TSTP Solution File: GRP432-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP432-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:47:27 EDT 2022
% Result : Unsatisfiable 21.03s 21.21s
% Output : Refutation 21.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 91 RR)
% Number of literals : 91 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(v,multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,v))),u)))),x),
file('GRP432-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP432-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,v))),y))),multiply(multiply(multiply(z,inverse(z)),inverse(x)),u)))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,x))),multiply(y,inverse(y))),multiply(w,u)))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,z)))))),inverse(multiply(z,w))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(9,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(w))),multiply(multiply(multiply(multiply(x,inverse(x)),inverse(multiply(y,v))),multiply(z,inverse(z))),u)))),multiply(y,multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(16,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(w))),multiply(x,u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(v,x))),multiply(z,inverse(z)))),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(30,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,multiply(w,inverse(multiply(multiply(x,multiply(y,inverse(y))),multiply(v,w))))))),x),
inference(spr,[status(thm),theory(equality)],[16,1]),
[iquote('0:SpR:16.0,1.0')] ).
cnf(35,plain,
equal(multiply(u,inverse(multiply(multiply(v,inverse(multiply(multiply(w,multiply(x,inverse(x))),multiply(y,v)))),multiply(w,u)))),y),
inference(spr,[status(thm),theory(equality)],[16,4]),
[iquote('0:SpR:16.0,4.0')] ).
cnf(101,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(multiply(x,inverse(x)),inverse(multiply(v,multiply(w,multiply(y,inverse(y))))))),
inference(spr,[status(thm),theory(equality)],[1,35]),
[iquote('0:SpR:1.0,35.0')] ).
cnf(131,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,w))),multiply(multiply(x,inverse(x)),inverse(multiply(v,w)))),
inference(spr,[status(thm),theory(equality)],[4,30]),
[iquote('0:SpR:4.0,30.0')] ).
cnf(173,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(multiply(multiply(y,inverse(y)),inverse(multiply(v,w))))),u)))),multiply(z,inverse(z))),
inference(spr,[status(thm),theory(equality)],[131,1]),
[iquote('0:SpR:131.0,1.0')] ).
cnf(213,plain,
equal(multiply(multiply(u,inverse(u)),inverse(v)),multiply(multiply(w,inverse(w)),inverse(v))),
inference(spr,[status(thm),theory(equality)],[1,131]),
[iquote('0:SpR:1.0,131.0')] ).
cnf(227,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[1,173]),
[iquote('0:Rew:1.0,173.0')] ).
cnf(236,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(multiply(w,inverse(w)),u)))),v),
inference(spr,[status(thm),theory(equality)],[227,1]),
[iquote('0:SpR:227.0,1.0')] ).
cnf(237,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(x,u)))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[227,4]),
[iquote('0:SpR:227.0,4.0')] ).
cnf(263,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))),u)))),v),
inference(spr,[status(thm),theory(equality)],[227,1]),
[iquote('0:SpR:227.0,1.0')] ).
cnf(289,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(inverse(w),u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,w)))))),inverse(multiply(z,inverse(z)))),y),
inference(spr,[status(thm),theory(equality)],[227,6]),
[iquote('0:SpR:227.0,6.0')] ).
cnf(362,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,inverse(w)))),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(multiply(z,inverse(z)),inverse(multiply(y,v))))),
inference(spr,[status(thm),theory(equality)],[227,3]),
[iquote('0:SpR:227.0,3.0')] ).
cnf(398,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(inverse(w),multiply(multiply(z,inverse(z)),multiply(multiply(x1,inverse(x1)),inverse(multiply(y,v))))))),
inference(spr,[status(thm),theory(equality)],[236,3]),
[iquote('0:SpR:236.0,3.0')] ).
cnf(437,plain,
equal(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),
inference(spr,[status(thm),theory(equality)],[213,227]),
[iquote('0:SpR:213.0,227.0')] ).
cnf(508,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(x),u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(multiply(z,inverse(z)),inverse(x)))),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[213,16]),
[iquote('0:SpR:213.0,16.0')] ).
cnf(526,plain,
equal(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(multiply(v,inverse(v)),inverse(w)))),multiply(x,inverse(x))),inverse(inverse(w))),
inference(rew,[status(thm),theory(equality)],[237,508]),
[iquote('0:Rew:237.0,508.0')] ).
cnf(575,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(multiply(v,inverse(v)),inverse(multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))))),multiply(y,inverse(y))),multiply(z,u)))),inverse(z)),
inference(spr,[status(thm),theory(equality)],[437,4]),
[iquote('0:SpR:437.0,4.0')] ).
cnf(583,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(v))),multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))),y))),multiply(multiply(multiply(z,inverse(z)),inverse(multiply(x1,inverse(x1)))),u)))),y),
inference(spr,[status(thm),theory(equality)],[437,3]),
[iquote('0:SpR:437.0,3.0')] ).
cnf(623,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(multiply(x,inverse(x))),u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(z,inverse(z)))),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[437,16]),
[iquote('0:SpR:437.0,16.0')] ).
cnf(643,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,u)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[526,575]),
[iquote('0:Rew:526.0,575.0')] ).
cnf(645,plain,
equal(inverse(inverse(multiply(u,inverse(u)))),multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))),multiply(x,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[237,623]),
[iquote('0:Rew:237.0,623.0')] ).
cnf(648,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))),x)),x),
inference(rew,[status(thm),theory(equality)],[263,583]),
[iquote('0:Rew:263.0,583.0')] ).
cnf(750,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(u,multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(1040,plain,
equal(inverse(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(inverse(multiply(w,inverse(w)))))))),v),
inference(spr,[status(thm),theory(equality)],[643,1]),
[iquote('0:SpR:643.0,1.0')] ).
cnf(1075,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[227,643]),
[iquote('0:SpR:227.0,643.0')] ).
cnf(1526,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(multiply(x,inverse(inverse(multiply(y,inverse(y)))))),u)))),multiply(multiply(multiply(z,inverse(z)),x),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[1040,16]),
[iquote('0:SpR:1040.0,16.0')] ).
cnf(1567,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),v)),
inference(spr,[status(thm),theory(equality)],[1040,213]),
[iquote('0:SpR:1040.0,213.0')] ).
cnf(1629,plain,
equal(inverse(inverse(multiply(u,inverse(inverse(multiply(v,inverse(v))))))),multiply(multiply(multiply(w,inverse(w)),u),multiply(x,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[237,1526]),
[iquote('0:Rew:237.0,1526.0')] ).
cnf(1966,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))))),u),
inference(spr,[status(thm),theory(equality)],[1040,1075]),
[iquote('0:SpR:1040.0,1075.0')] ).
cnf(1986,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(inverse(multiply(x,inverse(x)))),u)))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[1966,4]),
[iquote('0:SpR:1966.0,4.0')] ).
cnf(2003,plain,
equal(multiply(u,inverse(u)),multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1966,227]),
[iquote('0:SpR:1966.0,227.0')] ).
cnf(2088,plain,
equal(inverse(inverse(inverse(multiply(u,inverse(u))))),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[237,1986]),
[iquote('0:Rew:237.0,1986.0')] ).
cnf(2382,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(u,inverse(inverse(inverse(multiply(w,inverse(w))))))),
inference(spr,[status(thm),theory(equality)],[2088,750]),
[iquote('0:SpR:2088.0,750.0')] ).
cnf(2415,plain,
equal(inverse(inverse(inverse(multiply(u,inverse(u))))),inverse(inverse(inverse(multiply(v,inverse(v)))))),
inference(spr,[status(thm),theory(equality)],[2088]),
[iquote('0:SpR:2088.0,2088.0')] ).
cnf(2446,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(w,inverse(w))),inverse(inverse(inverse(multiply(x,inverse(x)))))))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(v,u))),multiply(z,inverse(z)))),
inference(spr,[status(thm),theory(equality)],[2088,16]),
[iquote('0:SpR:2088.0,16.0')] ).
cnf(2449,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(inverse(w),u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,w)))))),inverse(inverse(inverse(inverse(multiply(z,inverse(z))))))),y),
inference(spr,[status(thm),theory(equality)],[2088,6]),
[iquote('0:SpR:2088.0,6.0')] ).
cnf(2760,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(inverse(multiply(v,inverse(v))))),multiply(multiply(w,inverse(w)),u)))),inverse(inverse(multiply(x,inverse(x))))),
inference(spr,[status(thm),theory(equality)],[2415,236]),
[iquote('0:SpR:2415.0,236.0')] ).
cnf(2834,plain,
equal(inverse(inverse(multiply(u,inverse(u)))),inverse(inverse(multiply(v,inverse(v))))),
inference(rew,[status(thm),theory(equality)],[236,2760]),
[iquote('0:Rew:236.0,2760.0')] ).
cnf(2961,plain,
equal(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(multiply(v,inverse(v))))),w),multiply(multiply(x,inverse(x)),w)),
inference(spr,[status(thm),theory(equality)],[2834,1567]),
[iquote('0:SpR:2834.0,1567.0')] ).
cnf(3837,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[2003,1966]),
[iquote('0:SpR:2003.0,1966.0')] ).
cnf(4179,plain,
equal(inverse(inverse(multiply(u,inverse(u)))),multiply(multiply(v,inverse(v)),multiply(w,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[3837,645]),
[iquote('0:Rew:3837.0,645.0')] ).
cnf(4181,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(v,inverse(v)),w)),w),
inference(rew,[status(thm),theory(equality)],[3837,648]),
[iquote('0:Rew:3837.0,648.0')] ).
cnf(4230,plain,
equal(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(inverse(w),u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,w)))))),y),
inference(rew,[status(thm),theory(equality)],[3837,289]),
[iquote('0:Rew:3837.0,289.0')] ).
cnf(4325,plain,
equal(multiply(u,inverse(inverse(inverse(inverse(multiply(v,inverse(v))))))),u),
inference(rew,[status(thm),theory(equality)],[4230,2449]),
[iquote('0:Rew:4230.0,2449.0')] ).
cnf(5151,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(multiply(multiply(multiply(w,inverse(w)),inverse(multiply(inverse(multiply(x,inverse(x))),y))),multiply(z,inverse(z))),v))),y),
inference(spr,[status(thm),theory(equality)],[4181,4]),
[iquote('0:SpR:4181.0,4.0')] ).
cnf(5156,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(multiply(w,multiply(x,inverse(x))),v))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(w,inverse(multiply(z,inverse(z)))))),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[4181,16]),
[iquote('0:SpR:4181.0,16.0')] ).
cnf(5282,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(multiply(w,multiply(x,inverse(x))),v))),multiply(multiply(multiply(y,inverse(y)),inverse(w)),multiply(z,inverse(z)))),
inference(rew,[status(thm),theory(equality)],[3837,5156]),
[iquote('0:Rew:3837.0,5156.0')] ).
cnf(6780,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(v,inverse(v)),multiply(w,inverse(w)))))),u),
inference(spr,[status(thm),theory(equality)],[4179,4325]),
[iquote('0:SpR:4179.0,4325.0')] ).
cnf(6788,plain,
equal(inverse(multiply(multiply(u,inverse(u)),multiply(v,inverse(v)))),multiply(w,inverse(w))),
inference(spr,[status(thm),theory(equality)],[4179,2088]),
[iquote('0:SpR:4179.0,2088.0')] ).
cnf(6796,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(inverse(v),inverse(inverse(multiply(w,inverse(w))))))),v),
inference(spr,[status(thm),theory(equality)],[4179,1]),
[iquote('0:SpR:4179.0,1.0')] ).
cnf(7218,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(v,inverse(v)),inverse(inverse(inverse(multiply(w,inverse(w))))))))),u),
inference(spr,[status(thm),theory(equality)],[2088,6780]),
[iquote('0:SpR:2088.0,6780.0')] ).
cnf(7297,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(multiply(v,inverse(v)),multiply(multiply(multiply(w,inverse(w)),multiply(x,inverse(x))),y))),multiply(multiply(multiply(z,inverse(z)),inverse(multiply(x1,inverse(x1)))),u)))),y),
inference(spr,[status(thm),theory(equality)],[6788,3]),
[iquote('0:SpR:6788.0,3.0')] ).
cnf(7334,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(v,inverse(v)),multiply(multiply(multiply(w,inverse(w)),multiply(x,inverse(x))),multiply(y,inverse(y))))))),u),
inference(spr,[status(thm),theory(equality)],[6788,6780]),
[iquote('0:SpR:6788.0,6780.0')] ).
cnf(7669,plain,
equal(multiply(multiply(u,inverse(u)),multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),x)),x),
inference(rew,[status(thm),theory(equality)],[236,7297,3837]),
[iquote('0:Rew:236.0,7297.0,3837.0,7297.0')] ).
cnf(7672,plain,
equal(multiply(u,inverse(inverse(multiply(v,inverse(v))))),u),
inference(rew,[status(thm),theory(equality)],[7669,7334]),
[iquote('0:Rew:7669.0,7334.0')] ).
cnf(7675,plain,
equal(inverse(multiply(multiply(u,inverse(u)),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[7672,1040]),
[iquote('0:Rew:7672.0,1040.0')] ).
cnf(7679,plain,
equal(multiply(multiply(u,inverse(u)),inverse(inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[7672,6796]),
[iquote('0:Rew:7672.0,6796.0')] ).
cnf(7821,plain,
equal(multiply(inverse(multiply(u,inverse(u))),v),multiply(multiply(w,inverse(w)),v)),
inference(rew,[status(thm),theory(equality)],[7672,2961]),
[iquote('0:Rew:7672.0,2961.0')] ).
cnf(7859,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w))),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[7672,1629]),
[iquote('0:Rew:7672.0,1629.0')] ).
cnf(7953,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(v,inverse(v)))))),u),
inference(rew,[status(thm),theory(equality)],[7675,7218]),
[iquote('0:Rew:7675.0,7218.0')] ).
cnf(8008,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,inverse(w)))),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),multiply(y,v)),
inference(rew,[status(thm),theory(equality)],[7675,362]),
[iquote('0:Rew:7675.0,362.0')] ).
cnf(8100,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[7953,2382]),
[iquote('0:Rew:7953.0,2382.0')] ).
cnf(8194,plain,
equal(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(w))))),multiply(multiply(multiply(x,inverse(x)),inverse(multiply(v,u))),multiply(y,inverse(y)))),
inference(rew,[status(thm),theory(equality)],[7953,2446]),
[iquote('0:Rew:7953.0,2446.0')] ).
cnf(8740,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(multiply(multiply(w,inverse(w)),inverse(multiply(inverse(multiply(x,inverse(x))),y))),v))),y),
inference(rew,[status(thm),theory(equality)],[8100,5151]),
[iquote('0:Rew:8100.0,5151.0')] ).
cnf(9298,plain,
equal(multiply(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),w)),w),
inference(rew,[status(thm),theory(equality)],[8100,7669]),
[iquote('0:Rew:8100.0,7669.0')] ).
cnf(9302,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(multiply(w,multiply(x,inverse(x))),v))),multiply(multiply(y,inverse(y)),inverse(w))),
inference(rew,[status(thm),theory(equality)],[8100,5282]),
[iquote('0:Rew:8100.0,5282.0')] ).
cnf(9594,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(multiply(x,inverse(x)),inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[8100,101]),
[iquote('0:Rew:8100.0,101.0')] ).
cnf(9676,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(inverse(w),inverse(multiply(y,v))))),
inference(rew,[status(thm),theory(equality)],[9298,398]),
[iquote('0:Rew:9298.0,398.0')] ).
cnf(9703,plain,
equal(multiply(multiply(u,inverse(u)),v),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[8100,7859]),
[iquote('0:Rew:8100.0,7859.0')] ).
cnf(9711,plain,
equal(multiply(inverse(multiply(u,inverse(u))),v),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[9703,7821]),
[iquote('0:Rew:9703.0,7821.0')] ).
cnf(9733,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[9703,7679]),
[iquote('0:Rew:9703.0,7679.0')] ).
cnf(10101,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),inverse(inverse(inverse(multiply(v,w))))),
inference(rew,[status(thm),theory(equality)],[9703,9594]),
[iquote('0:Rew:9703.0,9594.0')] ).
cnf(10399,plain,
equal(inverse(inverse(inverse(multiply(inverse(u),inverse(inverse(inverse(v))))))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[10101,8008,8100,9703]),
[iquote('0:Rew:10101.0,8008.0,8100.0,8008.0,9703.0,8008.0')] ).
cnf(10421,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(v,u))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[9703,9302,8100]),
[iquote('0:Rew:9703.0,9302.0,8100.0,9302.0,9703.0,9302.0')] ).
cnf(10445,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),multiply(inverse(v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[8100,8194,9703]),
[iquote('0:Rew:8100.0,8194.0,8100.0,8194.0,9703.0,8194.0')] ).
cnf(10457,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(inverse(w),inverse(v))),
inference(rew,[status(thm),theory(equality)],[10445,10101]),
[iquote('0:Rew:10445.0,10101.0')] ).
cnf(10466,plain,
equal(multiply(inverse(inverse(inverse(inverse(u)))),inverse(inverse(v))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[10445,10399]),
[iquote('0:Rew:10445.0,10399.0')] ).
cnf(10474,plain,
equal(multiply(u,inverse(inverse(v))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[9733,10466]),
[iquote('0:Rew:9733.0,10466.0')] ).
cnf(10502,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[9733,8740,10421,9703,10474,9711]),
[iquote('0:Rew:9733.0,8740.0,10421.0,8740.0,9703.0,8740.0,9703.0,8740.0,10474.0,8740.0,9711.0,8740.0')] ).
cnf(10517,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[10502,9703]),
[iquote('0:Rew:10502.0,9703.0')] ).
cnf(10529,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[10502,10445]),
[iquote('0:Rew:10502.0,10445.0')] ).
cnf(10540,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),inverse(multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[10529,10457]),
[iquote('0:Rew:10529.0,10457.0')] ).
cnf(10637,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[10502,9676,10529,10540,10517]),
[iquote('0:Rew:10502.0,9676.0,10529.0,9676.0,10540.0,9676.0,10517.0,9676.0,10502.0,9676.0,10529.0,9676.0')] ).
cnf(10638,plain,
$false,
inference(unc,[status(thm)],[10637,2]),
[iquote('0:UnC:10637.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP432-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 20:56:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 21.03/21.21
% 21.03/21.21 SPASS V 3.9
% 21.03/21.21 SPASS beiseite: Proof found.
% 21.03/21.21 % SZS status Theorem
% 21.03/21.21 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.03/21.21 SPASS derived 8929 clauses, backtracked 0 clauses, performed 0 splits and kept 2839 clauses.
% 21.03/21.21 SPASS allocated 93418 KBytes.
% 21.03/21.21 SPASS spent 0:0:20.85 on the problem.
% 21.03/21.21 0:00:00.03 for the input.
% 21.03/21.21 0:00:00.00 for the FLOTTER CNF translation.
% 21.03/21.21 0:00:00.08 for inferences.
% 21.03/21.21 0:00:00.00 for the backtracking.
% 21.03/21.21 0:0:20.71 for the reduction.
% 21.03/21.21
% 21.03/21.21
% 21.03/21.21 Here is a proof with depth 13, length 91 :
% 21.03/21.21 % SZS output start Refutation
% See solution above
% 21.23/21.40 Formulae used in the proof : single_axiom prove_these_axioms_3
% 21.23/21.40
%------------------------------------------------------------------------------