%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN940+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 3.55s 3.72s % Output : Proof 3.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYN940+1 : TPTP v9.2.0. Released v3.1.0. % 0.06/0.14 % Command : duper %s % 0.13/0.35 % Computer : n025.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 15:38:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.55/3.72 SZS status Theorem for theBenchmark.p % 3.55/3.72 SZS output start Proof for theBenchmark.p % 3.55/3.72 Clause #0 (by assumption #[]): Eq % 3.55/3.72 (Not % 3.55/3.72 (∀ (B C : Iota), % 3.55/3.72 (∀ (Z : Iota), q (f Z)) → % 3.55/3.72 Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r B) (r C))) (q X))) % 3.55/3.72 True % 3.55/3.72 Clause #1 (by clausification #[0]): Eq % 3.55/3.72 (∀ (B C : Iota), % 3.55/3.72 (∀ (Z : Iota), q (f Z)) → Exists fun X => Exists fun Y => And (p (f Y) → And (p X) (r Y → And (r B) (r C))) (q X)) % 3.55/3.72 False % 3.55/3.72 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.55/3.72 Eq % 3.55/3.72 (Not % 3.55/3.72 (∀ (C : Iota), % 3.55/3.72 (∀ (Z : Iota), q (f Z)) → % 3.55/3.72 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))) % 3.55/3.72 True % 3.55/3.72 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.55/3.72 Eq % 3.55/3.72 (∀ (C : Iota), % 3.55/3.72 (∀ (Z : Iota), q (f Z)) → % 3.55/3.72 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)) % 3.55/3.72 False % 3.55/3.72 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.55/3.72 Eq % 3.55/3.72 (Not % 3.55/3.72 ((∀ (Z : Iota), q (f Z)) → % 3.55/3.72 Exists fun X => % 3.55/3.72 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))) % 3.55/3.72 True % 3.55/3.72 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.55/3.72 Eq % 3.55/3.72 ((∀ (Z : Iota), q (f Z)) → % 3.55/3.72 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)) % 3.55/3.72 False % 3.55/3.72 Clause #6 (by clausification #[5]): Eq (∀ (Z : Iota), q (f Z)) True % 3.55/3.72 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), % 3.55/3.72 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)) % 3.55/3.72 False % 3.55/3.72 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (q (f a)) True % 3.55/3.72 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.55/3.72 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 % 3.55/3.72 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.72 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 % 3.55/3.72 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.72 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) % 3.55/3.72 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (q a) False) (Eq (p (f a_1)) True) % 3.55/3.72 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.72 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) % 3.55/3.72 Clause #14 (by superposition #[12, 8]): ∀ (a : Iota), Or (Eq (p (f a)) True) (Eq False True) % 3.55/3.72 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (p (f a)) True % 3.55/3.72 Clause #16 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.72 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)) % 3.55/3.72 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (q a) False) (Or (Eq (p a) False) (Eq (r a_1) True)) % 3.55/3.72 Clause #18 (by clausification #[16]): ∀ (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)) % 3.55/3.72 Clause #19 (by superposition #[17, 8]): ∀ (a a_1 : Iota), Or (Eq (p (f a)) False) (Or (Eq (r a_1) True) (Eq False True)) % 3.55/3.72 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (p (f a)) False) (Eq (r a_1) True) % 3.55/3.72 Clause #21 (by superposition #[20, 15]): ∀ (a : Iota), Or (Eq (r a) True) (Eq False True) % 3.55/3.72 Clause #22 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 3.55/3.72 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))) % 3.55/3.72 Clause #24 (by clausification #[21]): ∀ (a : Iota), Eq (r a) True % 3.55/3.72 Clause #25 (by backward demodulation #[24, 22]): ∀ (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))) % 3.55/3.72 Clause #26 (by clausification #[25]): ∀ (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)) % 3.55/3.72 Clause #27 (by superposition #[26, 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)) % 3.55/3.72 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (f a)) False) (Eq (r (skS.0 1 a_1 a_2)) False) % 3.55/3.72 Clause #29 (by superposition #[28, 15]): ∀ (a a_1 : Iota), Or (Eq (r (skS.0 1 a a_1)) False) (Eq False True) % 3.55/3.72 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (r (skS.0 1 a a_1)) False % 3.55/3.72 Clause #31 (by superposition #[30, 24]): Eq False True % 3.55/3.72 Clause #32 (by clausification #[31]): False % 3.55/3.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------