%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO039-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 06:21:47 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (  12 unt;   0 nHn;  14 RR)
%            Number of literals    :   16 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    between(u__dfg,w__dfg,x__dfg),
    file('GEO039-2.p',unknown),
    [] ).

cnf(2,axiom,
    equal(x__dfg,u__dfg),
    file('GEO039-2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ between(v__dfg,w__dfg,x__dfg),
    file('GEO039-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ equidistant(u,v,w,w)
    | equal(u,v) ),
    file('GEO039-2.p',unknown),
    [] ).

cnf(7,axiom,
    between(u,v,extension(u,v,w,x)),
    file('GEO039-2.p',unknown),
    [] ).

cnf(8,axiom,
    equidistant(u,extension(v,u,w,x),w,x),
    file('GEO039-2.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ between(u,v,u)
    | equal(u,v) ),
    file('GEO039-2.p',unknown),
    [] ).

cnf(22,plain,
    between(u__dfg,w__dfg,u__dfg),
    inference(rew,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Rew:2.0,1.0')] ).

cnf(23,plain,
    ~ between(v__dfg,w__dfg,u__dfg),
    inference(rew,[status(thm),theory(equality)],[2,3]),
    [iquote('0:Rew:2.0,3.0')] ).

cnf(30,plain,
    equal(w__dfg,u__dfg),
    inference(res,[status(thm),theory(equality)],[22,10]),
    [iquote('0:Res:22.0,10.0')] ).

cnf(33,plain,
    ~ between(v__dfg,u__dfg,u__dfg),
    inference(rew,[status(thm),theory(equality)],[30,23]),
    [iquote('0:Rew:30.0,23.0')] ).

cnf(38,plain,
    equal(extension(u,v,w,w),v),
    inference(res,[status(thm),theory(equality)],[8,6]),
    [iquote('0:Res:8.0,6.0')] ).

cnf(41,plain,
    between(u,v,v),
    inference(spr,[status(thm),theory(equality)],[38,7]),
    [iquote('0:SpR:38.0,7.0')] ).

cnf(44,plain,
    $false,
    inference(unc,[status(thm)],[41,33]),
    [iquote('0:UnC:41.0,33.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO039-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n016.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 : Sat Jun 18 05:55:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.40  
% 0.19/0.40  SPASS V 3.9 
% 0.19/0.40  SPASS beiseite: Proof found.
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 19 clauses, backtracked 0 clauses, performed 1 splits and kept 32 clauses.
% 0.19/0.40  SPASS allocated 63134 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.40  		0:00:00.03 for the input.
% 0.19/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40  		0:00:00.00 for inferences.
% 0.19/0.40  		0:00:00.00 for the backtracking.
% 0.19/0.40  		0:00:00.00 for the reduction.
% 0.19/0.40  
% 0.19/0.40  
% 0.19/0.40  Here is a proof with depth 2, length 14 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : w_between_u_and_x u_is_x prove_corollary identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness
% 0.19/0.40  
%------------------------------------------------------------------------------