TSTP Solution File: GRP187-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP187-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art08.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 39.5s
% Output : Assurance 39.5s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP187-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: ueq
%
% strategies selected:
% (binary-posweight-kb-big-order 60 #f 4 1)
% (binary-posweight-lex-big-order 30 #f 4 1)
% (binary 30 #t)
% (binary-posweight-kb-big-order 180 #f)
% (binary-posweight-lex-big-order 120 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-posweight-kb-small-order 60 #f)
% (binary-posweight-lex-small-order 60 #f)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(18,40,0,36,0,0,13466,3,3004)
%
%
% START OF PROOF
% 20 [] equal(multiply(identity,X),X).
% 21 [] equal(multiply(inverse(X),X),identity).
% 22 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 23 [] equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)).
% 24 [] equal(least_upper_bound(X,Y),least_upper_bound(Y,X)).
% 25 [] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)).
% 26 [] equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)).
% 29 [] equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X).
% 30 [] equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X).
% 31 [] equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))).
% 32 [] equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))).
% 33 [] equal(multiply(least_upper_bound(X,Y),Z),least_upper_bound(multiply(X,Z),multiply(Y,Z))).
% 34 [] equal(multiply(greatest_lower_bound(X,Y),Z),greatest_lower_bound(multiply(X,Z),multiply(Y,Z))).
% 35 [] equal(greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b))),identity).
% 36 [] -equal(multiply(a,b),multiply(b,a)).
% 37 [para:23.1.1,35.1.1] equal(greatest_lower_bound(least_upper_bound(b,inverse(b)),least_upper_bound(a,inverse(a))),identity).
% 38 [para:24.1.1,35.1.1.1] equal(greatest_lower_bound(least_upper_bound(inverse(a),a),least_upper_bound(b,inverse(b))),identity).
% 41 [para:23.1.1,29.1.1.2] equal(least_upper_bound(X,greatest_lower_bound(Y,X)),X).
% 42 [para:29.1.1,24.1.1] equal(X,least_upper_bound(greatest_lower_bound(X,Y),X)).
% 44 [para:24.1.1,30.1.1.2] equal(greatest_lower_bound(X,least_upper_bound(Y,X)),X).
% 45 [para:21.1.1,22.1.1.1,demod:20] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 50 [para:42.1.2,30.1.1.2,demod:25] equal(greatest_lower_bound(X,greatest_lower_bound(Y,X)),greatest_lower_bound(X,Y)).
% 55 [para:25.1.2,23.1.1] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(Z,greatest_lower_bound(X,Y))).
% 57 [para:23.1.1,25.1.2.1,demod:25] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(Y,greatest_lower_bound(X,Z))).
% 59 [para:30.1.1,25.1.2.1] equal(greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)),greatest_lower_bound(X,Z)).
% 63 [para:44.1.1,25.1.2.1] equal(greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(Y,X),Z)),greatest_lower_bound(X,Z)).
% 67 [para:21.1.1,45.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 68 [para:22.1.1,45.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 69 [para:45.1.2,45.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 80 [para:26.1.2,44.1.1.2] equal(greatest_lower_bound(X,least_upper_bound(Y,least_upper_bound(Z,X))),X).
% 87 [para:50.1.1,41.1.1.2] equal(least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)),greatest_lower_bound(X,Y)).
% 100 [para:31.1.2,24.1.1,demod:31] equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))).
% 113 [para:21.1.1,32.1.2.1] equal(multiply(inverse(X),greatest_lower_bound(X,Y)),greatest_lower_bound(identity,multiply(inverse(X),Y))).
% 114 [para:21.1.1,32.1.2.2] equal(multiply(inverse(X),greatest_lower_bound(Y,X)),greatest_lower_bound(multiply(inverse(X),Y),identity)).
% 117 [para:45.1.2,32.1.2.1] equal(multiply(inverse(X),greatest_lower_bound(multiply(X,Y),Z)),greatest_lower_bound(Y,multiply(inverse(X),Z))).
% 118 [para:45.1.2,32.1.2.2] equal(multiply(inverse(X),greatest_lower_bound(Y,multiply(X,Z))),greatest_lower_bound(multiply(inverse(X),Y),Z)).
% 128 [para:20.1.1,33.1.2.1] equal(multiply(least_upper_bound(identity,X),Y),least_upper_bound(Y,multiply(X,Y))).
% 148 [para:20.1.1,34.1.2.1] equal(multiply(greatest_lower_bound(identity,X),Y),greatest_lower_bound(Y,multiply(X,Y))).
% 149 [para:20.1.1,34.1.2.2] equal(multiply(greatest_lower_bound(X,identity),Y),greatest_lower_bound(multiply(X,Y),Y)).
% 150 [para:21.1.1,34.1.2.1] equal(multiply(greatest_lower_bound(inverse(X),Y),X),greatest_lower_bound(identity,multiply(Y,X))).
% 160 [para:69.1.2,21.1.1] equal(multiply(X,inverse(X)),identity).
% 162 [para:69.1.2,67.1.2] equal(X,multiply(X,identity)).
% 165 [para:162.1.2,67.1.2] equal(X,inverse(inverse(X))).
% 168 [para:160.1.1,32.1.2.1] equal(multiply(X,greatest_lower_bound(inverse(X),Y)),greatest_lower_bound(identity,multiply(X,Y))).
% 172 [para:160.1.1,34.1.2.1] equal(multiply(greatest_lower_bound(X,Y),inverse(X)),greatest_lower_bound(identity,multiply(Y,inverse(X)))).
% 173 [para:160.1.1,34.1.2.2] equal(multiply(greatest_lower_bound(X,Y),inverse(Y)),greatest_lower_bound(multiply(X,inverse(Y)),identity)).
% 175 [para:29.1.1,80.1.1.2.2,demod:25] equal(greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(Z,X))),greatest_lower_bound(X,Y)).
% 197 [para:23.1.1,55.1.2.2] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(Z,greatest_lower_bound(Y,X))).
% 227 [para:35.1.1,59.1.1.2] equal(greatest_lower_bound(a,identity),greatest_lower_bound(a,least_upper_bound(b,inverse(b)))).
% 230 [para:37.1.1,59.1.1.2] equal(greatest_lower_bound(b,identity),greatest_lower_bound(b,least_upper_bound(a,inverse(a)))).
% 233 [para:38.1.1,59.1.1.2] equal(greatest_lower_bound(inverse(a),identity),greatest_lower_bound(inverse(a),least_upper_bound(b,inverse(b)))).
% 237 [para:227.1.2,23.1.1] equal(greatest_lower_bound(a,identity),greatest_lower_bound(least_upper_bound(b,inverse(b)),a)).
% 239 [para:227.1.2,55.1.1.2] equal(greatest_lower_bound(X,greatest_lower_bound(a,identity)),greatest_lower_bound(least_upper_bound(b,inverse(b)),greatest_lower_bound(X,a))).
% 240 [para:230.1.2,23.1.1] equal(greatest_lower_bound(b,identity),greatest_lower_bound(least_upper_bound(a,inverse(a)),b)).
% 243 [para:230.1.2,55.1.1.2] equal(greatest_lower_bound(X,greatest_lower_bound(b,identity)),greatest_lower_bound(least_upper_bound(a,inverse(a)),greatest_lower_bound(X,b))).
% 247 [para:237.1.2,25.1.2.1,demod:25] equal(greatest_lower_bound(least_upper_bound(b,inverse(b)),greatest_lower_bound(a,X)),greatest_lower_bound(a,greatest_lower_bound(identity,X))).
% 248 [para:237.1.2,59.1.1.2] equal(greatest_lower_bound(b,greatest_lower_bound(a,identity)),greatest_lower_bound(b,a)).
% 260 [para:248.1.1,57.1.1] equal(greatest_lower_bound(b,a),greatest_lower_bound(a,greatest_lower_bound(b,identity))).
% 332 [para:37.1.1,63.1.1.2] equal(greatest_lower_bound(inverse(b),identity),greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a)))).
% 338 [para:237.1.2,63.1.1.2] equal(greatest_lower_bound(inverse(b),greatest_lower_bound(a,identity)),greatest_lower_bound(inverse(b),a)).
% 364 [para:160.1.1,68.1.2.2.2,demod:162] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 366 [para:45.1.2,364.1.2.1.1] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 408 [para:240.1.2,25.1.2.1,demod:25] equal(greatest_lower_bound(least_upper_bound(a,inverse(a)),greatest_lower_bound(b,X)),greatest_lower_bound(b,greatest_lower_bound(identity,X))).
% 409 [para:240.1.2,63.1.1.2] equal(greatest_lower_bound(inverse(a),greatest_lower_bound(b,identity)),greatest_lower_bound(inverse(a),b)).
% 530 [para:100.1.1,364.1.2.1.1,demod:364] equal(inverse(least_upper_bound(X,Y)),inverse(least_upper_bound(Y,X))).
% 538 [para:87.1.1,530.1.1.1,demod:87] equal(inverse(greatest_lower_bound(X,Y)),inverse(greatest_lower_bound(Y,X))).
% 542 [para:538.1.1,45.1.2.1] equal(X,multiply(inverse(greatest_lower_bound(Y,Z)),multiply(greatest_lower_bound(Z,Y),X))).
% 1420 [para:41.1.1,128.1.1.1,demod:20] equal(X,least_upper_bound(X,multiply(greatest_lower_bound(Y,identity),X))).
% 1519 [para:1420.1.2,44.1.1.2] equal(greatest_lower_bound(multiply(greatest_lower_bound(X,identity),Y),Y),multiply(greatest_lower_bound(X,identity),Y)).
% 1523 [para:1420.1.2,63.1.1.2.1] equal(greatest_lower_bound(multiply(greatest_lower_bound(X,identity),Y),greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(greatest_lower_bound(X,identity),Y),Z)).
% 1700 [para:160.1.1,148.1.2.2] equal(multiply(greatest_lower_bound(identity,X),inverse(X)),greatest_lower_bound(inverse(X),identity)).
% 1857 [para:113.1.2,23.1.1] equal(multiply(inverse(X),greatest_lower_bound(X,Y)),greatest_lower_bound(multiply(inverse(X),Y),identity)).
% 1866 [para:248.1.1,113.1.1.2] equal(multiply(inverse(b),greatest_lower_bound(b,a)),greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,identity)))).
% 1870 [para:260.1.2,113.1.1.2] equal(multiply(inverse(a),greatest_lower_bound(b,a)),greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(b,identity)))).
% 3172 [para:1700.1.1,45.1.2.2] equal(inverse(X),multiply(inverse(greatest_lower_bound(identity,X)),greatest_lower_bound(inverse(X),identity))).
% 4022 [para:172.1.2,23.1.1] equal(multiply(greatest_lower_bound(X,Y),inverse(X)),greatest_lower_bound(multiply(Y,inverse(X)),identity)).
% 4048 [para:172.1.2,118.1.1.2,demod:162] equal(multiply(inverse(X),multiply(greatest_lower_bound(Y,X),inverse(Y))),greatest_lower_bound(inverse(X),inverse(Y))).
% 4080 [para:366.1.2,173.1.2.1] equal(multiply(greatest_lower_bound(inverse(X),Y),inverse(Y)),greatest_lower_bound(inverse(multiply(Y,X)),identity)).
% 4085 [para:173.1.2,117.1.1.2,demod:162] equal(multiply(inverse(X),multiply(greatest_lower_bound(X,Y),inverse(Y))),greatest_lower_bound(inverse(Y),inverse(X))).
% 4868 [para:233.1.2,175.1.1.2] equal(greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),identity)),greatest_lower_bound(inverse(b),inverse(a))).
% 4888 [para:332.1.2,175.1.1.2] equal(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),identity)),greatest_lower_bound(inverse(a),inverse(b))).
% 5510 [para:149.1.2,239.1.2.2] equal(greatest_lower_bound(multiply(X,a),greatest_lower_bound(a,identity)),greatest_lower_bound(least_upper_bound(b,inverse(b)),multiply(greatest_lower_bound(X,identity),a))).
% 5547 [para:149.1.2,243.1.2.2] equal(greatest_lower_bound(multiply(X,b),greatest_lower_bound(b,identity)),greatest_lower_bound(least_upper_bound(a,inverse(a)),multiply(greatest_lower_bound(X,identity),b))).
% 6412 [para:338.1.1,4022.1.1.1,demod:150,165] equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(multiply(greatest_lower_bound(a,identity),b),identity)).
% 6415 [para:409.1.1,4022.1.1.1,demod:150,165] equal(greatest_lower_bound(identity,multiply(b,a)),greatest_lower_bound(multiply(greatest_lower_bound(b,identity),a),identity)).
% 6500 [para:1519.1.1,239.1.2.2,demod:5510,1523] equal(greatest_lower_bound(multiply(greatest_lower_bound(X,identity),a),identity),greatest_lower_bound(multiply(X,a),greatest_lower_bound(a,identity))).
% 6501 [para:1519.1.1,243.1.2.2,demod:5547,1523] equal(greatest_lower_bound(multiply(greatest_lower_bound(X,identity),b),identity),greatest_lower_bound(multiply(X,b),greatest_lower_bound(b,identity))).
% 7337 [para:4868.1.1,197.1.1] equal(greatest_lower_bound(inverse(b),inverse(a)),greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b)))).
% 7349 [para:4868.1.1,4022.1.1.1,demod:6501,150,165] equal(greatest_lower_bound(identity,multiply(inverse(a),b)),greatest_lower_bound(multiply(inverse(a),b),greatest_lower_bound(b,identity))).
% 7399 [para:4888.1.1,4022.1.1.1,demod:6500,150,165] equal(greatest_lower_bound(identity,multiply(inverse(b),a)),greatest_lower_bound(multiply(inverse(b),a),greatest_lower_bound(a,identity))).
% 8024 [para:149.1.1,6412.1.2.1,demod:25] equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,identity))).
% 8026 [para:149.1.1,6415.1.2.1,demod:25] equal(greatest_lower_bound(identity,multiply(b,a)),greatest_lower_bound(multiply(b,a),greatest_lower_bound(a,identity))).
% 8644 [para:8024.1.2,117.1.1.2,demod:162,118] equal(greatest_lower_bound(inverse(a),b),greatest_lower_bound(b,multiply(inverse(a),greatest_lower_bound(b,identity)))).
% 8661 [para:8644.1.2,408.1.1.2,demod:1870,409,243] equal(greatest_lower_bound(inverse(a),b),greatest_lower_bound(b,multiply(inverse(a),greatest_lower_bound(b,a)))).
% 8681 [para:8661.1.2,23.1.1] equal(greatest_lower_bound(inverse(a),b),greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(b,a)),b)).
% 8687 [para:8661.1.2,172.1.1.1,demod:7337,4048,22,4080] equal(greatest_lower_bound(inverse(multiply(b,a)),identity),greatest_lower_bound(inverse(b),inverse(a))).
% 8700 [para:8026.1.2,117.1.1.2,demod:162,118] equal(greatest_lower_bound(inverse(b),a),greatest_lower_bound(a,multiply(inverse(b),greatest_lower_bound(a,identity)))).
% 8720 [para:114.1.1,8681.1.2.1,demod:25] equal(greatest_lower_bound(inverse(a),b),greatest_lower_bound(multiply(inverse(a),b),greatest_lower_bound(identity,b))).
% 8732 [para:8700.1.2,247.1.1.2,demod:1866,338,239] equal(greatest_lower_bound(inverse(b),a),greatest_lower_bound(a,multiply(inverse(b),greatest_lower_bound(b,a)))).
% 8733 [para:23.1.1,8720.1.2.2,demod:7349] equal(greatest_lower_bound(inverse(a),b),greatest_lower_bound(identity,multiply(inverse(a),b))).
% 8754 [para:8733.1.2,118.1.1.2,demod:162,168,165] equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(a,b)).
% 9329 [para:8732.1.2,23.1.1] equal(greatest_lower_bound(inverse(b),a),greatest_lower_bound(multiply(inverse(b),greatest_lower_bound(b,a)),a)).
% 9335 [para:8732.1.2,172.1.1.1,demod:7337,4085,22,4080] equal(greatest_lower_bound(inverse(multiply(a,b)),identity),greatest_lower_bound(inverse(b),inverse(a))).
% 9344 [para:9335.1.1,3172.1.2.2,demod:8754] equal(inverse(multiply(a,b)),multiply(inverse(greatest_lower_bound(a,b)),greatest_lower_bound(inverse(b),inverse(a)))).
% 10112 [para:1857.1.1,9329.1.2.1,demod:25] equal(greatest_lower_bound(inverse(b),a),greatest_lower_bound(multiply(inverse(b),a),greatest_lower_bound(identity,a))).
% 10257 [para:23.1.1,10112.1.2.2,demod:7399] equal(greatest_lower_bound(inverse(b),a),greatest_lower_bound(identity,multiply(inverse(b),a))).
% 10277 [para:10257.1.2,118.1.1.2,demod:162,168,165] equal(greatest_lower_bound(identity,multiply(b,a)),greatest_lower_bound(b,a)).
% 10314 [para:10277.1.1,1700.1.1.1,demod:8687] equal(multiply(greatest_lower_bound(b,a),inverse(multiply(b,a))),greatest_lower_bound(inverse(b),inverse(a))).
% 14770 [para:10314.1.1,542.1.2.2,demod:9344] equal(inverse(multiply(b,a)),inverse(multiply(a,b))).
% 14773 [para:14770.1.2,67.1.2.1.1,demod:162,22,165,cut:36] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using unit paramodulation strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% clause length limited to 1
% clause depth limited to 4
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 2274
% derived clauses: 1613862
% kept clauses: 14736
% kept size sum: 253857
% kept mid-nuclei: 0
% kept new demods: 12926
% forw unit-subs: 806277
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 68
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 41.43
% process. runtime: 40.90
% specific non-discr-tree subsumption statistics:
% tried: 0
% length fails: 0
% strength fails: 0
% predlist fails: 0
% aux str. fails: 0
% by-lit fails: 0
% full subs tried: 0
% full subs fail: 0
%
% ; 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/GRP/GRP187-1+eq_r.in")
%
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