%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS179+1 : TPTP v9.2.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 07:52:45 PM UTC 2025 % Result : Theorem 54.53s 54.75s % Output : Proof 54.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS179+1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n027.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 10:20:23 EDT 2025 % 0.13/0.34 % CPUTime : % 54.53/54.75 SZS status Theorem for theBenchmark.p % 54.53/54.75 SZS output start Proof for theBenchmark.p % 54.53/54.75 Clause #1 (by assumption #[]): Eq (∀ (S1 S2 : Iota), Iff (∀ (Ax C : Iota), status Ax C S1 → status Ax C S2) (isa S1 S2)) True % 54.53/54.75 Clause #13 (by assumption #[]): Eq (Not (∀ (S1 S2 S3 : Iota), And (isa S1 S2) (isa S2 S3) → isa S1 S3)) True % 54.53/54.75 Clause #16 (by clausification #[13]): Eq (∀ (S1 S2 S3 : Iota), And (isa S1 S2) (isa S2 S3) → isa S1 S3) False % 54.53/54.75 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (Not (∀ (S2 S3 : Iota), And (isa (skS.0 1 a) S2) (isa S2 S3) → isa (skS.0 1 a) S3)) True % 54.53/54.75 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (S2 S3 : Iota), And (isa (skS.0 1 a) S2) (isa S2 S3) → isa (skS.0 1 a) S3) False % 54.53/54.75 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 54.53/54.75 Eq (Not (∀ (S3 : Iota), And (isa (skS.0 1 a) (skS.0 2 a a_1)) (isa (skS.0 2 a a_1) S3) → isa (skS.0 1 a) S3)) True % 54.53/54.75 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 54.53/54.75 Eq (∀ (S3 : Iota), And (isa (skS.0 1 a) (skS.0 2 a a_1)) (isa (skS.0 2 a a_1) S3) → isa (skS.0 1 a) S3) False % 54.53/54.75 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 54.53/54.75 Eq % 54.53/54.75 (Not % 54.53/54.75 (And (isa (skS.0 1 a) (skS.0 2 a a_1)) (isa (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) → % 54.53/54.75 isa (skS.0 1 a) (skS.0 3 a a_1 a_2))) % 54.53/54.75 True % 54.53/54.75 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 54.53/54.75 Eq % 54.53/54.75 (And (isa (skS.0 1 a) (skS.0 2 a a_1)) (isa (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) → % 54.53/54.75 isa (skS.0 1 a) (skS.0 3 a a_1 a_2)) % 54.53/54.75 False % 54.53/54.75 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (And (isa (skS.0 1 a) (skS.0 2 a a_1)) (isa (skS.0 2 a a_1) (skS.0 3 a a_1 a_2))) True % 54.53/54.75 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (isa (skS.0 1 a) (skS.0 3 a a_1 a_2)) False % 54.53/54.75 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (isa (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) True % 54.53/54.75 Clause #26 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (isa (skS.0 1 a) (skS.0 2 a a_1)) True % 54.53/54.75 Clause #53 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (S2 : Iota), Iff (∀ (Ax C : Iota), status Ax C a → status Ax C S2) (isa a S2)) True % 54.53/54.75 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (Iff (∀ (Ax C : Iota), status Ax C a → status Ax C a_1) (isa a a_1)) True % 54.53/54.75 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (∀ (Ax C : Iota), status Ax C a → status Ax C a_1) True) (Eq (isa a a_1) False) % 54.53/54.75 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (∀ (Ax C : Iota), status Ax C a → status Ax C a_1) False) (Eq (isa a a_1) True) % 54.53/54.75 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (isa a a_1) False) (Eq (∀ (C : Iota), status a_2 C a → status a_2 C a_1) True) % 54.53/54.75 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (isa a a_1) False) (Eq (status a_2 a_3 a → status a_2 a_3 a_1) True) % 54.53/54.75 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (isa a a_1) False) (Or (Eq (status a_2 a_3 a) False) (Eq (status a_2 a_3 a_1) True)) % 54.53/54.75 Clause #60 (by superposition #[59, 25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 54.53/54.75 Or (Eq (status a a_1 (skS.0 2 a_2 a_3)) False) (Or (Eq (status a a_1 (skS.0 3 a_2 a_3 a_4)) True) (Eq False True)) % 54.53/54.75 Clause #61 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 54.53/54.75 Or (Eq (isa a a_1) True) % 54.53/54.75 (Eq (Not (∀ (C : Iota), status (skS.0 7 a a_1 a_2) C a → status (skS.0 7 a a_1 a_2) C a_1)) True) % 54.53/54.75 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 54.53/54.75 Or (Eq (isa a a_1) True) (Eq (∀ (C : Iota), status (skS.0 7 a a_1 a_2) C a → status (skS.0 7 a a_1 a_2) C a_1) False) % 54.53/54.75 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 54.53/54.75 Or (Eq (isa a a_1) True) % 54.53/54.75 (Eq % 54.53/54.75 (Not % 54.53/54.75 (status (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3) a → status (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3) a_1)) % 54.53/54.75 True) % 54.53/54.75 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), % 54.53/54.75 Or (Eq (isa a a_1) True) % 54.53/54.75 (Eq (status (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3) a → status (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3) a_1) % 54.53/54.75 False) % 54.53/54.75 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (isa a a_1) True) (Eq (status (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3) a) True) % 54.66/54.85 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (isa a a_1) True) (Eq (status (skS.0 7 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3) a_1) False) % 54.66/54.85 Clause #81 (by superposition #[26, 59]): ∀ (a a_1 a_2 a_3 : Iota), % 54.66/54.85 Or (Eq (status a a_1 (skS.0 1 a_2)) False) (Or (Eq (status a a_1 (skS.0 2 a_2 a_3)) True) (Eq False True)) % 54.66/54.85 Clause #157 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (status a a_1 (skS.0 1 a_2)) False) (Eq (status a a_1 (skS.0 2 a_2 a_3)) True) % 54.66/54.85 Clause #158 (by superposition #[157, 65]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 54.66/54.85 Or (Eq (status (skS.0 7 (skS.0 1 a) a_1 a_2) (skS.0 8 (skS.0 1 a) a_1 a_2 a_3) (skS.0 2 a a_4)) True) % 54.66/54.85 (Or (Eq (isa (skS.0 1 a) a_1) True) (Eq False True)) % 54.66/54.85 Clause #162 (by clausification #[60]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 54.66/54.85 Or (Eq (status a a_1 (skS.0 2 a_2 a_3)) False) (Eq (status a a_1 (skS.0 3 a_2 a_3 a_4)) True) % 54.66/54.85 Clause #292 (by clausification #[158]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 54.66/54.85 Or (Eq (status (skS.0 7 (skS.0 1 a) a_1 a_2) (skS.0 8 (skS.0 1 a) a_1 a_2 a_3) (skS.0 2 a a_4)) True) % 54.66/54.85 (Eq (isa (skS.0 1 a) a_1) True) % 54.66/54.85 Clause #293 (by superposition #[292, 162]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 54.66/54.85 Or (Eq (isa (skS.0 1 a) a_1) True) % 54.66/54.85 (Or (Eq True False) % 54.66/54.85 (Eq (status (skS.0 7 (skS.0 1 a) a_1 a_2) (skS.0 8 (skS.0 1 a) a_1 a_2 a_3) (skS.0 3 a a_4 a_5)) True)) % 54.66/54.85 Clause #2852 (by clausification #[293]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 54.66/54.85 Or (Eq (isa (skS.0 1 a) a_1) True) % 54.66/54.85 (Eq (status (skS.0 7 (skS.0 1 a) a_1 a_2) (skS.0 8 (skS.0 1 a) a_1 a_2 a_3) (skS.0 3 a a_4 a_5)) True) % 54.66/54.85 Clause #2853 (by superposition #[2852, 66]): ∀ (a a_1 a_2 : Iota), % 54.66/54.85 Or (Eq (isa (skS.0 1 a) (skS.0 3 a a_1 a_2)) True) % 54.66/54.85 (Or (Eq (isa (skS.0 1 a) (skS.0 3 a a_1 a_2)) True) (Eq True False)) % 54.66/54.85 Clause #8343 (by clausification #[2853]): ∀ (a a_1 a_2 : Iota), Or (Eq (isa (skS.0 1 a) (skS.0 3 a a_1 a_2)) True) (Eq (isa (skS.0 1 a) (skS.0 3 a a_1 a_2)) True) % 54.66/54.85 Clause #8344 (by eliminate duplicate literals #[8343]): ∀ (a a_1 a_2 : Iota), Eq (isa (skS.0 1 a) (skS.0 3 a a_1 a_2)) True % 54.66/54.85 Clause #8345 (by superposition #[8344, 24]): Eq True False % 54.66/54.85 Clause #8347 (by clausification #[8345]): False % 54.66/54.85 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------