TSTP Solution File: GRP077-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP077-1 : TPTP v3.4.2. Bugfixed v2.3.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art09.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 :
%------------------------------------------------------------------------------
%----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/GRP077-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 7 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 7 5)
% (binary-posweight-lex-big-order 30 #f 7 5)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(inverse(a1),a1),identity) | -equal(multiply(identity,a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% was split for some strategies as:
% -equal(multiply(inverse(a1),a1),identity).
% -equal(multiply(identity,a2),a2).
% -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(6,40,0,12,0,0,338,4,758)
%
%
% START OF PROOF
% 7 [] equal(X,X).
% 8 [] equal(double_divide(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),double_divide(Y,Z))),Y),identity)),Z).
% 9 [] equal(multiply(X,Y),double_divide(double_divide(Y,X),identity)).
% 10 [] equal(inverse(X),double_divide(X,identity)).
% 11 [] equal(identity,double_divide(X,inverse(X))).
% 12 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity) | -equal(multiply(identity,a2),a2).
% 13 [para:9.1.2,10.1.2] equal(inverse(double_divide(X,Y)),multiply(Y,X)).
% 14 [para:10.1.2,9.1.2.1,demod:10] equal(multiply(identity,X),inverse(inverse(X))).
% 15 [para:11.1.2,9.1.2.1,demod:10] equal(multiply(inverse(X),X),inverse(identity)).
% 16 [para:9.1.2,9.1.2.1,demod:10] equal(multiply(identity,double_divide(X,Y)),inverse(multiply(Y,X))).
% 17 [para:14.1.2,11.1.2.2] equal(identity,double_divide(inverse(X),multiply(identity,X))).
% 21 [para:13.1.1,11.1.2.2] equal(identity,double_divide(double_divide(X,Y),multiply(Y,X))).
% 26 [para:10.1.2,8.1.1.2,demod:13,10] equal(double_divide(X,multiply(Y,double_divide(identity,double_divide(inverse(X),double_divide(Y,Z))))),Z).
% 27 [para:10.1.2,8.1.1.2.1,demod:13,10] equal(double_divide(X,inverse(multiply(double_divide(inverse(X),double_divide(identity,Y)),identity))),Y).
% 29 [para:11.1.2,8.1.1.2.1.1.2.2,demod:9,14,10] equal(double_divide(X,multiply(Y,double_divide(identity,multiply(identity,X)))),inverse(Y)).
% 30 [para:8.1.1,9.1.2.1,demod:9,10] equal(multiply(multiply(X,double_divide(identity,double_divide(inverse(Y),double_divide(X,Z)))),Y),inverse(Z)).
% 31 [para:9.1.2,8.1.1.2.1.1.2.1,demod:9] equal(double_divide(double_divide(X,Y),multiply(Z,double_divide(identity,double_divide(multiply(Y,X),double_divide(Z,U))))),U).
% 34 [para:8.1.1,8.1.1.2.1.1.2.2,demod:9,10] equal(double_divide(X,multiply(Y,double_divide(identity,double_divide(inverse(X),Z)))),multiply(U,double_divide(identity,double_divide(inverse(Y),double_divide(U,Z))))).
% 39 [para:29.1.1,9.1.2.1,demod:14,10] equal(multiply(multiply(X,double_divide(identity,multiply(identity,Y))),Y),multiply(identity,X)).
% 40 [para:15.1.1,29.1.1.2,demod:13] equal(double_divide(X,inverse(identity)),inverse(multiply(multiply(identity,X),identity))).
% 41 [para:29.1.1,8.1.1.2.1.1.2.2,demod:9,10] equal(double_divide(X,multiply(Y,double_divide(identity,double_divide(inverse(X),inverse(Z))))),multiply(Z,double_divide(identity,multiply(identity,Y)))).
% 42 [para:16.1.1,29.1.1.2,demod:40] equal(double_divide(X,double_divide(X,inverse(identity))),inverse(identity)).
% 46 [para:42.1.1,8.1.1.2.1.1.2,demod:9,10,11] equal(double_divide(X,multiply(inverse(X),identity)),inverse(identity)).
% 47 [para:46.1.1,9.1.2.1,demod:14,10] equal(multiply(multiply(inverse(X),identity),X),multiply(identity,identity)).
% 49 [para:15.1.1,46.1.1.2,demod:11] equal(identity,inverse(identity)).
% 50 [para:46.1.1,13.1.1.1,demod:47,49] equal(identity,multiply(identity,identity)).
% 53 [para:46.1.1,8.1.1.2.1.1.2.2,demod:29,9,14,49,10] equal(inverse(X),multiply(inverse(X),identity)).
% 54 [para:50.1.2,29.1.1.2.2.2,demod:49,10] equal(double_divide(identity,multiply(X,identity)),inverse(X)).
% 61 [para:13.1.1,53.1.2.1,demod:13] equal(multiply(X,Y),multiply(multiply(X,Y),identity)).
% 64 [para:54.1.1,9.1.2.1,demod:14,10,61] equal(multiply(X,identity),multiply(identity,X)).
% 65 [para:54.1.1,13.1.1.1,demod:61,14] equal(multiply(identity,X),multiply(X,identity)).
% 71 [para:53.1.2,54.1.1.2,demod:14] equal(double_divide(identity,inverse(X)),multiply(identity,X)).
% 73 [para:64.1.2,16.1.1] equal(multiply(double_divide(X,Y),identity),inverse(multiply(Y,X))).
% 83 [para:64.1.2,29.1.1.2.2.2,demod:54] equal(double_divide(X,multiply(Y,inverse(X))),inverse(Y)).
% 85 [para:64.1.1,53.1.2] equal(inverse(X),multiply(identity,inverse(X))).
% 88 [para:13.1.1,85.1.2.2,demod:13] equal(multiply(X,Y),multiply(identity,multiply(X,Y))).
% 92 [para:65.1.1,26.1.1.2,demod:13,83,88,14,73] equal(multiply(X,identity),X).
% 98 [para:29.1.1,27.1.1.2.1.1.2,demod:92,49,10,50,83,88,14,73] equal(multiply(identity,X),X).
% 101 [para:92.1.1,29.1.1.2.2.2,demod:92,49,10] equal(double_divide(identity,X),inverse(X)).
% 104 [para:98.1.1,17.1.2.2] equal(identity,double_divide(inverse(X),X)).
% 106 [para:98.1.1,16.1.1] equal(double_divide(X,Y),inverse(multiply(Y,X))).
% 107 [para:101.1.1,8.1.1,demod:9,106,13,49,101] equal(double_divide(double_divide(X,Y),X),Y).
% 119 [para:107.1.1,9.1.2.1,demod:10] equal(multiply(X,double_divide(X,Y)),inverse(Y)).
% 122 [para:8.1.1,107.1.1.1,demod:9,13,101,10] equal(double_divide(X,Y),multiply(Z,multiply(double_divide(Z,X),inverse(Y)))).
% 123 [para:29.1.1,107.1.1.1,demod:101,98] equal(double_divide(inverse(X),Y),multiply(X,inverse(Y))).
% 125 [para:26.1.1,107.1.1.1,demod:123,13,101] equal(double_divide(X,Y),multiply(Z,double_divide(multiply(X,Z),Y))).
% 126 [para:107.1.1,107.1.1.1] equal(double_divide(X,double_divide(Y,X)),Y).
% 127 [para:126.1.1,9.1.2.1,demod:10] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 128 [para:126.1.1,8.1.1.2.1.1.2.2,demod:9,123,13,101,10] equal(double_divide(X,multiply(Y,double_divide(inverse(Z),X))),double_divide(Z,Y)).
% 132 [para:8.1.1,30.1.1.1.2.2.2,demod:125,9,10,123,13,101] equal(multiply(multiply(X,double_divide(inverse(Y),Z)),Z),multiply(X,Y)).
% 133 [para:30.1.1,29.1.1.2,demod:106,13,14,101,98] equal(double_divide(X,inverse(Y)),double_divide(multiply(double_divide(Z,Y),X),Z)).
% 134 [para:29.1.1,30.1.1.1.2.2.2,demod:98,14,123,13,101] equal(multiply(multiply(X,double_divide(Y,Z)),Z),double_divide(inverse(X),Y)).
% 139 [para:8.1.1,31.1.1.2.2.2.2,demod:125,9,123,10,13,101] equal(double_divide(double_divide(X,Y),multiply(Z,multiply(U,multiply(Y,X)))),double_divide(U,Z)).
% 143 [para:119.1.1,29.1.1.2.2.2,demod:98,71,101] equal(double_divide(inverse(X),multiply(Y,X)),inverse(Y)).
% 144 [para:127.1.1,29.1.1.2,demod:13,101,98] equal(double_divide(X,inverse(Y)),multiply(inverse(X),Y)).
% 151 [para:83.1.1,8.1.1.2.1.1.2.2,demod:123,9,98,14,144,13,101,10] equal(double_divide(X,multiply(Y,double_divide(Z,X))),double_divide(inverse(Z),Y)).
% 153 [para:14.1.2,123.1.2.2,demod:98] equal(double_divide(inverse(X),inverse(Y)),multiply(X,Y)).
% 154 [para:13.1.1,123.1.2.2] equal(double_divide(inverse(X),double_divide(Y,Z)),multiply(X,multiply(Z,Y))).
% 158 [para:106.1.2,123.1.2.2] equal(double_divide(inverse(X),multiply(Y,Z)),multiply(X,double_divide(Z,Y))).
% 159 [para:143.1.1,8.1.1.2.1.1.2.2,demod:13,144,9,106,101,153,10] equal(double_divide(X,double_divide(Y,multiply(X,Z))),multiply(Z,Y)).
% 160 [para:143.1.1,126.1.1.2] equal(double_divide(multiply(X,Y),inverse(X)),inverse(Y)).
% 161 [para:143.1.1,30.1.1.1.2.2.2,demod:13,144,106,101,153] equal(multiply(double_divide(X,multiply(Y,Z)),Y),double_divide(X,Z)).
% 165 [para:34.1.2,21.1.2.2,demod:128,123,13,106,101,154] equal(identity,double_divide(double_divide(double_divide(multiply(X,Y),Z),Y),double_divide(X,Z))).
% 166 [para:34.1.1,8.1.1.2.1.1.2.2,demod:123,13,151,9,125,106,101,154,10] equal(double_divide(double_divide(X,Y),Z),multiply(Y,double_divide(inverse(X),Z))).
% 167 [para:8.1.1,34.1.1.2.2.2,demod:125,106,154,144,9,133,13,98,14,10,123,101] equal(double_divide(X,double_divide(inverse(Y),Z)),double_divide(double_divide(Z,inverse(X)),Y)).
% 169 [para:29.1.1,34.1.1.2.2.2,demod:125,106,101,154,85,98,71] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Z,X),Y)).
% 171 [para:34.1.1,26.1.1.2.2.2.2,demod:166,123,13,119,169,106,101,154] equal(double_divide(X,multiply(Y,double_divide(Z,multiply(X,U)))),double_divide(double_divide(Z,U),Y)).
% 180 [para:106.1.2,34.1.2.2.2.1,demod:126,166,123,13,101] equal(double_divide(X,multiply(Y,Z)),multiply(U,multiply(double_divide(U,X),double_divide(Z,Y)))).
% 181 [para:127.1.1,34.1.1.2,demod:126,166,169,123,13,101] equal(double_divide(X,inverse(Y)),multiply(Z,multiply(double_divide(Z,X),Y))).
% 183 [para:34.1.1,34.1.1.2.2.2,demod:98,14,13,119,169,106,101,154] equal(double_divide(X,multiply(Y,multiply(Z,U))),double_divide(X,multiply(multiply(Y,Z),U))).
% 184 [para:34.1.1,34.1.2.2.2.2,demod:119,171,169,106,154,166,123,13,101] equal(double_divide(double_divide(double_divide(X,Y),Z),U),multiply(Z,double_divide(X,multiply(U,Y)))).
% 190 [para:144.1.2,34.1.1.2,demod:181,98,14,123,13,101] equal(double_divide(X,double_divide(Y,double_divide(inverse(X),Z))),double_divide(Z,inverse(Y))).
% 191 [para:160.1.1,34.1.2.2.2.2,demod:151,106,101,153] equal(double_divide(inverse(X),Y),multiply(multiply(X,Z),double_divide(Z,Y))).
% 194 [para:16.1.1,39.1.1.1.2.2,demod:98,13,101,106] equal(multiply(multiply(X,multiply(Y,Z)),double_divide(Z,Y)),X).
% 195 [para:88.1.2,39.1.1.1.2.2,demod:98,106,101] equal(multiply(multiply(X,double_divide(Y,Z)),multiply(Z,Y)),X).
% 199 [para:159.1.1,30.1.1.1.2.2.2,demod:13,154,134,106,101,158] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 201 [para:159.1.1,34.1.2.2.2.2,demod:158,126,184,169,106,101,199,154] equal(double_divide(double_divide(X,multiply(Y,Z)),U),multiply(Y,double_divide(double_divide(X,Z),U))).
% 204 [para:119.1.1,161.1.1.1.2] equal(multiply(double_divide(X,inverse(Y)),Z),double_divide(X,double_divide(Z,Y))).
% 209 [para:119.1.1,169.1.2.1] equal(double_divide(double_divide(X,Y),multiply(Z,X)),double_divide(inverse(Y),Z)).
% 211 [para:194.1.1,125.1.2.2.1,demod:199,169] equal(double_divide(X,multiply(Y,multiply(Z,U))),multiply(double_divide(X,U),double_divide(Z,Y))).
% 215 [para:41.1.1,34.1.2.2.2.2,demod:166,154,123,98,126,184,13,201,158,106,101,153] equal(double_divide(double_divide(X,Y),multiply(Z,U)),multiply(Y,multiply(X,double_divide(U,Z)))).
% 216 [para:161.1.1,195.1.1.1] equal(multiply(double_divide(X,Y),multiply(Z,U)),double_divide(X,multiply(double_divide(U,Z),Y))).
% 219 [para:123.1.2,199.1.2.1,demod:144] equal(multiply(X,double_divide(Y,inverse(Z))),multiply(double_divide(inverse(X),Y),Z)).
% 224 [para:31.1.1,122.1.2.2.1,demod:144,211,123,107,184,216,199,13,101,169] equal(double_divide(double_divide(X,double_divide(Y,Z)),U),double_divide(Y,multiply(U,double_divide(X,inverse(Z))))).
% 236 [para:190.1.1,122.1.2.2.1,demod:204] equal(double_divide(double_divide(X,double_divide(inverse(Y),Z)),U),multiply(Y,double_divide(Z,double_divide(inverse(U),X)))).
% 239 [para:132.1.1,165.1.2.1.1.1,demod:166,169] equal(identity,double_divide(double_divide(double_divide(X,multiply(Y,Z)),U),double_divide(double_divide(double_divide(X,Z),U),Y))).
% 246 [para:161.1.1,139.1.1.2.2,demod:199] equal(double_divide(double_divide(X,Y),multiply(Z,double_divide(U,V))),double_divide(double_divide(U,multiply(Y,multiply(X,V))),Z)).
% 248 [para:132.1.1,139.1.1.2.2,demod:215,158] equal(double_divide(double_divide(X,Y),multiply(Z,multiply(U,V))),double_divide(double_divide(double_divide(V,U),multiply(Y,X)),Z)).
% 249 [para:134.1.1,139.1.1.2.2,demod:184,166] equal(double_divide(double_divide(X,Y),double_divide(double_divide(Z,U),V)),double_divide(double_divide(double_divide(double_divide(V,X),Z),Y),U)).
% 252 [para:34.1.2,171.1.1.2.2.2,demod:169,106,154,126,166,123,13,101] equal(double_divide(X,multiply(Y,double_divide(Z,double_divide(U,V)))),double_divide(double_divide(Z,double_divide(X,multiply(V,U))),Y)).
% 256 [para:171.1.1,209.1.1.1,demod:201,13,184] equal(double_divide(double_divide(double_divide(X,Y),Z),multiply(U,V)),double_divide(double_divide(double_divide(X,multiply(V,Y)),Z),U)).
% 261 [para:159.1.1,180.1.2.2.1,demod:249,184,215,199] equal(double_divide(double_divide(X,multiply(Y,Z)),multiply(U,V)),double_divide(double_divide(Z,Y),double_divide(double_divide(V,U),X))).
% 262 [para:183.1.2,219.1.2.1,demod:184,158,204,144,169,199] equal(multiply(X,double_divide(Y,double_divide(Z,double_divide(U,V)))),multiply(double_divide(double_divide(double_divide(Y,U),X),V),Z)).
% 265 [para:166.1.2,184.1.2.2.2] equal(double_divide(double_divide(double_divide(X,double_divide(inverse(Y),Z)),U),V),multiply(U,double_divide(X,double_divide(double_divide(Y,V),Z)))).
% 266 [para:191.1.2,184.1.2.2.2,demod:236] equal(double_divide(double_divide(double_divide(X,double_divide(Y,Z)),U),multiply(V,Y)),double_divide(double_divide(Z,double_divide(inverse(U),X)),V)).
% 282 [para:215.1.2,184.1.2.2.2,demod:256] equal(double_divide(double_divide(double_divide(X,double_divide(Y,Z)),U),multiply(V,W)),multiply(U,double_divide(X,double_divide(double_divide(W,V),multiply(Z,Y))))).
% 290 [para:224.1.2,201.1.2.2,demod:201,167,261] equal(double_divide(double_divide(X,Y),double_divide(double_divide(Z,double_divide(inverse(U),V)),W)),double_divide(double_divide(V,double_divide(double_divide(W,multiply(Y,X)),Z)),U)).
% 305 [para:201.1.2,239.1.2.1.1.2] equal(identity,double_divide(double_divide(double_divide(X,double_divide(double_divide(Y,multiply(Z,U)),V)),W),double_divide(double_divide(double_divide(X,double_divide(double_divide(Y,U),V)),W),Z))).
% 312 [para:236.1.2,248.1.2.1.2,demod:290,282,246,265] equal(double_divide(double_divide(double_divide(X,double_divide(double_divide(Y,Z),U)),V),multiply(W,X1)),double_divide(double_divide(double_divide(X,double_divide(double_divide(Y,multiply(X1,Z)),U)),V),W)).
% 326 [para:266.1.1,252.1.2.1.2] equal(double_divide(double_divide(double_divide(X,double_divide(Y,Z)),U),multiply(V,double_divide(W,double_divide(Y,X1)))),double_divide(double_divide(W,double_divide(double_divide(Z,double_divide(inverse(U),X)),X1)),V)).
% 339 [input:12,cut:98] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity).
% 340 [para:305.1.1,339.2.2,demod:199,104,107,326,126,262,312,11,144,cut:7,cut:7] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 7
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 313
% derived clauses: 119471
% kept clauses: 323
% kept size sum: 5177
% kept mid-nuclei: 2
% kept new demods: 323
% forw unit-subs: 112538
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 6
% fast unit cutoff: 4
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.60
% process. runtime: 7.58
% 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/GRP077-1+eq_r.in")
%
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