%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 06:21:29 EDT 2022

% Result   : Unsatisfiable 0.21s 0.44s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (   8 unt;   2 nHn;  14 RR)
%            Number of literals    :   21 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(27,axiom,
    ( ~ between(u,v,w)
    | between(w,v,u) ),
    file('GEO006-3.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ between(u,v,w)
    | ~ between(u,w,v)
    | equal(w,v) ),
    file('GEO006-3.p',unknown),
    [] ).

cnf(31,axiom,
    ~ equal(c,a),
    file('GEO006-3.p',unknown),
    [] ).

cnf(33,axiom,
    ~ equal(d,c),
    file('GEO006-3.p',unknown),
    [] ).

cnf(34,axiom,
    between(a,c,d),
    file('GEO006-3.p',unknown),
    [] ).

cnf(35,axiom,
    ( between(a,d,c)
    | between(c,a,d) ),
    file('GEO006-3.p',unknown),
    [] ).

cnf(89,plain,
    between(d,c,a),
    inference(res,[status(thm),theory(equality)],[34,27]),
    [iquote('0:Res:34.0,27.0')] ).

cnf(95,plain,
    ( between(a,d,c)
    | between(d,a,c) ),
    inference(res,[status(thm),theory(equality)],[35,27]),
    [iquote('0:Res:35.1,27.0')] ).

cnf(333,plain,
    ( ~ between(a,d,c)
    | equal(d,c) ),
    inference(res,[status(thm),theory(equality)],[34,30]),
    [iquote('0:Res:34.0,30.0')] ).

cnf(342,plain,
    ( ~ between(d,a,c)
    | equal(c,a) ),
    inference(res,[status(thm),theory(equality)],[89,30]),
    [iquote('0:Res:89.0,30.0')] ).

cnf(344,plain,
    ~ between(a,d,c),
    inference(mrr,[status(thm)],[333,33]),
    [iquote('0:MRR:333.1,33.0')] ).

cnf(346,plain,
    between(d,a,c),
    inference(mrr,[status(thm)],[95,344]),
    [iquote('0:MRR:95.0,344.0')] ).

cnf(347,plain,
    ~ between(d,a,c),
    inference(mrr,[status(thm)],[342,31]),
    [iquote('0:MRR:342.1,31.0')] ).

cnf(348,plain,
    $false,
    inference(mrr,[status(thm)],[347,346]),
    [iquote('0:MRR:347.0,346.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GEO006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n010.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 : Sat Jun 18 14:31:53 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.44  
% 0.21/0.44  SPASS V 3.9 
% 0.21/0.44  SPASS beiseite: Proof found.
% 0.21/0.44  % SZS status Theorem
% 0.21/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.44  SPASS derived 288 clauses, backtracked 0 clauses, performed 0 splits and kept 91 clauses.
% 0.21/0.44  SPASS allocated 63282 KBytes.
% 0.21/0.44  SPASS spent	0:00:00.07 on the problem.
% 0.21/0.44  		0:00:00.03 for the input.
% 0.21/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.44  		0:00:00.00 for inferences.
% 0.21/0.44  		0:00:00.00 for the backtracking.
% 0.21/0.44  		0:00:00.01 for the reduction.
% 0.21/0.44  
% 0.21/0.44  
% 0.21/0.44  Here is a proof with depth 2, length 14 :
% 0.21/0.44  % SZS output start Refutation
% See solution above
% 0.21/0.44  Formulae used in the proof : t1 b3 a_not_c c_not_d c_between_a_and_d prove_not_between_others
% 0.21/0.44  
%------------------------------------------------------------------------------