TSTP Solution File: GRP102-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP102-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:45:18 EDT 2022
% Result : Unsatisfiable 0.70s 0.90s
% Output : Refutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of clauses : 117 ( 109 unt; 0 nHn; 117 RR)
% Number of literals : 135 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(v,u),w),double_divide(v,identity))),double_divide(identity,identity)),w),
file('GRP102-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP102-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP102-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP102-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP102-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(v,u),w),inverse(v))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.2')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(21,plain,
equal(double_divide(double_divide(double_divide(u,double_divide(identity,v)),w),inverse(u)),double_divide(double_divide(v,w),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(24,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,v),inverse(u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(26,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),inverse(double_divide(v,u))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(27,plain,
equal(double_divide(double_divide(u,double_divide(inverse(double_divide(v,u)),inverse(v))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(28,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,26]),
[iquote('0:Rew:6.0,26.0')] ).
cnf(29,plain,
equal(double_divide(double_divide(u,double_divide(multiply(u,v),inverse(v))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,27]),
[iquote('0:Rew:6.0,27.0')] ).
cnf(66,plain,
equal(multiply(inverse(identity),double_divide(u,double_divide(identity,inverse(v)))),inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[28,6]),
[iquote('0:SpR:28.0,6.0')] ).
cnf(68,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(u,v),w),inverse(double_divide(u,double_divide(identity,inverse(v)))))),inverse(identity)),w),
inference(spr,[status(thm),theory(equality)],[28,7]),
[iquote('0:SpR:28.0,7.0')] ).
cnf(71,plain,
equal(double_divide(double_divide(u,multiply(double_divide(identity,u),v)),inverse(identity)),double_divide(identity,inverse(v))),
inference(spr,[status(thm),theory(equality)],[28,7]),
[iquote('0:SpR:28.0,7.0')] ).
cnf(74,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[4,28]),
[iquote('0:SpR:4.0,28.0')] ).
cnf(75,plain,
equal(double_divide(inverse(u),inverse(identity)),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[3,74]),
[iquote('0:Rew:3.0,74.0')] ).
cnf(78,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(u,v),w),multiply(double_divide(identity,inverse(v)),u))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[6,68]),
[iquote('0:Rew:6.0,68.0')] ).
cnf(84,plain,
equal(double_divide(multiply(u,v),inverse(identity)),multiply(double_divide(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,75]),
[iquote('0:SpR:6.0,75.0')] ).
cnf(131,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(u,v),inverse(double_divide(inverse(w),double_divide(double_divide(identity,u),inverse(w)))))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[24,7]),
[iquote('0:SpR:24.0,7.0')] ).
cnf(138,plain,
equal(double_divide(double_divide(inverse(double_divide(identity,u)),identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,24]),
[iquote('0:SpR:4.0,24.0')] ).
cnf(140,plain,
equal(double_divide(double_divide(inverse(identity),multiply(identity,u)),inverse(identity)),double_divide(identity,inverse(u))),
inference(spr,[status(thm),theory(equality)],[28,24]),
[iquote('0:SpR:28.0,24.0')] ).
cnf(141,plain,
equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(multiply(identity,u),inverse(u))),
inference(spr,[status(thm),theory(equality)],[29,24]),
[iquote('0:SpR:29.0,24.0')] ).
cnf(143,plain,
equal(multiply(multiply(u,identity),identity),u),
inference(rew,[status(thm),theory(equality)],[75,138,3,6]),
[iquote('0:Rew:75.0,138.0,3.0,138.0,6.0,138.0')] ).
cnf(145,plain,
equal(double_divide(double_divide(inverse(identity),inverse(inverse(u))),inverse(identity)),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[13,140]),
[iquote('0:Rew:13.0,140.0')] ).
cnf(146,plain,
equal(double_divide(inverse(inverse(u)),inverse(u)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[12,141,75,3,13]),
[iquote('0:Rew:12.0,141.0,75.0,141.0,3.0,141.0,13.0,141.0')] ).
cnf(152,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(u,v),multiply(double_divide(double_divide(identity,u),inverse(w)),inverse(w)))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[6,131]),
[iquote('0:Rew:6.0,131.0')] ).
cnf(160,plain,
equal(multiply(inverse(inverse(identity)),identity),identity),
inference(spr,[status(thm),theory(equality)],[13,143]),
[iquote('0:SpR:13.0,143.0')] ).
cnf(163,plain,
equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),double_divide(identity,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[160,84]),
[iquote('0:SpR:160.0,84.0')] ).
cnf(169,plain,
equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),identity),
inference(rew,[status(thm),theory(equality)],[4,163]),
[iquote('0:Rew:4.0,163.0')] ).
cnf(175,plain,
equal(double_divide(identity,inverse(inverse(identity))),multiply(identity,identity)),
inference(spr,[status(thm),theory(equality)],[169,143]),
[iquote('0:SpR:169.0,143.0')] ).
cnf(177,plain,
equal(double_divide(identity,inverse(inverse(identity))),inverse(inverse(identity))),
inference(rew,[status(thm),theory(equality)],[13,175]),
[iquote('0:Rew:13.0,175.0')] ).
cnf(187,plain,
equal(multiply(inverse(inverse(identity)),identity),inverse(inverse(inverse(identity)))),
inference(spr,[status(thm),theory(equality)],[177,6]),
[iquote('0:SpR:177.0,6.0')] ).
cnf(194,plain,
equal(inverse(inverse(inverse(identity))),identity),
inference(rew,[status(thm),theory(equality)],[160,187]),
[iquote('0:Rew:160.0,187.0')] ).
cnf(248,plain,
equal(double_divide(inverse(identity),identity),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[194,146]),
[iquote('0:SpR:194.0,146.0')] ).
cnf(252,plain,
equal(inverse(inverse(identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[3,248]),
[iquote('0:Rew:3.0,248.0')] ).
cnf(255,plain,
equal(inverse(inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[252,194]),
[iquote('0:Rew:252.0,194.0')] ).
cnf(263,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[252,255]),
[iquote('0:Rew:252.0,255.0')] ).
cnf(265,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(v,u),w),inverse(v))),identity),w),
inference(rew,[status(thm),theory(equality)],[263,7]),
[iquote('0:Rew:263.0,7.0')] ).
cnf(267,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),identity),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[263,28]),
[iquote('0:Rew:263.0,28.0')] ).
cnf(268,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[263,15]),
[iquote('0:Rew:263.0,15.2')] ).
cnf(269,plain,
equal(double_divide(inverse(u),identity),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[263,75]),
[iquote('0:Rew:263.0,75.0')] ).
cnf(273,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,v),inverse(u))),identity),v),
inference(rew,[status(thm),theory(equality)],[263,24]),
[iquote('0:Rew:263.0,24.0')] ).
cnf(277,plain,
equal(double_divide(double_divide(double_divide(u,double_divide(identity,v)),w),inverse(u)),double_divide(double_divide(v,w),identity)),
inference(rew,[status(thm),theory(equality)],[263,21]),
[iquote('0:Rew:263.0,21.0')] ).
cnf(282,plain,
equal(multiply(identity,double_divide(u,double_divide(identity,inverse(v)))),inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[263,66]),
[iquote('0:Rew:263.0,66.0')] ).
cnf(283,plain,
equal(double_divide(double_divide(u,multiply(double_divide(identity,u),v)),identity),double_divide(identity,inverse(v))),
inference(rew,[status(thm),theory(equality)],[263,71]),
[iquote('0:Rew:263.0,71.0')] ).
cnf(286,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(multiply(u,v),w),multiply(double_divide(identity,inverse(v)),u))),identity),w),
inference(rew,[status(thm),theory(equality)],[263,78]),
[iquote('0:Rew:263.0,78.0')] ).
cnf(296,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),identity),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[263,145]),
[iquote('0:Rew:263.0,145.0')] ).
cnf(300,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(u,v),multiply(double_divide(double_divide(identity,u),inverse(w)),inverse(w)))),identity),v),
inference(rew,[status(thm),theory(equality)],[263,152]),
[iquote('0:Rew:263.0,152.0')] ).
cnf(321,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,269]),
[iquote('0:Rew:3.0,269.0')] ).
cnf(322,plain,
equal(inverse(inverse(multiply(u,identity))),u),
inference(rew,[status(thm),theory(equality)],[321,143]),
[iquote('0:Rew:321.0,143.0')] ).
cnf(325,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[321,322]),
[iquote('0:Rew:321.0,322.0')] ).
cnf(355,plain,
equal(multiply(double_divide(identity,inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,267,3]),
[iquote('0:Rew:6.0,267.0,3.0,267.0')] ).
cnf(363,plain,
equal(multiply(inverse(inverse(u)),identity),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,296,3]),
[iquote('0:Rew:6.0,296.0,3.0,296.0')] ).
cnf(364,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[325,363,321]),
[iquote('0:Rew:325.0,363.0,321.0,363.0')] ).
cnf(365,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[364,355]),
[iquote('0:Rew:364.0,355.0')] ).
cnf(379,plain,
equal(multiply(double_divide(double_divide(identity,u),inverse(v)),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[6,273,3]),
[iquote('0:Rew:6.0,273.0,3.0,273.0')] ).
cnf(380,plain,
equal(multiply(inverse(u),double_divide(double_divide(identity,v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[365,379]),
[iquote('0:Rew:365.0,379.0')] ).
cnf(384,plain,
equal(inverse(multiply(double_divide(identity,inverse(u)),v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[6,282,13]),
[iquote('0:Rew:6.0,282.0,13.0,282.0')] ).
cnf(385,plain,
equal(inverse(multiply(u,v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[364,384]),
[iquote('0:Rew:364.0,384.0')] ).
cnf(393,plain,
equal(multiply(double_divide(double_divide(double_divide(u,v),w),inverse(u)),v),w),
inference(rew,[status(thm),theory(equality)],[6,265,3]),
[iquote('0:Rew:6.0,265.0,3.0,265.0')] ).
cnf(394,plain,
equal(multiply(u,double_divide(double_divide(double_divide(v,u),w),inverse(v))),w),
inference(rew,[status(thm),theory(equality)],[365,393]),
[iquote('0:Rew:365.0,393.0')] ).
cnf(395,plain,
equal(multiply(multiply(double_divide(identity,u),v),u),double_divide(identity,inverse(v))),
inference(rew,[status(thm),theory(equality)],[6,283,3]),
[iquote('0:Rew:6.0,283.0,3.0,283.0')] ).
cnf(396,plain,
equal(multiply(u,multiply(double_divide(identity,u),v)),v),
inference(rew,[status(thm),theory(equality)],[365,395,364]),
[iquote('0:Rew:365.0,395.0,364.0,395.0')] ).
cnf(427,plain,
equal(double_divide(double_divide(double_divide(u,double_divide(identity,v)),w),inverse(u)),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[6,277,3]),
[iquote('0:Rew:6.0,277.0,3.0,277.0')] ).
cnf(435,plain,
equal(multiply(double_divide(double_divide(multiply(u,v),w),multiply(double_divide(identity,inverse(v)),u)),identity),w),
inference(rew,[status(thm),theory(equality)],[6,286,3]),
[iquote('0:Rew:6.0,286.0,3.0,286.0')] ).
cnf(436,plain,
equal(multiply(identity,double_divide(double_divide(multiply(u,v),w),multiply(v,u))),w),
inference(rew,[status(thm),theory(equality)],[365,435,364]),
[iquote('0:Rew:365.0,435.0,364.0,435.0')] ).
cnf(437,plain,
equal(inverse(multiply(multiply(u,v),double_divide(multiply(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[6,436,13]),
[iquote('0:Rew:6.0,436.0,13.0,436.0')] ).
cnf(441,plain,
equal(multiply(double_divide(double_divide(u,v),multiply(double_divide(double_divide(identity,u),inverse(w)),inverse(w))),identity),v),
inference(rew,[status(thm),theory(equality)],[6,300,3]),
[iquote('0:Rew:6.0,300.0,3.0,300.0')] ).
cnf(442,plain,
equal(multiply(identity,double_divide(double_divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[365,441,380]),
[iquote('0:Rew:365.0,441.0,380.0,441.0,365.0,441.0')] ).
cnf(443,plain,
equal(inverse(multiply(u,double_divide(u,v))),v),
inference(rew,[status(thm),theory(equality)],[6,442,13]),
[iquote('0:Rew:6.0,442.0,13.0,442.0')] ).
cnf(451,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[268]),
[iquote('0:Obv:268.2')] ).
cnf(452,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[365,451]),
[iquote('0:Rew:365.0,451.2,365.0,451.1')] ).
cnf(453,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[452]),
[iquote('0:Obv:452.1')] ).
cnf(458,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(spr,[status(thm),theory(equality)],[364,6]),
[iquote('0:SpR:364.0,6.0')] ).
cnf(464,plain,
equal(multiply(identity,inverse(u)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[365,458]),
[iquote('0:Rew:365.0,458.0')] ).
cnf(465,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[13,464]),
[iquote('0:Rew:13.0,464.0')] ).
cnf(466,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[465,325]),
[iquote('0:Rew:465.0,325.0')] ).
cnf(470,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[466,453]),
[iquote('0:Rew:466.0,453.0')] ).
cnf(478,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[470]),
[iquote('0:Obv:470.0')] ).
cnf(480,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[466,364]),
[iquote('0:SpR:466.0,364.0')] ).
cnf(483,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,466]),
[iquote('0:SpR:6.0,466.0')] ).
cnf(489,plain,
equal(double_divide(double_divide(double_divide(u,inverse(v)),w),inverse(u)),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[480,427]),
[iquote('0:Rew:480.0,427.0')] ).
cnf(490,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[480,396]),
[iquote('0:Rew:480.0,396.0')] ).
cnf(494,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[483,443]),
[iquote('0:Rew:483.0,443.0')] ).
cnf(495,plain,
equal(inverse(multiply(u,v)),double_divide(u,v)),
inference(rew,[status(thm),theory(equality)],[483,385]),
[iquote('0:Rew:483.0,385.0')] ).
cnf(496,plain,
equal(double_divide(double_divide(multiply(u,v),w),multiply(v,u)),w),
inference(rew,[status(thm),theory(equality)],[483,437]),
[iquote('0:Rew:483.0,437.0')] ).
cnf(497,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[483,495]),
[iquote('0:Rew:483.0,495.0')] ).
cnf(501,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[497,494]),
[iquote('0:Rew:497.0,494.0')] ).
cnf(504,plain,
equal(multiply(u,double_divide(inverse(v),double_divide(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[497,394]),
[iquote('0:Rew:497.0,394.0')] ).
cnf(508,plain,
equal(double_divide(multiply(u,v),double_divide(multiply(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[497,496]),
[iquote('0:Rew:497.0,496.0')] ).
cnf(509,plain,
equal(double_divide(inverse(u),double_divide(double_divide(u,inverse(v)),w)),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[497,489]),
[iquote('0:Rew:497.0,489.0')] ).
cnf(567,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[501,6]),
[iquote('0:SpR:501.0,6.0')] ).
cnf(572,plain,
equal(multiply(u,double_divide(inverse(v),w)),double_divide(double_divide(v,u),w)),
inference(spr,[status(thm),theory(equality)],[501,504]),
[iquote('0:SpR:501.0,504.0')] ).
cnf(575,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[497,501]),
[iquote('0:SpR:497.0,501.0')] ).
cnf(580,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[365,567]),
[iquote('0:Rew:365.0,567.0')] ).
cnf(701,plain,
equal(double_divide(u,inverse(v)),multiply(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[509,575]),
[iquote('0:SpR:509.0,575.0')] ).
cnf(763,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[580,490]),
[iquote('0:SpR:580.0,490.0')] ).
cnf(778,plain,
equal(multiply(u,multiply(v,inverse(w))),double_divide(double_divide(v,u),w)),
inference(rew,[status(thm),theory(equality)],[763,572]),
[iquote('0:Rew:763.0,572.0')] ).
cnf(1504,plain,
equal(inverse(double_divide(multiply(u,v),w)),multiply(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[508,580]),
[iquote('0:SpR:508.0,580.0')] ).
cnf(1527,plain,
equal(double_divide(multiply(u,v),double_divide(w,multiply(v,u))),w),
inference(spr,[status(thm),theory(equality)],[497,508]),
[iquote('0:SpR:497.0,508.0')] ).
cnf(1559,plain,
equal(multiply(u,multiply(v,w)),multiply(multiply(w,v),u)),
inference(rew,[status(thm),theory(equality)],[6,1504]),
[iquote('0:Rew:6.0,1504.0')] ).
cnf(2472,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[1527,580]),
[iquote('0:SpR:1527.0,580.0')] ).
cnf(2541,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[6,2472]),
[iquote('0:Rew:6.0,2472.0')] ).
cnf(4511,plain,
equal(double_divide(double_divide(u,v),inverse(w)),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[466,778]),
[iquote('0:SpR:466.0,778.0')] ).
cnf(4538,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,4511,701]),
[iquote('0:Rew:6.0,4511.0,701.0,4511.0')] ).
cnf(4540,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[4538,1559]),
[iquote('0:Rew:4538.0,1559.0')] ).
cnf(4597,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[4538,2541]),
[iquote('0:Rew:4538.0,2541.0')] ).
cnf(4605,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[4540,478]),
[iquote('0:Rew:4540.0,478.0')] ).
cnf(4619,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[4538,4597]),
[iquote('0:Rew:4538.0,4597.0')] ).
cnf(4644,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[4619,4605]),
[iquote('0:Rew:4619.0,4605.0')] ).
cnf(4645,plain,
$false,
inference(obv,[status(thm),theory(equality)],[4644]),
[iquote('0:Obv:4644.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP102-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 05:42:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/0.90
% 0.70/0.90 SPASS V 3.9
% 0.70/0.90 SPASS beiseite: Proof found.
% 0.70/0.90 % SZS status Theorem
% 0.70/0.90 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.70/0.90 SPASS derived 2322 clauses, backtracked 0 clauses, performed 0 splits and kept 500 clauses.
% 0.70/0.90 SPASS allocated 67449 KBytes.
% 0.70/0.90 SPASS spent 0:00:00.55 on the problem.
% 0.70/0.90 0:00:00.03 for the input.
% 0.70/0.90 0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.90 0:00:00.02 for inferences.
% 0.70/0.90 0:00:00.00 for the backtracking.
% 0.70/0.90 0:00:00.48 for the reduction.
% 0.70/0.90
% 0.70/0.90
% 0.70/0.90 Here is a proof with depth 7, length 117 :
% 0.70/0.90 % SZS output start Refutation
% See solution above
% 0.73/0.92 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.73/0.92
%------------------------------------------------------------------------------