%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN076+1 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 07:57:49 PM UTC 2025 % Result : Theorem 190.71s 191.01s % Output : Proof 191.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUN076+1 : TPTP v9.2.0. Released v7.3.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n016.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 11:41:38 EDT 2025 % 0.13/0.35 % CPUTime : % 190.71/191.01 SZS status Theorem for theBenchmark.p % 190.71/191.01 SZS output start Proof for theBenchmark.p % 190.71/191.01 Clause #0 (by assumption #[]): Eq (Exists fun Y24 => ∀ (X19 : Iota), Or (And (id X19 Y24) (r1 X19)) (And (Not (r1 X19)) (Not (id X19 Y24)))) True % 190.71/191.01 Clause #1 (by assumption #[]): Eq % 190.71/191.01 (∀ (X11 : Iota), % 190.71/191.01 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21)))) % 190.71/191.01 True % 190.71/191.01 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True % 190.71/191.01 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True % 190.71/191.01 Clause #6 (by assumption #[]): Eq (∀ (X23 X24 X25 : Iota), Or (Or (Not (id X23 X24)) (id X23 X25)) (Not (id X24 X25))) True % 190.71/191.01 Clause #7 (by assumption #[]): Eq (∀ (X26 X27 : Iota), Or (Or (Not (id X26 X27)) (And (Not (r1 X26)) (Not (r1 X27)))) (And (r1 X26) (r1 X27))) True % 190.71/191.01 Clause #8 (by assumption #[]): Eq % 190.71/191.01 (∀ (X28 X29 X30 X31 : Iota), % 190.71/191.01 Or (Or (Or (Not (id X28 X30)) (Not (id X29 X31))) (And (Not (r2 X28 X29)) (Not (r2 X30 X31)))) % 190.71/191.01 (And (r2 X28 X29) (r2 X30 X31))) % 190.71/191.01 True % 190.71/191.01 Clause #9 (by assumption #[]): Eq % 190.71/191.01 (∀ (X32 X33 X34 X35 X36 X37 : Iota), % 190.71/191.01 Or % 190.71/191.01 (Or (Or (Or (Not (id X32 X35)) (Not (id X33 X36))) (Not (id X34 X37))) % 190.71/191.01 (And (Not (r3 X32 X33 X34)) (Not (r3 X35 X36 X37)))) % 190.71/191.01 (And (r3 X32 X33 X34) (r3 X35 X36 X37))) % 190.71/191.01 True % 190.71/191.01 Clause #10 (by assumption #[]): Eq % 190.71/191.01 (∀ (X38 X39 X40 X41 X42 X43 : Iota), % 190.71/191.01 Or % 190.71/191.01 (Or (Or (Or (Not (id X38 X41)) (Not (id X39 X42))) (Not (id X40 X43))) % 190.71/191.01 (And (Not (r4 X38 X39 X40)) (Not (r4 X41 X42 X43)))) % 190.71/191.01 (And (r4 X38 X39 X40) (r4 X41 X42 X43))) % 190.71/191.01 True % 190.71/191.01 Clause #14 (by assumption #[]): Eq (∀ (X4 : Iota), Exists fun Y9 => And (id Y9 X4) (Exists fun Y16 => And (r1 Y16) (r3 X4 Y16 Y9))) True % 190.71/191.01 Clause #15 (by assumption #[]): Eq % 190.71/191.01 (∀ (X5 : Iota), % 190.71/191.01 Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 X5 Y17 Y8)) (Exists fun Y18 => And (id Y8 Y18) (r1 Y18))) % 190.71/191.01 True % 190.71/191.01 Clause #18 (by assumption #[]): Eq % 190.71/191.01 (Not % 190.71/191.01 (Exists fun Y1 => % 190.71/191.01 Exists fun Y2 => % 190.71/191.01 Exists fun Y3 => % 190.71/191.01 And % 190.71/191.01 (Exists fun Y4 => % 190.71/191.01 And (id Y4 Y1) % 190.71/191.01 (Exists fun Y6 => % 190.71/191.01 And (r4 Y6 Y2 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.71/191.01 (Exists fun Y5 => And (id Y5 Y1) (r3 Y2 Y3 Y5)))) % 190.71/191.01 True % 190.71/191.01 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True % 190.71/191.01 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True % 190.71/191.01 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True % 190.71/191.01 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True) % 190.71/191.01 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False) % 190.71/191.01 Clause #25 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (X24 X25 : Iota), Or (Or (Not (id a X24)) (id a X25)) (Not (id X24 X25))) True % 190.71/191.01 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (X25 : Iota), Or (Or (Not (id a a_1)) (id a X25)) (Not (id a_1 X25))) True % 190.71/191.01 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (Or (Or (Not (id a a_1)) (id a a_2)) (Not (id a_1 a_2))) True % 190.71/191.01 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (id a a_1)) (id a a_2)) True) (Eq (Not (id a_1 a_2)) True) % 190.71/191.01 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (Not (id a_2 a)) True) (Eq (id a_2 a_1) True)) % 190.71/191.01 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (id a a_2) True) (Eq (id a_1 a_2) False)) % 190.71/191.01 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a a_1) True) (Or (Eq (id a_2 a_1) False) (Eq (id a a_2) False)) % 190.71/191.01 Clause #34 (by clausification #[0]): ∀ (a : Iota), % 190.71/191.01 Eq (∀ (X19 : Iota), Or (And (id X19 (skS.0 0 a)) (r1 X19)) (And (Not (r1 X19)) (Not (id X19 (skS.0 0 a))))) True % 190.71/191.01 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Or (And (id a (skS.0 0 a_1)) (r1 a)) (And (Not (r1 a)) (Not (id a (skS.0 0 a_1))))) True % 190.81/191.05 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (And (id a (skS.0 0 a_1)) (r1 a)) True) (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) % 190.81/191.05 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) (Eq (r1 a) True) % 190.81/191.05 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (id a (skS.0 0 a_1)))) True) (Eq (id a (skS.0 0 a_1)) True) % 190.81/191.05 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True) % 190.81/191.05 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False) % 190.81/191.05 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True) % 190.81/191.05 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True % 190.81/191.05 Clause #53 (by clausification #[14]): ∀ (a : Iota), Eq (Exists fun Y9 => And (id Y9 a) (Exists fun Y16 => And (r1 Y16) (r3 a Y16 Y9))) True % 190.81/191.05 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (And (id (skS.0 1 a a_1) a) (Exists fun Y16 => And (r1 Y16) (r3 a Y16 (skS.0 1 a a_1)))) True % 190.81/191.05 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (Exists fun Y16 => And (r1 Y16) (r3 a Y16 (skS.0 1 a a_1))) True % 190.81/191.05 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True % 190.81/191.05 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 2 a a_1 a_2)) (r3 a (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) True % 190.81/191.05 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (r3 a (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 190.81/191.05 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 2 a a_1 a_2)) True % 190.81/191.05 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False) % 190.81/191.05 Clause #63 (by clausification #[1]): ∀ (a : Iota), % 190.81/191.05 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True % 190.81/191.05 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 190.81/191.05 Eq % 190.81/191.05 (∀ (X12 : Iota), Or (And (id X12 (skS.0 3 a a_1)) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 (skS.0 3 a a_1))))) % 190.81/191.05 True % 190.81/191.05 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 190.81/191.05 Eq (Or (And (id a (skS.0 3 a_1 a_2)) (r2 a_1 a)) (And (Not (r2 a_1 a)) (Not (id a (skS.0 3 a_1 a_2))))) True % 190.81/191.05 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 190.81/191.05 Or (Eq (And (id a (skS.0 3 a_1 a_2)) (r2 a_1 a)) True) (Eq (And (Not (r2 a_1 a)) (Not (id a (skS.0 3 a_1 a_2)))) True) % 190.81/191.05 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 3 a a_2)))) True) (Eq (r2 a a_1) True) % 190.81/191.05 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (Not (id a_1 (skS.0 3 a a_2))) True) % 190.81/191.05 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Eq (id a_1 (skS.0 3 a a_2)) False) % 190.81/191.05 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True) % 190.81/191.05 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True % 190.81/191.05 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True % 190.81/191.05 Clause #120 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (X27 : Iota), Or (Or (Not (id a X27)) (And (Not (r1 a)) (Not (r1 X27)))) (And (r1 a) (r1 X27))) True % 190.81/191.05 Clause #121 (by clausification #[120]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) (And (r1 a) (r1 a_1))) True % 190.81/191.05 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (id a a_1)) (And (Not (r1 a)) (Not (r1 a_1)))) True) (Eq (And (r1 a) (r1 a_1)) True) % 190.81/191.05 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), % 190.81/191.05 Or (Eq (And (r1 a) (r1 a_1)) True) (Or (Eq (Not (id a a_1)) True) (Eq (And (Not (r1 a)) (Not (r1 a_1))) True)) % 190.81/191.05 Clause #125 (by clausification #[123]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Eq (r1 a) True)) % 190.81/191.05 Clause #139 (by clausification #[8]): ∀ (a : Iota), % 190.81/191.08 Eq % 190.81/191.08 (∀ (X29 X30 X31 : Iota), % 190.81/191.08 Or (Or (Or (Not (id a X30)) (Not (id X29 X31))) (And (Not (r2 a X29)) (Not (r2 X30 X31)))) % 190.81/191.08 (And (r2 a X29) (r2 X30 X31))) % 190.81/191.08 True % 190.81/191.08 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), % 190.81/191.08 Eq % 190.81/191.08 (∀ (X30 X31 : Iota), % 190.81/191.08 Or (Or (Or (Not (id a X30)) (Not (id a_1 X31))) (And (Not (r2 a a_1)) (Not (r2 X30 X31)))) % 190.81/191.08 (And (r2 a a_1) (r2 X30 X31))) % 190.81/191.08 True % 190.81/191.08 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota), % 190.81/191.08 Eq % 190.81/191.08 (∀ (X31 : Iota), % 190.81/191.08 Or (Or (Or (Not (id a a_1)) (Not (id a_2 X31))) (And (Not (r2 a a_2)) (Not (r2 a_1 X31)))) % 190.81/191.08 (And (r2 a a_2) (r2 a_1 X31))) % 190.81/191.08 True % 190.81/191.08 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Eq % 190.81/191.08 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (And (Not (r2 a a_2)) (Not (r2 a_1 a_3)))) % 190.81/191.08 (And (r2 a a_2) (r2 a_1 a_3))) % 190.81/191.08 True % 190.81/191.08 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (And (Not (r2 a a_2)) (Not (r2 a_1 a_3)))) True) % 190.81/191.08 (Eq (And (r2 a a_2) (r2 a_1 a_3)) True) % 190.81/191.08 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (And (r2 a a_1) (r2 a_2 a_3)) True) % 190.81/191.08 (Or (Eq (Or (Not (id a a_2)) (Not (id a_1 a_3))) True) (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True)) % 190.81/191.08 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (Or (Not (id a a_1)) (Not (id a_2 a_3))) True) % 190.81/191.08 (Or (Eq (And (Not (r2 a a_2)) (Not (r2 a_1 a_3))) True) (Eq (r2 a_1 a_3) True)) % 190.81/191.08 Clause #147 (by clausification #[145]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True) % 190.81/191.08 (Or (Eq (r2 a_2 a_3) True) (Or (Eq (Not (id a a_2)) True) (Eq (Not (id a_1 a_3)) True))) % 190.81/191.08 Clause #149 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a_2 a)) True) (Or (Eq (Not (id a_3 a_1)) True) (Eq (Not (r2 a_2 a_3)) True))) % 190.81/191.08 Clause #153 (by clausification #[125]): ∀ (a a_1 : Iota), Or (Eq (And (Not (r1 a)) (Not (r1 a_1))) True) (Or (Eq (r1 a) True) (Eq (id a a_1) False)) % 190.81/191.08 Clause #154 (by clausification #[153]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a a_1) False) (Eq (Not (r1 a_1)) True)) % 190.81/191.08 Clause #156 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Or (Eq (id a a_1) False) (Eq (r1 a_1) False)) % 190.81/191.08 Clause #158 (by clausification #[149]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a_2 a_1)) True) (Or (Eq (Not (r2 a_3 a_2)) True) (Eq (id a_3 a) False))) % 190.81/191.08 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (r2 a a_1) True) (Or (Eq (Not (r2 a_2 a_3)) True) (Or (Eq (id a_2 a) False) (Eq (id a_3 a_1) False))) % 190.81/191.08 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Or (Eq (r2 a a_1) True) (Or (Eq (id a_2 a) False) (Or (Eq (id a_3 a_1) False) (Eq (r2 a_2 a_3) False))) % 190.81/191.08 Clause #168 (by clausification #[9]): ∀ (a : Iota), % 190.81/191.08 Eq % 190.81/191.08 (∀ (X33 X34 X35 X36 X37 : Iota), % 190.81/191.08 Or % 190.81/191.08 (Or (Or (Or (Not (id a X35)) (Not (id X33 X36))) (Not (id X34 X37))) % 190.81/191.08 (And (Not (r3 a X33 X34)) (Not (r3 X35 X36 X37)))) % 190.81/191.08 (And (r3 a X33 X34) (r3 X35 X36 X37))) % 190.81/191.08 True % 190.81/191.08 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), % 190.81/191.08 Eq % 190.81/191.08 (∀ (X34 X35 X36 X37 : Iota), % 190.81/191.08 Or % 190.81/191.08 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id X34 X37))) % 190.81/191.08 (And (Not (r3 a a_1 X34)) (Not (r3 X35 X36 X37)))) % 190.81/191.08 (And (r3 a a_1 X34) (r3 X35 X36 X37))) % 190.81/191.08 True % 190.81/191.08 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota), % 190.81/191.08 Eq % 190.81/191.08 (∀ (X35 X36 X37 : Iota), % 190.81/191.08 Or % 190.81/191.08 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id a_2 X37))) % 190.81/191.08 (And (Not (r3 a a_1 a_2)) (Not (r3 X35 X36 X37)))) % 190.81/191.08 (And (r3 a a_1 a_2) (r3 X35 X36 X37))) % 190.81/191.08 True % 190.81/191.08 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 a_3 : Iota), % 190.81/191.08 Eq % 190.81/191.08 (∀ (X36 X37 : Iota), % 190.81/191.08 Or % 190.81/191.08 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X36))) (Not (id a_3 X37))) % 190.81/191.08 (And (Not (r3 a a_2 a_3)) (Not (r3 a_1 X36 X37)))) % 190.81/191.08 (And (r3 a a_2 a_3) (r3 a_1 X36 X37))) % 190.89/191.11 True % 190.89/191.11 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 190.89/191.11 Eq % 190.89/191.11 (∀ (X37 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X37))) % 190.89/191.11 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 X37)))) % 190.89/191.11 (And (r3 a a_2 a_4) (r3 a_1 a_3 X37))) % 190.89/191.11 True % 190.89/191.11 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Eq % 190.89/191.11 (Or % 190.89/191.11 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 190.89/191.11 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5)))) % 190.89/191.11 (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5))) % 190.89/191.11 True % 190.89/191.11 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Eq % 190.89/191.11 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 190.89/191.11 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5)))) % 190.89/191.11 True) % 190.89/191.11 (Eq (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5)) True) % 190.89/191.11 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Or (Eq (And (r3 a a_1 a_2) (r3 a_3 a_4 a_5)) True) % 190.89/191.11 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True) % 190.89/191.11 (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True)) % 190.89/191.11 Clause #177 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True) % 190.89/191.11 (Or (Eq (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))) True) (Eq (r3 a a_2 a_4) True)) % 190.89/191.11 Clause #193 (by clausification #[10]): ∀ (a : Iota), % 190.89/191.11 Eq % 190.89/191.11 (∀ (X39 X40 X41 X42 X43 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Or (Or (Or (Not (id a X41)) (Not (id X39 X42))) (Not (id X40 X43))) % 190.89/191.11 (And (Not (r4 a X39 X40)) (Not (r4 X41 X42 X43)))) % 190.89/191.11 (And (r4 a X39 X40) (r4 X41 X42 X43))) % 190.89/191.11 True % 190.89/191.11 Clause #194 (by clausification #[193]): ∀ (a a_1 : Iota), % 190.89/191.11 Eq % 190.89/191.11 (∀ (X40 X41 X42 X43 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Or (Or (Or (Not (id a X41)) (Not (id a_1 X42))) (Not (id X40 X43))) % 190.89/191.11 (And (Not (r4 a a_1 X40)) (Not (r4 X41 X42 X43)))) % 190.89/191.11 (And (r4 a a_1 X40) (r4 X41 X42 X43))) % 190.89/191.11 True % 190.89/191.11 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 : Iota), % 190.89/191.11 Eq % 190.89/191.11 (∀ (X41 X42 X43 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Or (Or (Or (Not (id a X41)) (Not (id a_1 X42))) (Not (id a_2 X43))) % 190.89/191.11 (And (Not (r4 a a_1 a_2)) (Not (r4 X41 X42 X43)))) % 190.89/191.11 (And (r4 a a_1 a_2) (r4 X41 X42 X43))) % 190.89/191.11 True % 190.89/191.11 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 : Iota), % 190.89/191.11 Eq % 190.89/191.11 (∀ (X42 X43 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X42))) (Not (id a_3 X43))) % 190.89/191.11 (And (Not (r4 a a_2 a_3)) (Not (r4 a_1 X42 X43)))) % 190.89/191.11 (And (r4 a a_2 a_3) (r4 a_1 X42 X43))) % 190.89/191.11 True % 190.89/191.11 Clause #197 (by clausification #[196]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 190.89/191.11 Eq % 190.89/191.11 (∀ (X43 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X43))) % 190.89/191.11 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 X43)))) % 190.89/191.11 (And (r4 a a_2 a_4) (r4 a_1 a_3 X43))) % 190.89/191.11 True % 190.89/191.11 Clause #198 (by clausification #[197]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Eq % 190.89/191.11 (Or % 190.89/191.11 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 190.89/191.11 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5)))) % 190.89/191.11 (And (r4 a a_2 a_4) (r4 a_1 a_3 a_5))) % 190.89/191.11 True % 190.89/191.11 Clause #199 (by clausification #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Or % 190.89/191.11 (Eq % 190.89/191.11 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) % 190.89/191.11 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5)))) % 190.89/191.11 True) % 190.89/191.11 (Eq (And (r4 a a_2 a_4) (r4 a_1 a_3 a_5)) True) % 190.89/191.11 Clause #200 (by clausification #[199]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Or (Eq (And (r4 a a_1 a_2) (r4 a_3 a_4 a_5)) True) % 190.89/191.11 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True) % 190.89/191.11 (Eq (And (Not (r4 a a_1 a_2)) (Not (r4 a_3 a_4 a_5))) True)) % 190.89/191.11 Clause #202 (by clausification #[200]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.89/191.11 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True) % 190.89/191.11 (Or (Eq (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5))) True) (Eq (r4 a a_2 a_4) True)) % 190.89/191.11 Clause #309 (by clausification #[15]): ∀ (a : Iota), % 190.89/191.11 Eq (Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 Y8)) (Exists fun Y18 => And (id Y8 Y18) (r1 Y18))) % 190.89/191.14 True % 190.89/191.14 Clause #310 (by clausification #[309]): ∀ (a a_1 : Iota), % 190.89/191.14 Eq % 190.89/191.14 (And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) % 190.89/191.14 (Exists fun Y18 => And (id (skS.0 10 a a_1) Y18) (r1 Y18))) % 190.89/191.14 True % 190.89/191.14 Clause #311 (by clausification #[310]): ∀ (a a_1 : Iota), Eq (Exists fun Y18 => And (id (skS.0 10 a a_1) Y18) (r1 Y18)) True % 190.89/191.14 Clause #312 (by clausification #[310]): ∀ (a a_1 : Iota), Eq (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1))) True % 190.89/191.14 Clause #313 (by clausification #[311]): ∀ (a a_1 a_2 : Iota), Eq (And (id (skS.0 10 a a_1) (skS.0 11 a a_1 a_2)) (r1 (skS.0 11 a a_1 a_2))) True % 190.89/191.14 Clause #314 (by clausification #[313]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 11 a a_1 a_2)) True % 190.89/191.14 Clause #315 (by clausification #[313]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 11 a a_1 a_2)) True % 190.89/191.14 Clause #318 (by clausification #[312]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 (skS.0 12 a a_1 a_2)) (r4 a (skS.0 12 a a_1 a_2) (skS.0 10 a a_1))) True % 190.89/191.14 Clause #319 (by clausification #[318]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 12 a a_1 a_2) (skS.0 10 a a_1)) True % 190.89/191.14 Clause #320 (by clausification #[318]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 12 a a_1 a_2)) True % 190.89/191.14 Clause #327 (by superposition #[315, 156]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) True) (Or (Eq True False) (Eq (r1 (skS.0 11 a a_1 a_2)) False)) % 190.89/191.14 Clause #372 (by clausification #[18]): Eq % 190.89/191.14 (Exists fun Y1 => % 190.89/191.14 Exists fun Y2 => % 190.89/191.14 Exists fun Y3 => % 190.89/191.14 And % 190.89/191.14 (Exists fun Y4 => % 190.89/191.14 And (id Y4 Y1) % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 Y2 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.89/191.14 (Exists fun Y5 => And (id Y5 Y1) (r3 Y2 Y3 Y5))) % 190.89/191.14 False % 190.89/191.14 Clause #373 (by clausification #[372]): ∀ (a : Iota), % 190.89/191.14 Eq % 190.89/191.14 (Exists fun Y2 => % 190.89/191.14 Exists fun Y3 => % 190.89/191.14 And % 190.89/191.14 (Exists fun Y4 => % 190.89/191.14 And (id Y4 a) % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 Y2 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.89/191.14 (Exists fun Y5 => And (id Y5 a) (r3 Y2 Y3 Y5))) % 190.89/191.14 False % 190.89/191.14 Clause #374 (by clausification #[373]): ∀ (a a_1 : Iota), % 190.89/191.14 Eq % 190.89/191.14 (Exists fun Y3 => % 190.89/191.14 And % 190.89/191.14 (Exists fun Y4 => % 190.89/191.14 And (id Y4 a) % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 a_1 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.89/191.14 (Exists fun Y5 => And (id Y5 a) (r3 a_1 Y3 Y5))) % 190.89/191.14 False % 190.89/191.14 Clause #375 (by clausification #[374]): ∀ (a a_1 a_2 : Iota), % 190.89/191.14 Eq % 190.89/191.14 (And % 190.89/191.14 (Exists fun Y4 => % 190.89/191.14 And (id Y4 a) % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 a_1 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.89/191.14 (Exists fun Y5 => And (id Y5 a) (r3 a_1 a_2 Y5))) % 190.89/191.14 False % 190.89/191.14 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota), % 190.89/191.14 Or % 190.89/191.14 (Eq % 190.89/191.14 (Exists fun Y4 => % 190.89/191.14 And (id Y4 a) % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 a_1 Y4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.89/191.14 False) % 190.89/191.14 (Eq (Exists fun Y5 => And (id Y5 a) (r3 a_1 a_2 Y5)) False) % 190.89/191.14 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 : Iota), % 190.89/191.14 Or (Eq (Exists fun Y5 => And (id Y5 a) (r3 a_1 a_2 Y5)) False) % 190.89/191.14 (Eq % 190.89/191.14 (And (id a_3 a) % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 a_1 a_3) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.89/191.14 False) % 190.89/191.14 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 190.89/191.14 Or % 190.89/191.14 (Eq % 190.89/191.14 (And (id a a_1) % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 a_2 a) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))))) % 190.89/191.14 False) % 190.89/191.14 (Eq (And (id a_3 a_1) (r3 a_2 a_4 a_3)) False) % 190.89/191.14 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 190.89/191.14 Or (Eq (And (id a a_1) (r3 a_2 a_3 a)) False) % 190.89/191.14 (Or (Eq (id a_4 a_1) False) % 190.89/191.14 (Eq % 190.89/191.14 (Exists fun Y6 => % 190.89/191.14 And (r4 Y6 a_2 a_4) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) % 190.97/191.17 False)) % 190.97/191.17 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 190.97/191.17 Or (Eq (id a a_1) False) % 190.97/191.17 (Or % 190.97/191.17 (Eq % 190.97/191.17 (Exists fun Y6 => And (r4 Y6 a_2 a) (Exists fun Y7 => And (r2 Y7 Y6) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) % 190.97/191.17 False) % 190.97/191.17 (Or (Eq (id a_3 a_1) False) (Eq (r3 a_2 a_4 a_3) False))) % 190.97/191.17 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.97/191.17 Or (Eq (id a a_1) False) % 190.97/191.17 (Or (Eq (id a_2 a_1) False) % 190.97/191.17 (Or (Eq (r3 a_3 a_4 a_2) False) % 190.97/191.17 (Eq (And (r4 a_5 a_3 a) (Exists fun Y7 => And (r2 Y7 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7)))) False))) % 190.97/191.17 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.97/191.17 Or (Eq (id a a_1) False) % 190.97/191.17 (Or (Eq (id a_2 a_1) False) % 190.97/191.17 (Or (Eq (r3 a_3 a_4 a_2) False) % 190.97/191.17 (Or (Eq (r4 a_5 a_3 a) False) % 190.97/191.17 (Eq (Exists fun Y7 => And (r2 Y7 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 Y7))) False)))) % 190.97/191.17 Clause #383 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 190.97/191.17 Or (Eq (id a a_1) False) % 190.97/191.17 (Or (Eq (id a_2 a_1) False) % 190.97/191.17 (Or (Eq (r3 a_3 a_4 a_2) False) % 190.97/191.17 (Or (Eq (r4 a_5 a_3 a) False) (Eq (And (r2 a_6 a_5) (Exists fun Y8 => And (r1 Y8) (r2 Y8 a_6))) False)))) % 190.97/191.17 Clause #384 (by clausification #[383]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 190.97/191.17 Or (Eq (id a a_1) False) % 190.97/191.17 (Or (Eq (id a_2 a_1) False) % 190.97/191.17 (Or (Eq (r3 a_3 a_4 a_2) False) % 190.97/191.17 (Or (Eq (r4 a_5 a_3 a) False) % 190.97/191.17 (Or (Eq (r2 a_6 a_5) False) (Eq (Exists fun Y8 => And (r1 Y8) (r2 Y8 a_6)) False))))) % 190.97/191.17 Clause #385 (by clausification #[384]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 190.97/191.17 Or (Eq (id a a_1) False) % 190.97/191.17 (Or (Eq (id a_2 a_1) False) % 190.97/191.17 (Or (Eq (r3 a_3 a_4 a_2) False) % 190.97/191.17 (Or (Eq (r4 a_5 a_3 a) False) (Or (Eq (r2 a_6 a_5) False) (Eq (And (r1 a_7) (r2 a_7 a_6)) False))))) % 190.97/191.17 Clause #386 (by clausification #[385]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 190.97/191.17 Or (Eq (id a a_1) False) % 190.97/191.17 (Or (Eq (id a_2 a_1) False) % 190.97/191.17 (Or (Eq (r3 a_3 a_4 a_2) False) % 190.97/191.17 (Or (Eq (r4 a_5 a_3 a) False) (Or (Eq (r2 a_6 a_5) False) (Or (Eq (r1 a_7) False) (Eq (r2 a_7 a_6) False)))))) % 190.97/191.17 Clause #390 (by superposition #[386, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 190.97/191.17 Or (Eq (id a (skS.0 1 a_1 a_2)) False) % 190.97/191.17 (Or (Eq (r3 a_3 a_4 a) False) % 190.97/191.17 (Or (Eq (r4 a_5 a_3 a_1) False) % 190.97/191.17 (Or (Eq (r2 a_6 a_5) False) (Or (Eq (r1 a_7) False) (Or (Eq (r2 a_7 a_6) False) (Eq False True)))))) % 190.97/191.17 Clause #402 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True) % 190.97/191.17 Clause #404 (by clausification #[402]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False) % 190.97/191.17 Clause #405 (by superposition #[404, 44]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 0 a_1)) True) (Eq False True) % 190.97/191.17 Clause #406 (by superposition #[404, 59]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True) (Eq False True) % 190.97/191.17 Clause #410 (by superposition #[404, 320]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 12 a a_1 a_2) (skS.0 0 a_3)) True) (Eq False True) % 190.97/191.17 Clause #418 (by clausification #[405]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a) (skS.0 0 a_1)) True % 190.97/191.17 Clause #424 (by superposition #[418, 160]): ∀ (a a_1 a_2 a_3 : Iota), % 190.97/191.17 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq True False) (Or (Eq (id a_2 a_1) False) (Eq (r2 (skS.0 0 a_3) a_2) False))) % 190.97/191.17 Clause #447 (by clausification #[410]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 12 a a_1 a_2) (skS.0 0 a_3)) True % 190.97/191.17 Clause #511 (by clausification #[406]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True % 190.97/191.17 Clause #513 (by superposition #[511, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 2 a_1 a_2 a_3)) True) (Eq True False) % 190.97/191.17 Clause #562 (by clausification #[513]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 2 a_1 a_2 a_3)) True % 190.97/191.17 Clause #571 (by clausification #[177]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 190.97/191.17 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True) % 190.97/191.17 (Or (Eq (r3 a a_1 a_2) True) (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) (Eq (Not (id a_2 a_5)) True))) % 191.00/191.21 Clause #572 (by clausification #[571]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r3 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) % 191.00/191.21 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r3 a_3 a_4 a_5)) True))) % 191.00/191.21 Clause #574 (by clausification #[572]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r3 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (id a_2 a_3)) True) % 191.00/191.21 (Or (Eq (Not (r3 a_4 a_5 a_3)) True) (Or (Eq (Not (id a a_4)) True) (Eq (Not (id a_1 a_5)) True)))) % 191.00/191.21 Clause #575 (by clausification #[574]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r3 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (r3 a_3 a_4 a_5)) True) % 191.00/191.21 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False)))) % 191.00/191.21 Clause #576 (by clausification #[575]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r3 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (id a a_3)) True) % 191.00/191.21 (Or (Eq (Not (id a_1 a_4)) True) (Or (Eq (id a_2 a_5) False) (Eq (r3 a_3 a_4 a_5) False)))) % 191.00/191.21 Clause #577 (by clausification #[576]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r3 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (id a_1 a_3)) True) % 191.00/191.21 (Or (Eq (id a_2 a_4) False) (Or (Eq (r3 a_5 a_3 a_4) False) (Eq (id a a_5) False)))) % 191.00/191.21 Clause #578 (by clausification #[577]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r3 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (id a_2 a_3) False) (Or (Eq (r3 a_4 a_5 a_3) False) (Or (Eq (id a a_4) False) (Eq (id a_1 a_5) False)))) % 191.00/191.21 Clause #590 (by superposition #[578, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r3 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (r3 a_3 a_4 (skS.0 1 a_2 a_5)) False) % 191.00/191.21 (Or (Eq (id a a_3) False) (Or (Eq (id a_1 a_4) False) (Eq False True)))) % 191.00/191.21 Clause #693 (by clausification #[202]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (And (Not (r4 a a_1 a_2)) (Not (r4 a_3 a_4 a_5))) True) % 191.00/191.21 (Or (Eq (r4 a a_1 a_2) True) (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) (Eq (Not (id a_2 a_5)) True))) % 191.00/191.21 Clause #694 (by clausification #[693]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) % 191.00/191.21 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r4 a_3 a_4 a_5)) True))) % 191.00/191.21 Clause #696 (by clausification #[694]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (id a_2 a_3)) True) % 191.00/191.21 (Or (Eq (Not (r4 a_4 a_5 a_3)) True) (Or (Eq (Not (id a a_4)) True) (Eq (Not (id a_1 a_5)) True)))) % 191.00/191.21 Clause #697 (by clausification #[696]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (r4 a_3 a_4 a_5)) True) % 191.00/191.21 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False)))) % 191.00/191.21 Clause #698 (by clausification #[697]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (id a a_3)) True) % 191.00/191.21 (Or (Eq (Not (id a_1 a_4)) True) (Or (Eq (id a_2 a_5) False) (Eq (r4 a_3 a_4 a_5) False)))) % 191.00/191.21 Clause #699 (by clausification #[698]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (Not (id a_1 a_3)) True) % 191.00/191.21 (Or (Eq (id a_2 a_4) False) (Or (Eq (r4 a_5 a_3 a_4) False) (Eq (id a a_5) False)))) % 191.00/191.21 Clause #700 (by clausification #[699]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (id a_2 a_3) False) (Or (Eq (r4 a_4 a_5 a_3) False) (Or (Eq (id a a_4) False) (Eq (id a_1 a_5) False)))) % 191.00/191.21 Clause #719 (by superposition #[700, 19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) % 191.00/191.21 (Or (Eq (r4 a_3 a_4 a_2) False) (Or (Eq (id a a_3) False) (Or (Eq (id a_1 a_4) False) (Eq False True)))) % 191.00/191.21 Clause #720 (by clausification #[719]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 a_2) True) (Or (Eq (r4 a_3 a_4 a_2) False) (Or (Eq (id a a_3) False) (Eq (id a_1 a_4) False))) % 191.00/191.21 Clause #721 (by superposition #[720, 319]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 191.00/191.21 Or (Eq (r4 a a_1 (skS.0 10 a_2 a_3)) True) % 191.00/191.21 (Or (Eq (id a a_2) False) (Or (Eq (id a_1 (skS.0 12 a_2 a_3 a_4)) False) (Eq False True))) % 191.00/191.21 Clause #725 (by clausification #[424]): ∀ (a a_1 a_2 a_3 : Iota), % 191.02/191.24 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (id a_2 a_1) False) (Eq (r2 (skS.0 0 a_3) a_2) False)) % 191.02/191.24 Clause #744 (by superposition #[725, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (r2 (skS.0 0 a_2) a_1) False) (Eq False True)) % 191.02/191.24 Clause #745 (by clausification #[744]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) True) (Eq (r2 (skS.0 0 a_2) a_1) False) % 191.02/191.24 Clause #746 (by superposition #[745, 78]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) True) (Eq False True) % 191.02/191.24 Clause #750 (by clausification #[746]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) True % 191.02/191.24 Clause #900 (by clausification #[327]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) True) (Eq (r1 (skS.0 11 a a_1 a_2)) False) % 191.02/191.24 Clause #901 (by superposition #[900, 314]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) True) (Eq False True) % 191.02/191.24 Clause #902 (by clausification #[901]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 10 a a_1)) True % 191.02/191.24 Clause #906 (by superposition #[902, 404]): ∀ (a a_1 a_2 : Iota), Or (Eq (id (skS.0 10 a a_1) (skS.0 0 a_2)) True) (Eq True False) % 191.02/191.24 Clause #937 (by clausification #[906]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 0 a_2)) True % 191.02/191.24 Clause #939 (by superposition #[937, 23]): ∀ (a a_1 a_2 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 10 a_1 a_2)) True) (Eq True False) % 191.02/191.24 Clause #962 (by clausification #[939]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 0 a) (skS.0 10 a_1 a_2)) True % 191.02/191.24 Clause #963 (by superposition #[962, 31]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 10 a_1 a_2)) True) (Or (Eq True False) (Eq (id a (skS.0 0 a_3)) False)) % 191.02/191.24 Clause #984 (by clausification #[963]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 10 a_1 a_2)) True) (Eq (id a (skS.0 0 a_3)) False) % 191.02/191.24 Clause #986 (by superposition #[984, 447]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (id (skS.0 12 a a_1 a_2) (skS.0 10 a_3 a_4)) True) (Eq False True) % 191.02/191.24 Clause #1140 (by clausification #[986]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (id (skS.0 12 a a_1 a_2) (skS.0 10 a_3 a_4)) True % 191.02/191.24 Clause #1141 (by superposition #[1140, 23]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (id (skS.0 10 a a_1) (skS.0 12 a_2 a_3 a_4)) True) (Eq True False) % 191.02/191.24 Clause #1165 (by clausification #[1141]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 12 a_2 a_3 a_4)) True % 191.02/191.24 Clause #3905 (by clausification #[590]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.02/191.24 Or (Eq (r3 a a_1 a_2) True) % 191.02/191.24 (Or (Eq (r3 a_3 a_4 (skS.0 1 a_2 a_5)) False) (Or (Eq (id a a_3) False) (Eq (id a_1 a_4) False))) % 191.02/191.24 Clause #3906 (by superposition #[3905, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 191.02/191.24 Or (Eq (r3 a a_1 a_2) True) (Or (Eq (id a a_2) False) (Or (Eq (id a_1 (skS.0 2 a_2 a_3 a_4)) False) (Eq False True))) % 191.02/191.24 Clause #3907 (by clausification #[3906]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 191.02/191.24 Or (Eq (r3 a a_1 a_2) True) (Or (Eq (id a a_2) False) (Eq (id a_1 (skS.0 2 a_2 a_3 a_4)) False)) % 191.02/191.24 Clause #3978 (by superposition #[3907, 19]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a) True) (Or (Eq (id a_1 (skS.0 2 a a_2 a_3)) False) (Eq False True)) % 191.02/191.24 Clause #3979 (by clausification #[3978]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a) True) (Eq (id a_1 (skS.0 2 a a_2 a_3)) False) % 191.02/191.24 Clause #3980 (by superposition #[3979, 562]): ∀ (a a_1 : Iota), Or (Eq (r3 a (skS.0 0 a_1) a) True) (Eq False True) % 191.02/191.24 Clause #3995 (by clausification #[3980]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 0 a_1) a) True % 191.02/191.24 Clause #7166 (by clausification #[390]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 191.02/191.24 Or (Eq (id a (skS.0 1 a_1 a_2)) False) % 191.02/191.24 (Or (Eq (r3 a_3 a_4 a) False) % 191.02/191.24 (Or (Eq (r4 a_5 a_3 a_1) False) (Or (Eq (r2 a_6 a_5) False) (Or (Eq (r1 a_7) False) (Eq (r2 a_7 a_6) False))))) % 191.02/191.24 Clause #7172 (by superposition #[7166, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.02/191.24 Or (Eq (r3 a a_1 a_2) False) % 191.02/191.24 (Or (Eq (r4 a_3 a a_2) False) % 191.02/191.24 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Or (Eq (r2 a_5 a_4) False) (Eq False True))))) % 191.02/191.24 Clause #7187 (by clausification #[7172]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 191.02/191.24 Or (Eq (r3 a a_1 a_2) False) % 191.02/191.24 (Or (Eq (r4 a_3 a a_2) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False)))) % 191.32/191.59 Clause #7199 (by superposition #[7187, 3995]): ∀ (a a_1 a_2 a_3 : Iota), % 191.32/191.59 Or (Eq (r4 a a_1 a_1) False) % 191.32/191.59 (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_2) False) (Eq False True)))) % 191.32/191.59 Clause #7201 (by clausification #[7199]): ∀ (a a_1 a_2 a_3 : Iota), % 191.32/191.59 Or (Eq (r4 a a_1 a_1) False) (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Eq (r2 a_3 a_2) False))) % 191.32/191.59 Clause #30950 (by clausification #[721]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 191.32/191.59 Or (Eq (r4 a a_1 (skS.0 10 a_2 a_3)) True) (Or (Eq (id a a_2) False) (Eq (id a_1 (skS.0 12 a_2 a_3 a_4)) False)) % 191.32/191.59 Clause #31109 (by superposition #[30950, 19]): ∀ (a a_1 a_2 a_3 : Iota), % 191.32/191.59 Or (Eq (r4 a a_1 (skS.0 10 a a_2)) True) (Or (Eq (id a_1 (skS.0 12 a a_2 a_3)) False) (Eq False True)) % 191.32/191.59 Clause #31110 (by clausification #[31109]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a_1 (skS.0 10 a a_2)) True) (Eq (id a_1 (skS.0 12 a a_2 a_3)) False) % 191.32/191.59 Clause #31112 (by superposition #[31110, 1165]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a (skS.0 10 a_1 a_2) (skS.0 10 a a_3)) True) (Eq False True) % 191.32/191.59 Clause #31154 (by clausification #[31112]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r4 a (skS.0 10 a_1 a_2) (skS.0 10 a a_3)) True % 191.32/191.59 Clause #31160 (by superposition #[31154, 7201]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a) False))) % 191.32/191.59 Clause #31163 (by clausification #[31160]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a) False)) % 191.32/191.59 Clause #31182 (by superposition #[31163, 78]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True)) % 191.32/191.59 Clause #31183 (by clausification #[31182]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False) % 191.32/191.59 Clause #31184 (by superposition #[31183, 44]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Eq False True) % 191.32/191.59 Clause #31394 (by clausification #[31184]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 0 a) a_1) False % 191.32/191.59 Clause #31395 (by superposition #[31394, 750]): Eq False True % 191.32/191.59 Clause #31396 (by clausification #[31395]): False % 191.32/191.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------