TSTP Solution File: GRP050-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP050-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:45:00 EDT 2022
% Result : Unsatisfiable 34.20s 34.39s
% Output : Refutation 34.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 81 ( 76 unt; 0 nHn; 81 RR)
% Number of literals : 89 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(v),multiply(inverse(v),v))))),w),
file('GRP050-1.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('GRP050-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(inverse(w),multiply(inverse(w),w))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),v)),multiply(inverse(x),multiply(inverse(x),x))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(v),w)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),multiply(inverse(x),multiply(inverse(x),x))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),multiply(inverse(x),multiply(inverse(x),x))))),inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),multiply(inverse(x),multiply(inverse(x),x))))))))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(21,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(w),multiply(inverse(v),multiply(inverse(v),v)))))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(57,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(v),multiply(inverse(v),v)))))),x)),multiply(inverse(w),y))),multiply(inverse(x),multiply(inverse(x),x)))),y),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(104,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(u),w))),multiply(inverse(v),multiply(inverse(v),v)))),w),
inference(rew,[status(thm),theory(equality)],[1,57]),
[iquote('0:Rew:1.0,57.0')] ).
cnf(131,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(inverse(x),v)),multiply(inverse(x),w))),
inference(spr,[status(thm),theory(equality)],[104,21]),
[iquote('0:SpR:104.0,21.0')] ).
cnf(140,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),multiply(inverse(v),multiply(inverse(v),v)))),w),
inference(spr,[status(thm),theory(equality)],[104]),
[iquote('0:SpR:104.0,104.0')] ).
cnf(191,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[131]),
[iquote('0:SpR:131.0,131.0')] ).
cnf(197,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(multiply(w,x)),multiply(w,multiply(inverse(v),v)))))),multiply(inverse(v),x)),
inference(spr,[status(thm),theory(equality)],[131,21]),
[iquote('0:SpR:131.0,21.0')] ).
cnf(219,plain,
equal(multiply(inverse(multiply(u,multiply(v,inverse(multiply(inverse(w),multiply(inverse(x),multiply(inverse(x),x))))))),multiply(u,y)),multiply(inverse(w),multiply(inverse(multiply(v,x)),y))),
inference(spr,[status(thm),theory(equality)],[21,131]),
[iquote('0:SpR:21.0,131.0')] ).
cnf(255,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,multiply(v,w))),x)),multiply(inverse(multiply(v,w)),multiply(inverse(multiply(y,w)),multiply(y,w)))))),x),
inference(spr,[status(thm),theory(equality)],[191,1]),
[iquote('0:SpR:191.0,1.0')] ).
cnf(256,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,inverse(multiply(inverse(x),multiply(inverse(multiply(v,w)),multiply(inverse(multiply(y,w)),multiply(y,w))))))),x),
inference(spr,[status(thm),theory(equality)],[191,21]),
[iquote('0:SpR:191.0,21.0')] ).
cnf(276,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,x))),multiply(inverse(multiply(inverse(multiply(w,y)),v)),multiply(inverse(multiply(z,y)),multiply(z,x)))),
inference(spr,[status(thm),theory(equality)],[191]),
[iquote('0:SpR:191.0,191.0')] ).
cnf(277,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x)),multiply(inverse(multiply(inverse(multiply(y,z)),multiply(y,w))),multiply(inverse(multiply(v,z)),x))),
inference(spr,[status(thm),theory(equality)],[191]),
[iquote('0:SpR:191.0,191.0')] ).
cnf(288,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(w,x)),y)),multiply(inverse(x),multiply(inverse(x),x)))))),multiply(inverse(multiply(w,v)),y)),
inference(spr,[status(thm),theory(equality)],[1,191]),
[iquote('0:SpR:1.0,191.0')] ).
cnf(292,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,w)),x)),multiply(inverse(w),multiply(inverse(w),w)))))),multiply(u,y)),multiply(inverse(x),multiply(v,y))),
inference(spr,[status(thm),theory(equality)],[1,191]),
[iquote('0:SpR:1.0,191.0')] ).
cnf(326,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(v),multiply(inverse(v),v)))),multiply(u,w)),multiply(x,multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,x))),w))),
inference(spr,[status(thm),theory(equality)],[140,191]),
[iquote('0:SpR:140.0,191.0')] ).
cnf(456,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(u),multiply(inverse(u),u)))),inverse(multiply(inverse(multiply(w,v)),multiply(w,multiply(inverse(u),u))))),
inference(spr,[status(thm),theory(equality)],[197,140]),
[iquote('0:SpR:197.0,140.0')] ).
cnf(617,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,multiply(inverse(w),w)))),inverse(multiply(inverse(multiply(x,v)),multiply(x,multiply(inverse(w),w))))),
inference(spr,[status(thm),theory(equality)],[191,456]),
[iquote('0:SpR:191.0,456.0')] ).
cnf(1772,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,multiply(v,x))),multiply(inverse(multiply(y,multiply(z,w))),multiply(y,multiply(z,x)))),
inference(spr,[status(thm),theory(equality)],[276,277]),
[iquote('0:SpR:276.0,277.0')] ).
cnf(3043,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(w,x)))),multiply(u,inverse(multiply(inverse(multiply(y,z)),multiply(y,multiply(inverse(multiply(x1,multiply(x2,x))),multiply(x1,multiply(x2,x)))))))),multiply(inverse(multiply(v,multiply(w,x))),z)),
inference(spr,[status(thm),theory(equality)],[1772,197]),
[iquote('0:SpR:1772.0,197.0')] ).
cnf(3861,plain,
equal(multiply(inverse(multiply(u,v)),inverse(multiply(w,multiply(inverse(multiply(u,w)),multiply(inverse(multiply(x,w)),multiply(x,w)))))),multiply(inverse(v),multiply(inverse(v),v))),
inference(spr,[status(thm),theory(equality)],[140,255]),
[iquote('0:SpR:140.0,255.0')] ).
cnf(4849,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,inverse(x))))),multiply(u,inverse(multiply(inverse(multiply(y,multiply(inverse(w),multiply(inverse(w),w)))),multiply(y,multiply(inverse(multiply(z,multiply(v,inverse(x)))),multiply(z,multiply(v,inverse(x))))))))),x),
inference(spr,[status(thm),theory(equality)],[326,256]),
[iquote('0:SpR:326.0,256.0')] ).
cnf(5098,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),multiply(inverse(v),multiply(inverse(v),v))),w),
inference(rew,[status(thm),theory(equality)],[3043,4849]),
[iquote('0:Rew:3043.0,4849.0')] ).
cnf(5141,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(v),multiply(inverse(v),v)))),multiply(u,multiply(inverse(v),multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[5098,326]),
[iquote('0:SpR:5098.0,326.0')] ).
cnf(5184,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(inverse(w),multiply(inverse(w),w)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(x,w)),multiply(x,inverse(y)))),v)),y)),
inference(spr,[status(thm),theory(equality)],[5098,191]),
[iquote('0:SpR:5098.0,191.0')] ).
cnf(5361,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[5141]),
[iquote('0:SpR:5141.0,5141.0')] ).
cnf(5740,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),multiply(inverse(v),v)))),v),
inference(spr,[status(thm),theory(equality)],[5361,140]),
[iquote('0:SpR:5361.0,140.0')] ).
cnf(5814,plain,
equal(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w)),multiply(inverse(multiply(x,v)),multiply(x,u))),
inference(spr,[status(thm),theory(equality)],[5361,191]),
[iquote('0:SpR:5361.0,191.0')] ).
cnf(5871,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(w),multiply(inverse(v),multiply(inverse(x),x)))))),w),
inference(spr,[status(thm),theory(equality)],[5361,21]),
[iquote('0:SpR:5361.0,21.0')] ).
cnf(5879,plain,
equal(multiply(u,inverse(multiply(inverse(v),v))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),multiply(inverse(w),multiply(inverse(w),w)))),multiply(inverse(x),multiply(inverse(x),x))))),
inference(spr,[status(thm),theory(equality)],[5361,3]),
[iquote('0:SpR:5361.0,3.0')] ).
cnf(5924,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(inverse(w),multiply(inverse(w),w))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),v)),multiply(inverse(x),multiply(inverse(y),y))))),
inference(spr,[status(thm),theory(equality)],[5361,3]),
[iquote('0:SpR:5361.0,3.0')] ).
cnf(5941,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),multiply(inverse(u),multiply(inverse(u),u))))),w),
inference(spr,[status(thm),theory(equality)],[5361,1]),
[iquote('0:SpR:5361.0,1.0')] ).
cnf(5955,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),multiply(inverse(multiply(v,w)),multiply(inverse(multiply(x,w)),multiply(x,w)))))),multiply(v,w))),multiply(inverse(y),y)),u),
inference(spr,[status(thm),theory(equality)],[5361,256]),
[iquote('0:SpR:5361.0,256.0')] ).
cnf(5981,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,multiply(inverse(w),w)))),inverse(multiply(inverse(multiply(inverse(x),x)),multiply(inverse(v),multiply(inverse(w),w))))),
inference(spr,[status(thm),theory(equality)],[5361,617]),
[iquote('0:SpR:5361.0,617.0')] ).
cnf(5984,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(x),multiply(inverse(v),v)))))),multiply(inverse(v),x)),
inference(spr,[status(thm),theory(equality)],[5361,197]),
[iquote('0:SpR:5361.0,197.0')] ).
cnf(6030,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)],[5361,2]),
[iquote('0:SpL:5361.0,2.2')] ).
cnf(6397,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),multiply(inverse(w),w)))),v),
inference(spr,[status(thm),theory(equality)],[5361,5740]),
[iquote('0:SpR:5361.0,5740.0')] ).
cnf(6444,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,multiply(inverse(w),w)))),v),
inference(rew,[status(thm),theory(equality)],[6397,5981]),
[iquote('0:Rew:6397.0,5981.0')] ).
cnf(6445,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[6397,5984]),
[iquote('0:Rew:6397.0,5984.0')] ).
cnf(6447,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,x))),multiply(inverse(multiply(inverse(multiply(w,y)),v)),multiply(inverse(y),x))),
inference(rew,[status(thm),theory(equality)],[6445,276]),
[iquote('0:Rew:6445.0,276.0')] ).
cnf(7448,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(inverse(w),multiply(inverse(w),w)))),multiply(inverse(multiply(inverse(multiply(inverse(w),inverse(x))),v)),x)),
inference(rew,[status(thm),theory(equality)],[6445,5184]),
[iquote('0:Rew:6445.0,5184.0')] ).
cnf(7462,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),multiply(inverse(u),multiply(inverse(w),w))))),v),
inference(rew,[status(thm),theory(equality)],[6445,5871]),
[iquote('0:Rew:6445.0,5871.0')] ).
cnf(7514,plain,
equal(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[6445,5814]),
[iquote('0:Rew:6445.0,5814.0')] ).
cnf(7560,plain,
equal(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(v),multiply(inverse(v),v))))),x),multiply(inverse(w),multiply(u,x))),
inference(rew,[status(thm),theory(equality)],[6445,292]),
[iquote('0:Rew:6445.0,292.0')] ).
cnf(7753,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(multiply(v,w)),x)),multiply(inverse(w),multiply(inverse(w),w))))),multiply(inverse(multiply(v,u)),x)),
inference(rew,[status(thm),theory(equality)],[6445,288]),
[iquote('0:Rew:6445.0,288.0')] ).
cnf(7797,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),multiply(inverse(w),multiply(inverse(w),w)))))),x),multiply(inverse(v),multiply(inverse(multiply(u,w)),x))),
inference(rew,[status(thm),theory(equality)],[6445,219]),
[iquote('0:Rew:6445.0,219.0')] ).
cnf(7856,plain,
equal(multiply(inverse(multiply(u,v)),inverse(multiply(w,multiply(inverse(multiply(u,w)),multiply(inverse(w),w))))),multiply(inverse(v),multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[6445,3861]),
[iquote('0:Rew:6445.0,3861.0')] ).
cnf(7858,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),multiply(inverse(multiply(v,w)),multiply(inverse(w),w))))),multiply(v,w))),multiply(inverse(x),x)),u),
inference(rew,[status(thm),theory(equality)],[6445,5955]),
[iquote('0:Rew:6445.0,5955.0')] ).
cnf(7953,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[6445,6444]),
[iquote('0:Rew:6445.0,6444.0')] ).
cnf(8048,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[7462,5941]),
[iquote('0:Rew:7462.0,5941.0')] ).
cnf(8085,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(v),x)),multiply(inverse(w),multiply(u,x))),
inference(rew,[status(thm),theory(equality)],[6445,6447]),
[iquote('0:Rew:6445.0,6447.0')] ).
cnf(8090,plain,
equal(multiply(u,inverse(multiply(inverse(v),v))),inverse(multiply(inverse(multiply(inverse(w),multiply(inverse(w),w))),multiply(inverse(multiply(u,w)),multiply(inverse(x),x))))),
inference(rew,[status(thm),theory(equality)],[8085,5879]),
[iquote('0:Rew:8085.0,5879.0')] ).
cnf(8181,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(inverse(w),multiply(inverse(w),w))))),inverse(multiply(inverse(v),multiply(inverse(multiply(u,w)),multiply(inverse(x),x))))),
inference(rew,[status(thm),theory(equality)],[8085,5924]),
[iquote('0:Rew:8085.0,5924.0')] ).
cnf(8339,plain,
equal(multiply(inverse(u),multiply(inverse(v),multiply(inverse(v),v))),multiply(inverse(multiply(inverse(multiply(inverse(v),inverse(w))),u)),w)),
inference(rew,[status(thm),theory(equality)],[6445,7448]),
[iquote('0:Rew:6445.0,7448.0')] ).
cnf(8341,plain,
equal(multiply(inverse(inverse(multiply(inverse(u),multiply(v,multiply(inverse(w),w))))),x),multiply(inverse(u),multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[8085,7560]),
[iquote('0:Rew:8085.0,7560.0')] ).
cnf(8343,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),multiply(w,multiply(inverse(x),x))))),multiply(inverse(multiply(w,u)),v)),
inference(rew,[status(thm),theory(equality)],[8085,7753]),
[iquote('0:Rew:8085.0,7753.0')] ).
cnf(8349,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[7953,7858,6445,8341]),
[iquote('0:Rew:7953.0,7858.0,6445.0,7858.0,8341.0,7858.0')] ).
cnf(8350,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),w))),multiply(inverse(multiply(w,u)),v)),
inference(rew,[status(thm),theory(equality)],[8349,8343]),
[iquote('0:Rew:8349.0,8343.0')] ).
cnf(8359,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[8349,7953]),
[iquote('0:Rew:8349.0,7953.0')] ).
cnf(8371,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),inverse(w))))),x),multiply(inverse(v),multiply(inverse(multiply(u,w)),x))),
inference(rew,[status(thm),theory(equality)],[8349,7797]),
[iquote('0:Rew:8349.0,7797.0')] ).
cnf(8377,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),inverse(v))),w)),v),multiply(inverse(w),inverse(u))),
inference(rew,[status(thm),theory(equality)],[8349,8339]),
[iquote('0:Rew:8349.0,8339.0')] ).
cnf(8380,plain,
equal(multiply(inverse(multiply(u,v)),inverse(multiply(w,multiply(inverse(multiply(u,w)),multiply(inverse(w),w))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[8349,7856]),
[iquote('0:Rew:8349.0,7856.0')] ).
cnf(8382,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[8349,7514]),
[iquote('0:Rew:8349.0,7514.0')] ).
cnf(8388,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[8382,8048]),
[iquote('0:Rew:8382.0,8048.0')] ).
cnf(8395,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)],[8388,6030]),
[iquote('0:Rew:8388.0,6030.2')] ).
cnf(8399,plain,
equal(multiply(inverse(u),multiply(inverse(v),w)),multiply(inverse(multiply(v,u)),w)),
inference(rew,[status(thm),theory(equality)],[8382,8350]),
[iquote('0:Rew:8382.0,8350.0')] ).
cnf(8404,plain,
equal(multiply(inverse(multiply(multiply(u,v),w)),u),multiply(inverse(w),inverse(v))),
inference(rew,[status(thm),theory(equality)],[8359,8377,8382]),
[iquote('0:Rew:8359.0,8377.0,8382.0,8377.0')] ).
cnf(8408,plain,
equal(multiply(inverse(multiply(u,v)),inverse(multiply(w,inverse(multiply(u,w))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[8349,8380]),
[iquote('0:Rew:8349.0,8380.0')] ).
cnf(8409,plain,
equal(multiply(inverse(multiply(multiply(u,v),w)),x),multiply(inverse(multiply(u,multiply(v,w))),x)),
inference(rew,[status(thm),theory(equality)],[8359,8371,8382,8399]),
[iquote('0:Rew:8359.0,8371.0,8382.0,8371.0,8399.0,8371.0')] ).
cnf(8410,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),u),multiply(inverse(w),inverse(v))),
inference(rew,[status(thm),theory(equality)],[8409,8404]),
[iquote('0:Rew:8409.0,8404.0')] ).
cnf(8423,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)],[8395]),
[iquote('0:Obv:8395.2')] ).
cnf(8433,plain,
equal(inverse(multiply(u,inverse(multiply(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[8349,8090,8382,8359]),
[iquote('0:Rew:8349.0,8090.0,8382.0,8090.0,8359.0,8090.0,8349.0,8090.0,8349.0,8090.0')] ).
cnf(8434,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[8433,8408]),
[iquote('0:Rew:8433.0,8408.0')] ).
cnf(8436,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[8434,8410]),
[iquote('0:Rew:8434.0,8410.0')] ).
cnf(8438,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[8359,8181,8436,8349]),
[iquote('0:Rew:8359.0,8181.0,8436.0,8181.0,8349.0,8181.0,8359.0,8181.0,8436.0,8181.0,8349.0,8181.0')] ).
cnf(8440,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)],[8438,8423]),
[iquote('0:Rew:8438.0,8423.1')] ).
cnf(8445,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[8440]),
[iquote('0:Obv:8440.1')] ).
cnf(8446,plain,
$false,
inference(unc,[status(thm)],[8445,5361]),
[iquote('0:UnC:8445.0,5361.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP050-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 00:45:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 34.20/34.39
% 34.20/34.39 SPASS V 3.9
% 34.20/34.39 SPASS beiseite: Proof found.
% 34.20/34.39 % SZS status Theorem
% 34.20/34.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.20/34.39 SPASS derived 7645 clauses, backtracked 0 clauses, performed 0 splits and kept 2497 clauses.
% 34.20/34.39 SPASS allocated 115725 KBytes.
% 34.20/34.39 SPASS spent 0:0:34.03 on the problem.
% 34.20/34.39 0:00:00.04 for the input.
% 34.20/34.39 0:00:00.00 for the FLOTTER CNF translation.
% 34.20/34.39 0:00:00.14 for inferences.
% 34.20/34.39 0:00:00.00 for the backtracking.
% 34.20/34.39 0:0:33.83 for the reduction.
% 34.20/34.39
% 34.20/34.39
% 34.20/34.39 Here is a proof with depth 10, length 81 :
% 34.20/34.39 % SZS output start Refutation
% See solution above
% 34.50/34.72 Formulae used in the proof : single_axiom prove_these_axioms
% 34.50/34.72
%------------------------------------------------------------------------------