%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.45s 0.62s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 27 RR)
% Number of literals : 27 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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(greatest_lower_bound(inverse(u),inverse(v)),inverse(least_upper_bound(u,v))),
file('GRP167-5.p',unknown),
[] ).
cnf(2,axiom,
equal(least_upper_bound(u,identity),positive_part(u)),
file('GRP167-5.p',unknown),
[] ).
cnf(3,axiom,
equal(greatest_lower_bound(u,identity),negative_part(u)),
file('GRP167-5.p',unknown),
[] ).
cnf(6,axiom,
~ equal(multiply(positive_part(a),negative_part(a)),a),
file('GRP167-5.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(identity,u),u),
file('GRP167-5.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP167-5.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP167-5.p',unknown),
[] ).
cnf(10,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP167-5.p',unknown),
[] ).
cnf(11,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP167-5.p',unknown),
[] ).
cnf(21,axiom,
equal(greatest_lower_bound(multiply(u,v),multiply(w,v)),multiply(greatest_lower_bound(u,w),v)),
file('GRP167-5.p',unknown),
[] ).
cnf(47,plain,
equal(least_upper_bound(identity,u),positive_part(u)),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.0,2.0')] ).
cnf(66,plain,
equal(greatest_lower_bound(identity,u),negative_part(u)),
inference(spr,[status(thm),theory(equality)],[10,3]),
[iquote('0:SpR:10.0,3.0')] ).
cnf(550,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[8,9]),
[iquote('0:SpR:8.0,9.0')] ).
cnf(551,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[7,550]),
[iquote('0:Rew:7.0,550.0')] ).
cnf(554,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[551]),
[iquote('0:SpR:551.0,551.0')] ).
cnf(557,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[8,551]),
[iquote('0:SpR:8.0,551.0')] ).
cnf(561,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[554,557]),
[iquote('0:Rew:554.0,557.0')] ).
cnf(564,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[561,8]),
[iquote('0:SpR:561.0,8.0')] ).
cnf(573,plain,
equal(greatest_lower_bound(identity,inverse(u)),inverse(least_upper_bound(identity,u))),
inference(spr,[status(thm),theory(equality)],[564,1]),
[iquote('0:SpR:564.0,1.0')] ).
cnf(578,plain,
equal(negative_part(inverse(u)),inverse(positive_part(u))),
inference(rew,[status(thm),theory(equality)],[66,573,47]),
[iquote('0:Rew:66.0,573.0,47.0,573.0')] ).
cnf(602,plain,
equal(greatest_lower_bound(multiply(u,v),v),multiply(greatest_lower_bound(u,identity),v)),
inference(spr,[status(thm),theory(equality)],[7,21]),
[iquote('0:SpR:7.0,21.0')] ).
cnf(613,plain,
equal(greatest_lower_bound(u,multiply(v,u)),multiply(negative_part(v),u)),
inference(rew,[status(thm),theory(equality)],[10,602,3]),
[iquote('0:Rew:10.0,602.0,3.0,602.0')] ).
cnf(2204,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(spr,[status(thm),theory(equality)],[554,551]),
[iquote('0:SpR:554.0,551.0')] ).
cnf(3372,plain,
equal(multiply(negative_part(inverse(u)),u),greatest_lower_bound(u,identity)),
inference(spr,[status(thm),theory(equality)],[8,613]),
[iquote('0:SpR:8.0,613.0')] ).
cnf(3384,plain,
equal(multiply(inverse(positive_part(u)),u),negative_part(u)),
inference(rew,[status(thm),theory(equality)],[578,3372,3]),
[iquote('0:Rew:578.0,3372.0,3.0,3372.0')] ).
cnf(3410,plain,
equal(multiply(positive_part(u),negative_part(u)),u),
inference(spr,[status(thm),theory(equality)],[3384,2204]),
[iquote('0:SpR:3384.0,2204.0')] ).
cnf(3422,plain,
$false,
inference(unc,[status(thm)],[3410,6]),
[iquote('0:UnC:3410.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 14:09:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.45/0.62
% 0.45/0.62 SPASS V 3.9
% 0.45/0.62 SPASS beiseite: Proof found.
% 0.45/0.62 % SZS status Theorem
% 0.45/0.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.62 SPASS derived 2206 clauses, backtracked 0 clauses, performed 0 splits and kept 501 clauses.
% 0.45/0.62 SPASS allocated 65901 KBytes.
% 0.45/0.62 SPASS spent 0:00:00.26 on the problem.
% 0.45/0.62 0:00:00.03 for the input.
% 0.45/0.62 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.62 0:00:00.02 for inferences.
% 0.45/0.62 0:00:00.00 for the backtracking.
% 0.45/0.62 0:00:00.20 for the reduction.
% 0.45/0.62
% 0.45/0.62
% 0.45/0.62 Here is a proof with depth 4, length 27 :
% 0.45/0.62 % SZS output start Refutation
% See solution above
% 0.45/0.62 Formulae used in the proof : p10 lat4_1 lat4_2 prove_lat4 left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub monotony_glb2
% 0.45/0.62
%------------------------------------------------------------------------------