%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN057^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 3.59s 3.76s % Output : Proof 3.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYN057^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : duper %s % 0.14/0.36 % Computer : n013.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 15:13:08 EDT 2025 % 0.14/0.36 % CPUTime : % 3.59/3.76 SZS status Theorem for theBenchmark.p % 3.59/3.76 SZS output start Proof for theBenchmark.p % 3.59/3.76 Clause #0 (by assumption #[]): Eq % 3.59/3.76 (Not % 3.59/3.76 (And % 3.59/3.76 (And (And (Exists fun Xx => And (cF Xx) (Not (cG Xx))) (∀ (Xx : Iota), cF Xx → cH Xx)) % 3.59/3.76 (∀ (Xx : Iota), And (cJ Xx) (cI Xx) → cF Xx)) % 3.59/3.76 ((Exists fun Xx => And (cH Xx) (Not (cG Xx))) → ∀ (Xx : Iota), cI Xx → Not (cH Xx)) → % 3.59/3.76 ∀ (Xx : Iota), cJ Xx → Not (cI Xx))) % 3.59/3.76 True % 3.59/3.76 Clause #1 (by clausification #[0]): Eq % 3.59/3.76 (And % 3.59/3.76 (And (And (Exists fun Xx => And (cF Xx) (Not (cG Xx))) (∀ (Xx : Iota), cF Xx → cH Xx)) % 3.59/3.76 (∀ (Xx : Iota), And (cJ Xx) (cI Xx) → cF Xx)) % 3.59/3.76 ((Exists fun Xx => And (cH Xx) (Not (cG Xx))) → ∀ (Xx : Iota), cI Xx → Not (cH Xx)) → % 3.59/3.76 ∀ (Xx : Iota), cJ Xx → Not (cI Xx)) % 3.59/3.76 False % 3.59/3.76 Clause #2 (by clausification #[1]): Eq % 3.59/3.76 (And % 3.59/3.76 (And (And (Exists fun Xx => And (cF Xx) (Not (cG Xx))) (∀ (Xx : Iota), cF Xx → cH Xx)) % 3.59/3.76 (∀ (Xx : Iota), And (cJ Xx) (cI Xx) → cF Xx)) % 3.59/3.76 ((Exists fun Xx => And (cH Xx) (Not (cG Xx))) → ∀ (Xx : Iota), cI Xx → Not (cH Xx))) % 3.59/3.76 True % 3.59/3.76 Clause #3 (by clausification #[1]): Eq (∀ (Xx : Iota), cJ Xx → Not (cI Xx)) False % 3.59/3.76 Clause #4 (by clausification #[2]): Eq ((Exists fun Xx => And (cH Xx) (Not (cG Xx))) → ∀ (Xx : Iota), cI Xx → Not (cH Xx)) True % 3.59/3.76 Clause #5 (by clausification #[2]): Eq % 3.59/3.76 (And (And (Exists fun Xx => And (cF Xx) (Not (cG Xx))) (∀ (Xx : Iota), cF Xx → cH Xx)) % 3.59/3.76 (∀ (Xx : Iota), And (cJ Xx) (cI Xx) → cF Xx)) % 3.59/3.76 True % 3.59/3.76 Clause #6 (by clausification #[4]): Or (Eq (Exists fun Xx => And (cH Xx) (Not (cG Xx))) False) (Eq (∀ (Xx : Iota), cI Xx → Not (cH Xx)) True) % 3.59/3.76 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), cI Xx → Not (cH Xx)) True) (Eq (And (cH a) (Not (cG a))) False) % 3.59/3.76 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (And (cH a) (Not (cG a))) False) (Eq (cI a_1 → Not (cH a_1)) True) % 3.59/3.76 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cI a → Not (cH a)) True) (Or (Eq (cH a_1) False) (Eq (Not (cG a_1)) False)) % 3.59/3.76 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (cH a) False) (Or (Eq (Not (cG a)) False) (Or (Eq (cI a_1) False) (Eq (Not (cH a_1)) True))) % 3.59/3.76 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cH a) False) (Or (Eq (cI a_1) False) (Or (Eq (Not (cH a_1)) True) (Eq (cG a) True))) % 3.59/3.76 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (cH a) False) (Or (Eq (cI a_1) False) (Or (Eq (cG a) True) (Eq (cH a_1) False))) % 3.59/3.76 Clause #13 (by clausification #[3]): ∀ (a : Iota), Eq (Not (cJ (skS.0 0 a) → Not (cI (skS.0 0 a)))) True % 3.59/3.76 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (cJ (skS.0 0 a) → Not (cI (skS.0 0 a))) False % 3.59/3.76 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (cJ (skS.0 0 a)) True % 3.59/3.76 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Not (cI (skS.0 0 a))) False % 3.59/3.76 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (cI (skS.0 0 a)) True % 3.59/3.76 Clause #18 (by clausification #[5]): Eq (∀ (Xx : Iota), And (cJ Xx) (cI Xx) → cF Xx) True % 3.59/3.76 Clause #19 (by clausification #[5]): Eq (And (Exists fun Xx => And (cF Xx) (Not (cG Xx))) (∀ (Xx : Iota), cF Xx → cH Xx)) True % 3.59/3.76 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (And (cJ a) (cI a) → cF a) True % 3.59/3.76 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (And (cJ a) (cI a)) False) (Eq (cF a) True) % 3.59/3.76 Clause #22 (by clausification #[21]): ∀ (a : Iota), Or (Eq (cF a) True) (Or (Eq (cJ a) False) (Eq (cI a) False)) % 3.59/3.76 Clause #23 (by superposition #[22, 15]): ∀ (a : Iota), Or (Eq (cF (skS.0 0 a)) True) (Or (Eq (cI (skS.0 0 a)) False) (Eq False True)) % 3.59/3.76 Clause #24 (by clausification #[19]): Eq (∀ (Xx : Iota), cF Xx → cH Xx) True % 3.59/3.76 Clause #25 (by clausification #[19]): Eq (Exists fun Xx => And (cF Xx) (Not (cG Xx))) True % 3.59/3.76 Clause #26 (by clausification #[24]): ∀ (a : Iota), Eq (cF a → cH a) True % 3.59/3.76 Clause #27 (by clausification #[26]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq (cH a) True) % 3.59/3.76 Clause #28 (by clausification #[23]): ∀ (a : Iota), Or (Eq (cF (skS.0 0 a)) True) (Eq (cI (skS.0 0 a)) False) % 3.61/3.77 Clause #29 (by superposition #[28, 17]): ∀ (a : Iota), Or (Eq (cF (skS.0 0 a)) True) (Eq False True) % 3.61/3.77 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (cF (skS.0 0 a)) True % 3.61/3.77 Clause #32 (by superposition #[30, 27]): ∀ (a : Iota), Or (Eq True False) (Eq (cH (skS.0 0 a)) True) % 3.61/3.77 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (cH (skS.0 0 a)) True % 3.61/3.77 Clause #35 (by clausification #[25]): ∀ (a : Iota), Eq (And (cF (skS.0 1 a)) (Not (cG (skS.0 1 a)))) True % 3.61/3.77 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (Not (cG (skS.0 1 a))) True % 3.61/3.77 Clause #37 (by clausification #[35]): ∀ (a : Iota), Eq (cF (skS.0 1 a)) True % 3.61/3.77 Clause #38 (by clausification #[36]): ∀ (a : Iota), Eq (cG (skS.0 1 a)) False % 3.61/3.77 Clause #39 (by superposition #[37, 27]): ∀ (a : Iota), Or (Eq True False) (Eq (cH (skS.0 1 a)) True) % 3.61/3.77 Clause #42 (by clausification #[39]): ∀ (a : Iota), Eq (cH (skS.0 1 a)) True % 3.61/3.77 Clause #43 (by superposition #[42, 12]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cI a) False) (Or (Eq (cG (skS.0 1 a_1)) True) (Eq (cH a) False))) % 3.61/3.77 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (cI a) False) (Or (Eq (cG (skS.0 1 a_1)) True) (Eq (cH a) False)) % 3.61/3.77 Clause #45 (by superposition #[44, 17]): ∀ (a a_1 : Iota), Or (Eq (cG (skS.0 1 a)) True) (Or (Eq (cH (skS.0 0 a_1)) False) (Eq False True)) % 3.61/3.77 Clause #49 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (cG (skS.0 1 a)) True) (Eq (cH (skS.0 0 a_1)) False) % 3.61/3.77 Clause #50 (by superposition #[49, 33]): ∀ (a : Iota), Or (Eq (cG (skS.0 1 a)) True) (Eq False True) % 3.61/3.77 Clause #51 (by clausification #[50]): ∀ (a : Iota), Eq (cG (skS.0 1 a)) True % 3.61/3.77 Clause #52 (by superposition #[51, 38]): Eq True False % 3.61/3.77 Clause #53 (by clausification #[52]): False % 3.61/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------