%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV412^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:03:09 PM UTC 2025 % Result : Theorem 4.79s 4.97s % Output : Proof 4.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEV412^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n017.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 01:29:53 EDT 2025 % 0.15/0.35 % CPUTime : % 4.79/4.97 SZS status Theorem for theBenchmark.p % 4.79/4.97 SZS output start Proof for theBenchmark.p % 4.79/4.97 Clause #0 (by assumption #[]): Eq % 4.79/4.97 (Not % 4.79/4.97 (Or ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) → % 4.79/4.97 (∀ (Xx : Iota), cA Xx → cB Xx) → cG)) % 4.79/4.97 True % 4.79/4.97 Clause #1 (by clausification #[0]): Eq % 4.79/4.97 (Or ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) → (∀ (Xx : Iota), cA Xx → cB Xx) → cG) % 4.79/4.97 False % 4.79/4.97 Clause #2 (by clausification #[1]): Eq (Or ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) ((∀ (Xx : Iota), cA Xx → cB Xx) → cG)) True % 4.79/4.97 Clause #3 (by clausification #[1]): Eq ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) False % 4.79/4.97 Clause #4 (by clausification #[2]): Or (Eq ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) True) (Eq ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) True) % 4.79/4.97 Clause #5 (by clausification #[4]): Or (Eq ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) True) (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Eq cG True)) % 4.79/4.97 Clause #6 (by clausification #[5]): Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) % 4.79/4.97 (Or (Eq cG True) (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Eq cG True))) % 4.79/4.97 Clause #7 (by clausification #[6]): ∀ (a : Iota), % 4.79/4.97 Or (Eq cG True) % 4.79/4.97 (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Or (Eq cG True) (Eq (Not (cA (skS.0 0 a) → cB (skS.0 0 a))) True))) % 4.79/4.97 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.79/4.97 Or (Eq cG True) % 4.79/4.97 (Or (Eq cG True) % 4.79/4.97 (Or (Eq (Not (cA (skS.0 0 a) → cB (skS.0 0 a))) True) (Eq (Not (cA (skS.0 1 a_1) → cB (skS.0 1 a_1))) True))) % 4.79/4.97 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 4.79/4.97 Or (Eq cG True) % 4.79/4.97 (Or (Eq cG True) % 4.79/4.97 (Or (Eq (Not (cA (skS.0 1 a) → cB (skS.0 1 a))) True) (Eq (cA (skS.0 0 a_1) → cB (skS.0 0 a_1)) False))) % 4.79/4.97 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.79/4.97 Or (Eq cG True) % 4.79/4.97 (Or (Eq cG True) (Or (Eq (cA (skS.0 0 a) → cB (skS.0 0 a)) False) (Eq (cA (skS.0 1 a_1) → cB (skS.0 1 a_1)) False))) % 4.79/4.97 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.79/4.97 Or (Eq cG True) (Or (Eq cG True) (Or (Eq (cA (skS.0 1 a) → cB (skS.0 1 a)) False) (Eq (cA (skS.0 0 a_1)) True))) % 4.79/4.97 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.79/4.97 Or (Eq cG True) (Or (Eq cG True) (Or (Eq (cA (skS.0 1 a) → cB (skS.0 1 a)) False) (Eq (cB (skS.0 0 a_1)) False))) % 4.79/4.97 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Eq (cA (skS.0 1 a_1)) True))) % 4.79/4.97 Clause #14 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 1 a_1)) False))) % 4.79/4.97 Clause #15 (by eliminate duplicate literals #[13]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Eq (cA (skS.0 1 a_1)) True)) % 4.79/4.97 Clause #16 (by clausification #[3]): Eq (∀ (Xx : Iota), cA Xx → cB Xx) True % 4.79/4.97 Clause #17 (by clausification #[3]): Eq cG False % 4.79/4.97 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (cA a → cB a) True % 4.79/4.97 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (cA a) False) (Eq (cB a) True) % 4.79/4.97 Clause #22 (by backward demodulation #[17, 15]): ∀ (a a_1 : Iota), Or (Eq False True) (Or (Eq (cA (skS.0 0 a)) True) (Eq (cA (skS.0 1 a_1)) True)) % 4.79/4.97 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 4.79/4.97 Clause #25 (by superposition #[23, 19]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq True False) (Eq (cB (skS.0 1 a_1)) True)) % 4.79/4.97 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 1 a_1)) True) % 4.79/4.97 Clause #27 (by superposition #[26, 19]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq True False) (Eq (cB (skS.0 0 a_1)) True)) % 4.79/4.97 Clause #28 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Eq (cA (skS.0 1 a_1)) True))) % 4.79/4.97 Clause #29 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Eq (cB (skS.0 1 a_1)) False))) % 4.79/4.97 Clause #30 (by eliminate duplicate literals #[28]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Eq (cA (skS.0 1 a_1)) True)) % 4.81/5.00 Clause #31 (by forward demodulation #[30, 17]): ∀ (a a_1 : Iota), Or (Eq False True) (Or (Eq (cB (skS.0 0 a)) False) (Eq (cA (skS.0 1 a_1)) True)) % 4.81/5.00 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Eq (cA (skS.0 1 a_1)) True) % 4.81/5.00 Clause #33 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Eq (cB (skS.0 0 a_1)) True) % 4.81/5.00 Clause #34 (by superposition #[33, 32]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq True False) (Eq (cA (skS.0 1 a_1)) True)) % 4.81/5.00 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 4.81/5.00 Clause #36 (by superposition #[35, 19]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq True False) (Eq (cB (skS.0 1 a_1)) True)) % 4.81/5.00 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Eq (cB (skS.0 1 a_1)) True) % 4.81/5.00 Clause #38 (by equality factoring #[37]): ∀ (a : Iota), Or (Ne True True) (Eq (cB (skS.0 1 a)) True) % 4.81/5.00 Clause #39 (by clausification #[38]): ∀ (a : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 4.81/5.00 Clause #41 (by clausification #[39]): ∀ (a : Iota), Or (Eq (cB (skS.0 1 a)) True) (Eq True False) % 4.81/5.00 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (cB (skS.0 1 a)) True % 4.81/5.00 Clause #43 (by eliminate duplicate literals #[14]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 1 a_1)) False)) % 4.81/5.00 Clause #44 (by forward demodulation #[43, 17]): ∀ (a a_1 : Iota), Or (Eq False True) (Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 1 a_1)) False)) % 4.81/5.00 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 1 a_1)) False) % 4.81/5.00 Clause #46 (by superposition #[45, 42]): ∀ (a : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq False True) % 4.81/5.00 Clause #47 (by clausification #[46]): ∀ (a : Iota), Eq (cA (skS.0 0 a)) True % 4.81/5.00 Clause #48 (by superposition #[47, 19]): ∀ (a : Iota), Or (Eq True False) (Eq (cB (skS.0 0 a)) True) % 4.81/5.00 Clause #49 (by clausification #[48]): ∀ (a : Iota), Eq (cB (skS.0 0 a)) True % 4.81/5.00 Clause #57 (by eliminate duplicate literals #[29]): ∀ (a a_1 : Iota), Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Eq (cB (skS.0 1 a_1)) False)) % 4.81/5.00 Clause #58 (by forward demodulation #[57, 17]): ∀ (a a_1 : Iota), Or (Eq False True) (Or (Eq (cB (skS.0 0 a)) False) (Eq (cB (skS.0 1 a_1)) False)) % 4.81/5.00 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Eq (cB (skS.0 1 a_1)) False) % 4.81/5.00 Clause #60 (by superposition #[59, 49]): ∀ (a : Iota), Or (Eq (cB (skS.0 1 a)) False) (Eq False True) % 4.81/5.00 Clause #61 (by clausification #[60]): ∀ (a : Iota), Eq (cB (skS.0 1 a)) False % 4.81/5.00 Clause #62 (by superposition #[61, 42]): Eq False True % 4.81/5.00 Clause #63 (by clausification #[62]): False % 4.81/5.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------