%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP407-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:47:14 EDT 2022
% Result : Unsatisfiable 37.03s 37.24s
% Output : Refutation 37.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 48 RR)
% Number of literals : 48 ( 0 equ; 2 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(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(v),multiply(inverse(v),v))))),w),
file('GRP407-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP407-1.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(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(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(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(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(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(6029,plain,
~ equal(multiply(multiply(inverse(u),u),a2),a2),
inference(spl,[status(thm),theory(equality)],[5361,2]),
[iquote('0:SpL:5361.0,2.0')] ).
cnf(6413,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(6461,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,multiply(inverse(w),w)))),v),
inference(rew,[status(thm),theory(equality)],[6413,5981]),
[iquote('0:Rew:6413.0,5981.0')] ).
cnf(6462,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[6413,5984]),
[iquote('0:Rew:6413.0,5984.0')] ).
cnf(6464,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)],[6462,276]),
[iquote('0:Rew:6462.0,276.0')] ).
cnf(7479,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),multiply(inverse(u),multiply(inverse(w),w))))),v),
inference(rew,[status(thm),theory(equality)],[6462,5871]),
[iquote('0:Rew:6462.0,5871.0')] ).
cnf(7531,plain,
equal(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[6462,5814]),
[iquote('0:Rew:6462.0,5814.0')] ).
cnf(7577,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)],[6462,292]),
[iquote('0:Rew:6462.0,292.0')] ).
cnf(7876,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)],[6462,5955]),
[iquote('0:Rew:6462.0,5955.0')] ).
cnf(7971,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[6462,6461]),
[iquote('0:Rew:6462.0,6461.0')] ).
cnf(8066,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[7479,5941]),
[iquote('0:Rew:7479.0,5941.0')] ).
cnf(8105,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)],[6462,6464]),
[iquote('0:Rew:6462.0,6464.0')] ).
cnf(8361,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)],[8105,7577]),
[iquote('0:Rew:8105.0,7577.0')] ).
cnf(8369,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[7971,7876,6462,8361]),
[iquote('0:Rew:7971.0,7876.0,6462.0,7876.0,8361.0,7876.0')] ).
cnf(8403,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[8369,7531]),
[iquote('0:Rew:8369.0,7531.0')] ).
cnf(8409,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[8403,8066]),
[iquote('0:Rew:8403.0,8066.0')] ).
cnf(8416,plain,
$false,
inference(unc,[status(thm)],[8409,6029]),
[iquote('0:UnC:8409.0,6029.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP407-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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 17:21:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 37.03/37.24
% 37.03/37.24 SPASS V 3.9
% 37.03/37.24 SPASS beiseite: Proof found.
% 37.03/37.24 % SZS status Theorem
% 37.03/37.24 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.03/37.24 SPASS derived 7671 clauses, backtracked 0 clauses, performed 0 splits and kept 2595 clauses.
% 37.03/37.24 SPASS allocated 115722 KBytes.
% 37.03/37.24 SPASS spent 0:0:36.87 on the problem.
% 37.03/37.24 0:00:00.03 for the input.
% 37.03/37.24 0:00:00.00 for the FLOTTER CNF translation.
% 37.03/37.24 0:00:00.15 for inferences.
% 37.03/37.24 0:00:00.00 for the backtracking.
% 37.03/37.24 0:0:36.66 for the reduction.
% 37.03/37.24
% 37.03/37.24
% 37.03/37.24 Here is a proof with depth 10, length 48 :
% 37.03/37.24 % SZS output start Refutation
% See solution above
% 37.34/37.56 Formulae used in the proof : single_axiom prove_these_axioms_2
% 37.34/37.56
%------------------------------------------------------------------------------