%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP170-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:46:04 EDT 2022
% Result : Unsatisfiable 7.06s 7.26s
% Output : Refutation 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(a,b),b),
file('GRP170-3.p',unknown),
[] ).
cnf(2,axiom,
equal(least_upper_bound(c,d),d),
file('GRP170-3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
file('GRP170-3.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('GRP170-3.p',unknown),
[] ).
cnf(14,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP170-3.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP170-3.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP170-3.p',unknown),
[] ).
cnf(438,plain,
equal(least_upper_bound(multiply(a,u),multiply(b,u)),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(783,plain,
equal(least_upper_bound(multiply(u,c),multiply(u,d)),multiply(u,d)),
inference(spr,[status(thm),theory(equality)],[2,15]),
[iquote('0:SpR:2.0,15.0')] ).
cnf(1131,plain,
equal(least_upper_bound(multiply(a,u),least_upper_bound(multiply(b,u),v)),least_upper_bound(multiply(b,u),v)),
inference(spr,[status(thm),theory(equality)],[438,10]),
[iquote('0:SpR:438.0,10.0')] ).
cnf(25032,plain,
equal(least_upper_bound(multiply(a,c),multiply(b,d)),multiply(b,d)),
inference(spr,[status(thm),theory(equality)],[783,1131]),
[iquote('0:SpR:783.0,1131.0')] ).
cnf(25099,plain,
equal(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
inference(spr,[status(thm),theory(equality)],[25032,14]),
[iquote('0:SpR:25032.0,14.0')] ).
cnf(25128,plain,
$false,
inference(mrr,[status(thm)],[25099,3]),
[iquote('0:MRR:25099.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP170-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 09:57:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 7.06/7.26
% 7.06/7.26 SPASS V 3.9
% 7.06/7.26 SPASS beiseite: Proof found.
% 7.06/7.26 % SZS status Theorem
% 7.06/7.26 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.06/7.26 SPASS derived 16570 clauses, backtracked 0 clauses, performed 0 splits and kept 2875 clauses.
% 7.06/7.26 SPASS allocated 87343 KBytes.
% 7.06/7.26 SPASS spent 0:00:06.77 on the problem.
% 7.06/7.26 0:00:00.04 for the input.
% 7.06/7.26 0:00:00.00 for the FLOTTER CNF translation.
% 7.06/7.26 0:00:00.11 for inferences.
% 7.06/7.26 0:00:00.00 for the backtracking.
% 7.06/7.26 0:00:06.59 for the reduction.
% 7.06/7.26
% 7.06/7.26
% 7.06/7.26 Here is a proof with depth 4, length 13 :
% 7.06/7.26 % SZS output start Refutation
% See solution above
% 7.06/7.26 Formulae used in the proof : p03c_1 p03c_2 prove_p03c associativity_of_lub glb_absorbtion monotony_lub1 monotony_lub2
% 7.06/7.26
%------------------------------------------------------------------------------