TSTP Solution File: NUN080+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUN080+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n001.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 4.58s 4.80s
% Output : Proof 4.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN080+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 09:58:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.58/4.80 SZS status Theorem for theBenchmark.p
% 4.58/4.80 SZS output start Proof for theBenchmark.p
% 4.58/4.80 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
% 4.58/4.80 Clause #1 (by assumption #[]): Eq
% 4.58/4.80 (∀ (X11 : Iota),
% 4.58/4.80 Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 X11 X12)) (And (Not (r2 X11 X12)) (Not (id X12 Y21))))
% 4.58/4.80 True
% 4.58/4.80 Clause #2 (by assumption #[]): Eq
% 4.58/4.80 (∀ (X13 X14 : Iota),
% 4.58/4.80 Exists fun Y22 =>
% 4.58/4.80 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 X13 X14 X15)) (And (Not (r3 X13 X14 X15)) (Not (id X15 Y22))))
% 4.58/4.80 True
% 4.58/4.80 Clause #4 (by assumption #[]): Eq (∀ (X20 : Iota), id X20 X20) True
% 4.58/4.80 Clause #5 (by assumption #[]): Eq (∀ (X21 X22 : Iota), Or (Not (id X21 X22)) (id X22 X21)) True
% 4.58/4.80 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
% 4.58/4.80 Clause #18 (by assumption #[]): Eq
% 4.58/4.80 (Not
% 4.58/4.80 (Exists fun Y1 =>
% 4.58/4.80 Exists fun Y2 =>
% 4.58/4.80 Exists fun Y3 =>
% 4.58/4.80 And (id Y3 Y2)
% 4.58/4.80 (Exists fun Y4 =>
% 4.58/4.80 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))))
% 4.58/4.80 True
% 4.58/4.80 Clause #19 (by clausification #[4]): ∀ (a : Iota), Eq (id a a) True
% 4.58/4.80 Clause #20 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X22 : Iota), Or (Not (id a X22)) (id X22 a)) True
% 4.58/4.80 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Not (id a a_1)) (id a_1 a)) True
% 4.58/4.80 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Not (id a a_1)) True) (Eq (id a_1 a) True)
% 4.58/4.80 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (id a a_1) True) (Eq (id a_1 a) False)
% 4.58/4.80 Clause #34 (by clausification #[0]): ∀ (a : Iota),
% 4.58/4.80 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
% 4.58/4.80 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
% 4.58/4.80 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)
% 4.58/4.80 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)
% 4.58/4.80 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (Not (id a (skS.0 0 a_1))) True)
% 4.58/4.80 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (r1 a) True) (Eq (id a (skS.0 0 a_1)) False)
% 4.58/4.80 Clause #42 (by superposition #[41, 19]): ∀ (a : Iota), Or (Eq (r1 (skS.0 0 a)) True) (Eq False True)
% 4.58/4.80 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (r1 (skS.0 0 a)) True
% 4.58/4.80 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
% 4.58/4.80 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
% 4.58/4.80 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (id (skS.0 1 a a_1) a) True
% 4.58/4.80 Clause #61 (by superposition #[56, 23]): ∀ (a a_1 : Iota), Or (Eq (id a (skS.0 1 a a_1)) True) (Eq True False)
% 4.58/4.80 Clause #63 (by clausification #[1]): ∀ (a : Iota),
% 4.58/4.80 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (id X12 Y21) (r2 a X12)) (And (Not (r2 a X12)) (Not (id X12 Y21)))) True
% 4.58/4.80 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 4.58/4.80 Eq
% 4.58/4.80 (∀ (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)))))
% 4.58/4.80 True
% 4.58/4.80 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 4.58/4.80 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
% 4.58/4.80 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 4.58/4.80 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)
% 4.58/4.80 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)
% 4.58/4.80 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)
% 4.67/4.83 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)
% 4.67/4.83 Clause #73 (by superposition #[71, 19]): ∀ (a a_1 : Iota), Or (Eq (r2 a (skS.0 3 a a_1)) True) (Eq False True)
% 4.67/4.83 Clause #75 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (id a (skS.0 1 a a_1)) True
% 4.67/4.83 Clause #78 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 3 a a_1)) True
% 4.67/4.83 Clause #80 (by clausification #[2]): ∀ (a : Iota),
% 4.67/4.83 Eq
% 4.67/4.83 (∀ (X14 : Iota),
% 4.67/4.83 Exists fun Y22 =>
% 4.67/4.83 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 a X14 X15)) (And (Not (r3 a X14 X15)) (Not (id X15 Y22))))
% 4.67/4.83 True
% 4.67/4.83 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota),
% 4.67/4.83 Eq
% 4.67/4.83 (Exists fun Y22 =>
% 4.67/4.83 ∀ (X15 : Iota), Or (And (id X15 Y22) (r3 a a_1 X15)) (And (Not (r3 a a_1 X15)) (Not (id X15 Y22))))
% 4.67/4.83 True
% 4.67/4.83 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota),
% 4.67/4.83 Eq
% 4.67/4.83 (∀ (X15 : Iota),
% 4.67/4.83 Or (And (id X15 (skS.0 4 a a_1 a_2)) (r3 a a_1 X15))
% 4.67/4.83 (And (Not (r3 a a_1 X15)) (Not (id X15 (skS.0 4 a a_1 a_2)))))
% 4.67/4.83 True
% 4.67/4.83 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.67/4.83 Eq
% 4.67/4.83 (Or (And (id a (skS.0 4 a_1 a_2 a_3)) (r3 a_1 a_2 a)) (And (Not (r3 a_1 a_2 a)) (Not (id a (skS.0 4 a_1 a_2 a_3)))))
% 4.67/4.83 True
% 4.67/4.83 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.67/4.83 Or (Eq (And (id a (skS.0 4 a_1 a_2 a_3)) (r3 a_1 a_2 a)) True)
% 4.67/4.83 (Eq (And (Not (r3 a_1 a_2 a)) (Not (id a (skS.0 4 a_1 a_2 a_3)))) True)
% 4.67/4.83 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.67/4.83 Or (Eq (And (Not (r3 a a_1 a_2)) (Not (id a_2 (skS.0 4 a a_1 a_3)))) True) (Eq (r3 a a_1 a_2) True)
% 4.67/4.83 Clause #87 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Eq (Not (id a_2 (skS.0 4 a a_1 a_3))) True)
% 4.67/4.83 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r3 a a_1 a_2) True) (Eq (id a_2 (skS.0 4 a a_1 a_3)) False)
% 4.67/4.83 Clause #91 (by superposition #[89, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True) (Eq False True)
% 4.67/4.83 Clause #97 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), Eq (r3 a a_1 (skS.0 4 a a_1 a_2)) True
% 4.67/4.83 Clause #372 (by clausification #[18]): Eq
% 4.67/4.83 (Exists fun Y1 =>
% 4.67/4.83 Exists fun Y2 =>
% 4.67/4.83 Exists fun Y3 =>
% 4.67/4.83 And (id Y3 Y2)
% 4.67/4.83 (Exists fun Y4 =>
% 4.67/4.83 And (r3 Y1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.67/4.83 False
% 4.67/4.83 Clause #373 (by clausification #[372]): ∀ (a : Iota),
% 4.67/4.83 Eq
% 4.67/4.83 (Exists fun Y2 =>
% 4.67/4.83 Exists fun Y3 =>
% 4.67/4.83 And (id Y3 Y2)
% 4.67/4.83 (Exists fun Y4 =>
% 4.67/4.83 And (r3 a Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.67/4.83 False
% 4.67/4.83 Clause #374 (by clausification #[373]): ∀ (a a_1 : Iota),
% 4.67/4.83 Eq
% 4.67/4.83 (Exists fun Y3 =>
% 4.67/4.83 And (id Y3 a)
% 4.67/4.83 (Exists fun Y4 =>
% 4.67/4.83 And (r3 a_1 Y4 Y3) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.67/4.83 False
% 4.67/4.83 Clause #375 (by clausification #[374]): ∀ (a a_1 a_2 : Iota),
% 4.67/4.83 Eq
% 4.67/4.83 (And (id a a_1)
% 4.67/4.83 (Exists fun Y4 => And (r3 a_2 Y4 a) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))))
% 4.67/4.83 False
% 4.67/4.83 Clause #376 (by clausification #[375]): ∀ (a a_1 a_2 : Iota),
% 4.67/4.83 Or (Eq (id a a_1) False)
% 4.67/4.83 (Eq (Exists fun Y4 => And (r3 a_2 Y4 a) (Exists fun Y5 => And (r2 Y5 Y4) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))))
% 4.67/4.83 False)
% 4.67/4.83 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.67/4.83 Or (Eq (id a a_1) False)
% 4.67/4.83 (Eq (And (r3 a_2 a_3 a) (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5)))) False)
% 4.67/4.83 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.67/4.83 Or (Eq (id a a_1) False)
% 4.67/4.83 (Or (Eq (r3 a_2 a_3 a) False)
% 4.67/4.83 (Eq (Exists fun Y5 => And (r2 Y5 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 Y5))) False))
% 4.67/4.83 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.67/4.83 Or (Eq (id a a_1) False)
% 4.67/4.83 (Or (Eq (r3 a_2 a_3 a) False) (Eq (And (r2 a_4 a_3) (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_4))) False))
% 4.67/4.84 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.67/4.84 Or (Eq (id a a_1) False)
% 4.67/4.84 (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Eq (Exists fun Y6 => And (r1 Y6) (r2 Y6 a_4)) False)))
% 4.67/4.84 Clause #381 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.67/4.84 Or (Eq (id a a_1) False)
% 4.67/4.84 (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Eq (And (r1 a_5) (r2 a_5 a_4)) False)))
% 4.67/4.84 Clause #382 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.67/4.84 Or (Eq (id a a_1) False)
% 4.67/4.84 (Or (Eq (r3 a_2 a_3 a) False) (Or (Eq (r2 a_4 a_3) False) (Or (Eq (r1 a_5) False) (Eq (r2 a_5 a_4) False))))
% 4.67/4.84 Clause #386 (by superposition #[382, 75]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.67/4.84 Or (Eq (r3 a a_1 a_2) False)
% 4.67/4.84 (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Or (Eq (r2 a_4 a_3) False) (Eq False True))))
% 4.67/4.84 Clause #389 (by clausification #[386]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.67/4.84 Or (Eq (r3 a a_1 a_2) False) (Or (Eq (r2 a_3 a_1) False) (Or (Eq (r1 a_4) False) (Eq (r2 a_4 a_3) False)))
% 4.67/4.84 Clause #391 (by superposition #[389, 97]): ∀ (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)))
% 4.67/4.84 Clause #392 (by clausification #[391]): ∀ (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))
% 4.67/4.84 Clause #395 (by superposition #[392, 78]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Or (Eq (r2 a a_1) False) (Eq False True))
% 4.67/4.84 Clause #396 (by clausification #[395]): ∀ (a a_1 : Iota), Or (Eq (r1 a) False) (Eq (r2 a a_1) False)
% 4.67/4.84 Clause #397 (by superposition #[396, 44]): ∀ (a a_1 : Iota), Or (Eq (r2 (skS.0 0 a) a_1) False) (Eq False True)
% 4.67/4.84 Clause #407 (by clausification #[397]): ∀ (a a_1 : Iota), Eq (r2 (skS.0 0 a) a_1) False
% 4.67/4.84 Clause #408 (by superposition #[407, 78]): Eq False True
% 4.67/4.84 Clause #409 (by clausification #[408]): False
% 4.67/4.84 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------