TSTP Solution File: GRP167-2 by Gandalf---c-2.6
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% File : Gandalf---c-2.6
% Problem : GRP167-2 : 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 : art05.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
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP167-2+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 3 1)
% (binary-posweight-lex-big-order 30 #f 3 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(24,40,0,48,0,0,169,50,12,193,0,12)
%
%
% START OF PROOF
% 170 [] equal(X,X).
% 171 [] equal(multiply(identity,X),X).
% 172 [] equal(multiply(inverse(X),X),identity).
% 173 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 174 [] equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)).
% 175 [] equal(least_upper_bound(X,Y),least_upper_bound(Y,X)).
% 178 [] equal(least_upper_bound(X,X),X).
% 180 [] equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X).
% 181 [] equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X).
% 182 [] equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))).
% 183 [] equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))).
% 184 [] equal(multiply(least_upper_bound(X,Y),Z),least_upper_bound(multiply(X,Z),multiply(Y,Z))).
% 185 [] equal(multiply(greatest_lower_bound(X,Y),Z),greatest_lower_bound(multiply(X,Z),multiply(Y,Z))).
% 187 [] equal(inverse(inverse(X)),X).
% 188 [] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 189 [] equal(positive_part(X),least_upper_bound(X,identity)).
% 190 [] equal(negative_part(X),greatest_lower_bound(X,identity)).
% 191 [] equal(least_upper_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z))).
% 192 [] equal(greatest_lower_bound(X,least_upper_bound(Y,Z)),least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z))).
% 193 [] -equal(a,multiply(positive_part(a),negative_part(a))).
% 194 [para:187.1.1,172.1.1.1] equal(multiply(X,inverse(X)),identity).
% 195 [para:189.1.2,178.1.1] equal(positive_part(identity),identity).
% 197 [para:172.1.1,173.1.1.1,demod:171] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 199 [para:174.1.1,190.1.2] equal(negative_part(X),greatest_lower_bound(identity,X)).
% 200 [para:175.1.1,189.1.2] equal(positive_part(X),least_upper_bound(identity,X)).
% 208 [para:190.1.2,180.1.1.2] equal(least_upper_bound(X,negative_part(X)),X).
% 210 [para:199.1.2,180.1.1.2,demod:200] equal(positive_part(negative_part(X)),identity).
% 212 [para:208.1.1,175.1.1] equal(X,least_upper_bound(negative_part(X),X)).
% 225 [para:181.1.1,199.1.2,demod:200] equal(negative_part(positive_part(X)),identity).
% 229 [para:225.1.1,212.1.2.1,demod:200] equal(positive_part(X),positive_part(positive_part(X))).
% 235 [para:172.1.1,182.1.2.1,demod:200] equal(multiply(inverse(X),least_upper_bound(X,Y)),positive_part(multiply(inverse(X),Y))).
% 259 [para:171.1.1,184.1.2.1,demod:200] equal(multiply(positive_part(X),Y),least_upper_bound(Y,multiply(X,Y))).
% 271 [para:171.1.1,185.1.2.1,demod:199] equal(multiply(negative_part(X),Y),greatest_lower_bound(Y,multiply(X,Y))).
% 281 [para:172.1.1,197.1.2.2,demod:187] equal(X,multiply(X,identity)).
% 287 [para:197.1.2,184.1.2.1] equal(multiply(least_upper_bound(inverse(X),Y),multiply(X,Z)),least_upper_bound(Z,multiply(Y,multiply(X,Z)))).
% 291 [para:281.1.2,182.1.2.1,demod:200] equal(multiply(X,positive_part(Y)),least_upper_bound(X,multiply(X,Y))).
% 293 [para:281.1.2,183.1.2.1,demod:199] equal(multiply(X,negative_part(Y)),greatest_lower_bound(X,multiply(X,Y))).
% 315 [para:188.1.2,197.1.2.2,demod:187] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 326 [para:189.1.2,191.1.2.1,demod:199] equal(least_upper_bound(X,negative_part(Y)),greatest_lower_bound(positive_part(X),least_upper_bound(X,Y))).
% 332 [para:200.1.2,191.1.2.1,demod:200] equal(positive_part(greatest_lower_bound(X,Y)),greatest_lower_bound(positive_part(X),positive_part(Y))).
% 372 [para:199.1.2,192.1.2.1,demod:199] equal(negative_part(least_upper_bound(X,Y)),least_upper_bound(negative_part(X),negative_part(Y))).
% 466 [para:315.1.2,315.1.2.2.1,demod:187] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 572 [para:172.1.1,259.1.2.2,demod:189] equal(multiply(positive_part(inverse(X)),X),positive_part(X)).
% 573 [para:173.1.1,259.1.2.2] equal(multiply(positive_part(multiply(X,Y)),Z),least_upper_bound(Z,multiply(X,multiply(Y,Z)))).
% 574 [para:194.1.1,259.1.2.2,demod:189] equal(multiply(positive_part(X),inverse(X)),positive_part(inverse(X))).
% 592 [para:572.1.1,466.1.2.1.1] equal(inverse(X),multiply(inverse(positive_part(X)),positive_part(inverse(X)))).
% 603 [para:229.1.2,574.1.1.1,demod:194] equal(identity,positive_part(inverse(positive_part(X)))).
% 675 [para:172.1.1,271.1.2.2,demod:190] equal(multiply(negative_part(inverse(X)),X),negative_part(X)).
% 707 [para:189.1.2,235.1.1.2,demod:281] equal(multiply(inverse(X),positive_part(X)),positive_part(inverse(X))).
% 754 [para:707.1.1,271.1.2.2,demod:332] equal(multiply(negative_part(inverse(X)),positive_part(X)),positive_part(greatest_lower_bound(X,inverse(X)))).
% 818 [para:291.1.2,259.1.2] equal(multiply(positive_part(X),X),multiply(X,positive_part(X))).
% 822 [para:675.1.1,291.1.2.2,demod:372,754] equal(positive_part(greatest_lower_bound(X,inverse(X))),negative_part(least_upper_bound(inverse(X),X))).
% 914 [para:818.1.1,293.1.2.2,demod:271] equal(multiply(positive_part(X),negative_part(X)),multiply(negative_part(X),positive_part(X))).
% 1073 [para:592.1.2,291.1.2.2,demod:592,229] equal(inverse(X),least_upper_bound(inverse(positive_part(X)),inverse(X))).
% 1606 [para:1073.1.2,326.1.2.2,demod:199,603] equal(least_upper_bound(inverse(positive_part(X)),negative_part(inverse(X))),negative_part(inverse(X))).
% 1939 [para:822.1.2,210.1.1.1,demod:229] equal(positive_part(greatest_lower_bound(X,inverse(X))),identity).
% 2233 [para:1606.1.1,287.1.1.1,demod:171,195,1939,754,573] equal(multiply(negative_part(inverse(X)),multiply(positive_part(X),Y)),Y).
% 2235 [para:572.1.1,2233.1.1.2,demod:914,187] equal(multiply(positive_part(X),negative_part(X)),X).
% 2262 [para:2235.1.1,193.1.2,cut:170] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos 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:
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% given clauses: 493
% derived clauses: 63497
% kept clauses: 2189
% kept size sum: 31049
% kept mid-nuclei: 0
% kept new demods: 1723
% forw unit-subs: 35363
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 2
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 0.80
% process. runtime: 0.80
% 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/GRP167-2+eq_r.in")
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