%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS105+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 07:52:38 PM UTC 2025 % Result : Unsatisfiable 3.61s 3.79s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : KRS105+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n017.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 10:16:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.61/3.79 SZS status Theorem for theBenchmark.p % 3.61/3.79 SZS output start Proof for theBenchmark.p % 3.61/3.79 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), cUnsatisfiable X → cdxcomp X) True % 3.61/3.79 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), cUnsatisfiable X → cc X) True % 3.61/3.79 Clause #4 (by assumption #[]): Eq (∀ (X : Iota), cc X → ∀ (Y : Iota), rr X Y → cc Y) True % 3.61/3.79 Clause #5 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.61/3.79 Clause #6 (by assumption #[]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.61/3.79 Clause #7 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax2 X) (∀ (Y : Iota), rr X Y → cc Y)) True % 3.61/3.79 Clause #8 (by assumption #[]): Eq (∀ (X : Iota), ca_Ax2 X → cd X) True % 3.61/3.79 Clause #9 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_20_53634) True % 3.61/3.79 Clause #10 (by clausification #[8]): ∀ (a : Iota), Eq (ca_Ax2 a → cd a) True % 3.61/3.79 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (cd a) True) % 3.61/3.79 Clause #12 (by clausification #[3]): ∀ (a : Iota), Eq (cUnsatisfiable a → cc a) True % 3.61/3.79 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cc a) True) % 3.61/3.79 Clause #14 (by superposition #[13, 9]): Or (Eq (cc i2003_11_14_17_20_53634) True) (Eq False True) % 3.61/3.79 Clause #15 (by clausification #[14]): Eq (cc i2003_11_14_17_20_53634) True % 3.61/3.79 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (cUnsatisfiable a → cdxcomp a) True % 3.61/3.79 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cdxcomp a) True) % 3.61/3.79 Clause #18 (by superposition #[17, 9]): Or (Eq (cdxcomp i2003_11_14_17_20_53634) True) (Eq False True) % 3.61/3.79 Clause #23 (by clausification #[18]): Eq (cdxcomp i2003_11_14_17_20_53634) True % 3.61/3.79 Clause #24 (by clausification #[4]): ∀ (a : Iota), Eq (cc a → ∀ (Y : Iota), rr a Y → cc Y) True % 3.61/3.79 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (cc a) False) (Eq (∀ (Y : Iota), rr a Y → cc Y) True) % 3.61/3.79 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (cc a) False) (Eq (rr a a_1 → cc a_1) True) % 3.61/3.79 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (cc a) False) (Or (Eq (rr a a_1) False) (Eq (cc a_1) True)) % 3.61/3.79 Clause #28 (by superposition #[27, 15]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_53634 a) False) (Or (Eq (cc a) True) (Eq False True)) % 3.61/3.79 Clause #35 (by betaEtaReduce #[5]): Eq (∀ (X : Iota), Iff (cd X) (Not (Exists (ra_Px1 X)))) True % 3.61/3.79 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (Iff (cd a) (Not (Exists (ra_Px1 a)))) True % 3.61/3.79 Clause #38 (by clausification #[36]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.61/3.79 Clause #42 (by clausification #[38]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists (ra_Px1 a)) False) % 3.61/3.79 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (ra_Px1 a a_1) False) % 3.61/3.79 Clause #44 (by clausification #[28]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_53634 a) False) (Eq (cc a) True) % 3.61/3.79 Clause #45 (by clausification #[7]): ∀ (a : Iota), Eq (Iff (ca_Ax2 a) (∀ (Y : Iota), rr a Y → cc Y)) True % 3.61/3.79 Clause #46 (by clausification #[45]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) True) (Eq (∀ (Y : Iota), rr a Y → cc Y) False) % 3.61/3.79 Clause #48 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) True) (Eq (Not (rr a (skS.0 1 a a_1) → cc (skS.0 1 a a_1))) True) % 3.61/3.79 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) True) (Eq (rr a (skS.0 1 a a_1) → cc (skS.0 1 a a_1)) False) % 3.61/3.79 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) True) (Eq (rr a (skS.0 1 a a_1)) True) % 3.61/3.79 Clause #51 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) True) (Eq (cc (skS.0 1 a a_1)) False) % 3.61/3.79 Clause #52 (by superposition #[50, 44]): ∀ (a : Iota), % 3.61/3.79 Or (Eq (ca_Ax2 i2003_11_14_17_20_53634) True) (Or (Eq True False) (Eq (cc (skS.0 1 i2003_11_14_17_20_53634 a)) True)) % 3.61/3.79 Clause #55 (by betaEtaReduce #[6]): Eq (∀ (X : Iota), Iff (cdxcomp X) (Exists (ra_Px1 X))) True % 3.61/3.79 Clause #56 (by clausification #[55]): ∀ (a : Iota), Eq (Iff (cdxcomp a) (Exists (ra_Px1 a))) True % 3.63/3.79 Clause #58 (by clausification #[56]): ∀ (a : Iota), Or (Eq (cdxcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.63/3.79 Clause #62 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (cdxcomp a) False) (Eq (ra_Px1 a (skS.0 2 a a_1)) True) % 3.63/3.79 Clause #63 (by superposition #[62, 23]): ∀ (a : Iota), Or (Eq (ra_Px1 i2003_11_14_17_20_53634 (skS.0 2 i2003_11_14_17_20_53634 a)) True) (Eq False True) % 3.63/3.79 Clause #65 (by clausification #[63]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_20_53634 (skS.0 2 i2003_11_14_17_20_53634 a)) True % 3.63/3.79 Clause #67 (by clausification #[52]): ∀ (a : Iota), Or (Eq (ca_Ax2 i2003_11_14_17_20_53634) True) (Eq (cc (skS.0 1 i2003_11_14_17_20_53634 a)) True) % 3.63/3.79 Clause #68 (by superposition #[67, 51]): Or (Eq (ca_Ax2 i2003_11_14_17_20_53634) True) (Or (Eq (ca_Ax2 i2003_11_14_17_20_53634) True) (Eq True False)) % 3.63/3.79 Clause #70 (by clausification #[68]): Or (Eq (ca_Ax2 i2003_11_14_17_20_53634) True) (Eq (ca_Ax2 i2003_11_14_17_20_53634) True) % 3.63/3.79 Clause #71 (by eliminate duplicate literals #[70]): Eq (ca_Ax2 i2003_11_14_17_20_53634) True % 3.63/3.79 Clause #73 (by superposition #[71, 11]): Or (Eq True False) (Eq (cd i2003_11_14_17_20_53634) True) % 3.63/3.79 Clause #75 (by clausification #[73]): Eq (cd i2003_11_14_17_20_53634) True % 3.63/3.79 Clause #76 (by superposition #[75, 43]): ∀ (a : Iota), Or (Eq True False) (Eq (ra_Px1 i2003_11_14_17_20_53634 a) False) % 3.63/3.79 Clause #77 (by clausification #[76]): ∀ (a : Iota), Eq (ra_Px1 i2003_11_14_17_20_53634 a) False % 3.63/3.79 Clause #78 (by superposition #[77, 65]): Eq False True % 3.63/3.79 Clause #80 (by clausification #[78]): False % 3.63/3.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------