%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP482-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:47:41 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 2 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; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(double_divide(u,double_divide(v,identity)),double_divide(double_divide(w,double_divide(x,double_divide(x,identity))),double_divide(u,identity))),v),w),
file('GRP482-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP482-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP482-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP482-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP482-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(double_divide(u,inverse(v)),double_divide(inverse(w),inverse(u))),v),w),
inference(rew,[status(thm),theory(equality)],[3,1,4]),
[iquote('0:Rew:3.0,1.0,3.0,1.0,4.0,1.0,3.0,1.0,3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
cnf(46,plain,
equal(inverse(double_divide(double_divide(u,inverse(identity)),double_divide(inverse(v),inverse(u)))),v),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(53,plain,
equal(double_divide(double_divide(double_divide(inverse(u),inverse(v)),identity),v),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(56,plain,
equal(double_divide(multiply(inverse(u),inverse(v)),u),v),
inference(rew,[status(thm),theory(equality)],[6,53,3]),
[iquote('0:Rew:6.0,53.0,3.0,53.0')] ).
cnf(57,plain,
equal(multiply(double_divide(inverse(u),inverse(v)),double_divide(v,inverse(identity))),u),
inference(rew,[status(thm),theory(equality)],[6,46]),
[iquote('0:Rew:6.0,46.0')] ).
cnf(69,plain,
equal(double_divide(inverse(identity),inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[12,56]),
[iquote('0:SpR:12.0,56.0')] ).
cnf(72,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[69,4]),
[iquote('0:SpR:69.0,4.0')] ).
cnf(74,plain,
equal(multiply(inverse(u),inverse(identity)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[69,6]),
[iquote('0:SpR:69.0,6.0')] ).
cnf(83,plain,
equal(multiply(double_divide(inverse(u),inverse(v)),double_divide(v,identity)),u),
inference(rew,[status(thm),theory(equality)],[72,57]),
[iquote('0:Rew:72.0,57.0')] ).
cnf(86,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[72,74]),
[iquote('0:Rew:72.0,74.0')] ).
cnf(90,plain,
equal(multiply(double_divide(inverse(u),inverse(v)),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[3,83]),
[iquote('0:Rew:3.0,83.0')] ).
cnf(117,plain,
equal(multiply(double_divide(inverse(u),identity),identity),u),
inference(spr,[status(thm),theory(equality)],[72,90]),
[iquote('0:SpR:72.0,90.0')] ).
cnf(124,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(rew,[status(thm),theory(equality)],[3,117]),
[iquote('0:Rew:3.0,117.0')] ).
cnf(125,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[86,124]),
[iquote('0:Rew:86.0,124.0')] ).
cnf(126,plain,
$false,
inference(unc,[status(thm)],[125,14]),
[iquote('0:UnC:125.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP482-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 05:44:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 79 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.18/0.41 SPASS allocated 63259 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 4, length 24 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.18/0.41
%------------------------------------------------------------------------------