TSTP Solution File: GRP191-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP191-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:46:15 EDT 2022
% Result : Unsatisfiable 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(greatest_lower_bound(a,b),b),
file('GRP191-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)),
file('GRP191-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(identity,u),u),
file('GRP191-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP191-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP191-1.p',unknown),
[] ).
cnf(6,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP191-1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP191-1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP191-1.p',unknown),
[] ).
cnf(247,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(248,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[3,247]),
[iquote('0:Rew:3.0,247.0')] ).
cnf(251,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[248]),
[iquote('0:SpR:248.0,248.0')] ).
cnf(254,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[4,248]),
[iquote('0:SpR:4.0,248.0')] ).
cnf(256,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[251,254]),
[iquote('0:Rew:251.0,254.0')] ).
cnf(271,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[251,4]),
[iquote('0:SpR:251.0,4.0')] ).
cnf(288,plain,
equal(greatest_lower_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(998,plain,
equal(greatest_lower_bound(multiply(a,inverse(b)),identity),identity),
inference(spr,[status(thm),theory(equality)],[271,288]),
[iquote('0:SpR:271.0,288.0')] ).
cnf(1009,plain,
equal(greatest_lower_bound(identity,multiply(a,inverse(b))),identity),
inference(rew,[status(thm),theory(equality)],[6,998]),
[iquote('0:Rew:6.0,998.0')] ).
cnf(1026,plain,
equal(greatest_lower_bound(multiply(u,identity),multiply(u,multiply(a,inverse(b)))),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[1009,15]),
[iquote('0:SpR:1009.0,15.0')] ).
cnf(1032,plain,
equal(greatest_lower_bound(u,multiply(u,multiply(a,inverse(b)))),u),
inference(rew,[status(thm),theory(equality)],[256,1026]),
[iquote('0:Rew:256.0,1026.0')] ).
cnf(1143,plain,
equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)),
inference(spr,[status(thm),theory(equality)],[248,1032]),
[iquote('0:SpR:248.0,1032.0')] ).
cnf(1144,plain,
$false,
inference(mrr,[status(thm)],[1143,2]),
[iquote('0:MRR:1143.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP191-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 23:22:21 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.52
% 0.21/0.52 SPASS V 3.9
% 0.21/0.52 SPASS beiseite: Proof found.
% 0.21/0.52 % SZS status Theorem
% 0.21/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.52 SPASS derived 814 clauses, backtracked 0 clauses, performed 0 splits and kept 203 clauses.
% 0.21/0.52 SPASS allocated 64363 KBytes.
% 0.21/0.52 SPASS spent 0:00:00.14 on the problem.
% 0.21/0.52 0:00:00.04 for the input.
% 0.21/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.52 0:00:00.01 for inferences.
% 0.21/0.52 0:00:00.00 for the backtracking.
% 0.21/0.52 0:00:00.08 for the reduction.
% 0.21/0.52
% 0.21/0.52
% 0.21/0.52 Here is a proof with depth 6, length 21 :
% 0.21/0.52 % SZS output start Refutation
% See solution above
% 0.21/0.52 Formulae used in the proof : p39b_1 prove_p39b left_identity left_inverse associativity symmetry_of_glb monotony_glb1 monotony_glb2
% 0.21/0.52
%------------------------------------------------------------------------------