TSTP Solution File: HEN009-1 by Gandalf---c-2.6
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% File : Gandalf---c-2.6
% Problem : HEN009-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art02.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 0.0s
% Output : Assurance 0.0s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
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%----NO SOLUTION OUTPUT BY SYSTEM
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%----ORIGINAL SYSTEM OUTPUT
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% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/HEN/HEN009-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: heq
% detected subclass: medium
% detected subclass: long
%
% strategies selected:
% (hyper 58 #f 2 11)
% (binary-posweight-order 29 #f 2 11)
% (binary-unit 29 #f 2 11)
% (binary-double 29 #f 2 11)
% (binary 29 #t 2 11)
% (hyper 29 #t)
% (hyper 105 #f)
% (binary-unit-uniteq 17 #f)
% (binary-weightorder 23 #f)
% (binary-posweight-order 70 #f)
% (binary-posweight-lex-big-order 29 #f)
% (binary-posweight-lex-small-order 11 #f)
% (binary-order 29 #f)
% (binary-unit 46 #f)
% (binary 67 #t)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(14,40,0,28,0,0,2306,50,8,2320,0,8)
%
%
% START OF PROOF
% 2308 [] quotient(X,Y,zero) | -less_equal(X,Y).
% 2309 [] -quotient(X,Y,zero) | less_equal(X,Y).
% 2310 [] -quotient(X,Y,Z) | less_equal(Z,X).
% 2311 [] -quotient(Z,U,X2) | -quotient(V,W,X1) | -quotient(Y,U,W) | -quotient(X,U,V) | -quotient(X,Y,Z) | less_equal(X1,X2).
% 2312 [] less_equal(zero,X).
% 2313 [] -less_equal(Y,X) | -less_equal(X,Y) | equal(X,Y).
% 2314 [] less_equal(X,identity).
% 2315 [] quotient(X,Y,divide(X,Y)).
% 2316 [] -quotient(X,Y,U) | -quotient(X,Y,Z) | equal(Z,U).
% 2317 [] quotient(identity,a,id^qa).
% 2318 [] quotient(identity,id^qa,id^q_id^qa).
% 2319 [] quotient(identity,id^q_id^qa,id^q__id^q_id^qa).
% 2320 [] -equal(id^qa,id^q__id^q_id^qa).
% 2321 [hyper:2308,2312] quotient(zero,X,zero).
% 2324 [hyper:2308,2314] quotient(X,identity,zero).
% 2448 [hyper:2310,2315] less_equal(divide(X,Y),X).
% 2501 [hyper:2311,2315,2315,2315,2315,2324] less_equal(divide(divide(X,Y),divide(identity,Y)),divide(zero,Y)).
% 2507 [hyper:2311,2315,2315,2315,2319,2318] less_equal(divide(id^q__id^q_id^qa,divide(id^qa,id^q_id^qa)),divide(id^q_id^qa,id^q_id^qa)).
% 2524 [hyper:2311,2315,2315,2315,2317,2315] less_equal(divide(id^qa,divide(X,a)),divide(divide(identity,X),a)).
% 2865 [hyper:2311,2315,2324,2321,2315,2317] less_equal(divide(divide(X,a),id^qa),zero).
% 2866 [hyper:2311,2315,2324,2321,2315,2318] less_equal(divide(divide(X,id^qa),id^q_id^qa),zero).
% 2867 [hyper:2311,2315,2324,2321,2315,2319] less_equal(divide(divide(X,id^q_id^qa),id^q__id^q_id^qa),zero).
% 2871 [hyper:2311,2315,2324,2321,2318,2318] less_equal(divide(id^q_id^qa,id^q_id^qa),zero).
% 2873 [hyper:2311,2315,2324,2321,2317,2317] less_equal(divide(id^qa,id^qa),zero).
% 3068 [hyper:2316,2315,2321] equal(zero,divide(zero,X)).
% 3074 [hyper:2308,2448] quotient(divide(X,Y),X,zero).
% 3081 [hyper:2313,2871,cut:2312] equal(zero,divide(id^q_id^qa,id^q_id^qa)).
% 3083 [hyper:2313,2873,cut:2312] equal(zero,divide(id^qa,id^qa)).
% 3460 [hyper:2311,2315,2318,2315,2315,2317,demod:3083] less_equal(divide(id^q_id^qa,divide(a,id^qa)),zero).
% 4338 [hyper:2316,3074,2315] equal(divide(divide(X,Y),X),zero).
% 6550 [hyper:2313,2501,demod:3068,cut:2312] equal(zero,divide(divide(X,Y),divide(identity,Y))).
% 6552 [hyper:2313,2865,cut:2312] equal(zero,divide(divide(X,a),id^qa)).
% 6554 [hyper:2313,2866,cut:2312] equal(zero,divide(divide(X,id^qa),id^q_id^qa)).
% 6556 [hyper:2313,2867,cut:2312] equal(zero,divide(divide(X,id^q_id^qa),id^q__id^q_id^qa)).
% 6562 [para:6552.1.2,2315.1.3] quotient(divide(X,a),id^qa,zero).
% 6563 [hyper:2309,6562] less_equal(divide(X,a),id^qa).
% 6827 [para:6554.1.2,2315.1.3] quotient(divide(X,id^qa),id^q_id^qa,zero).
% 6833 [hyper:2309,6827] less_equal(divide(X,id^qa),id^q_id^qa).
% 7103 [para:6556.1.2,2315.1.3] quotient(divide(X,id^q_id^qa),id^q__id^q_id^qa,zero).
% 7104 [hyper:2309,7103] less_equal(divide(X,id^q_id^qa),id^q__id^q_id^qa).
% 7115 [hyper:2311,7103,2315,2315,2315,2315] less_equal(divide(divide(X,id^q__id^q_id^qa),divide(id^q_id^qa,id^q__id^q_id^qa)),zero).
% 7367 [hyper:2313,2507,demod:3081,cut:2312] equal(zero,divide(id^q__id^q_id^qa,divide(id^qa,id^q_id^qa))).
% 7378 [hyper:2313,3460,cut:2312] equal(zero,divide(id^q_id^qa,divide(a,id^qa))).
% 7389 [para:7367.1.2,2315.1.3] quotient(id^q__id^q_id^qa,divide(id^qa,id^q_id^qa),zero).
% 7395 [hyper:2309,7389] less_equal(id^q__id^q_id^qa,divide(id^qa,id^q_id^qa)).
% 7737 [hyper:2313,7395,cut:7104] equal(divide(id^qa,id^q_id^qa),id^q__id^q_id^qa).
% 7739 [para:7737.1.1,2448.1.1] less_equal(id^q__id^q_id^qa,id^qa).
% 8918 [para:7378.1.2,2315.1.3] quotient(id^q_id^qa,divide(a,id^qa),zero).
% 8919 [hyper:2309,8918] less_equal(id^q_id^qa,divide(a,id^qa)).
% 9257 [hyper:2313,8919,cut:6833] equal(divide(a,id^qa),id^q_id^qa).
% 9260 [para:9257.1.1,3074.1.1] quotient(id^q_id^qa,a,zero).
% 10083 [hyper:2311,9260,2315,2315,2315,2315,demod:3068] less_equal(divide(divide(id^q_id^qa,X),divide(a,X)),zero).
% 22389 [para:6550.1.2,2315.1.3] quotient(divide(X,Y),divide(identity,Y),zero).
% 22390 [hyper:2309,22389] less_equal(divide(X,Y),divide(identity,Y)).
% 22860 [hyper:2313,10083,cut:2312] equal(zero,divide(divide(id^q_id^qa,X),divide(a,X))).
% 23477 [para:22860.1.2,2315.1.3] quotient(divide(id^q_id^qa,X),divide(a,X),zero).
% 23478 [hyper:2309,23477] less_equal(divide(id^q_id^qa,X),divide(a,X)).
% 24003 [hyper:2313,7115,cut:2312] equal(zero,divide(divide(X,id^q__id^q_id^qa),divide(id^q_id^qa,id^q__id^q_id^qa))).
% 24004 [para:24003.1.2,2315.1.3] quotient(divide(X,id^q__id^q_id^qa),divide(id^q_id^qa,id^q__id^q_id^qa),zero).
% 24005 [hyper:2309,24004] less_equal(divide(X,id^q__id^q_id^qa),divide(id^q_id^qa,id^q__id^q_id^qa)).
% 24451 [hyper:2313,24005,22390] equal(divide(id^q_id^qa,id^q__id^q_id^qa),divide(identity,id^q__id^q_id^qa)).
% 24452 [hyper:2313,24005,23478] equal(divide(id^q_id^qa,id^q__id^q_id^qa),divide(a,id^q__id^q_id^qa)).
% 24464 [para:24451.1.2,2524.1.2.1,demod:4338,24452] less_equal(divide(id^qa,divide(id^q__id^q_id^qa,a)),zero).
% 25456 [hyper:2313,24464,cut:2312] equal(zero,divide(id^qa,divide(id^q__id^q_id^qa,a))).
% 25459 [para:25456.1.2,2315.1.3] quotient(id^qa,divide(id^q__id^q_id^qa,a),zero).
% 25462 [hyper:2309,25459] less_equal(id^qa,divide(id^q__id^q_id^qa,a)).
% 25912 [hyper:2313,25462,cut:6563] equal(divide(id^q__id^q_id^qa,a),id^qa).
% 25914 [para:25912.1.1,2448.1.1] less_equal(id^qa,id^q__id^q_id^qa).
% 25920 [hyper:2313,25914,cut:7739] equal(id^qa,id^q__id^q_id^qa).
% 25945 [hyper:2320,25920] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 11
% clause depth limited to 3
% seconds given: 58
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 248
% derived clauses: 95666
% kept clauses: 321
% kept size sum: 2388
% kept mid-nuclei: 25543
% kept new demods: 53
% forw unit-subs: 53113
% forw double-subs: 14491
% forw overdouble-subs: 0
% backward subs: 9
% fast unit cutoff: 621
% full unit cutoff: 26
% dbl unit cutoff: 0
% real runtime : 1.17
% process. runtime: 1.15
% specific non-discr-tree subsumption statistics:
% tried: 20430
% length fails: 0
% strength fails: 7653
% predlist fails: 4194
% aux str. fails: 8369
% by-lit fails: 0
% full subs tried: 214
% full subs fail: 214
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/HEN/HEN009-1+eq_r.in")
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