TSTP Solution File: GRP056-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP056-1 : 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 : art07.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/GRP056-1+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 9 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 9 5)
% (binary-posweight-lex-big-order 30 #f 9 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),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% was split for some strategies as:
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(3,40,0,6,0,0,12,50,0,15,0,0,34,50,5,37,0,5,1635,4,683)
%
%
% START OF PROOF
% 35 [] equal(X,X).
% 36 [] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Z)))),multiply(X,inverse(Z)))),inverse(multiply(inverse(Z),Z))),Y).
% 37 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% 38 [para:36.1.1,36.1.1.1.1.1.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),Z)))),multiply(U,inverse(Z)))).
% 40 [para:38.1.1,36.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),inverse(multiply(inverse(Z),Z)))),Z)))),multiply(X,inverse(Z))),Y).
% 41 [para:38.1.2,36.1.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(Z),Z))),Y).
% 42 [para:36.1.1,38.1.2.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Y),Y)))))),inverse(multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Y),Y))))),multiply(inverse(Z),multiply(inverse(multiply(inverse(multiply(U,inverse(multiply(inverse(Z),Y)))),multiply(U,inverse(Y)))),inverse(Y)))).
% 43 [para:36.1.1,38.1.2.2] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(Z),Z))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(Z),Z)))),inverse(multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(Z),Z)))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(U,inverse(multiply(inverse(V),Z)))),multiply(U,inverse(Z)))),inverse(multiply(inverse(Y),multiply(inverse(Z),Z))))),V)).
% 44 [para:38.1.1,38.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Z)))),multiply(X,inverse(Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),Z)))),multiply(U,inverse(Z)))).
% 46 [?] ?
% 48 [para:41.1.1,40.1.1.1.1.2.1.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Z)))),multiply(X,inverse(Z))),multiply(inverse(multiply(inverse(multiply(U,inverse(Y))),multiply(U,inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))).
% 58 [para:40.1.1,44.1.1.1.1.2.1,demod:40] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(Z,inverse(U))))),multiply(inverse(multiply(V,inverse(Y))),multiply(V,inverse(multiply(Z,inverse(U)))))).
% 59 [para:44.1.1,44.1.1.1.1.2.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),U)))),multiply(Y,inverse(U)))))),multiply(X,inverse(multiply(V,inverse(U))))),multiply(inverse(multiply(W,inverse(multiply(inverse(multiply(V,inverse(multiply(inverse(Z),U)))),multiply(V,inverse(U)))))),multiply(W,inverse(multiply(V,inverse(U)))))).
% 63 [para:36.1.1,58.1.1.2.2.1,demod:36] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(Z))),multiply(inverse(multiply(U,inverse(Y))),multiply(U,inverse(Z)))).
% 67 [para:38.1.1,58.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z)))))),inverse(U))),multiply(inverse(multiply(V,inverse(multiply(inverse(Y),Z)))),multiply(V,inverse(Z)))),multiply(inverse(multiply(W,inverse(U))),multiply(W,inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))).
% 70 [para:63.1.1,36.1.1.1.1.1.1.2.1,demod:46] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y,inverse(Z))),multiply(Y,inverse(U)))),inverse(multiply(inverse(U),U)))),U))),multiply(X,inverse(Z))).
% 71 [para:63.1.1,36.1.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(Z,inverse(U)))))),multiply(X,inverse(multiply(Z,inverse(U)))))),inverse(multiply(inverse(multiply(V,inverse(U))),multiply(V,inverse(U))))),Y).
% 72 [para:36.1.1,63.1.1.1.1] equal(multiply(inverse(X),multiply(inverse(multiply(inverse(multiply(Y,inverse(multiply(inverse(X),Z)))),multiply(Y,inverse(Z)))),inverse(U))),multiply(inverse(multiply(V,inverse(multiply(inverse(Z),Z)))),multiply(V,inverse(U)))).
% 73 [para:36.1.1,63.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Z)))),multiply(X,inverse(Z)))),inverse(U))),Y),multiply(inverse(multiply(V,inverse(U))),multiply(V,inverse(multiply(inverse(Z),Z))))).
% 79 [para:63.1.1,38.1.2.1.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(Z))))),multiply(X,inverse(inverse(multiply(inverse(multiply(Y,inverse(U))),multiply(Y,inverse(U)))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(U))),multiply(Y,inverse(U))))),inverse(multiply(inverse(multiply(Y,inverse(U))),multiply(Y,inverse(U))))))),multiply(inverse(multiply(V,inverse(multiply(inverse(multiply(W,inverse(Z))),multiply(W,inverse(U)))))),multiply(V,inverse(multiply(Y,inverse(U)))))).
% 80 [para:38.1.1,63.1.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Z)))),multiply(X,inverse(Z)))),multiply(inverse(multiply(inverse(multiply(U,inverse(Y))),multiply(U,inverse(inverse(multiply(inverse(Z),Z)))))),inverse(V))),multiply(inverse(multiply(W,inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))),multiply(W,inverse(V)))).
% 83 [para:70.1.1,41.1.1.1.1.1.1.1.1,demod:41] equal(X,multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,inverse(Z)))),inverse(multiply(inverse(Z),Z)))),Z)).
% 107 [para:70.1.1,71.1.1.1.1.2,demod:83] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Z)))),multiply(X,inverse(Z)))),inverse(multiply(inverse(multiply(U,inverse(V))),multiply(U,inverse(V))))),Y).
% 111 [para:36.1.1,107.1.1.2.1.1.1,demod:36] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Z)))),multiply(X,inverse(Z)))),inverse(multiply(inverse(U),U))),Y).
% 126 [para:43.1.1,42.1.1,demod:111] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 158 [para:126.1.1,83.1.2.1.1.1.1] equal(X,multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(X),X)))),X)).
% 193 [para:126.1.1,158.1.2.1.1.2.1] equal(X,multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z)))),X)).
% 195 [para:193.1.2,63.1.1.1.1,demod:193] equal(multiply(inverse(inverse(X)),inverse(Y)),multiply(inverse(multiply(Z,inverse(X))),multiply(Z,inverse(Y)))).
% 200 [para:193.1.2,193.1.2.1.1.1.1,demod:193] equal(X,multiply(inverse(inverse(multiply(inverse(Y),Y))),X)).
% 202 [para:200.1.2,126.1.1] equal(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)).
% 206 [para:200.1.2,200.1.2.1.1.1] equal(X,multiply(inverse(inverse(inverse(multiply(inverse(Y),Y)))),X)).
% 208 [para:202.1.1,63.1.1.1.1.2,demod:200,195] equal(multiply(inverse(multiply(X,multiply(inverse(Y),Y))),multiply(X,inverse(Z))),inverse(Z)).
% 209 [para:202.1.2,63.1.1.2,demod:195] equal(multiply(inverse(multiply(inverse(inverse(X)),inverse(Y))),inverse(multiply(inverse(Z),Z))),multiply(inverse(inverse(Y)),inverse(X))).
% 212 [para:202.1.1,126.1.1.1] equal(multiply(multiply(inverse(X),X),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
% 213 [para:202.1.1,126.1.2.1] equal(multiply(inverse(X),X),multiply(multiply(inverse(Y),Y),multiply(inverse(Z),Z))).
% 221 [para:202.1.2,200.1.2] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 222 [para:202.1.1,200.1.2.1.1] equal(X,multiply(inverse(multiply(inverse(Y),Y)),X)).
% 224 [para:200.1.2,202.1.1.1] equal(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)).
% 227 [para:202.1.1,222.1.2.1] equal(X,multiply(multiply(inverse(Y),Y),X)).
% 229 [para:206.1.2,193.1.2.1.1.2.1,demod:222] equal(X,multiply(inverse(inverse(inverse(inverse(multiply(inverse(Y),Y))))),X)).
% 230 [para:206.1.2,202.1.1.1] equal(inverse(inverse(inverse(multiply(inverse(X),X)))),multiply(inverse(Y),Y)).
% 238 [para:224.1.2,63.1.1.2,demod:195] equal(multiply(inverse(multiply(inverse(inverse(X)),inverse(Y))),inverse(inverse(multiply(inverse(Z),Z)))),multiply(inverse(inverse(Y)),inverse(X))).
% 247 [para:229.1.2,224.1.1.1.1] equal(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X),X)))))),multiply(inverse(Y),Y)).
% 252 [para:230.1.2,63.1.1.2,demod:195] equal(multiply(inverse(multiply(inverse(inverse(X)),inverse(Y))),inverse(inverse(inverse(multiply(inverse(Z),Z))))),multiply(inverse(inverse(Y)),inverse(X))).
% 261 [para:48.1.1,63.1.1,demod:206,238,200,195] equal(inverse(X),multiply(inverse(inverse(multiply(inverse(X),Y))),inverse(Y))).
% 264 [para:63.1.1,48.1.1.1.1.2.1,demod:206,238,200,195] equal(multiply(inverse(inverse(multiply(inverse(inverse(X)),inverse(Y)))),inverse(multiply(Z,inverse(Y)))),inverse(multiply(Z,inverse(X)))).
% 270 [para:221.1.1,48.1.1.2.2,demod:206,238,200,222,195] equal(multiply(inverse(inverse(multiply(inverse(X),multiply(inverse(Y),Y)))),inverse(multiply(inverse(Z),Z))),inverse(X)).
% 279 [para:48.1.1,48.1.1.1.1.2.1,demod:264,206,238,200,195] equal(multiply(inverse(inverse(inverse(X))),inverse(multiply(Y,inverse(Z)))),inverse(multiply(Y,inverse(multiply(inverse(X),Z))))).
% 281 [para:48.1.1,48.1.2.1.1,demod:229,252,206,200,261,195] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),multiply(inverse(inverse(X)),inverse(inverse(multiply(inverse(Y),Y))))).
% 295 [para:202.1.1,261.1.2.2] equal(inverse(X),multiply(inverse(inverse(multiply(inverse(X),multiply(inverse(Y),Y)))),multiply(inverse(Z),Z))).
% 298 [para:261.1.2,48.1.1.1.1.2.1,demod:261,264,281,195] equal(multiply(inverse(inverse(inverse(X))),inverse(inverse(Y))),inverse(inverse(multiply(inverse(X),Y)))).
% 357 [para:126.1.1,208.1.1.2] equal(multiply(inverse(multiply(inverse(inverse(X)),multiply(inverse(Y),Y))),multiply(inverse(Z),Z)),inverse(X)).
% 363 [para:208.1.1,48.1.1.1.1.2.1,demod:261,264,281,279,195] equal(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),inverse(multiply(X,multiply(inverse(Z),Z)))).
% 758 [para:295.1.2,357.1.1.1.1] equal(multiply(inverse(inverse(X)),multiply(inverse(Y),Y)),inverse(multiply(inverse(X),multiply(inverse(Z),Z)))).
% 765 [para:67.1.1,48.1.1.1.1.2.1,demod:264,209,298,261,281,195,200] equal(inverse(inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),Z))),inverse(multiply(inverse(inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y))))),inverse(X)))).
% 774 [para:67.1.2,59.1.1,demod:298,200,261,765,270,281,195] equal(inverse(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y)))),inverse(inverse(multiply(inverse(X),multiply(inverse(Y),Y))))).
% 980 [para:758.1.2,208.1.1.1] equal(multiply(multiply(inverse(inverse(X)),multiply(inverse(Y),Y)),multiply(inverse(X),inverse(Z))),inverse(Z)).
% 1035 [para:758.1.1,295.1.2] equal(inverse(X),inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(Y),Y))),multiply(inverse(Z),Z)))).
% 1281 [?] ?
% 1287 [para:72.1.1,48.1.1.1.1.2.1,demod:264,281,774,279,261,200,195] equal(inverse(inverse(multiply(inverse(X),multiply(inverse(Y),Y)))),inverse(X)).
% 1295 [para:261.1.2,72.1.2.2,demod:1287,774,1281,261,195] equal(inverse(X),multiply(inverse(multiply(inverse(Y),X)),inverse(Y))).
% 1301 [para:212.1.2,72.1.2.2,demod:227,1287,774,1281,261,195] equal(inverse(X),multiply(inverse(X),multiply(inverse(Y),Y))).
% 1302 [para:213.1.1,72.1.2.2,demod:227,1301,774,1281,261,195] equal(inverse(X),inverse(inverse(inverse(X)))).
% 1303 [para:247.1.2,72.1.2.2,demod:1302,1301,774,1281,261,195] equal(inverse(X),multiply(inverse(X),inverse(multiply(inverse(Y),Y)))).
% 1367 [para:1302.1.2,298.1.1.1] equal(multiply(inverse(X),inverse(inverse(Y))),inverse(inverse(multiply(inverse(X),Y)))).
% 1376 [para:1301.1.2,63.1.1,demod:195] equal(inverse(multiply(inverse(inverse(X)),inverse(Y))),multiply(inverse(inverse(Y)),inverse(X))).
% 1398 [para:1295.1.2,261.1.2.1.1.1,demod:1302] equal(inverse(multiply(inverse(X),Y)),multiply(inverse(Y),inverse(inverse(X)))).
% 1411 [para:1295.1.2,72.1.1.2,demod:222,1398,1367,195] equal(multiply(inverse(X),inverse(multiply(Y,inverse(Z)))),inverse(multiply(Y,inverse(multiply(inverse(X),Z))))).
% 1417 [?] ?
% 1426 [?] ?
% 1430 [para:202.1.1,73.1.2.2.2,demod:1426,1376,1417,1411] equal(inverse(inverse(X)),multiply(inverse(multiply(Y,inverse(X))),multiply(Y,multiply(inverse(Z),Z)))).
% 1431 [para:73.1.2,48.1.1,demod:1303,195,222,1302,1367,1398,1301,1417,1411] equal(multiply(multiply(inverse(X),inverse(Y)),Y),inverse(X)).
% 1455 [para:126.1.1,1431.1.1.1,demod:227] equal(X,inverse(inverse(X))).
% 1474 [para:1431.1.1,67.1.2.1.1,demod:227,1295,1417,1411,1430,1455,1367] equal(X,multiply(Y,multiply(multiply(inverse(Y),X),multiply(inverse(Z),Z)))).
% 1479 [para:1035.1.2,1431.1.1.1.1,demod:1455,1301,1431] equal(inverse(X),inverse(multiply(X,multiply(inverse(Y),Y)))).
% 1481 [?] ?
% 1483 [para:1295.1.2,1431.1.1.1] equal(multiply(inverse(X),Y),inverse(multiply(inverse(Y),X))).
% 1486 [para:1431.1.1,73.1.2.1.1,demod:1474,1455,1483] equal(multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(Y),Z))),inverse(U))),Z),U).
% 1487 [para:1431.1.1,73.1.2.2,demod:1455,1301,1486,1483] equal(X,multiply(multiply(X,Y),inverse(Y))).
% 1490 [para:1455.1.2,193.1.2.1.1.1.1.1,demod:1455,1301,1483] equal(X,multiply(multiply(Y,inverse(Y)),X)).
% 1497 [para:1455.1.2,261.1.2.2,demod:1455,1483] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 1499 [para:1455.1.2,208.1.1.2.2,demod:1455,1479] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 1500 [para:1455.1.2,298.1.1.2.1,demod:1483,1455] equal(multiply(inverse(X),inverse(Y)),inverse(multiply(Y,X))).
% 1504 [para:363.1.1,1455.1.2.1,demod:1455,1479,1483] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 1505 [para:1455.1.2,195.1.2.1.1.2,demod:1500,1455] equal(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,Y)),multiply(Z,inverse(X)))).
% 1507 [para:1455.1.2,295.1.2.2.1,demod:1455,1301] equal(inverse(X),multiply(inverse(X),multiply(Y,inverse(Y)))).
% 1510 [para:1455.1.2,758.1.1.2.1,demod:1301,1455] equal(multiply(X,multiply(Y,inverse(Y))),X).
% 1511 [para:1455.1.2,980.1.1.1.1,demod:1500,1504] equal(multiply(X,inverse(multiply(Y,X))),inverse(Y)).
% 1512 [para:1455.1.2,980.1.1.2.2,demod:1504,1455] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 1515 [para:1455.1.2,1431.1.1.1.1,demod:1455] equal(multiply(multiply(X,inverse(Y)),Y),X).
% 1518 [para:48.1.1,1487.1.2.1,demod:1500,1301,227,1455,1497,1504,1483] equal(inverse(multiply(X,multiply(inverse(Y),Z))),inverse(multiply(multiply(X,inverse(Y)),Z))).
% 1524 [para:67.1.2,1487.1.2.1,demod:227,1487,1512,1505,1500,1455,1497,1504,1483] equal(inverse(multiply(X,inverse(Y))),multiply(Y,inverse(X))).
% 1525 [para:1490.1.2,59.1.1.1.1,demod:1490,1524,1455,1512,1505,1483] equal(multiply(inverse(X),multiply(Y,inverse(Z))),multiply(inverse(multiply(U,X)),multiply(U,multiply(Y,inverse(Z))))).
% 1530 [para:195.1.2,1499.1.1.2,demod:1455,1524] equal(multiply(multiply(X,inverse(Y)),multiply(Y,inverse(Z))),multiply(X,inverse(Z))).
% 1537 [para:1504.1.1,59.1.1,demod:1525,1518,1455,1512,1505,1483,1524] equal(inverse(multiply(X,multiply(inverse(Y),Z))),multiply(inverse(Z),multiply(Y,inverse(X)))).
% 1540 [para:1504.1.1,59.1.2.1.1.2.1,demod:1497,1512,1515,1510,1455,1524,1537,1483] equal(multiply(multiply(inverse(X),multiply(Y,inverse(Z))),multiply(Z,inverse(Y))),inverse(X)).
% 1542 [para:1515.1.1,195.1.2.2,demod:1524,1455] equal(multiply(X,inverse(Y)),multiply(multiply(X,inverse(multiply(Z,Y))),Z)).
% 1555 [para:1511.1.1,59.1.1.1.1,demod:1525,1455,1540,1530,1518,1524,1537,1483] equal(multiply(multiply(inverse(X),multiply(Y,inverse(Z))),multiply(Z,inverse(U))),multiply(inverse(X),multiply(Y,inverse(U)))).
% 1556 [?] ?
% 1558 [para:1511.1.1,195.1.2.1.1,demod:1455] equal(multiply(multiply(X,Y),inverse(Z)),multiply(X,multiply(Y,inverse(Z)))).
% 1559 [para:1511.1.1,73.1.1.1.1,demod:1504,1558,1524,1507,1555,1537,1483,1455] equal(multiply(X,Y),multiply(multiply(X,multiply(Y,inverse(Z))),Z)).
% 1579 [para:1500.1.1,48.1.1.1.1.2.1,demod:1507,1490,1515,1510,1524,1455] equal(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,Y)),inverse(Z)).
% 1583 [para:48.1.2,79.1.1.1.1.2.2.1.1.1.1,demod:1490,1497,1510,1301,227,1507,1555,1537,1455,1500,1515,1504,1483,1524] equal(multiply(X,Y),multiply(multiply(X,inverse(Z)),multiply(Z,Y))).
% 1584 [para:79.1.2,261.1.2.1.1.1,demod:1559,1500,1558,1490,1497,1510,1583,1524] equal(inverse(multiply(X,multiply(Y,inverse(Z)))),multiply(Z,inverse(multiply(X,Y)))).
% 1587 [para:261.1.2,79.1.1.1.1.2.2.1.1.1.1,demod:1584,1583,1490,1537,1518,1497,1510,1507,1455,1524,1556,1483] equal(multiply(multiply(X,inverse(Y)),Z),multiply(multiply(X,inverse(multiply(U,Y))),multiply(U,Z))).
% 1588 [para:298.1.1,79.1.1.1.1.1.1.2.1,demod:1505,1490,1559,1510,1524,1511,1558,1500,1455,1537,1483] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,multiply(U,X))),multiply(Z,multiply(U,Y)))).
% 1596 [para:79.1.2,1499.1.1.2,demod:1490,1542,1510,1558,1584,1583,1524] equal(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,inverse(U))),multiply(X,multiply(Y,inverse(U)))).
% 1615 [?] ?
% 1619 [para:73.1.1,1559.1.2.1.2,demod:1615,1504,1483,1500,1510,1596,1558,1524,1455] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 1620 [para:1559.1.2,79.1.1.1.1.1.1.2.1,demod:1619,1500,1615,1587,1584,1507,1490,1559,1510,1583,1588,1455,1558,1524] equal(inverse(multiply(X,Y)),multiply(Z,inverse(multiply(X,multiply(Y,Z))))).
% 1625 [para:1497.1.2,1619.1.2.1] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(Y),Z)).
% 1628 [para:1579.1.1,80.1.1.1.1.1.1.2.1,demod:1481,227,1500,1559,1504,1483,1625,1558,1524,1619,1505,1455] equal(multiply(X,multiply(Y,multiply(Z,inverse(multiply(U,multiply(X,multiply(Y,Z))))))),inverse(U)).
% 1632 [para:1620.1.2,80.1.2.2,demod:227,1619,1500,1615,1504,1524,1455,1507,1555,1537,1483] equal(multiply(X,inverse(multiply(Y,multiply(Z,multiply(U,X))))),inverse(multiply(Y,multiply(Z,U)))).
% 1636 [input:37,cut:126] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 1637 [para:1628.1.2,1636.1.1.1.1,demod:1619,227,1511,1620,1632,cut:35,cut:35] 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 11
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 308
% derived clauses: 239825
% kept clauses: 1618
% kept size sum: 40584
% kept mid-nuclei: 2
% kept new demods: 564
% forw unit-subs: 232107
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 78
% fast unit cutoff: 2
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 6.91
% process. runtime: 6.84
% 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/GRP056-1+eq_r.in")
%
%------------------------------------------------------------------------------