TSTP Solution File: NUN059+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.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 : Thu Aug 31 12:47:15 EDT 2023
% Result : Theorem 184.01s 184.18s
% Output : Proof 184.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.00/0.13 % Command : duper %s
% 0.17/0.34 % Computer : n012.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sun Aug 27 09:31:25 EDT 2023
% 0.17/0.35 % CPUTime :
% 184.01/184.18 SZS status Theorem for theBenchmark.p
% 184.01/184.18 SZS output start Proof for theBenchmark.p
% 184.01/184.18 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
% 184.01/184.18 Clause #3 (by assumption #[]): Eq
% 184.01/184.18 (∀ (X16 X17 : Iota),
% 184.01/184.18 Exists fun Y23 =>
% 184.01/184.18 ∀ (X18 : Iota), Or (And (id X18 Y23) (r4 X16 X17 X18)) (And (Not (r4 X16 X17 X18)) (Not (id X18 Y23))))
% 184.01/184.18 True
% 184.01/184.18 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True
% 184.01/184.18 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True
% 184.01/184.18 Clause #6 (by assumption #[]): Eq (∀ (X23 X24 X25 : Iota), Or (Or (Not (id X23 X24)) (id X23 X25)) (Not (id X24 X25))) True
% 184.01/184.18 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
% 184.01/184.18 Clause #9 (by assumption #[]): Eq
% 184.01/184.18 (∀ (X32 X33 X34 X35 X36 X37 : Iota),
% 184.01/184.18 Or
% 184.01/184.18 (Or (Or (Or (Not (id X32 X35)) (Not (id X33 X36))) (Not (id X34 X37)))
% 184.01/184.18 (And (Not (r3 X32 X33 X34)) (Not (r3 X35 X36 X37))))
% 184.01/184.18 (And (r3 X32 X33 X34) (r3 X35 X36 X37)))
% 184.01/184.18 True
% 184.01/184.18 Clause #10 (by assumption #[]): Eq
% 184.01/184.18 (∀ (X38 X39 X40 X41 X42 X43 : Iota),
% 184.01/184.18 Or
% 184.01/184.18 (Or (Or (Or (Not (id X38 X41)) (Not (id X39 X42))) (Not (id X40 X43)))
% 184.01/184.18 (And (Not (r4 X38 X39 X40)) (Not (r4 X41 X42 X43))))
% 184.01/184.18 (And (r4 X38 X39 X40) (r4 X41 X42 X43)))
% 184.01/184.18 True
% 184.01/184.18 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
% 184.01/184.18 Clause #15 (by assumption #[]): Eq
% 184.01/184.18 (∀ (X5 : Iota),
% 184.01/184.18 Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 X5 Y17 Y8)) (Exists fun Y18 => And (id Y8 Y18) (r1 Y18)))
% 184.01/184.18 True
% 184.01/184.18 Clause #18 (by assumption #[]): Eq
% 184.01/184.18 (Not
% 184.01/184.18 (Exists fun Y1 =>
% 184.01/184.18 Exists fun Y3 =>
% 184.01/184.18 Exists fun Y2 =>
% 184.01/184.18 Exists fun Y4 =>
% 184.01/184.18 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5))
% 184.01/184.18 (Exists fun Y6 => And (r4 Y3 Y3 Y6) (Exists fun Y7 => And (r4 Y1 Y1 Y7) (r3 Y7 Y6 Y4)))))
% 184.01/184.18 True
% 184.01/184.18 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True
% 184.01/184.18 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True
% 184.01/184.18 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True
% 184.01/184.18 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True)
% 184.01/184.18 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False)
% 184.01/184.18 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
% 184.01/184.18 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
% 184.01/184.18 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
% 184.01/184.18 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)
% 184.01/184.18 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))
% 184.01/184.18 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))
% 184.01/184.18 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))
% 184.01/184.18 Clause #34 (by clausification #[0]): ∀ (a : Iota),
% 184.01/184.18 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
% 184.01/184.18 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
% 184.01/184.18 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)
% 184.01/184.18 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)
% 184.01/184.21 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)
% 184.01/184.21 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True)
% 184.01/184.21 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False)
% 184.01/184.21 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True)
% 184.01/184.21 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True
% 184.01/184.21 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
% 184.01/184.21 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
% 184.01/184.21 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
% 184.01/184.21 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True
% 184.01/184.21 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
% 184.01/184.21 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
% 184.01/184.21 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 2 a a_1 a_2)) True
% 184.01/184.21 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False)
% 184.01/184.21 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True
% 184.01/184.21 Clause #99 (by clausification #[3]): ∀ (a : Iota),
% 184.01/184.21 Eq
% 184.01/184.21 (∀ (X17 : Iota),
% 184.01/184.21 Exists fun Y23 =>
% 184.01/184.21 ∀ (X18 : Iota), Or (And (id X18 Y23) (r4 a X17 X18)) (And (Not (r4 a X17 X18)) (Not (id X18 Y23))))
% 184.01/184.21 True
% 184.01/184.21 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota),
% 184.01/184.21 Eq
% 184.01/184.21 (Exists fun Y23 =>
% 184.01/184.21 ∀ (X18 : Iota), Or (And (id X18 Y23) (r4 a a_1 X18)) (And (Not (r4 a a_1 X18)) (Not (id X18 Y23))))
% 184.01/184.21 True
% 184.01/184.21 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota),
% 184.01/184.21 Eq
% 184.01/184.21 (∀ (X18 : Iota),
% 184.01/184.21 Or (And (id X18 (skS.0 5 a a_1 a_2)) (r4 a a_1 X18))
% 184.01/184.21 (And (Not (r4 a a_1 X18)) (Not (id X18 (skS.0 5 a a_1 a_2)))))
% 184.01/184.21 True
% 184.01/184.21 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.01/184.21 Eq
% 184.01/184.21 (Or (And (id a (skS.0 5 a_1 a_2 a_3)) (r4 a_1 a_2 a)) (And (Not (r4 a_1 a_2 a)) (Not (id a (skS.0 5 a_1 a_2 a_3)))))
% 184.01/184.21 True
% 184.01/184.21 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.01/184.21 Or (Eq (And (id a (skS.0 5 a_1 a_2 a_3)) (r4 a_1 a_2 a)) True)
% 184.01/184.21 (Eq (And (Not (r4 a_1 a_2 a)) (Not (id a (skS.0 5 a_1 a_2 a_3)))) True)
% 184.01/184.21 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.01/184.21 Or (Eq (And (Not (r4 a a_1 a_2)) (Not (id a_2 (skS.0 5 a a_1 a_3)))) True) (Eq (r4 a a_1 a_2) True)
% 184.01/184.21 Clause #105 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.01/184.21 Or (Eq (And (Not (r4 a a_1 a_2)) (Not (id a_2 (skS.0 5 a a_1 a_3)))) True) (Eq (id a_2 (skS.0 5 a a_1 a_3)) True)
% 184.01/184.21 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a_1 a_2) True) (Eq (Not (id a_2 (skS.0 5 a a_1 a_3))) True)
% 184.01/184.21 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a_1 a_2) True) (Eq (id a_2 (skS.0 5 a a_1 a_3)) False)
% 184.01/184.21 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
% 184.01/184.21 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
% 184.01/184.21 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)
% 184.01/184.21 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota),
% 184.01/184.21 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))
% 184.01/184.21 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))
% 184.01/184.24 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))
% 184.01/184.24 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))
% 184.01/184.24 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))
% 184.01/184.24 Clause #168 (by clausification #[9]): ∀ (a : Iota),
% 184.01/184.24 Eq
% 184.01/184.24 (∀ (X33 X34 X35 X36 X37 : Iota),
% 184.01/184.24 Or
% 184.01/184.24 (Or (Or (Or (Not (id a X35)) (Not (id X33 X36))) (Not (id X34 X37)))
% 184.01/184.24 (And (Not (r3 a X33 X34)) (Not (r3 X35 X36 X37))))
% 184.01/184.24 (And (r3 a X33 X34) (r3 X35 X36 X37)))
% 184.01/184.24 True
% 184.01/184.24 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota),
% 184.01/184.24 Eq
% 184.01/184.24 (∀ (X34 X35 X36 X37 : Iota),
% 184.01/184.24 Or
% 184.01/184.24 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id X34 X37)))
% 184.01/184.24 (And (Not (r3 a a_1 X34)) (Not (r3 X35 X36 X37))))
% 184.01/184.24 (And (r3 a a_1 X34) (r3 X35 X36 X37)))
% 184.01/184.24 True
% 184.01/184.24 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota),
% 184.01/184.24 Eq
% 184.01/184.24 (∀ (X35 X36 X37 : Iota),
% 184.01/184.24 Or
% 184.01/184.24 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id a_2 X37)))
% 184.01/184.24 (And (Not (r3 a a_1 a_2)) (Not (r3 X35 X36 X37))))
% 184.01/184.24 (And (r3 a a_1 a_2) (r3 X35 X36 X37)))
% 184.01/184.24 True
% 184.01/184.24 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.01/184.24 Eq
% 184.01/184.24 (∀ (X36 X37 : Iota),
% 184.01/184.24 Or
% 184.01/184.24 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X36))) (Not (id a_3 X37)))
% 184.01/184.24 (And (Not (r3 a a_2 a_3)) (Not (r3 a_1 X36 X37))))
% 184.01/184.24 (And (r3 a a_2 a_3) (r3 a_1 X36 X37)))
% 184.01/184.24 True
% 184.01/184.24 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.01/184.24 Eq
% 184.01/184.24 (∀ (X37 : Iota),
% 184.01/184.24 Or
% 184.01/184.24 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X37)))
% 184.01/184.24 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 X37))))
% 184.01/184.24 (And (r3 a a_2 a_4) (r3 a_1 a_3 X37)))
% 184.01/184.24 True
% 184.01/184.24 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.01/184.24 Eq
% 184.01/184.24 (Or
% 184.01/184.24 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5)))
% 184.01/184.24 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))))
% 184.01/184.24 (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5)))
% 184.01/184.24 True
% 184.01/184.24 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.01/184.24 Or
% 184.01/184.24 (Eq
% 184.01/184.24 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5)))
% 184.01/184.24 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))))
% 184.01/184.24 True)
% 184.01/184.24 (Eq (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5)) True)
% 184.01/184.24 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.01/184.24 Or (Eq (And (r3 a a_1 a_2) (r3 a_3 a_4 a_5)) True)
% 184.01/184.24 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True)
% 184.01/184.24 (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True))
% 184.01/184.24 Clause #176 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.01/184.24 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True)
% 184.01/184.24 (Or (Eq (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))) True) (Eq (r3 a_1 a_3 a_5) True))
% 184.01/184.24 Clause #177 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.01/184.24 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True)
% 184.01/184.24 (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))
% 184.01/184.24 Clause #178 (by clausification #[176]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.01/184.24 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True)
% 184.01/184.24 (Or (Eq (r3 a_3 a_4 a_5) True) (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True) (Eq (Not (id a_2 a_5)) True)))
% 184.01/184.24 Clause #180 (by clausification #[178]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.01/184.24 Or (Eq (r3 a a_1 a_2) True)
% 184.01/184.24 (Or (Eq (Or (Not (id a_3 a)) (Not (id a_4 a_1))) True)
% 184.01/184.24 (Or (Eq (Not (id a_5 a_2)) True) (Eq (Not (r3 a_3 a_4 a_5)) True)))
% 184.01/184.24 Clause #193 (by clausification #[10]): ∀ (a : Iota),
% 184.01/184.24 Eq
% 184.01/184.24 (∀ (X39 X40 X41 X42 X43 : Iota),
% 184.01/184.24 Or
% 184.01/184.24 (Or (Or (Or (Not (id a X41)) (Not (id X39 X42))) (Not (id X40 X43)))
% 184.01/184.24 (And (Not (r4 a X39 X40)) (Not (r4 X41 X42 X43))))
% 184.01/184.24 (And (r4 a X39 X40) (r4 X41 X42 X43)))
% 184.11/184.27 True
% 184.11/184.27 Clause #194 (by clausification #[193]): ∀ (a a_1 : Iota),
% 184.11/184.27 Eq
% 184.11/184.27 (∀ (X40 X41 X42 X43 : Iota),
% 184.11/184.27 Or
% 184.11/184.27 (Or (Or (Or (Not (id a X41)) (Not (id a_1 X42))) (Not (id X40 X43)))
% 184.11/184.27 (And (Not (r4 a a_1 X40)) (Not (r4 X41 X42 X43))))
% 184.11/184.27 (And (r4 a a_1 X40) (r4 X41 X42 X43)))
% 184.11/184.27 True
% 184.11/184.27 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 : Iota),
% 184.11/184.27 Eq
% 184.11/184.27 (∀ (X41 X42 X43 : Iota),
% 184.11/184.27 Or
% 184.11/184.27 (Or (Or (Or (Not (id a X41)) (Not (id a_1 X42))) (Not (id a_2 X43)))
% 184.11/184.27 (And (Not (r4 a a_1 a_2)) (Not (r4 X41 X42 X43))))
% 184.11/184.27 (And (r4 a a_1 a_2) (r4 X41 X42 X43)))
% 184.11/184.27 True
% 184.11/184.27 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.11/184.27 Eq
% 184.11/184.27 (∀ (X42 X43 : Iota),
% 184.11/184.27 Or
% 184.11/184.27 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X42))) (Not (id a_3 X43)))
% 184.11/184.27 (And (Not (r4 a a_2 a_3)) (Not (r4 a_1 X42 X43))))
% 184.11/184.27 (And (r4 a a_2 a_3) (r4 a_1 X42 X43)))
% 184.11/184.27 True
% 184.11/184.27 Clause #197 (by clausification #[196]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.27 Eq
% 184.11/184.27 (∀ (X43 : Iota),
% 184.11/184.27 Or
% 184.11/184.27 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X43)))
% 184.11/184.27 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 X43))))
% 184.11/184.27 (And (r4 a a_2 a_4) (r4 a_1 a_3 X43)))
% 184.11/184.27 True
% 184.11/184.27 Clause #198 (by clausification #[197]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.27 Eq
% 184.11/184.27 (Or
% 184.11/184.27 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5)))
% 184.11/184.27 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5))))
% 184.11/184.27 (And (r4 a a_2 a_4) (r4 a_1 a_3 a_5)))
% 184.11/184.27 True
% 184.11/184.27 Clause #199 (by clausification #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.27 Or
% 184.11/184.27 (Eq
% 184.11/184.27 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5)))
% 184.11/184.27 (And (Not (r4 a a_2 a_4)) (Not (r4 a_1 a_3 a_5))))
% 184.11/184.27 True)
% 184.11/184.27 (Eq (And (r4 a a_2 a_4) (r4 a_1 a_3 a_5)) True)
% 184.11/184.27 Clause #200 (by clausification #[199]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.27 Or (Eq (And (r4 a a_1 a_2) (r4 a_3 a_4 a_5)) True)
% 184.11/184.27 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True)
% 184.11/184.27 (Eq (And (Not (r4 a a_1 a_2)) (Not (r4 a_3 a_4 a_5))) True))
% 184.11/184.27 Clause #202 (by clausification #[200]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.27 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True)
% 184.11/184.27 (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))
% 184.11/184.27 Clause #309 (by clausification #[15]): ∀ (a : Iota),
% 184.11/184.27 Eq (Exists fun Y8 => And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 Y8)) (Exists fun Y18 => And (id Y8 Y18) (r1 Y18)))
% 184.11/184.27 True
% 184.11/184.27 Clause #310 (by clausification #[309]): ∀ (a a_1 : Iota),
% 184.11/184.27 Eq
% 184.11/184.27 (And (Exists fun Y17 => And (r1 Y17) (r4 a Y17 (skS.0 10 a a_1)))
% 184.11/184.27 (Exists fun Y18 => And (id (skS.0 10 a a_1) Y18) (r1 Y18)))
% 184.11/184.27 True
% 184.11/184.27 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
% 184.11/184.27 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
% 184.11/184.27 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
% 184.11/184.27 Clause #314 (by clausification #[313]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 11 a a_1 a_2)) True
% 184.11/184.27 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
% 184.11/184.27 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
% 184.11/184.27 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
% 184.11/184.27 Clause #320 (by clausification #[318]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 12 a a_1 a_2)) True
% 184.11/184.27 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))
% 184.11/184.27 Clause #372 (by clausification #[18]): Eq
% 184.11/184.27 (Exists fun Y1 =>
% 184.11/184.27 Exists fun Y3 =>
% 184.11/184.27 Exists fun Y2 =>
% 184.11/184.27 Exists fun Y4 =>
% 184.11/184.27 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5))
% 184.11/184.27 (Exists fun Y6 => And (r4 Y3 Y3 Y6) (Exists fun Y7 => And (r4 Y1 Y1 Y7) (r3 Y7 Y6 Y4))))
% 184.11/184.29 False
% 184.11/184.29 Clause #373 (by clausification #[372]): ∀ (a : Iota),
% 184.11/184.29 Eq
% 184.11/184.29 (Exists fun Y3 =>
% 184.11/184.29 Exists fun Y2 =>
% 184.11/184.29 Exists fun Y4 =>
% 184.11/184.29 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5))
% 184.11/184.29 (Exists fun Y6 => And (r4 Y3 Y3 Y6) (Exists fun Y7 => And (r4 a a Y7) (r3 Y7 Y6 Y4))))
% 184.11/184.29 False
% 184.11/184.29 Clause #374 (by clausification #[373]): ∀ (a a_1 : Iota),
% 184.11/184.29 Eq
% 184.11/184.29 (Exists fun Y2 =>
% 184.11/184.29 Exists fun Y4 =>
% 184.11/184.29 And (Exists fun Y5 => And (id Y4 Y5) (r4 Y2 Y2 Y5))
% 184.11/184.29 (Exists fun Y6 => And (r4 a a Y6) (Exists fun Y7 => And (r4 a_1 a_1 Y7) (r3 Y7 Y6 Y4))))
% 184.11/184.29 False
% 184.11/184.29 Clause #375 (by clausification #[374]): ∀ (a a_1 a_2 : Iota),
% 184.11/184.29 Eq
% 184.11/184.29 (Exists fun Y4 =>
% 184.11/184.29 And (Exists fun Y5 => And (id Y4 Y5) (r4 a a Y5))
% 184.11/184.29 (Exists fun Y6 => And (r4 a_1 a_1 Y6) (Exists fun Y7 => And (r4 a_2 a_2 Y7) (r3 Y7 Y6 Y4))))
% 184.11/184.29 False
% 184.11/184.29 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.11/184.29 Eq
% 184.11/184.29 (And (Exists fun Y5 => And (id a Y5) (r4 a_1 a_1 Y5))
% 184.11/184.29 (Exists fun Y6 => And (r4 a_2 a_2 Y6) (Exists fun Y7 => And (r4 a_3 a_3 Y7) (r3 Y7 Y6 a))))
% 184.11/184.29 False
% 184.11/184.29 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.11/184.29 Or (Eq (Exists fun Y5 => And (id a Y5) (r4 a_1 a_1 Y5)) False)
% 184.11/184.29 (Eq (Exists fun Y6 => And (r4 a_2 a_2 Y6) (Exists fun Y7 => And (r4 a_3 a_3 Y7) (r3 Y7 Y6 a))) False)
% 184.11/184.29 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.29 Or (Eq (Exists fun Y6 => And (r4 a a Y6) (Exists fun Y7 => And (r4 a_1 a_1 Y7) (r3 Y7 Y6 a_2))) False)
% 184.11/184.29 (Eq (And (id a_2 a_3) (r4 a_4 a_4 a_3)) False)
% 184.11/184.29 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.29 Or (Eq (And (id a a_1) (r4 a_2 a_2 a_1)) False)
% 184.11/184.29 (Eq (And (r4 a_3 a_3 a_4) (Exists fun Y7 => And (r4 a_5 a_5 Y7) (r3 Y7 a_4 a))) False)
% 184.11/184.29 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.29 Or (Eq (And (r4 a a a_1) (Exists fun Y7 => And (r4 a_2 a_2 Y7) (r3 Y7 a_1 a_3))) False)
% 184.11/184.29 (Or (Eq (id a_3 a_4) False) (Eq (r4 a_5 a_5 a_4) False))
% 184.11/184.29 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.29 Or (Eq (id a a_1) False)
% 184.11/184.29 (Or (Eq (r4 a_2 a_2 a_1) False)
% 184.11/184.29 (Or (Eq (r4 a_3 a_3 a_4) False) (Eq (Exists fun Y7 => And (r4 a_5 a_5 Y7) (r3 Y7 a_4 a)) False)))
% 184.11/184.29 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 184.11/184.29 Or (Eq (id a a_1) False)
% 184.11/184.29 (Or (Eq (r4 a_2 a_2 a_1) False) (Or (Eq (r4 a_3 a_3 a_4) False) (Eq (And (r4 a_5 a_5 a_6) (r3 a_6 a_4 a)) False)))
% 184.11/184.29 Clause #383 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 184.11/184.29 Or (Eq (id a a_1) False)
% 184.11/184.29 (Or (Eq (r4 a_2 a_2 a_1) False)
% 184.11/184.29 (Or (Eq (r4 a_3 a_3 a_4) False) (Or (Eq (r4 a_5 a_5 a_6) False) (Eq (r3 a_6 a_4 a) False))))
% 184.11/184.29 Clause #403 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True)
% 184.11/184.29 Clause #408 (by clausification #[403]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False)
% 184.11/184.29 Clause #409 (by superposition #[408, 44]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 0 a_1)) True) (Eq False True)
% 184.11/184.29 Clause #410 (by superposition #[408, 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)
% 184.11/184.29 Clause #414 (by superposition #[408, 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)
% 184.11/184.29 Clause #425 (by clausification #[409]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a) (skS.0 0 a_1)) True
% 184.11/184.29 Clause #435 (by superposition #[425, 383]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 184.11/184.29 Or (Eq True False)
% 184.11/184.29 (Or (Eq (r4 a a (skS.0 0 a_1)) False)
% 184.11/184.29 (Or (Eq (r4 a_2 a_2 a_3) False) (Or (Eq (r4 a_4 a_4 a_5) False) (Eq (r3 a_5 a_3 (skS.0 0 a_6)) False))))
% 184.11/184.29 Clause #448 (by clausification #[410]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True
% 184.11/184.29 Clause #450 (by superposition #[448, 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)
% 184.11/184.29 Clause #461 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 5 a_1 a_2 a_3)) True) (Eq (Not (r4 a_1 a_2 a)) True)
% 184.11/184.32 Clause #463 (by clausification #[461]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 5 a_1 a_2 a_3)) True) (Eq (r4 a_1 a_2 a) False)
% 184.11/184.32 Clause #468 (by clausification #[450]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 2 a_1 a_2 a_3)) True
% 184.11/184.32 Clause #492 (by clausification #[414]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 12 a a_1 a_2) (skS.0 0 a_3)) True
% 184.11/184.32 Clause #494 (by superposition #[492, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 12 a_1 a_2 a_3)) True) (Eq True False)
% 184.11/184.32 Clause #504 (by clausification #[494]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 12 a_1 a_2 a_3)) True
% 184.11/184.32 Clause #571 (by clausification #[177]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True)
% 184.11/184.32 (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)))
% 184.11/184.32 Clause #572 (by clausification #[571]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True)
% 184.11/184.32 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r3 a_3 a_4 a_5)) True)))
% 184.11/184.32 Clause #574 (by clausification #[572]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (id a_2 a_3)) True)
% 184.11/184.32 (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))))
% 184.11/184.32 Clause #575 (by clausification #[574]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (r3 a_3 a_4 a_5)) True)
% 184.11/184.32 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False))))
% 184.11/184.32 Clause #576 (by clausification #[575]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (id a a_3)) True)
% 184.11/184.32 (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))))
% 184.11/184.32 Clause #577 (by clausification #[576]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (id a_1 a_3)) True)
% 184.11/184.32 (Or (Eq (id a_2 a_4) False) (Or (Eq (r3 a_5 a_3 a_4) False) (Eq (id a a_5) False))))
% 184.11/184.32 Clause #578 (by clausification #[577]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (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))))
% 184.11/184.32 Clause #590 (by superposition #[578, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (r3 a_3 a_4 (skS.0 1 a_2 a_5)) False)
% 184.11/184.32 (Or (Eq (id a a_3) False) (Or (Eq (id a_1 a_4) False) (Eq False True))))
% 184.11/184.32 Clause #626 (by clausification #[180]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (id a_3 a_2)) True)
% 184.11/184.32 (Or (Eq (Not (r3 a_4 a_5 a_3)) True) (Or (Eq (Not (id a_4 a)) True) (Eq (Not (id a_5 a_1)) True))))
% 184.11/184.32 Clause #627 (by clausification #[626]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (r3 a_3 a_4 a_5)) True)
% 184.11/184.32 (Or (Eq (Not (id a_3 a)) True) (Or (Eq (Not (id a_4 a_1)) True) (Eq (id a_5 a_2) False))))
% 184.11/184.32 Clause #628 (by clausification #[627]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (id a_3 a)) True)
% 184.11/184.32 (Or (Eq (Not (id a_4 a_1)) True) (Or (Eq (id a_5 a_2) False) (Eq (r3 a_3 a_4 a_5) False))))
% 184.11/184.32 Clause #629 (by clausification #[628]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (Not (id a_3 a_1)) True)
% 184.11/184.32 (Or (Eq (id a_4 a_2) False) (Or (Eq (r3 a_5 a_3 a_4) False) (Eq (id a_5 a) False))))
% 184.11/184.32 Clause #630 (by clausification #[629]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (id a_3 a_2) False) (Or (Eq (r3 a_4 a_5 a_3) False) (Or (Eq (id a_4 a) False) (Eq (id a_5 a_1) False))))
% 184.11/184.32 Clause #647 (by superposition #[630, 19]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.32 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.32 (Or (Eq (r3 a_3 a_4 a_2) False) (Or (Eq (id a_3 a) False) (Or (Eq (id a_4 a_1) False) (Eq False True))))
% 184.11/184.32 Clause #648 (by clausification #[647]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.35 Or (Eq (r3 a a_1 a_2) True) (Or (Eq (r3 a_3 a_4 a_2) False) (Or (Eq (id a_3 a) False) (Eq (id a_4 a_1) False)))
% 184.11/184.35 Clause #692 (by clausification #[202]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (And (Not (r4 a a_1 a_2)) (Not (r4 a_3 a_4 a_5))) True)
% 184.11/184.35 (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)))
% 184.11/184.35 Clause #693 (by clausification #[692]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 a_2) True)
% 184.11/184.35 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True)
% 184.11/184.35 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r4 a_3 a_4 a_5)) True)))
% 184.11/184.35 Clause #695 (by clausification #[693]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 a_2) True)
% 184.11/184.35 (Or (Eq (Not (id a_2 a_3)) True)
% 184.11/184.35 (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))))
% 184.11/184.35 Clause #696 (by clausification #[695]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 a_2) True)
% 184.11/184.35 (Or (Eq (Not (r4 a_3 a_4 a_5)) True)
% 184.11/184.35 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False))))
% 184.11/184.35 Clause #697 (by clausification #[696]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 a_2) True)
% 184.11/184.35 (Or (Eq (Not (id a a_3)) True)
% 184.11/184.35 (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))))
% 184.11/184.35 Clause #698 (by clausification #[697]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 a_2) True)
% 184.11/184.35 (Or (Eq (Not (id a_1 a_3)) True)
% 184.11/184.35 (Or (Eq (id a_2 a_4) False) (Or (Eq (r4 a_5 a_3 a_4) False) (Eq (id a a_5) False))))
% 184.11/184.35 Clause #699 (by clausification #[698]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 a_2) True)
% 184.11/184.35 (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))))
% 184.11/184.35 Clause #718 (by superposition #[699, 19]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 a_2) True)
% 184.11/184.35 (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))))
% 184.11/184.35 Clause #719 (by clausification #[718]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.35 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)))
% 184.11/184.35 Clause #720 (by superposition #[719, 319]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.35 Or (Eq (r4 a a_1 (skS.0 10 a_2 a_3)) True)
% 184.11/184.35 (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)))
% 184.11/184.35 Clause #1314 (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)
% 184.11/184.35 Clause #1315 (by superposition #[1314, 314]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 10 a a_1)) True) (Eq False True)
% 184.11/184.35 Clause #1316 (by clausification #[1315]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 10 a a_1)) True
% 184.11/184.35 Clause #1320 (by superposition #[1316, 408]): ∀ (a a_1 a_2 : Iota), Or (Eq (id (skS.0 10 a a_1) (skS.0 0 a_2)) True) (Eq True False)
% 184.11/184.35 Clause #1321 (by clausification #[1320]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 0 a_2)) True
% 184.11/184.35 Clause #1326 (by superposition #[1321, 31]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (id a (skS.0 10 a_2 a_3)) False))
% 184.11/184.35 Clause #1674 (by clausification #[1326]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (id a (skS.0 10 a_2 a_3)) False)
% 184.11/184.35 Clause #4859 (by clausification #[590]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 184.11/184.35 Or (Eq (r3 a a_1 a_2) True)
% 184.11/184.35 (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)))
% 184.11/184.35 Clause #4860 (by superposition #[4859, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.35 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)))
% 184.11/184.35 Clause #4861 (by clausification #[4860]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.11/184.35 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))
% 184.11/184.35 Clause #4942 (by superposition #[4861, 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))
% 184.11/184.35 Clause #4943 (by clausification #[4942]): ∀ (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)
% 184.21/184.37 Clause #4944 (by superposition #[4943, 468]): ∀ (a a_1 : Iota), Or (Eq (r3 a (skS.0 0 a_1) a) True) (Eq False True)
% 184.21/184.37 Clause #4959 (by clausification #[4944]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 0 a_1) a) True
% 184.21/184.37 Clause #4963 (by superposition #[4959, 648]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.21/184.37 Or (Eq (r3 a a_1 a_2) True) (Or (Eq True False) (Or (Eq (id a_2 a) False) (Eq (id (skS.0 0 a_3) a_1) False)))
% 184.21/184.37 Clause #4998 (by clausification #[4963]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Or (Eq (id a_2 a) False) (Eq (id (skS.0 0 a_3) a_1) False))
% 184.21/184.37 Clause #5000 (by superposition #[4998, 425]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.21/184.37 Or (Eq (r3 (skS.0 0 a) a_1 (skS.0 0 a_2)) True) (Or (Eq (id (skS.0 0 a_3) a_1) False) (Eq False True))
% 184.21/184.37 Clause #8338 (by clausification #[5000]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 (skS.0 0 a) a_1 (skS.0 0 a_2)) True) (Eq (id (skS.0 0 a_3) a_1) False)
% 184.21/184.37 Clause #8339 (by superposition #[8338, 425]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) True) (Eq False True)
% 184.21/184.37 Clause #8366 (by clausification #[8339]): ∀ (a a_1 a_2 : Iota), Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) True
% 184.21/184.37 Clause #9212 (by clausification #[435]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 184.21/184.37 Or (Eq (r4 a a (skS.0 0 a_1)) False)
% 184.21/184.37 (Or (Eq (r4 a_2 a_2 a_3) False) (Or (Eq (r4 a_4 a_4 a_5) False) (Eq (r3 a_5 a_3 (skS.0 0 a_6)) False)))
% 184.21/184.37 Clause #30058 (by clausification #[720]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.21/184.37 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))
% 184.21/184.37 Clause #30223 (by superposition #[30058, 19]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.21/184.37 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))
% 184.21/184.37 Clause #30224 (by clausification #[30223]): ∀ (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)
% 184.21/184.37 Clause #30225 (by superposition #[30224, 504]): ∀ (a a_1 a_2 : Iota), Or (Eq (r4 a (skS.0 0 a_1) (skS.0 10 a a_2)) True) (Eq False True)
% 184.21/184.37 Clause #30261 (by clausification #[30225]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 0 a_1) (skS.0 10 a a_2)) True
% 184.21/184.37 Clause #30265 (by superposition #[30261, 463]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 10 a a_1) (skS.0 5 a (skS.0 0 a_2) a_3)) True) (Eq True False)
% 184.21/184.37 Clause #31228 (by clausification #[30265]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 10 a a_1) (skS.0 5 a (skS.0 0 a_2) a_3)) True
% 184.21/184.37 Clause #31235 (by superposition #[31228, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 10 a a_3)) True) (Eq True False)
% 184.21/184.37 Clause #31585 (by clausification #[31235]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 10 a a_3)) True
% 184.21/184.37 Clause #31586 (by superposition #[31585, 1674]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 0 a_3)) True) (Eq True False)
% 184.21/184.37 Clause #31663 (by clausification #[31586]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 5 a (skS.0 0 a_1) a_2) (skS.0 0 a_3)) True
% 184.21/184.37 Clause #31677 (by superposition #[31663, 23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 5 a_1 (skS.0 0 a_2) a_3)) True) (Eq True False)
% 184.21/184.37 Clause #32044 (by clausification #[31677]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 5 a_1 (skS.0 0 a_2) a_3)) True
% 184.21/184.37 Clause #32045 (by superposition #[32044, 108]): ∀ (a a_1 a_2 : Iota), Or (Eq (r4 a (skS.0 0 a_1) (skS.0 0 a_2)) True) (Eq True False)
% 184.21/184.37 Clause #32119 (by clausification #[32045]): ∀ (a a_1 a_2 : Iota), Eq (r4 a (skS.0 0 a_1) (skS.0 0 a_2)) True
% 184.21/184.37 Clause #32120 (by superposition #[32119, 9212]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.21/184.37 Or (Eq True False) (Or (Eq (r4 a a a_1) False) (Or (Eq (r4 a_2 a_2 a_3) False) (Eq (r3 a_3 a_1 (skS.0 0 a_4)) False)))
% 184.21/184.37 Clause #32138 (by clausification #[32120]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 184.21/184.37 Or (Eq (r4 a a a_1) False) (Or (Eq (r4 a_2 a_2 a_3) False) (Eq (r3 a_3 a_1 (skS.0 0 a_4)) False))
% 184.21/184.37 Clause #32156 (by superposition #[32138, 32119]): ∀ (a a_1 a_2 a_3 : Iota),
% 184.51/184.67 Or (Eq (r4 a a a_1) False) (Or (Eq (r3 a_1 (skS.0 0 a_2) (skS.0 0 a_3)) False) (Eq False True))
% 184.51/184.67 Clause #32163 (by clausification #[32156]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r4 a a a_1) False) (Eq (r3 a_1 (skS.0 0 a_2) (skS.0 0 a_3)) False)
% 184.51/184.67 Clause #32181 (by superposition #[32163, 32119]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) False) (Eq False True)
% 184.51/184.67 Clause #32188 (by clausification #[32181]): ∀ (a a_1 a_2 : Iota), Eq (r3 (skS.0 0 a) (skS.0 0 a_1) (skS.0 0 a_2)) False
% 184.51/184.67 Clause #32189 (by superposition #[32188, 8366]): Eq False True
% 184.51/184.67 Clause #32225 (by clausification #[32189]): False
% 184.51/184.67 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------