TSTP Solution File: GRP063-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP063-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:45:06 EDT 2022
% Result : Unsatisfiable 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of clauses : 65 ( 60 unt; 0 nHn; 65 RR)
% Number of literals : 73 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(divide(divide(divide(u,u),v),w),divide(divide(divide(u,u),u),w))),v),
file('GRP063-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP063-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP063-1.p',unknown),
[] ).
cnf(4,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('GRP063-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(6,plain,
equal(divide(u,divide(divide(inverse(v),w),divide(inverse(u),w))),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(9,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(11,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(14,plain,
equal(multiply(inverse(divide(u,u)),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(20,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(22,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[20,4]),
[iquote('0:Rew:20.0,4.2')] ).
cnf(27,plain,
equal(divide(u,divide(divide(inverse(v),divide(divide(inverse(w),x),divide(inverse(inverse(u)),x))),w)),v),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(28,plain,
equal(divide(u,divide(v,divide(inverse(u),divide(divide(inverse(v),w),divide(inverse(inverse(x)),w))))),x),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(29,plain,
equal(divide(u,divide(divide(inverse(v),inverse(w)),multiply(inverse(u),w))),v),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(30,plain,
equal(divide(divide(u,u),divide(divide(inverse(v),w),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(33,plain,
equal(divide(u,inverse(divide(inverse(u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(34,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[5,33]),
[iquote('0:Rew:5.0,33.0,5.0,33.0')] ).
cnf(35,plain,
equal(inverse(multiply(divide(inverse(u),v),v)),u),
inference(rew,[status(thm),theory(equality)],[3,30,5]),
[iquote('0:Rew:3.0,30.0,5.0,30.0')] ).
cnf(37,plain,
equal(divide(u,divide(multiply(inverse(v),w),multiply(inverse(u),w))),v),
inference(rew,[status(thm),theory(equality)],[5,29]),
[iquote('0:Rew:5.0,29.0')] ).
cnf(44,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[34]),
[iquote('0:SpR:34.0,34.0')] ).
cnf(45,plain,
equal(inverse(inverse(multiply(inverse(divide(u,u)),v))),v),
inference(spr,[status(thm),theory(equality)],[11,34]),
[iquote('0:SpR:11.0,34.0')] ).
cnf(51,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[14,45]),
[iquote('0:Rew:14.0,45.0')] ).
cnf(53,plain,
equal(multiply(u,inverse(inverse(inverse(v)))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[51,5]),
[iquote('0:SpR:51.0,5.0')] ).
cnf(57,plain,
equal(multiply(inverse(inverse(inverse(u))),multiply(u,v)),v),
inference(spr,[status(thm),theory(equality)],[51,34]),
[iquote('0:SpR:51.0,34.0')] ).
cnf(62,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[44,57]),
[iquote('0:Rew:44.0,57.0')] ).
cnf(82,plain,
equal(inverse(multiply(inverse(u),u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[7,35]),
[iquote('0:SpR:7.0,35.0')] ).
cnf(107,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[82]),
[iquote('0:SpR:82.0,82.0')] ).
cnf(130,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[107,5]),
[iquote('0:SpR:107.0,5.0')] ).
cnf(159,plain,
equal(divide(u,divide(multiply(v,w),multiply(inverse(u),w))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[44,37]),
[iquote('0:SpR:44.0,37.0')] ).
cnf(160,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[107,37]),
[iquote('0:SpR:107.0,37.0')] ).
cnf(167,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[159,37]),
[iquote('0:Rew:159.0,37.0')] ).
cnf(168,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)],[167,22]),
[iquote('0:Rew:167.0,22.2')] ).
cnf(172,plain,
equal(divide(u,divide(v,divide(inverse(u),divide(divide(inverse(v),w),divide(x,w))))),x),
inference(rew,[status(thm),theory(equality)],[167,28]),
[iquote('0:Rew:167.0,28.0')] ).
cnf(173,plain,
equal(divide(u,divide(divide(inverse(v),divide(divide(inverse(w),x),divide(u,x))),w)),v),
inference(rew,[status(thm),theory(equality)],[167,27]),
[iquote('0:Rew:167.0,27.0')] ).
cnf(179,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[167,53]),
[iquote('0:Rew:167.0,53.0')] ).
cnf(202,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)],[168]),
[iquote('0:Obv:168.2')] ).
cnf(316,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[130]),
[iquote('0:SpR:130.0,130.0')] ).
cnf(363,plain,
equal(multiply(inverse(u),divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[179,62]),
[iquote('0:SpR:179.0,62.0')] ).
cnf(417,plain,
equal(divide(u,divide(v,inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[160,172]),
[iquote('0:SpR:160.0,172.0')] ).
cnf(418,plain,
equal(divide(divide(u,u),divide(v,inverse(divide(divide(inverse(v),w),divide(x,w))))),x),
inference(spr,[status(thm),theory(equality)],[7,172]),
[iquote('0:SpR:7.0,172.0')] ).
cnf(422,plain,
equal(divide(u,multiply(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[5,417]),
[iquote('0:Rew:5.0,417.0')] ).
cnf(440,plain,
equal(inverse(multiply(u,divide(divide(inverse(u),v),divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[3,418,5]),
[iquote('0:Rew:3.0,418.0,5.0,418.0')] ).
cnf(576,plain,
equal(divide(multiply(u,v),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[62,422]),
[iquote('0:SpR:62.0,422.0')] ).
cnf(585,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[167,576]),
[iquote('0:Rew:167.0,576.0')] ).
cnf(639,plain,
equal(divide(u,divide(divide(v,divide(divide(inverse(w),x),divide(u,x))),w)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[167,173]),
[iquote('0:SpR:167.0,173.0')] ).
cnf(721,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[585,5]),
[iquote('0:SpR:585.0,5.0')] ).
cnf(736,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[179,721]),
[iquote('0:Rew:179.0,721.0')] ).
cnf(750,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[736,422]),
[iquote('0:SpR:736.0,422.0')] ).
cnf(778,plain,
equal(divide(u,divide(v,w)),multiply(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[750,5]),
[iquote('0:SpR:750.0,5.0')] ).
cnf(792,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5,750]),
[iquote('0:SpR:5.0,750.0')] ).
cnf(824,plain,
equal(divide(u,divide(divide(v,divide(inverse(multiply(w,x)),divide(u,w))),x)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[792,639]),
[iquote('0:Rew:792.0,639.0')] ).
cnf(833,plain,
equal(inverse(multiply(u,divide(inverse(multiply(v,u)),divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[792,440]),
[iquote('0:Rew:792.0,440.0')] ).
cnf(852,plain,
equal(inverse(multiply(u,inverse(multiply(divide(v,w),multiply(w,u))))),v),
inference(rew,[status(thm),theory(equality)],[792,833]),
[iquote('0:Rew:792.0,833.0')] ).
cnf(853,plain,
equal(divide(multiply(divide(u,v),multiply(v,w)),w),u),
inference(rew,[status(thm),theory(equality)],[750,852,179]),
[iquote('0:Rew:750.0,852.0,179.0,852.0')] ).
cnf(876,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,multiply(divide(u,x),multiply(x,v)))))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[792,824,778]),
[iquote('0:Rew:792.0,824.0,778.0,824.0,778.0,824.0,792.0,824.0')] ).
cnf(877,plain,
equal(multiply(u,divide(v,multiply(w,multiply(divide(u,x),multiply(x,v))))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[179,876]),
[iquote('0:Rew:179.0,876.0')] ).
cnf(939,plain,
equal(multiply(divide(u,v),multiply(v,w)),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[853,736]),
[iquote('0:SpR:853.0,736.0')] ).
cnf(971,plain,
equal(multiply(u,divide(v,multiply(w,multiply(u,v)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[939,877]),
[iquote('0:Rew:939.0,877.0')] ).
cnf(1069,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[585,363]),
[iquote('0:SpR:585.0,363.0')] ).
cnf(1190,plain,
equal(inverse(inverse(multiply(multiply(u,v),w))),multiply(u,divide(v,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1069,971]),
[iquote('0:SpR:1069.0,971.0')] ).
cnf(1275,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[167,1190,5]),
[iquote('0:Rew:167.0,1190.0,5.0,1190.0')] ).
cnf(1276,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)],[1275,202]),
[iquote('0:Rew:1275.0,202.1')] ).
cnf(1313,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[1276]),
[iquote('0:Obv:1276.1')] ).
cnf(1314,plain,
$false,
inference(unc,[status(thm)],[1313,316]),
[iquote('0:UnC:1313.0,316.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP063-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 : Mon Jun 13 05:47:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 817 clauses, backtracked 0 clauses, performed 0 splits and kept 187 clauses.
% 0.18/0.51 SPASS allocated 64610 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.51 0:00:00.04 for the input.
% 0.18/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.09 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 10, length 65 :
% 0.18/0.51 % SZS output start Refutation
% See solution above
% 0.18/0.51 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms
% 0.18/0.51
%------------------------------------------------------------------------------