TSTP Solution File: GEO205+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 0.47s 0.64s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   40 (  17 unt;  16 nHn;  40 RR)
%            Number of literals    :   83 (   0 equ;  27 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+2.p',unknown),
    [] ).

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

cnf(3,axiom,
    ~ distinct_points(u,u),
    file('GEO205+2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ convergent_lines(u,v)
    | distinct_lines(u,v) ),
    file('GEO205+2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ distinct_points(u,v)
    | distinct_points(v,w)
    | distinct_points(u,w) ),
    file('GEO205+2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ convergent_lines(u,v)
    | convergent_lines(v,w)
    | convergent_lines(u,w) ),
    file('GEO205+2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ apart_point_and_line(u,v)
    | distinct_lines(v,w)
    | apart_point_and_line(u,w) ),
    file('GEO205+2.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ convergent_lines(skc5,skc4)
    | distinct_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)) ),
    file('GEO205+2.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(w,u)
    | distinct_points(w,intersection_point(u,v)) ),
    file('GEO205+2.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(w,v)
    | distinct_points(w,intersection_point(u,v)) ),
    file('GEO205+2.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+2.p',unknown),
    [] ).

cnf(18,plain,
    ( convergent_lines(skc3,u)
    | convergent_lines(skc5,u) ),
    inference(res,[status(thm),theory(equality)],[1,9]),
    [iquote('0:Res:1.0,9.0')] ).

cnf(19,plain,
    distinct_lines(skc5,skc3),
    inference(res,[status(thm),theory(equality)],[1,6]),
    [iquote('0:Res:1.0,6.0')] ).

cnf(20,plain,
    ( ~ apart_point_and_line(u,skc5)
    | distinct_points(u,intersection_point(skc5,skc3)) ),
    inference(res,[status(thm),theory(equality)],[1,15]),
    [iquote('0:Res:1.0,15.1')] ).

cnf(21,plain,
    ( ~ apart_point_and_line(u,skc3)
    | distinct_points(u,intersection_point(skc5,skc3)) ),
    inference(res,[status(thm),theory(equality)],[1,16]),
    [iquote('0:Res:1.0,16.1')] ).

cnf(22,plain,
    ~ convergent_lines(skc3,skc4),
    inference(res,[status(thm),theory(equality)],[6,2]),
    [iquote('0:Res:6.1,2.0')] ).

cnf(25,plain,
    ( ~ apart_point_and_line(u,skc3)
    | apart_point_and_line(u,skc4) ),
    inference(res,[status(thm),theory(equality)],[11,2]),
    [iquote('0:Res:11.2,2.0')] ).

cnf(28,plain,
    convergent_lines(skc5,skc4),
    inference(res,[status(thm),theory(equality)],[18,22]),
    [iquote('0:Res:18.0,22.0')] ).

cnf(30,plain,
    distinct_points(intersection_point(skc5,skc3),intersection_point(skc5,skc4)),
    inference(mrr,[status(thm)],[12,28]),
    [iquote('0:MRR:12.0,28.0')] ).

cnf(42,plain,
    ~ apart_point_and_line(intersection_point(skc5,skc3),skc3),
    inference(res,[status(thm),theory(equality)],[21,3]),
    [iquote('0:Res:21.1,3.0')] ).

cnf(49,plain,
    ~ apart_point_and_line(intersection_point(skc5,skc3),skc5),
    inference(res,[status(thm),theory(equality)],[20,3]),
    [iquote('0:Res:20.1,3.0')] ).

cnf(75,plain,
    ( distinct_points(intersection_point(skc5,skc4),u)
    | distinct_points(intersection_point(skc5,skc3),u) ),
    inference(res,[status(thm),theory(equality)],[30,7]),
    [iquote('0:Res:30.0,7.0')] ).

cnf(162,plain,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(w,v)
    | distinct_points(intersection_point(u,v),x)
    | distinct_points(w,x) ),
    inference(res,[status(thm),theory(equality)],[16,7]),
    [iquote('0:Res:16.2,7.0')] ).

cnf(182,plain,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(w,u)
    | distinct_points(intersection_point(u,v),x)
    | distinct_points(w,x) ),
    inference(res,[status(thm),theory(equality)],[15,7]),
    [iquote('0:Res:15.2,7.0')] ).

cnf(302,plain,
    ( ~ distinct_points(u,v)
    | apart_point_and_line(v,skc5)
    | apart_point_and_line(v,skc3)
    | apart_point_and_line(u,skc3)
    | apart_point_and_line(u,skc5) ),
    inference(res,[status(thm),theory(equality)],[19,17]),
    [iquote('0:Res:19.0,17.0')] ).

cnf(395,plain,
    distinct_points(intersection_point(skc5,skc4),intersection_point(skc5,skc3)),
    inference(res,[status(thm),theory(equality)],[75,3]),
    [iquote('0:Res:75.1,3.0')] ).

cnf(574,plain,
    ( ~ apart_point_and_line(u,skc4)
    | distinct_points(intersection_point(skc5,skc4),v)
    | distinct_points(u,v) ),
    inference(res,[status(thm),theory(equality)],[28,162]),
    [iquote('0:Res:28.0,162.0')] ).

cnf(637,plain,
    ( ~ apart_point_and_line(u,skc5)
    | distinct_points(intersection_point(skc5,skc4),v)
    | distinct_points(u,v) ),
    inference(res,[status(thm),theory(equality)],[28,182]),
    [iquote('0:Res:28.0,182.0')] ).

cnf(1048,plain,
    ( apart_point_and_line(intersection_point(skc5,skc3),skc5)
    | apart_point_and_line(intersection_point(skc5,skc3),skc3)
    | apart_point_and_line(intersection_point(skc5,skc4),skc3)
    | apart_point_and_line(intersection_point(skc5,skc4),skc5) ),
    inference(res,[status(thm),theory(equality)],[395,302]),
    [iquote('0:Res:395.0,302.0')] ).

cnf(1055,plain,
    ( apart_point_and_line(intersection_point(skc5,skc4),skc3)
    | apart_point_and_line(intersection_point(skc5,skc4),skc5) ),
    inference(mrr,[status(thm)],[1048,49,42]),
    [iquote('0:MRR:1048.0,1048.1,49.0,42.0')] ).

cnf(1061,plain,
    ( apart_point_and_line(intersection_point(skc5,skc4),skc5)
    | apart_point_and_line(intersection_point(skc5,skc4),skc4) ),
    inference(res,[status(thm),theory(equality)],[1055,25]),
    [iquote('0:Res:1055.0,25.0')] ).

cnf(1066,plain,
    apart_point_and_line(intersection_point(skc5,skc4),skc5),
    inference(spt,[spt(split,[position(s1)])],[1061]),
    [iquote('1:Spt:1061.0')] ).

cnf(1067,plain,
    ( distinct_points(intersection_point(skc5,skc4),u)
    | distinct_points(intersection_point(skc5,skc4),u) ),
    inference(res,[status(thm),theory(equality)],[1066,637]),
    [iquote('1:Res:1066.0,637.0')] ).

cnf(1076,plain,
    distinct_points(intersection_point(skc5,skc4),u),
    inference(obv,[status(thm),theory(equality)],[1067]),
    [iquote('1:Obv:1067.0')] ).

cnf(1077,plain,
    $false,
    inference(unc,[status(thm)],[1076,3]),
    [iquote('1:UnC:1076.0,3.0')] ).

cnf(1078,plain,
    ~ apart_point_and_line(intersection_point(skc5,skc4),skc5),
    inference(spt,[spt(split,[position(sa)])],[1077,1066]),
    [iquote('1:Spt:1077.0,1061.0,1066.0')] ).

cnf(1079,plain,
    apart_point_and_line(intersection_point(skc5,skc4),skc4),
    inference(spt,[spt(split,[position(s2)])],[1061]),
    [iquote('1:Spt:1077.0,1061.1')] ).

cnf(1085,plain,
    ( distinct_points(intersection_point(skc5,skc4),u)
    | distinct_points(intersection_point(skc5,skc4),u) ),
    inference(res,[status(thm),theory(equality)],[1079,574]),
    [iquote('1:Res:1079.0,574.0')] ).

cnf(1091,plain,
    distinct_points(intersection_point(skc5,skc4),u),
    inference(obv,[status(thm),theory(equality)],[1085]),
    [iquote('1:Obv:1085.0')] ).

cnf(1092,plain,
    $false,
    inference(unc,[status(thm)],[1091,3]),
    [iquote('1:UnC:1091.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15  % Problem  : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15  % Command  : run_spass %d %s
% 0.16/0.37  % Computer : n029.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 600
% 0.16/0.37  % DateTime : Sat Jun 18 16:12:59 EDT 2022
% 0.16/0.37  % CPUTime  : 
% 0.47/0.64  
% 0.47/0.64  SPASS V 3.9 
% 0.47/0.64  SPASS beiseite: Proof found.
% 0.47/0.64  % SZS status Theorem
% 0.47/0.64  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.47/0.64  SPASS derived 1003 clauses, backtracked 7 clauses, performed 1 splits and kept 476 clauses.
% 0.47/0.64  SPASS allocated 85629 KBytes.
% 0.47/0.64  SPASS spent	0:00:00.25 on the problem.
% 0.47/0.64  		0:00:00.03 for the input.
% 0.47/0.64  		0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.64  		0:00:00.02 for inferences.
% 0.47/0.64  		0:00:00.00 for the backtracking.
% 0.47/0.64  		0:00:00.15 for the reduction.
% 0.47/0.64  
% 0.47/0.64  
% 0.47/0.64  Here is a proof with depth 6, length 40 :
% 0.47/0.64  % SZS output start Refutation
% See solution above
% 0.47/0.65  Formulae used in the proof : con apart1 ceq3 apart4 apart6 ceq2 con2 cu1
% 0.47/0.65  
%------------------------------------------------------------------------------