%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN941+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:08:17 PM UTC 2025 % Result : Theorem 3.42s 3.58s % Output : Proof 3.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN941+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.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 15:41:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.42/3.58 SZS status Theorem for theBenchmark.p % 3.42/3.58 SZS output start Proof for theBenchmark.p % 3.42/3.58 Clause #0 (by assumption #[]): Eq % 3.42/3.58 (Not % 3.42/3.58 (∀ (B C : Iota), q (f B) → Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r B) (r C))) (q X))) % 3.42/3.58 True % 3.42/3.58 Clause #1 (by clausification #[0]): Eq (∀ (B C : Iota), q (f B) → Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r B) (r C))) (q X)) % 3.42/3.58 False % 3.42/3.58 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.42/3.58 Eq % 3.42/3.58 (Not % 3.42/3.58 (∀ (C : Iota), % 3.42/3.58 q (f (skS.0 0 a)) → % 3.42/3.58 Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r (skS.0 0 a)) (r C))) (q X))) % 3.42/3.58 True % 3.42/3.58 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.42/3.58 Eq % 3.42/3.58 (∀ (C : Iota), % 3.42/3.58 q (f (skS.0 0 a)) → % 3.42/3.58 Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r (skS.0 0 a)) (r C))) (q X)) % 3.42/3.58 False % 3.42/3.58 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.42/3.58 Eq % 3.42/3.58 (Not % 3.42/3.58 (q (f (skS.0 0 a)) → % 3.42/3.58 Exists fun X => % 3.42/3.58 Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r (skS.0 0 a)) (r (skS.0 1 a a_1)))) (q X))) % 3.42/3.58 True % 3.42/3.58 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.42/3.58 Eq % 3.42/3.58 (q (f (skS.0 0 a)) → % 3.42/3.58 Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r (skS.0 0 a)) (r (skS.0 1 a a_1)))) (q X)) % 3.42/3.58 False % 3.42/3.58 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (q (f (skS.0 0 a))) True % 3.42/3.58 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), % 3.42/3.58 Eq (Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r (skS.0 0 a)) (r (skS.0 1 a a_1)))) (q X)) % 3.42/3.58 False % 3.42/3.58 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.42/3.58 Eq (Exists fun Y => And (p (f Y) → And (p a) (r Y → And (r (skS.0 0 a_1)) (r (skS.0 1 a_1 a_2)))) (q a)) False % 3.42/3.58 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.42/3.58 Eq (And (p (f a) → And (p a_1) (r a → And (r (skS.0 0 a_2)) (r (skS.0 1 a_2 a_3)))) (q a_1)) False % 3.42/3.58 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.42/3.58 Or (Eq (p (f a) → And (p a_1) (r a → And (r (skS.0 0 a_2)) (r (skS.0 1 a_2 a_3)))) False) (Eq (q a_1) False) % 3.42/3.58 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (q a) False) (Eq (p (f a_1)) True) % 3.42/3.58 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota), % 3.42/3.58 Or (Eq (q a) False) (Eq (And (p a) (r a_1 → And (r (skS.0 0 a_2)) (r (skS.0 1 a_2 a_3)))) False) % 3.42/3.58 Clause #13 (by superposition #[11, 6]): ∀ (a : Iota), Or (Eq (p (f a)) True) (Eq False True) % 3.42/3.58 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (p (f a)) True % 3.42/3.58 Clause #15 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 3.42/3.58 Or (Eq (q a) False) (Or (Eq (p a) False) (Eq (r a_1 → And (r (skS.0 0 a_2)) (r (skS.0 1 a_2 a_3))) False)) % 3.42/3.58 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Eq (r a_1) True)) % 3.42/3.58 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Eq (And (r (skS.0 0 a_1)) (r (skS.0 1 a_1 a_2))) False)) % 3.42/3.58 Clause #18 (by superposition #[16, 6]): ∀ (a a_1 : Iota), Or (Eq (p (f (skS.0 0 a))) False) (Or (Eq (r a_1) True) (Eq False True)) % 3.42/3.58 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (p (f (skS.0 0 a))) False) (Eq (r a_1) True) % 3.42/3.58 Clause #20 (by superposition #[19, 14]): ∀ (a : Iota), Or (Eq (r a) True) (Eq False True) % 3.42/3.58 Clause #21 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.42/3.58 Or (Eq (q a) False) (Or (Eq (p a) False) (Or (Eq (r (skS.0 0 a_1)) False) (Eq (r (skS.0 1 a_1 a_2)) False))) % 3.42/3.58 Clause #23 (by clausification #[20]): ∀ (a : Iota), Eq (r a) True % 3.42/3.58 Clause #24 (by backward demodulation #[23, 21]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Or (Eq True False) (Eq (r (skS.0 1 a_1 a_2)) False))) % 3.42/3.58 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Eq (r (skS.0 1 a_1 a_2)) False)) % 3.42/3.58 Clause #26 (by superposition #[25, 6]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f (skS.0 0 a))) False) (Or (Eq (r (skS.0 1 a_1 a_2)) False) (Eq False True)) % 3.42/3.58 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f (skS.0 0 a))) False) (Eq (r (skS.0 1 a_1 a_2)) False) % 3.42/3.59 Clause #28 (by superposition #[27, 14]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 1 a a_1)) False) (Eq False True) % 3.42/3.59 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (r (skS.0 1 a a_1)) False % 3.42/3.59 Clause #30 (by superposition #[29, 23]): Eq False True % 3.42/3.59 Clause #31 (by clausification #[30]): False % 3.42/3.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------