TSTP Solution File: GRP530-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP530-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:47:54 EDT 2022
% Result : Unsatisfiable 0.15s 0.44s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 11 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,divide(v,w)),divide(u,v)),w),
file('GRP530-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP530-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP530-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP530-1.p',unknown),
[] ).
cnf(5,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(10,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(18,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(43,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(46,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[43,10]),
[iquote('0:Rew:43.0,10.0')] ).
cnf(58,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[5,46]),
[iquote('0:SpR:5.0,46.0')] ).
cnf(61,plain,
$false,
inference(unc,[status(thm)],[58,4]),
[iquote('0:UnC:58.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP530-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 03:40:39 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.44
% 0.15/0.44 SPASS V 3.9
% 0.15/0.44 SPASS beiseite: Proof found.
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 SPASS derived 47 clauses, backtracked 0 clauses, performed 0 splits and kept 33 clauses.
% 0.15/0.44 SPASS allocated 63170 KBytes.
% 0.15/0.44 SPASS spent 0:00:00.06 on the problem.
% 0.15/0.44 0:00:00.03 for the input.
% 0.15/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.44 0:00:00.00 for inferences.
% 0.15/0.44 0:00:00.00 for the backtracking.
% 0.15/0.44 0:00:00.00 for the reduction.
% 0.15/0.44
% 0.15/0.44
% 0.15/0.44 Here is a proof with depth 2, length 11 :
% 0.15/0.44 % SZS output start Refutation
% See solution above
% 0.15/0.44 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.15/0.44
%------------------------------------------------------------------------------