TSTP Solution File: GRP083-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP083-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:45:13 EDT 2022
% Result : Unsatisfiable 175.74s 175.93s
% Output : Refutation 176.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 3
% Syntax : Number of clauses : 165 ( 162 unt; 0 nHn; 165 RR)
% Number of literals : 171 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,inverse(double_divide(v,w))),double_divide(inverse(v),inverse(double_divide(x,double_divide(u,x))))),w),
file('GRP083-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP083-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP083-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(double_divide(u,multiply(v,w)),double_divide(inverse(w),multiply(double_divide(u,x),x))),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(double_divide(inverse(u),multiply(double_divide(v,w),w)),double_divide(v,multiply(x,u))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(9,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(w,x))),double_divide(multiply(x,w),multiply(double_divide(u,y),y))),v),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,inverse(v)),double_divide(inverse(double_divide(w,multiply(v,x))),multiply(double_divide(u,y),y))),double_divide(inverse(x),multiply(double_divide(w,z),z))),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(double_divide(inverse(double_divide(u,multiply(v,w))),multiply(double_divide(x,y),y)),double_divide(x,inverse(v))),inverse(double_divide(inverse(w),multiply(double_divide(u,z),z)))),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(14,plain,
equal(multiply(double_divide(multiply(u,v),multiply(double_divide(w,x),x)),double_divide(w,multiply(y,double_divide(v,u)))),inverse(y)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(15,plain,
equal(double_divide(double_divide(u,inverse(v)),double_divide(multiply(multiply(v,w),x),multiply(double_divide(u,y),y))),double_divide(inverse(w),multiply(double_divide(x,z),z))),
inference(rew,[status(thm),theory(equality)],[2,10]),
[iquote('0:Rew:2.0,10.0')] ).
cnf(16,plain,
equal(multiply(double_divide(multiply(multiply(u,v),w),multiply(double_divide(x,y),y)),double_divide(x,inverse(u))),multiply(multiply(double_divide(w,z),z),inverse(v))),
inference(rew,[status(thm),theory(equality)],[2,12]),
[iquote('0:Rew:2.0,12.0,2.0,12.0')] ).
cnf(18,plain,
equal(double_divide(double_divide(double_divide(u,multiply(v,double_divide(w,x))),multiply(y,z)),double_divide(inverse(z),multiply(v,double_divide(multiply(x,w),multiply(double_divide(u,x1),x1))))),y),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(21,plain,
equal(multiply(double_divide(inverse(u),multiply(v,double_divide(multiply(w,x),multiply(double_divide(y,z),z)))),double_divide(double_divide(y,multiply(v,double_divide(x,w))),multiply(x1,u))),inverse(x1)),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(84,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,w),w)),double_divide(inverse(u),multiply(double_divide(v,x),x))),
inference(spr,[status(thm),theory(equality)],[15]),
[iquote('0:SpR:15.0,15.0')] ).
cnf(126,plain,
equal(inverse(double_divide(inverse(u),multiply(double_divide(v,w),w))),multiply(multiply(double_divide(v,x),x),inverse(u))),
inference(spr,[status(thm),theory(equality)],[84,2]),
[iquote('0:SpR:84.0,2.0')] ).
cnf(186,plain,
equal(multiply(multiply(double_divide(u,v),v),inverse(w)),multiply(multiply(double_divide(u,x),x),inverse(w))),
inference(rew,[status(thm),theory(equality)],[2,126]),
[iquote('0:Rew:2.0,126.0')] ).
cnf(256,plain,
equal(double_divide(double_divide(u,multiply(multiply(double_divide(v,w),w),inverse(x))),double_divide(inverse(inverse(x)),multiply(double_divide(u,y),y))),multiply(double_divide(v,z),z)),
inference(spr,[status(thm),theory(equality)],[186,4]),
[iquote('0:SpR:186.0,4.0')] ).
cnf(259,plain,
equal(multiply(double_divide(inverse(inverse(u)),multiply(double_divide(v,w),w)),double_divide(v,multiply(multiply(double_divide(x,y),y),inverse(u)))),inverse(multiply(double_divide(x,z),z))),
inference(spr,[status(thm),theory(equality)],[186,6]),
[iquote('0:SpR:186.0,6.0')] ).
cnf(285,plain,
equal(multiply(double_divide(u,v),v),multiply(double_divide(u,w),w)),
inference(rew,[status(thm),theory(equality)],[4,256]),
[iquote('0:Rew:4.0,256.0')] ).
cnf(287,plain,
equal(inverse(multiply(double_divide(u,v),v)),inverse(multiply(double_divide(u,w),w))),
inference(rew,[status(thm),theory(equality)],[6,259]),
[iquote('0:Rew:6.0,259.0')] ).
cnf(321,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,w),w)),double_divide(inverse(x),multiply(double_divide(u,y),y))),double_divide(v,x)),
inference(spr,[status(thm),theory(equality)],[285,4]),
[iquote('0:SpR:285.0,4.0')] ).
cnf(324,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,w),w)),double_divide(multiply(x,y),multiply(double_divide(u,z),z))),double_divide(v,double_divide(y,x))),
inference(spr,[status(thm),theory(equality)],[285,9]),
[iquote('0:SpR:285.0,9.0')] ).
cnf(341,plain,
equal(multiply(double_divide(inverse(u),multiply(double_divide(v,w),w)),double_divide(v,multiply(double_divide(x,y),y))),inverse(double_divide(x,u))),
inference(spr,[status(thm),theory(equality)],[285,6]),
[iquote('0:SpR:285.0,6.0')] ).
cnf(342,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(w,double_divide(x,w)))),double_divide(multiply(double_divide(x,y),y),multiply(double_divide(u,z),z))),v),
inference(spr,[status(thm),theory(equality)],[285,9]),
[iquote('0:SpR:285.0,9.0')] ).
cnf(344,plain,
equal(multiply(double_divide(multiply(u,v),multiply(double_divide(w,x),x)),double_divide(w,multiply(double_divide(y,z),z))),inverse(double_divide(y,double_divide(v,u)))),
inference(spr,[status(thm),theory(equality)],[285,14]),
[iquote('0:SpR:285.0,14.0')] ).
cnf(357,plain,
equal(multiply(double_divide(double_divide(u,multiply(v,w)),x),x),multiply(v,double_divide(inverse(w),multiply(double_divide(u,y),y)))),
inference(spr,[status(thm),theory(equality)],[4,285]),
[iquote('0:SpR:4.0,285.0')] ).
cnf(358,plain,
equal(multiply(double_divide(double_divide(u,multiply(v,double_divide(w,x))),y),y),multiply(v,double_divide(multiply(x,w),multiply(double_divide(u,z),z)))),
inference(spr,[status(thm),theory(equality)],[9,285]),
[iquote('0:SpR:9.0,285.0')] ).
cnf(361,plain,
equal(multiply(double_divide(inverse(u),multiply(double_divide(v,w),w)),double_divide(v,multiply(double_divide(x,y),y))),multiply(u,x)),
inference(rew,[status(thm),theory(equality)],[2,341]),
[iquote('0:Rew:2.0,341.0')] ).
cnf(363,plain,
equal(multiply(double_divide(multiply(u,v),multiply(double_divide(w,x),x)),double_divide(w,multiply(double_divide(y,z),z))),multiply(double_divide(v,u),y)),
inference(rew,[status(thm),theory(equality)],[2,344]),
[iquote('0:Rew:2.0,344.0')] ).
cnf(405,plain,
equal(inverse(multiply(double_divide(double_divide(u,multiply(v,w)),x),x)),inverse(multiply(v,double_divide(inverse(w),multiply(double_divide(u,y),y))))),
inference(spr,[status(thm),theory(equality)],[4,287]),
[iquote('0:SpR:4.0,287.0')] ).
cnf(752,plain,
equal(multiply(double_divide(double_divide(u,multiply(double_divide(inverse(v),multiply(double_divide(inverse(w),x),x)),w)),y),y),inverse(double_divide(u,v))),
inference(spr,[status(thm),theory(equality)],[357,6]),
[iquote('0:SpR:357.0,6.0')] ).
cnf(810,plain,
equal(multiply(double_divide(double_divide(u,multiply(double_divide(inverse(v),multiply(double_divide(inverse(w),x),x)),w)),y),y),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,752]),
[iquote('0:Rew:2.0,752.0')] ).
cnf(885,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,w),w)),double_divide(inverse(multiply(double_divide(x,y),y)),multiply(double_divide(u,z),z))),double_divide(v,multiply(double_divide(x,x1),x1))),
inference(spr,[status(thm),theory(equality)],[287,321]),
[iquote('0:SpR:287.0,321.0')] ).
cnf(895,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(multiply(w,x),multiply(double_divide(y,z),z)))),double_divide(inverse(x1),multiply(double_divide(u,x2),x2))),double_divide(double_divide(y,multiply(v,double_divide(x,w))),x1)),
inference(spr,[status(thm),theory(equality)],[9,321]),
[iquote('0:SpR:9.0,321.0')] ).
cnf(908,plain,
equal(double_divide(u,multiply(double_divide(v,w),w)),double_divide(u,multiply(double_divide(v,x),x))),
inference(rew,[status(thm),theory(equality)],[321,885]),
[iquote('0:Rew:321.0,885.0')] ).
cnf(2436,plain,
equal(multiply(double_divide(double_divide(u,multiply(double_divide(inverse(v),multiply(double_divide(inverse(w),x),x)),w)),multiply(double_divide(y,z),z)),multiply(double_divide(y,x1),x1)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[908,810]),
[iquote('0:SpR:908.0,810.0')] ).
cnf(4535,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,w),w)),double_divide(multiply(double_divide(x,y),y),multiply(double_divide(u,z),z))),double_divide(v,double_divide(x1,double_divide(x,x1)))),
inference(spr,[status(thm),theory(equality)],[908,342]),
[iquote('0:SpR:908.0,342.0')] ).
cnf(4539,plain,
equal(double_divide(u,double_divide(v,double_divide(w,v))),double_divide(u,double_divide(x,double_divide(w,x)))),
inference(rew,[status(thm),theory(equality)],[324,4535]),
[iquote('0:Rew:324.0,4535.0')] ).
cnf(4574,plain,
equal(inverse(double_divide(u,double_divide(v,double_divide(w,v)))),multiply(double_divide(x,double_divide(w,x)),u)),
inference(spr,[status(thm),theory(equality)],[4539,2]),
[iquote('0:SpR:4539.0,2.0')] ).
cnf(4762,plain,
equal(multiply(double_divide(u,double_divide(v,u)),w),multiply(double_divide(x,double_divide(v,x)),w)),
inference(rew,[status(thm),theory(equality)],[2,4574]),
[iquote('0:Rew:2.0,4574.0')] ).
cnf(5129,plain,
equal(multiply(double_divide(u,double_divide(v,u)),double_divide(v,w)),multiply(double_divide(w,x),x)),
inference(spr,[status(thm),theory(equality)],[4762,285]),
[iquote('0:SpR:4762.0,285.0')] ).
cnf(5200,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,double_divide(w,v)),x)),double_divide(inverse(x),multiply(double_divide(u,y),y))),double_divide(z,double_divide(w,z))),
inference(spr,[status(thm),theory(equality)],[4762,4]),
[iquote('0:SpR:4762.0,4.0')] ).
cnf(5246,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,double_divide(w,v)),double_divide(w,x))),double_divide(inverse(y),multiply(double_divide(u,z),z))),double_divide(x,y)),
inference(spr,[status(thm),theory(equality)],[4762,321]),
[iquote('0:SpR:4762.0,321.0')] ).
cnf(5270,plain,
equal(multiply(double_divide(inverse(u),multiply(double_divide(v,w),w)),double_divide(v,multiply(double_divide(x,double_divide(y,x)),double_divide(y,z)))),multiply(u,z)),
inference(spr,[status(thm),theory(equality)],[4762,361]),
[iquote('0:SpR:4762.0,361.0')] ).
cnf(5358,plain,
equal(double_divide(u,double_divide(v,u)),double_divide(w,double_divide(v,w))),
inference(rew,[status(thm),theory(equality)],[4,5200]),
[iquote('0:Rew:4.0,5200.0')] ).
cnf(5572,plain,
equal(double_divide(double_divide(u,double_divide(v,u)),double_divide(w,double_divide(x,double_divide(v,x)))),double_divide(y,double_divide(w,y))),
inference(spr,[status(thm),theory(equality)],[4539,5358]),
[iquote('0:SpR:4539.0,5358.0')] ).
cnf(5575,plain,
equal(double_divide(multiply(double_divide(u,v),v),double_divide(w,multiply(double_divide(u,x),x))),double_divide(y,double_divide(w,y))),
inference(spr,[status(thm),theory(equality)],[908,5358]),
[iquote('0:SpR:908.0,5358.0')] ).
cnf(5711,plain,
equal(multiply(double_divide(multiply(multiply(double_divide(u,v),v),w),multiply(double_divide(x,y),y)),double_divide(x,inverse(double_divide(z,double_divide(x1,z))))),multiply(multiply(double_divide(w,x2),x2),inverse(double_divide(x1,u)))),
inference(spr,[status(thm),theory(equality)],[5129,16]),
[iquote('0:SpR:5129.0,16.0')] ).
cnf(5928,plain,
equal(multiply(double_divide(multiply(multiply(double_divide(u,v),v),w),multiply(double_divide(x,y),y)),double_divide(x,multiply(double_divide(z,x1),x1))),multiply(multiply(double_divide(w,x2),x2),multiply(u,z))),
inference(rew,[status(thm),theory(equality)],[2,5711]),
[iquote('0:Rew:2.0,5711.0,2.0,5711.0')] ).
cnf(5929,plain,
equal(multiply(double_divide(u,multiply(double_divide(v,w),w)),x),multiply(multiply(double_divide(u,y),y),multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[363,5928]),
[iquote('0:Rew:363.0,5928.0')] ).
cnf(9223,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,double_divide(w,v)),double_divide(w,double_divide(x,double_divide(y,x))))),double_divide(inverse(z),multiply(double_divide(u,x1),x1))),double_divide(double_divide(x2,double_divide(y,x2)),z)),
inference(spr,[status(thm),theory(equality)],[5572,321]),
[iquote('0:SpR:5572.0,321.0')] ).
cnf(9270,plain,
equal(multiply(double_divide(inverse(u),multiply(double_divide(v,w),w)),double_divide(v,multiply(double_divide(x,double_divide(y,x)),double_divide(y,double_divide(z,double_divide(x1,z)))))),multiply(u,double_divide(x2,double_divide(x1,x2)))),
inference(spr,[status(thm),theory(equality)],[5572,361]),
[iquote('0:SpR:5572.0,361.0')] ).
cnf(9576,plain,
equal(multiply(u,double_divide(v,double_divide(w,v))),multiply(u,double_divide(x,double_divide(w,x)))),
inference(rew,[status(thm),theory(equality)],[5270,9270]),
[iquote('0:Rew:5270.0,9270.0')] ).
cnf(9577,plain,
equal(double_divide(double_divide(u,double_divide(v,u)),w),double_divide(double_divide(x,double_divide(v,x)),w)),
inference(rew,[status(thm),theory(equality)],[5246,9223]),
[iquote('0:Rew:5246.0,9223.0')] ).
cnf(11117,plain,
equal(double_divide(double_divide(u,multiply(double_divide(v,double_divide(w,v)),double_divide(w,multiply(double_divide(x,y),y)))),double_divide(inverse(z),multiply(double_divide(u,x1),x1))),double_divide(multiply(double_divide(x,x2),x2),z)),
inference(spr,[status(thm),theory(equality)],[5575,321]),
[iquote('0:SpR:5575.0,321.0')] ).
cnf(11544,plain,
equal(double_divide(multiply(double_divide(u,v),v),w),double_divide(multiply(double_divide(u,x),x),w)),
inference(rew,[status(thm),theory(equality)],[5246,11117]),
[iquote('0:Rew:5246.0,11117.0')] ).
cnf(14723,plain,
equal(multiply(multiply(double_divide(inverse(u),v),v),multiply(w,double_divide(w,multiply(x,u)))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[5929,6]),
[iquote('0:SpR:5929.0,6.0')] ).
cnf(15042,plain,
equal(multiply(double_divide(double_divide(u,multiply(double_divide(inverse(v),multiply(double_divide(inverse(w),x),x)),w)),multiply(double_divide(y,z),z)),x1),multiply(multiply(v,u),multiply(y,x1))),
inference(spr,[status(thm),theory(equality)],[810,5929]),
[iquote('0:SpR:810.0,5929.0')] ).
cnf(15056,plain,
equal(multiply(multiply(u,v),multiply(w,multiply(double_divide(w,x),x))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[15042,2436]),
[iquote('0:Rew:15042.0,2436.0')] ).
cnf(15969,plain,
equal(multiply(inverse(u),multiply(v,multiply(double_divide(v,w),w))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[6,15056]),
[iquote('0:SpR:6.0,15056.0')] ).
cnf(16161,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(multiply(w,double_divide(w,multiply(x,y))),multiply(double_divide(inverse(y),z),z)))),double_divide(inverse(x),multiply(double_divide(u,x1),x1))),v),
inference(spr,[status(thm),theory(equality)],[14723,9]),
[iquote('0:SpR:14723.0,9.0')] ).
cnf(16359,plain,
equal(double_divide(double_divide(inverse(u),multiply(v,double_divide(double_divide(w,multiply(x,u)),w))),x),v),
inference(rew,[status(thm),theory(equality)],[895,16161]),
[iquote('0:Rew:895.0,16161.0')] ).
cnf(16419,plain,
equal(multiply(double_divide(double_divide(inverse(u),multiply(v,double_divide(double_divide(w,multiply(x,u)),w))),y),y),multiply(v,x)),
inference(spr,[status(thm),theory(equality)],[16359,285]),
[iquote('0:SpR:16359.0,285.0')] ).
cnf(16438,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(double_divide(double_divide(inverse(w),multiply(u,double_divide(double_divide(x,multiply(multiply(double_divide(y,z),z),w)),x))),x1),x1))),double_divide(y,v)),
inference(spr,[status(thm),theory(equality)],[16359,321]),
[iquote('0:SpR:16359.0,321.0')] ).
cnf(16442,plain,
equal(multiply(multiply(double_divide(double_divide(inverse(u),multiply(v,double_divide(double_divide(w,multiply(multiply(double_divide(x,y),y),u)),w))),z),z),multiply(x,x1)),multiply(v,x1)),
inference(spr,[status(thm),theory(equality)],[16359,5929]),
[iquote('0:SpR:16359.0,5929.0')] ).
cnf(16474,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,double_divide(multiply(w,double_divide(w,multiply(multiply(x,v),y))),multiply(double_divide(inverse(y),z),z))))),x),
inference(spr,[status(thm),theory(equality)],[16359,18]),
[iquote('0:SpR:16359.0,18.0')] ).
cnf(16477,plain,
equal(multiply(u,double_divide(multiply(v,double_divide(v,multiply(w,x))),multiply(double_divide(inverse(x),y),y))),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[16359,358]),
[iquote('0:SpR:16359.0,358.0')] ).
cnf(16478,plain,
equal(multiply(double_divide(inverse(u),multiply(v,double_divide(multiply(w,double_divide(w,multiply(multiply(x,u),y))),multiply(double_divide(inverse(y),z),z)))),v),inverse(x)),
inference(spr,[status(thm),theory(equality)],[16359,21]),
[iquote('0:SpR:16359.0,21.0')] ).
cnf(16744,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,multiply(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[16477,16474]),
[iquote('0:Rew:16477.0,16474.0')] ).
cnf(16750,plain,
equal(multiply(double_divide(inverse(u),multiply(v,multiply(w,u))),v),inverse(w)),
inference(rew,[status(thm),theory(equality)],[16477,16478]),
[iquote('0:Rew:16477.0,16478.0')] ).
cnf(16797,plain,
equal(multiply(multiply(u,multiply(double_divide(v,w),w)),multiply(v,x)),multiply(u,x)),
inference(rew,[status(thm),theory(equality)],[16419,16442]),
[iquote('0:Rew:16419.0,16442.0')] ).
cnf(16816,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,multiply(double_divide(w,x),x)))),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[16419,16438]),
[iquote('0:Rew:16419.0,16438.0')] ).
cnf(17787,plain,
equal(double_divide(inverse(u),double_divide(inverse(multiply(double_divide(v,w),w)),inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[15969,16744]),
[iquote('0:SpR:15969.0,16744.0')] ).
cnf(17940,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(w))),v),inverse(double_divide(inverse(x),multiply(u,multiply(w,x))))),
inference(spr,[status(thm),theory(equality)],[16750]),
[iquote('0:SpR:16750.0,16750.0')] ).
cnf(18036,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(w))),v),multiply(multiply(u,multiply(w,x)),inverse(x))),
inference(rew,[status(thm),theory(equality)],[2,17940]),
[iquote('0:Rew:2.0,17940.0')] ).
cnf(18138,plain,
equal(double_divide(u,double_divide(inverse(multiply(double_divide(v,w),w)),u)),v),
inference(spr,[status(thm),theory(equality)],[17787,5358]),
[iquote('0:SpR:17787.0,5358.0')] ).
cnf(18534,plain,
equal(multiply(double_divide(inverse(multiply(double_divide(u,v),v)),w),w),inverse(u)),
inference(spr,[status(thm),theory(equality)],[18138,2]),
[iquote('0:SpR:18138.0,2.0')] ).
cnf(19696,plain,
equal(multiply(double_divide(inverse(inverse(u)),v),v),inverse(inverse(multiply(double_divide(u,w),w)))),
inference(spr,[status(thm),theory(equality)],[18534]),
[iquote('0:SpR:18534.0,18534.0')] ).
cnf(19725,plain,
equal(double_divide(u,double_divide(inverse(inverse(v)),u)),inverse(multiply(double_divide(v,w),w))),
inference(spr,[status(thm),theory(equality)],[18534,18138]),
[iquote('0:SpR:18534.0,18138.0')] ).
cnf(19816,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(w))),v),inverse(double_divide(inverse(multiply(double_divide(w,x),x)),u))),
inference(spr,[status(thm),theory(equality)],[18534,16750]),
[iquote('0:SpR:18534.0,16750.0')] ).
cnf(19942,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(w))),v),multiply(u,inverse(multiply(double_divide(w,x),x)))),
inference(rew,[status(thm),theory(equality)],[2,19816]),
[iquote('0:Rew:2.0,19816.0')] ).
cnf(20234,plain,
equal(multiply(u,inverse(multiply(double_divide(v,w),w))),multiply(u,double_divide(x,double_divide(inverse(inverse(v)),x)))),
inference(spr,[status(thm),theory(equality)],[19725,9576]),
[iquote('0:SpR:19725.0,9576.0')] ).
cnf(20323,plain,
equal(inverse(multiply(double_divide(double_divide(u,multiply(v,multiply(double_divide(w,x),x))),y),y)),inverse(multiply(v,double_divide(double_divide(z,double_divide(inverse(inverse(w)),z)),multiply(double_divide(u,x1),x1))))),
inference(spr,[status(thm),theory(equality)],[19725,405]),
[iquote('0:SpR:19725.0,405.0')] ).
cnf(20364,plain,
equal(multiply(double_divide(double_divide(u,double_divide(inverse(inverse(v)),u)),w),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[19725,18534]),
[iquote('0:SpR:19725.0,18534.0')] ).
cnf(20369,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(inverse(inverse(w)),v)),u)),w),
inference(spr,[status(thm),theory(equality)],[19725,18138]),
[iquote('0:SpR:19725.0,18138.0')] ).
cnf(20445,plain,
equal(double_divide(u,double_divide(inverse(inverse(double_divide(v,double_divide(w,v)))),u)),inverse(multiply(double_divide(double_divide(x,double_divide(w,x)),y),y))),
inference(spr,[status(thm),theory(equality)],[9577,19725]),
[iquote('0:SpR:9577.0,19725.0')] ).
cnf(20490,plain,
equal(inverse(multiply(double_divide(double_divide(u,double_divide(v,u)),w),w)),v),
inference(rew,[status(thm),theory(equality)],[18138,20445,2]),
[iquote('0:Rew:18138.0,20445.0,2.0,20445.0')] ).
cnf(20556,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,w),w))),u),
inference(spr,[status(thm),theory(equality)],[20490,15969]),
[iquote('0:SpR:20490.0,15969.0')] ).
cnf(20769,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(v,w),w))),multiply(double_divide(u,x),x)),
inference(spr,[status(thm),theory(equality)],[20556,285]),
[iquote('0:SpR:20556.0,285.0')] ).
cnf(20772,plain,
equal(multiply(double_divide(inverse(double_divide(u,multiply(v,multiply(double_divide(v,w),w)))),x),x),inverse(u)),
inference(spr,[status(thm),theory(equality)],[20556,18534]),
[iquote('0:SpR:20556.0,18534.0')] ).
cnf(20796,plain,
equal(double_divide(u,double_divide(inverse(double_divide(v,multiply(w,multiply(double_divide(w,x),x)))),u)),v),
inference(spr,[status(thm),theory(equality)],[20556,18138]),
[iquote('0:SpR:20556.0,18138.0')] ).
cnf(20800,plain,
equal(inverse(double_divide(double_divide(u,double_divide(v,u)),multiply(w,multiply(double_divide(w,x),x)))),v),
inference(spr,[status(thm),theory(equality)],[20556,20490]),
[iquote('0:SpR:20556.0,20490.0')] ).
cnf(20820,plain,
equal(double_divide(u,multiply(double_divide(v,w),w)),multiply(multiply(double_divide(u,x),x),multiply(v,multiply(y,multiply(double_divide(y,z),z))))),
inference(spr,[status(thm),theory(equality)],[20556,5929]),
[iquote('0:SpR:20556.0,5929.0')] ).
cnf(20937,plain,
equal(multiply(u,multiply(inverse(multiply(double_divide(v,w),w)),inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[18534,20556]),
[iquote('0:SpR:18534.0,20556.0')] ).
cnf(20971,plain,
equal(double_divide(u,double_divide(multiply(multiply(v,multiply(double_divide(v,w),w)),x),u)),x),
inference(rew,[status(thm),theory(equality)],[2,20796]),
[iquote('0:Rew:2.0,20796.0')] ).
cnf(20972,plain,
equal(multiply(multiply(u,multiply(double_divide(u,v),v)),double_divide(w,double_divide(x,w))),x),
inference(rew,[status(thm),theory(equality)],[2,20800]),
[iquote('0:Rew:2.0,20800.0')] ).
cnf(20974,plain,
equal(multiply(double_divide(multiply(multiply(u,multiply(double_divide(u,v),v)),w),x),x),inverse(w)),
inference(rew,[status(thm),theory(equality)],[2,20772]),
[iquote('0:Rew:2.0,20772.0')] ).
cnf(20985,plain,
equal(double_divide(u,multiply(double_divide(v,w),w)),multiply(multiply(double_divide(u,x),x),v)),
inference(rew,[status(thm),theory(equality)],[20556,20820]),
[iquote('0:Rew:20556.0,20820.0')] ).
cnf(21624,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(inverse(multiply(w,x)),v)),u)),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[2,20369]),
[iquote('0:SpR:2.0,20369.0')] ).
cnf(21966,plain,
equal(multiply(u,multiply(inverse(double_divide(v,multiply(w,multiply(double_divide(w,x),x)))),inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[20556,20937]),
[iquote('0:SpR:20556.0,20937.0')] ).
cnf(21978,plain,
equal(multiply(u,multiply(multiply(multiply(v,multiply(double_divide(v,w),w)),x),inverse(x))),u),
inference(rew,[status(thm),theory(equality)],[2,21966]),
[iquote('0:Rew:2.0,21966.0')] ).
cnf(22228,plain,
equal(multiply(double_divide(double_divide(u,double_divide(inverse(v),u)),w),w),v),
inference(spr,[status(thm),theory(equality)],[20490,20364]),
[iquote('0:SpR:20490.0,20364.0')] ).
cnf(22422,plain,
equal(multiply(double_divide(double_divide(u,double_divide(inverse(v),u)),multiply(double_divide(w,x),x)),y),multiply(v,multiply(w,y))),
inference(spr,[status(thm),theory(equality)],[22228,5929]),
[iquote('0:SpR:22228.0,5929.0')] ).
cnf(22548,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,w))),double_divide(double_divide(x,double_divide(inverse(w),x)),v)),
inference(spr,[status(thm),theory(equality)],[22228,16744]),
[iquote('0:SpR:22228.0,16744.0')] ).
cnf(23646,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,inverse(inverse(multiply(double_divide(w,x),x)))))),double_divide(inverse(inverse(w)),v)),
inference(spr,[status(thm),theory(equality)],[19696,16744]),
[iquote('0:SpR:19696.0,16744.0')] ).
cnf(23647,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(inverse(multiply(double_divide(w,x),x))))),v),inverse(double_divide(inverse(inverse(w)),u))),
inference(spr,[status(thm),theory(equality)],[19696,16750]),
[iquote('0:SpR:19696.0,16750.0')] ).
cnf(23836,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(inverse(multiply(double_divide(w,x),x))))),v),multiply(u,inverse(inverse(w)))),
inference(rew,[status(thm),theory(equality)],[2,23647]),
[iquote('0:Rew:2.0,23647.0')] ).
cnf(25600,plain,
equal(multiply(multiply(u,multiply(double_divide(double_divide(v,w),x),x)),y),multiply(multiply(u,w),multiply(v,y))),
inference(spr,[status(thm),theory(equality)],[16797]),
[iquote('0:SpR:16797.0,16797.0')] ).
cnf(25674,plain,
equal(multiply(multiply(u,multiply(double_divide(v,w),w)),v),multiply(u,multiply(x,multiply(double_divide(x,y),y)))),
inference(spr,[status(thm),theory(equality)],[20556,16797]),
[iquote('0:SpR:20556.0,16797.0')] ).
cnf(25723,plain,
equal(multiply(multiply(u,multiply(double_divide(multiply(double_divide(v,w),w),x),x)),multiply(multiply(double_divide(v,y),y),z)),multiply(u,z)),
inference(spr,[status(thm),theory(equality)],[11544,16797]),
[iquote('0:SpR:11544.0,16797.0')] ).
cnf(25801,plain,
equal(multiply(multiply(u,multiply(double_divide(v,w),w)),v),u),
inference(rew,[status(thm),theory(equality)],[20556,25674]),
[iquote('0:Rew:20556.0,25674.0')] ).
cnf(26038,plain,
equal(multiply(double_divide(u,multiply(double_divide(v,w),w)),double_divide(v,inverse(u))),multiply(multiply(double_divide(x,y),y),inverse(multiply(double_divide(x,z),z)))),
inference(spr,[status(thm),theory(equality)],[25801,16]),
[iquote('0:SpR:25801.0,16.0')] ).
cnf(26063,plain,
equal(multiply(u,multiply(double_divide(multiply(double_divide(v,w),w),x),x)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[25801]),
[iquote('0:SpR:25801.0,25801.0')] ).
cnf(26082,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,w))),multiply(w,multiply(double_divide(v,x),x))),
inference(spr,[status(thm),theory(equality)],[25801,16744]),
[iquote('0:SpR:25801.0,16744.0')] ).
cnf(26175,plain,
equal(double_divide(inverse(multiply(double_divide(u,v),v)),multiply(double_divide(w,x),x)),multiply(inverse(u),w)),
inference(spr,[status(thm),theory(equality)],[18534,25801]),
[iquote('0:SpR:18534.0,25801.0')] ).
cnf(26176,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),u)),multiply(double_divide(w,x),x)),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[22228,25801]),
[iquote('0:SpR:22228.0,25801.0')] ).
cnf(26196,plain,
equal(multiply(u,multiply(double_divide(double_divide(v,w),x),x)),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[16797,25801]),
[iquote('0:SpR:16797.0,25801.0')] ).
cnf(26202,plain,
equal(multiply(multiply(u,v),multiply(multiply(double_divide(v,w),w),x)),multiply(u,x)),
inference(rew,[status(thm),theory(equality)],[26063,25723]),
[iquote('0:Rew:26063.0,25723.0')] ).
cnf(26264,plain,
equal(multiply(multiply(multiply(u,v),w),x),multiply(multiply(u,v),multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[26196,25600]),
[iquote('0:Rew:26196.0,25600.0')] ).
cnf(26369,plain,
equal(multiply(u,multiply(multiply(v,multiply(double_divide(v,w),w)),multiply(x,inverse(x)))),u),
inference(rew,[status(thm),theory(equality)],[26264,21978]),
[iquote('0:Rew:26264.0,21978.0')] ).
cnf(26455,plain,
equal(inverse(multiply(double_divide(double_divide(u,multiply(v,multiply(double_divide(w,x),x))),y),y)),inverse(multiply(v,multiply(inverse(w),u)))),
inference(rew,[status(thm),theory(equality)],[26176,20323]),
[iquote('0:Rew:26176.0,20323.0')] ).
cnf(26461,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[26176,22422]),
[iquote('0:Rew:26176.0,22422.0')] ).
cnf(26477,plain,
equal(multiply(double_divide(u,multiply(double_divide(v,w),w)),x),multiply(double_divide(u,y),multiply(y,multiply(v,x)))),
inference(rew,[status(thm),theory(equality)],[26461,5929]),
[iquote('0:Rew:26461.0,5929.0')] ).
cnf(26485,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(inverse(b2),multiply(b2,a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[26461,3]),
[iquote('0:Rew:26461.0,3.2')] ).
cnf(26789,plain,
equal(multiply(u,multiply(multiply(double_divide(u,v),v),double_divide(w,double_divide(x,w)))),x),
inference(rew,[status(thm),theory(equality)],[26461,20972]),
[iquote('0:Rew:26461.0,20972.0')] ).
cnf(27330,plain,
equal(multiply(multiply(u,v),multiply(double_divide(v,w),multiply(w,x))),multiply(u,x)),
inference(rew,[status(thm),theory(equality)],[26461,26202]),
[iquote('0:Rew:26461.0,26202.0')] ).
cnf(27340,plain,
equal(double_divide(u,double_divide(multiply(v,multiply(multiply(double_divide(v,w),w),x)),u)),x),
inference(rew,[status(thm),theory(equality)],[26461,20971]),
[iquote('0:Rew:26461.0,20971.0')] ).
cnf(27640,plain,
equal(double_divide(u,multiply(double_divide(v,w),w)),multiply(double_divide(u,x),multiply(x,v))),
inference(rew,[status(thm),theory(equality)],[26461,20985]),
[iquote('0:Rew:26461.0,20985.0')] ).
cnf(28424,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(w))),v),multiply(u,multiply(multiply(w,x),inverse(x)))),
inference(rew,[status(thm),theory(equality)],[26461,18036]),
[iquote('0:Rew:26461.0,18036.0')] ).
cnf(28427,plain,
equal(multiply(double_divide(multiply(u,multiply(multiply(double_divide(u,v),v),w)),x),x),inverse(w)),
inference(rew,[status(thm),theory(equality)],[26461,20974]),
[iquote('0:Rew:26461.0,20974.0')] ).
cnf(29326,plain,
equal(multiply(u,multiply(double_divide(u,v),multiply(v,double_divide(w,double_divide(x,w))))),x),
inference(rew,[status(thm),theory(equality)],[26461,26789]),
[iquote('0:Rew:26461.0,26789.0')] ).
cnf(29327,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,w),multiply(w,x)))),multiply(u,x)),
inference(rew,[status(thm),theory(equality)],[26461,27330]),
[iquote('0:Rew:26461.0,27330.0')] ).
cnf(29329,plain,
equal(double_divide(u,double_divide(multiply(v,multiply(double_divide(v,w),multiply(w,x))),u)),x),
inference(rew,[status(thm),theory(equality)],[26461,27340]),
[iquote('0:Rew:26461.0,27340.0')] ).
cnf(29332,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[29327,26369,26461]),
[iquote('0:Rew:29327.0,26369.0,26461.0,26369.0,26461.0,26369.0')] ).
cnf(29338,plain,
equal(multiply(double_divide(multiply(u,multiply(double_divide(u,v),multiply(v,w))),x),x),inverse(w)),
inference(rew,[status(thm),theory(equality)],[26461,28427]),
[iquote('0:Rew:26461.0,28427.0')] ).
cnf(29434,plain,
equal(multiply(double_divide(inverse(u),multiply(v,inverse(w))),v),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[29332,28424,26461]),
[iquote('0:Rew:29332.0,28424.0,26461.0,28424.0')] ).
cnf(29435,plain,
equal(multiply(u,inverse(multiply(double_divide(v,w),w))),multiply(u,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[29434,23836]),
[iquote('0:Rew:29434.0,23836.0')] ).
cnf(29437,plain,
equal(multiply(u,inverse(multiply(double_divide(v,w),w))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[29434,19942]),
[iquote('0:Rew:29434.0,19942.0')] ).
cnf(29469,plain,
equal(multiply(u,double_divide(v,double_divide(inverse(inverse(w)),v))),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[29437,20234]),
[iquote('0:Rew:29437.0,20234.0')] ).
cnf(29545,plain,
equal(multiply(u,inverse(inverse(v))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[29437,29435]),
[iquote('0:Rew:29437.0,29435.0')] ).
cnf(29690,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,multiply(double_divide(w,x),x)))),double_divide(inverse(inverse(w)),v)),
inference(rew,[status(thm),theory(equality)],[29545,23646]),
[iquote('0:Rew:29545.0,23646.0')] ).
cnf(29705,plain,
equal(double_divide(inverse(inverse(u)),v),double_divide(u,v)),
inference(rew,[status(thm),theory(equality)],[16816,29690]),
[iquote('0:Rew:16816.0,29690.0')] ).
cnf(29707,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(w,v)),u)),w),
inference(rew,[status(thm),theory(equality)],[29705,20369]),
[iquote('0:Rew:29705.0,20369.0')] ).
cnf(30071,plain,
equal(multiply(u,double_divide(v,double_divide(w,v))),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[29705,29469]),
[iquote('0:Rew:29705.0,29469.0')] ).
cnf(30166,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[29707,21624]),
[iquote('0:Rew:29707.0,21624.0')] ).
cnf(31048,plain,
equal(double_divide(double_divide(u,double_divide(v,u)),multiply(double_divide(w,x),x)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[30166,26175]),
[iquote('0:Rew:30166.0,26175.0')] ).
cnf(31868,plain,
equal(multiply(u,multiply(double_divide(u,v),multiply(v,w))),w),
inference(rew,[status(thm),theory(equality)],[30071,29326]),
[iquote('0:Rew:30071.0,29326.0')] ).
cnf(31888,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[31868,29338]),
[iquote('0:Rew:31868.0,29338.0')] ).
cnf(31891,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[31868,29329]),
[iquote('0:Rew:31868.0,29329.0')] ).
cnf(31905,plain,
equal(multiply(double_divide(inverse(u),v),v),u),
inference(rew,[status(thm),theory(equality)],[31891,22228]),
[iquote('0:Rew:31891.0,22228.0')] ).
cnf(33303,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,w))),double_divide(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[31891,22548]),
[iquote('0:Rew:31891.0,22548.0')] ).
cnf(34130,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(u,w))),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[31888,26082]),
[iquote('0:Rew:31888.0,26082.0')] ).
cnf(34225,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[31888,27640]),
[iquote('0:Rew:31888.0,27640.0')] ).
cnf(34233,plain,
equal(double_divide(u,multiply(v,inverse(v))),multiply(double_divide(u,w),w)),
inference(rew,[status(thm),theory(equality)],[31888,20769]),
[iquote('0:Rew:31888.0,20769.0')] ).
cnf(34789,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[31888,31905]),
[iquote('0:Rew:31888.0,31905.0')] ).
cnf(34866,plain,
equal(double_divide(u,multiply(v,inverse(v))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[31888,34233]),
[iquote('0:Rew:31888.0,34233.0')] ).
cnf(34886,plain,
equal(multiply(u,inverse(v)),double_divide(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[33303,34130]),
[iquote('0:Rew:33303.0,34130.0')] ).
cnf(34893,plain,
equal(double_divide(u,double_divide(inverse(v),v)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[34886,34866]),
[iquote('0:Rew:34886.0,34866.0')] ).
cnf(35056,plain,
equal(multiply(inverse(u),v),double_divide(u,inverse(v))),
inference(rew,[status(thm),theory(equality)],[31891,31048,31888]),
[iquote('0:Rew:31891.0,31048.0,31888.0,31048.0')] ).
cnf(35392,plain,
equal(multiply(double_divide(u,inverse(v)),w),double_divide(u,double_divide(w,v))),
inference(rew,[status(thm),theory(equality)],[31888,26477,30166,34225]),
[iquote('0:Rew:31888.0,26477.0,30166.0,26477.0,34225.0,26477.0')] ).
cnf(36187,plain,
equal(double_divide(double_divide(u,inverse(v)),w),double_divide(v,double_divide(inverse(w),u))),
inference(rew,[status(thm),theory(equality)],[34789,26455,31888,34886,30166,35056]),
[iquote('0:Rew:34789.0,26455.0,31888.0,26455.0,34886.0,26455.0,31888.0,26455.0,30166.0,26455.0,35056.0,26455.0')] ).
cnf(37350,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[34893,26038,36187,35392,31888,35056,34789]),
[iquote('0:Rew:34893.0,26038.0,36187.0,26038.0,35392.0,26038.0,31888.0,26038.0,35056.0,26038.0,31888.0,26038.0,34789.0,26038.0,31888.0,26038.0')] ).
cnf(39622,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[31891,26485,30166,35056,26461]),
[iquote('0:Rew:31891.0,26485.2,30166.0,26485.2,35056.0,26485.2,26461.0,26485.1,35056.0,26485.0,35056.0,26485.0')] ).
cnf(39623,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[39622]),
[iquote('0:Obv:39622.2')] ).
cnf(39624,plain,
$false,
inference(unc,[status(thm)],[39623,37350]),
[iquote('0:UnC:39623.0,37350.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP083-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 03:24:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 175.74/175.93
% 175.74/175.93 SPASS V 3.9
% 175.74/175.93 SPASS beiseite: Proof found.
% 175.74/175.93 % SZS status Theorem
% 175.74/175.93 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 175.74/175.93 SPASS derived 30686 clauses, backtracked 0 clauses, performed 0 splits and kept 9840 clauses.
% 175.74/175.93 SPASS allocated 169978 KBytes.
% 175.74/175.93 SPASS spent 0:2:55.49 on the problem.
% 175.74/175.93 0:00:00.04 for the input.
% 175.74/175.93 0:00:00.00 for the FLOTTER CNF translation.
% 175.74/175.93 0:00:00.28 for inferences.
% 175.74/175.93 0:00:00.00 for the backtracking.
% 175.74/175.93 0:2:55.14 for the reduction.
% 175.74/175.93
% 175.74/175.93
% 175.74/175.93 Here is a proof with depth 22, length 165 :
% 175.74/175.93 % SZS output start Refutation
% See solution above
% 176.71/176.92 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 176.71/176.92
%------------------------------------------------------------------------------