%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 06:21:24 EDT 2022

% Result   : Unsatisfiable 0.19s 0.54s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   16 (   8 unt;   0 nHn;  16 RR)
%            Number of literals    :   31 (   0 equ;  16 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    between(a,b,c),
    file('GEO001-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ between(c,b,a),
    file('GEO001-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ equidistant(u,v,w,w)
    | equal(u,v) ),
    file('GEO001-2.p',unknown),
    [] ).

cnf(6,axiom,
    between(u,v,extension(u,v,w,x)),
    file('GEO001-2.p',unknown),
    [] ).

cnf(7,axiom,
    equidistant(u,extension(v,u,w,x),w,x),
    file('GEO001-2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ between(u,v,u)
    | equal(u,v) ),
    file('GEO001-2.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(y,inner_pasch(x,y,w,v,u),u) ),
    file('GEO001-2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(v,inner_pasch(x,y,w,v,u),x) ),
    file('GEO001-2.p',unknown),
    [] ).

cnf(28,plain,
    equal(extension(u,v,w,w),v),
    inference(res,[status(thm),theory(equality)],[7,5]),
    [iquote('0:Res:7.0,5.0')] ).

cnf(29,plain,
    between(u,v,v),
    inference(spr,[status(thm),theory(equality)],[28,6]),
    [iquote('0:SpR:28.0,6.0')] ).

cnf(38,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | equal(inner_pasch(v,x,w,v,u),v) ),
    inference(res,[status(thm),theory(equality)],[11,9]),
    [iquote('0:Res:11.2,9.0')] ).

cnf(433,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | ~ between(u,v,w)
    | ~ between(v,x,w)
    | between(x,v,u) ),
    inference(spr,[status(thm),theory(equality)],[38,10]),
    [iquote('0:SpR:38.2,10.2')] ).

cnf(435,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | between(x,v,u) ),
    inference(obv,[status(thm),theory(equality)],[433]),
    [iquote('0:Obv:433.1')] ).

cnf(500,plain,
    ( ~ between(b,u,c)
    | between(u,b,a) ),
    inference(res,[status(thm),theory(equality)],[1,435]),
    [iquote('0:Res:1.0,435.0')] ).

cnf(508,plain,
    between(c,b,a),
    inference(res,[status(thm),theory(equality)],[29,500]),
    [iquote('0:Res:29.0,500.0')] ).

cnf(511,plain,
    $false,
    inference(mrr,[status(thm)],[508,2]),
    [iquote('0:MRR:508.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n009.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jun 18 13:19:52 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.54  
% 0.19/0.54  SPASS V 3.9 
% 0.19/0.54  SPASS beiseite: Proof found.
% 0.19/0.54  % SZS status Theorem
% 0.19/0.54  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.54  SPASS derived 424 clauses, backtracked 0 clauses, performed 1 splits and kept 238 clauses.
% 0.19/0.54  SPASS allocated 63744 KBytes.
% 0.19/0.54  SPASS spent	0:00:00.18 on the problem.
% 0.19/0.54  		0:00:00.03 for the input.
% 0.19/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.54  		0:00:00.01 for inferences.
% 0.19/0.54  		0:00:00.00 for the backtracking.
% 0.19/0.54  		0:00:00.11 for the reduction.
% 0.19/0.54  
% 0.19/0.54  
% 0.19/0.54  Here is a proof with depth 4, length 16 :
% 0.19/0.54  % SZS output start Refutation
% See solution above
% 0.19/0.54  Formulae used in the proof : b_between_a_and_c prove_b_between_c_and_a identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2
% 0.19/0.54  
%------------------------------------------------------------------------------