%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 11:46:03 EDT 2022
% Result : Unsatisfiable 1.08s 1.26s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 28 RR)
% Number of literals : 28 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)),
file('GRP169-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(greatest_lower_bound(a,b),b),
file('GRP169-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(identity,u),u),
file('GRP169-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP169-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP169-2.p',unknown),
[] ).
cnf(6,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP169-2.p',unknown),
[] ).
cnf(7,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP169-2.p',unknown),
[] ).
cnf(12,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP169-2.p',unknown),
[] ).
cnf(13,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP169-2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP169-2.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP169-2.p',unknown),
[] ).
cnf(29,plain,
equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(335,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(336,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[3,335]),
[iquote('0:Rew:3.0,335.0')] ).
cnf(339,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[336]),
[iquote('0:SpR:336.0,336.0')] ).
cnf(342,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[4,336]),
[iquote('0:SpR:4.0,336.0')] ).
cnf(344,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[339,342]),
[iquote('0:Rew:339.0,342.0')] ).
cnf(363,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(spr,[status(thm),theory(equality)],[339,336]),
[iquote('0:SpR:339.0,336.0')] ).
cnf(385,plain,
equal(greatest_lower_bound(multiply(inverse(a),u),multiply(inverse(b),u)),multiply(inverse(a),u)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(6570,plain,
equal(greatest_lower_bound(multiply(inverse(a),b),identity),multiply(inverse(a),b)),
inference(spr,[status(thm),theory(equality)],[4,385]),
[iquote('0:SpR:4.0,385.0')] ).
cnf(6597,plain,
equal(greatest_lower_bound(identity,multiply(inverse(a),b)),multiply(inverse(a),b)),
inference(rew,[status(thm),theory(equality)],[6,6570]),
[iquote('0:Rew:6.0,6570.0')] ).
cnf(6755,plain,
equal(least_upper_bound(identity,multiply(inverse(a),b)),identity),
inference(spr,[status(thm),theory(equality)],[6597,12]),
[iquote('0:SpR:6597.0,12.0')] ).
cnf(6822,plain,
equal(least_upper_bound(multiply(u,identity),multiply(u,multiply(inverse(a),b))),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[6755,14]),
[iquote('0:SpR:6755.0,14.0')] ).
cnf(6841,plain,
equal(least_upper_bound(u,multiply(u,multiply(inverse(a),b))),u),
inference(rew,[status(thm),theory(equality)],[344,6822]),
[iquote('0:Rew:344.0,6822.0')] ).
cnf(7388,plain,
equal(least_upper_bound(a,b),a),
inference(spr,[status(thm),theory(equality)],[363,6841]),
[iquote('0:SpR:363.0,6841.0')] ).
cnf(7437,plain,
equal(greatest_lower_bound(b,a),b),
inference(spr,[status(thm),theory(equality)],[7388,29]),
[iquote('0:SpR:7388.0,29.0')] ).
cnf(7452,plain,
equal(greatest_lower_bound(a,b),b),
inference(rew,[status(thm),theory(equality)],[6,7437]),
[iquote('0:Rew:6.0,7437.0')] ).
cnf(7453,plain,
$false,
inference(mrr,[status(thm)],[7452,2]),
[iquote('0:MRR:7452.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 12:03:57 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.08/1.26
% 1.08/1.26 SPASS V 3.9
% 1.08/1.26 SPASS beiseite: Proof found.
% 1.08/1.26 % SZS status Theorem
% 1.08/1.26 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.08/1.26 SPASS derived 4891 clauses, backtracked 0 clauses, performed 0 splits and kept 714 clauses.
% 1.08/1.26 SPASS allocated 69404 KBytes.
% 1.08/1.26 SPASS spent 0:00:00.88 on the problem.
% 1.08/1.26 0:00:00.04 for the input.
% 1.08/1.26 0:00:00.00 for the FLOTTER CNF translation.
% 1.08/1.26 0:00:00.04 for inferences.
% 1.08/1.26 0:00:00.00 for the backtracking.
% 1.08/1.26 0:00:00.77 for the reduction.
% 1.08/1.26
% 1.08/1.26
% 1.08/1.26 Here is a proof with depth 6, length 28 :
% 1.08/1.26 % SZS output start Refutation
% See solution above
% 1.08/1.26 Formulae used in the proof : p02b_1 prove_p02b left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion monotony_lub1 monotony_glb2
% 1.08/1.26
%------------------------------------------------------------------------------