%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO040-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 06:21:48 EDT 2022

% Result   : Unsatisfiable 0.35s 0.53s
% Output   : Refutation 0.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   6 unt;   0 nHn;  13 RR)
%            Number of literals    :   27 (   0 equ;  16 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(1,axiom,
    between(u__dfg,v__dfg,w__dfg),
    file('GEO040-2.p',unknown),
    [] ).

cnf(2,axiom,
    between(v__dfg,u__dfg,w__dfg),
    file('GEO040-2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(v__dfg,u__dfg),
    file('GEO040-2.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ between(u,v,u)
    | equal(u,v) ),
    file('GEO040-2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(y,inner_pasch(x,y,w,v,u),u) ),
    file('GEO040-2.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ between(u,v,w)
    | ~ between(x,y,w)
    | between(v,inner_pasch(x,y,w,v,u),x) ),
    file('GEO040-2.p',unknown),
    [] ).

cnf(27,plain,
    ~ between(v__dfg,u__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[10,3]),
    [iquote('0:Res:10.1,3.0')] ).

cnf(46,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | equal(inner_pasch(v,x,w,v,u),v) ),
    inference(res,[status(thm),theory(equality)],[12,10]),
    [iquote('0:Res:12.2,10.0')] ).

cnf(426,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)],[46,11]),
    [iquote('0:SpR:46.2,11.2')] ).

cnf(428,plain,
    ( ~ between(u,v,w)
    | ~ between(v,x,w)
    | between(x,v,u) ),
    inference(obv,[status(thm),theory(equality)],[426]),
    [iquote('0:Obv:426.1')] ).

cnf(493,plain,
    ( ~ between(u__dfg,u,w__dfg)
    | between(u,u__dfg,v__dfg) ),
    inference(res,[status(thm),theory(equality)],[2,428]),
    [iquote('0:Res:2.0,428.0')] ).

cnf(502,plain,
    between(v__dfg,u__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[1,493]),
    [iquote('0:Res:1.0,493.0')] ).

cnf(506,plain,
    $false,
    inference(mrr,[status(thm)],[502,27]),
    [iquote('0:MRR:502.0,27.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GEO040-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.11/0.33  % Computer : n022.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Fri Jun 17 19:34:47 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.35/0.53  
% 0.35/0.53  SPASS V 3.9 
% 0.35/0.53  SPASS beiseite: Proof found.
% 0.35/0.53  % SZS status Theorem
% 0.35/0.53  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.35/0.53  SPASS derived 418 clauses, backtracked 0 clauses, performed 0 splits and kept 237 clauses.
% 0.35/0.53  SPASS allocated 63709 KBytes.
% 0.35/0.53  SPASS spent	0:00:00.18 on the problem.
% 0.35/0.53  		0:00:00.04 for the input.
% 0.35/0.53  		0:00:00.00 for the FLOTTER CNF translation.
% 0.35/0.53  		0:00:00.01 for inferences.
% 0.35/0.53  		0:00:00.00 for the backtracking.
% 0.35/0.53  		0:00:00.11 for the reduction.
% 0.35/0.53  
% 0.35/0.53  
% 0.35/0.53  Here is a proof with depth 4, length 13 :
% 0.35/0.53  % SZS output start Refutation
% See solution above
% 0.35/0.53  Formulae used in the proof : v_between_u_and_w u_between_v_and_w prove_u_is_v identity_for_betweeness inner_pasch1 inner_pasch2
% 0.35/0.53  
%------------------------------------------------------------------------------