (by superposition #[113, 58]): ∀ (a a_1 : Iota), % 3.71/3.90 Or (Eq True False) % 3.71/3.90 (Eq (ra_Px1 (skS.0 5 i2003_11_14_17_22_10903 a) (skS.0 1 (skS.0 5 i2003_11_14_17_22_10903 a) a_1)) True) % 3.71/3.90 Clause #115 (by clausification #[109]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_22_10903 a) a_1) False % 3.71/3.90 Clause #123 (by clausification #[114]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_22_10903 a) (skS.0 1 (skS.0 5 i2003_11_14_17_22_10903 a) a_1)) True % 3.71/3.90 Clause #124 (by superposition #[123, 115]): Eq True False % 3.71/3.90 Clause #126 (by clausification #[124]): False % 3.71/3.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------