TSTP Solution File: GRP171-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP171-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:46:05 EDT 2022
% Result : Unsatisfiable 0.24s 0.48s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 15 RR)
% Number of literals : 15 ( 0 equ; 1 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(identity,a),a),
file('GRP171-2.p',unknown),
[] ).
cnf(2,axiom,
equal(least_upper_bound(identity,b),b),
file('GRP171-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(greatest_lower_bound(identity,multiply(a,b)),identity),
file('GRP171-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP171-2.p',unknown),
[] ).
cnf(9,axiom,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(u,greatest_lower_bound(v,w))),
file('GRP171-2.p',unknown),
[] ).
cnf(14,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP171-2.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP171-2.p',unknown),
[] ).
cnf(26,plain,
equal(greatest_lower_bound(identity,b),identity),
inference(spr,[status(thm),theory(equality)],[2,14]),
[iquote('0:SpR:2.0,14.0')] ).
cnf(27,plain,
equal(greatest_lower_bound(identity,a),identity),
inference(spr,[status(thm),theory(equality)],[1,14]),
[iquote('0:SpR:1.0,14.0')] ).
cnf(247,plain,
equal(greatest_lower_bound(identity,greatest_lower_bound(b,u)),greatest_lower_bound(identity,u)),
inference(spr,[status(thm),theory(equality)],[26,9]),
[iquote('0:SpR:26.0,9.0')] ).
cnf(392,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(a,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[27,18]),
[iquote('0:SpR:27.0,18.0')] ).
cnf(402,plain,
equal(greatest_lower_bound(u,multiply(a,u)),u),
inference(rew,[status(thm),theory(equality)],[4,392]),
[iquote('0:Rew:4.0,392.0')] ).
cnf(463,plain,
equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(identity,b)),
inference(spr,[status(thm),theory(equality)],[402,247]),
[iquote('0:SpR:402.0,247.0')] ).
cnf(469,plain,
equal(greatest_lower_bound(identity,multiply(a,b)),identity),
inference(rew,[status(thm),theory(equality)],[26,463]),
[iquote('0:Rew:26.0,463.0')] ).
cnf(470,plain,
$false,
inference(mrr,[status(thm)],[469,3]),
[iquote('0:MRR:469.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : GRP171-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.14 % Command : run_spass %d %s
% 0.15/0.38 % Computer : n019.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 600
% 0.15/0.38 % DateTime : Mon Jun 13 08:29:09 EDT 2022
% 0.15/0.38 % CPUTime :
% 0.24/0.48
% 0.24/0.48 SPASS V 3.9
% 0.24/0.48 SPASS beiseite: Proof found.
% 0.24/0.48 % SZS status Theorem
% 0.24/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.48 SPASS derived 358 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.24/0.48 SPASS allocated 63511 KBytes.
% 0.24/0.48 SPASS spent 0:00:00.08 on the problem.
% 0.24/0.48 0:00:00.03 for the input.
% 0.24/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.24/0.48 0:00:00.00 for inferences.
% 0.24/0.48 0:00:00.00 for the backtracking.
% 0.24/0.48 0:00:00.02 for the reduction.
% 0.24/0.48
% 0.24/0.48
% 0.24/0.48 Here is a proof with depth 3, length 15 :
% 0.24/0.48 % SZS output start Refutation
% See solution above
% 0.24/0.48 Formulae used in the proof : p04c_1 p04c_2 prove_p04c left_identity associativity_of_glb glb_absorbtion monotony_glb2
% 0.24/0.48
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