%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP185-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:46:13 EDT 2022
% Result : Unsatisfiable 0.52s 0.72s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(identity),identity),
file('GRP185-4.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(inverse(u)),u),
file('GRP185-4.p',unknown),
[] ).
cnf(3,axiom,
equal(inverse(multiply(u,v)),multiply(inverse(v),inverse(u))),
file('GRP185-4.p',unknown),
[] ).
cnf(4,axiom,
~ equal(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),least_upper_bound(multiply(a,b),identity)),
file('GRP185-4.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(identity,u),u),
file('GRP185-4.p',unknown),
[] ).
cnf(9,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP185-4.p',unknown),
[] ).
cnf(11,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP185-4.p',unknown),
[] ).
cnf(15,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP185-4.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP185-4.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP185-4.p',unknown),
[] ).
cnf(20,plain,
~ equal(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,least_upper_bound(b,least_upper_bound(multiply(a,identity),multiply(a,b))))),least_upper_bound(identity,multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[11,4,5,16,18,9]),
[iquote('0:Rew:11.0,4.0,5.0,4.0,5.0,4.0,16.0,4.0,16.0,4.0,18.0,4.0,9.0,4.0,9.0,4.0,9.0,4.0')] ).
cnf(96,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(102,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[5,96]),
[iquote('0:Rew:5.0,96.0')] ).
cnf(113,plain,
equal(multiply(u,identity),u),
inference(spr,[status(thm),theory(equality)],[2,102]),
[iquote('0:SpR:2.0,102.0')] ).
cnf(115,plain,
~ equal(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,least_upper_bound(b,least_upper_bound(a,multiply(a,b))))),least_upper_bound(identity,multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[113,20]),
[iquote('0:Rew:113.0,20.0')] ).
cnf(147,plain,
equal(greatest_lower_bound(least_upper_bound(u,v),least_upper_bound(u,least_upper_bound(v,w))),least_upper_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[11,15]),
[iquote('0:SpR:11.0,15.0')] ).
cnf(148,plain,
equal(least_upper_bound(u,least_upper_bound(v,w)),least_upper_bound(w,least_upper_bound(u,v))),
inference(spr,[status(thm),theory(equality)],[11,9]),
[iquote('0:SpR:11.0,9.0')] ).
cnf(158,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)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(164,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)],[11,158]),
[iquote('0:Rew:11.0,158.0')] ).
cnf(165,plain,
~ equal(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,multiply(a,b))))),least_upper_bound(identity,multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[164,115]),
[iquote('0:Rew:164.0,115.0')] ).
cnf(709,plain,
equal(least_upper_bound(u,least_upper_bound(v,w)),least_upper_bound(w,least_upper_bound(v,u))),
inference(spr,[status(thm),theory(equality)],[9,148]),
[iquote('0:SpR:9.0,148.0')] ).
cnf(3200,plain,
equal(greatest_lower_bound(least_upper_bound(u,v),least_upper_bound(u,least_upper_bound(w,least_upper_bound(x,v)))),least_upper_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[709,147]),
[iquote('0:SpR:709.0,147.0')] ).
cnf(3263,plain,
$false,
inference(unc,[status(thm)],[3200,165]),
[iquote('0:UnC:3200.0,165.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP185-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n006.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 : Tue Jun 14 13:35:41 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.52/0.72
% 0.52/0.72 SPASS V 3.9
% 0.52/0.72 SPASS beiseite: Proof found.
% 0.52/0.72 % SZS status Theorem
% 0.52/0.72 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.72 SPASS derived 2140 clauses, backtracked 0 clauses, performed 0 splits and kept 313 clauses.
% 0.52/0.72 SPASS allocated 65771 KBytes.
% 0.52/0.72 SPASS spent 0:00:00.35 on the problem.
% 0.52/0.72 0:00:00.04 for the input.
% 0.52/0.72 0:00:00.00 for the FLOTTER CNF translation.
% 0.52/0.72 0:00:00.02 for inferences.
% 0.52/0.72 0:00:00.00 for the backtracking.
% 0.52/0.72 0:00:00.28 for the reduction.
% 0.52/0.72
% 0.52/0.72
% 0.52/0.72 Here is a proof with depth 3, length 23 :
% 0.52/0.72 % SZS output start Refutation
% See solution above
% 0.52/0.72 Formulae used in the proof : p22b_1 p22b_2 p22b_3 prove_p22b left_identity symmetry_of_lub associativity_of_lub glb_absorbtion monotony_lub1 monotony_lub2
% 0.52/0.72
%------------------------------------------------------------------------------