TSTP Solution File: NUN070+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN070+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n026.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 12:47:19 EDT 2023
% Result : Theorem 35.19s 35.45s
% Output : Proof 35.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN070+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 10:04:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 35.19/35.45 SZS status Theorem for theBenchmark.p
% 35.19/35.45 SZS output start Proof for theBenchmark.p
% 35.19/35.45 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
% 35.19/35.45 Clause #1 (by assumption #[]): Eq
% 35.19/35.45 (∀ (X11 : Iota),
% 35.19/35.45 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21))))
% 35.19/35.45 True
% 35.19/35.45 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True
% 35.19/35.45 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True
% 35.19/35.45 Clause #8 (by assumption #[]): Eq
% 35.19/35.45 (∀ (X28 X29 X30 X31 : Iota),
% 35.19/35.45 Or (Or (Or (Not (id X28 X30)) (Not (id X29 X31))) (And (Not (r2 X28 X29)) (Not (r2 X30 X31))))
% 35.19/35.45 (And (r2 X28 X29) (r2 X30 X31)))
% 35.19/35.45 True
% 35.19/35.45 Clause #9 (by assumption #[]): Eq
% 35.19/35.45 (∀ (X32 X33 X34 X35 X36 X37 : Iota),
% 35.19/35.45 Or
% 35.19/35.45 (Or (Or (Or (Not (id X32 X35)) (Not (id X33 X36))) (Not (id X34 X37)))
% 35.19/35.45 (And (Not (r3 X32 X33 X34)) (Not (r3 X35 X36 X37))))
% 35.19/35.45 (And (r3 X32 X33 X34) (r3 X35 X36 X37)))
% 35.19/35.45 True
% 35.19/35.45 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
% 35.19/35.45 Clause #18 (by assumption #[]): Eq
% 35.19/35.45 (Not
% 35.19/35.45 (Exists fun Y1 =>
% 35.19/35.45 And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 Y1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2)))
% 35.19/35.45 (Exists fun Y3 => And (id Y1 Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3)))))
% 35.19/35.45 True
% 35.19/35.45 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True
% 35.19/35.45 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True
% 35.19/35.45 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True
% 35.19/35.45 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True)
% 35.19/35.45 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False)
% 35.19/35.45 Clause #34 (by clausification #[0]): ∀ (a : Iota),
% 35.19/35.45 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
% 35.19/35.45 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
% 35.19/35.45 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)
% 35.19/35.45 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)
% 35.19/35.45 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)
% 35.19/35.45 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True)
% 35.19/35.45 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False)
% 35.19/35.45 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True)
% 35.19/35.45 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True
% 35.19/35.45 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
% 35.19/35.45 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
% 35.19/35.45 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
% 35.19/35.45 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True
% 35.19/35.45 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
% 35.19/35.45 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
% 35.19/35.45 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 2 a a_1 a_2)) True
% 35.19/35.45 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False)
% 35.19/35.48 Clause #63 (by clausification #[1]): ∀ (a : Iota),
% 35.19/35.48 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True
% 35.19/35.48 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 35.19/35.48 Eq
% 35.19/35.48 (∀ (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)))))
% 35.19/35.48 True
% 35.19/35.48 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 35.19/35.48 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
% 35.19/35.48 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 35.19/35.48 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)
% 35.19/35.48 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)
% 35.19/35.48 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)
% 35.19/35.48 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)
% 35.19/35.48 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True)
% 35.19/35.48 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True
% 35.19/35.48 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True
% 35.19/35.48 Clause #139 (by clausification #[8]): ∀ (a : Iota),
% 35.19/35.48 Eq
% 35.19/35.48 (∀ (X29 X30 X31 : Iota),
% 35.19/35.48 Or (Or (Or (Not (id a X30)) (Not (id X29 X31))) (And (Not (r2 a X29)) (Not (r2 X30 X31))))
% 35.19/35.48 (And (r2 a X29) (r2 X30 X31)))
% 35.19/35.48 True
% 35.19/35.48 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota),
% 35.19/35.48 Eq
% 35.19/35.48 (∀ (X30 X31 : Iota),
% 35.19/35.48 Or (Or (Or (Not (id a X30)) (Not (id a_1 X31))) (And (Not (r2 a a_1)) (Not (r2 X30 X31))))
% 35.19/35.48 (And (r2 a a_1) (r2 X30 X31)))
% 35.19/35.48 True
% 35.19/35.48 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota),
% 35.19/35.48 Eq
% 35.19/35.48 (∀ (X31 : Iota),
% 35.19/35.48 Or (Or (Or (Not (id a a_1)) (Not (id a_2 X31))) (And (Not (r2 a a_2)) (Not (r2 a_1 X31))))
% 35.19/35.48 (And (r2 a a_2) (r2 a_1 X31)))
% 35.19/35.48 True
% 35.19/35.48 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 Eq
% 35.19/35.48 (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))))
% 35.19/35.48 (And (r2 a a_2) (r2 a_1 a_3)))
% 35.19/35.48 True
% 35.19/35.48 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 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)
% 35.19/35.48 (Eq (And (r2 a a_2) (r2 a_1 a_3)) True)
% 35.19/35.48 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 Or (Eq (And (r2 a a_1) (r2 a_2 a_3)) True)
% 35.19/35.48 (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))
% 35.19/35.48 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 Or (Eq (Or (Not (id a a_1)) (Not (id a_2 a_3))) True)
% 35.19/35.48 (Or (Eq (And (Not (r2 a a_2)) (Not (r2 a_1 a_3))) True) (Eq (r2 a_1 a_3) True))
% 35.19/35.48 Clause #147 (by clausification #[145]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 Or (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True)
% 35.19/35.48 (Or (Eq (r2 a_2 a_3) True) (Or (Eq (Not (id a a_2)) True) (Eq (Not (id a_1 a_3)) True)))
% 35.19/35.48 Clause #149 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 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)))
% 35.19/35.48 Clause #158 (by clausification #[149]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 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)))
% 35.19/35.48 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 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)))
% 35.19/35.48 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.48 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)))
% 35.19/35.48 Clause #168 (by clausification #[9]): ∀ (a : Iota),
% 35.19/35.48 Eq
% 35.19/35.48 (∀ (X33 X34 X35 X36 X37 : Iota),
% 35.19/35.48 Or
% 35.19/35.48 (Or (Or (Or (Not (id a X35)) (Not (id X33 X36))) (Not (id X34 X37)))
% 35.19/35.52 (And (Not (r3 a X33 X34)) (Not (r3 X35 X36 X37))))
% 35.19/35.52 (And (r3 a X33 X34) (r3 X35 X36 X37)))
% 35.19/35.52 True
% 35.19/35.52 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota),
% 35.19/35.52 Eq
% 35.19/35.52 (∀ (X34 X35 X36 X37 : Iota),
% 35.19/35.52 Or
% 35.19/35.52 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id X34 X37)))
% 35.19/35.52 (And (Not (r3 a a_1 X34)) (Not (r3 X35 X36 X37))))
% 35.19/35.52 (And (r3 a a_1 X34) (r3 X35 X36 X37)))
% 35.19/35.52 True
% 35.19/35.52 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Iota),
% 35.19/35.52 Eq
% 35.19/35.52 (∀ (X35 X36 X37 : Iota),
% 35.19/35.52 Or
% 35.19/35.52 (Or (Or (Or (Not (id a X35)) (Not (id a_1 X36))) (Not (id a_2 X37)))
% 35.19/35.52 (And (Not (r3 a a_1 a_2)) (Not (r3 X35 X36 X37))))
% 35.19/35.52 (And (r3 a a_1 a_2) (r3 X35 X36 X37)))
% 35.19/35.52 True
% 35.19/35.52 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.19/35.52 Eq
% 35.19/35.52 (∀ (X36 X37 : Iota),
% 35.19/35.52 Or
% 35.19/35.52 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 X36))) (Not (id a_3 X37)))
% 35.19/35.52 (And (Not (r3 a a_2 a_3)) (Not (r3 a_1 X36 X37))))
% 35.19/35.52 (And (r3 a a_2 a_3) (r3 a_1 X36 X37)))
% 35.19/35.52 True
% 35.19/35.52 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.19/35.52 Eq
% 35.19/35.52 (∀ (X37 : Iota),
% 35.19/35.52 Or
% 35.19/35.52 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 X37)))
% 35.19/35.52 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 X37))))
% 35.19/35.52 (And (r3 a a_2 a_4) (r3 a_1 a_3 X37)))
% 35.19/35.52 True
% 35.19/35.52 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.19/35.52 Eq
% 35.19/35.52 (Or
% 35.19/35.52 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5)))
% 35.19/35.52 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))))
% 35.19/35.52 (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5)))
% 35.19/35.52 True
% 35.19/35.52 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.19/35.52 Or
% 35.19/35.52 (Eq
% 35.19/35.52 (Or (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5)))
% 35.19/35.52 (And (Not (r3 a a_2 a_4)) (Not (r3 a_1 a_3 a_5))))
% 35.19/35.52 True)
% 35.19/35.52 (Eq (And (r3 a a_2 a_4) (r3 a_1 a_3 a_5)) True)
% 35.19/35.52 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.19/35.52 Or (Eq (And (r3 a a_1 a_2) (r3 a_3 a_4 a_5)) True)
% 35.19/35.52 (Or (Eq (Or (Or (Not (id a a_3)) (Not (id a_1 a_4))) (Not (id a_2 a_5))) True)
% 35.19/35.52 (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True))
% 35.19/35.52 Clause #177 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.19/35.52 Or (Eq (Or (Or (Not (id a a_1)) (Not (id a_2 a_3))) (Not (id a_4 a_5))) True)
% 35.19/35.52 (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))
% 35.19/35.52 Clause #372 (by clausification #[18]): Eq
% 35.19/35.52 (Exists fun Y1 =>
% 35.19/35.52 And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 Y1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2)))
% 35.19/35.52 (Exists fun Y3 => And (id Y1 Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))))
% 35.19/35.52 False
% 35.19/35.52 Clause #373 (by clausification #[372]): ∀ (a : Iota),
% 35.19/35.52 Eq
% 35.19/35.52 (And (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2)))
% 35.19/35.52 (Exists fun Y3 => And (id a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))))
% 35.19/35.52 False
% 35.19/35.52 Clause #374 (by clausification #[373]): ∀ (a : Iota),
% 35.19/35.52 Or
% 35.19/35.52 (Eq (Exists fun Y2 => And (Exists fun Y4 => And (r1 Y4) (r3 Y2 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 Y2)))
% 35.19/35.52 False)
% 35.19/35.52 (Eq (Exists fun Y3 => And (id a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))) False)
% 35.19/35.52 Clause #375 (by clausification #[374]): ∀ (a a_1 : Iota),
% 35.19/35.52 Or (Eq (Exists fun Y3 => And (id a Y3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y3))) False)
% 35.19/35.52 (Eq (And (Exists fun Y4 => And (r1 Y4) (r3 a_1 Y4 a)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 a_1))) False)
% 35.19/35.52 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota),
% 35.19/35.52 Or (Eq (And (Exists fun Y4 => And (r1 Y4) (r3 a Y4 a_1)) (Exists fun Y5 => And (r1 Y5) (r2 Y5 a))) False)
% 35.19/35.52 (Eq (And (id a_1 a_2) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2))) False)
% 35.19/35.52 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 : Iota),
% 35.19/35.52 Or (Eq (And (id a a_1) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_1))) False)
% 35.19/35.52 (Or (Eq (Exists fun Y4 => And (r1 Y4) (r3 a_2 Y4 a)) False) (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a_2)) False))
% 35.19/35.52 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 : Iota),
% 35.35/35.55 Or (Eq (Exists fun Y4 => And (r1 Y4) (r3 a Y4 a_1)) False)
% 35.35/35.55 (Or (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a)) False)
% 35.35/35.55 (Or (Eq (id a_1 a_2) False) (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2)) False)))
% 35.35/35.55 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.35/35.55 Or (Eq (Exists fun Y5 => And (r1 Y5) (r2 Y5 a)) False)
% 35.35/35.55 (Or (Eq (id a_1 a_2) False)
% 35.35/35.55 (Or (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_2)) False) (Eq (And (r1 a_3) (r3 a a_3 a_1)) False)))
% 35.35/35.55 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.35/35.55 Or (Eq (id a a_1) False)
% 35.35/35.55 (Or (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_1)) False)
% 35.35/35.55 (Or (Eq (And (r1 a_2) (r3 a_3 a_2 a)) False) (Eq (And (r1 a_4) (r2 a_4 a_3)) False)))
% 35.35/35.55 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (id a a_1) False)
% 35.35/35.55 (Or (Eq (And (r1 a_2) (r3 a_3 a_2 a)) False)
% 35.35/35.55 (Or (Eq (And (r1 a_4) (r2 a_4 a_3)) False) (Eq (And (r1 a_5) (r2 a_5 a_1)) False)))
% 35.35/35.55 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (id a a_1) False)
% 35.35/35.55 (Or (Eq (And (r1 a_2) (r2 a_2 a_3)) False)
% 35.35/35.55 (Or (Eq (And (r1 a_4) (r2 a_4 a_1)) False) (Or (Eq (r1 a_5) False) (Eq (r3 a_3 a_5 a) False))))
% 35.35/35.55 Clause #383 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (id a a_1) False)
% 35.35/35.55 (Or (Eq (And (r1 a_2) (r2 a_2 a_1)) False)
% 35.35/35.55 (Or (Eq (r1 a_3) False) (Or (Eq (r3 a_4 a_3 a) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False)))))
% 35.35/35.55 Clause #384 (by clausification #[383]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (id a a_1) False)
% 35.35/35.55 (Or (Eq (r1 a_2) False)
% 35.35/35.55 (Or (Eq (r3 a_3 a_2 a) False)
% 35.35/35.55 (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_1) False))))))
% 35.35/35.55 Clause #393 (by superposition #[384, 19]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.35/35.55 Or (Eq (r1 a) False)
% 35.35/35.55 (Or (Eq (r3 a_1 a a_2) False)
% 35.35/35.55 (Or (Eq (r1 a_3) False)
% 35.35/35.55 (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_2) False) (Eq False True))))))
% 35.35/35.55 Clause #400 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True)
% 35.35/35.55 Clause #402 (by clausification #[400]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False)
% 35.35/35.55 Clause #403 (by superposition #[402, 44]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 0 a_1)) True) (Eq False True)
% 35.35/35.55 Clause #404 (by superposition #[402, 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)
% 35.35/35.55 Clause #416 (by clausification #[403]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a) (skS.0 0 a_1)) True
% 35.35/35.55 Clause #422 (by superposition #[416, 160]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.35/35.55 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)))
% 35.35/35.55 Clause #509 (by clausification #[404]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True
% 35.35/35.55 Clause #511 (by superposition #[509, 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)
% 35.35/35.55 Clause #560 (by clausification #[511]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 0 a) (skS.0 2 a_1 a_2 a_3)) True
% 35.35/35.55 Clause #569 (by clausification #[177]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (r3 a_3 a_4 a_5))) True)
% 35.35/35.55 (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)))
% 35.35/35.55 Clause #570 (by clausification #[569]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (r3 a a_1 a_2) True)
% 35.35/35.55 (Or (Eq (Or (Not (id a a_3)) (Not (id a_1 a_4))) True)
% 35.35/35.55 (Or (Eq (Not (id a_2 a_5)) True) (Eq (Not (r3 a_3 a_4 a_5)) True)))
% 35.35/35.55 Clause #572 (by clausification #[570]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (r3 a a_1 a_2) True)
% 35.35/35.55 (Or (Eq (Not (id a_2 a_3)) True)
% 35.35/35.55 (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))))
% 35.35/35.55 Clause #573 (by clausification #[572]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.35/35.55 Or (Eq (r3 a a_1 a_2) True)
% 35.35/35.55 (Or (Eq (Not (r3 a_3 a_4 a_5)) True)
% 35.41/35.58 (Or (Eq (Not (id a a_3)) True) (Or (Eq (Not (id a_1 a_4)) True) (Eq (id a_2 a_5) False))))
% 35.41/35.58 Clause #574 (by clausification #[573]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.41/35.58 Or (Eq (r3 a a_1 a_2) True)
% 35.41/35.58 (Or (Eq (Not (id a a_3)) True)
% 35.41/35.58 (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))))
% 35.41/35.58 Clause #575 (by clausification #[574]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.41/35.58 Or (Eq (r3 a a_1 a_2) True)
% 35.41/35.58 (Or (Eq (Not (id a_1 a_3)) True)
% 35.41/35.58 (Or (Eq (id a_2 a_4) False) (Or (Eq (r3 a_5 a_3 a_4) False) (Eq (id a a_5) False))))
% 35.41/35.58 Clause #576 (by clausification #[575]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.41/35.58 Or (Eq (r3 a a_1 a_2) True)
% 35.41/35.58 (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))))
% 35.41/35.58 Clause #588 (by superposition #[576, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.41/35.58 Or (Eq (r3 a a_1 a_2) True)
% 35.41/35.58 (Or (Eq (r3 a_3 a_4 (skS.0 1 a_2 a_5)) False)
% 35.41/35.58 (Or (Eq (id a a_3) False) (Or (Eq (id a_1 a_4) False) (Eq False True))))
% 35.41/35.58 Clause #723 (by clausification #[422]): ∀ (a a_1 a_2 a_3 : Iota),
% 35.41/35.58 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))
% 35.41/35.58 Clause #742 (by superposition #[723, 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))
% 35.41/35.58 Clause #743 (by clausification #[742]): ∀ (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)
% 35.41/35.58 Clause #744 (by superposition #[743, 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)
% 35.41/35.58 Clause #748 (by clausification #[744]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) True
% 35.41/35.58 Clause #1745 (by clausification #[393]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.41/35.58 Or (Eq (r1 a) False)
% 35.41/35.58 (Or (Eq (r3 a_1 a a_2) False)
% 35.41/35.58 (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_2) False)))))
% 35.41/35.58 Clause #1746 (by superposition #[1745, 44]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.41/35.58 Or (Eq (r3 a (skS.0 0 a_1) a_2) False)
% 35.41/35.58 (Or (Eq (r1 a_3) False)
% 35.41/35.58 (Or (Eq (r2 a_3 a) False) (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_2) False) (Eq False True)))))
% 35.41/35.58 Clause #2890 (by clausification #[1746]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.41/35.58 Or (Eq (r3 a (skS.0 0 a_1) a_2) False)
% 35.41/35.58 (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_2) False))))
% 35.41/35.58 Clause #3887 (by clausification #[588]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 35.41/35.58 Or (Eq (r3 a a_1 a_2) True)
% 35.41/35.58 (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)))
% 35.41/35.58 Clause #3888 (by superposition #[3887, 58]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.41/35.58 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)))
% 35.41/35.58 Clause #3902 (by clausification #[3888]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 35.41/35.58 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))
% 35.41/35.58 Clause #3972 (by superposition #[3902, 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))
% 35.41/35.58 Clause #3973 (by clausification #[3972]): ∀ (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)
% 35.41/35.58 Clause #3974 (by superposition #[3973, 560]): ∀ (a a_1 : Iota), Or (Eq (r3 a (skS.0 0 a_1) a) True) (Eq False True)
% 35.41/35.58 Clause #3988 (by clausification #[3974]): ∀ (a a_1 : Iota), Eq (r3 a (skS.0 0 a_1) a) True
% 35.41/35.58 Clause #3990 (by superposition #[3988, 2890]): ∀ (a a_1 a_2 : Iota),
% 35.41/35.58 Or (Eq True False) (Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False))))
% 35.41/35.58 Clause #4018 (by clausification #[3990]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False)))
% 35.41/35.58 Clause #4019 (by superposition #[4018, 44]): ∀ (a a_1 a_2 : Iota),
% 35.41/35.58 Or (Eq (r2 (skS.0 0 a) a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a_1) False) (Eq False True)))
% 35.41/35.58 Clause #4055 (by clausification #[4019]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Or (Eq (r1 a_2) False) (Eq (r2 a_2 a_1) False))
% 35.41/35.63 Clause #4056 (by superposition #[4055, 748]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a (skS.0 3 (skS.0 0 a_1) a_2)) False) (Eq False True))
% 35.41/35.63 Clause #4382 (by clausification #[4056]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a) False) (Eq (r2 a (skS.0 3 (skS.0 0 a_1) a_2)) False)
% 35.41/35.63 Clause #4383 (by superposition #[4382, 44]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) False) (Eq False True)
% 35.41/35.63 Clause #4828 (by clausification #[4383]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) False
% 35.41/35.63 Clause #4829 (by superposition #[4828, 748]): Eq False True
% 35.41/35.63 Clause #4830 (by clausification #[4829]): False
% 35.41/35.63 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------