%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN058^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:07:05 PM UTC 2025 % Result : Theorem 3.63s 3.78s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SYN058^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : duper %s % 0.14/0.35 % Computer : n014.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 15:35:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.63/3.78 SZS status Theorem for theBenchmark.p % 3.63/3.78 SZS output start Proof for theBenchmark.p % 3.63/3.78 Clause #0 (by assumption #[]): Eq % 3.63/3.78 (Not % 3.63/3.78 (And % 3.63/3.78 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0) % 3.63/3.78 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx))) % 3.63/3.78 ((Exists fun Xx => cS Xx) → ∀ (Xx : Iota), cF Xx → cG Xx) → % 3.63/3.78 ∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx)) % 3.63/3.78 True % 3.63/3.78 Clause #1 (by betaEtaReduce #[0]): Eq % 3.63/3.78 (Not % 3.63/3.78 (And % 3.63/3.78 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0) % 3.63/3.78 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx))) % 3.63/3.78 (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx) → % 3.63/3.78 ∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx)) % 3.63/3.78 True % 3.63/3.78 Clause #2 (by clausification #[1]): Eq % 3.63/3.78 (And % 3.63/3.78 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0) % 3.63/3.78 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx))) % 3.63/3.78 (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx) → % 3.63/3.78 ∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx) % 3.63/3.78 False % 3.63/3.78 Clause #3 (by clausification #[2]): Eq % 3.63/3.78 (And % 3.63/3.78 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0) % 3.63/3.78 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx))) % 3.63/3.78 (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx)) % 3.63/3.78 True % 3.63/3.78 Clause #4 (by clausification #[2]): Eq (∀ (Xx : Iota), And (cP Xx) (cF Xx) → cG Xx) False % 3.63/3.78 Clause #5 (by clausification #[3]): Eq (Exists cS → ∀ (Xx : Iota), cF Xx → cG Xx) True % 3.63/3.78 Clause #6 (by clausification #[3]): Eq % 3.63/3.78 (And (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0) % 3.63/3.78 ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx))) % 3.63/3.78 True % 3.63/3.78 Clause #7 (by clausification #[5]): Or (Eq (Exists cS) False) (Eq (∀ (Xx : Iota), cF Xx → cG Xx) True) % 3.63/3.78 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cF Xx → cG Xx) True) (Eq (cS a) False) % 3.63/3.78 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cS a) False) (Eq (cF a_1 → cG a_1) True) % 3.63/3.78 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (cS a) False) (Or (Eq (cF a_1) False) (Eq (cG a_1) True)) % 3.63/3.78 Clause #11 (by clausification #[4]): ∀ (a : Iota), Eq (Not (And (cP (skS.0 0 a)) (cF (skS.0 0 a)) → cG (skS.0 0 a))) True % 3.63/3.78 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (And (cP (skS.0 0 a)) (cF (skS.0 0 a)) → cG (skS.0 0 a)) False % 3.63/3.78 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (And (cP (skS.0 0 a)) (cF (skS.0 0 a))) True % 3.63/3.78 Clause #14 (by clausification #[12]): ∀ (a : Iota), Eq (cG (skS.0 0 a)) False % 3.63/3.78 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (cF (skS.0 0 a)) True % 3.63/3.78 Clause #16 (by clausification #[13]): ∀ (a : Iota), Eq (cP (skS.0 0 a)) True % 3.63/3.78 Clause #17 (by clausification #[6]): Eq ((∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) → Exists fun Xx => And (cQ Xx) (cS Xx)) True % 3.63/3.78 Clause #18 (by clausification #[6]): Eq (∀ (Xx : Iota), cP Xx → ∀ (Xx0 : Iota), cQ Xx0) True % 3.63/3.78 Clause #19 (by clausification #[17]): Or (Eq (∀ (Xx : Iota), Or (cQ Xx) (cR Xx)) False) (Eq (Exists fun Xx => And (cQ Xx) (cS Xx)) True) % 3.63/3.78 Clause #20 (by clausification #[19]): ∀ (a : Iota), Or (Eq (Exists fun Xx => And (cQ Xx) (cS Xx)) True) (Eq (Not (Or (cQ (skS.0 1 a)) (cR (skS.0 1 a)))) True) % 3.63/3.78 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 3.63/3.78 Or (Eq (Not (Or (cQ (skS.0 1 a)) (cR (skS.0 1 a)))) True) (Eq (And (cQ (skS.0 2 a_1)) (cS (skS.0 2 a_1))) True) % 3.63/3.78 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 3.63/3.78 Or (Eq (And (cQ (skS.0 2 a)) (cS (skS.0 2 a))) True) (Eq (Or (cQ (skS.0 1 a_1)) (cR (skS.0 1 a_1))) False) % 3.63/3.78 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (Or (cQ (skS.0 1 a)) (cR (skS.0 1 a))) False) (Eq (cS (skS.0 2 a_1)) True) % 3.63/3.78 Clause #26 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq (cQ (skS.0 1 a_1)) False) % 3.63/3.78 Clause #27 (by clausification #[18]): ∀ (a : Iota), Eq (cP a → ∀ (Xx0 : Iota), cQ Xx0) True % 3.63/3.78 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (∀ (Xx0 : Iota), cQ Xx0) True) % 3.63/3.78 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cQ a_1) True) % 3.63/3.78 Clause #30 (by superposition #[29, 16]): ∀ (a : Iota), Or (Eq (cQ a) True) (Eq False True) % 3.63/3.78 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (cQ a) True % 3.63/3.78 Clause #32 (by superposition #[26, 31]): ∀ (a : Iota), Or (Eq (cS (skS.0 2 a)) True) (Eq True False) % 3.63/3.78 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (cS (skS.0 2 a)) True % 3.63/3.78 Clause #34 (by superposition #[33, 10]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (cF a) False) (Eq (cG a) True)) % 3.63/3.78 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq (cG a) True) % 3.63/3.78 Clause #36 (by superposition #[35, 15]): ∀ (a : Iota), Or (Eq (cG (skS.0 0 a)) True) (Eq False True) % 3.63/3.78 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (cG (skS.0 0 a)) True % 3.63/3.78 Clause #38 (by superposition #[37, 14]): Eq True False % 3.63/3.78 Clause #41 (by clausification #[38]): False % 3.63/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------