%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO001-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 8.33s 8.55s
% Output   : Refutation 8.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   5 unt;   0 nHn;  12 RR)
%            Number of literals    :   26 (   0 equ;  15 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(25,axiom,
    between(u,v,v),
    file('GEO001-3.p',unknown),
    [] ).

cnf(27,axiom,
    between(a,b,c),
    file('GEO001-3.p',unknown),
    [] ).

cnf(28,axiom,
    ~ between(c,b,a),
    file('GEO001-3.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ between(u,v,u)
    | equal(u,v) ),
    file('GEO001-3.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(y,inner_pasch(x,y,w,v,u),u) ),
    file('GEO001-3.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(v,inner_pasch(x,y,w,v,u),x) ),
    file('GEO001-3.p',unknown),
    [] ).

cnf(497,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | equal(inner_pasch(v,x,w,v,u),v) ),
    inference(res,[status(thm),theory(equality)],[37,35]),
    [iquote('0:Res:37.2,35.0')] ).

cnf(2750,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)],[497,36]),
    [iquote('0:SpR:497.2,36.2')] ).

cnf(2752,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | between(x,v,u) ),
    inference(obv,[status(thm),theory(equality)],[2750]),
    [iquote('0:Obv:2750.1')] ).

cnf(11206,plain,
    ( ~ between(b,u,c)
    | between(u,b,a) ),
    inference(res,[status(thm),theory(equality)],[27,2752]),
    [iquote('0:Res:27.0,2752.0')] ).

cnf(11222,plain,
    between(c,b,a),
    inference(res,[status(thm),theory(equality)],[25,11206]),
    [iquote('0:Res:25.0,11206.0')] ).

cnf(11229,plain,
    $false,
    inference(mrr,[status(thm)],[11222,28]),
    [iquote('0:MRR:11222.0,28.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO001-3 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n006.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jun 18 07:15:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 8.33/8.55  
% 8.33/8.55  SPASS V 3.9 
% 8.33/8.55  SPASS beiseite: Proof found.
% 8.33/8.55  % SZS status Theorem
% 8.33/8.55  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 8.33/8.55  SPASS derived 9367 clauses, backtracked 0 clauses, performed 1 splits and kept 2747 clauses.
% 8.33/8.55  SPASS allocated 71876 KBytes.
% 8.33/8.55  SPASS spent	0:00:08.09 on the problem.
% 8.33/8.55  		0:00:00.03 for the input.
% 8.33/8.55  		0:00:00.00 for the FLOTTER CNF translation.
% 8.33/8.55  		0:00:00.12 for inferences.
% 8.33/8.55  		0:00:00.01 for the backtracking.
% 8.33/8.55  		0:00:07.88 for the reduction.
% 8.33/8.55  
% 8.33/8.55  
% 8.33/8.55  Here is a proof with depth 4, length 12 :
% 8.33/8.55  % SZS output start Refutation
% See solution above
% 8.33/8.55  Formulae used in the proof : t3 b_between_a_and_c prove_b_between_c_and_a identity_for_betweeness inner_pasch1 inner_pasch2
% 8.33/8.55  
%------------------------------------------------------------------------------