%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO039-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (  10 unt;   0 nHn;  12 RR)
%            Number of literals    :   14 (   0 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(10,axiom,
    equal(extension(u,v,w,w),v),
    file('GEO039-3.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ equal(u,extension(v,w,x,y))
    | between(v,w,u) ),
    file('GEO039-3.p',unknown),
    [] ).

cnf(26,axiom,
    between(u__dfg,w__dfg,x__dfg),
    file('GEO039-3.p',unknown),
    [] ).

cnf(27,axiom,
    equal(x__dfg,u__dfg),
    file('GEO039-3.p',unknown),
    [] ).

cnf(28,axiom,
    ~ between(v__dfg,w__dfg,x__dfg),
    file('GEO039-3.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ between(u,v,u)
    | equal(u,v) ),
    file('GEO039-3.p',unknown),
    [] ).

cnf(48,plain,
    between(u__dfg,w__dfg,u__dfg),
    inference(rew,[status(thm),theory(equality)],[27,26]),
    [iquote('0:Rew:27.0,26.0')] ).

cnf(49,plain,
    ~ between(v__dfg,w__dfg,u__dfg),
    inference(rew,[status(thm),theory(equality)],[27,28]),
    [iquote('0:Rew:27.0,28.0')] ).

cnf(53,plain,
    ~ equal(extension(v__dfg,w__dfg,u,v),u__dfg),
    inference(res,[status(thm),theory(equality)],[11,49]),
    [iquote('0:Res:11.1,49.0')] ).

cnf(75,plain,
    ~ equal(w__dfg,u__dfg),
    inference(spl,[status(thm),theory(equality)],[10,53]),
    [iquote('0:SpL:10.0,53.0')] ).

cnf(76,plain,
    equal(w__dfg,u__dfg),
    inference(res,[status(thm),theory(equality)],[48,35]),
    [iquote('0:Res:48.0,35.0')] ).

cnf(78,plain,
    $false,
    inference(mrr,[status(thm)],[76,75]),
    [iquote('0:MRR:76.0,75.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GEO039-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n018.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 05:26:18 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.41  
% 0.18/0.41  SPASS V 3.9 
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 26 clauses, backtracked 0 clauses, performed 1 splits and kept 53 clauses.
% 0.18/0.41  SPASS allocated 63170 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.41  		0:00:00.04 for the input.
% 0.18/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.00 for the reduction.
% 0.18/0.41  
% 0.18/0.41  
% 0.18/0.41  Here is a proof with depth 2, length 12 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : e1 b0 w_between_u_and_x u_is_x prove_corollary identity_for_betweeness
% 0.18/0.41  
%------------------------------------------------------------------------------