TSTP Solution File: GEO205+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 06:23:23 EDT 2022

% Result   : Theorem 0.41s 0.56s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   49 (  22 unt;  22 nHn;  49 RR)
%            Number of literals    :   98 (   0 equ;  21 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    convergent_lines(skc5,skc3),
    file('GEO205+1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ distinct_lines(skc3,skc4),
    file('GEO205+1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ distinct_points(u,u),
    file('GEO205+1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ convergent_lines(u,u),
    file('GEO205+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ distinct_points(u,v)
    | distinct_points(v,w)
    | distinct_points(u,w) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ convergent_lines(u,v)
    | convergent_lines(v,w)
    | convergent_lines(u,w) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(intersection_point(u,v),u) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(intersection_point(u,v),v) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ apart_point_and_line(u,v)
    | distinct_lines(v,w)
    | apart_point_and_line(u,w) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ convergent_lines(u,v)
    | distinct_lines(v,w)
    | convergent_lines(u,w) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ convergent_lines(skc5,skc4)
    | distinct_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ distinct_lines(u,v)
    | ~ distinct_points(w,x)
    | apart_point_and_line(x,u)
    | apart_point_and_line(x,v)
    | apart_point_and_line(w,v)
    | apart_point_and_line(w,u) ),
    file('GEO205+1.p',unknown),
    [] ).

cnf(18,plain,
    ( convergent_lines(skc3,u)
    | convergent_lines(skc5,u) ),
    inference(res,[status(thm),theory(equality)],[1,8]),
    [iquote('0:Res:1.0,8.0')] ).

cnf(19,plain,
    ~ apart_point_and_line(intersection_point(skc5,skc3),skc5),
    inference(res,[status(thm),theory(equality)],[1,11]),
    [iquote('0:Res:1.0,11.0')] ).

cnf(20,plain,
    ~ apart_point_and_line(intersection_point(skc5,skc3),skc3),
    inference(res,[status(thm),theory(equality)],[1,12]),
    [iquote('0:Res:1.0,12.0')] ).

cnf(21,plain,
    ( distinct_lines(skc3,u)
    | convergent_lines(skc5,u) ),
    inference(res,[status(thm),theory(equality)],[1,15]),
    [iquote('0:Res:1.0,15.0')] ).

cnf(24,plain,
    ( ~ apart_point_and_line(u,skc3)
    | apart_point_and_line(u,skc4) ),
    inference(res,[status(thm),theory(equality)],[14,2]),
    [iquote('0:Res:14.2,2.0')] ).

cnf(25,plain,
    ( ~ convergent_lines(u,skc3)
    | convergent_lines(u,skc4) ),
    inference(res,[status(thm),theory(equality)],[15,2]),
    [iquote('0:Res:15.2,2.0')] ).

cnf(26,plain,
    convergent_lines(skc5,skc4),
    inference(res,[status(thm),theory(equality)],[1,25]),
    [iquote('0:Res:1.0,25.0')] ).

cnf(30,plain,
    distinct_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)),
    inference(mrr,[status(thm)],[16,26]),
    [iquote('0:MRR:16.0,26.0')] ).

cnf(41,plain,
    ( distinct_points(intersection_point(skc5,skc4),u)
    | distinct_points(intersection_point(skc5,skc3),u) ),
    inference(res,[status(thm),theory(equality)],[30,6]),
    [iquote('0:Res:30.0,6.0')] ).

cnf(42,plain,
    distinct_points(intersection_point(skc5,skc4),intersection_point(skc5,skc3)),
    inference(res,[status(thm),theory(equality)],[41,3]),
    [iquote('0:Res:41.1,3.0')] ).

cnf(94,plain,
    ( convergent_lines(skc5,u)
    | convergent_lines(u,v)
    | convergent_lines(skc3,v) ),
    inference(res,[status(thm),theory(equality)],[18,8]),
    [iquote('0:Res:18.0,8.0')] ).

cnf(106,plain,
    ( convergent_lines(skc5,u)
    | convergent_lines(u,skc3) ),
    inference(res,[status(thm),theory(equality)],[94,5]),
    [iquote('0:Res:94.2,5.0')] ).

cnf(111,plain,
    ( convergent_lines(u,skc3)
    | convergent_lines(u,v)
    | convergent_lines(skc5,v) ),
    inference(res,[status(thm),theory(equality)],[106,8]),
    [iquote('0:Res:106.0,8.0')] ).

cnf(135,plain,
    ( ~ distinct_points(u,v)
    | convergent_lines(skc5,w)
    | apart_point_and_line(v,skc3)
    | apart_point_and_line(v,w)
    | apart_point_and_line(u,w)
    | apart_point_and_line(u,skc3) ),
    inference(res,[status(thm),theory(equality)],[21,17]),
    [iquote('0:Res:21.0,17.0')] ).

cnf(160,plain,
    ( convergent_lines(u,skc3)
    | convergent_lines(u,skc5) ),
    inference(res,[status(thm),theory(equality)],[111,5]),
    [iquote('0:Res:111.2,5.0')] ).

cnf(170,plain,
    ( convergent_lines(u,skc5)
    | distinct_lines(skc3,v)
    | convergent_lines(u,v) ),
    inference(res,[status(thm),theory(equality)],[160,15]),
    [iquote('0:Res:160.0,15.0')] ).

cnf(171,plain,
    ( convergent_lines(u,skc5)
    | convergent_lines(u,skc4) ),
    inference(res,[status(thm),theory(equality)],[160,25]),
    [iquote('0:Res:160.0,25.0')] ).

cnf(183,plain,
    ( convergent_lines(u,skc5)
    | distinct_lines(skc4,v)
    | convergent_lines(u,v) ),
    inference(res,[status(thm),theory(equality)],[171,15]),
    [iquote('0:Res:171.1,15.0')] ).

cnf(195,plain,
    ( convergent_lines(skc5,u)
    | apart_point_and_line(intersection_point(skc5,skc3),skc3)
    | apart_point_and_line(intersection_point(skc5,skc3),u)
    | apart_point_and_line(intersection_point(skc5,skc4),u)
    | apart_point_and_line(intersection_point(skc5,skc4),skc3) ),
    inference(res,[status(thm),theory(equality)],[42,135]),
    [iquote('0:Res:42.0,135.0')] ).

cnf(199,plain,
    ( convergent_lines(skc5,u)
    | apart_point_and_line(intersection_point(skc5,skc3),u)
    | apart_point_and_line(intersection_point(skc5,skc4),u)
    | apart_point_and_line(intersection_point(skc5,skc4),skc3) ),
    inference(mrr,[status(thm)],[195,20]),
    [iquote('0:MRR:195.1,20.0')] ).

cnf(346,plain,
    ( distinct_lines(skc3,skc5)
    | convergent_lines(u,skc5) ),
    inference(fac,[status(thm)],[170]),
    [iquote('0:Fac:170.0,170.2')] ).

cnf(359,plain,
    convergent_lines(u,skc5),
    inference(spt,[spt(split,[position(s1)])],[346]),
    [iquote('1:Spt:346.1')] ).

cnf(360,plain,
    $false,
    inference(unc,[status(thm)],[359,5]),
    [iquote('1:UnC:359.0,5.0')] ).

cnf(361,plain,
    distinct_lines(skc3,skc5),
    inference(spt,[spt(split,[position(s2)])],[346]),
    [iquote('1:Spt:360.0,346.0')] ).

cnf(410,plain,
    ( distinct_lines(skc4,skc5)
    | convergent_lines(u,skc5) ),
    inference(fac,[status(thm)],[183]),
    [iquote('0:Fac:183.0,183.2')] ).

cnf(421,plain,
    convergent_lines(u,skc5),
    inference(spt,[spt(split,[position(s2s1)])],[410]),
    [iquote('2:Spt:410.1')] ).

cnf(422,plain,
    $false,
    inference(unc,[status(thm)],[421,5]),
    [iquote('2:UnC:421.0,5.0')] ).

cnf(423,plain,
    distinct_lines(skc4,skc5),
    inference(spt,[spt(split,[position(s2s2)])],[410]),
    [iquote('2:Spt:422.0,410.0')] ).

cnf(963,plain,
    ( convergent_lines(skc5,u)
    | apart_point_and_line(intersection_point(skc5,skc3),u)
    | apart_point_and_line(intersection_point(skc5,skc4),u) ),
    inference(spt,[spt(split,[position(s2s2s1)])],[199]),
    [iquote('3:Spt:199.0,199.1,199.2')] ).

cnf(965,plain,
    ( convergent_lines(skc5,skc5)
    | apart_point_and_line(intersection_point(skc5,skc4),skc5) ),
    inference(res,[status(thm),theory(equality)],[963,19]),
    [iquote('3:Res:963.1,19.0')] ).

cnf(973,plain,
    apart_point_and_line(intersection_point(skc5,skc4),skc5),
    inference(mrr,[status(thm)],[965,5]),
    [iquote('3:MRR:965.0,5.0')] ).

cnf(974,plain,
    ~ convergent_lines(skc5,skc4),
    inference(res,[status(thm),theory(equality)],[973,11]),
    [iquote('3:Res:973.0,11.1')] ).

cnf(977,plain,
    $false,
    inference(mrr,[status(thm)],[974,26]),
    [iquote('3:MRR:974.0,26.0')] ).

cnf(978,plain,
    apart_point_and_line(intersection_point(skc5,skc4),skc3),
    inference(spt,[spt(split,[position(s2s2s2)])],[199]),
    [iquote('3:Spt:977.0,199.3')] ).

cnf(979,plain,
    apart_point_and_line(intersection_point(skc5,skc4),skc4),
    inference(res,[status(thm),theory(equality)],[978,24]),
    [iquote('3:Res:978.0,24.0')] ).

cnf(982,plain,
    ~ convergent_lines(skc5,skc4),
    inference(res,[status(thm),theory(equality)],[979,12]),
    [iquote('3:Res:979.0,12.1')] ).

cnf(985,plain,
    $false,
    inference(mrr,[status(thm)],[982,26]),
    [iquote('3:MRR:982.0,26.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14  % Command  : run_spass %d %s
% 0.15/0.36  % Computer : n012.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Sat Jun 18 16:21:23 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.41/0.56  
% 0.41/0.56  SPASS V 3.9 
% 0.41/0.56  SPASS beiseite: Proof found.
% 0.41/0.56  % SZS status Theorem
% 0.41/0.56  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.41/0.56  SPASS derived 903 clauses, backtracked 3 clauses, performed 3 splits and kept 382 clauses.
% 0.41/0.56  SPASS allocated 85549 KBytes.
% 0.41/0.56  SPASS spent	0:00:00.19 on the problem.
% 0.41/0.56  		0:00:00.03 for the input.
% 0.41/0.56  		0:00:00.03 for the FLOTTER CNF translation.
% 0.41/0.56  		0:00:00.01 for inferences.
% 0.41/0.56  		0:00:00.00 for the backtracking.
% 0.41/0.56  		0:00:00.09 for the reduction.
% 0.41/0.56  
% 0.41/0.56  
% 0.41/0.56  Here is a proof with depth 9, length 49 :
% 0.41/0.56  % SZS output start Refutation
% See solution above
% 0.41/0.56  Formulae used in the proof : con apart1 apart3 apart4 ax6 ci3 ci4 ceq2 ceq3 cu1
% 0.41/0.56  
%------------------------------------------------------------------------------