TSTP Solution File: NUN073+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN073+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 12:47:20 EDT 2023
% Result : Theorem 15.89s 16.07s
% Output : Proof 15.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN073+1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14 % Command : duper %s
% 0.13/0.34 % Computer : n005.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 09:32:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 15.89/16.07 SZS status Theorem for theBenchmark.p
% 15.89/16.07 SZS output start Proof for theBenchmark.p
% 15.89/16.07 Clause #1 (by assumption #[]): Eq
% 15.89/16.07 (∀ (X11 : Iota),
% 15.89/16.07 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21))))
% 15.89/16.07 True
% 15.89/16.07 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True
% 15.89/16.07 Clause #8 (by assumption #[]): Eq
% 15.89/16.07 (∀ (X28 X29 X30 X31 : Iota),
% 15.89/16.07 Or (Or (Or (Not (id X28 X30)) (Not (id X29 X31))) (And (Not (r2 X28 X29)) (Not (r2 X30 X31))))
% 15.89/16.07 (And (r2 X28 X29) (r2 X30 X31)))
% 15.89/16.07 True
% 15.89/16.07 Clause #13 (by assumption #[]): Eq
% 15.89/16.07 (∀ (X3 X10 : Iota),
% 15.89/16.07 Or (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 X3 Y13))) (Not (r2 X10 Y12))) (id X3 X10))
% 15.89/16.07 True
% 15.89/16.07 Clause #17 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 X7 Y10))) True
% 15.89/16.07 Clause #18 (by assumption #[]): Eq
% 15.89/16.07 (Not
% 15.89/16.07 (∀ (Y1 : Iota),
% 15.89/16.07 Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 Y1)))
% 15.89/16.07 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 Y1)))))
% 15.89/16.07 True
% 15.89/16.07 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True
% 15.89/16.07 Clause #45 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (id Y20 Y10)) (Not (r1 Y20))) (Not (r2 a Y10))) True
% 15.89/16.07 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Or (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) (Not (r2 a_1 a))) True
% 15.89/16.07 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (∀ (Y20 : Iota), Or (Not (id Y20 a)) (Not (r1 Y20))) True) (Eq (Not (r2 a_1 a)) True)
% 15.89/16.07 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r2 a a_1)) True) (Eq (Or (Not (id a_2 a_1)) (Not (r1 a_2))) True)
% 15.89/16.07 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (id a a_1)) (Not (r1 a))) True) (Eq (r2 a_2 a_1) False)
% 15.89/16.07 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (id a_2 a_1)) True) (Eq (Not (r1 a_2)) True))
% 15.89/16.07 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (r1 a_2)) True) (Eq (id a_2 a_1) False))
% 15.89/16.07 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (id a_2 a_1) False) (Eq (r1 a_2) False))
% 15.89/16.07 Clause #63 (by clausification #[1]): ∀ (a : Iota),
% 15.89/16.07 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True
% 15.89/16.07 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 15.89/16.07 Eq
% 15.89/16.07 (∀ (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)))))
% 15.89/16.07 True
% 15.89/16.07 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 15.89/16.07 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
% 15.89/16.07 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 15.89/16.07 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)
% 15.89/16.07 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)
% 15.89/16.07 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota),
% 15.89/16.07 Or (Eq (And (Not (r2 a a_1)) (Not (id a_1 (skS.0 3 a a_2)))) True) (Eq (id a_1 (skS.0 3 a a_2)) True)
% 15.89/16.07 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)
% 15.89/16.07 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)
% 15.89/16.07 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True)
% 15.89/16.07 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True
% 15.89/16.07 Clause #139 (by clausification #[8]): ∀ (a : Iota),
% 15.89/16.07 Eq
% 15.89/16.07 (∀ (X29 X30 X31 : Iota),
% 15.89/16.07 Or (Or (Or (Not (id a X30)) (Not (id X29 X31))) (And (Not (r2 a X29)) (Not (r2 X30 X31))))
% 15.89/16.07 (And (r2 a X29) (r2 X30 X31)))
% 15.89/16.07 True
% 15.89/16.09 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota),
% 15.89/16.09 Eq
% 15.89/16.09 (∀ (X30 X31 : Iota),
% 15.89/16.09 Or (Or (Or (Not (id a X30)) (Not (id a_1 X31))) (And (Not (r2 a a_1)) (Not (r2 X30 X31))))
% 15.89/16.09 (And (r2 a a_1) (r2 X30 X31)))
% 15.89/16.09 True
% 15.89/16.09 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota),
% 15.89/16.09 Eq
% 15.89/16.09 (∀ (X31 : Iota),
% 15.89/16.09 Or (Or (Or (Not (id a a_1)) (Not (id a_2 X31))) (And (Not (r2 a a_2)) (Not (r2 a_1 X31))))
% 15.89/16.09 (And (r2 a a_2) (r2 a_1 X31)))
% 15.89/16.09 True
% 15.89/16.09 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 Eq
% 15.89/16.09 (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))))
% 15.89/16.09 (And (r2 a a_2) (r2 a_1 a_3)))
% 15.89/16.09 True
% 15.89/16.09 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 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)
% 15.89/16.09 (Eq (And (r2 a a_2) (r2 a_1 a_3)) True)
% 15.89/16.09 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 Or (Eq (And (r2 a a_1) (r2 a_2 a_3)) True)
% 15.89/16.09 (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))
% 15.89/16.09 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 Or (Eq (Or (Not (id a a_1)) (Not (id a_2 a_3))) True)
% 15.89/16.09 (Or (Eq (And (Not (r2 a a_2)) (Not (r2 a_1 a_3))) True) (Eq (r2 a_1 a_3) True))
% 15.89/16.09 Clause #147 (by clausification #[145]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 Or (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True)
% 15.89/16.09 (Or (Eq (r2 a_2 a_3) True) (Or (Eq (Not (id a a_2)) True) (Eq (Not (id a_1 a_3)) True)))
% 15.89/16.09 Clause #149 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 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)))
% 15.89/16.09 Clause #158 (by clausification #[149]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 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)))
% 15.89/16.09 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 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)))
% 15.89/16.09 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 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)))
% 15.89/16.09 Clause #163 (by superposition #[160, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Or (Eq (id a_2 a_1) False) (Or (Eq (r2 a a_2) False) (Eq False True)))
% 15.89/16.09 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Or (Eq (id a_2 a_1) False) (Eq (r2 a a_2) False))
% 15.89/16.09 Clause #284 (by clausification #[13]): ∀ (a : Iota),
% 15.89/16.09 Eq
% 15.89/16.09 (∀ (X10 : Iota),
% 15.89/16.09 Or (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 a Y13))) (Not (r2 X10 Y12))) (id a X10))
% 15.89/16.09 True
% 15.89/16.09 Clause #285 (by clausification #[284]): ∀ (a a_1 : Iota),
% 15.89/16.09 Eq (Or (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 a Y13))) (Not (r2 a_1 Y12))) (id a a_1))
% 15.89/16.09 True
% 15.89/16.09 Clause #286 (by clausification #[285]): ∀ (a a_1 : Iota),
% 15.89/16.09 Or (Eq (∀ (Y12 : Iota), Or (∀ (Y13 : Iota), Or (Not (id Y13 Y12)) (Not (r2 a Y13))) (Not (r2 a_1 Y12))) True)
% 15.89/16.09 (Eq (id a a_1) True)
% 15.89/16.09 Clause #287 (by clausification #[286]): ∀ (a a_1 a_2 : Iota),
% 15.89/16.09 Or (Eq (id a a_1) True) (Eq (Or (∀ (Y13 : Iota), Or (Not (id Y13 a_2)) (Not (r2 a Y13))) (Not (r2 a_1 a_2))) True)
% 15.89/16.09 Clause #288 (by clausification #[287]): ∀ (a a_1 a_2 : Iota),
% 15.89/16.09 Or (Eq (id a a_1) True)
% 15.89/16.09 (Or (Eq (∀ (Y13 : Iota), Or (Not (id Y13 a_2)) (Not (r2 a Y13))) True) (Eq (Not (r2 a_1 a_2)) True))
% 15.89/16.09 Clause #289 (by clausification #[288]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 Or (Eq (id a a_1) True) (Or (Eq (Not (r2 a_1 a_2)) True) (Eq (Or (Not (id a_3 a_2)) (Not (r2 a a_3))) True))
% 15.89/16.09 Clause #290 (by clausification #[289]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 Or (Eq (id a a_1) True) (Or (Eq (Or (Not (id a_2 a_3)) (Not (r2 a a_2))) True) (Eq (r2 a_1 a_3) False))
% 15.89/16.09 Clause #291 (by clausification #[290]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.09 Or (Eq (id a a_1) True) (Or (Eq (r2 a_1 a_2) False) (Or (Eq (Not (id a_3 a_2)) True) (Eq (Not (r2 a a_3)) True)))
% 15.89/16.12 Clause #292 (by clausification #[291]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.12 Or (Eq (id a a_1) True) (Or (Eq (r2 a_1 a_2) False) (Or (Eq (Not (r2 a a_3)) True) (Eq (id a_3 a_2) False)))
% 15.89/16.12 Clause #293 (by clausification #[292]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.12 Or (Eq (id a a_1) True) (Or (Eq (r2 a_1 a_2) False) (Or (Eq (id a_3 a_2) False) (Eq (r2 a a_3) False)))
% 15.89/16.12 Clause #295 (by superposition #[293, 78]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.89/16.12 Or (Eq (id a a_1) True) (Or (Eq (id a_2 (skS.0 3 a_1 a_3)) False) (Or (Eq (r2 a a_2) False) (Eq False True)))
% 15.89/16.12 Clause #298 (by clausification #[295]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id a a_1) True) (Or (Eq (id a_2 (skS.0 3 a_1 a_3)) False) (Eq (r2 a a_2) False))
% 15.89/16.12 Clause #372 (by clausification #[18]): Eq
% 15.89/16.12 (∀ (Y1 : Iota),
% 15.89/16.12 Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 Y1)))
% 15.89/16.12 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 Y1))))
% 15.89/16.12 False
% 15.89/16.12 Clause #373 (by clausification #[372]): ∀ (a : Iota),
% 15.89/16.12 Eq
% 15.89/16.12 (Not
% 15.89/16.12 (Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 (skS.0 16 a))))
% 15.89/16.12 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 (skS.0 16 a))))))
% 15.89/16.12 True
% 15.89/16.12 Clause #374 (by clausification #[373]): ∀ (a : Iota),
% 15.89/16.12 Eq
% 15.89/16.12 (Or (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 (skS.0 16 a))))
% 15.89/16.12 (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 (skS.0 16 a)))))
% 15.89/16.12 False
% 15.89/16.12 Clause #375 (by clausification #[374]): ∀ (a : Iota), Eq (∀ (Y3 : Iota), Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 Y3))) (Not (r2 Y3 (skS.0 16 a)))) False
% 15.89/16.12 Clause #376 (by clausification #[374]): ∀ (a : Iota), Eq (∀ (Y2 : Iota), Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 Y2))) (Not (id Y2 (skS.0 16 a)))) False
% 15.89/16.12 Clause #377 (by clausification #[375]): ∀ (a a_1 : Iota),
% 15.89/16.12 Eq
% 15.89/16.12 (Not (Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 (skS.0 17 a a_1)))) (Not (r2 (skS.0 17 a a_1) (skS.0 16 a)))))
% 15.89/16.12 True
% 15.89/16.12 Clause #378 (by clausification #[377]): ∀ (a a_1 : Iota),
% 15.89/16.12 Eq (Or (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 (skS.0 17 a a_1)))) (Not (r2 (skS.0 17 a a_1) (skS.0 16 a))))
% 15.89/16.12 False
% 15.89/16.12 Clause #379 (by clausification #[378]): ∀ (a a_1 : Iota), Eq (Not (r2 (skS.0 17 a a_1) (skS.0 16 a))) False
% 15.89/16.12 Clause #380 (by clausification #[378]): ∀ (a a_1 : Iota), Eq (∀ (Y5 : Iota), Or (Not (r1 Y5)) (Not (r2 Y5 (skS.0 17 a a_1)))) False
% 15.89/16.12 Clause #381 (by clausification #[379]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 17 a a_1) (skS.0 16 a)) True
% 15.89/16.12 Clause #391 (by clausification #[380]): ∀ (a a_1 a_2 : Iota),
% 15.89/16.12 Eq (Not (Or (Not (r1 (skS.0 18 a a_1 a_2))) (Not (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1))))) True
% 15.89/16.12 Clause #392 (by clausification #[391]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 18 a a_1 a_2))) (Not (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1)))) False
% 15.89/16.12 Clause #393 (by clausification #[392]): ∀ (a a_1 a_2 : Iota), Eq (Not (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1))) False
% 15.89/16.12 Clause #395 (by clausification #[393]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 18 a a_1 a_2) (skS.0 17 a a_1)) True
% 15.89/16.12 Clause #396 (by superposition #[395, 52]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (id a (skS.0 17 a_1 a_2)) False) (Eq (r1 a) False))
% 15.89/16.12 Clause #403 (by clausification #[396]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 17 a_1 a_2)) False) (Eq (r1 a) False)
% 15.89/16.12 Clause #434 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 3 a_1 a_2)) True) (Eq (Not (r2 a_1 a)) True)
% 15.89/16.12 Clause #436 (by clausification #[434]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 3 a_1 a_2)) True) (Eq (r2 a_1 a) False)
% 15.89/16.12 Clause #439 (by superposition #[436, 381]): ∀ (a a_1 a_2 : Iota), Or (Eq (id (skS.0 16 a) (skS.0 3 (skS.0 17 a a_1) a_2)) True) (Eq False True)
% 15.89/16.12 Clause #556 (by clausification #[376]): ∀ (a a_1 : Iota),
% 15.89/16.12 Eq
% 15.89/16.12 (Not (Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 19 a a_1)))) (Not (id (skS.0 19 a a_1) (skS.0 16 a)))))
% 15.89/16.12 True
% 15.89/16.12 Clause #557 (by clausification #[556]): ∀ (a a_1 : Iota),
% 15.98/16.16 Eq (Or (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 19 a a_1)))) (Not (id (skS.0 19 a a_1) (skS.0 16 a))))
% 15.98/16.16 False
% 15.98/16.16 Clause #558 (by clausification #[557]): ∀ (a a_1 : Iota), Eq (Not (id (skS.0 19 a a_1) (skS.0 16 a))) False
% 15.98/16.16 Clause #559 (by clausification #[557]): ∀ (a a_1 : Iota), Eq (∀ (Y4 : Iota), Or (Not (r1 Y4)) (Not (r2 Y4 (skS.0 19 a a_1)))) False
% 15.98/16.16 Clause #560 (by clausification #[558]): ∀ (a a_1 : Iota), Eq (id (skS.0 19 a a_1) (skS.0 16 a)) True
% 15.98/16.16 Clause #568 (by superposition #[560, 164]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a (skS.0 16 a_1)) True) (Or (Eq True False) (Eq (r2 a (skS.0 19 a_1 a_2)) False))
% 15.98/16.16 Clause #572 (by clausification #[559]): ∀ (a a_1 a_2 : Iota),
% 15.98/16.16 Eq (Not (Or (Not (r1 (skS.0 20 a a_1 a_2))) (Not (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1))))) True
% 15.98/16.16 Clause #573 (by clausification #[572]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 20 a a_1 a_2))) (Not (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1)))) False
% 15.98/16.16 Clause #574 (by clausification #[573]): ∀ (a a_1 a_2 : Iota), Eq (Not (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1))) False
% 15.98/16.16 Clause #575 (by clausification #[573]): ∀ (a a_1 a_2 : Iota), Eq (Not (r1 (skS.0 20 a a_1 a_2))) False
% 15.98/16.16 Clause #576 (by clausification #[574]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 20 a a_1 a_2) (skS.0 19 a a_1)) True
% 15.98/16.16 Clause #582 (by clausification #[575]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 20 a a_1 a_2)) True
% 15.98/16.16 Clause #911 (by clausification #[568]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a (skS.0 16 a_1)) True) (Eq (r2 a (skS.0 19 a_1 a_2)) False)
% 15.98/16.16 Clause #912 (by superposition #[911, 576]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 (skS.0 20 a a_1 a_2) (skS.0 16 a)) True) (Eq False True)
% 15.98/16.16 Clause #915 (by clausification #[912]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 20 a a_1 a_2) (skS.0 16 a)) True
% 15.98/16.16 Clause #3205 (by clausification #[439]): ∀ (a a_1 a_2 : Iota), Eq (id (skS.0 16 a) (skS.0 3 (skS.0 17 a a_1) a_2)) True
% 15.98/16.16 Clause #3206 (by superposition #[3205, 298]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 17 a_1 a_2)) True) (Or (Eq True False) (Eq (r2 a (skS.0 16 a_1)) False))
% 15.98/16.16 Clause #3241 (by clausification #[3206]): ∀ (a a_1 a_2 : Iota), Or (Eq (id a (skS.0 17 a_1 a_2)) True) (Eq (r2 a (skS.0 16 a_1)) False)
% 15.98/16.16 Clause #3243 (by superposition #[3241, 915]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (id (skS.0 20 a a_1 a_2) (skS.0 17 a a_3)) True) (Eq False True)
% 15.98/16.16 Clause #3316 (by clausification #[3243]): ∀ (a a_1 a_2 a_3 : Iota), Eq (id (skS.0 20 a a_1 a_2) (skS.0 17 a a_3)) True
% 15.98/16.16 Clause #3317 (by superposition #[3316, 403]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (r1 (skS.0 20 a a_1 a_2)) False)
% 15.98/16.16 Clause #3350 (by clausification #[3317]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 20 a a_1 a_2)) False
% 15.98/16.16 Clause #3351 (by superposition #[3350, 582]): Eq False True
% 15.98/16.16 Clause #3365 (by clausification #[3351]): False
% 15.98/16.16 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------