%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS100+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 3.67s 3.82s % Output : Proof 3.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : KRS100+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.14 % Command : duper %s % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 10:14:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.67/3.82 SZS status Theorem for theBenchmark.p % 3.67/3.82 SZS output start Proof for theBenchmark.p % 3.67/3.82 Clause #2 (by assumption #[]): Eq % 3.67/3.82 (∀ (X : Iota), % 3.67/3.82 Iff (cUnsatisfiable X) % 3.67/3.82 (And (And (∀ (Y : Iota), rr X Y → Or (ce Y) (Not (cd Y))) (∀ (Y : Iota), rr X Y → cd Y)) % 3.67/3.82 (Exists fun Y => And (rr X Y) (Not (ce Y))))) % 3.67/3.82 True % 3.67/3.82 Clause #4 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_20_32704) True % 3.67/3.82 Clause #17 (by clausification #[2]): ∀ (a : Iota), % 3.67/3.82 Eq % 3.67/3.82 (Iff (cUnsatisfiable a) % 3.67/3.82 (And (And (∀ (Y : Iota), rr a Y → Or (ce Y) (Not (cd Y))) (∀ (Y : Iota), rr a Y → cd Y)) % 3.67/3.82 (Exists fun Y => And (rr a Y) (Not (ce Y))))) % 3.67/3.82 True % 3.67/3.82 Clause #19 (by clausification #[17]): ∀ (a : Iota), % 3.67/3.82 Or (Eq (cUnsatisfiable a) False) % 3.67/3.82 (Eq % 3.67/3.82 (And (And (∀ (Y : Iota), rr a Y → Or (ce Y) (Not (cd Y))) (∀ (Y : Iota), rr a Y → cd Y)) % 3.67/3.82 (Exists fun Y => And (rr a Y) (Not (ce Y)))) % 3.67/3.82 True) % 3.67/3.82 Clause #33 (by clausification #[19]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (Not (ce Y))) True) % 3.67/3.82 Clause #34 (by clausification #[19]): ∀ (a : Iota), % 3.67/3.82 Or (Eq (cUnsatisfiable a) False) % 3.67/3.82 (Eq (And (∀ (Y : Iota), rr a Y → Or (ce Y) (Not (cd Y))) (∀ (Y : Iota), rr a Y → cd Y)) True) % 3.67/3.82 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 2 a a_1)) (Not (ce (skS.0 2 a a_1)))) True) % 3.67/3.82 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (ce (skS.0 2 a a_1))) True) % 3.67/3.82 Clause #37 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 2 a a_1)) True) % 3.67/3.82 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ce (skS.0 2 a a_1)) False) % 3.67/3.82 Clause #39 (by superposition #[38, 4]): ∀ (a : Iota), Or (Eq (ce (skS.0 2 i2003_11_14_17_20_32704 a)) False) (Eq False True) % 3.67/3.82 Clause #40 (by clausification #[39]): ∀ (a : Iota), Eq (ce (skS.0 2 i2003_11_14_17_20_32704 a)) False % 3.67/3.82 Clause #41 (by superposition #[37, 4]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_32704 (skS.0 2 i2003_11_14_17_20_32704 a)) True) (Eq False True) % 3.67/3.82 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (rr i2003_11_14_17_20_32704 (skS.0 2 i2003_11_14_17_20_32704 a)) True % 3.67/3.82 Clause #50 (by clausification #[34]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rr a Y → cd Y) True) % 3.67/3.82 Clause #51 (by clausification #[34]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rr a Y → Or (ce Y) (Not (cd Y))) True) % 3.67/3.82 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a a_1 → cd a_1) True) % 3.67/3.82 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Eq (cd a_1) True)) % 3.67/3.82 Clause #54 (by superposition #[53, 4]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_32704 a) False) (Or (Eq (cd a) True) (Eq False True)) % 3.67/3.82 Clause #55 (by clausification #[54]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_32704 a) False) (Eq (cd a) True) % 3.67/3.82 Clause #56 (by superposition #[55, 42]): ∀ (a : Iota), Or (Eq (cd (skS.0 2 i2003_11_14_17_20_32704 a)) True) (Eq False True) % 3.67/3.82 Clause #57 (by clausification #[56]): ∀ (a : Iota), Eq (cd (skS.0 2 i2003_11_14_17_20_32704 a)) True % 3.67/3.82 Clause #58 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a a_1 → Or (ce a_1) (Not (cd a_1))) True) % 3.67/3.82 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Eq (Or (ce a_1) (Not (cd a_1))) True)) % 3.67/3.82 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), % 3.67/3.82 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (ce a_1) True) (Eq (Not (cd a_1)) True))) % 3.67/3.82 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), % 3.67/3.82 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rr a a_1) False) (Or (Eq (ce a_1) True) (Eq (cd a_1) False))) % 3.67/3.82 Clause #62 (by superposition #[61, 4]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_32704 a) False) (Or (Eq (ce a) True) (Or (Eq (cd a) False) (Eq False True))) % 3.67/3.82 Clause #63 (by clausification #[62]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_20_32704 a) False) (Or (Eq (ce a) True) (Eq (cd a) False)) % 3.67/3.82 Clause #64 (by superposition #[63, 42]): ∀ (a : Iota), % 3.67/3.82 Or (Eq (ce (skS.0 2 i2003_11_14_17_20_32704 a)) True) % 3.67/3.82 (Or (Eq (cd (skS.0 2 i2003_11_14_17_20_32704 a)) False) (Eq False True)) % 3.67/3.82 Clause #66 (by clausification #[64]): ∀ (a : Iota), Or (Eq (ce (skS.0 2 i2003_11_14_17_20_32704 a)) True) (Eq (cd (skS.0 2 i2003_11_14_17_20_32704 a)) False) % 3.67/3.82 Clause #67 (by forward demodulation #[66, 57]): ∀ (a : Iota), Or (Eq (ce (skS.0 2 i2003_11_14_17_20_32704 a)) True) (Eq True False) % 3.67/3.82 Clause #68 (by clausification #[67]): ∀ (a : Iota), Eq (ce (skS.0 2 i2003_11_14_17_20_32704 a)) True % 3.67/3.82 Clause #69 (by superposition #[68, 40]): Eq True False % 3.67/3.82 Clause #70 (by clausification #[69]): False % 3.67/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------