TSTP Solution File: NUN081+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN081+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 12:47:22 EDT 2023
% Result : Theorem 26.50s 26.83s
% Output : Proof 26.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : NUN081+1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.15 % Command : duper %s
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 09:24:18 EDT 2023
% 0.15/0.35 % CPUTime :
% 26.50/26.83 SZS status Theorem for theBenchmark.p
% 26.50/26.83 SZS output start Proof for theBenchmark.p
% 26.50/26.83 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
% 26.50/26.83 Clause #1 (by assumption #[]): Eq
% 26.50/26.83 (∀ (X11 : Iota),
% 26.50/26.83 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21))))
% 26.50/26.83 True
% 26.50/26.83 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True
% 26.50/26.83 Clause #8 (by assumption #[]): Eq
% 26.50/26.83 (∀ (X28 X29 X30 X31 : Iota),
% 26.50/26.83 Or (Or (Or (Not (id X28 X30)) (Not (id X29 X31))) (And (Not (r2 X28 X29)) (Not (r2 X30 X31))))
% 26.50/26.83 (And (r2 X28 X29) (r2 X30 X31)))
% 26.50/26.83 True
% 26.50/26.83 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
% 26.50/26.83 Clause #18 (by assumption #[]): Eq
% 26.50/26.83 (Not
% 26.50/26.83 (Exists fun Y1 =>
% 26.50/26.83 Exists fun Y2 =>
% 26.50/26.83 Exists fun Y3 =>
% 26.50/26.83 And (r3 Y1 Y2 Y3)
% 26.50/26.83 (Exists fun Y4 =>
% 26.50/26.83 And (id Y3 Y4)
% 26.50/26.83 (Exists fun Y5 =>
% 26.50/26.83 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))))
% 26.50/26.83 True
% 26.50/26.83 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True
% 26.50/26.83 Clause #34 (by clausification #[0]): ∀ (a : Iota),
% 26.50/26.83 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
% 26.50/26.83 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
% 26.50/26.83 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)
% 26.50/26.83 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)
% 26.50/26.83 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)
% 26.50/26.83 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True)
% 26.50/26.83 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False)
% 26.50/26.83 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True)
% 26.50/26.83 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True
% 26.50/26.83 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
% 26.50/26.83 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
% 26.50/26.83 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
% 26.50/26.83 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True
% 26.50/26.83 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
% 26.50/26.83 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
% 26.50/26.83 Clause #63 (by clausification #[1]): ∀ (a : Iota),
% 26.50/26.83 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True
% 26.50/26.83 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 26.50/26.83 Eq
% 26.50/26.83 (∀ (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)))))
% 26.50/26.83 True
% 26.50/26.83 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 26.50/26.83 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
% 26.50/26.83 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 26.50/26.83 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)
% 26.50/26.83 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)
% 26.50/26.83 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)
% 26.67/26.86 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)
% 26.67/26.86 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True)
% 26.67/26.86 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True
% 26.67/26.86 Clause #139 (by clausification #[8]): ∀ (a : Iota),
% 26.67/26.86 Eq
% 26.67/26.86 (∀ (X29 X30 X31 : Iota),
% 26.67/26.86 Or (Or (Or (Not (id a X30)) (Not (id X29 X31))) (And (Not (r2 a X29)) (Not (r2 X30 X31))))
% 26.67/26.86 (And (r2 a X29) (r2 X30 X31)))
% 26.67/26.86 True
% 26.67/26.86 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota),
% 26.67/26.86 Eq
% 26.67/26.86 (∀ (X30 X31 : Iota),
% 26.67/26.86 Or (Or (Or (Not (id a X30)) (Not (id a_1 X31))) (And (Not (r2 a a_1)) (Not (r2 X30 X31))))
% 26.67/26.86 (And (r2 a a_1) (r2 X30 X31)))
% 26.67/26.86 True
% 26.67/26.86 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota),
% 26.67/26.86 Eq
% 26.67/26.86 (∀ (X31 : Iota),
% 26.67/26.86 Or (Or (Or (Not (id a a_1)) (Not (id a_2 X31))) (And (Not (r2 a a_2)) (Not (r2 a_1 X31))))
% 26.67/26.86 (And (r2 a a_2) (r2 a_1 X31)))
% 26.67/26.86 True
% 26.67/26.86 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.86 Eq
% 26.67/26.86 (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))))
% 26.67/26.86 (And (r2 a a_2) (r2 a_1 a_3)))
% 26.67/26.86 True
% 26.67/26.86 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.86 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)
% 26.67/26.86 (Eq (And (r2 a a_2) (r2 a_1 a_3)) True)
% 26.67/26.86 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.86 Or (Eq (And (r2 a a_1) (r2 a_2 a_3)) True)
% 26.67/26.86 (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))
% 26.67/26.86 Clause #146 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.86 Or (Eq (Or (Not (id a a_1)) (Not (id a_2 a_3))) True)
% 26.67/26.86 (Or (Eq (And (Not (r2 a a_2)) (Not (r2 a_1 a_3))) True) (Eq (r2 a a_2) True))
% 26.67/26.86 Clause #372 (by clausification #[18]): Eq
% 26.67/26.86 (Exists fun Y1 =>
% 26.67/26.86 Exists fun Y2 =>
% 26.67/26.86 Exists fun Y3 =>
% 26.67/26.86 And (r3 Y1 Y2 Y3)
% 26.67/26.86 (Exists fun Y4 =>
% 26.67/26.86 And (id Y3 Y4)
% 26.67/26.86 (Exists fun Y5 =>
% 26.67/26.86 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 26.67/26.86 False
% 26.67/26.86 Clause #373 (by clausification #[372]): ∀ (a : Iota),
% 26.67/26.86 Eq
% 26.67/26.86 (Exists fun Y2 =>
% 26.67/26.86 Exists fun Y3 =>
% 26.67/26.86 And (r3 a Y2 Y3)
% 26.67/26.86 (Exists fun Y4 =>
% 26.67/26.86 And (id Y3 Y4)
% 26.67/26.86 (Exists fun Y5 =>
% 26.67/26.86 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 26.67/26.86 False
% 26.67/26.86 Clause #374 (by clausification #[373]): ∀ (a a_1 : Iota),
% 26.67/26.86 Eq
% 26.67/26.86 (Exists fun Y3 =>
% 26.67/26.86 And (r3 a a_1 Y3)
% 26.67/26.86 (Exists fun Y4 =>
% 26.67/26.86 And (id Y3 Y4)
% 26.67/26.86 (Exists fun Y5 =>
% 26.67/26.86 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 26.67/26.86 False
% 26.67/26.86 Clause #375 (by clausification #[374]): ∀ (a a_1 a_2 : Iota),
% 26.67/26.86 Eq
% 26.67/26.86 (And (r3 a a_1 a_2)
% 26.67/26.86 (Exists fun Y4 =>
% 26.67/26.86 And (id a_2 Y4)
% 26.67/26.86 (Exists fun Y5 =>
% 26.67/26.86 And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))))
% 26.67/26.86 False
% 26.67/26.86 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota),
% 26.67/26.86 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.86 (Eq
% 26.67/26.86 (Exists fun Y4 =>
% 26.67/26.86 And (id a_2 Y4)
% 26.67/26.86 (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))
% 26.67/26.86 False)
% 26.67/26.86 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.86 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.86 (Eq
% 26.67/26.86 (And (id a_2 a_3)
% 26.67/26.86 (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))))
% 26.67/26.86 False)
% 26.67/26.86 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.86 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.86 (Or (Eq (id a_2 a_3) False)
% 26.67/26.86 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r2 Y6 Y5) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))))
% 26.67/26.86 False))
% 26.67/26.86 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 26.67/26.89 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.89 (Or (Eq (id a_2 a_3) False)
% 26.67/26.89 (Eq (And (r2 a_4 a_3) (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6)))) False))
% 26.67/26.89 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 26.67/26.89 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.89 (Or (Eq (id a_2 a_3) False)
% 26.67/26.89 (Or (Eq (r2 a_4 a_3) False)
% 26.67/26.89 (Eq (Exists fun Y6 => And (r2 Y6 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 Y6))) False)))
% 26.67/26.89 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 26.67/26.89 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.89 (Or (Eq (id a_2 a_3) False)
% 26.67/26.89 (Or (Eq (r2 a_4 a_3) False) (Eq (And (r2 a_5 a_4) (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5))) False)))
% 26.67/26.89 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 26.67/26.89 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.89 (Or (Eq (id a_2 a_3) False)
% 26.67/26.89 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (Exists fun Y7 => And (r1 Y7) (r2 Y7 a_5)) False))))
% 26.67/26.89 Clause #383 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 26.67/26.89 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.89 (Or (Eq (id a_2 a_3) False)
% 26.67/26.89 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Eq (And (r1 a_6) (r2 a_6 a_5)) False))))
% 26.67/26.89 Clause #384 (by clausification #[383]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 26.67/26.89 Or (Eq (r3 a a_1 a_2) False)
% 26.67/26.89 (Or (Eq (id a_2 a_3) False)
% 26.67/26.89 (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r2 a_5 a_4) False) (Or (Eq (r1 a_6) False) (Eq (r2 a_6 a_5) False)))))
% 26.67/26.89 Clause #385 (by superposition #[384, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 26.67/26.89 Or (Eq (id (skS.0 1 a a_1) a_2) False)
% 26.67/26.89 (Or (Eq (r2 a_3 a_2) False)
% 26.67/26.89 (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)))))
% 26.67/26.89 Clause #395 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (Not (r1 a)) True)
% 26.67/26.89 Clause #397 (by clausification #[395]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 0 a_1)) True) (Eq (r1 a) False)
% 26.67/26.89 Clause #398 (by superposition #[397, 44]): ∀ (a a_1 : Iota), Or (Eq (id (skS.0 0 a) (skS.0 0 a_1)) True) (Eq False True)
% 26.67/26.89 Clause #411 (by clausification #[398]): ∀ (a a_1 : Iota), Eq (id (skS.0 0 a) (skS.0 0 a_1)) True
% 26.67/26.89 Clause #516 (by clausification #[146]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.89 Or (Eq (And (Not (r2 a a_1)) (Not (r2 a_2 a_3))) True)
% 26.67/26.89 (Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a a_2)) True) (Eq (Not (id a_1 a_3)) True)))
% 26.67/26.89 Clause #517 (by clausification #[516]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.89 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a a_2)) True) (Or (Eq (Not (id a_1 a_3)) True) (Eq (Not (r2 a_2 a_3)) True)))
% 26.67/26.89 Clause #519 (by clausification #[517]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.89 Or (Eq (r2 a a_1) True) (Or (Eq (Not (id a_1 a_2)) True) (Or (Eq (Not (r2 a_3 a_2)) True) (Eq (id a a_3) False)))
% 26.67/26.89 Clause #520 (by clausification #[519]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.89 Or (Eq (r2 a a_1) True) (Or (Eq (Not (r2 a_2 a_3)) True) (Or (Eq (id a a_2) False) (Eq (id a_1 a_3) False)))
% 26.67/26.89 Clause #521 (by clausification #[520]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.89 Or (Eq (r2 a a_1) True) (Or (Eq (id a a_2) False) (Or (Eq (id a_1 a_3) False) (Eq (r2 a_2 a_3) False)))
% 26.67/26.89 Clause #525 (by superposition #[521, 411]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.89 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (id a_1 a_2) False) (Or (Eq (r2 (skS.0 0 a_3) a_2) False) (Eq False True)))
% 26.67/26.89 Clause #1030 (by clausification #[525]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.67/26.89 Or (Eq (r2 (skS.0 0 a) a_1) True) (Or (Eq (id a_1 a_2) False) (Eq (r2 (skS.0 0 a_3) a_2) False))
% 26.67/26.89 Clause #1059 (by superposition #[1030, 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))
% 26.67/26.89 Clause #1090 (by clausification #[1059]): ∀ (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)
% 26.67/26.89 Clause #1091 (by superposition #[1090, 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)
% 26.67/26.89 Clause #1095 (by clausification #[1091]): ∀ (a a_1 a_2 : Iota), Eq (r2 (skS.0 0 a) (skS.0 3 (skS.0 0 a_1) a_2)) True
% 26.67/26.89 Clause #5751 (by clausification #[385]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 26.73/26.93 Or (Eq (id (skS.0 1 a a_1) a_2) False)
% 26.73/26.93 (Or (Eq (r2 a_3 a_2) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False))))
% 26.73/26.93 Clause #5771 (by superposition #[5751, 56]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.73/26.93 Or (Eq (r2 a a_1) False)
% 26.73/26.93 (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Or (Eq (r2 a_3 a_2) False) (Eq False True))))
% 26.73/26.93 Clause #5772 (by clausification #[5771]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.73/26.93 Or (Eq (r2 a a_1) False) (Or (Eq (r2 a_2 a) False) (Or (Eq (r1 a_3) False) (Eq (r2 a_3 a_2) False)))
% 26.73/26.93 Clause #5784 (by superposition #[5772, 78]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Or (Eq (r2 a_2 a) False) (Eq False True)))
% 26.73/26.93 Clause #5785 (by clausification #[5784]): ∀ (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))
% 26.73/26.93 Clause #5797 (by superposition #[5785, 78]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True))
% 26.73/26.93 Clause #5798 (by clausification #[5797]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False)
% 26.73/26.93 Clause #5799 (by superposition #[5798, 44]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Eq False True)
% 26.73/26.93 Clause #5828 (by clausification #[5799]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 0 a) a_1) False
% 26.73/26.93 Clause #5829 (by superposition #[5828, 1095]): Eq False True
% 26.73/26.93 Clause #5830 (by clausification #[5829]): False
% 26.73/26.93 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------