TSTP Solution File: GRP178-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:46:08 EDT 2022
% Result : Unsatisfiable 3.63s 3.82s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 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(3,axiom,
equal(greatest_lower_bound(identity,c),identity),
file('GRP178-2.p',unknown),
[] ).
cnf(4,axiom,
equal(greatest_lower_bound(a,b),identity),
file('GRP178-2.p',unknown),
[] ).
cnf(5,axiom,
~ equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),
file('GRP178-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(identity,u),u),
file('GRP178-2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP178-2.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP178-2.p',unknown),
[] ).
cnf(11,axiom,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(u,greatest_lower_bound(v,w))),
file('GRP178-2.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP178-2.p',unknown),
[] ).
cnf(20,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP178-2.p',unknown),
[] ).
cnf(258,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(259,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[6,258]),
[iquote('0:Rew:6.0,258.0')] ).
cnf(277,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[259]),
[iquote('0:SpR:259.0,259.0')] ).
cnf(280,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[7,259]),
[iquote('0:SpR:7.0,259.0')] ).
cnf(282,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[277,280]),
[iquote('0:Rew:277.0,280.0')] ).
cnf(301,plain,
equal(greatest_lower_bound(multiply(a,u),multiply(b,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,20]),
[iquote('0:SpR:4.0,20.0')] ).
cnf(319,plain,
equal(greatest_lower_bound(multiply(a,u),multiply(b,u)),u),
inference(rew,[status(thm),theory(equality)],[6,301]),
[iquote('0:Rew:6.0,301.0')] ).
cnf(510,plain,
equal(greatest_lower_bound(multiply(u,identity),multiply(u,c)),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(533,plain,
equal(greatest_lower_bound(u,multiply(u,c)),u),
inference(rew,[status(thm),theory(equality)],[282,510]),
[iquote('0:Rew:282.0,510.0')] ).
cnf(704,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(multiply(u,c),v)),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[533,11]),
[iquote('0:SpR:533.0,11.0')] ).
cnf(15846,plain,
equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)),
inference(spr,[status(thm),theory(equality)],[319,704]),
[iquote('0:SpR:319.0,704.0')] ).
cnf(15863,plain,
$false,
inference(mrr,[status(thm)],[15846,5]),
[iquote('0:MRR:15846.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.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 08:22:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.63/3.82
% 3.63/3.82 SPASS V 3.9
% 3.63/3.82 SPASS beiseite: Proof found.
% 3.63/3.82 % SZS status Theorem
% 3.63/3.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.63/3.82 SPASS derived 10929 clauses, backtracked 0 clauses, performed 0 splits and kept 2379 clauses.
% 3.63/3.82 SPASS allocated 77091 KBytes.
% 3.63/3.82 SPASS spent 0:00:03.37 on the problem.
% 3.63/3.82 0:00:00.03 for the input.
% 3.63/3.82 0:00:00.00 for the FLOTTER CNF translation.
% 3.63/3.82 0:00:00.07 for inferences.
% 3.63/3.82 0:00:00.00 for the backtracking.
% 3.63/3.82 0:00:03.23 for the reduction.
% 3.63/3.82
% 3.63/3.82
% 3.63/3.82 Here is a proof with depth 3, length 21 :
% 3.63/3.82 % SZS output start Refutation
% See solution above
% 3.63/3.82 Formulae used in the proof : p09b_3 p09b_4 prove_p09b left_identity left_inverse associativity associativity_of_glb monotony_glb1 monotony_glb2
% 3.63/3.82
%------------------------------------------------------------------------------