TSTP Solution File: ARI646_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI646_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Tue Sep 6 17:02:26 EDT 2022
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ARI646_1 : TPTP v8.1.0. Released v6.3.0.
% 0.04/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 30 01:11:04 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37 Usage: tptp [options] [-file:]file
% 0.15/0.37 -h, -? prints this message.
% 0.15/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.37 -m, -model generate model.
% 0.15/0.37 -p, -proof generate proof.
% 0.15/0.37 -c, -core generate unsat core of named formulas.
% 0.15/0.37 -st, -statistics display statistics.
% 0.15/0.37 -t:timeout set timeout (in second).
% 0.15/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37 -<param>:<value> configuration parameter and value.
% 0.15/0.37 -o:<output-file> file to place output in.
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(a_type, type, (
% 0.22/0.41 a: $int)).
% 0.22/0.41 tff(1,assumption,(~$greatereq(a, 10)), introduced(assumption)).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 ($lesseq(a, 9) | $greatereq(a, 10)),
% 0.22/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 ($lesseq(a, 9)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.22/0.41 tff(4,assumption,(~((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))))), introduced(assumption)).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 4)) | (~$greatereq(a, 4)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 ((~$lesseq(a, 4)) | (~$greatereq(a, 4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 3)) | (~$greatereq(a, 3)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(8,plain,
% 0.22/0.41 ((~$lesseq(a, 3)) | (~$greatereq(a, 3))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[7, 4])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 2)) | (~$greatereq(a, 2)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 ((~$lesseq(a, 2)) | (~$greatereq(a, 2))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[9, 4])).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 1)) | (~$greatereq(a, 1)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 ((~$lesseq(a, 1)) | (~$greatereq(a, 1))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[11, 4])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 0)) | (~$greatereq(a, 0)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(14,plain,
% 0.22/0.42 ((~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[13, 4])).
% 0.22/0.42 tff(15,plain,
% 0.22/0.42 ((($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))) <=> (($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(16,plain,
% 0.22/0.42 ((($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))) <=> (($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(17,plain,
% 0.22/0.42 ((($lesseq(10, a) | (~$lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))) <=> (($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(18,plain,
% 0.22/0.42 ((($lesseq(10, a) | (~$lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))) <=> (($lesseq(10, a) | (~$lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(19,plain,
% 0.22/0.42 (((~((~$lesseq(10, a)) & $lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))) <=> (($lesseq(10, a) | (~$lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(20,plain,
% 0.22/0.42 ((~(((~$lesseq(10, a)) & $lesseq(0, a)) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))) <=> ((~((~$lesseq(10, a)) & $lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(21,plain,
% 0.22/0.42 ((($greater(10, a) & $lesseq(0, a)) <=> ((((((((((a = 9) | (a = 8)) | (a = 7)) | (a = 6)) | (a = 5)) | (a = 4)) | (a = 3)) | (a = 2)) | (a = 1)) | (a = 0))) <=> (((~$lesseq(10, a)) & $lesseq(0, a)) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(22,plain,
% 0.22/0.42 ((~(($greater(10, a) & $lesseq(0, a)) <=> ((((((((((a = 9) | (a = 8)) | (a = 7)) | (a = 6)) | (a = 5)) | (a = 4)) | (a = 3)) | (a = 2)) | (a = 1)) | (a = 0)))) <=> (~(((~$lesseq(10, a)) & $lesseq(0, a)) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.22/0.42 tff(23,plain,
% 0.22/0.42 ((~(($greater(10, a) & $lesseq(0, a)) <=> ((((((((((a = 9) | (a = 8)) | (a = 7)) | (a = 6)) | (a = 5)) | (a = 4)) | (a = 3)) | (a = 2)) | (a = 1)) | (a = 0)))) <=> ((~((~$lesseq(10, a)) & $lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[22, 20])).
% 0.22/0.42 tff(24,axiom,(~(($greater(10, a) & $lesseq(0, a)) <=> ((((((((((a = 9) | (a = 8)) | (a = 7)) | (a = 6)) | (a = 5)) | (a = 4)) | (a = 3)) | (a = 2)) | (a = 1)) | (a = 0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 ((~((~$lesseq(10, a)) & $lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.22/0.42 tff(26,plain,
% 0.22/0.42 (($lesseq(10, a) | (~$lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (($lesseq(10, a) | (~$lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.22/0.42 tff(28,plain,
% 0.22/0.42 (($lesseq(10, a) | (~$lesseq(0, a))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[27, 18])).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.22/0.42 tff(31,plain,
% 0.22/0.42 (($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((a = 9) | (a = 8) | (a = 7) | (a = 6) | (a = 5) | (a = 4) | (a = 3) | (a = 2) | (a = 1) | (a = 0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[30, 16])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 15])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 ((~($greatereq(a, 10) | (~$greatereq(a, 0)))) | ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | (~(($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 ((~($greatereq(a, 10) | (~$greatereq(a, 0)))) | ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (~($greatereq(a, 10) | (~$greatereq(a, 0)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[34, 4])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (($greatereq(a, 10) | (~$greatereq(a, 0))) | $greatereq(a, 0)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 ($greatereq(a, 0)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 ((~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(39,plain,
% 0.22/0.43 (~$lesseq(a, 0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[38, 37, 14])).
% 0.22/0.43 tff(40,plain,
% 0.22/0.43 ($lesseq(a, 0) | $greatereq(a, 1)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(41,plain,
% 0.22/0.43 ($greatereq(a, 1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.22/0.43 tff(42,plain,
% 0.22/0.43 ((~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~$lesseq(a, 1)) | (~$greatereq(a, 1))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(43,plain,
% 0.22/0.43 (~$lesseq(a, 1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[42, 41, 12])).
% 0.22/0.43 tff(44,plain,
% 0.22/0.43 ($lesseq(a, 1) | $greatereq(a, 2)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 ($greatereq(a, 2)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 ((~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~$lesseq(a, 2)) | (~$greatereq(a, 2))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 (~$lesseq(a, 2)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[46, 45, 10])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 ($lesseq(a, 2) | $greatereq(a, 3)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(49,plain,
% 0.22/0.43 ($greatereq(a, 3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 ((~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~$lesseq(a, 3)) | (~$greatereq(a, 3))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(51,plain,
% 0.22/0.43 (~$lesseq(a, 3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[50, 49, 8])).
% 0.22/0.43 tff(52,plain,
% 0.22/0.43 ($lesseq(a, 3) | $greatereq(a, 4)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 ($greatereq(a, 4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 5)) | (~$greatereq(a, 5)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(55,plain,
% 0.22/0.43 ((~$lesseq(a, 5)) | (~$greatereq(a, 5))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[54, 4])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 6)) | (~$greatereq(a, 6)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 ((~$lesseq(a, 6)) | (~$greatereq(a, 6))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[56, 4])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 7)) | (~$greatereq(a, 7)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 ((~$lesseq(a, 7)) | (~$greatereq(a, 7))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[58, 4])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 8)) | (~$greatereq(a, 8)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 ((~$lesseq(a, 8)) | (~$greatereq(a, 8))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[60, 4])).
% 0.22/0.43 tff(62,assumption,($lesseq(a, 9)), introduced(assumption)).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | ((~$lesseq(a, 9)) | (~$greatereq(a, 9)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 ((~$lesseq(a, 9)) | (~$greatereq(a, 9))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[63, 4])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~$lesseq(a, 9)) | (~$greatereq(a, 9))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (~$greatereq(a, 9)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[65, 64, 62])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 ($lesseq(a, 8) | $greatereq(a, 9)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 ($lesseq(a, 8)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 ((~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~$lesseq(a, 8)) | (~$greatereq(a, 8))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (~$greatereq(a, 8)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[69, 68, 61])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 ($lesseq(a, 7) | $greatereq(a, 8)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 ($lesseq(a, 7)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 ((~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~$lesseq(a, 7)) | (~$greatereq(a, 7))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 (~$greatereq(a, 7)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[73, 72, 59])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 ($lesseq(a, 6) | $greatereq(a, 7)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(76,plain,
% 0.22/0.43 ($lesseq(a, 6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 ((~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~$lesseq(a, 6)) | (~$greatereq(a, 6))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 (~$greatereq(a, 6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[77, 76, 57])).
% 0.22/0.43 tff(79,plain,
% 0.22/0.43 ($lesseq(a, 5) | $greatereq(a, 6)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 ($lesseq(a, 5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.22/0.43 tff(81,plain,
% 0.22/0.43 ((~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~$lesseq(a, 5)) | (~$greatereq(a, 5))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(82,plain,
% 0.22/0.43 (~$greatereq(a, 5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[81, 80, 55])).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 ($lesseq(a, 4) | $greatereq(a, 5)),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 ($lesseq(a, 4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 ((~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~$lesseq(a, 4)) | (~$greatereq(a, 4))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[85, 84, 53, 6])).
% 0.22/0.43 tff(87,plain,(((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))) | (~$lesseq(a, 9))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(88,plain,
% 0.22/0.43 ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[87, 3])).
% 0.22/0.43 tff(89,plain,
% 0.22/0.43 (($greatereq(a, 10) | (~$greatereq(a, 0))) | (~((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))))) | (~(($greatereq(a, 10) | (~$greatereq(a, 0))) <=> ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(90,plain,
% 0.22/0.43 (($greatereq(a, 10) | (~$greatereq(a, 0))) | (~((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[89, 32])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 ($greatereq(a, 10) | (~$greatereq(a, 0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[90, 88])).
% 0.22/0.43 tff(92,plain,
% 0.22/0.43 ((~($greatereq(a, 10) | (~$greatereq(a, 0)))) | $greatereq(a, 10) | (~$greatereq(a, 0))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 (~$greatereq(a, 0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[92, 91, 1])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 ($greatereq(a, 0) | (~$greatereq(a, 1))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(95,plain,
% 0.22/0.43 (~$greatereq(a, 1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 ($greatereq(a, 1) | (~$greatereq(a, 2))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(97,plain,
% 0.22/0.43 (~$greatereq(a, 2)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 ($greatereq(a, 2) | (~$greatereq(a, 3))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 (~$greatereq(a, 3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.22/0.43 tff(100,plain,
% 0.22/0.43 ($greatereq(a, 3) | (~$greatereq(a, 4))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(101,plain,
% 0.22/0.43 (~$greatereq(a, 4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 ($greatereq(a, 4) | (~$greatereq(a, 5))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 (~$greatereq(a, 5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 ($greatereq(a, 5) | (~$greatereq(a, 6))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 (~$greatereq(a, 6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 ($greatereq(a, 6) | (~$greatereq(a, 7))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 (~$greatereq(a, 7)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 ($greatereq(a, 7) | (~$greatereq(a, 8))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 (~$greatereq(a, 8)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 ($greatereq(a, 8) | (~$greatereq(a, 9))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 (~$greatereq(a, 9)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 (((~$lesseq(a, 7)) | (~$greatereq(a, 7))) | $greatereq(a, 7)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(113,plain,
% 0.22/0.43 ((~$lesseq(a, 7)) | (~$greatereq(a, 7))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[112, 107])).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 (((~$lesseq(a, 0)) | (~$greatereq(a, 0))) | $greatereq(a, 0)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 ((~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[114, 93])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 (((~$lesseq(a, 1)) | (~$greatereq(a, 1))) | $greatereq(a, 1)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(117,plain,
% 0.22/0.43 ((~$lesseq(a, 1)) | (~$greatereq(a, 1))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[116, 95])).
% 0.22/0.43 tff(118,plain,
% 0.22/0.43 (((~$lesseq(a, 2)) | (~$greatereq(a, 2))) | $greatereq(a, 2)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 ((~$lesseq(a, 2)) | (~$greatereq(a, 2))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[118, 97])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (((~$lesseq(a, 3)) | (~$greatereq(a, 3))) | $greatereq(a, 3)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 ((~$lesseq(a, 3)) | (~$greatereq(a, 3))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[120, 99])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 (((~$lesseq(a, 4)) | (~$greatereq(a, 4))) | $greatereq(a, 4)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 ((~$lesseq(a, 4)) | (~$greatereq(a, 4))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[122, 101])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (((~$lesseq(a, 5)) | (~$greatereq(a, 5))) | $greatereq(a, 5)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 ((~$lesseq(a, 5)) | (~$greatereq(a, 5))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[124, 103])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 (((~$lesseq(a, 6)) | (~$greatereq(a, 6))) | $greatereq(a, 6)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 ((~$lesseq(a, 6)) | (~$greatereq(a, 6))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[126, 105])).
% 0.22/0.43 tff(128,plain,
% 0.22/0.43 (((~$lesseq(a, 8)) | (~$greatereq(a, 8))) | $greatereq(a, 8)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(129,plain,
% 0.22/0.43 ((~$lesseq(a, 8)) | (~$greatereq(a, 8))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[128, 109])).
% 0.22/0.43 tff(130,plain,
% 0.22/0.43 ((~((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0)))))) | (~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(131,plain,
% 0.22/0.43 (~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[130, 129, 88, 127, 125, 123, 121, 119, 117, 115, 113])).
% 0.22/0.43 tff(132,plain,
% 0.22/0.43 (((~$lesseq(a, 9)) | (~$greatereq(a, 9))) | $greatereq(a, 9)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(133,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[132, 131, 111])).
% 0.22/0.43 tff(134,plain,($greatereq(a, 10)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(135,plain,
% 0.22/0.43 ($greatereq(a, 9) | (~$greatereq(a, 10))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(136,plain,
% 0.22/0.43 ($greatereq(a, 9)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.22/0.43 tff(137,plain,
% 0.22/0.43 ($greatereq(a, 8)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[110, 136])).
% 0.22/0.43 tff(138,plain,
% 0.22/0.43 ((~$lesseq(a, 7)) | (~$greatereq(a, 8))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(139,plain,
% 0.22/0.43 (~$lesseq(a, 7)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.22/0.43 tff(140,plain,
% 0.22/0.43 (((~$lesseq(a, 7)) | (~$greatereq(a, 7))) | $lesseq(a, 7)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(141,plain,
% 0.22/0.43 ((~$lesseq(a, 7)) | (~$greatereq(a, 7))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.22/0.43 tff(142,plain,
% 0.22/0.43 ($greatereq(a, 7)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[108, 137])).
% 0.22/0.43 tff(143,plain,
% 0.22/0.43 ($greatereq(a, 6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[106, 142])).
% 0.22/0.43 tff(144,plain,
% 0.22/0.43 ($greatereq(a, 5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[104, 143])).
% 0.22/0.43 tff(145,plain,
% 0.22/0.43 ($greatereq(a, 4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[102, 144])).
% 0.22/0.43 tff(146,plain,
% 0.22/0.43 ($greatereq(a, 3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[100, 145])).
% 0.22/0.43 tff(147,plain,
% 0.22/0.43 ((~$lesseq(a, 2)) | (~$greatereq(a, 3))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(148,plain,
% 0.22/0.43 (~$lesseq(a, 2)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.22/0.43 tff(149,plain,
% 0.22/0.43 (((~$lesseq(a, 2)) | (~$greatereq(a, 2))) | $lesseq(a, 2)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(150,plain,
% 0.22/0.43 ((~$lesseq(a, 2)) | (~$greatereq(a, 2))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.22/0.43 tff(151,plain,
% 0.22/0.43 ((~$lesseq(a, 3)) | (~$greatereq(a, 4))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(152,plain,
% 0.22/0.43 (~$lesseq(a, 3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[151, 145])).
% 0.22/0.43 tff(153,plain,
% 0.22/0.43 (((~$lesseq(a, 3)) | (~$greatereq(a, 3))) | $lesseq(a, 3)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(154,plain,
% 0.22/0.43 ((~$lesseq(a, 3)) | (~$greatereq(a, 3))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.22/0.43 tff(155,plain,
% 0.22/0.43 ((~$lesseq(a, 4)) | (~$greatereq(a, 5))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(156,plain,
% 0.22/0.43 (~$lesseq(a, 4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[155, 144])).
% 0.22/0.43 tff(157,plain,
% 0.22/0.43 (((~$lesseq(a, 4)) | (~$greatereq(a, 4))) | $lesseq(a, 4)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(158,plain,
% 0.22/0.43 ((~$lesseq(a, 4)) | (~$greatereq(a, 4))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.22/0.43 tff(159,plain,
% 0.22/0.43 ((~$lesseq(a, 5)) | (~$greatereq(a, 6))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(160,plain,
% 0.22/0.43 (~$lesseq(a, 5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[159, 143])).
% 0.22/0.43 tff(161,plain,
% 0.22/0.43 (((~$lesseq(a, 5)) | (~$greatereq(a, 5))) | $lesseq(a, 5)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(162,plain,
% 0.22/0.43 ((~$lesseq(a, 5)) | (~$greatereq(a, 5))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.22/0.43 tff(163,plain,
% 0.22/0.43 ((~$lesseq(a, 6)) | (~$greatereq(a, 7))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(164,plain,
% 0.22/0.43 (~$lesseq(a, 6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[163, 142])).
% 0.22/0.43 tff(165,plain,
% 0.22/0.43 (((~$lesseq(a, 6)) | (~$greatereq(a, 6))) | $lesseq(a, 6)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(166,plain,
% 0.22/0.43 ((~$lesseq(a, 6)) | (~$greatereq(a, 6))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.22/0.43 tff(167,plain,
% 0.22/0.43 ((~$lesseq(a, 8)) | (~$greatereq(a, 9))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(168,plain,
% 0.22/0.43 (~$lesseq(a, 8)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[167, 136])).
% 0.22/0.43 tff(169,plain,
% 0.22/0.43 (((~$lesseq(a, 8)) | (~$greatereq(a, 8))) | $lesseq(a, 8)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(170,plain,
% 0.22/0.43 ((~$lesseq(a, 8)) | (~$greatereq(a, 8))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.22/0.43 tff(171,plain,
% 0.22/0.43 ((~$lesseq(a, 9)) | (~$greatereq(a, 10))),
% 0.22/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.43 tff(172,plain,
% 0.22/0.43 (~$lesseq(a, 9)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[171, 134])).
% 0.22/0.43 tff(173,plain,
% 0.22/0.43 (((~$lesseq(a, 9)) | (~$greatereq(a, 9))) | $lesseq(a, 9)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(174,plain,
% 0.22/0.43 ((~$lesseq(a, 9)) | (~$greatereq(a, 9))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.22/0.44 tff(175,plain,
% 0.22/0.44 (($greatereq(a, 10) | (~$greatereq(a, 0))) | (~$greatereq(a, 10))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(176,plain,
% 0.22/0.44 ($greatereq(a, 10) | (~$greatereq(a, 0))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[175, 134])).
% 0.22/0.44 tff(177,plain,
% 0.22/0.44 ((~((~$lesseq(a, 9)) | (~$greatereq(a, 9)))) | (~((~$lesseq(a, 8)) | (~$greatereq(a, 8)))) | (~((~$lesseq(a, 7)) | (~$greatereq(a, 7)))) | (~((~$lesseq(a, 6)) | (~$greatereq(a, 6)))) | (~((~$lesseq(a, 5)) | (~$greatereq(a, 5)))) | (~((~$lesseq(a, 4)) | (~$greatereq(a, 4)))) | (~((~$lesseq(a, 3)) | (~$greatereq(a, 3)))) | (~((~$lesseq(a, 2)) | (~$greatereq(a, 2)))) | (~((~$lesseq(a, 1)) | (~$greatereq(a, 1)))) | (~((~$lesseq(a, 0)) | (~$greatereq(a, 0))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[34, 176])).
% 0.22/0.44 tff(178,plain,
% 0.22/0.44 ($greatereq(a, 2)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[98, 146])).
% 0.22/0.44 tff(179,plain,
% 0.22/0.44 ((~$lesseq(a, 1)) | (~$greatereq(a, 2))),
% 0.22/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.44 tff(180,plain,
% 0.22/0.44 (~$lesseq(a, 1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.22/0.44 tff(181,plain,
% 0.22/0.44 (((~$lesseq(a, 1)) | (~$greatereq(a, 1))) | $lesseq(a, 1)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(182,plain,
% 0.22/0.44 ((~$lesseq(a, 1)) | (~$greatereq(a, 1))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.22/0.44 tff(183,plain,
% 0.22/0.44 ($greatereq(a, 1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[96, 178])).
% 0.22/0.44 tff(184,plain,
% 0.22/0.44 ((~$lesseq(a, 0)) | (~$greatereq(a, 1))),
% 0.22/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.44 tff(185,plain,
% 0.22/0.44 (~$lesseq(a, 0)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.22/0.44 tff(186,plain,
% 0.22/0.44 (((~$lesseq(a, 0)) | (~$greatereq(a, 0))) | $lesseq(a, 0)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(187,plain,
% 0.22/0.44 ((~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.22/0.44 tff(188,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[130, 187, 182, 177, 174, 170, 166, 162, 158, 154, 150, 141])).
% 0.22/0.44 % SZS output end Proof
%------------------------------------------------------------------------------