%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN979+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:08:21 PM UTC 2025 % Result : Theorem 3.58s 3.77s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SYN979+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.15 % Command : duper %s % 0.14/0.36 % Computer : n026.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 15:27:08 EDT 2025 % 0.14/0.36 % CPUTime : % 3.58/3.77 SZS status Theorem for theBenchmark.p % 3.58/3.77 SZS output start Proof for theBenchmark.p % 3.58/3.77 Clause #0 (by assumption #[]): Eq % 3.58/3.77 (Not % 3.58/3.77 (∀ (A B : Iota), % 3.58/3.77 Exists fun X => % 3.58/3.77 Exists fun Y => % 3.58/3.77 And (And (And (And (And (And (And (q X → p X A) (q A)) (q B)) (r Y → p B Y)) (r A)) (r B)) (s A → p X Y)) % 3.58/3.77 (s A) → % 3.58/3.77 p A B)) % 3.58/3.77 True % 3.58/3.77 Clause #1 (by clausification #[0]): Eq % 3.58/3.77 (∀ (A B : Iota), % 3.58/3.77 Exists fun X => % 3.58/3.77 Exists fun Y => % 3.58/3.77 And (And (And (And (And (And (And (q X → p X A) (q A)) (q B)) (r Y → p B Y)) (r A)) (r B)) (s A → p X Y)) % 3.58/3.77 (s A) → % 3.58/3.77 p A B) % 3.58/3.77 False % 3.58/3.77 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.58/3.77 Eq % 3.58/3.77 (Not % 3.58/3.77 (∀ (B : Iota), % 3.58/3.77 Exists fun X => % 3.58/3.77 Exists fun Y => % 3.58/3.77 And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And (And (And (And (q X → p X (skS.0 0 a)) (q (skS.0 0 a))) (q B)) (r Y → p B Y)) (r (skS.0 0 a))) % 3.58/3.77 (r B)) % 3.58/3.77 (s (skS.0 0 a) → p X Y)) % 3.58/3.77 (s (skS.0 0 a)) → % 3.58/3.77 p (skS.0 0 a) B)) % 3.58/3.77 True % 3.58/3.77 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.58/3.77 Eq % 3.58/3.77 (∀ (B : Iota), % 3.58/3.77 Exists fun X => % 3.58/3.77 Exists fun Y => % 3.58/3.77 And % 3.58/3.77 (And % 3.58/3.77 (And (And (And (And (And (q X → p X (skS.0 0 a)) (q (skS.0 0 a))) (q B)) (r Y → p B Y)) (r (skS.0 0 a))) % 3.58/3.77 (r B)) % 3.58/3.77 (s (skS.0 0 a) → p X Y)) % 3.58/3.77 (s (skS.0 0 a)) → % 3.58/3.77 p (skS.0 0 a) B) % 3.58/3.77 False % 3.58/3.77 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.58/3.77 Eq % 3.58/3.77 (Not % 3.58/3.77 (Exists fun X => % 3.58/3.77 Exists fun Y => % 3.58/3.77 And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And (And (And (q X → p X (skS.0 0 a)) (q (skS.0 0 a))) (q (skS.0 1 a a_1))) % 3.58/3.77 (r Y → p (skS.0 1 a a_1) Y)) % 3.58/3.77 (r (skS.0 0 a))) % 3.58/3.77 (r (skS.0 1 a a_1))) % 3.58/3.77 (s (skS.0 0 a) → p X Y)) % 3.58/3.77 (s (skS.0 0 a)) → % 3.58/3.77 p (skS.0 0 a) (skS.0 1 a a_1))) % 3.58/3.77 True % 3.58/3.77 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.58/3.77 Eq % 3.58/3.77 (Exists fun X => % 3.58/3.77 Exists fun Y => % 3.58/3.77 And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And (And (And (q X → p X (skS.0 0 a)) (q (skS.0 0 a))) (q (skS.0 1 a a_1))) % 3.58/3.77 (r Y → p (skS.0 1 a a_1) Y)) % 3.58/3.77 (r (skS.0 0 a))) % 3.58/3.77 (r (skS.0 1 a a_1))) % 3.58/3.77 (s (skS.0 0 a) → p X Y)) % 3.58/3.77 (s (skS.0 0 a)) → % 3.58/3.77 p (skS.0 0 a) (skS.0 1 a a_1)) % 3.58/3.77 False % 3.58/3.77 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.58/3.77 Eq % 3.58/3.77 (Exists fun Y => % 3.58/3.77 And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And (And (And (q a → p a (skS.0 0 a_1)) (q (skS.0 0 a_1))) (q (skS.0 1 a_1 a_2))) % 3.58/3.77 (r Y → p (skS.0 1 a_1 a_2) Y)) % 3.58/3.77 (r (skS.0 0 a_1))) % 3.58/3.77 (r (skS.0 1 a_1 a_2))) % 3.58/3.77 (s (skS.0 0 a_1) → p a Y)) % 3.58/3.77 (s (skS.0 0 a_1)) → % 3.58/3.77 p (skS.0 0 a_1) (skS.0 1 a_1 a_2)) % 3.58/3.77 False % 3.58/3.77 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.77 Eq % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And (And (And (q a → p a (skS.0 0 a_1)) (q (skS.0 0 a_1))) (q (skS.0 1 a_1 a_2))) % 3.58/3.77 (r a_3 → p (skS.0 1 a_1 a_2) a_3)) % 3.58/3.77 (r (skS.0 0 a_1))) % 3.58/3.77 (r (skS.0 1 a_1 a_2))) % 3.58/3.77 (s (skS.0 0 a_1) → p a a_3)) % 3.58/3.77 (s (skS.0 0 a_1)) → % 3.58/3.77 p (skS.0 0 a_1) (skS.0 1 a_1 a_2)) % 3.58/3.77 False % 3.58/3.77 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.77 Eq % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And % 3.58/3.77 (And (And (And (q a → p a (skS.0 0 a_1)) (q (skS.0 0 a_1))) (q (skS.0 1 a_1 a_2))) % 3.58/3.77 (r a_3 → p (skS.0 1 a_1 a_2) a_3)) % 3.58/3.77 (r (skS.0 0 a_1))) % 3.58/3.77 (r (skS.0 1 a_1 a_2))) % 3.58/3.77 (s (skS.0 0 a_1) → p a a_3)) % 3.58/3.77 (s (skS.0 0 a_1))) % 3.58/3.77 True % 3.58/3.77 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (p (skS.0 0 a) (skS.0 1 a a_1)) False % 3.58/3.77 Clause #10 (by clausification #[8]): ∀ (a : Iota), Eq (s (skS.0 0 a)) True % 3.58/3.78 Clause #11 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.78 Eq % 3.58/3.78 (And % 3.58/3.78 (And % 3.58/3.78 (And % 3.58/3.78 (And (And (And (q a → p a (skS.0 0 a_1)) (q (skS.0 0 a_1))) (q (skS.0 1 a_1 a_2))) % 3.58/3.78 (r a_3 → p (skS.0 1 a_1 a_2) a_3)) % 3.58/3.78 (r (skS.0 0 a_1))) % 3.58/3.78 (r (skS.0 1 a_1 a_2))) % 3.58/3.78 (s (skS.0 0 a_1) → p a a_3)) % 3.58/3.78 True % 3.58/3.78 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (s (skS.0 0 a) → p a_1 a_2) True % 3.58/3.78 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (s (skS.0 0 a)) False) (Eq (p a_1 a_2) True) % 3.58/3.78 Clause #15 (by superposition #[14, 10]): ∀ (a a_1 : Iota), Or (Eq (p a a_1) True) (Eq False True) % 3.58/3.78 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (p a a_1) True % 3.58/3.78 Clause #17 (by superposition #[16, 9]): Eq True False % 3.58/3.78 Clause #18 (by clausification #[17]): False % 3.58/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------