TSTP Solution File: GRP107-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP107-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:45:20 EDT 2022
% Result : Unsatisfiable 1.38s 1.58s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 3
% Syntax : Number of clauses : 117 ( 105 unt; 0 nHn; 117 RR)
% Number of literals : 138 ( 0 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,v),inverse(double_divide(u,inverse(double_divide(inverse(w),v))))),w),
file('GRP107-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP107-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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('GRP107-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(double_divide(u,v),multiply(multiply(v,inverse(w)),u)),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(multiply(u,inverse(v)),w),double_divide(w,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(u,multiply(multiply(multiply(multiply(v,inverse(u)),w),inverse(x)),double_divide(w,v))),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(double_divide(inverse(u),v),multiply(v,inverse(w))),inverse(w)),u),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(13,plain,
equal(multiply(multiply(multiply(multiply(multiply(u,inverse(v)),w),inverse(x)),double_divide(w,u)),v),inverse(x)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(14,plain,
equal(multiply(multiply(multiply(u,multiply(v,w)),x),double_divide(x,u)),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(72,plain,
equal(multiply(multiply(multiply(multiply(multiply(multiply(multiply(u,inverse(v)),w),inverse(x)),double_divide(w,u)),inverse(y)),v),x),inverse(y)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(76,plain,
equal(double_divide(u,multiply(multiply(multiply(multiply(multiply(multiply(v,inverse(w)),x),inverse(u)),double_divide(x,v)),inverse(y)),w)),y),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(139,plain,
equal(double_divide(double_divide(double_divide(inverse(u),multiply(multiply(multiply(multiply(v,inverse(inverse(w))),x),inverse(y)),double_divide(x,v))),inverse(y)),inverse(w)),u),
inference(spr,[status(thm),theory(equality)],[13,10]),
[iquote('0:SpR:13.0,10.0')] ).
cnf(150,plain,
equal(double_divide(u,multiply(inverse(u),double_divide(double_divide(v,w),multiply(multiply(w,inverse(inverse(x))),v)))),x),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
cnf(151,plain,
equal(multiply(multiply(inverse(u),double_divide(double_divide(v,w),multiply(multiply(w,inverse(inverse(x))),v))),u),inverse(x)),
inference(spr,[status(thm),theory(equality)],[13]),
[iquote('0:SpR:13.0,13.0')] ).
cnf(170,plain,
equal(double_divide(u,multiply(inverse(u),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[4,150]),
[iquote('0:Rew:4.0,150.0')] ).
cnf(171,plain,
equal(multiply(multiply(inverse(u),inverse(v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4,151]),
[iquote('0:Rew:4.0,151.0')] ).
cnf(216,plain,
equal(double_divide(u,multiply(multiply(multiply(inverse(v),inverse(u)),inverse(w)),v)),w),
inference(spr,[status(thm),theory(equality)],[170,4]),
[iquote('0:SpR:170.0,4.0')] ).
cnf(231,plain,
equal(double_divide(double_divide(u,v),multiply(multiply(v,u),inverse(w))),w),
inference(spr,[status(thm),theory(equality)],[2,170]),
[iquote('0:SpR:2.0,170.0')] ).
cnf(238,plain,
equal(double_divide(double_divide(u,inverse(u)),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[171,4]),
[iquote('0:SpR:171.0,4.0')] ).
cnf(240,plain,
equal(multiply(inverse(u),double_divide(v,inverse(v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[171,6]),
[iquote('0:SpR:171.0,6.0')] ).
cnf(273,plain,
equal(double_divide(double_divide(u,inverse(u)),multiply(v,w)),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[2,238]),
[iquote('0:SpR:2.0,238.0')] ).
cnf(416,plain,
equal(double_divide(double_divide(inverse(u),inverse(inverse(v))),inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[171,231]),
[iquote('0:SpR:171.0,231.0')] ).
cnf(464,plain,
equal(double_divide(double_divide(inverse(u),inverse(multiply(v,w))),inverse(u)),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[2,416]),
[iquote('0:SpR:2.0,416.0')] ).
cnf(635,plain,
equal(double_divide(inverse(u),multiply(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[273,231]),
[iquote('0:SpR:273.0,231.0')] ).
cnf(694,plain,
equal(multiply(multiply(inverse(u),u),inverse(v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[635,2]),
[iquote('0:SpR:635.0,2.0')] ).
cnf(695,plain,
equal(double_divide(u,multiply(multiply(multiply(inverse(v),v),inverse(w)),inverse(u))),w),
inference(spr,[status(thm),theory(equality)],[635,4]),
[iquote('0:SpR:635.0,4.0')] ).
cnf(704,plain,
equal(multiply(multiply(multiply(multiply(inverse(u),u),inverse(v)),inverse(w)),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[635,6]),
[iquote('0:SpR:635.0,6.0')] ).
cnf(717,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[694,695]),
[iquote('0:Rew:694.0,695.0')] ).
cnf(720,plain,
equal(multiply(multiply(inverse(u),inverse(v)),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[694,704]),
[iquote('0:Rew:694.0,704.0')] ).
cnf(753,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[717,635]),
[iquote('0:SpR:717.0,635.0')] ).
cnf(756,plain,
equal(double_divide(double_divide(inverse(u),v),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[753,416]),
[iquote('0:Rew:753.0,416.0')] ).
cnf(799,plain,
equal(double_divide(double_divide(double_divide(inverse(u),multiply(multiply(multiply(multiply(v,w),x),inverse(y)),double_divide(x,v))),inverse(y)),inverse(w)),u),
inference(rew,[status(thm),theory(equality)],[753,139]),
[iquote('0:Rew:753.0,139.0')] ).
cnf(813,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[756,464]),
[iquote('0:Rew:756.0,464.0')] ).
cnf(878,plain,
equal(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(u,inverse(v)),w),inverse(x)),double_divide(w,u)),inverse(y)),v),multiply(z,x1)),x),y),multiply(z,x1)),
inference(spr,[status(thm),theory(equality)],[76,14]),
[iquote('0:SpR:76.0,14.0')] ).
cnf(931,plain,
equal(double_divide(double_divide(u,v),multiply(multiply(v,w),u)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[753,4]),
[iquote('0:SpR:753.0,4.0')] ).
cnf(940,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(spr,[status(thm),theory(equality)],[753,171]),
[iquote('0:SpR:753.0,171.0')] ).
cnf(944,plain,
equal(double_divide(u,multiply(v,inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[753,717]),
[iquote('0:SpR:753.0,717.0')] ).
cnf(955,plain,
equal(multiply(u,double_divide(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[753,240]),
[iquote('0:SpR:753.0,240.0')] ).
cnf(994,plain,
equal(multiply(multiply(u,v),inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[753,940]),
[iquote('0:SpR:753.0,940.0')] ).
cnf(995,plain,
equal(multiply(multiply(double_divide(u,v),w),multiply(v,u)),w),
inference(spr,[status(thm),theory(equality)],[813,940]),
[iquote('0:SpR:813.0,940.0')] ).
cnf(996,plain,
equal(multiply(inverse(double_divide(u,inverse(u))),v),v),
inference(spr,[status(thm),theory(equality)],[955,940]),
[iquote('0:SpR:955.0,940.0')] ).
cnf(997,plain,
equal(multiply(inverse(u),u),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[955,940]),
[iquote('0:SpR:955.0,940.0')] ).
cnf(1001,plain,
equal(multiply(u,double_divide(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[753,955]),
[iquote('0:SpR:753.0,955.0')] ).
cnf(1003,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[2,996]),
[iquote('0:Rew:2.0,996.0')] ).
cnf(1004,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[1003,3]),
[iquote('0:Rew:1003.0,3.3')] ).
cnf(1010,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[1004]),
[iquote('0:Obv:1004.3')] ).
cnf(1013,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[994]),
[iquote('0:SpR:994.0,994.0')] ).
cnf(1021,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[813,1013]),
[iquote('0:Rew:813.0,1013.0')] ).
cnf(1024,plain,
equal(multiply(inverse(double_divide(inverse(u),u)),v),v),
inference(spr,[status(thm),theory(equality)],[1001,940]),
[iquote('0:SpR:1001.0,940.0')] ).
cnf(1032,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[2,1024]),
[iquote('0:Rew:2.0,1024.0')] ).
cnf(1051,plain,
equal(multiply(inverse(u),v),double_divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[1021,940]),
[iquote('0:SpR:1021.0,940.0')] ).
cnf(1052,plain,
equal(double_divide(double_divide(u,v),u),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[1021,813]),
[iquote('0:SpR:1021.0,813.0')] ).
cnf(1058,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),double_divide(inverse(b1),b1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1051,1010]),
[iquote('0:Rew:1051.0,1010.1')] ).
cnf(1083,plain,
equal(double_divide(inverse(u),u),double_divide(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[1051,997]),
[iquote('0:Rew:1051.0,997.0')] ).
cnf(1145,plain,
equal(multiply(double_divide(inverse(inverse(u)),v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1051,720]),
[iquote('0:Rew:1051.0,720.0')] ).
cnf(1152,plain,
equal(double_divide(u,multiply(multiply(double_divide(inverse(inverse(u)),v),inverse(w)),v)),w),
inference(rew,[status(thm),theory(equality)],[1051,216]),
[iquote('0:Rew:1051.0,216.0')] ).
cnf(1168,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[753,1052]),
[iquote('0:Rew:753.0,1052.0')] ).
cnf(1173,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[753,1145]),
[iquote('0:Rew:753.0,1145.0')] ).
cnf(1177,plain,
equal(double_divide(u,multiply(multiply(double_divide(u,v),inverse(w)),v)),w),
inference(rew,[status(thm),theory(equality)],[753,1152]),
[iquote('0:Rew:753.0,1152.0')] ).
cnf(1269,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(double_divide(inverse(b1),b1),double_divide(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1051,1058]),
[iquote('0:Rew:1051.0,1058.1')] ).
cnf(1276,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1168]),
[iquote('0:SpR:1168.0,1168.0')] ).
cnf(1344,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(v)),w),inverse(x))),multiply(multiply(double_divide(w,u),v),x)),
inference(spr,[status(thm),theory(equality)],[994,72]),
[iquote('0:SpR:994.0,72.0')] ).
cnf(1345,plain,
equal(inverse(multiply(multiply(multiply(multiply(u,inverse(v)),w),inverse(x)),double_divide(w,u))),multiply(v,x)),
inference(spr,[status(thm),theory(equality)],[1032,72]),
[iquote('0:SpR:1032.0,72.0')] ).
cnf(1351,plain,
equal(double_divide(inverse(u),multiply(multiply(v,inverse(w)),x)),multiply(multiply(double_divide(x,v),w),u)),
inference(rew,[status(thm),theory(equality)],[813,1344]),
[iquote('0:Rew:813.0,1344.0')] ).
cnf(1354,plain,
equal(double_divide(double_divide(multiply(multiply(double_divide(double_divide(u,v),multiply(multiply(v,w),u)),x),y),inverse(x)),inverse(w)),y),
inference(rew,[status(thm),theory(equality)],[1351,799]),
[iquote('0:Rew:1351.0,799.0')] ).
cnf(1358,plain,
equal(double_divide(double_divide(u,v),multiply(multiply(multiply(v,inverse(w)),u),inverse(x))),multiply(w,x)),
inference(rew,[status(thm),theory(equality)],[813,1345]),
[iquote('0:Rew:813.0,1345.0')] ).
cnf(1371,plain,
equal(double_divide(double_divide(multiply(double_divide(inverse(u),v),w),inverse(u)),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[1051,1354,931]),
[iquote('0:Rew:1051.0,1354.0,931.0,1354.0')] ).
cnf(1403,plain,
equal(double_divide(u,double_divide(u,v)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[1173,813]),
[iquote('0:SpR:1173.0,813.0')] ).
cnf(1410,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[1276,1173]),
[iquote('0:SpR:1276.0,1173.0')] ).
cnf(1411,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,1410]),
[iquote('0:Rew:2.0,1410.0')] ).
cnf(1413,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(double_divide(inverse(b1),b1),double_divide(inverse(a1),a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1411,1269]),
[iquote('0:Rew:1411.0,1269.2')] ).
cnf(1427,plain,
equal(multiply(multiply(u,v),multiply(double_divide(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[1411,995]),
[iquote('0:Rew:1411.0,995.0')] ).
cnf(1456,plain,
equal(multiply(multiply(u,multiply(multiply(multiply(multiply(multiply(multiply(multiply(v,inverse(w)),x),inverse(u)),double_divide(x,v)),inverse(y)),w),multiply(z,x1))),y),multiply(z,x1)),
inference(rew,[status(thm),theory(equality)],[1411,878]),
[iquote('0:Rew:1411.0,878.0')] ).
cnf(1566,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(u,v),inverse(w)))),w),
inference(rew,[status(thm),theory(equality)],[1411,1177]),
[iquote('0:Rew:1411.0,1177.0')] ).
cnf(1570,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[753,1403]),
[iquote('0:Rew:753.0,1403.0')] ).
cnf(1645,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(double_divide(inverse(b1),b1),double_divide(inverse(a1),a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1411,1413]),
[iquote('0:Rew:1411.0,1413.0')] ).
cnf(1646,plain,
( ~ equal(double_divide(inverse(b1),b1),double_divide(inverse(a1),a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[1645]),
[iquote('0:Obv:1645.0')] ).
cnf(1648,plain,
equal(multiply(u,multiply(v,multiply(multiply(w,multiply(multiply(double_divide(x,y),multiply(multiply(multiply(y,inverse(w)),x),inverse(v))),inverse(u))),multiply(z,x1)))),multiply(z,x1)),
inference(rew,[status(thm),theory(equality)],[1411,1456]),
[iquote('0:Rew:1411.0,1456.0,1411.0,1456.0,1411.0,1456.0')] ).
cnf(1678,plain,
equal(inverse(multiply(u,v)),double_divide(u,v)),
inference(spr,[status(thm),theory(equality)],[1411,813]),
[iquote('0:SpR:1411.0,813.0')] ).
cnf(1690,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[813,1678]),
[iquote('0:Rew:813.0,1678.0')] ).
cnf(1694,plain,
( ~ equal(double_divide(inverse(a1),a1),double_divide(b1,inverse(b1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1690,1646]),
[iquote('0:Rew:1690.0,1646.0')] ).
cnf(1721,plain,
equal(double_divide(double_divide(inverse(u),multiply(double_divide(inverse(u),v),w)),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[1690,1371]),
[iquote('0:Rew:1690.0,1371.0')] ).
cnf(1742,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[1690,1083]),
[iquote('0:Rew:1690.0,1083.0')] ).
cnf(1770,plain,
equal(double_divide(inverse(u),double_divide(inverse(v),multiply(double_divide(inverse(v),u),w))),w),
inference(rew,[status(thm),theory(equality)],[1690,1721]),
[iquote('0:Rew:1690.0,1721.0')] ).
cnf(1783,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1690,1694]),
[iquote('0:Rew:1690.0,1694.0')] ).
cnf(2028,plain,
equal(multiply(u,inverse(v)),double_divide(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[944,1570]),
[iquote('0:SpR:944.0,1570.0')] ).
cnf(2072,plain,
equal(double_divide(u,multiply(v,double_divide(w,inverse(double_divide(u,v))))),w),
inference(rew,[status(thm),theory(equality)],[2028,1566]),
[iquote('0:Rew:2028.0,1566.0')] ).
cnf(2099,plain,
equal(multiply(u,multiply(v,multiply(multiply(w,multiply(multiply(double_divide(x,y),multiply(multiply(double_divide(w,inverse(y)),x),inverse(v))),inverse(u))),multiply(z,x1)))),multiply(z,x1)),
inference(rew,[status(thm),theory(equality)],[2028,1648]),
[iquote('0:Rew:2028.0,1648.0')] ).
cnf(2139,plain,
equal(double_divide(double_divide(u,v),multiply(multiply(double_divide(w,inverse(v)),u),inverse(x))),multiply(w,x)),
inference(rew,[status(thm),theory(equality)],[2028,1358]),
[iquote('0:Rew:2028.0,1358.0')] ).
cnf(2235,plain,
equal(double_divide(u,multiply(v,double_divide(w,multiply(v,u)))),w),
inference(rew,[status(thm),theory(equality)],[2,2072]),
[iquote('0:Rew:2.0,2072.0')] ).
cnf(2262,plain,
equal(double_divide(double_divide(u,v),double_divide(w,inverse(multiply(double_divide(x,inverse(v)),u)))),multiply(x,w)),
inference(rew,[status(thm),theory(equality)],[2028,2139]),
[iquote('0:Rew:2028.0,2139.0')] ).
cnf(2263,plain,
equal(double_divide(double_divide(u,v),double_divide(w,double_divide(u,double_divide(x,inverse(v))))),multiply(x,w)),
inference(rew,[status(thm),theory(equality)],[813,2262]),
[iquote('0:Rew:813.0,2262.0')] ).
cnf(2466,plain,
equal(multiply(u,multiply(v,multiply(multiply(w,double_divide(u,inverse(multiply(double_divide(x,y),double_divide(v,inverse(multiply(double_divide(w,inverse(y)),x))))))),multiply(z,x1)))),multiply(z,x1)),
inference(rew,[status(thm),theory(equality)],[2028,2099]),
[iquote('0:Rew:2028.0,2099.0,2028.0,2099.0')] ).
cnf(2467,plain,
equal(multiply(u,multiply(v,multiply(multiply(w,double_divide(u,double_divide(double_divide(x,y),double_divide(v,double_divide(x,double_divide(w,inverse(y))))))),multiply(z,x1)))),multiply(z,x1)),
inference(rew,[status(thm),theory(equality)],[1690,2466,813]),
[iquote('0:Rew:1690.0,2466.0,813.0,2466.0,813.0,2466.0')] ).
cnf(2468,plain,
equal(multiply(u,multiply(v,multiply(multiply(w,double_divide(u,multiply(w,v))),multiply(x,y)))),multiply(x,y)),
inference(rew,[status(thm),theory(equality)],[2263,2467]),
[iquote('0:Rew:2263.0,2467.0')] ).
cnf(2556,plain,
equal(double_divide(inverse(u),double_divide(v,w)),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[2,1051]),
[iquote('0:SpR:2.0,1051.0')] ).
cnf(2589,plain,
equal(multiply(multiply(multiply(double_divide(inverse(u),v),w),inverse(u)),v),w),
inference(rew,[status(thm),theory(equality)],[2556,1770]),
[iquote('0:Rew:2556.0,1770.0')] ).
cnf(2608,plain,
equal(multiply(u,double_divide(v,double_divide(w,double_divide(inverse(v),u)))),w),
inference(rew,[status(thm),theory(equality)],[1411,2589,1690,813,1051]),
[iquote('0:Rew:1411.0,2589.0,1690.0,2589.0,813.0,2589.0,1051.0,2589.0,1411.0,2589.0')] ).
cnf(2696,plain,
equal(multiply(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),w),
inference(spr,[status(thm),theory(equality)],[753,2608]),
[iquote('0:SpR:753.0,2608.0')] ).
cnf(2713,plain,
equal(multiply(u,multiply(multiply(double_divide(v,u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[2556,2696]),
[iquote('0:Rew:2556.0,2696.0')] ).
cnf(2714,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[1411,2713]),
[iquote('0:Rew:1411.0,2713.0')] ).
cnf(3101,plain,
equal(double_divide(u,double_divide(v,double_divide(inverse(u),double_divide(w,x)))),multiply(multiply(x,w),v)),
inference(spr,[status(thm),theory(equality)],[2608,1427]),
[iquote('0:SpR:2608.0,1427.0')] ).
cnf(3154,plain,
equal(double_divide(u,double_divide(v,multiply(multiply(w,x),u))),multiply(multiply(w,x),v)),
inference(rew,[status(thm),theory(equality)],[2556,3101]),
[iquote('0:Rew:2556.0,3101.0')] ).
cnf(3314,plain,
equal(multiply(double_divide(double_divide(u,multiply(v,w)),v),x),multiply(u,multiply(w,x))),
inference(spr,[status(thm),theory(equality)],[1427,2468]),
[iquote('0:SpR:1427.0,2468.0')] ).
cnf(3319,plain,
equal(multiply(double_divide(u,double_divide(v,multiply(u,w))),x),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[1690,3314]),
[iquote('0:Rew:1690.0,3314.0')] ).
cnf(3547,plain,
equal(inverse(multiply(u,double_divide(v,multiply(u,w)))),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[2235,1021]),
[iquote('0:SpR:2235.0,1021.0')] ).
cnf(3605,plain,
equal(double_divide(u,double_divide(v,multiply(u,w))),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[1690,3547,813]),
[iquote('0:Rew:1690.0,3547.0,813.0,3547.0')] ).
cnf(3606,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[3605,3319]),
[iquote('0:Rew:3605.0,3319.0')] ).
cnf(3679,plain,
equal(double_divide(u,double_divide(v,multiply(w,multiply(x,u)))),multiply(multiply(x,w),v)),
inference(rew,[status(thm),theory(equality)],[3606,3154]),
[iquote('0:Rew:3606.0,3154.0')] ).
cnf(3681,plain,
equal(double_divide(inverse(u),double_divide(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[3606,2556]),
[iquote('0:Rew:3606.0,2556.0')] ).
cnf(3753,plain,
equal(double_divide(u,double_divide(v,multiply(w,multiply(x,u)))),multiply(w,multiply(x,v))),
inference(rew,[status(thm),theory(equality)],[3606,3679]),
[iquote('0:Rew:3606.0,3679.0')] ).
cnf(4035,plain,
equal(double_divide(u,double_divide(v,double_divide(inverse(u),double_divide(w,x)))),multiply(x,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[2608,2714]),
[iquote('0:SpR:2608.0,2714.0')] ).
cnf(4116,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[3753,4035,3681]),
[iquote('0:Rew:3753.0,4035.0,3681.0,4035.0')] ).
cnf(4118,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[4116,1783]),
[iquote('0:Rew:4116.0,1783.1')] ).
cnf(4143,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1411,4118]),
[iquote('0:Rew:1411.0,4118.1')] ).
cnf(4144,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[4143]),
[iquote('0:Obv:4143.1')] ).
cnf(4145,plain,
$false,
inference(unc,[status(thm)],[4144,1742]),
[iquote('0:UnC:4144.0,1742.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP107-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 04:32:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.38/1.58
% 1.38/1.58 SPASS V 3.9
% 1.38/1.58 SPASS beiseite: Proof found.
% 1.38/1.58 % SZS status Theorem
% 1.38/1.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.38/1.58 SPASS derived 2478 clauses, backtracked 0 clauses, performed 0 splits and kept 1192 clauses.
% 1.38/1.58 SPASS allocated 72073 KBytes.
% 1.38/1.58 SPASS spent 0:00:01.21 on the problem.
% 1.38/1.58 0:00:00.03 for the input.
% 1.38/1.58 0:00:00.00 for the FLOTTER CNF translation.
% 1.38/1.58 0:00:00.02 for inferences.
% 1.38/1.58 0:00:00.00 for the backtracking.
% 1.38/1.58 0:00:01.14 for the reduction.
% 1.38/1.58
% 1.38/1.58
% 1.38/1.58 Here is a proof with depth 15, length 117 :
% 1.38/1.58 % SZS output start Refutation
% See solution above
% 1.46/1.62 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 1.46/1.62
%------------------------------------------------------------------------------