%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV416^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 6.14s 6.32s % Output : Proof 6.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEV416^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n021.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 : Fri Oct 3 01:25:08 EDT 2025 % 0.14/0.35 % CPUTime : % 6.14/6.32 SZS status Theorem for theBenchmark.p % 6.14/6.32 SZS output start Proof for theBenchmark.p % 6.14/6.32 Clause #0 (by assumption #[]): Eq % 6.14/6.32 (Not % 6.14/6.32 (Or (And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx) → cG) ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) → % 6.14/6.32 (∀ (Xx : Iota), cA Xx → cB Xx) → cG)) % 6.14/6.32 True % 6.14/6.32 Clause #1 (by clausification #[0]): Eq % 6.14/6.32 (Or (And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx) → cG) ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) → % 6.14/6.32 (∀ (Xx : Iota), cA Xx → cB Xx) → cG) % 6.14/6.32 False % 6.14/6.32 Clause #2 (by clausification #[1]): Eq (Or (And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx) → cG) ((∀ (Xx : Iota), cA Xx → cB Xx) → cG)) % 6.14/6.32 True % 6.14/6.32 Clause #3 (by clausification #[1]): Eq ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) False % 6.14/6.32 Clause #4 (by clausification #[2]): Or (Eq (And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx) → cG) True) % 6.14/6.32 (Eq ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) True) % 6.14/6.32 Clause #5 (by clausification #[4]): Or (Eq ((∀ (Xx : Iota), cA Xx → cB Xx) → cG) True) % 6.14/6.32 (Or (Eq (And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx)) False) (Eq cG True)) % 6.14/6.32 Clause #6 (by clausification #[5]): Or (Eq (And (∀ (Xx : Iota), cA Xx → cB Xx) (∀ (Xx : Iota), cA Xx → cB Xx)) False) % 6.14/6.32 (Or (Eq cG True) (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Eq cG True))) % 6.14/6.32 Clause #7 (by clausification #[6]): Or (Eq cG True) % 6.14/6.32 (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) % 6.14/6.32 (Or (Eq cG True) (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False)))) % 6.14/6.32 Clause #8 (by clausification #[7]): ∀ (a : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) % 6.14/6.32 (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) (Eq (Not (cA (skS.0 0 a) → cB (skS.0 0 a))) True)))) % 6.14/6.32 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (∀ (Xx : Iota), cA Xx → cB Xx) False) % 6.14/6.32 (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)))) % 6.14/6.32 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (Not (cA (skS.0 0 a) → cB (skS.0 0 a))) True) % 6.14/6.32 (Or (Eq (Not (cA (skS.0 1 a_1) → cB (skS.0 1 a_1))) True) % 6.14/6.32 (Eq (Not (cA (skS.0 2 a_2) → cB (skS.0 2 a_2))) True)))) % 6.14/6.32 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (Not (cA (skS.0 1 a) → cB (skS.0 1 a))) True) % 6.14/6.32 (Or (Eq (Not (cA (skS.0 2 a_1) → cB (skS.0 2 a_1))) True) (Eq (cA (skS.0 0 a_2) → cB (skS.0 0 a_2)) False)))) % 6.14/6.32 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (Not (cA (skS.0 2 a) → cB (skS.0 2 a))) True) % 6.14/6.32 (Or (Eq (cA (skS.0 0 a_1) → cB (skS.0 0 a_1)) False) (Eq (cA (skS.0 1 a_2) → cB (skS.0 1 a_2)) False)))) % 6.14/6.32 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (cA (skS.0 0 a) → cB (skS.0 0 a)) False) % 6.14/6.32 (Or (Eq (cA (skS.0 1 a_1) → cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2) → cB (skS.0 2 a_2)) False)))) % 6.14/6.32 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (cA (skS.0 1 a) → cB (skS.0 1 a)) False) % 6.14/6.32 (Or (Eq (cA (skS.0 2 a_1) → cB (skS.0 2 a_1)) False) (Eq (cA (skS.0 0 a_2)) True)))) % 6.14/6.32 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (cA (skS.0 1 a) → cB (skS.0 1 a)) False) % 6.14/6.32 (Or (Eq (cA (skS.0 2 a_1) → cB (skS.0 2 a_1)) False) (Eq (cB (skS.0 0 a_2)) False)))) % 6.14/6.32 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 6.14/6.32 Or (Eq cG True) % 6.14/6.32 (Or (Eq cG True) % 6.14/6.32 (Or (Eq (cA (skS.0 2 a) → cB (skS.0 2 a)) False) (Or (Eq (cA (skS.0 0 a_1)) True) (Eq (cA (skS.0 1 a_2)) True)))) % 6.14/6.32 Clause #17 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) % 6.14/6.35 (Or (Eq (cA (skS.0 2 a) → cB (skS.0 2 a)) False) (Or (Eq (cA (skS.0 0 a_1)) True) (Eq (cB (skS.0 1 a_2)) False)))) % 6.14/6.35 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True)))) % 6.14/6.35 Clause #19 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False)))) % 6.14/6.35 Clause #20 (by eliminate duplicate literals #[18]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.35 Clause #21 (by clausification #[3]): Eq (∀ (Xx : Iota), cA Xx → cB Xx) True % 6.14/6.35 Clause #22 (by clausification #[3]): Eq cG False % 6.14/6.35 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (cA a → cB a) True % 6.14/6.35 Clause #24 (by clausification #[23]): ∀ (a : Iota), Or (Eq (cA a) False) (Eq (cB a) True) % 6.14/6.35 Clause #28 (by backward demodulation #[22, 20]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq False True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.35 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True)) % 6.14/6.35 Clause #30 (by superposition #[29, 24]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 2 a_1)) True) (Or (Eq True False) (Eq (cB (skS.0 0 a_2)) True))) % 6.14/6.35 Clause #32 (by superposition #[29, 24]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq True False) (Eq (cB (skS.0 2 a_2)) True))) % 6.14/6.35 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) True)) % 6.14/6.35 Clause #34 (by superposition #[33, 24]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cB (skS.0 2 a_1)) True) (Or (Eq True False) (Eq (cB (skS.0 0 a_2)) True))) % 6.14/6.35 Clause #36 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) % 6.14/6.35 (Or (Eq (cA (skS.0 2 a) → cB (skS.0 2 a)) False) (Or (Eq (cB (skS.0 0 a_1)) False) (Eq (cA (skS.0 1 a_2)) True)))) % 6.14/6.35 Clause #37 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) % 6.14/6.35 (Or (Eq (cA (skS.0 2 a) → cB (skS.0 2 a)) False) % 6.14/6.35 (Or (Eq (cB (skS.0 0 a_1)) False) (Eq (cB (skS.0 1 a_2)) False)))) % 6.14/6.35 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True)))) % 6.14/6.35 Clause #39 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False)))) % 6.14/6.35 Clause #40 (by eliminate duplicate literals #[38]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.35 Clause #41 (by forward demodulation #[40, 22]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq False True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.35 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True)) % 6.14/6.35 Clause #47 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cB (skS.0 2 a_1)) True) (Eq (cB (skS.0 0 a_2)) True)) % 6.14/6.35 Clause #49 (by superposition #[47, 42]): ∀ (a a_1 a_2 a_3 : Iota), % 6.14/6.35 Or (Eq (cA (skS.0 1 a)) True) % 6.14/6.35 (Or (Eq (cB (skS.0 2 a_1)) True) % 6.14/6.35 (Or (Eq True False) (Or (Eq (cA (skS.0 1 a_2)) True) (Eq (cA (skS.0 2 a_3)) True)))) % 6.14/6.35 Clause #54 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 6.14/6.35 Or (Eq cG True) % 6.14/6.35 (Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True)))) % 6.14/6.35 Clause #55 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) % 6.14/6.38 (Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False)))) % 6.14/6.38 Clause #56 (by eliminate duplicate literals #[54]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.38 Clause #57 (by forward demodulation #[56, 22]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq False True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.38 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True)) % 6.14/6.38 Clause #63 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 2 a_1)) True) (Eq (cB (skS.0 0 a_2)) True)) % 6.14/6.38 Clause #66 (by superposition #[63, 42]): ∀ (a a_1 a_2 a_3 : Iota), % 6.14/6.38 Or (Eq (cA (skS.0 1 a)) True) % 6.14/6.38 (Or (Eq (cA (skS.0 2 a_1)) True) % 6.14/6.38 (Or (Eq True False) (Or (Eq (cA (skS.0 1 a_2)) True) (Eq (cA (skS.0 2 a_3)) True)))) % 6.14/6.38 Clause #73 (by eliminate duplicate literals #[19]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #74 (by forward demodulation #[73, 22]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq False True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False)) % 6.14/6.38 Clause #90 (by eliminate duplicate literals #[55]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #91 (by forward demodulation #[90, 22]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq False True) (Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False)) % 6.14/6.38 Clause #97 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) % 6.14/6.38 (Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True)))) % 6.14/6.38 Clause #98 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) % 6.14/6.38 (Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False)))) % 6.14/6.38 Clause #99 (by eliminate duplicate literals #[97]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.38 Clause #100 (by forward demodulation #[99, 22]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq False True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True))) % 6.14/6.38 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cA (skS.0 2 a_2)) True)) % 6.14/6.38 Clause #106 (by eliminate duplicate literals #[98]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #107 (by forward demodulation #[106, 22]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq False True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #108 (by clausification #[107]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cB (skS.0 1 a_1)) False) (Eq (cB (skS.0 2 a_2)) False)) % 6.14/6.38 Clause #113 (by eliminate duplicate literals #[39]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq cG True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #114 (by forward demodulation #[113, 22]): ∀ (a a_1 a_2 : Iota), % 6.14/6.38 Or (Eq False True) (Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False))) % 6.14/6.38 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 0 a)) False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False)) % 6.25/6.41 Clause #141 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 6.25/6.41 Or (Eq (cA (skS.0 1 a)) True) % 6.25/6.41 (Or (Eq (cB (skS.0 2 a_1)) True) (Or (Eq (cA (skS.0 1 a_2)) True) (Eq (cA (skS.0 2 a_3)) True))) % 6.25/6.41 Clause #146 (by equality factoring #[141]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 2 a_1)) True) (Or (Ne True True) (Eq (cA (skS.0 1 a_2)) True))) % 6.25/6.41 Clause #147 (by clausification #[146]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cB (skS.0 2 a)) True) % 6.25/6.41 (Or (Eq (cA (skS.0 2 a_1)) True) (Or (Eq (cA (skS.0 1 a_2)) True) (Or (Eq True False) (Eq True False)))) % 6.25/6.41 Clause #149 (by clausification #[147]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 2 a_1)) True) (Or (Eq (cA (skS.0 1 a_2)) True) (Eq True False))) % 6.25/6.41 Clause #150 (by clausification #[149]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 2 a_1)) True) (Eq (cA (skS.0 1 a_2)) True)) % 6.25/6.41 Clause #153 (by superposition #[150, 24]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 2 a_1)) True) (Or (Eq True False) (Eq (cB (skS.0 1 a_2)) True))) % 6.25/6.41 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 2 a_1)) True) (Eq (cB (skS.0 1 a_2)) True)) % 6.25/6.41 Clause #156 (by superposition #[154, 24]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cB (skS.0 1 a_1)) True) (Or (Eq True False) (Eq (cB (skS.0 2 a_2)) True))) % 6.25/6.41 Clause #159 (by clausification #[156]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cB (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) True)) % 6.25/6.41 Clause #164 (by equality factoring #[159]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Ne True True) (Eq (cB (skS.0 2 a_1)) True)) % 6.25/6.41 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq (cB (skS.0 2 a_1)) True) (Or (Eq True False) (Eq True False))) % 6.25/6.41 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Or (Eq (cB (skS.0 2 a_1)) True) (Eq True False)) % 6.25/6.41 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) True) (Eq (cB (skS.0 2 a_1)) True) % 6.25/6.41 Clause #169 (by superposition #[168, 58]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (cA (skS.0 2 a_2)) True))) % 6.25/6.41 Clause #178 (by clausification #[169]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 0 a_1)) True) (Eq (cA (skS.0 2 a_2)) True)) % 6.25/6.41 Clause #181 (by superposition #[178, 24]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (cB (skS.0 2 a_2)) True))) % 6.25/6.41 Clause #182 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), Or (Eq (cB (skS.0 2 a)) True) (Or (Eq (cA (skS.0 0 a_1)) True) (Eq (cB (skS.0 2 a_2)) True)) % 6.25/6.41 Clause #186 (by equality factoring #[182]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Ne True True) (Eq (cB (skS.0 2 a_1)) True)) % 6.25/6.41 Clause #187 (by clausification #[186]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 2 a_1)) True) (Or (Eq True False) (Eq True False))) % 6.25/6.41 Clause #189 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cB (skS.0 2 a_1)) True) (Eq True False)) % 6.25/6.41 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 2 a_1)) True) % 6.25/6.41 Clause #191 (by superposition #[190, 24]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 2 a)) True) (Or (Eq True False) (Eq (cB (skS.0 0 a_1)) True)) % 6.25/6.41 Clause #193 (by clausification #[191]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 2 a)) True) (Eq (cB (skS.0 0 a_1)) True) % 6.25/6.41 Clause #240 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 6.25/6.41 Or (Eq (cA (skS.0 1 a)) True) % 6.25/6.41 (Or (Eq (cA (skS.0 2 a_1)) True) (Or (Eq (cA (skS.0 1 a_2)) True) (Eq (cA (skS.0 2 a_3)) True))) % 6.25/6.41 Clause #246 (by equality factoring #[240]): ∀ (a a_1 a_2 : Iota), % 6.25/6.41 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Ne True True) (Eq (cA (skS.0 2 a_2)) True))) % 6.25/6.44 Clause #248 (by clausification #[246]): ∀ (a a_1 a_2 : Iota), % 6.25/6.44 Or (Eq (cA (skS.0 1 a)) True) % 6.25/6.44 (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq (cA (skS.0 2 a_2)) True) (Or (Eq True False) (Eq True False)))) % 6.25/6.44 Clause #250 (by clausification #[248]): ∀ (a a_1 a_2 : Iota), % 6.25/6.44 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq (cA (skS.0 2 a_2)) True) (Eq True False))) % 6.25/6.44 Clause #251 (by clausification #[250]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 2 a_2)) True)) % 6.25/6.44 Clause #254 (by equality factoring #[251]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 2 a)) True) (Or (Ne True True) (Eq (cA (skS.0 1 a_1)) True)) % 6.25/6.44 Clause #255 (by clausification #[254]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 2 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False))) % 6.25/6.44 Clause #257 (by clausification #[255]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 2 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq True False)) % 6.25/6.44 Clause #258 (by clausification #[257]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 2 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 6.25/6.44 Clause #259 (by superposition #[258, 24]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq True False) (Eq (cB (skS.0 2 a_1)) True)) % 6.25/6.44 Clause #265 (by clausification #[259]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Eq (cB (skS.0 2 a_1)) True) % 6.25/6.44 Clause #267 (by superposition #[265, 75]): ∀ (a a_1 a_2 : Iota), % 6.25/6.44 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 0 a_1)) True) (Or (Eq (cA (skS.0 1 a_2)) True) (Eq True False))) % 6.25/6.44 Clause #272 (by clausification #[267]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 0 a_1)) True) (Eq (cA (skS.0 1 a_2)) True)) % 6.25/6.44 Clause #276 (by equality factoring #[272]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Ne True True) (Eq (cA (skS.0 1 a_1)) True)) % 6.25/6.44 Clause #277 (by clausification #[276]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False))) % 6.25/6.44 Clause #279 (by clausification #[277]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq True False)) % 6.25/6.44 Clause #280 (by clausification #[279]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 6.25/6.44 Clause #281 (by superposition #[280, 24]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq True False) (Eq (cB (skS.0 0 a_1)) True)) % 6.25/6.44 Clause #292 (by clausification #[281]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Eq (cB (skS.0 0 a_1)) True) % 6.25/6.44 Clause #296 (by superposition #[292, 115]): ∀ (a a_1 a_2 : Iota), % 6.25/6.44 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq True False) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False))) % 6.25/6.44 Clause #309 (by clausification #[296]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cB (skS.0 2 a_2)) False)) % 6.25/6.44 Clause #313 (by superposition #[309, 265]): ∀ (a a_1 a_2 : Iota), % 6.25/6.44 Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq (cA (skS.0 1 a_2)) True) (Eq False True))) % 6.25/6.44 Clause #315 (by clausification #[313]): ∀ (a a_1 a_2 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq (cA (skS.0 1 a_2)) True)) % 6.25/6.44 Clause #317 (by equality factoring #[315]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Ne True True) (Eq (cA (skS.0 1 a_1)) True)) % 6.25/6.44 Clause #318 (by clausification #[317]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False))) % 6.25/6.44 Clause #320 (by clausification #[318]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq (cA (skS.0 1 a_1)) True) (Eq True False)) % 6.25/6.44 Clause #321 (by clausification #[320]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 1 a)) True) (Eq (cA (skS.0 1 a_1)) True) % 6.25/6.44 Clause #323 (by equality factoring #[321]): ∀ (a : Iota), Or (Ne True True) (Eq (cA (skS.0 1 a)) True) % 6.25/6.44 Clause #324 (by clausification #[323]): ∀ (a : Iota), Or (Eq (cA (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 6.25/6.44 Clause #326 (by clausification #[324]): ∀ (a : Iota), Or (Eq (cA (skS.0 1 a)) True) (Eq True False) % 6.25/6.46 Clause #327 (by clausification #[326]): ∀ (a : Iota), Eq (cA (skS.0 1 a)) True % 6.25/6.46 Clause #328 (by superposition #[327, 24]): ∀ (a : Iota), Or (Eq True False) (Eq (cB (skS.0 1 a)) True) % 6.25/6.46 Clause #329 (by clausification #[328]): ∀ (a : Iota), Eq (cB (skS.0 1 a)) True % 6.25/6.46 Clause #330 (by superposition #[329, 92]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq True False) (Eq (cB (skS.0 2 a_1)) False)) % 6.25/6.46 Clause #332 (by clausification #[330]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 2 a_1)) False) % 6.25/6.46 Clause #334 (by superposition #[332, 193]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Or (Eq False True) (Eq (cB (skS.0 0 a_1)) True)) % 6.25/6.46 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Or (Eq (cA (skS.0 0 a)) True) (Eq (cB (skS.0 0 a_1)) True) % 6.25/6.46 Clause #336 (by superposition #[335, 24]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Eq True False) (Eq (cB (skS.0 0 a_1)) True)) % 6.25/6.46 Clause #339 (by clausification #[336]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 0 a)) True) (Eq (cB (skS.0 0 a_1)) True) % 6.25/6.46 Clause #342 (by equality factoring #[339]): ∀ (a : Iota), Or (Ne True True) (Eq (cB (skS.0 0 a)) True) % 6.25/6.46 Clause #343 (by clausification #[342]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 6.25/6.46 Clause #345 (by clausification #[343]): ∀ (a : Iota), Or (Eq (cB (skS.0 0 a)) True) (Eq True False) % 6.25/6.46 Clause #346 (by clausification #[345]): ∀ (a : Iota), Eq (cB (skS.0 0 a)) True % 6.25/6.46 Clause #347 (by superposition #[346, 101]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cB (skS.0 1 a)) False) (Eq (cA (skS.0 2 a_1)) True)) % 6.25/6.46 Clause #348 (by superposition #[346, 108]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cB (skS.0 1 a)) False) (Eq (cB (skS.0 2 a_1)) False)) % 6.25/6.46 Clause #350 (by clausification #[348]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) False) (Eq (cB (skS.0 2 a_1)) False) % 6.25/6.46 Clause #351 (by superposition #[350, 329]): ∀ (a : Iota), Or (Eq (cB (skS.0 2 a)) False) (Eq False True) % 6.25/6.46 Clause #352 (by clausification #[351]): ∀ (a : Iota), Eq (cB (skS.0 2 a)) False % 6.25/6.46 Clause #356 (by clausification #[347]): ∀ (a a_1 : Iota), Or (Eq (cB (skS.0 1 a)) False) (Eq (cA (skS.0 2 a_1)) True) % 6.25/6.46 Clause #357 (by superposition #[356, 329]): ∀ (a : Iota), Or (Eq (cA (skS.0 2 a)) True) (Eq False True) % 6.25/6.46 Clause #359 (by clausification #[357]): ∀ (a : Iota), Eq (cA (skS.0 2 a)) True % 6.25/6.46 Clause #360 (by superposition #[359, 24]): ∀ (a : Iota), Or (Eq True False) (Eq (cB (skS.0 2 a)) True) % 6.25/6.46 Clause #361 (by clausification #[360]): ∀ (a : Iota), Eq (cB (skS.0 2 a)) True % 6.25/6.46 Clause #362 (by superposition #[361, 352]): Eq True False % 6.25/6.46 Clause #363 (by clausification #[362]): False % 6.25/6.46 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------