%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN055^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:07:04 PM UTC 2025 % Result : Theorem 3.84s 3.98s % Output : Proof 3.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYN055^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.15/0.36 % Computer : n023.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Thu Oct 2 15:04:23 EDT 2025 % 0.15/0.36 % CPUTime : % 3.84/3.98 SZS status Theorem for theBenchmark.p % 3.84/3.98 SZS output start Proof for theBenchmark.p % 3.84/3.98 Clause #0 (by assumption #[]): Eq % 3.84/3.98 (Not % 3.84/3.98 (And % 3.84/3.98 (And (And (Exists fun Xx => cP Xx) (∀ (Xx : Iota), cF Xx → And (Not (cG Xx)) (cR Xx))) % 3.84/3.98 (∀ (Xx : Iota), cP Xx → And (cG Xx) (cF Xx))) % 3.84/3.98 (Or (∀ (Xx : Iota), cP Xx → cQ Xx) (Exists fun Xx => And (cP Xx) (cR Xx))) → % 3.84/3.98 Exists fun Xx => And (cQ Xx) (cP Xx))) % 3.84/3.98 True % 3.84/3.98 Clause #1 (by betaEtaReduce #[0]): Eq % 3.84/3.98 (Not % 3.84/3.98 (And % 3.84/3.98 (And (And (Exists cP) (∀ (Xx : Iota), cF Xx → And (Not (cG Xx)) (cR Xx))) % 3.84/3.98 (∀ (Xx : Iota), cP Xx → And (cG Xx) (cF Xx))) % 3.84/3.98 (Or (∀ (Xx : Iota), cP Xx → cQ Xx) (Exists fun Xx => And (cP Xx) (cR Xx))) → % 3.84/3.98 Exists fun Xx => And (cQ Xx) (cP Xx))) % 3.84/3.98 True % 3.84/3.98 Clause #2 (by clausification #[1]): Eq % 3.84/3.98 (And % 3.84/3.98 (And (And (Exists cP) (∀ (Xx : Iota), cF Xx → And (Not (cG Xx)) (cR Xx))) % 3.84/3.98 (∀ (Xx : Iota), cP Xx → And (cG Xx) (cF Xx))) % 3.84/3.98 (Or (∀ (Xx : Iota), cP Xx → cQ Xx) (Exists fun Xx => And (cP Xx) (cR Xx))) → % 3.84/3.98 Exists fun Xx => And (cQ Xx) (cP Xx)) % 3.84/3.98 False % 3.84/3.98 Clause #3 (by clausification #[2]): Eq % 3.84/3.98 (And % 3.84/3.98 (And (And (Exists cP) (∀ (Xx : Iota), cF Xx → And (Not (cG Xx)) (cR Xx))) % 3.84/3.98 (∀ (Xx : Iota), cP Xx → And (cG Xx) (cF Xx))) % 3.84/3.98 (Or (∀ (Xx : Iota), cP Xx → cQ Xx) (Exists fun Xx => And (cP Xx) (cR Xx)))) % 3.84/3.98 True % 3.84/3.98 Clause #6 (by clausification #[3]): Eq % 3.84/3.98 (And (And (Exists cP) (∀ (Xx : Iota), cF Xx → And (Not (cG Xx)) (cR Xx))) % 3.84/3.98 (∀ (Xx : Iota), cP Xx → And (cG Xx) (cF Xx))) % 3.84/3.98 True % 3.84/3.98 Clause #15 (by clausification #[6]): Eq (∀ (Xx : Iota), cP Xx → And (cG Xx) (cF Xx)) True % 3.84/3.98 Clause #16 (by clausification #[6]): Eq (And (Exists cP) (∀ (Xx : Iota), cF Xx → And (Not (cG Xx)) (cR Xx))) True % 3.84/3.98 Clause #17 (by clausification #[15]): ∀ (a : Iota), Eq (cP a → And (cG a) (cF a)) True % 3.84/3.98 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (And (cG a) (cF a)) True) % 3.84/3.98 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (cF a) True) % 3.84/3.98 Clause #20 (by clausification #[18]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (cG a) True) % 3.84/3.98 Clause #21 (by clausification #[16]): Eq (∀ (Xx : Iota), cF Xx → And (Not (cG Xx)) (cR Xx)) True % 3.84/3.98 Clause #22 (by clausification #[16]): Eq (Exists cP) True % 3.84/3.98 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (cF a → And (Not (cG a)) (cR a)) True % 3.84/3.98 Clause #24 (by clausification #[23]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq (And (Not (cG a)) (cR a)) True) % 3.84/3.98 Clause #26 (by clausification #[24]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq (Not (cG a)) True) % 3.84/3.98 Clause #27 (by clausification #[22]): ∀ (a : Iota), Eq (cP (skS.0 1 a)) True % 3.84/3.98 Clause #30 (by superposition #[27, 19]): ∀ (a : Iota), Or (Eq True False) (Eq (cF (skS.0 1 a)) True) % 3.84/3.98 Clause #31 (by superposition #[27, 20]): ∀ (a : Iota), Or (Eq True False) (Eq (cG (skS.0 1 a)) True) % 3.84/3.98 Clause #32 (by clausification #[26]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq (cG a) False) % 3.84/3.98 Clause #33 (by clausification #[31]): ∀ (a : Iota), Eq (cG (skS.0 1 a)) True % 3.84/3.98 Clause #34 (by clausification #[30]): ∀ (a : Iota), Eq (cF (skS.0 1 a)) True % 3.84/3.98 Clause #36 (by superposition #[34, 32]): ∀ (a : Iota), Or (Eq True False) (Eq (cG (skS.0 1 a)) False) % 3.84/3.98 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (cG (skS.0 1 a)) False % 3.84/3.98 Clause #38 (by superposition #[37, 33]): Eq False True % 3.84/3.98 Clause #41 (by clausification #[38]): False % 3.84/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------