TSTP Solution File: GRP167-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP167-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:46:01 EDT 2022
% Result : Unsatisfiable 11.95s 12.27s
% Output : Refutation 12.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of clauses : 106 ( 106 unt; 0 nHn; 106 RR)
% Number of literals : 106 ( 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(u,identity),positive_part(u)),
file('GRP167-1.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(u,identity),negative_part(u)),
file('GRP167-1.p',unknown),
[] ).
cnf(3,axiom,
equal(greatest_lower_bound(least_upper_bound(u,v),least_upper_bound(u,w)),least_upper_bound(u,greatest_lower_bound(v,w))),
file('GRP167-1.p',unknown),
[] ).
cnf(4,axiom,
equal(least_upper_bound(greatest_lower_bound(u,v),greatest_lower_bound(u,w)),greatest_lower_bound(u,least_upper_bound(v,w))),
file('GRP167-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(positive_part(a),negative_part(a)),a),
file('GRP167-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(identity,u),u),
file('GRP167-1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP167-1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP167-1.p',unknown),
[] ).
cnf(9,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP167-1.p',unknown),
[] ).
cnf(10,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP167-1.p',unknown),
[] ).
cnf(12,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP167-1.p',unknown),
[] ).
cnf(15,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP167-1.p',unknown),
[] ).
cnf(16,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP167-1.p',unknown),
[] ).
cnf(17,axiom,
equal(least_upper_bound(multiply(u,v),multiply(u,w)),multiply(u,least_upper_bound(v,w))),
file('GRP167-1.p',unknown),
[] ).
cnf(18,axiom,
equal(greatest_lower_bound(multiply(u,v),multiply(u,w)),multiply(u,greatest_lower_bound(v,w))),
file('GRP167-1.p',unknown),
[] ).
cnf(19,axiom,
equal(least_upper_bound(multiply(u,v),multiply(w,v)),multiply(least_upper_bound(u,w),v)),
file('GRP167-1.p',unknown),
[] ).
cnf(20,axiom,
equal(greatest_lower_bound(multiply(u,v),multiply(w,v)),multiply(greatest_lower_bound(u,w),v)),
file('GRP167-1.p',unknown),
[] ).
cnf(46,plain,
equal(least_upper_bound(identity,u),positive_part(u)),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(57,plain,
equal(greatest_lower_bound(identity,positive_part(u)),identity),
inference(spr,[status(thm),theory(equality)],[46,16]),
[iquote('0:SpR:46.0,16.0')] ).
cnf(59,plain,
equal(positive_part(greatest_lower_bound(identity,u)),identity),
inference(spr,[status(thm),theory(equality)],[46,15]),
[iquote('0:SpR:46.0,15.0')] ).
cnf(65,plain,
equal(greatest_lower_bound(identity,u),negative_part(u)),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(74,plain,
equal(positive_part(negative_part(u)),identity),
inference(rew,[status(thm),theory(equality)],[65,59]),
[iquote('0:Rew:65.0,59.0')] ).
cnf(75,plain,
equal(negative_part(positive_part(u)),identity),
inference(rew,[status(thm),theory(equality)],[65,57]),
[iquote('0:Rew:65.0,57.0')] ).
cnf(152,plain,
equal(least_upper_bound(u,least_upper_bound(v,identity)),positive_part(least_upper_bound(u,v))),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(170,plain,
equal(least_upper_bound(u,positive_part(v)),positive_part(least_upper_bound(u,v))),
inference(rew,[status(thm),theory(equality)],[1,152]),
[iquote('0:Rew:1.0,152.0')] ).
cnf(183,plain,
equal(greatest_lower_bound(u,positive_part(least_upper_bound(u,v))),u),
inference(spr,[status(thm),theory(equality)],[170,16]),
[iquote('0:SpR:170.0,16.0')] ).
cnf(192,plain,
equal(positive_part(least_upper_bound(u,negative_part(v))),least_upper_bound(u,identity)),
inference(spr,[status(thm),theory(equality)],[74,170]),
[iquote('0:SpR:74.0,170.0')] ).
cnf(199,plain,
equal(positive_part(least_upper_bound(u,negative_part(v))),positive_part(u)),
inference(rew,[status(thm),theory(equality)],[1,192]),
[iquote('0:Rew:1.0,192.0')] ).
cnf(213,plain,
equal(positive_part(least_upper_bound(negative_part(u),v)),positive_part(v)),
inference(spr,[status(thm),theory(equality)],[10,199]),
[iquote('0:SpR:10.0,199.0')] ).
cnf(420,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(421,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[6,420]),
[iquote('0:Rew:6.0,420.0')] ).
cnf(424,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[421]),
[iquote('0:SpR:421.0,421.0')] ).
cnf(427,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[7,421]),
[iquote('0:SpR:7.0,421.0')] ).
cnf(429,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[424,427]),
[iquote('0:Rew:424.0,427.0')] ).
cnf(485,plain,
equal(greatest_lower_bound(multiply(u,v),v),multiply(greatest_lower_bound(u,identity),v)),
inference(spr,[status(thm),theory(equality)],[6,20]),
[iquote('0:SpR:6.0,20.0')] ).
cnf(491,plain,
equal(multiply(greatest_lower_bound(inverse(u),v),u),greatest_lower_bound(identity,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[7,20]),
[iquote('0:SpR:7.0,20.0')] ).
cnf(496,plain,
equal(greatest_lower_bound(u,multiply(v,u)),multiply(negative_part(v),u)),
inference(rew,[status(thm),theory(equality)],[9,485,2]),
[iquote('0:Rew:9.0,485.0,2.0,485.0')] ).
cnf(501,plain,
equal(multiply(greatest_lower_bound(inverse(u),v),u),negative_part(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[65,491]),
[iquote('0:Rew:65.0,491.0')] ).
cnf(678,plain,
equal(least_upper_bound(multiply(u,v),v),multiply(least_upper_bound(u,identity),v)),
inference(spr,[status(thm),theory(equality)],[6,19]),
[iquote('0:SpR:6.0,19.0')] ).
cnf(689,plain,
equal(least_upper_bound(u,multiply(v,u)),multiply(positive_part(v),u)),
inference(rew,[status(thm),theory(equality)],[10,678,1]),
[iquote('0:Rew:10.0,678.0,1.0,678.0')] ).
cnf(738,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[424,7]),
[iquote('0:SpR:424.0,7.0')] ).
cnf(743,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[424,429]),
[iquote('0:SpR:424.0,429.0')] ).
cnf(744,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(spr,[status(thm),theory(equality)],[424,421]),
[iquote('0:SpR:424.0,421.0')] ).
cnf(749,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[429,743]),
[iquote('0:Rew:429.0,743.0')] ).
cnf(769,plain,
equal(multiply(u,multiply(v,inverse(multiply(u,v)))),identity),
inference(spr,[status(thm),theory(equality)],[738,8]),
[iquote('0:SpR:738.0,8.0')] ).
cnf(797,plain,
equal(greatest_lower_bound(multiply(u,v),u),multiply(u,greatest_lower_bound(v,identity))),
inference(spr,[status(thm),theory(equality)],[429,18]),
[iquote('0:SpR:429.0,18.0')] ).
cnf(809,plain,
equal(greatest_lower_bound(u,multiply(u,v)),multiply(u,negative_part(v))),
inference(rew,[status(thm),theory(equality)],[9,797,2]),
[iquote('0:Rew:9.0,797.0,2.0,797.0')] ).
cnf(1008,plain,
equal(multiply(inverse(u),least_upper_bound(v,u)),least_upper_bound(multiply(inverse(u),v),identity)),
inference(spr,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpR:7.0,17.0')] ).
cnf(1033,plain,
equal(multiply(inverse(u),least_upper_bound(v,u)),positive_part(multiply(inverse(u),v))),
inference(rew,[status(thm),theory(equality)],[46,1008,10]),
[iquote('0:Rew:46.0,1008.0,10.0,1008.0')] ).
cnf(1264,plain,
equal(least_upper_bound(greatest_lower_bound(identity,u),negative_part(v)),greatest_lower_bound(identity,least_upper_bound(u,v))),
inference(spr,[status(thm),theory(equality)],[65,4]),
[iquote('0:SpR:65.0,4.0')] ).
cnf(1295,plain,
equal(least_upper_bound(negative_part(u),negative_part(v)),negative_part(least_upper_bound(u,v))),
inference(rew,[status(thm),theory(equality)],[65,1264]),
[iquote('0:Rew:65.0,1264.0,65.0,1264.0')] ).
cnf(1634,plain,
equal(greatest_lower_bound(least_upper_bound(identity,u),positive_part(v)),least_upper_bound(identity,greatest_lower_bound(u,v))),
inference(spr,[status(thm),theory(equality)],[46,3]),
[iquote('0:SpR:46.0,3.0')] ).
cnf(1668,plain,
equal(greatest_lower_bound(positive_part(u),positive_part(v)),positive_part(greatest_lower_bound(u,v))),
inference(rew,[status(thm),theory(equality)],[46,1634]),
[iquote('0:Rew:46.0,1634.0,46.0,1634.0')] ).
cnf(2049,plain,
equal(multiply(negative_part(u),inverse(u)),greatest_lower_bound(inverse(u),identity)),
inference(spr,[status(thm),theory(equality)],[738,496]),
[iquote('0:SpR:738.0,496.0')] ).
cnf(2057,plain,
equal(multiply(negative_part(u),inverse(u)),negative_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[65,2049,9]),
[iquote('0:Rew:65.0,2049.0,9.0,2049.0')] ).
cnf(2108,plain,
equal(multiply(identity,inverse(positive_part(u))),negative_part(inverse(positive_part(u)))),
inference(spr,[status(thm),theory(equality)],[75,2057]),
[iquote('0:SpR:75.0,2057.0')] ).
cnf(2115,plain,
equal(negative_part(inverse(positive_part(u))),inverse(positive_part(u))),
inference(rew,[status(thm),theory(equality)],[6,2108]),
[iquote('0:Rew:6.0,2108.0')] ).
cnf(2158,plain,
equal(positive_part(least_upper_bound(inverse(positive_part(u)),v)),positive_part(v)),
inference(spr,[status(thm),theory(equality)],[2115,213]),
[iquote('0:SpR:2115.0,213.0')] ).
cnf(2182,plain,
equal(greatest_lower_bound(u,positive_part(multiply(positive_part(v),u))),u),
inference(spr,[status(thm),theory(equality)],[689,183]),
[iquote('0:SpR:689.0,183.0')] ).
cnf(2196,plain,
equal(multiply(u,least_upper_bound(v,multiply(u,v))),multiply(positive_part(u),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[689,17]),
[iquote('0:SpR:689.0,17.0')] ).
cnf(2198,plain,
equal(multiply(positive_part(inverse(u)),u),least_upper_bound(u,identity)),
inference(spr,[status(thm),theory(equality)],[7,689]),
[iquote('0:SpR:7.0,689.0')] ).
cnf(2203,plain,
equal(multiply(positive_part(u),inverse(u)),least_upper_bound(inverse(u),identity)),
inference(spr,[status(thm),theory(equality)],[738,689]),
[iquote('0:SpR:738.0,689.0')] ).
cnf(2210,plain,
equal(multiply(positive_part(inverse(u)),u),positive_part(u)),
inference(rew,[status(thm),theory(equality)],[1,2198]),
[iquote('0:Rew:1.0,2198.0')] ).
cnf(2211,plain,
equal(multiply(positive_part(u),inverse(u)),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[46,2203,10]),
[iquote('0:Rew:46.0,2203.0,10.0,2203.0')] ).
cnf(2218,plain,
equal(multiply(positive_part(u),multiply(u,v)),multiply(u,multiply(positive_part(u),v))),
inference(rew,[status(thm),theory(equality)],[689,2196]),
[iquote('0:Rew:689.0,2196.0')] ).
cnf(2904,plain,
equal(positive_part(multiply(positive_part(u),inverse(positive_part(v)))),positive_part(multiply(u,inverse(positive_part(v))))),
inference(spr,[status(thm),theory(equality)],[689,2158]),
[iquote('0:SpR:689.0,2158.0')] ).
cnf(5620,plain,
equal(multiply(u,inverse(multiply(v,u))),multiply(inverse(v),identity)),
inference(spr,[status(thm),theory(equality)],[769,421]),
[iquote('0:SpR:769.0,421.0')] ).
cnf(5661,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[429,5620]),
[iquote('0:Rew:429.0,5620.0')] ).
cnf(5841,plain,
equal(multiply(inverse(multiply(u,v)),inverse(inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5661]),
[iquote('0:SpR:5661.0,5661.0')] ).
cnf(5845,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5661,421]),
[iquote('0:SpR:5661.0,421.0')] ).
cnf(5854,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[5661,744]),
[iquote('0:SpR:5661.0,744.0')] ).
cnf(5859,plain,
equal(multiply(u,inverse(positive_part(u))),inverse(positive_part(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[2210,5661]),
[iquote('0:SpR:2210.0,5661.0')] ).
cnf(5895,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[749,5841]),
[iquote('0:Rew:749.0,5841.0')] ).
cnf(6180,plain,
equal(multiply(positive_part(inverse(multiply(u,v))),u),least_upper_bound(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[5895,689]),
[iquote('0:SpR:5895.0,689.0')] ).
cnf(6614,plain,
equal(least_upper_bound(inverse(positive_part(u)),inverse(positive_part(inverse(u)))),multiply(positive_part(u),inverse(positive_part(u)))),
inference(spr,[status(thm),theory(equality)],[5859,689]),
[iquote('0:SpR:5859.0,689.0')] ).
cnf(6662,plain,
equal(least_upper_bound(inverse(positive_part(u)),inverse(positive_part(inverse(u)))),identity),
inference(rew,[status(thm),theory(equality)],[738,6614]),
[iquote('0:Rew:738.0,6614.0')] ).
cnf(12928,plain,
equal(multiply(positive_part(inverse(u)),negative_part(u)),greatest_lower_bound(positive_part(inverse(u)),positive_part(u))),
inference(spr,[status(thm),theory(equality)],[2210,809]),
[iquote('0:SpR:2210.0,809.0')] ).
cnf(12938,plain,
equal(multiply(u,negative_part(inverse(u))),greatest_lower_bound(u,identity)),
inference(spr,[status(thm),theory(equality)],[738,809]),
[iquote('0:SpR:738.0,809.0')] ).
cnf(12954,plain,
equal(multiply(positive_part(u),negative_part(inverse(u))),greatest_lower_bound(positive_part(u),positive_part(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[2211,809]),
[iquote('0:SpR:2211.0,809.0')] ).
cnf(12966,plain,
equal(multiply(u,negative_part(inverse(u))),negative_part(u)),
inference(rew,[status(thm),theory(equality)],[2,12938]),
[iquote('0:Rew:2.0,12938.0')] ).
cnf(12980,plain,
equal(multiply(positive_part(inverse(u)),negative_part(u)),positive_part(greatest_lower_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[9,12928,1668]),
[iquote('0:Rew:9.0,12928.0,1668.0,12928.0')] ).
cnf(12982,plain,
equal(multiply(positive_part(u),negative_part(inverse(u))),positive_part(greatest_lower_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[1668,12954]),
[iquote('0:Rew:1668.0,12954.0')] ).
cnf(13017,plain,
equal(multiply(positive_part(u),negative_part(inverse(u))),least_upper_bound(negative_part(inverse(u)),negative_part(u))),
inference(spr,[status(thm),theory(equality)],[12966,689]),
[iquote('0:SpR:12966.0,689.0')] ).
cnf(13069,plain,
equal(multiply(positive_part(u),negative_part(inverse(u))),negative_part(least_upper_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[10,13017,1295]),
[iquote('0:Rew:10.0,13017.0,1295.0,13017.0')] ).
cnf(13070,plain,
equal(negative_part(least_upper_bound(u,inverse(u))),positive_part(greatest_lower_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[12982,13069]),
[iquote('0:Rew:12982.0,13069.0')] ).
cnf(15490,plain,
equal(multiply(inverse(u),positive_part(u)),positive_part(multiply(inverse(u),identity))),
inference(spr,[status(thm),theory(equality)],[46,1033]),
[iquote('0:SpR:46.0,1033.0')] ).
cnf(15502,plain,
equal(positive_part(multiply(inverse(inverse(positive_part(inverse(u)))),inverse(positive_part(u)))),multiply(inverse(inverse(positive_part(inverse(u)))),identity)),
inference(spr,[status(thm),theory(equality)],[6662,1033]),
[iquote('0:SpR:6662.0,1033.0')] ).
cnf(15517,plain,
equal(multiply(inverse(u),positive_part(u)),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[429,15490]),
[iquote('0:Rew:429.0,15490.0')] ).
cnf(15556,plain,
equal(positive_part(multiply(positive_part(inverse(u)),inverse(positive_part(u)))),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[429,15502,749]),
[iquote('0:Rew:429.0,15502.0,749.0,15502.0')] ).
cnf(15557,plain,
equal(positive_part(multiply(inverse(u),inverse(positive_part(u)))),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[2904,15556]),
[iquote('0:Rew:2904.0,15556.0')] ).
cnf(15558,plain,
equal(positive_part(inverse(multiply(positive_part(u),u))),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[5845,15557]),
[iquote('0:Rew:5845.0,15557.0')] ).
cnf(15978,plain,
equal(multiply(positive_part(u),inverse(positive_part(inverse(u)))),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[15517,5661]),
[iquote('0:SpR:15517.0,5661.0')] ).
cnf(16061,plain,
equal(multiply(positive_part(u),inverse(positive_part(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[749,15978]),
[iquote('0:Rew:749.0,15978.0')] ).
cnf(18254,plain,
equal(positive_part(inverse(multiply(positive_part(inverse(u)),inverse(multiply(positive_part(u),u))))),positive_part(inverse(inverse(multiply(positive_part(u),u))))),
inference(spr,[status(thm),theory(equality)],[15558]),
[iquote('0:SpR:15558.0,15558.0')] ).
cnf(18355,plain,
equal(positive_part(multiply(positive_part(u),multiply(u,inverse(positive_part(inverse(u)))))),positive_part(multiply(positive_part(u),u))),
inference(rew,[status(thm),theory(equality)],[8,18254,5854,749]),
[iquote('0:Rew:8.0,18254.0,5854.0,18254.0,749.0,18254.0')] ).
cnf(18356,plain,
equal(positive_part(multiply(u,multiply(positive_part(u),inverse(positive_part(inverse(u)))))),positive_part(multiply(positive_part(u),u))),
inference(rew,[status(thm),theory(equality)],[2218,18355]),
[iquote('0:Rew:2218.0,18355.0')] ).
cnf(18357,plain,
equal(positive_part(multiply(positive_part(u),u)),positive_part(multiply(u,u))),
inference(rew,[status(thm),theory(equality)],[16061,18356]),
[iquote('0:Rew:16061.0,18356.0')] ).
cnf(27785,plain,
equal(greatest_lower_bound(u,positive_part(multiply(u,u))),u),
inference(spr,[status(thm),theory(equality)],[18357,2182]),
[iquote('0:SpR:18357.0,2182.0')] ).
cnf(27937,plain,
equal(negative_part(multiply(positive_part(multiply(inverse(u),inverse(u))),u)),multiply(inverse(u),u)),
inference(spr,[status(thm),theory(equality)],[27785,501]),
[iquote('0:SpR:27785.0,501.0')] ).
cnf(27989,plain,
equal(negative_part(multiply(positive_part(inverse(multiply(u,u))),u)),identity),
inference(rew,[status(thm),theory(equality)],[5845,27937,7]),
[iquote('0:Rew:5845.0,27937.0,7.0,27937.0')] ).
cnf(27990,plain,
equal(positive_part(greatest_lower_bound(u,inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[13070,27989,6180]),
[iquote('0:Rew:13070.0,27989.0,6180.0,27989.0')] ).
cnf(27991,plain,
equal(multiply(positive_part(inverse(u)),negative_part(u)),identity),
inference(rew,[status(thm),theory(equality)],[27990,12980]),
[iquote('0:Rew:27990.0,12980.0')] ).
cnf(28769,plain,
equal(multiply(inverse(positive_part(inverse(u))),identity),negative_part(u)),
inference(spr,[status(thm),theory(equality)],[27991,421]),
[iquote('0:SpR:27991.0,421.0')] ).
cnf(28854,plain,
equal(inverse(positive_part(inverse(u))),negative_part(u)),
inference(rew,[status(thm),theory(equality)],[429,28769]),
[iquote('0:Rew:429.0,28769.0')] ).
cnf(28860,plain,
equal(multiply(positive_part(u),negative_part(u)),u),
inference(rew,[status(thm),theory(equality)],[28854,16061]),
[iquote('0:Rew:28854.0,16061.0')] ).
cnf(29073,plain,
$false,
inference(unc,[status(thm)],[28860,5]),
[iquote('0:UnC:28860.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP167-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jun 13 10:00:05 EDT 2022
% 0.12/0.32 % CPUTime :
% 11.95/12.27
% 11.95/12.27 SPASS V 3.9
% 11.95/12.27 SPASS beiseite: Proof found.
% 11.95/12.27 % SZS status Theorem
% 11.95/12.27 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.95/12.27 SPASS derived 17888 clauses, backtracked 0 clauses, performed 0 splits and kept 3957 clauses.
% 11.95/12.27 SPASS allocated 91041 KBytes.
% 11.95/12.27 SPASS spent 0:0:11.90 on the problem.
% 11.95/12.27 0:00:00.03 for the input.
% 11.95/12.27 0:00:00.00 for the FLOTTER CNF translation.
% 11.95/12.27 0:00:00.16 for inferences.
% 11.95/12.27 0:00:00.00 for the backtracking.
% 11.95/12.27 0:0:11.66 for the reduction.
% 11.95/12.27
% 11.95/12.27
% 11.95/12.27 Here is a proof with depth 11, length 106 :
% 11.95/12.27 % SZS output start Refutation
% See solution above
% 12.25/12.56 Formulae used in the proof : lat4_1 lat4_2 lat4_3 lat4_4 prove_lat4 left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub associativity_of_lub lub_absorbtion glb_absorbtion monotony_lub1 monotony_glb1 monotony_lub2 monotony_glb2
% 12.25/12.56
%------------------------------------------------------------------------------