%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP481-1 : 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 11:47:41 EDT 2022

% Result   : Unsatisfiable 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;  14 RR)
%            Number of literals    :   14 (   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('GRP481-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP481-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP481-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP481-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(inverse(a1),a1),identity),
    file('GRP481-1.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(14,plain,
    ~ equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[12,5]),
    [iquote('0:Rew:12.0,5.0')] ).

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(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(80,plain,
    $false,
    inference(mrr,[status(thm)],[72,14]),
    [iquote('0:MRR:72.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP481-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 13 09:49:09 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.43  
% 0.21/0.43  SPASS V 3.9 
% 0.21/0.43  SPASS beiseite: Proof found.
% 0.21/0.43  % SZS status Theorem
% 0.21/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.43  SPASS derived 53 clauses, backtracked 0 clauses, performed 0 splits and kept 29 clauses.
% 0.21/0.43  SPASS allocated 63209 KBytes.
% 0.21/0.43  SPASS spent	0:00:00.07 on the problem.
% 0.21/0.43  		0:00:00.04 for the input.
% 0.21/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43  		0:00:00.00 for inferences.
% 0.21/0.43  		0:00:00.00 for the backtracking.
% 0.21/0.43  		0:00:00.00 for the reduction.
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  Here is a proof with depth 3, length 14 :
% 0.21/0.43  % SZS output start Refutation
% See solution above
% 0.21/0.43  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.21/0.43  
%------------------------------------------------------------------------------