TSTP Solution File: GRP417-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP417-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 11:47:23 EDT 2022
% Result : Unsatisfiable 21.23s 21.45s
% Output : Refutation 21.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 2
% Syntax : Number of clauses : 119 ( 119 unt; 0 nHn; 119 RR)
% Number of literals : 119 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 21 ( 4 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,inverse(w)))),inverse(multiply(inverse(u),u)))))),w),
file('GRP417-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP417-1.p',unknown),
[] ).
cnf(4,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v)))),inverse(multiply(inverse(multiply(w,multiply(v,inverse(x)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v)))))))))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,w))),inverse(multiply(inverse(u),u)))))),multiply(x,inverse(multiply(inverse(multiply(inverse(multiply(y,x)),multiply(y,inverse(w)))),inverse(multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(11,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,inverse(inverse(w))))),inverse(multiply(inverse(u),u))))),w),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(21,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,w))),inverse(multiply(inverse(u),u))))))),w),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(107,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),w)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(inverse(w))))),inverse(multiply(inverse(v),v)))),
inference(spr,[status(thm),theory(equality)],[11,1]),
[iquote('0:SpR:11.0,1.0')] ).
cnf(113,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),w)),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(inverse(w))))),inverse(multiply(inverse(v),v))))),
inference(spr,[status(thm),theory(equality)],[11,21]),
[iquote('0:SpR:11.0,21.0')] ).
cnf(151,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(inverse(multiply(v,inverse(w))))))),inverse(multiply(inverse(v),v))),w),
inference(spr,[status(thm),theory(equality)],[107,1]),
[iquote('0:SpR:107.0,1.0')] ).
cnf(153,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(inverse(multiply(v,w)))))),inverse(multiply(inverse(v),v)))),w),
inference(spr,[status(thm),theory(equality)],[107,21]),
[iquote('0:SpR:107.0,21.0')] ).
cnf(182,plain,
equal(multiply(u,inverse(inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(inverse(v),v)))))))),w),
inference(spr,[status(thm),theory(equality)],[107,11]),
[iquote('0:SpR:107.0,11.0')] ).
cnf(268,plain,
equal(inverse(multiply(inverse(multiply(u,multiply(v,inverse(w)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(u)))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(u)))),inverse(multiply(inverse(v),v)))))))),multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(u)))),inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(w,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))),
inference(spr,[status(thm),theory(equality)],[4,182]),
[iquote('0:SpR:4.0,182.0')] ).
cnf(269,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(x)))),inverse(multiply(inverse(inverse(multiply(v,w))),inverse(multiply(v,w)))))),multiply(v,inverse(inverse(multiply(w,inverse(multiply(x,inverse(multiply(inverse(w),w))))))))),
inference(spr,[status(thm),theory(equality)],[1,182]),
[iquote('0:SpR:1.0,182.0')] ).
cnf(287,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v)))),multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(x,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))))))))),x),
inference(rew,[status(thm),theory(equality)],[268,4]),
[iquote('0:Rew:268.0,4.0')] ).
cnf(390,plain,
equal(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(u,inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))),inverse(multiply(w,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))))))))))),w),
inference(spr,[status(thm),theory(equality)],[287]),
[iquote('0:SpR:287.0,287.0')] ).
cnf(494,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,inverse(inverse(multiply(w,inverse(x))))))),u)),x)),inverse(multiply(inverse(u),u)))))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[151,1]),
[iquote('0:SpR:151.0,1.0')] ).
cnf(537,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(inverse(v),v))),multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,w))),inverse(multiply(inverse(v),v)))),
inference(spr,[status(thm),theory(equality)],[21,151]),
[iquote('0:SpR:21.0,151.0')] ).
cnf(1617,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))),multiply(inverse(u),u)),
inference(spr,[status(thm),theory(equality)],[153,494]),
[iquote('0:SpR:153.0,494.0')] ).
cnf(1658,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))),w),
inference(spr,[status(thm),theory(equality)],[1617,11]),
[iquote('0:SpR:1617.0,11.0')] ).
cnf(1667,plain,
equal(multiply(inverse(u),inverse(inverse(multiply(u,inverse(multiply(multiply(inverse(u),u),inverse(multiply(inverse(u),u)))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))),
inference(spr,[status(thm),theory(equality)],[1617,182]),
[iquote('0:SpR:1617.0,182.0')] ).
cnf(1673,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),inverse(multiply(inverse(multiply(multiply(inverse(u),u),w)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))))))))),w),
inference(spr,[status(thm),theory(equality)],[1617,182]),
[iquote('0:SpR:1617.0,182.0')] ).
cnf(1674,plain,
equal(inverse(multiply(inverse(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))))),w),
inference(spr,[status(thm),theory(equality)],[1617,153]),
[iquote('0:SpR:1617.0,153.0')] ).
cnf(1675,plain,
equal(multiply(inverse(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),inverse(w))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))))),w),
inference(spr,[status(thm),theory(equality)],[1617,151]),
[iquote('0:SpR:1617.0,151.0')] ).
cnf(1679,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))))))),
inference(spr,[status(thm),theory(equality)],[1617,107]),
[iquote('0:SpR:1617.0,107.0')] ).
cnf(1917,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),w)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))))),inverse(multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(v),v)))),multiply(x,inverse(inverse(w))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),
inference(spr,[status(thm),theory(equality)],[1617,113]),
[iquote('0:SpR:1617.0,113.0')] ).
cnf(2000,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))))))),
inference(spr,[status(thm),theory(equality)],[1617,113]),
[iquote('0:SpR:1617.0,113.0')] ).
cnf(2071,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),w)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))))),multiply(inverse(v),inverse(inverse(multiply(v,inverse(multiply(inverse(w),inverse(multiply(inverse(v),v))))))))),
inference(rew,[status(thm),theory(equality)],[269,1917]),
[iquote('0:Rew:269.0,1917.0')] ).
cnf(2073,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(u),inverse(inverse(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(u),u))))))))),v),
inference(rew,[status(thm),theory(equality)],[2071,1673]),
[iquote('0:Rew:2071.0,1673.0')] ).
cnf(2509,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(u),v)),multiply(inverse(multiply(w,u)),multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[21,2073]),
[iquote('0:SpR:21.0,2073.0')] ).
cnf(2594,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(inverse(multiply(v,inverse(multiply(inverse(w),inverse(multiply(inverse(v),v))))))))),w),
inference(spr,[status(thm),theory(equality)],[2509,2073]),
[iquote('0:SpR:2509.0,2073.0')] ).
cnf(2601,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[2509]),
[iquote('0:SpR:2509.0,2509.0')] ).
cnf(3067,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,inverse(x)))),inverse(multiply(inverse(w),w)))))),multiply(u,y)),multiply(x,multiply(w,y))),
inference(spr,[status(thm),theory(equality)],[1,2601]),
[iquote('0:SpR:1.0,2601.0')] ).
cnf(3223,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[1617,2594]),
[iquote('0:SpR:1617.0,2594.0')] ).
cnf(3724,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[3223]),
[iquote('0:SpR:3223.0,3223.0')] ).
cnf(4029,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(u),u))))))),u),
inference(spr,[status(thm),theory(equality)],[3724,21]),
[iquote('0:SpR:3724.0,21.0')] ).
cnf(4102,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[3724,2601]),
[iquote('0:SpR:3724.0,2601.0')] ).
cnf(4112,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(inverse(w),v)),multiply(inverse(x),x))),
inference(spr,[status(thm),theory(equality)],[3724,2601]),
[iquote('0:SpR:3724.0,2601.0')] ).
cnf(4137,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(u)),inverse(u))))))),u),
inference(spr,[status(thm),theory(equality)],[3724,1]),
[iquote('0:SpR:3724.0,1.0')] ).
cnf(4204,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(u,inverse(v))))),u)),multiply(inverse(w),w))),inverse(multiply(inverse(u),u))),v),
inference(spr,[status(thm),theory(equality)],[3724,151]),
[iquote('0:SpR:3724.0,151.0')] ).
cnf(4212,plain,
equal(multiply(inverse(u),inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),inverse(multiply(inverse(u),u)))))))),w),
inference(spr,[status(thm),theory(equality)],[3724,182]),
[iquote('0:SpR:3724.0,182.0')] ).
cnf(4229,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w))),inverse(multiply(inverse(v),v))),multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,u))),inverse(multiply(inverse(v),v)))),
inference(spr,[status(thm),theory(equality)],[3724,537]),
[iquote('0:SpR:3724.0,537.0')] ).
cnf(4287,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(w),w))))))),u),
inference(spr,[status(thm),theory(equality)],[3724,4029]),
[iquote('0:SpR:3724.0,4029.0')] ).
cnf(4417,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),v)),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[4102,3724]),
[iquote('0:SpR:4102.0,3724.0')] ).
cnf(4418,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),v))),multiply(inverse(w),x)),multiply(inverse(multiply(y,w)),multiply(y,x))),
inference(spr,[status(thm),theory(equality)],[4102]),
[iquote('0:SpR:4102.0,4102.0')] ).
cnf(4424,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(w),w))),inverse(multiply(inverse(x),x))))))),u),
inference(spr,[status(thm),theory(equality)],[4102,4287]),
[iquote('0:SpR:4102.0,4287.0')] ).
cnf(4574,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),v))),multiply(inverse(w),x)),multiply(inverse(multiply(inverse(x),w)),multiply(inverse(y),y))),
inference(spr,[status(thm),theory(equality)],[4417,4112]),
[iquote('0:SpR:4417.0,4112.0')] ).
cnf(4598,plain,
equal(multiply(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(w)),inverse(w))))))),multiply(inverse(x),x)),multiply(w,multiply(inverse(w),u))),
inference(spr,[status(thm),theory(equality)],[4137,4112]),
[iquote('0:SpR:4137.0,4112.0')] ).
cnf(4616,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(w),w)))))),u),
inference(spr,[status(thm),theory(equality)],[3724,4137]),
[iquote('0:SpR:3724.0,4137.0')] ).
cnf(4636,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))),w),
inference(rew,[status(thm),theory(equality)],[4616,1658]),
[iquote('0:Rew:4616.0,1658.0')] ).
cnf(4641,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),w)),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))),multiply(inverse(v),inverse(inverse(multiply(v,inverse(multiply(inverse(w),inverse(multiply(inverse(v),v))))))))),
inference(rew,[status(thm),theory(equality)],[4616,2071]),
[iquote('0:Rew:4616.0,2071.0')] ).
cnf(4643,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))))),
inference(rew,[status(thm),theory(equality)],[4616,1679]),
[iquote('0:Rew:4616.0,1679.0')] ).
cnf(4644,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))))),
inference(rew,[status(thm),theory(equality)],[4616,2000]),
[iquote('0:Rew:4616.0,2000.0')] ).
cnf(4646,plain,
equal(multiply(inverse(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),inverse(w))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))),w),
inference(rew,[status(thm),theory(equality)],[4616,1675]),
[iquote('0:Rew:4616.0,1675.0')] ).
cnf(4647,plain,
equal(inverse(multiply(inverse(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),w)))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))),w),
inference(rew,[status(thm),theory(equality)],[4616,1674]),
[iquote('0:Rew:4616.0,1674.0')] ).
cnf(4651,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(w),u))),
inference(rew,[status(thm),theory(equality)],[4616,4598]),
[iquote('0:Rew:4616.0,4598.0')] ).
cnf(4652,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),w),
inference(rew,[status(thm),theory(equality)],[4616,4636]),
[iquote('0:Rew:4616.0,4636.0')] ).
cnf(4654,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),w))))),w),
inference(rew,[status(thm),theory(equality)],[4616,4647]),
[iquote('0:Rew:4616.0,4647.0')] ).
cnf(4656,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),u),
inference(rew,[status(thm),theory(equality)],[4654,4646]),
[iquote('0:Rew:4654.0,4646.0')] ).
cnf(4659,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(multiply(inverse(v),v),w)))),multiply(inverse(v),inverse(inverse(multiply(v,inverse(multiply(inverse(w),inverse(multiply(inverse(v),v))))))))),
inference(rew,[status(thm),theory(equality)],[4616,4641]),
[iquote('0:Rew:4616.0,4641.0')] ).
cnf(4662,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u))))))),multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),
inference(rew,[status(thm),theory(equality)],[4616,4644]),
[iquote('0:Rew:4616.0,4644.0')] ).
cnf(4861,plain,
equal(multiply(u,multiply(inverse(u),inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[4651,3724]),
[iquote('0:SpR:4651.0,3724.0')] ).
cnf(4890,plain,
equal(multiply(u,multiply(inverse(u),v)),multiply(w,multiply(inverse(w),v))),
inference(spr,[status(thm),theory(equality)],[4651]),
[iquote('0:SpR:4651.0,4651.0')] ).
cnf(4905,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[4651]),
[iquote('0:SpR:4651.0,4651.0')] ).
cnf(4923,plain,
equal(multiply(multiply(u,v),multiply(inverse(w),w)),multiply(multiply(u,x),multiply(inverse(multiply(y,x)),multiply(y,v)))),
inference(spr,[status(thm),theory(equality)],[2601,4651]),
[iquote('0:SpR:2601.0,4651.0')] ).
cnf(4925,plain,
equal(multiply(multiply(inverse(u),v),multiply(inverse(w),w)),multiply(multiply(inverse(x),x),multiply(inverse(multiply(y,u)),multiply(y,v)))),
inference(spr,[status(thm),theory(equality)],[4102,4651]),
[iquote('0:SpR:4102.0,4651.0')] ).
cnf(4938,plain,
equal(multiply(u,multiply(inverse(u),multiply(inverse(inverse(v)),w))),multiply(v,multiply(x,multiply(inverse(x),w)))),
inference(spr,[status(thm),theory(equality)],[4890]),
[iquote('0:SpR:4890.0,4890.0')] ).
cnf(4962,plain,
equal(multiply(inverse(multiply(u,v)),multiply(w,multiply(inverse(w),x))),multiply(inverse(multiply(y,v)),multiply(y,multiply(inverse(u),x)))),
inference(spr,[status(thm),theory(equality)],[4890,2601]),
[iquote('0:SpR:4890.0,2601.0')] ).
cnf(4989,plain,
equal(multiply(u,multiply(inverse(u),multiply(inverse(v),w))),multiply(multiply(inverse(x),x),multiply(inverse(multiply(y,v)),multiply(y,w)))),
inference(spr,[status(thm),theory(equality)],[4102,4890]),
[iquote('0:SpR:4102.0,4890.0')] ).
cnf(5105,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(w),multiply(inverse(inverse(u)),inverse(multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[4861,4890]),
[iquote('0:SpR:4861.0,4890.0')] ).
cnf(5367,plain,
equal(inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))),inverse(multiply(v,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),multiply(inverse(w),w))),v),
inference(spr,[status(thm),theory(equality)],[4905,390]),
[iquote('0:SpR:4905.0,390.0')] ).
cnf(5368,plain,
equal(inverse(multiply(u,multiply(inverse(u),inverse(multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))),inverse(multiply(w,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))),w),
inference(spr,[status(thm),theory(equality)],[4651,390]),
[iquote('0:SpR:4651.0,390.0')] ).
cnf(5388,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(multiply(inverse(w),w)),inverse(multiply(inverse(x),x)))))))),u),
inference(spr,[status(thm),theory(equality)],[4616]),
[iquote('0:SpR:4616.0,4616.0')] ).
cnf(5448,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[4616,5388]),
[iquote('0:Rew:4616.0,5388.0')] ).
cnf(5449,plain,
equal(multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))),inverse(multiply(v,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))),v),
inference(rew,[status(thm),theory(equality)],[5448,5367]),
[iquote('0:Rew:5448.0,5367.0')] ).
cnf(5451,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),w))))))),u),
inference(rew,[status(thm),theory(equality)],[5448,4424]),
[iquote('0:Rew:5448.0,4424.0')] ).
cnf(5456,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(inverse(v),v))),multiply(multiply(inverse(w),v),inverse(multiply(inverse(v),v)))),
inference(rew,[status(thm),theory(equality)],[5448,4229]),
[iquote('0:Rew:5448.0,4229.0')] ).
cnf(5463,plain,
equal(multiply(multiply(inverse(inverse(inverse(multiply(u,inverse(v))))),u),inverse(multiply(inverse(u),u))),v),
inference(rew,[status(thm),theory(equality)],[5448,4204]),
[iquote('0:Rew:5448.0,4204.0')] ).
cnf(5509,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(v),w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[5448,4418]),
[iquote('0:Rew:5448.0,4418.0')] ).
cnf(5510,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(v),w)),multiply(inverse(multiply(inverse(w),v)),multiply(inverse(x),x))),
inference(rew,[status(thm),theory(equality)],[5448,4574]),
[iquote('0:Rew:5448.0,4574.0')] ).
cnf(5527,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[5451,1667]),
[iquote('0:Rew:5451.0,1667.0')] ).
cnf(5538,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[5527,4656]),
[iquote('0:Rew:5527.0,4656.0')] ).
cnf(5539,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(v),v),u)),w)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[5527,4643]),
[iquote('0:Rew:5527.0,4643.0')] ).
cnf(5540,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(v),v),u)),w)),inverse(multiply(inverse(u),u))))))),multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),
inference(rew,[status(thm),theory(equality)],[5527,4662]),
[iquote('0:Rew:5527.0,4662.0')] ).
cnf(5544,plain,
equal(multiply(multiply(inverse(u),u),multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v))))),v),
inference(rew,[status(thm),theory(equality)],[5527,4652]),
[iquote('0:Rew:5527.0,4652.0')] ).
cnf(5547,plain,
equal(multiply(inverse(u),inverse(inverse(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(u),u)))))))),inverse(inverse(multiply(multiply(inverse(u),u),multiply(multiply(inverse(u),u),v))))),
inference(rew,[status(thm),theory(equality)],[5527,4659]),
[iquote('0:Rew:5527.0,4659.0')] ).
cnf(6275,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(multiply(inverse(inverse(v)),w),inverse(multiply(inverse(w),w)))))),multiply(u,x)),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[5456,3067]),
[iquote('0:Rew:5456.0,3067.0')] ).
cnf(6476,plain,
equal(inverse(inverse(multiply(multiply(inverse(u),u),multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(v),v)),w))))),w),
inference(rew,[status(thm),theory(equality)],[5547,4212]),
[iquote('0:Rew:5547.0,4212.0')] ).
cnf(6685,plain,
equal(inverse(multiply(u,multiply(inverse(u),inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[5449,5368]),
[iquote('0:Rew:5449.0,5368.0')] ).
cnf(6710,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(v),v),u)),w)),inverse(multiply(inverse(u),u)))))),multiply(inverse(w),multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[6685,5539]),
[iquote('0:Rew:6685.0,5539.0')] ).
cnf(6715,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v)))),inverse(multiply(inverse(v),multiply(inverse(u),u)))),
inference(rew,[status(thm),theory(equality)],[6710,5540]),
[iquote('0:Rew:6710.0,5540.0')] ).
cnf(6716,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[5448,6715]),
[iquote('0:Rew:5448.0,6715.0')] ).
cnf(6717,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[6716,5544]),
[iquote('0:Rew:6716.0,5544.0')] ).
cnf(6731,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[6717,6716]),
[iquote('0:Rew:6717.0,6716.0')] ).
cnf(6733,plain,
equal(inverse(inverse(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(v),v)),w)))),w),
inference(rew,[status(thm),theory(equality)],[6717,6476]),
[iquote('0:Rew:6717.0,6476.0')] ).
cnf(6737,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[6717,5509]),
[iquote('0:Rew:6717.0,5509.0')] ).
cnf(6738,plain,
equal(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[6717,5510]),
[iquote('0:Rew:6717.0,5510.0')] ).
cnf(6739,plain,
equal(multiply(u,multiply(inverse(u),multiply(inverse(v),w))),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[6717,4989]),
[iquote('0:Rew:6717.0,4989.0')] ).
cnf(6765,plain,
equal(multiply(multiply(inverse(u),v),multiply(inverse(w),w)),multiply(inverse(multiply(x,u)),multiply(x,v))),
inference(rew,[status(thm),theory(equality)],[6717,4925]),
[iquote('0:Rew:6717.0,4925.0')] ).
cnf(6935,plain,
equal(multiply(inverse(multiply(u,v)),multiply(w,multiply(inverse(w),x))),multiply(inverse(v),multiply(inverse(u),x))),
inference(rew,[status(thm),theory(equality)],[6737,4962]),
[iquote('0:Rew:6737.0,4962.0')] ).
cnf(6958,plain,
equal(multiply(multiply(u,v),multiply(inverse(w),w)),multiply(multiply(u,x),multiply(inverse(x),v))),
inference(rew,[status(thm),theory(equality)],[6737,4923]),
[iquote('0:Rew:6737.0,4923.0')] ).
cnf(6966,plain,
equal(multiply(inverse(inverse(multiply(multiply(inverse(inverse(u)),v),inverse(multiply(inverse(v),v))))),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6737,6275]),
[iquote('0:Rew:6737.0,6275.0')] ).
cnf(7121,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),v))),v),
inference(rew,[status(thm),theory(equality)],[6717,6733]),
[iquote('0:Rew:6717.0,6733.0')] ).
cnf(7172,plain,
equal(multiply(u,multiply(inverse(u),multiply(inverse(v),w))),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[6737,6739]),
[iquote('0:Rew:6737.0,6739.0')] ).
cnf(7175,plain,
equal(multiply(u,multiply(v,multiply(inverse(v),w))),multiply(inverse(inverse(u)),w)),
inference(rew,[status(thm),theory(equality)],[7172,4938]),
[iquote('0:Rew:7172.0,4938.0')] ).
cnf(7176,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(inverse(inverse(u)),inverse(multiply(inverse(w),w)))),
inference(rew,[status(thm),theory(equality)],[7172,5105]),
[iquote('0:Rew:7172.0,5105.0')] ).
cnf(7186,plain,
equal(multiply(multiply(inverse(u),v),multiply(inverse(w),w)),multiply(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[6737,6765]),
[iquote('0:Rew:6737.0,6765.0')] ).
cnf(7195,plain,
equal(multiply(inverse(inverse(inverse(multiply(u,v)))),w),multiply(inverse(v),multiply(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[7175,6935]),
[iquote('0:Rew:7175.0,6935.0')] ).
cnf(7227,plain,
equal(multiply(multiply(inverse(inverse(u)),multiply(inverse(v),v)),inverse(multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[7195,5463]),
[iquote('0:Rew:7195.0,5463.0')] ).
cnf(7228,plain,
equal(multiply(u,inverse(multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[5538,7227]),
[iquote('0:Rew:5538.0,7227.0')] ).
cnf(7306,plain,
equal(multiply(u,multiply(inverse(v),v)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[7228,7176]),
[iquote('0:Rew:7228.0,7176.0')] ).
cnf(7346,plain,
equal(multiply(multiply(u,v),multiply(inverse(v),w)),inverse(inverse(multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[7306,6958]),
[iquote('0:Rew:7306.0,6958.0')] ).
cnf(7347,plain,
equal(inverse(inverse(multiply(inverse(u),v))),multiply(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[7306,7186]),
[iquote('0:Rew:7306.0,7186.0')] ).
cnf(7353,plain,
equal(inverse(inverse(inverse(multiply(inverse(u),v)))),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[7306,6738]),
[iquote('0:Rew:7306.0,6738.0')] ).
cnf(7364,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[7347,7121]),
[iquote('0:Rew:7347.0,7121.0')] ).
cnf(7372,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[7364,6731]),
[iquote('0:Rew:7364.0,6731.0')] ).
cnf(7394,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[7372,7353]),
[iquote('0:Rew:7372.0,7353.0')] ).
cnf(7403,plain,
equal(multiply(multiply(u,v),multiply(inverse(v),w)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[7372,7346]),
[iquote('0:Rew:7372.0,7346.0')] ).
cnf(7455,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[7372,6966,7403,7394]),
[iquote('0:Rew:7372.0,6966.0,7403.0,6966.0,7372.0,6966.0,7394.0,6966.0')] ).
cnf(7456,plain,
$false,
inference(unc,[status(thm)],[7455,2]),
[iquote('0:UnC:7455.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP417-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 : Mon Jun 13 06:32:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 21.23/21.45
% 21.23/21.45 SPASS V 3.9
% 21.23/21.45 SPASS beiseite: Proof found.
% 21.23/21.45 % SZS status Theorem
% 21.23/21.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.23/21.45 SPASS derived 6718 clauses, backtracked 0 clauses, performed 0 splits and kept 2333 clauses.
% 21.23/21.45 SPASS allocated 115623 KBytes.
% 21.23/21.45 SPASS spent 0:0:21.10 on the problem.
% 21.23/21.45 0:00:00.04 for the input.
% 21.23/21.45 0:00:00.00 for the FLOTTER CNF translation.
% 21.23/21.45 0:00:00.14 for inferences.
% 21.23/21.45 0:00:00.00 for the backtracking.
% 21.23/21.45 0:0:20.90 for the reduction.
% 21.23/21.45
% 21.23/21.45
% 21.23/21.45 Here is a proof with depth 15, length 119 :
% 21.23/21.45 % SZS output start Refutation
% See solution above
% 21.52/21.75 Formulae used in the proof : single_axiom prove_these_axioms_3
% 21.52/21.75
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