%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS123+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 3.58s 3.74s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS123+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n031.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 10:11:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.58/3.74 SZS status Theorem for theBenchmark.p % 3.58/3.74 SZS output start Proof for theBenchmark.p % 3.58/3.74 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), Iff (cUnsatisfiable X) (And (cc X) (cd X))) True % 3.58/3.74 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), cc X → cdxcomp X) True % 3.58/3.74 Clause #6 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.58/3.74 Clause #7 (by assumption #[]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.58/3.74 Clause #12 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_22_02803) True % 3.58/3.74 Clause #25 (by clausification #[3]): ∀ (a : Iota), Eq (cc a → cdxcomp a) True % 3.58/3.74 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (cdxcomp a) True) % 3.58/3.74 Clause #34 (by clausification #[2]): ∀ (a : Iota), Eq (Iff (cUnsatisfiable a) (And (cc a) (cd a))) True % 3.58/3.74 Clause #36 (by clausification #[34]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (cc a) (cd a)) True) % 3.58/3.74 Clause #38 (by clausification #[36]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd a) True) % 3.58/3.74 Clause #39 (by clausification #[36]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cc a) True) % 3.58/3.74 Clause #40 (by superposition #[38, 12]): Or (Eq (cd i2003_11_14_17_22_02803) True) (Eq False True) % 3.58/3.74 Clause #41 (by clausification #[40]): Eq (cd i2003_11_14_17_22_02803) True % 3.58/3.74 Clause #42 (by superposition #[39, 12]): Or (Eq (cc i2003_11_14_17_22_02803) True) (Eq False True) % 3.58/3.74 Clause #43 (by clausification #[42]): Eq (cc i2003_11_14_17_22_02803) True % 3.58/3.74 Clause #44 (by superposition #[43, 26]): Or (Eq True False) (Eq (cdxcomp i2003_11_14_17_22_02803) True) % 3.58/3.74 Clause #46 (by clausification #[44]): Eq (cdxcomp i2003_11_14_17_22_02803) True % 3.58/3.74 Clause #47 (by betaEtaReduce #[6]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists (ra_Px1 X)))) True % 3.58/3.74 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (Iff (cd a) (Not (Exists (ra_Px1 a)))) True % 3.58/3.74 Clause #50 (by clausification #[48]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.58/3.74 Clause #55 (by clausification #[50]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists (ra_Px1 a)) False) % 3.58/3.74 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (ra_Px1 a a_1) False) % 3.58/3.74 Clause #57 (by superposition #[56, 41]): ∀ (a : Iota), Or (Eq (ra_Px1 i2003_11_14_17_22_02803 a) False) (Eq False True) % 3.58/3.74 Clause #58 (by clausification #[57]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_22_02803 a) False % 3.58/3.74 Clause #59 (by betaEtaReduce #[7]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists (ra_Px1 X))) True % 3.58/3.74 Clause #60 (by clausification #[59]): ∀ (a : Iota), Eq (Iff (cdxcomp a) (Exists (ra_Px1 a))) True % 3.58/3.74 Clause #62 (by clausification #[60]): ∀ (a : Iota), Or (Eq (cdxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.58/3.74 Clause #72 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (cdxcomp a) False) (Eq (ra_Px1 a (skS.0 2 a a_1)) True) % 3.58/3.74 Clause #73 (by superposition #[72, 46]): ∀ (a : Iota), Or (Eq (ra_Px1 i2003_11_14_17_22_02803 (skS.0 2 i2003_11_14_17_22_02803 a)) True) (Eq False True) % 3.58/3.74 Clause #86 (by clausification #[73]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_22_02803 (skS.0 2 i2003_11_14_17_22_02803 a)) True % 3.58/3.74 Clause #87 (by superposition #[86, 58]): Eq True False % 3.58/3.74 Clause #89 (by clausification #[87]): False % 3.58/3.74 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------