%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS090+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 07:52:36 PM UTC 2025 % Result : Unsatisfiable 3.63s 3.87s % Output : Proof 3.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : KRS090+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n014.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 10:21:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.63/3.87 SZS status Theorem for theBenchmark.p % 3.63/3.87 SZS output start Proof for theBenchmark.p % 3.63/3.87 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), cC2 X → And (Or (Not (cB X)) (cA X)) (Or (cB X) (cA X))) True % 3.63/3.87 Clause #4 (by assumption #[]): Eq (∀ (X : Iota), cC3 X → And (Or (Not (cB X)) (Not (cA X))) (Or (cB X) (Not (cA X)))) True % 3.63/3.87 Clause #5 (by assumption #[]): Eq (∀ (X : Iota), cC4 X → Exists fun Y => And (rR X Y) (cC2 Y)) True % 3.63/3.87 Clause #6 (by assumption #[]): Eq (∀ (X : Iota), cC5 X → ∀ (Y : Iota), rR X Y → cC3 Y) True % 3.63/3.87 Clause #7 (by assumption #[]): Eq (∀ (X : Iota), cTEST X → And (And (cC4 X) (cC1 X)) (cC5 X)) True % 3.63/3.87 Clause #8 (by assumption #[]): Eq (cTEST i2003_11_14_17_19_57994) True % 3.63/3.87 Clause #9 (by clausification #[6]): ∀ (a : Iota), Eq (cC5 a → ∀ (Y : Iota), rR a Y → cC3 Y) True % 3.63/3.87 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (cC5 a) False) (Eq (∀ (Y : Iota), rR a Y → cC3 Y) True) % 3.63/3.87 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cC5 a) False) (Eq (rR a a_1 → cC3 a_1) True) % 3.63/3.87 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (cC5 a) False) (Or (Eq (rR a a_1) False) (Eq (cC3 a_1) True)) % 3.63/3.87 Clause #27 (by clausification #[7]): ∀ (a : Iota), Eq (cTEST a → And (And (cC4 a) (cC1 a)) (cC5 a)) True % 3.63/3.87 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (cTEST a) False) (Eq (And (And (cC4 a) (cC1 a)) (cC5 a)) True) % 3.63/3.87 Clause #29 (by clausification #[28]): ∀ (a : Iota), Or (Eq (cTEST a) False) (Eq (cC5 a) True) % 3.63/3.87 Clause #30 (by clausification #[28]): ∀ (a : Iota), Or (Eq (cTEST a) False) (Eq (And (cC4 a) (cC1 a)) True) % 3.63/3.87 Clause #31 (by superposition #[29, 8]): Or (Eq (cC5 i2003_11_14_17_19_57994) True) (Eq False True) % 3.63/3.87 Clause #32 (by clausification #[31]): Eq (cC5 i2003_11_14_17_19_57994) True % 3.63/3.87 Clause #33 (by superposition #[32, 12]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (rR i2003_11_14_17_19_57994 a) False) (Eq (cC3 a) True)) % 3.63/3.87 Clause #35 (by clausification #[30]): ∀ (a : Iota), Or (Eq (cTEST a) False) (Eq (cC4 a) True) % 3.63/3.87 Clause #39 (by clausification #[3]): ∀ (a : Iota), Eq (cC2 a → And (Or (Not (cB a)) (cA a)) (Or (cB a) (cA a))) True % 3.63/3.87 Clause #40 (by clausification #[39]): ∀ (a : Iota), Or (Eq (cC2 a) False) (Eq (And (Or (Not (cB a)) (cA a)) (Or (cB a) (cA a))) True) % 3.63/3.87 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (cC2 a) False) (Eq (Or (cB a) (cA a)) True) % 3.63/3.87 Clause #42 (by clausification #[40]): ∀ (a : Iota), Or (Eq (cC2 a) False) (Eq (Or (Not (cB a)) (cA a)) True) % 3.63/3.87 Clause #43 (by clausification #[41]): ∀ (a : Iota), Or (Eq (cC2 a) False) (Or (Eq (cB a) True) (Eq (cA a) True)) % 3.63/3.87 Clause #44 (by superposition #[35, 8]): Or (Eq (cC4 i2003_11_14_17_19_57994) True) (Eq False True) % 3.63/3.87 Clause #45 (by clausification #[44]): Eq (cC4 i2003_11_14_17_19_57994) True % 3.63/3.87 Clause #47 (by clausification #[33]): ∀ (a : Iota), Or (Eq (rR i2003_11_14_17_19_57994 a) False) (Eq (cC3 a) True) % 3.63/3.87 Clause #48 (by clausification #[42]): ∀ (a : Iota), Or (Eq (cC2 a) False) (Or (Eq (Not (cB a)) True) (Eq (cA a) True)) % 3.63/3.87 Clause #49 (by clausification #[48]): ∀ (a : Iota), Or (Eq (cC2 a) False) (Or (Eq (cA a) True) (Eq (cB a) False)) % 3.63/3.87 Clause #50 (by clausification #[4]): ∀ (a : Iota), Eq (cC3 a → And (Or (Not (cB a)) (Not (cA a))) (Or (cB a) (Not (cA a)))) True % 3.63/3.87 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Eq (And (Or (Not (cB a)) (Not (cA a))) (Or (cB a) (Not (cA a)))) True) % 3.63/3.87 Clause #52 (by clausification #[51]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Eq (Or (cB a) (Not (cA a))) True) % 3.63/3.87 Clause #53 (by clausification #[51]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Eq (Or (Not (cB a)) (Not (cA a))) True) % 3.63/3.87 Clause #54 (by clausification #[52]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Or (Eq (cB a) True) (Eq (Not (cA a)) True)) % 3.63/3.87 Clause #55 (by clausification #[54]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Or (Eq (cB a) True) (Eq (cA a) False)) % 3.63/3.87 Clause #56 (by clausification #[53]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Or (Eq (Not (cB a)) True) (Eq (Not (cA a)) True)) % 3.63/3.87 Clause #57 (by clausification #[56]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Or (Eq (Not (cA a)) True) (Eq (cB a) False)) % 3.74/3.90 Clause #58 (by clausification #[57]): ∀ (a : Iota), Or (Eq (cC3 a) False) (Or (Eq (cB a) False) (Eq (cA a) False)) % 3.74/3.90 Clause #59 (by clausification #[5]): ∀ (a : Iota), Eq (cC4 a → Exists fun Y => And (rR a Y) (cC2 Y)) True % 3.74/3.90 Clause #60 (by clausification #[59]): ∀ (a : Iota), Or (Eq (cC4 a) False) (Eq (Exists fun Y => And (rR a Y) (cC2 Y)) True) % 3.74/3.90 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), Or (Eq (cC4 a) False) (Eq (And (rR a (skS.0 0 a a_1)) (cC2 (skS.0 0 a a_1))) True) % 3.74/3.90 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), Or (Eq (cC4 a) False) (Eq (cC2 (skS.0 0 a a_1)) True) % 3.74/3.90 Clause #63 (by clausification #[61]): ∀ (a a_1 : Iota), Or (Eq (cC4 a) False) (Eq (rR a (skS.0 0 a a_1)) True) % 3.74/3.90 Clause #64 (by superposition #[62, 45]): ∀ (a : Iota), Or (Eq (cC2 (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq False True) % 3.74/3.90 Clause #65 (by clausification #[64]): ∀ (a : Iota), Eq (cC2 (skS.0 0 i2003_11_14_17_19_57994 a)) True % 3.74/3.90 Clause #66 (by superposition #[65, 43]): ∀ (a : Iota), % 3.74/3.90 Or (Eq True False) % 3.74/3.90 (Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) True)) % 3.74/3.90 Clause #67 (by superposition #[65, 49]): ∀ (a : Iota), % 3.74/3.90 Or (Eq True False) % 3.74/3.90 (Or (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) False)) % 3.74/3.90 Clause #68 (by superposition #[63, 45]): ∀ (a : Iota), Or (Eq (rR i2003_11_14_17_19_57994 (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq False True) % 3.74/3.90 Clause #69 (by clausification #[68]): ∀ (a : Iota), Eq (rR i2003_11_14_17_19_57994 (skS.0 0 i2003_11_14_17_19_57994 a)) True % 3.74/3.90 Clause #70 (by superposition #[69, 47]): ∀ (a : Iota), Or (Eq True False) (Eq (cC3 (skS.0 0 i2003_11_14_17_19_57994 a)) True) % 3.74/3.90 Clause #76 (by clausification #[70]): ∀ (a : Iota), Eq (cC3 (skS.0 0 i2003_11_14_17_19_57994 a)) True % 3.74/3.90 Clause #77 (by superposition #[76, 55]): ∀ (a : Iota), % 3.74/3.90 Or (Eq True False) % 3.74/3.90 (Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) False)) % 3.74/3.90 Clause #78 (by superposition #[76, 58]): ∀ (a : Iota), % 3.74/3.90 Or (Eq True False) % 3.74/3.90 (Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) False) (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) False)) % 3.74/3.90 Clause #79 (by clausification #[66]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) True) % 3.74/3.90 Clause #80 (by clausification #[67]): ∀ (a : Iota), Or (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) False) % 3.74/3.90 Clause #81 (by clausification #[78]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) False) (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) False) % 3.74/3.90 Clause #87 (by clausification #[77]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) False) % 3.74/3.90 Clause #88 (by superposition #[87, 79]): ∀ (a : Iota), % 3.74/3.90 Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) % 3.74/3.90 (Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq False True)) % 3.74/3.90 Clause #89 (by clausification #[88]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True) % 3.74/3.90 Clause #90 (by eliminate duplicate literals #[89]): ∀ (a : Iota), Eq (cB (skS.0 0 i2003_11_14_17_19_57994 a)) True % 3.74/3.90 Clause #92 (by backward demodulation #[90, 80]): ∀ (a : Iota), Or (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) True) (Eq True False) % 3.74/3.90 Clause #93 (by backward demodulation #[90, 81]): ∀ (a : Iota), Or (Eq True False) (Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) False) % 3.74/3.90 Clause #95 (by clausification #[93]): ∀ (a : Iota), Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) False % 3.74/3.90 Clause #101 (by clausification #[92]): ∀ (a : Iota), Eq (cA (skS.0 0 i2003_11_14_17_19_57994 a)) True % 3.74/3.90 Clause #102 (by superposition #[101, 95]): Eq True False % 3.74/3.90 Clause #103 (by clausification #[102]): False % 3.74/3.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------