TSTP Solution File: GRP437-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:47:28 EDT 2022
% Result : Unsatisfiable 62.90s 63.08s
% Output : Refutation 63.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 2
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 81 RR)
% Number of literals : 81 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 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(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),u))))),x),
file('GRP437-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP437-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,x))),inverse(y))),multiply(y,multiply(w,u))))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),y)))),multiply(z,multiply(multiply(inverse(z),inverse(x)),u))))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(15,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,u))),x)))),inverse(multiply(multiply(y,multiply(multiply(inverse(y),inverse(multiply(x,z))),inverse(x1))),multiply(x1,w)))),z),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(17,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(x))),multiply(x,multiply(y,u))))),multiply(z,multiply(multiply(inverse(z),inverse(multiply(w,y))),inverse(v)))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(27,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,x))),w))),inverse(v))),x),
inference(spr,[status(thm),theory(equality)],[17,3]),
[iquote('0:SpR:17.0,3.0')] ).
cnf(83,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),y)))),multiply(z,multiply(multiply(inverse(z),inverse(x)),x1)))),multiply(x2,multiply(multiply(inverse(x2),inverse(y)),u))))),x1),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(104,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),multiply(y,multiply(multiply(inverse(y),inverse(multiply(multiply(inverse(z),inverse(multiply(multiply(inverse(w),inverse(multiply(x1,v))),x1))),x))),inverse(z)))),
inference(spr,[status(thm),theory(equality)],[27,17]),
[iquote('0:SpR:27.0,17.0')] ).
cnf(105,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(u),inverse(multiply(x,y))),x))),z))),inverse(w))),y))),z),
inference(spr,[status(thm),theory(equality)],[27,3]),
[iquote('0:SpR:27.0,3.0')] ).
cnf(117,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,y))),inverse(z))))),x1))),inverse(v))),inverse(multiply(multiply(z,multiply(x,inverse(x2))),multiply(x2,multiply(y,x1))))),
inference(spr,[status(thm),theory(equality)],[17,27]),
[iquote('0:SpR:17.0,27.0')] ).
cnf(119,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,inverse(multiply(w,multiply(x,multiply(multiply(inverse(x),inverse(multiply(y,w))),v))))))),inverse(z))),multiply(x1,multiply(multiply(inverse(x1),inverse(y)),inverse(z)))),
inference(spr,[status(thm),theory(equality)],[5,27]),
[iquote('0:SpR:5.0,27.0')] ).
cnf(122,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(v)),inverse(w))),multiply(x,multiply(multiply(inverse(x),inverse(v)),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[1,119]),
[iquote('0:Rew:1.0,119.0')] ).
cnf(161,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(y))))),z))),inverse(v))),multiply(multiply(inverse(z),inverse(x)),inverse(y))),
inference(spr,[status(thm),theory(equality)],[122,27]),
[iquote('0:SpR:122.0,27.0')] ).
cnf(181,plain,
equal(inverse(multiply(multiply(u,multiply(v,inverse(w))),multiply(w,multiply(x,y)))),multiply(multiply(inverse(y),inverse(multiply(v,x))),inverse(u))),
inference(rew,[status(thm),theory(equality)],[161,117]),
[iquote('0:Rew:161.0,117.0')] ).
cnf(304,plain,
equal(multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(multiply(inverse(w),inverse(multiply(x,y))),x))),z))),inverse(v)),inverse(multiply(y,multiply(w,multiply(z,u))))),
inference(spr,[status(thm),theory(equality)],[27,181]),
[iquote('0:SpR:27.0,181.0')] ).
cnf(307,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),multiply(y,inverse(multiply(v,multiply(w,multiply(x,y)))))),
inference(rew,[status(thm),theory(equality)],[304,104]),
[iquote('0:Rew:304.0,104.0')] ).
cnf(308,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,inverse(multiply(w,multiply(u,multiply(x,v))))),w))),x),
inference(rew,[status(thm),theory(equality)],[304,105]),
[iquote('0:Rew:304.0,105.0')] ).
cnf(322,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(multiply(x,multiply(y,multiply(v,w)))))))),inverse(y))),x),
inference(spr,[status(thm),theory(equality)],[308,27]),
[iquote('0:SpR:308.0,27.0')] ).
cnf(340,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,x))),w))),multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(y,x))),y)))),
inference(spr,[status(thm),theory(equality)],[27,308]),
[iquote('0:SpR:27.0,308.0')] ).
cnf(613,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(inverse(w),inverse(multiply(multiply(inverse(x),inverse(multiply(y,z))),y))))),inverse(w)))),inverse(v))),inverse(multiply(multiply(inverse(x),inverse(multiply(x1,z))),x1))),
inference(spr,[status(thm),theory(equality)],[340,27]),
[iquote('0:SpR:340.0,27.0')] ).
cnf(663,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,w))),v)),inverse(multiply(multiply(inverse(u),inverse(multiply(x,w))),x))),
inference(rew,[status(thm),theory(equality)],[27,613]),
[iquote('0:Rew:27.0,613.0')] ).
cnf(718,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(multiply(multiply(inverse(x),inverse(multiply(y,z))),y)))))),inverse(x1))),multiply(inverse(x),inverse(multiply(multiply(x1,multiply(v,w)),z)))),
inference(spr,[status(thm),theory(equality)],[663,322]),
[iquote('0:SpR:663.0,322.0')] ).
cnf(792,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(u)))))),v)),inverse(multiply(y,inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(multiply(x,z))),y))))))),
inference(spr,[status(thm),theory(equality)],[5,663]),
[iquote('0:SpR:5.0,663.0')] ).
cnf(803,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(u)))))),v)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[1,792]),
[iquote('0:Rew:1.0,792.0')] ).
cnf(1045,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),u))))),v)),inverse(x)),
inference(spr,[status(thm),theory(equality)],[307,803]),
[iquote('0:SpR:307.0,803.0')] ).
cnf(1130,plain,
equal(inverse(multiply(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(inverse(w),inverse(x))))),inverse(y))),multiply(y,multiply(v,inverse(w))))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[181,1045]),
[iquote('0:SpR:181.0,1045.0')] ).
cnf(1142,plain,
equal(multiply(multiply(inverse(inverse(u)),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(inverse(u),inverse(x))))),w))),inverse(v)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[181,1130]),
[iquote('0:Rew:181.0,1130.0')] ).
cnf(1281,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(inverse(w))),multiply(inverse(inverse(x)),inverse(multiply(multiply(inverse(y),inverse(multiply(z,multiply(inverse(x),inverse(w))))),z)))))),inverse(v))),inverse(y)),
inference(spr,[status(thm),theory(equality)],[1142,27]),
[iquote('0:SpR:1142.0,27.0')] ).
cnf(1343,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(inverse(w))),inverse(inverse(x)))),multiply(inverse(x),inverse(w))))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[718,1281]),
[iquote('0:Rew:718.0,1281.0')] ).
cnf(1767,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(x,multiply(multiply(inverse(x),inverse(inverse(y))),inverse(inverse(z)))),multiply(inverse(z),inverse(y))))),inverse(v)))),
inference(spr,[status(thm),theory(equality)],[1343,122]),
[iquote('0:SpR:1343.0,122.0')] ).
cnf(1785,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(inverse(v))),inverse(v))),inverse(multiply(multiply(inverse(u),inverse(multiply(w,inverse(multiply(multiply(x,multiply(multiply(inverse(x),inverse(inverse(y))),inverse(inverse(z)))),multiply(inverse(z),inverse(y))))))),w))),
inference(spr,[status(thm),theory(equality)],[1343,663]),
[iquote('0:SpR:1343.0,663.0')] ).
cnf(1848,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),multiply(w,multiply(inverse(w),inverse(v)))),
inference(rew,[status(thm),theory(equality)],[1343,1767]),
[iquote('0:Rew:1343.0,1767.0')] ).
cnf(1936,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(inverse(v),multiply(inverse(w),inverse(multiply(x,multiply(y,multiply(inverse(y),inverse(w))))))))),inverse(v))),x),
inference(spr,[status(thm),theory(equality)],[1848,322]),
[iquote('0:SpR:1848.0,322.0')] ).
cnf(1987,plain,
equal(multiply(u,multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(inverse(w))),inverse(inverse(x)))),multiply(inverse(x),inverse(w)))))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[1343,1848]),
[iquote('0:SpR:1343.0,1848.0')] ).
cnf(1995,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[1343,1987]),
[iquote('0:Rew:1343.0,1987.0')] ).
cnf(2007,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(w,multiply(inverse(w),inverse(inverse(u))))),
inference(spr,[status(thm),theory(equality)],[1995,1848]),
[iquote('0:SpR:1995.0,1848.0')] ).
cnf(2070,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(u,multiply(x,inverse(x)))))),w))),v),
inference(spr,[status(thm),theory(equality)],[1995,308]),
[iquote('0:SpR:1995.0,308.0')] ).
cnf(2079,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),x))),inverse(v))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[1995,27]),
[iquote('0:SpR:1995.0,27.0')] ).
cnf(2778,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(u,multiply(x,inverse(x)))))),w))),multiply(multiply(y,inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(v)),y))))),z)),
inference(spr,[status(thm),theory(equality)],[1045,2070]),
[iquote('0:SpR:1045.0,2070.0')] ).
cnf(2783,plain,
equal(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),inverse(u)))))),multiply(y,multiply(z,multiply(multiply(inverse(z),inverse(multiply(multiply(x1,inverse(x1)),y))),x)))),
inference(spr,[status(thm),theory(equality)],[15,2070]),
[iquote('0:SpR:15.0,2070.0')] ).
cnf(2820,plain,
equal(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(multiply(w,inverse(w)),u))),x))),x),
inference(rew,[status(thm),theory(equality)],[1,2783]),
[iquote('0:Rew:1.0,2783.0')] ).
cnf(2823,plain,
equal(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),u))))),v),x),
inference(rew,[status(thm),theory(equality)],[2070,2778]),
[iquote('0:Rew:2070.0,2778.0')] ).
cnf(3022,plain,
equal(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(x,inverse(x)),u))))),v),inverse(w)),
inference(spr,[status(thm),theory(equality)],[322,2820]),
[iquote('0:SpR:322.0,2820.0')] ).
cnf(3457,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(w)),inverse(x))),multiply(x,w)))),u),
inference(spr,[status(thm),theory(equality)],[2823,1]),
[iquote('0:SpR:2823.0,1.0')] ).
cnf(3592,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),v)),
inference(spr,[status(thm),theory(equality)],[2820,2823]),
[iquote('0:SpR:2820.0,2823.0')] ).
cnf(3610,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(inverse(v))),inverse(v))),inverse(multiply(multiply(inverse(u),inverse(w)),w))),
inference(rew,[status(thm),theory(equality)],[3457,1785]),
[iquote('0:Rew:3457.0,1785.0')] ).
cnf(3717,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))),
inference(spr,[status(thm),theory(equality)],[3592,1995]),
[iquote('0:SpR:3592.0,1995.0')] ).
cnf(3844,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(w,inverse(w)),multiply(inverse(multiply(x,inverse(x))),inverse(inverse(u))))),
inference(spr,[status(thm),theory(equality)],[3592,2007]),
[iquote('0:SpR:3592.0,2007.0')] ).
cnf(3957,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),multiply(x,inverse(x))))),inverse(v))),inverse(multiply(y,inverse(y)))),
inference(spr,[status(thm),theory(equality)],[3717,27]),
[iquote('0:SpR:3717.0,27.0')] ).
cnf(4081,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[2079,3957]),
[iquote('0:Rew:2079.0,3957.0')] ).
cnf(4145,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))))),
inference(spr,[status(thm),theory(equality)],[4081]),
[iquote('0:SpR:4081.0,4081.0')] ).
cnf(4973,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(inverse(v),multiply(w,multiply(multiply(x,inverse(x)),inverse(y)))))),inverse(v))),multiply(y,inverse(w))),
inference(spr,[status(thm),theory(equality)],[3022,122]),
[iquote('0:SpR:3022.0,122.0')] ).
cnf(5129,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(x),inverse(y)),y))),u))))),multiply(inverse(x),inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[3610,1]),
[iquote('0:SpR:3610.0,1.0')] ).
cnf(5149,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(multiply(inverse(multiply(v,inverse(v))),inverse(w)),w))),
inference(spr,[status(thm),theory(equality)],[3610,4145]),
[iquote('0:SpR:3610.0,4145.0')] ).
cnf(5419,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(multiply(x,inverse(x))),inverse(y)),y))),u))))),v),
inference(spr,[status(thm),theory(equality)],[5149,1]),
[iquote('0:SpR:5149.0,1.0')] ).
cnf(5536,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),multiply(inverse(multiply(x,inverse(x))),inverse(y))))),inverse(v))),y),
inference(spr,[status(thm),theory(equality)],[5149,27]),
[iquote('0:SpR:5149.0,27.0')] ).
cnf(5558,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(multiply(inverse(multiply(w,inverse(w))),inverse(x)),x),multiply(inverse(multiply(y,inverse(y))),inverse(inverse(u))))),
inference(spr,[status(thm),theory(equality)],[5149,2007]),
[iquote('0:SpR:5149.0,2007.0')] ).
cnf(5690,plain,
equal(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[5129,5419]),
[iquote('0:Rew:5129.0,5419.0')] ).
cnf(5692,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(w,inverse(w)),u)),
inference(rew,[status(thm),theory(equality)],[5690,3844]),
[iquote('0:Rew:5690.0,3844.0')] ).
cnf(5695,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(multiply(inverse(multiply(w,inverse(w))),inverse(x)),x),u)),
inference(rew,[status(thm),theory(equality)],[5690,5558]),
[iquote('0:Rew:5690.0,5558.0')] ).
cnf(5696,plain,
equal(inverse(multiply(inverse(multiply(u,inverse(u))),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[2079,5536]),
[iquote('0:Rew:2079.0,5536.0')] ).
cnf(6145,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(inverse(x),v))),y)))),multiply(multiply(z,inverse(z)),multiply(x,x1)))),multiply(x2,multiply(multiply(inverse(x2),inverse(y)),u))))),x1),
inference(spr,[status(thm),theory(equality)],[5690,83]),
[iquote('0:SpR:5690.0,83.0')] ).
cnf(6273,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),w),inverse(multiply(x,inverse(x)))))),inverse(v))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[5696,27]),
[iquote('0:SpR:5696.0,27.0')] ).
cnf(6428,plain,
equal(inverse(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u)))))),multiply(v,multiply(w,multiply(x,inverse(multiply(y,inverse(y))))))),
inference(spr,[status(thm),theory(equality)],[307,5696]),
[iquote('0:SpR:307.0,5696.0')] ).
cnf(6509,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(multiply(w,inverse(w)),x))),multiply(y,multiply(multiply(inverse(y),inverse(z)),u))))),inverse(multiply(inverse(x),inverse(multiply(z,v))))),
inference(spr,[status(thm),theory(equality)],[5692,5]),
[iquote('0:SpR:5692.0,5.0')] ).
cnf(6737,plain,
equal(inverse(multiply(inverse(multiply(u,v)),inverse(multiply(w,inverse(multiply(x,multiply(y,multiply(multiply(inverse(y),inverse(multiply(inverse(u),x))),w)))))))),v),
inference(rew,[status(thm),theory(equality)],[6509,6145]),
[iquote('0:Rew:6509.0,6145.0')] ).
cnf(6743,plain,
equal(inverse(multiply(inverse(multiply(u,v)),inverse(inverse(u)))),v),
inference(rew,[status(thm),theory(equality)],[1,6737]),
[iquote('0:Rew:1.0,6737.0')] ).
cnf(6930,plain,
equal(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,u))),x)))),inverse(multiply(inverse(w),inverse(inverse(x))))),
inference(spr,[status(thm),theory(equality)],[1,6743]),
[iquote('0:SpR:1.0,6743.0')] ).
cnf(6968,plain,
equal(multiply(u,inverse(multiply(inverse(v),inverse(inverse(u))))),v),
inference(rew,[status(thm),theory(equality)],[6930,1]),
[iquote('0:Rew:6930.0,1.0')] ).
cnf(10703,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[1995,6968]),
[iquote('0:SpR:1995.0,6968.0')] ).
cnf(10768,plain,
equal(inverse(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u)))))),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[10703,6428]),
[iquote('0:Rew:10703.0,6428.0')] ).
cnf(10780,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(inverse(v),w))),inverse(v))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[10703,6273]),
[iquote('0:Rew:10703.0,6273.0')] ).
cnf(11012,plain,
equal(inverse(multiply(u,multiply(multiply(v,inverse(v)),inverse(w)))),multiply(w,inverse(u))),
inference(rew,[status(thm),theory(equality)],[10780,4973]),
[iquote('0:Rew:10780.0,4973.0')] ).
cnf(11015,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(inverse(w),inverse(u))))))),v),
inference(rew,[status(thm),theory(equality)],[10780,1936]),
[iquote('0:Rew:10780.0,1936.0')] ).
cnf(11108,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[10768,11015]),
[iquote('0:Rew:10768.0,11015.0')] ).
cnf(11153,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[11108,5692]),
[iquote('0:Rew:11108.0,5692.0')] ).
cnf(11201,plain,
equal(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(v)),v),w),w),
inference(rew,[status(thm),theory(equality)],[11108,5695]),
[iquote('0:Rew:11108.0,5695.0')] ).
cnf(11556,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[11153,11012]),
[iquote('0:Rew:11153.0,11012.0')] ).
cnf(12376,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[11153,11201,11556]),
[iquote('0:Rew:11153.0,11201.0,11556.0,11201.0')] ).
cnf(12377,plain,
$false,
inference(unc,[status(thm)],[12376,2]),
[iquote('0:UnC:12376.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 20:55:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 62.90/63.08
% 62.90/63.08 SPASS V 3.9
% 62.90/63.08 SPASS beiseite: Proof found.
% 62.90/63.08 % SZS status Theorem
% 62.90/63.08 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.90/63.08 SPASS derived 10371 clauses, backtracked 0 clauses, performed 0 splits and kept 4559 clauses.
% 62.90/63.08 SPASS allocated 118964 KBytes.
% 62.90/63.08 SPASS spent 0:01:02.72 on the problem.
% 62.90/63.08 0:00:00.02 for the input.
% 62.90/63.08 0:00:00.00 for the FLOTTER CNF translation.
% 62.90/63.08 0:00:00.09 for inferences.
% 62.90/63.08 0:00:00.00 for the backtracking.
% 62.90/63.08 0:01:02.58 for the reduction.
% 62.90/63.08
% 62.90/63.08
% 62.90/63.08 Here is a proof with depth 22, length 81 :
% 62.90/63.08 % SZS output start Refutation
% See solution above
% 63.33/63.52 Formulae used in the proof : single_axiom prove_these_axioms_2
% 63.33/63.52
%------------------------------------------------------------------------------