TSTP Solution File: GRP184-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP184-2 : 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 11:46:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 0 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(identity),identity),
file('GRP184-2.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(inverse(u)),u),
file('GRP184-2.p',unknown),
[] ).
cnf(3,axiom,
equal(inverse(multiply(u,v)),multiply(inverse(v),inverse(u))),
file('GRP184-2.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))),
file('GRP184-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(identity,u),u),
file('GRP184-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP184-2.p',unknown),
[] ).
cnf(8,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP184-2.p',unknown),
[] ).
cnf(9,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP184-2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP184-2.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP184-2.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP184-2.p',unknown),
[] ).
cnf(19,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP184-2.p',unknown),
[] ).
cnf(20,plain,
~ equal(least_upper_bound(multiply(inverse(greatest_lower_bound(identity,a)),identity),multiply(inverse(greatest_lower_bound(identity,a)),a)),least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a))))),
inference(rew,[status(thm),theory(equality)],[16,4,5,18,9,8]),
[iquote('0:Rew:16.0,4.0,5.0,4.0,18.0,4.0,9.0,4.0,8.0,4.0')] ).
cnf(30,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
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(97,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(99,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
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(103,plain,
~ equal(least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)),least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a))))),
inference(rew,[status(thm),theory(equality)],[102,20]),
[iquote('0:Rew:102.0,20.0')] ).
cnf(110,plain,
~ equal(least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(inverse(multiply(inverse(identity),a)),multiply(inverse(a),a)))),least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a))))),
inference(rew,[status(thm),theory(equality)],[97,103,17]),
[iquote('0:Rew:97.0,103.0,17.0,103.0,97.0,103.0')] ).
cnf(111,plain,
~ equal(least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))),least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[8,110,5,1,6]),
[iquote('0:Rew:8.0,110.0,5.0,110.0,1.0,110.0,6.0,110.0')] ).
cnf(765,plain,
equal(inverse(greatest_lower_bound(multiply(u,inverse(v)),multiply(w,inverse(v)))),multiply(v,inverse(greatest_lower_bound(u,w)))),
inference(spr,[status(thm),theory(equality)],[19,99]),
[iquote('0:SpR:19.0,99.0')] ).
cnf(790,plain,
~ equal(least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(multiply(identity,inverse(a)),multiply(a,inverse(a))))),least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[765,111]),
[iquote('0:Rew:765.0,111.0')] ).
cnf(793,plain,
~ equal(least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a)))),least_upper_bound(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(identity,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[8,790,5,30]),
[iquote('0:Rew:8.0,790.0,5.0,790.0,30.0,790.0')] ).
cnf(794,plain,
$false,
inference(obv,[status(thm),theory(equality)],[793]),
[iquote('0:Obv:793.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP184-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 09:21:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 519 clauses, backtracked 0 clauses, performed 0 splits and kept 118 clauses.
% 0.20/0.47 SPASS allocated 63805 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.01 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.05 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 2, length 25 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : p21_1 p21_2 p21_3 prove_p21 left_identity left_inverse symmetry_of_glb symmetry_of_lub monotony_lub1 monotony_glb1 monotony_lub2 monotony_glb2
% 0.20/0.47
%------------------------------------------------------------------------------