TSTP Solution File: GRP053-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP053-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:45:03 EDT 2022
% Result : Unsatisfiable 21.82s 21.98s
% Output : Refutation 22.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 2
% Syntax : Number of clauses : 124 ( 119 unt; 0 nHn; 124 RR)
% Number of literals : 132 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 21 ( 4 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 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('GRP053-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP053-1.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(4273,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(u),u),a2),a2) ),
inference(spl,[status(thm),theory(equality)],[3724,2]),
[iquote('0:SpL:3724.0,2.2')] ).
cnf(4289,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(4419,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(4420,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(4426,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)],[4102,4289]),
[iquote('0:SpR:4102.0,4289.0')] ).
cnf(4576,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)],[4419,4112]),
[iquote('0:SpR:4419.0,4112.0')] ).
cnf(4600,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(4618,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(4638,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)],[4618,1658]),
[iquote('0:Rew:4618.0,1658.0')] ).
cnf(4643,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)],[4618,2071]),
[iquote('0:Rew:4618.0,2071.0')] ).
cnf(4645,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)],[4618,1679]),
[iquote('0:Rew:4618.0,1679.0')] ).
cnf(4646,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)],[4618,2000]),
[iquote('0:Rew:4618.0,2000.0')] ).
cnf(4648,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)],[4618,1675]),
[iquote('0:Rew:4618.0,1675.0')] ).
cnf(4649,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)],[4618,1674]),
[iquote('0:Rew:4618.0,1674.0')] ).
cnf(4653,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(w),u))),
inference(rew,[status(thm),theory(equality)],[4618,4600]),
[iquote('0:Rew:4618.0,4600.0')] ).
cnf(4654,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)],[4618,4638]),
[iquote('0:Rew:4618.0,4638.0')] ).
cnf(4656,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)],[4618,4649]),
[iquote('0:Rew:4618.0,4649.0')] ).
cnf(4658,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)],[4656,4648]),
[iquote('0:Rew:4656.0,4648.0')] ).
cnf(4661,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)],[4618,4643]),
[iquote('0:Rew:4618.0,4643.0')] ).
cnf(4664,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)],[4618,4646]),
[iquote('0:Rew:4618.0,4646.0')] ).
cnf(4863,plain,
equal(multiply(u,multiply(inverse(u),inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[4653,3724]),
[iquote('0:SpR:4653.0,3724.0')] ).
cnf(4892,plain,
equal(multiply(u,multiply(inverse(u),v)),multiply(w,multiply(inverse(w),v))),
inference(spr,[status(thm),theory(equality)],[4653]),
[iquote('0:SpR:4653.0,4653.0')] ).
cnf(4907,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[4653]),
[iquote('0:SpR:4653.0,4653.0')] ).
cnf(4925,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)],[2601,4653]),
[iquote('0:SpR:2601.0,4653.0')] ).
cnf(4927,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)],[4102,4653]),
[iquote('0:SpR:4102.0,4653.0')] ).
cnf(4940,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)],[4892]),
[iquote('0:SpR:4892.0,4892.0')] ).
cnf(4964,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)],[4892,2601]),
[iquote('0:SpR:4892.0,2601.0')] ).
cnf(4991,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)],[4102,4892]),
[iquote('0:SpR:4102.0,4892.0')] ).
cnf(5107,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)],[4863,4892]),
[iquote('0:SpR:4863.0,4892.0')] ).
cnf(5369,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)],[4907,390]),
[iquote('0:SpR:4907.0,390.0')] ).
cnf(5370,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)],[4653,390]),
[iquote('0:SpR:4653.0,390.0')] ).
cnf(5390,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)],[4618]),
[iquote('0:SpR:4618.0,4618.0')] ).
cnf(5450,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[4618,5390]),
[iquote('0:Rew:4618.0,5390.0')] ).
cnf(5451,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)],[5450,5369]),
[iquote('0:Rew:5450.0,5369.0')] ).
cnf(5453,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),w))))))),u),
inference(rew,[status(thm),theory(equality)],[5450,4426]),
[iquote('0:Rew:5450.0,4426.0')] ).
cnf(5458,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)],[5450,4229]),
[iquote('0:Rew:5450.0,4229.0')] ).
cnf(5465,plain,
equal(multiply(multiply(inverse(inverse(inverse(multiply(u,inverse(v))))),u),inverse(multiply(inverse(u),u))),v),
inference(rew,[status(thm),theory(equality)],[5450,4204]),
[iquote('0:Rew:5450.0,4204.0')] ).
cnf(5511,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)],[5450,4420]),
[iquote('0:Rew:5450.0,4420.0')] ).
cnf(5512,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)],[5450,4576]),
[iquote('0:Rew:5450.0,4576.0')] ).
cnf(5529,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)],[5453,1667]),
[iquote('0:Rew:5453.0,1667.0')] ).
cnf(5540,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[5529,4658]),
[iquote('0:Rew:5529.0,4658.0')] ).
cnf(5541,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)],[5529,4645]),
[iquote('0:Rew:5529.0,4645.0')] ).
cnf(5542,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)],[5529,4664]),
[iquote('0:Rew:5529.0,4664.0')] ).
cnf(5546,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)],[5529,4654]),
[iquote('0:Rew:5529.0,4654.0')] ).
cnf(5549,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)],[5529,4661]),
[iquote('0:Rew:5529.0,4661.0')] ).
cnf(6277,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)],[5458,3067]),
[iquote('0:Rew:5458.0,3067.0')] ).
cnf(6478,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)],[5549,4212]),
[iquote('0:Rew:5549.0,4212.0')] ).
cnf(6687,plain,
equal(inverse(multiply(u,multiply(inverse(u),inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[5451,5370]),
[iquote('0:Rew:5451.0,5370.0')] ).
cnf(6712,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)],[6687,5541]),
[iquote('0:Rew:6687.0,5541.0')] ).
cnf(6717,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)],[6712,5542]),
[iquote('0:Rew:6712.0,5542.0')] ).
cnf(6718,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[5450,6717]),
[iquote('0:Rew:5450.0,6717.0')] ).
cnf(6719,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[6718,5546]),
[iquote('0:Rew:6718.0,5546.0')] ).
cnf(6733,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[6719,6718]),
[iquote('0:Rew:6719.0,6718.0')] ).
cnf(6735,plain,
equal(inverse(inverse(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(v),v)),w)))),w),
inference(rew,[status(thm),theory(equality)],[6719,6478]),
[iquote('0:Rew:6719.0,6478.0')] ).
cnf(6739,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[6719,5511]),
[iquote('0:Rew:6719.0,5511.0')] ).
cnf(6740,plain,
equal(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[6719,5512]),
[iquote('0:Rew:6719.0,5512.0')] ).
cnf(6741,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)],[6719,4991]),
[iquote('0:Rew:6719.0,4991.0')] ).
cnf(6761,plain,
( ~ 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)],[6719,4273]),
[iquote('0:Rew:6719.0,4273.2')] ).
cnf(6768,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)],[6719,4927]),
[iquote('0:Rew:6719.0,4927.0')] ).
cnf(6938,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)],[6739,4964]),
[iquote('0:Rew:6739.0,4964.0')] ).
cnf(6961,plain,
equal(multiply(multiply(u,v),multiply(inverse(w),w)),multiply(multiply(u,x),multiply(inverse(x),v))),
inference(rew,[status(thm),theory(equality)],[6739,4925]),
[iquote('0:Rew:6739.0,4925.0')] ).
cnf(6969,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)],[6739,6277]),
[iquote('0:Rew:6739.0,6277.0')] ).
cnf(7124,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),v))),v),
inference(rew,[status(thm),theory(equality)],[6719,6735]),
[iquote('0:Rew:6719.0,6735.0')] ).
cnf(7175,plain,
equal(multiply(u,multiply(inverse(u),multiply(inverse(v),w))),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[6739,6741]),
[iquote('0:Rew:6739.0,6741.0')] ).
cnf(7178,plain,
equal(multiply(u,multiply(v,multiply(inverse(v),w))),multiply(inverse(inverse(u)),w)),
inference(rew,[status(thm),theory(equality)],[7175,4940]),
[iquote('0:Rew:7175.0,4940.0')] ).
cnf(7179,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(inverse(inverse(u)),inverse(multiply(inverse(w),w)))),
inference(rew,[status(thm),theory(equality)],[7175,5107]),
[iquote('0:Rew:7175.0,5107.0')] ).
cnf(7189,plain,
equal(multiply(multiply(inverse(u),v),multiply(inverse(w),w)),multiply(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[6739,6768]),
[iquote('0:Rew:6739.0,6768.0')] ).
cnf(7198,plain,
equal(multiply(inverse(inverse(inverse(multiply(u,v)))),w),multiply(inverse(v),multiply(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[7178,6938]),
[iquote('0:Rew:7178.0,6938.0')] ).
cnf(7230,plain,
equal(multiply(multiply(inverse(inverse(u)),multiply(inverse(v),v)),inverse(multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[7198,5465]),
[iquote('0:Rew:7198.0,5465.0')] ).
cnf(7231,plain,
equal(multiply(u,inverse(multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[5540,7230]),
[iquote('0:Rew:5540.0,7230.0')] ).
cnf(7309,plain,
equal(multiply(u,multiply(inverse(v),v)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[7231,7179]),
[iquote('0:Rew:7231.0,7179.0')] ).
cnf(7349,plain,
equal(multiply(multiply(u,v),multiply(inverse(v),w)),inverse(inverse(multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[7309,6961]),
[iquote('0:Rew:7309.0,6961.0')] ).
cnf(7350,plain,
equal(inverse(inverse(multiply(inverse(u),v))),multiply(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[7309,7189]),
[iquote('0:Rew:7309.0,7189.0')] ).
cnf(7356,plain,
equal(inverse(inverse(inverse(multiply(inverse(u),v)))),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[7309,6740]),
[iquote('0:Rew:7309.0,6740.0')] ).
cnf(7367,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[7350,7124]),
[iquote('0:Rew:7350.0,7124.0')] ).
cnf(7375,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[7367,6733]),
[iquote('0:Rew:7367.0,6733.0')] ).
cnf(7397,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[7375,7356]),
[iquote('0:Rew:7375.0,7356.0')] ).
cnf(7406,plain,
equal(multiply(multiply(u,v),multiply(inverse(v),w)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[7375,7349]),
[iquote('0:Rew:7375.0,7349.0')] ).
cnf(7458,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[7375,6969,7406,7397]),
[iquote('0:Rew:7375.0,6969.0,7406.0,6969.0,7375.0,6969.0,7397.0,6969.0')] ).
cnf(7547,plain,
( ~ 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)],[6761]),
[iquote('0:Obv:6761.2')] ).
cnf(7548,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[7458,7547]),
[iquote('0:Rew:7458.0,7547.1')] ).
cnf(7549,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[7548]),
[iquote('0:Obv:7548.1')] ).
cnf(7550,plain,
$false,
inference(unc,[status(thm)],[7549,3724]),
[iquote('0:UnC:7549.0,3724.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP053-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.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 02:34:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 21.82/21.98
% 21.82/21.98 SPASS V 3.9
% 21.82/21.98 SPASS beiseite: Proof found.
% 21.82/21.98 % SZS status Theorem
% 21.82/21.98 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.82/21.98 SPASS derived 6712 clauses, backtracked 0 clauses, performed 0 splits and kept 2314 clauses.
% 21.82/21.98 SPASS allocated 115628 KBytes.
% 21.82/21.98 SPASS spent 0:0:21.61 on the problem.
% 21.82/21.98 0:00:00.04 for the input.
% 21.82/21.98 0:00:00.00 for the FLOTTER CNF translation.
% 21.82/21.98 0:00:00.14 for inferences.
% 21.82/21.98 0:00:00.00 for the backtracking.
% 21.82/21.98 0:0:21.41 for the reduction.
% 21.82/21.98
% 21.82/21.98
% 21.82/21.98 Here is a proof with depth 15, length 124 :
% 21.82/21.98 % SZS output start Refutation
% See solution above
% 22.05/22.26 Formulae used in the proof : single_axiom prove_these_axioms
% 22.05/22.26
%------------------------------------------------------------------------------