%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN939+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:08:16 PM UTC 2025 % Result : Theorem 5.14s 5.31s % Output : Proof 5.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SYN939+1 : TPTP v9.2.0. Released v3.1.0. % 0.10/0.14 % Command : duper %s % 0.14/0.35 % Computer : n007.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 15:23:38 EDT 2025 % 0.14/0.35 % CPUTime : % 5.14/5.31 SZS status Theorem for theBenchmark.p % 5.14/5.31 SZS output start Proof for theBenchmark.p % 5.14/5.31 Clause #0 (by assumption #[]): Eq % 5.14/5.31 (Not % 5.14/5.31 (∀ (C B : Iota), % 5.14/5.31 (∀ (Z : Iota), q (f Z)) → % 5.14/5.31 Exists fun X => Exists fun Y => And (And (p (f Y) → p X) (r Y → And (r B) (r C))) (q X))) % 5.14/5.31 True % 5.14/5.31 Clause #1 (by clausification #[0]): Eq % 5.14/5.31 (∀ (C B : Iota), % 5.14/5.31 (∀ (Z : Iota), q (f Z)) → Exists fun X => Exists fun Y => And (And (p (f Y) → p X) (r Y → And (r B) (r C))) (q X)) % 5.14/5.31 False % 5.14/5.31 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 5.14/5.31 Eq % 5.14/5.31 (Not % 5.14/5.31 (∀ (B : Iota), % 5.14/5.31 (∀ (Z : Iota), q (f Z)) → % 5.14/5.31 Exists fun X => Exists fun Y => And (And (p (f Y) → p X) (r Y → And (r B) (r (skS.0 0 a)))) (q X))) % 5.14/5.31 True % 5.14/5.31 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 5.14/5.31 Eq % 5.14/5.31 (∀ (B : Iota), % 5.14/5.31 (∀ (Z : Iota), q (f Z)) → % 5.14/5.31 Exists fun X => Exists fun Y => And (And (p (f Y) → p X) (r Y → And (r B) (r (skS.0 0 a)))) (q X)) % 5.14/5.31 False % 5.14/5.31 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 5.14/5.31 Eq % 5.14/5.31 (Not % 5.14/5.31 ((∀ (Z : Iota), q (f Z)) → % 5.14/5.31 Exists fun X => % 5.14/5.31 Exists fun Y => And (And (p (f Y) → p X) (r Y → And (r (skS.0 1 a a_1)) (r (skS.0 0 a)))) (q X))) % 5.14/5.31 True % 5.14/5.31 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 5.14/5.31 Eq % 5.14/5.31 ((∀ (Z : Iota), q (f Z)) → % 5.14/5.31 Exists fun X => Exists fun Y => And (And (p (f Y) → p X) (r Y → And (r (skS.0 1 a a_1)) (r (skS.0 0 a)))) (q X)) % 5.14/5.31 False % 5.14/5.31 Clause #6 (by clausification #[5]): Eq (∀ (Z : Iota), q (f Z)) True % 5.14/5.31 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), % 5.14/5.31 Eq (Exists fun X => Exists fun Y => And (And (p (f Y) → p X) (r Y → And (r (skS.0 1 a a_1)) (r (skS.0 0 a)))) (q X)) % 5.14/5.31 False % 5.14/5.31 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (q (f a)) True % 5.14/5.31 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 5.14/5.31 Eq (Exists fun Y => And (And (p (f Y) → p a) (r Y → And (r (skS.0 1 a_1 a_2)) (r (skS.0 0 a_1)))) (q a)) False % 5.14/5.31 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 5.14/5.31 Eq (And (And (p (f a) → p a_1) (r a → And (r (skS.0 1 a_2 a_3)) (r (skS.0 0 a_2)))) (q a_1)) False % 5.14/5.31 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota), % 5.14/5.31 Or (Eq (And (p (f a) → p a_1) (r a → And (r (skS.0 1 a_2 a_3)) (r (skS.0 0 a_2)))) False) (Eq (q a_1) False) % 5.14/5.31 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota), % 5.14/5.31 Or (Eq (q a) False) (Or (Eq (p (f a_1) → p a) False) (Eq (r a_1 → And (r (skS.0 1 a_2 a_3)) (r (skS.0 0 a_2))) False)) % 5.14/5.31 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 5.14/5.31 Or (Eq (q a) False) (Or (Eq (r a_1 → And (r (skS.0 1 a_2 a_3)) (r (skS.0 0 a_2))) False) (Eq (p (f a_1)) True)) % 5.14/5.31 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 5.14/5.31 Or (Eq (q a) False) (Or (Eq (r a_1 → And (r (skS.0 1 a_2 a_3)) (r (skS.0 0 a_2))) False) (Eq (p a) False)) % 5.14/5.31 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (q a) False) (Or (Eq (p (f a_1)) True) (Eq (r a_1) True)) % 5.14/5.31 Clause #16 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 5.14/5.31 Or (Eq (q a) False) (Or (Eq (p (f a_1)) True) (Eq (And (r (skS.0 1 a_2 a_3)) (r (skS.0 0 a_2))) False)) % 5.14/5.31 Clause #17 (by superposition #[15, 8]): ∀ (a : Iota), Or (Eq (p (f a)) True) (Or (Eq (r a) True) (Eq False True)) % 5.14/5.31 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (p (f a)) True) (Eq (r a) True) % 5.14/5.31 Clause #19 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : Iota), % 5.14/5.31 Or (Eq (q a) False) (Or (Eq (p (f a_1)) True) (Or (Eq (r (skS.0 1 a_2 a_3)) False) (Eq (r (skS.0 0 a_2)) False))) % 5.14/5.31 Clause #20 (by superposition #[19, 8]): ∀ (a a_1 a_2 : Iota), % 5.14/5.31 Or (Eq (p (f a)) True) (Or (Eq (r (skS.0 1 a_1 a_2)) False) (Or (Eq (r (skS.0 0 a_1)) False) (Eq False True))) % 5.14/5.31 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f a)) True) (Or (Eq (r (skS.0 1 a_1 a_2)) False) (Eq (r (skS.0 0 a_1)) False)) % 5.14/5.31 Clause #22 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Eq (r a_1) True)) % 5.14/5.31 Clause #23 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Eq (And (r (skS.0 1 a_1 a_2)) (r (skS.0 0 a_1))) False)) % 5.18/5.34 Clause #24 (by superposition #[22, 8]): ∀ (a a_1 : Iota), Or (Eq (p (f a)) False) (Or (Eq (r a_1) True) (Eq False True)) % 5.18/5.34 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p (f a)) False) (Eq (r a_1) True) % 5.18/5.34 Clause #26 (by superposition #[25, 18]): ∀ (a a_1 : Iota), Or (Eq (r a) True) (Or (Eq False True) (Eq (r a_1) True)) % 5.18/5.34 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (r a) True) (Eq (r a_1) True) % 5.18/5.34 Clause #29 (by equality factoring #[27]): ∀ (a : Iota), Or (Ne True True) (Eq (r a) True) % 5.18/5.34 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (r a) True) (Or (Eq True False) (Eq True False)) % 5.18/5.34 Clause #32 (by clausification #[30]): ∀ (a : Iota), Or (Eq (r a) True) (Eq True False) % 5.18/5.34 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (r a) True % 5.18/5.34 Clause #34 (by backward demodulation #[33, 21]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f a)) True) (Or (Eq (r (skS.0 1 a_1 a_2)) False) (Eq True False)) % 5.18/5.34 Clause #36 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 5.18/5.34 Or (Eq (q a) False) (Or (Eq (p a) False) (Or (Eq (r (skS.0 1 a_1 a_2)) False) (Eq (r (skS.0 0 a_1)) False))) % 5.18/5.34 Clause #37 (by forward demodulation #[36, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Or (Eq (r (skS.0 1 a_1 a_2)) False) (Eq True False))) % 5.18/5.34 Clause #38 (by clausification #[37]): ∀ (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)) % 5.18/5.34 Clause #39 (by superposition #[38, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f a)) False) (Or (Eq (r (skS.0 1 a_1 a_2)) False) (Eq False True)) % 5.18/5.34 Clause #40 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f a)) True) (Eq (r (skS.0 1 a_1 a_2)) False) % 5.18/5.34 Clause #41 (by superposition #[40, 33]): ∀ (a : Iota), Or (Eq (p (f a)) True) (Eq False True) % 5.18/5.34 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (p (f a)) True % 5.18/5.34 Clause #43 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f a)) False) (Eq (r (skS.0 1 a_1 a_2)) False) % 5.18/5.34 Clause #44 (by superposition #[43, 42]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 1 a a_1)) False) (Eq False True) % 5.18/5.34 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (r (skS.0 1 a a_1)) False % 5.18/5.34 Clause #46 (by superposition #[45, 33]): Eq False True % 5.18/5.34 Clause #47 (by clausification #[46]): False % 5.18/5.34 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------