TSTP Solution File: GRP167-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP167-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:46:02 EDT 2022
% Result : Unsatisfiable 10.32s 10.51s
% Output : Refutation 10.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of clauses : 104 ( 104 unt; 0 nHn; 104 RR)
% Number of literals : 104 ( 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(inverse(identity),identity),
file('GRP167-2.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(inverse(u)),u),
file('GRP167-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
file('GRP167-2.p',unknown),
[] ).
cnf(4,axiom,
equal(least_upper_bound(u,identity),positive_part(u)),
file('GRP167-2.p',unknown),
[] ).
cnf(5,axiom,
equal(greatest_lower_bound(u,identity),negative_part(u)),
file('GRP167-2.p',unknown),
[] ).
cnf(6,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('GRP167-2.p',unknown),
[] ).
cnf(7,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('GRP167-2.p',unknown),
[] ).
cnf(8,axiom,
~ equal(multiply(positive_part(a),negative_part(a)),a),
file('GRP167-2.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(identity,u),u),
file('GRP167-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP167-2.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP167-2.p',unknown),
[] ).
cnf(12,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP167-2.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP167-2.p',unknown),
[] ).
cnf(15,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP167-2.p',unknown),
[] ).
cnf(18,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP167-2.p',unknown),
[] ).
cnf(19,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP167-2.p',unknown),
[] ).
cnf(20,axiom,
equal(least_upper_bound(multiply(u,v),multiply(u,w)),multiply(u,least_upper_bound(v,w))),
file('GRP167-2.p',unknown),
[] ).
cnf(21,axiom,
equal(greatest_lower_bound(multiply(u,v),multiply(u,w)),multiply(u,greatest_lower_bound(v,w))),
file('GRP167-2.p',unknown),
[] ).
cnf(22,axiom,
equal(least_upper_bound(multiply(u,v),multiply(w,v)),multiply(least_upper_bound(u,w),v)),
file('GRP167-2.p',unknown),
[] ).
cnf(23,axiom,
equal(greatest_lower_bound(multiply(u,v),multiply(w,v)),multiply(greatest_lower_bound(u,w),v)),
file('GRP167-2.p',unknown),
[] ).
cnf(33,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[2,10]),
[iquote('0:SpR:2.0,10.0')] ).
cnf(56,plain,
equal(least_upper_bound(identity,u),positive_part(u)),
inference(spr,[status(thm),theory(equality)],[13,4]),
[iquote('0:SpR:13.0,4.0')] ).
cnf(67,plain,
equal(greatest_lower_bound(identity,positive_part(u)),identity),
inference(spr,[status(thm),theory(equality)],[56,19]),
[iquote('0:SpR:56.0,19.0')] ).
cnf(69,plain,
equal(positive_part(greatest_lower_bound(identity,u)),identity),
inference(spr,[status(thm),theory(equality)],[56,18]),
[iquote('0:SpR:56.0,18.0')] ).
cnf(92,plain,
equal(greatest_lower_bound(identity,u),negative_part(u)),
inference(spr,[status(thm),theory(equality)],[12,5]),
[iquote('0:SpR:12.0,5.0')] ).
cnf(103,plain,
equal(positive_part(negative_part(u)),identity),
inference(rew,[status(thm),theory(equality)],[92,69]),
[iquote('0:Rew:92.0,69.0')] ).
cnf(104,plain,
equal(negative_part(positive_part(u)),identity),
inference(rew,[status(thm),theory(equality)],[92,67]),
[iquote('0:Rew:92.0,67.0')] ).
cnf(186,plain,
equal(multiply(inverse(u),identity),inverse(multiply(identity,u))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(189,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(192,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[9,186]),
[iquote('0:Rew:9.0,186.0')] ).
cnf(197,plain,
equal(multiply(u,identity),u),
inference(spr,[status(thm),theory(equality)],[2,192]),
[iquote('0:SpR:2.0,192.0')] ).
cnf(227,plain,
equal(least_upper_bound(u,least_upper_bound(v,identity)),positive_part(least_upper_bound(u,v))),
inference(spr,[status(thm),theory(equality)],[15,4]),
[iquote('0:SpR:15.0,4.0')] ).
cnf(247,plain,
equal(least_upper_bound(u,positive_part(v)),positive_part(least_upper_bound(u,v))),
inference(rew,[status(thm),theory(equality)],[4,227]),
[iquote('0:Rew:4.0,227.0')] ).
cnf(262,plain,
equal(greatest_lower_bound(u,positive_part(least_upper_bound(u,v))),u),
inference(spr,[status(thm),theory(equality)],[247,19]),
[iquote('0:SpR:247.0,19.0')] ).
cnf(271,plain,
equal(positive_part(least_upper_bound(u,negative_part(v))),least_upper_bound(u,identity)),
inference(spr,[status(thm),theory(equality)],[103,247]),
[iquote('0:SpR:103.0,247.0')] ).
cnf(278,plain,
equal(positive_part(least_upper_bound(u,negative_part(v))),positive_part(u)),
inference(rew,[status(thm),theory(equality)],[4,271]),
[iquote('0:Rew:4.0,271.0')] ).
cnf(292,plain,
equal(positive_part(least_upper_bound(negative_part(u),v)),positive_part(v)),
inference(spr,[status(thm),theory(equality)],[13,278]),
[iquote('0:SpR:13.0,278.0')] ).
cnf(513,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpR:10.0,11.0')] ).
cnf(519,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[9,513]),
[iquote('0:Rew:9.0,513.0')] ).
cnf(528,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3,519]),
[iquote('0:SpR:3.0,519.0')] ).
cnf(537,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[2,528]),
[iquote('0:Rew:2.0,528.0')] ).
cnf(656,plain,
equal(greatest_lower_bound(multiply(u,v),v),multiply(greatest_lower_bound(u,identity),v)),
inference(spr,[status(thm),theory(equality)],[9,23]),
[iquote('0:SpR:9.0,23.0')] ).
cnf(665,plain,
equal(multiply(greatest_lower_bound(inverse(u),v),u),greatest_lower_bound(identity,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[10,23]),
[iquote('0:SpR:10.0,23.0')] ).
cnf(673,plain,
equal(greatest_lower_bound(u,multiply(v,u)),multiply(negative_part(v),u)),
inference(rew,[status(thm),theory(equality)],[12,656,5]),
[iquote('0:Rew:12.0,656.0,5.0,656.0')] ).
cnf(678,plain,
equal(multiply(greatest_lower_bound(inverse(u),v),u),negative_part(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[92,665]),
[iquote('0:Rew:92.0,665.0')] ).
cnf(846,plain,
equal(least_upper_bound(multiply(u,v),v),multiply(least_upper_bound(u,identity),v)),
inference(spr,[status(thm),theory(equality)],[9,22]),
[iquote('0:SpR:9.0,22.0')] ).
cnf(863,plain,
equal(least_upper_bound(u,multiply(v,u)),multiply(positive_part(v),u)),
inference(rew,[status(thm),theory(equality)],[13,846,4]),
[iquote('0:Rew:13.0,846.0,4.0,846.0')] ).
cnf(880,plain,
equal(multiply(inverse(multiply(u,v)),inverse(inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[537]),
[iquote('0:SpR:537.0,537.0')] ).
cnf(906,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[2,880]),
[iquote('0:Rew:2.0,880.0')] ).
cnf(1068,plain,
equal(greatest_lower_bound(multiply(u,v),u),multiply(u,greatest_lower_bound(v,identity))),
inference(spr,[status(thm),theory(equality)],[197,21]),
[iquote('0:SpR:197.0,21.0')] ).
cnf(1086,plain,
equal(greatest_lower_bound(u,multiply(u,v)),multiply(u,negative_part(v))),
inference(rew,[status(thm),theory(equality)],[12,1068,5]),
[iquote('0:Rew:12.0,1068.0,5.0,1068.0')] ).
cnf(1313,plain,
equal(multiply(inverse(u),least_upper_bound(v,u)),least_upper_bound(multiply(inverse(u),v),identity)),
inference(spr,[status(thm),theory(equality)],[10,20]),
[iquote('0:SpR:10.0,20.0')] ).
cnf(1344,plain,
equal(multiply(inverse(u),least_upper_bound(v,u)),positive_part(multiply(inverse(u),v))),
inference(rew,[status(thm),theory(equality)],[56,1313,13]),
[iquote('0:Rew:56.0,1313.0,13.0,1313.0')] ).
cnf(1576,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)],[92,7]),
[iquote('0:SpR:92.0,7.0')] ).
cnf(1608,plain,
equal(least_upper_bound(negative_part(u),negative_part(v)),negative_part(least_upper_bound(u,v))),
inference(rew,[status(thm),theory(equality)],[92,1576]),
[iquote('0:Rew:92.0,1576.0,92.0,1576.0')] ).
cnf(1978,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)],[56,6]),
[iquote('0:SpR:56.0,6.0')] ).
cnf(2016,plain,
equal(greatest_lower_bound(positive_part(u),positive_part(v)),positive_part(greatest_lower_bound(u,v))),
inference(rew,[status(thm),theory(equality)],[56,1978]),
[iquote('0:Rew:56.0,1978.0,56.0,1978.0')] ).
cnf(2396,plain,
equal(multiply(negative_part(u),inverse(u)),greatest_lower_bound(inverse(u),identity)),
inference(spr,[status(thm),theory(equality)],[33,673]),
[iquote('0:SpR:33.0,673.0')] ).
cnf(2409,plain,
equal(multiply(negative_part(u),inverse(u)),negative_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[92,2396,12]),
[iquote('0:Rew:92.0,2396.0,12.0,2396.0')] ).
cnf(2473,plain,
equal(multiply(identity,inverse(positive_part(u))),negative_part(inverse(positive_part(u)))),
inference(spr,[status(thm),theory(equality)],[104,2409]),
[iquote('0:SpR:104.0,2409.0')] ).
cnf(2480,plain,
equal(negative_part(inverse(positive_part(u))),inverse(positive_part(u))),
inference(rew,[status(thm),theory(equality)],[9,2473]),
[iquote('0:Rew:9.0,2473.0')] ).
cnf(2529,plain,
equal(positive_part(least_upper_bound(inverse(positive_part(u)),v)),positive_part(v)),
inference(spr,[status(thm),theory(equality)],[2480,292]),
[iquote('0:SpR:2480.0,292.0')] ).
cnf(2555,plain,
equal(greatest_lower_bound(u,positive_part(multiply(positive_part(v),u))),u),
inference(spr,[status(thm),theory(equality)],[863,262]),
[iquote('0:SpR:863.0,262.0')] ).
cnf(2569,plain,
equal(multiply(u,least_upper_bound(v,multiply(u,v))),multiply(positive_part(u),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[863,20]),
[iquote('0:SpR:863.0,20.0')] ).
cnf(2571,plain,
equal(multiply(positive_part(inverse(u)),u),least_upper_bound(u,identity)),
inference(spr,[status(thm),theory(equality)],[10,863]),
[iquote('0:SpR:10.0,863.0')] ).
cnf(2572,plain,
equal(multiply(positive_part(inverse(multiply(u,v))),u),least_upper_bound(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[906,863]),
[iquote('0:SpR:906.0,863.0')] ).
cnf(2574,plain,
equal(multiply(positive_part(u),inverse(u)),least_upper_bound(inverse(u),identity)),
inference(spr,[status(thm),theory(equality)],[33,863]),
[iquote('0:SpR:33.0,863.0')] ).
cnf(2586,plain,
equal(multiply(positive_part(inverse(u)),u),positive_part(u)),
inference(rew,[status(thm),theory(equality)],[4,2571]),
[iquote('0:Rew:4.0,2571.0')] ).
cnf(2587,plain,
equal(multiply(positive_part(u),inverse(u)),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[56,2574,13]),
[iquote('0:Rew:56.0,2574.0,13.0,2574.0')] ).
cnf(2594,plain,
equal(multiply(positive_part(u),multiply(u,v)),multiply(u,multiply(positive_part(u),v))),
inference(rew,[status(thm),theory(equality)],[863,2569]),
[iquote('0:Rew:863.0,2569.0')] ).
cnf(2797,plain,
equal(multiply(u,inverse(positive_part(u))),inverse(positive_part(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[2586,537]),
[iquote('0:SpR:2586.0,537.0')] ).
cnf(3477,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)],[863,2529]),
[iquote('0:SpR:863.0,2529.0')] ).
cnf(5425,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)],[2797,863]),
[iquote('0:SpR:2797.0,863.0')] ).
cnf(5477,plain,
equal(least_upper_bound(inverse(positive_part(u)),inverse(positive_part(inverse(u)))),identity),
inference(rew,[status(thm),theory(equality)],[33,5425]),
[iquote('0:Rew:33.0,5425.0')] ).
cnf(11957,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)],[2586,1086]),
[iquote('0:SpR:2586.0,1086.0')] ).
cnf(11960,plain,
equal(multiply(u,negative_part(inverse(u))),greatest_lower_bound(u,identity)),
inference(spr,[status(thm),theory(equality)],[33,1086]),
[iquote('0:SpR:33.0,1086.0')] ).
cnf(11965,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)],[2587,1086]),
[iquote('0:SpR:2587.0,1086.0')] ).
cnf(11994,plain,
equal(multiply(u,negative_part(inverse(u))),negative_part(u)),
inference(rew,[status(thm),theory(equality)],[5,11960]),
[iquote('0:Rew:5.0,11960.0')] ).
cnf(12008,plain,
equal(multiply(positive_part(inverse(u)),negative_part(u)),positive_part(greatest_lower_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[12,11957,2016]),
[iquote('0:Rew:12.0,11957.0,2016.0,11957.0')] ).
cnf(12010,plain,
equal(multiply(positive_part(u),negative_part(inverse(u))),positive_part(greatest_lower_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[2016,11965]),
[iquote('0:Rew:2016.0,11965.0')] ).
cnf(12045,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)],[11994,863]),
[iquote('0:SpR:11994.0,863.0')] ).
cnf(12097,plain,
equal(multiply(positive_part(u),negative_part(inverse(u))),negative_part(least_upper_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[13,12045,1608]),
[iquote('0:Rew:13.0,12045.0,1608.0,12045.0')] ).
cnf(12098,plain,
equal(negative_part(least_upper_bound(u,inverse(u))),positive_part(greatest_lower_bound(u,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[12010,12097]),
[iquote('0:Rew:12010.0,12097.0')] ).
cnf(16641,plain,
equal(multiply(inverse(u),positive_part(u)),positive_part(multiply(inverse(u),identity))),
inference(spr,[status(thm),theory(equality)],[56,1344]),
[iquote('0:SpR:56.0,1344.0')] ).
cnf(16657,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)],[5477,1344]),
[iquote('0:SpR:5477.0,1344.0')] ).
cnf(16679,plain,
equal(multiply(inverse(u),positive_part(u)),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[197,16641]),
[iquote('0:Rew:197.0,16641.0')] ).
cnf(16757,plain,
equal(positive_part(multiply(positive_part(inverse(u)),inverse(positive_part(u)))),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[197,16657,2]),
[iquote('0:Rew:197.0,16657.0,2.0,16657.0')] ).
cnf(16758,plain,
equal(positive_part(multiply(inverse(u),inverse(positive_part(u)))),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3477,16757]),
[iquote('0:Rew:3477.0,16757.0')] ).
cnf(16759,plain,
equal(positive_part(inverse(multiply(positive_part(u),u))),positive_part(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,16758]),
[iquote('0:Rew:3.0,16758.0')] ).
cnf(16990,plain,
equal(multiply(positive_part(u),inverse(positive_part(inverse(u)))),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[16679,537]),
[iquote('0:SpR:16679.0,537.0')] ).
cnf(17088,plain,
equal(multiply(positive_part(u),inverse(positive_part(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,16990]),
[iquote('0:Rew:2.0,16990.0')] ).
cnf(18745,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)],[16759]),
[iquote('0:SpR:16759.0,16759.0')] ).
cnf(18849,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)],[11,18745,189,2]),
[iquote('0:Rew:11.0,18745.0,189.0,18745.0,2.0,18745.0')] ).
cnf(18850,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)],[2594,18849]),
[iquote('0:Rew:2594.0,18849.0')] ).
cnf(18851,plain,
equal(positive_part(multiply(positive_part(u),u)),positive_part(multiply(u,u))),
inference(rew,[status(thm),theory(equality)],[17088,18850]),
[iquote('0:Rew:17088.0,18850.0')] ).
cnf(35615,plain,
equal(greatest_lower_bound(u,positive_part(multiply(u,u))),u),
inference(spr,[status(thm),theory(equality)],[18851,2555]),
[iquote('0:SpR:18851.0,2555.0')] ).
cnf(35796,plain,
equal(negative_part(multiply(positive_part(multiply(inverse(u),inverse(u))),u)),multiply(inverse(u),u)),
inference(spr,[status(thm),theory(equality)],[35615,678]),
[iquote('0:SpR:35615.0,678.0')] ).
cnf(35858,plain,
equal(negative_part(multiply(positive_part(inverse(multiply(u,u))),u)),identity),
inference(rew,[status(thm),theory(equality)],[3,35796,10]),
[iquote('0:Rew:3.0,35796.0,10.0,35796.0')] ).
cnf(35859,plain,
equal(positive_part(greatest_lower_bound(u,inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[12098,35858,2572]),
[iquote('0:Rew:12098.0,35858.0,2572.0,35858.0')] ).
cnf(35860,plain,
equal(multiply(positive_part(inverse(u)),negative_part(u)),identity),
inference(rew,[status(thm),theory(equality)],[35859,12008]),
[iquote('0:Rew:35859.0,12008.0')] ).
cnf(36595,plain,
equal(multiply(inverse(positive_part(inverse(u))),identity),negative_part(u)),
inference(spr,[status(thm),theory(equality)],[35860,519]),
[iquote('0:SpR:35860.0,519.0')] ).
cnf(36690,plain,
equal(inverse(positive_part(inverse(u))),negative_part(u)),
inference(rew,[status(thm),theory(equality)],[197,36595]),
[iquote('0:Rew:197.0,36595.0')] ).
cnf(36696,plain,
equal(multiply(positive_part(u),negative_part(u)),u),
inference(rew,[status(thm),theory(equality)],[36690,17088]),
[iquote('0:Rew:36690.0,17088.0')] ).
cnf(36901,plain,
$false,
inference(unc,[status(thm)],[36696,8]),
[iquote('0:UnC:36696.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP167-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 04:06:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.32/10.51
% 10.32/10.51 SPASS V 3.9
% 10.32/10.51 SPASS beiseite: Proof found.
% 10.32/10.51 % SZS status Theorem
% 10.32/10.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.32/10.51 SPASS derived 22180 clauses, backtracked 0 clauses, performed 0 splits and kept 4763 clauses.
% 10.32/10.51 SPASS allocated 97675 KBytes.
% 10.32/10.51 SPASS spent 0:0:10.14 on the problem.
% 10.32/10.51 0:00:00.04 for the input.
% 10.32/10.51 0:00:00.00 for the FLOTTER CNF translation.
% 10.32/10.51 0:00:00.13 for inferences.
% 10.32/10.51 0:00:00.00 for the backtracking.
% 10.32/10.51 0:00:09.94 for the reduction.
% 10.32/10.51
% 10.32/10.51
% 10.32/10.51 Here is a proof with depth 8, length 104 :
% 10.32/10.51 % SZS output start Refutation
% See solution above
% 10.62/10.81 Formulae used in the proof : lat4_1 lat4_2 lat4_3 lat4_4 lat4_5 lat4_6 lat4_7 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
% 10.62/10.81
%------------------------------------------------------------------------------