%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS254+1 : TPTP v9.2.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 07:52:49 PM UTC 2025 % Result : Theorem 102.85s 103.07s % Output : Proof 103.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS254+1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n001.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 10:21:23 EDT 2025 % 0.13/0.35 % CPUTime : % 102.85/103.07 SZS status Theorem for theBenchmark.p % 102.85/103.07 SZS output start Proof for theBenchmark.p % 102.85/103.07 Clause #0 (by assumption #[]): Eq (∀ (Ax C : Iota), Iff (Not (Exists fun I1 => model I1 Ax) → Not (Exists fun I2 => model I2 C)) (status Ax C unp)) % 102.85/103.07 True % 102.85/103.07 Clause #4 (by assumption #[]): Eq (∀ (Ax C : Iota), Iff (∀ (I1 : Iota), model I1 Ax → model I1 C) (status Ax C thm)) True % 102.85/103.07 Clause #19 (by assumption #[]): Eq (∀ (S1 S2 : Iota), Iff (Exists fun Ax => Exists fun C => And (status Ax C S1) (status Ax C S2)) (mighta S1 S2)) True % 102.85/103.07 Clause #26 (by assumption #[]): Eq (Exists fun F => ∀ (I : Iota), model I F) True % 102.85/103.07 Clause #32 (by assumption #[]): Eq (Not (mighta unp thm)) True % 102.85/103.07 Clause #33 (by clausification #[32]): Eq (mighta unp thm) False % 102.85/103.07 Clause #34 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (I : Iota), model I (skS.0 0 a)) True % 102.85/103.07 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (model a (skS.0 0 a_1)) True % 102.85/103.07 Clause #47 (by clausification #[0]): ∀ (a : Iota), % 102.85/103.07 Eq (∀ (C : Iota), Iff (Not (Exists fun I1 => model I1 a) → Not (Exists fun I2 => model I2 C)) (status a C unp)) True % 102.85/103.07 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 102.85/103.07 Eq (Iff (Not (Exists fun I1 => model I1 a) → Not (Exists fun I2 => model I2 a_1)) (status a a_1 unp)) True % 102.85/103.07 Clause #50 (by clausification #[48]): ∀ (a a_1 : Iota), % 102.85/103.07 Or (Eq (Not (Exists fun I1 => model I1 a) → Not (Exists fun I2 => model I2 a_1)) False) (Eq (status a a_1 unp) True) % 102.85/103.07 Clause #110 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (∀ (I1 : Iota), model I1 a → model I1 C) (status a C thm)) True % 102.85/103.07 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), Eq (Iff (∀ (I1 : Iota), model I1 a → model I1 a_1) (status a a_1 thm)) True % 102.85/103.07 Clause #113 (by clausification #[111]): ∀ (a a_1 : Iota), Or (Eq (∀ (I1 : Iota), model I1 a → model I1 a_1) False) (Eq (status a a_1 thm) True) % 102.85/103.07 Clause #116 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), % 102.85/103.07 Or (Eq (status a a_1 thm) True) (Eq (Not (model (skS.0 6 a a_1 a_2) a → model (skS.0 6 a a_1 a_2) a_1)) True) % 102.85/103.07 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), % 102.85/103.07 Or (Eq (status a a_1 thm) True) (Eq (model (skS.0 6 a a_1 a_2) a → model (skS.0 6 a a_1 a_2) a_1) False) % 102.85/103.07 Clause #119 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), Or (Eq (status a a_1 thm) True) (Eq (model (skS.0 6 a a_1 a_2) a_1) False) % 102.85/103.07 Clause #197 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (status a a_1 unp) True) (Eq (Not (Exists fun I1 => model I1 a)) True) % 102.85/103.07 Clause #198 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (status a a_1 unp) True) (Eq (Not (Exists fun I2 => model I2 a_1)) False) % 102.85/103.07 Clause #199 (by clausification #[197]): ∀ (a a_1 : Iota), Or (Eq (status a a_1 unp) True) (Eq (Exists fun I1 => model I1 a) False) % 102.85/103.07 Clause #200 (by clausification #[199]): ∀ (a a_1 a_2 : Iota), Or (Eq (status a a_1 unp) True) (Eq (model a_2 a) False) % 102.85/103.07 Clause #248 (by clausification #[198]): ∀ (a a_1 : Iota), Or (Eq (status a a_1 unp) True) (Eq (Exists fun I2 => model I2 a_1) True) % 102.85/103.07 Clause #249 (by clausification #[248]): ∀ (a a_1 a_2 : Iota), Or (Eq (status a a_1 unp) True) (Eq (model (skS.0 13 a_1 a_2) a_1) True) % 102.85/103.07 Clause #256 (by superposition #[249, 200]): ∀ (a a_1 a_2 : Iota), Or (Eq (status a a_1 unp) True) (Or (Eq (status a_1 a_2 unp) True) (Eq True False)) % 102.85/103.07 Clause #257 (by clausification #[256]): ∀ (a a_1 a_2 : Iota), Or (Eq (status a a_1 unp) True) (Eq (status a_1 a_2 unp) True) % 102.85/103.07 Clause #260 (by equality factoring #[257]): ∀ (a : Iota), Or (Ne True True) (Eq (status a a unp) True) % 102.85/103.07 Clause #261 (by clausification #[260]): ∀ (a : Iota), Or (Eq (status a a unp) True) (Or (Eq True False) (Eq True False)) % 102.85/103.07 Clause #263 (by clausification #[261]): ∀ (a : Iota), Or (Eq (status a a unp) True) (Eq True False) % 102.85/103.07 Clause #264 (by clausification #[263]): ∀ (a : Iota), Eq (status a a unp) True % 102.85/103.07 Clause #546 (by clausification #[19]): ∀ (a : Iota), % 102.85/103.07 Eq (∀ (S2 : Iota), Iff (Exists fun Ax => Exists fun C => And (status Ax C a) (status Ax C S2)) (mighta a S2)) True % 102.85/103.07 Clause #547 (by clausification #[546]): ∀ (a a_1 : Iota), Eq (Iff (Exists fun Ax => Exists fun C => And (status Ax C a) (status Ax C a_1)) (mighta a a_1)) True % 103.01/103.25 Clause #549 (by clausification #[547]): ∀ (a a_1 : Iota), % 103.01/103.25 Or (Eq (Exists fun Ax => Exists fun C => And (status Ax C a) (status Ax C a_1)) False) (Eq (mighta a a_1) True) % 103.01/103.25 Clause #1410 (by superposition #[119, 35]): ∀ (a a_1 : Iota), Or (Eq (status a (skS.0 0 a_1) thm) True) (Eq False True) % 103.01/103.25 Clause #1428 (by clausification #[1410]): ∀ (a a_1 : Iota), Eq (status a (skS.0 0 a_1) thm) True % 103.01/103.25 Clause #16131 (by clausification #[549]): ∀ (a a_1 a_2 : Iota), Or (Eq (mighta a a_1) True) (Eq (Exists fun C => And (status a_2 C a) (status a_2 C a_1)) False) % 103.01/103.25 Clause #16132 (by clausification #[16131]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (mighta a a_1) True) (Eq (And (status a_2 a_3 a) (status a_2 a_3 a_1)) False) % 103.01/103.25 Clause #16133 (by clausification #[16132]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (mighta a a_1) True) (Or (Eq (status a_2 a_3 a) False) (Eq (status a_2 a_3 a_1) False)) % 103.01/103.25 Clause #16348 (by superposition #[16133, 264]): ∀ (a a_1 : Iota), Or (Eq (mighta unp a) True) (Or (Eq (status a_1 a_1 a) False) (Eq False True)) % 103.01/103.25 Clause #17632 (by clausification #[16348]): ∀ (a a_1 : Iota), Or (Eq (mighta unp a) True) (Eq (status a_1 a_1 a) False) % 103.01/103.25 Clause #17641 (by superposition #[17632, 1428]): Or (Eq (mighta unp thm) True) (Eq False True) % 103.01/103.25 Clause #18096 (by clausification #[17641]): Eq (mighta unp thm) True % 103.01/103.25 Clause #18097 (by superposition #[18096, 33]): Eq True False % 103.01/103.25 Clause #18100 (by clausification #[18097]): False % 103.01/103.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------