%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP149-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:45:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(greatest_lower_bound(a,c),a),
file('GRP149-1.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(b,c),b),
file('GRP149-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(least_upper_bound(least_upper_bound(a,b),c),c),
file('GRP149-1.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP149-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP149-1.p',unknown),
[] ).
cnf(10,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP149-1.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP149-1.p',unknown),
[] ).
cnf(19,plain,
equal(greatest_lower_bound(c,b),b),
inference(rew,[status(thm),theory(equality)],[7,2]),
[iquote('0:Rew:7.0,2.0')] ).
cnf(20,plain,
~ equal(least_upper_bound(c,least_upper_bound(a,b)),c),
inference(rew,[status(thm),theory(equality)],[8,3]),
[iquote('0:Rew:8.0,3.0')] ).
cnf(32,plain,
equal(least_upper_bound(c,b),c),
inference(spr,[status(thm),theory(equality)],[19,13]),
[iquote('0:SpR:19.0,13.0')] ).
cnf(46,plain,
equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(67,plain,
equal(least_upper_bound(c,a),c),
inference(spr,[status(thm),theory(equality)],[1,46]),
[iquote('0:SpR:1.0,46.0')] ).
cnf(74,plain,
equal(least_upper_bound(a,c),c),
inference(rew,[status(thm),theory(equality)],[8,67]),
[iquote('0:Rew:8.0,67.0')] ).
cnf(151,plain,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(v,least_upper_bound(u,w))),
inference(spr,[status(thm),theory(equality)],[8,10]),
[iquote('0:SpR:8.0,10.0')] ).
cnf(160,plain,
equal(least_upper_bound(u,least_upper_bound(v,w)),least_upper_bound(v,least_upper_bound(u,w))),
inference(rew,[status(thm),theory(equality)],[10,151]),
[iquote('0:Rew:10.0,151.0')] ).
cnf(161,plain,
~ equal(least_upper_bound(a,least_upper_bound(c,b)),c),
inference(rew,[status(thm),theory(equality)],[160,20]),
[iquote('0:Rew:160.0,20.0')] ).
cnf(162,plain,
~ equal(c,c),
inference(rew,[status(thm),theory(equality)],[74,161,32]),
[iquote('0:Rew:74.0,161.0,32.0,161.0')] ).
cnf(163,plain,
$false,
inference(obv,[status(thm),theory(equality)],[162]),
[iquote('0:Obv:162.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP149-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 23:45:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 128 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.20/0.42 SPASS allocated 63222 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.42 0:00:00.03 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.01 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 2, length 18 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : ax_lub1d_1 ax_lub1d_2 prove_ax_lub1d symmetry_of_glb symmetry_of_lub associativity_of_lub lub_absorbtion
% 0.20/0.42
%------------------------------------------------------------------------------