%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN381+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:07:33 PM UTC 2025 % Result : Theorem 3.40s 3.59s % Output : Proof 3.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYN381+1 : TPTP v9.2.0. Released v2.0.0. % 0.13/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.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 15:19:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.40/3.59 SZS status Theorem for theBenchmark.p % 3.40/3.59 SZS output start Proof for theBenchmark.p % 3.40/3.59 Clause #0 (by assumption #[]): Eq % 3.40/3.59 (Not % 3.40/3.59 (And (And (∀ (X : Iota), (Exists fun Y => big_q X Y) → big_p X) (∀ (V : Iota), Exists fun U => big_q U V)) % 3.40/3.59 (∀ (W Z : Iota), big_q W Z → Or (big_q Z W) (big_q Z Z)) → % 3.40/3.59 ∀ (Z : Iota), big_p Z)) % 3.40/3.59 True % 3.40/3.59 Clause #1 (by betaEtaReduce #[0]): Eq % 3.40/3.59 (Not % 3.40/3.59 (And (And (∀ (X : Iota), Exists (big_q X) → big_p X) (∀ (V : Iota), Exists fun U => big_q U V)) % 3.40/3.59 (∀ (W Z : Iota), big_q W Z → Or (big_q Z W) (big_q Z Z)) → % 3.40/3.59 ∀ (Z : Iota), big_p Z)) % 3.40/3.59 True % 3.40/3.59 Clause #2 (by clausification #[1]): Eq % 3.40/3.59 (And (And (∀ (X : Iota), Exists (big_q X) → big_p X) (∀ (V : Iota), Exists fun U => big_q U V)) % 3.40/3.59 (∀ (W Z : Iota), big_q W Z → Or (big_q Z W) (big_q Z Z)) → % 3.40/3.59 ∀ (Z : Iota), big_p Z) % 3.40/3.59 False % 3.40/3.59 Clause #3 (by clausification #[2]): Eq % 3.40/3.59 (And (And (∀ (X : Iota), Exists (big_q X) → big_p X) (∀ (V : Iota), Exists fun U => big_q U V)) % 3.40/3.59 (∀ (W Z : Iota), big_q W Z → Or (big_q Z W) (big_q Z Z))) % 3.40/3.59 True % 3.40/3.59 Clause #4 (by clausification #[2]): Eq (∀ (Z : Iota), big_p Z) False % 3.40/3.59 Clause #5 (by clausification #[3]): Eq (∀ (W Z : Iota), big_q W Z → Or (big_q Z W) (big_q Z Z)) True % 3.40/3.59 Clause #6 (by clausification #[3]): Eq (And (∀ (X : Iota), Exists (big_q X) → big_p X) (∀ (V : Iota), Exists fun U => big_q U V)) True % 3.40/3.59 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Z : Iota), big_q a Z → Or (big_q Z a) (big_q Z Z)) True % 3.40/3.59 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (big_q a a_1 → Or (big_q a_1 a) (big_q a_1 a_1)) True % 3.40/3.59 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (big_q a a_1) False) (Eq (Or (big_q a_1 a) (big_q a_1 a_1)) True) % 3.40/3.59 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (big_q a a_1) False) (Or (Eq (big_q a_1 a) True) (Eq (big_q a_1 a_1) True)) % 3.40/3.59 Clause #11 (by clausification #[4]): ∀ (a : Iota), Eq (Not (big_p (skS.0 0 a))) True % 3.40/3.59 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (big_p (skS.0 0 a)) False % 3.40/3.59 Clause #13 (by clausification #[6]): Eq (∀ (V : Iota), Exists fun U => big_q U V) True % 3.40/3.59 Clause #14 (by clausification #[6]): Eq (∀ (X : Iota), Exists (big_q X) → big_p X) True % 3.40/3.59 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (Exists fun U => big_q U a) True % 3.40/3.59 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (big_q (skS.0 1 a a_1) a) True % 3.40/3.59 Clause #17 (by superposition #[16, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_q a (skS.0 1 a a_1)) True) (Eq (big_q a a) True)) % 3.40/3.59 Clause #18 (by clausification #[14]): ∀ (a : Iota), Eq (Exists (big_q a) → big_p a) True % 3.40/3.59 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (Exists (big_q a)) False) (Eq (big_p a) True) % 3.40/3.59 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_q a a_1) False) % 3.40/3.59 Clause #23 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_q a (skS.0 1 a a_1)) True) (Eq (big_q a a) True) % 3.40/3.59 Clause #25 (by superposition #[23, 20]): ∀ (a : Iota), Or (Eq (big_q a a) True) (Or (Eq (big_p a) True) (Eq True False)) % 3.40/3.59 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (big_q a a) True) (Eq (big_p a) True) % 3.40/3.59 Clause #27 (by superposition #[26, 20]): ∀ (a : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a) True) (Eq True False)) % 3.40/3.59 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq (big_p a) True) % 3.40/3.59 Clause #29 (by eliminate duplicate literals #[28]): ∀ (a : Iota), Eq (big_p a) True % 3.40/3.59 Clause #32 (by superposition #[29, 12]): Eq True False % 3.40/3.59 Clause #33 (by clausification #[32]): False % 3.40/3.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------