%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP612-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:48:17 EDT 2022
% Result : Unsatisfiable 0.46s 0.70s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 51 RR)
% Number of literals : 51 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(double_divide(inverse(double_divide(inverse(double_divide(u,v)),w)),double_divide(u,w))),v),
file('GRP612-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP612-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP612-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(w,u))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),multiply(x,v)),double_divide(w,u)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(7,plain,
equal(multiply(double_divide(multiply(u,v),double_divide(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(multiply(u,x),double_divide(x,w))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(15,plain,
equal(double_divide(u,multiply(double_divide(multiply(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(32,plain,
equal(multiply(multiply(double_divide(multiply(u,v),w),u),v),inverse(w)),
inference(spr,[status(thm),theory(equality)],[15,2]),
[iquote('0:SpR:15.0,2.0')] ).
cnf(37,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),u),double_divide(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[15]),
[iquote('0:SpR:15.0,15.0')] ).
cnf(42,plain,
equal(double_divide(multiply(u,v),double_divide(v,multiply(w,u))),w),
inference(spr,[status(thm),theory(equality)],[6,15]),
[iquote('0:SpR:6.0,15.0')] ).
cnf(44,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(w,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[42,2]),
[iquote('0:SpR:42.0,2.0')] ).
cnf(61,plain,
equal(multiply(double_divide(u,multiply(double_divide(multiply(v,multiply(w,u)),x),v)),inverse(x)),w),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(68,plain,
equal(multiply(double_divide(multiply(u,inverse(v)),w),multiply(w,multiply(double_divide(multiply(x,y),v),x))),double_divide(y,u)),
inference(spr,[status(thm),theory(equality)],[32,6]),
[iquote('0:SpR:32.0,6.0')] ).
cnf(76,plain,
equal(multiply(double_divide(u,double_divide(u,multiply(v,w))),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[37,61]),
[iquote('0:Rew:37.0,61.0')] ).
cnf(80,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(w,inverse(x))),double_divide(v,multiply(x,u))),
inference(spr,[status(thm),theory(equality)],[44,4]),
[iquote('0:SpR:44.0,4.0')] ).
cnf(130,plain,
equal(multiply(multiply(double_divide(u,v),multiply(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(144,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(double_divide(multiply(w,x),y),w))),double_divide(multiply(u,x),y)),
inference(spr,[status(thm),theory(equality)],[15,9]),
[iquote('0:SpR:15.0,9.0')] ).
cnf(159,plain,
equal(double_divide(multiply(multiply(u,inverse(v)),w),v),double_divide(w,u)),
inference(rew,[status(thm),theory(equality)],[144,68]),
[iquote('0:Rew:144.0,68.0')] ).
cnf(174,plain,
equal(multiply(multiply(double_divide(u,v),multiply(double_divide(w,x),multiply(x,u))),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[130,32]),
[iquote('0:SpR:130.0,32.0')] ).
cnf(182,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,w)),x),u),multiply(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[4,130]),
[iquote('0:SpR:4.0,130.0')] ).
cnf(184,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,multiply(w,x))),inverse(w)),u),multiply(x,v)),
inference(spr,[status(thm),theory(equality)],[44,130]),
[iquote('0:SpR:44.0,130.0')] ).
cnf(190,plain,
equal(multiply(u,multiply(multiply(double_divide(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[7,130]),
[iquote('0:SpR:7.0,130.0')] ).
cnf(195,plain,
equal(multiply(multiply(u,v),multiply(inverse(u),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[182,184]),
[iquote('0:Rew:182.0,184.0')] ).
cnf(254,plain,
equal(multiply(double_divide(u,double_divide(u,v)),inverse(w)),multiply(multiply(double_divide(x,w),v),x)),
inference(spr,[status(thm),theory(equality)],[190,76]),
[iquote('0:SpR:190.0,76.0')] ).
cnf(284,plain,
equal(double_divide(multiply(u,multiply(multiply(v,inverse(multiply(w,u))),x)),double_divide(x,v)),w),
inference(spr,[status(thm),theory(equality)],[159,42]),
[iquote('0:SpR:159.0,42.0')] ).
cnf(290,plain,
equal(double_divide(u,multiply(double_divide(u,v),multiply(v,inverse(w)))),w),
inference(spr,[status(thm),theory(equality)],[159,15]),
[iquote('0:SpR:159.0,15.0')] ).
cnf(376,plain,
equal(multiply(double_divide(u,double_divide(u,multiply(v,w))),inverse(multiply(x,v))),multiply(inverse(x),w)),
inference(spr,[status(thm),theory(equality)],[195,76]),
[iquote('0:SpR:195.0,76.0')] ).
cnf(386,plain,
equal(multiply(u,multiply(inverse(double_divide(v,w)),x)),multiply(multiply(w,multiply(u,v)),x)),
inference(spr,[status(thm),theory(equality)],[4,195]),
[iquote('0:SpR:4.0,195.0')] ).
cnf(397,plain,
equal(multiply(multiply(u,multiply(v,w)),x),multiply(v,multiply(multiply(u,w),x))),
inference(rew,[status(thm),theory(equality)],[2,386]),
[iquote('0:Rew:2.0,386.0')] ).
cnf(409,plain,
equal(multiply(double_divide(u,v),multiply(multiply(double_divide(w,x),multiply(v,w)),u)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[397,174]),
[iquote('0:Rew:397.0,174.0')] ).
cnf(418,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(multiply(double_divide(w,x),w),u))),inverse(x)),
inference(rew,[status(thm),theory(equality)],[397,409]),
[iquote('0:Rew:397.0,409.0')] ).
cnf(419,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4,418]),
[iquote('0:Rew:4.0,418.0')] ).
cnf(434,plain,
equal(multiply(double_divide(u,v),multiply(v,inverse(w))),double_divide(u,w)),
inference(spr,[status(thm),theory(equality)],[419,4]),
[iquote('0:SpR:419.0,4.0')] ).
cnf(440,plain,
equal(double_divide(multiply(multiply(u,v),w),double_divide(w,v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[419,9]),
[iquote('0:SpR:419.0,9.0')] ).
cnf(447,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(w,u)),inverse(double_divide(w,v))),
inference(spr,[status(thm),theory(equality)],[419,44]),
[iquote('0:SpR:419.0,44.0')] ).
cnf(456,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[42,419]),
[iquote('0:SpR:42.0,419.0')] ).
cnf(460,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[434,80]),
[iquote('0:Rew:434.0,80.0')] ).
cnf(462,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[434,290]),
[iquote('0:Rew:434.0,290.0')] ).
cnf(467,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,u))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[462,376]),
[iquote('0:Rew:462.0,376.0')] ).
cnf(471,plain,
equal(multiply(multiply(double_divide(u,v),w),u),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[462,254]),
[iquote('0:Rew:462.0,254.0')] ).
cnf(529,plain,
equal(double_divide(multiply(multiply(u,inverse(multiply(v,w))),x),multiply(double_divide(x,u),w)),v),
inference(rew,[status(thm),theory(equality)],[460,284]),
[iquote('0:Rew:460.0,284.0')] ).
cnf(643,plain,
equal(double_divide(u,multiply(double_divide(u,v),multiply(w,v))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[460,440]),
[iquote('0:Rew:460.0,440.0')] ).
cnf(646,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2,456]),
[iquote('0:Rew:2.0,456.0')] ).
cnf(671,plain,
equal(multiply(double_divide(u,v),multiply(w,u)),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[646,471]),
[iquote('0:Rew:646.0,471.0')] ).
cnf(691,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(w,u)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[2,447]),
[iquote('0:Rew:2.0,447.0')] ).
cnf(692,plain,
equal(multiply(u,inverse(inverse(v))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[671,691]),
[iquote('0:Rew:671.0,691.0')] ).
cnf(701,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,u)))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[646,467]),
[iquote('0:Rew:646.0,467.0')] ).
cnf(750,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[643,529,701,646,460]),
[iquote('0:Rew:643.0,529.0,701.0,529.0,646.0,529.0,646.0,529.0,460.0,529.0,646.0,529.0,460.0,529.0,646.0,529.0')] ).
cnf(751,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[750,692]),
[iquote('0:Rew:750.0,692.0')] ).
cnf(752,plain,
$false,
inference(unc,[status(thm)],[751,3]),
[iquote('0:UnC:751.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP612-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 21:19:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.70
% 0.46/0.70 SPASS V 3.9
% 0.46/0.70 SPASS beiseite: Proof found.
% 0.46/0.70 % SZS status Theorem
% 0.46/0.70 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.70 SPASS derived 720 clauses, backtracked 0 clauses, performed 0 splits and kept 452 clauses.
% 0.46/0.70 SPASS allocated 64976 KBytes.
% 0.46/0.70 SPASS spent 0:00:00.33 on the problem.
% 0.46/0.70 0:00:00.04 for the input.
% 0.46/0.70 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.70 0:00:00.01 for inferences.
% 0.46/0.70 0:00:00.00 for the backtracking.
% 0.46/0.70 0:00:00.27 for the reduction.
% 0.46/0.70
% 0.46/0.70
% 0.46/0.70 Here is a proof with depth 6, length 51 :
% 0.46/0.70 % SZS output start Refutation
% See solution above
% 0.46/0.70 Formulae used in the proof : single_axiom multiply prove_these_axioms_4
% 0.46/0.70
%------------------------------------------------------------------------------