%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO058-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 06:21:58 EDT 2022

% Result   : Unsatisfiable 0.23s 0.44s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(8,axiom,
    ( ~ equidistant(u,v,w,x)
    | equidistant(x,w,v,u) ),
    file('GEO058-3.p',unknown),
    [] ).

cnf(13,axiom,
    equidistant(u,reflection(v,u),v,u),
    file('GEO058-3.p',unknown),
    [] ).

cnf(16,axiom,
    equal(reflection(u__dfg,v__dfg),v__dfg),
    file('GEO058-3.p',unknown),
    [] ).

cnf(17,axiom,
    ~ equal(u__dfg,v__dfg),
    file('GEO058-3.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ equidistant(u,v,w,w)
    | equal(u,v) ),
    file('GEO058-3.p',unknown),
    [] ).

cnf(48,plain,
    ~ equidistant(v__dfg,u__dfg,u,u),
    inference(res,[status(thm),theory(equality)],[20,17]),
    [iquote('0:Res:20.1,17.0')] ).

cnf(55,plain,
    equidistant(v__dfg,v__dfg,u__dfg,v__dfg),
    inference(spr,[status(thm),theory(equality)],[16,13]),
    [iquote('0:SpR:16.0,13.0')] ).

cnf(82,plain,
    equidistant(v__dfg,u__dfg,v__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[55,8]),
    [iquote('0:Res:55.0,8.0')] ).

cnf(84,plain,
    $false,
    inference(mrr,[status(thm)],[82,48]),
    [iquote('0:MRR:82.0,48.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : GEO058-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.15  % Command  : run_spass %d %s
% 0.15/0.36  % Computer : n029.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 : Sat Jun 18 00:39:43 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.23/0.44  
% 0.23/0.44  SPASS V 3.9 
% 0.23/0.44  SPASS beiseite: Proof found.
% 0.23/0.44  % SZS status Theorem
% 0.23/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.23/0.44  SPASS derived 47 clauses, backtracked 0 clauses, performed 0 splits and kept 60 clauses.
% 0.23/0.44  SPASS allocated 63175 KBytes.
% 0.23/0.44  SPASS spent	0:00:00.07 on the problem.
% 0.23/0.44  		0:00:00.04 for the input.
% 0.23/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.44  		0:00:00.00 for inferences.
% 0.23/0.44  		0:00:00.00 for the backtracking.
% 0.23/0.44  		0:00:00.00 for the reduction.
% 0.23/0.44  
% 0.23/0.44  
% 0.23/0.44  Here is a proof with depth 2, length 9 :
% 0.23/0.44  % SZS output start Refutation
% See solution above
% 0.23/0.44  Formulae used in the proof : d4_5 r2_2 v_equals_reflection prove_u_equals_v identity_for_equidistance
% 0.23/0.44  
%------------------------------------------------------------------------------