TSTP Solution File: GRP548-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:47:59 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 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(divide(divide(identity,divide(u,v)),divide(divide(v,w),u)),w),
file('GRP548-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP548-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP548-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP548-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP548-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,v)),divide(divide(v,w),u)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(29,plain,
equal(divide(inverse(divide(u,v)),divide(identity,u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(33,plain,
equal(divide(inverse(divide(divide(u,v),u)),identity),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(36,plain,
equal(divide(inverse(identity),divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(37,plain,
equal(divide(inverse(inverse(u)),divide(divide(u,v),identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(40,plain,
equal(multiply(inverse(divide(u,v)),u),v),
inference(rew,[status(thm),theory(equality)],[6,29,3]),
[iquote('0:Rew:6.0,29.0,3.0,29.0')] ).
cnf(41,plain,
equal(multiply(inverse(divide(divide(u,v),u)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,33]),
[iquote('0:Rew:15.0,33.0')] ).
cnf(42,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,36,9]),
[iquote('0:Rew:3.0,36.0,9.0,36.0')] ).
cnf(43,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[42,41]),
[iquote('0:Rew:42.0,41.0')] ).
cnf(44,plain,
equal(divide(u,identity),u),
inference(rew,[status(thm),theory(equality)],[43,15]),
[iquote('0:Rew:43.0,15.0')] ).
cnf(46,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[44,37]),
[iquote('0:Rew:44.0,37.0')] ).
cnf(66,plain,
equal(inverse(divide(identity,u)),u),
inference(spr,[status(thm),theory(equality)],[40,43]),
[iquote('0:SpR:40.0,43.0')] ).
cnf(73,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,66]),
[iquote('0:Rew:3.0,66.0')] ).
cnf(75,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[73,46]),
[iquote('0:Rew:73.0,46.0')] ).
cnf(102,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[75,40]),
[iquote('0:SpR:75.0,40.0')] ).
cnf(151,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[73,102]),
[iquote('0:SpR:73.0,102.0')] ).
cnf(153,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,151]),
[iquote('0:Rew:6.0,151.0')] ).
cnf(154,plain,
$false,
inference(unc,[status(thm)],[153,5]),
[iquote('0:UnC:153.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 09:27:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 104 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.20/0.41 SPASS allocated 63224 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.03 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.01 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 3, length 26 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.20/0.41
%------------------------------------------------------------------------------