%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN359+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:07:29 PM UTC 2025 % Result : Theorem 3.39s 3.57s % Output : Proof 3.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN359+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n009.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 15:43:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.39/3.57 SZS status Theorem for theBenchmark.p % 3.39/3.57 SZS output start Proof for theBenchmark.p % 3.39/3.57 Clause #0 (by assumption #[]): Eq % 3.39/3.57 (Not % 3.39/3.57 (And (And (Exists fun X => big_r X) (∀ (Y : Iota), big_r Y → Exists fun Z => big_q Y Z)) % 3.39/3.57 (∀ (X Y : Iota), big_q X Y → big_q X X) → % 3.39/3.57 Exists fun X => Exists fun Y => And (big_q X Y) (big_r Y))) % 3.39/3.57 True % 3.39/3.57 Clause #1 (by betaEtaReduce #[0]): Eq % 3.39/3.57 (Not % 3.39/3.57 (And (And (Exists big_r) (∀ (Y : Iota), big_r Y → Exists (big_q Y))) (∀ (X Y : Iota), big_q X Y → big_q X X) → % 3.39/3.57 Exists fun X => Exists fun Y => And (big_q X Y) (big_r Y))) % 3.39/3.57 True % 3.39/3.57 Clause #2 (by clausification #[1]): Eq % 3.39/3.57 (And (And (Exists big_r) (∀ (Y : Iota), big_r Y → Exists (big_q Y))) (∀ (X Y : Iota), big_q X Y → big_q X X) → % 3.39/3.57 Exists fun X => Exists fun Y => And (big_q X Y) (big_r Y)) % 3.39/3.57 False % 3.39/3.57 Clause #3 (by clausification #[2]): Eq (And (And (Exists big_r) (∀ (Y : Iota), big_r Y → Exists (big_q Y))) (∀ (X Y : Iota), big_q X Y → big_q X X)) True % 3.39/3.57 Clause #4 (by clausification #[2]): Eq (Exists fun X => Exists fun Y => And (big_q X Y) (big_r Y)) False % 3.39/3.57 Clause #5 (by clausification #[3]): Eq (∀ (X Y : Iota), big_q X Y → big_q X X) True % 3.39/3.57 Clause #6 (by clausification #[3]): Eq (And (Exists big_r) (∀ (Y : Iota), big_r Y → Exists (big_q Y))) True % 3.39/3.57 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y : Iota), big_q a Y → big_q a a) True % 3.39/3.57 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (big_q a a_1 → big_q a a) True % 3.39/3.57 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (big_q a a_1) False) (Eq (big_q a a) True) % 3.39/3.57 Clause #10 (by clausification #[6]): Eq (∀ (Y : Iota), big_r Y → Exists (big_q Y)) True % 3.39/3.57 Clause #11 (by clausification #[6]): Eq (Exists big_r) True % 3.39/3.57 Clause #12 (by clausification #[10]): ∀ (a : Iota), Eq (big_r a → Exists (big_q a)) True % 3.39/3.57 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (big_r a) False) (Eq (Exists (big_q a)) True) % 3.39/3.57 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_r a) False) (Eq (big_q a (skS.0 0 a a_1)) True) % 3.39/3.57 Clause #15 (by clausification #[11]): ∀ (a : Iota), Eq (big_r (skS.0 1 a)) True % 3.39/3.57 Clause #16 (by superposition #[15, 14]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_q (skS.0 1 a) (skS.0 0 (skS.0 1 a) a_1)) True) % 3.39/3.57 Clause #17 (by clausification #[4]): ∀ (a : Iota), Eq (Exists fun Y => And (big_q a Y) (big_r Y)) False % 3.39/3.57 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (And (big_q a a_1) (big_r a_1)) False % 3.39/3.57 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_q a a_1) False) (Eq (big_r a_1) False) % 3.39/3.57 Clause #20 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (big_q (skS.0 1 a) (skS.0 0 (skS.0 1 a) a_1)) True % 3.39/3.57 Clause #21 (by superposition #[20, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (big_q (skS.0 1 a) (skS.0 1 a)) True) % 3.39/3.57 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (big_q (skS.0 1 a) (skS.0 1 a)) True % 3.39/3.57 Clause #24 (by superposition #[23, 19]): ∀ (a : Iota), Or (Eq True False) (Eq (big_r (skS.0 1 a)) False) % 3.39/3.57 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (big_r (skS.0 1 a)) False % 3.39/3.57 Clause #26 (by superposition #[25, 15]): Eq False True % 3.39/3.57 Clause #27 (by clausification #[26]): False % 3.39/3.57 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------