TSTP Solution File: GEO201+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 06:23:20 EDT 2022

% Result   : Theorem 0.37s 0.55s
% Output   : Refutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   37 (  17 unt;  15 nHn;  37 RR)
%            Number of literals    :   77 (   0 equ;  25 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    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    convergent_lines(skc2,skc3),
    file('GEO201+2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ distinct_points(u,u),
    file('GEO201+2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ distinct_lines(u,u),
    file('GEO201+2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ convergent_lines(u,u),
    file('GEO201+2.p',unknown),
    [] ).

cnf(5,axiom,
    distinct_points(intersection_point(skc2,skc3),intersection_point(skc3,skc2)),
    file('GEO201+2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ convergent_lines(u,v)
    | distinct_lines(u,v) ),
    file('GEO201+2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ distinct_points(u,v)
    | distinct_points(v,w)
    | distinct_points(u,w) ),
    file('GEO201+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ distinct_lines(u,v)
    | distinct_lines(v,w)
    | distinct_lines(u,w) ),
    file('GEO201+2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ convergent_lines(u,v)
    | convergent_lines(v,w)
    | convergent_lines(u,w) ),
    file('GEO201+2.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(w,u)
    | distinct_points(w,intersection_point(u,v)) ),
    file('GEO201+2.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ convergent_lines(u,v)
    | ~ apart_point_and_line(w,v)
    | distinct_points(w,intersection_point(u,v)) ),
    file('GEO201+2.p',unknown),
    [] ).

cnf(16,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('GEO201+2.p',unknown),
    [] ).

cnf(17,plain,
    ( convergent_lines(skc3,u)
    | convergent_lines(skc2,u) ),
    inference(res,[status(thm),theory(equality)],[1,9]),
    [iquote('0:Res:1.0,9.0')] ).

cnf(18,plain,
    distinct_lines(skc2,skc3),
    inference(res,[status(thm),theory(equality)],[1,6]),
    [iquote('0:Res:1.0,6.0')] ).

cnf(19,plain,
    ( ~ apart_point_and_line(u,skc2)
    | distinct_points(u,intersection_point(skc2,skc3)) ),
    inference(res,[status(thm),theory(equality)],[1,14]),
    [iquote('0:Res:1.0,14.1')] ).

cnf(20,plain,
    ( ~ apart_point_and_line(u,skc3)
    | distinct_points(u,intersection_point(skc2,skc3)) ),
    inference(res,[status(thm),theory(equality)],[1,15]),
    [iquote('0:Res:1.0,15.1')] ).

cnf(21,plain,
    ( ~ distinct_lines(u,v)
    | apart_point_and_line(intersection_point(skc3,skc2),u)
    | apart_point_and_line(intersection_point(skc3,skc2),v)
    | apart_point_and_line(intersection_point(skc2,skc3),v)
    | apart_point_and_line(intersection_point(skc2,skc3),u) ),
    inference(res,[status(thm),theory(equality)],[5,16]),
    [iquote('0:Res:5.0,16.0')] ).

cnf(25,plain,
    convergent_lines(skc3,skc2),
    inference(res,[status(thm),theory(equality)],[17,4]),
    [iquote('0:Res:17.1,4.0')] ).

cnf(27,plain,
    ( distinct_lines(skc3,u)
    | distinct_lines(skc2,u) ),
    inference(res,[status(thm),theory(equality)],[18,8]),
    [iquote('0:Res:18.0,8.0')] ).

cnf(29,plain,
    distinct_lines(skc3,skc2),
    inference(res,[status(thm),theory(equality)],[27,3]),
    [iquote('0:Res:27.1,3.0')] ).

cnf(32,plain,
    ~ apart_point_and_line(intersection_point(skc2,skc3),skc3),
    inference(res,[status(thm),theory(equality)],[20,2]),
    [iquote('0:Res:20.1,2.0')] ).

cnf(36,plain,
    ~ apart_point_and_line(intersection_point(skc2,skc3),skc2),
    inference(res,[status(thm),theory(equality)],[19,2]),
    [iquote('0:Res:19.1,2.0')] ).

cnf(129,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)],[15,7]),
    [iquote('0:Res:15.2,7.0')] ).

cnf(154,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)],[14,7]),
    [iquote('0:Res:14.2,7.0')] ).

cnf(255,plain,
    ( ~ apart_point_and_line(u,skc2)
    | distinct_points(intersection_point(skc3,skc2),v)
    | distinct_points(u,v) ),
    inference(res,[status(thm),theory(equality)],[25,129]),
    [iquote('0:Res:25.0,129.0')] ).

cnf(314,plain,
    ( ~ apart_point_and_line(u,skc3)
    | distinct_points(intersection_point(skc3,skc2),v)
    | distinct_points(u,v) ),
    inference(res,[status(thm),theory(equality)],[25,154]),
    [iquote('0:Res:25.0,154.0')] ).

cnf(552,plain,
    ( apart_point_and_line(intersection_point(skc3,skc2),skc3)
    | apart_point_and_line(intersection_point(skc3,skc2),skc2)
    | apart_point_and_line(intersection_point(skc2,skc3),skc2)
    | apart_point_and_line(intersection_point(skc2,skc3),skc3) ),
    inference(res,[status(thm),theory(equality)],[29,21]),
    [iquote('0:Res:29.0,21.0')] ).

cnf(560,plain,
    ( apart_point_and_line(intersection_point(skc3,skc2),skc3)
    | apart_point_and_line(intersection_point(skc3,skc2),skc2) ),
    inference(mrr,[status(thm)],[552,36,32]),
    [iquote('0:MRR:552.2,552.3,36.0,32.0')] ).

cnf(590,plain,
    apart_point_and_line(intersection_point(skc3,skc2),skc3),
    inference(spt,[spt(split,[position(s1)])],[560]),
    [iquote('1:Spt:560.0')] ).

cnf(591,plain,
    ( distinct_points(intersection_point(skc3,skc2),u)
    | distinct_points(intersection_point(skc3,skc2),u) ),
    inference(res,[status(thm),theory(equality)],[590,314]),
    [iquote('1:Res:590.0,314.0')] ).

cnf(597,plain,
    distinct_points(intersection_point(skc3,skc2),u),
    inference(obv,[status(thm),theory(equality)],[591]),
    [iquote('1:Obv:591.0')] ).

cnf(598,plain,
    $false,
    inference(unc,[status(thm)],[597,2]),
    [iquote('1:UnC:597.0,2.0')] ).

cnf(599,plain,
    ~ apart_point_and_line(intersection_point(skc3,skc2),skc3),
    inference(spt,[spt(split,[position(sa)])],[598,590]),
    [iquote('1:Spt:598.0,560.0,590.0')] ).

cnf(600,plain,
    apart_point_and_line(intersection_point(skc3,skc2),skc2),
    inference(spt,[spt(split,[position(s2)])],[560]),
    [iquote('1:Spt:598.0,560.1')] ).

cnf(616,plain,
    ( distinct_points(intersection_point(skc3,skc2),u)
    | distinct_points(intersection_point(skc3,skc2),u) ),
    inference(res,[status(thm),theory(equality)],[600,255]),
    [iquote('1:Res:600.0,255.0')] ).

cnf(622,plain,
    distinct_points(intersection_point(skc3,skc2),u),
    inference(obv,[status(thm),theory(equality)],[616]),
    [iquote('1:Obv:616.0')] ).

cnf(623,plain,
    $false,
    inference(unc,[status(thm)],[622,2]),
    [iquote('1:UnC:622.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jun 17 17:13:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.37/0.55  
% 0.37/0.55  SPASS V 3.9 
% 0.37/0.55  SPASS beiseite: Proof found.
% 0.37/0.55  % SZS status Theorem
% 0.37/0.55  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.37/0.55  SPASS derived 529 clauses, backtracked 25 clauses, performed 1 splits and kept 337 clauses.
% 0.37/0.55  SPASS allocated 85480 KBytes.
% 0.37/0.55  SPASS spent	0:00:00.19 on the problem.
% 0.37/0.55  		0:00:00.03 for the input.
% 0.37/0.55  		0:00:00.03 for the FLOTTER CNF translation.
% 0.37/0.55  		0:00:00.01 for inferences.
% 0.37/0.55  		0:00:00.00 for the backtracking.
% 0.37/0.55  		0:00:00.10 for the reduction.
% 0.37/0.55  
% 0.37/0.55  
% 0.37/0.55  Here is a proof with depth 6, length 37 :
% 0.37/0.55  % SZS output start Refutation
% See solution above
% 0.37/0.55  Formulae used in the proof : con apart1 apart2 apart3 ceq3 apart4 apart5 apart6 con2 cu1
% 0.37/0.55  
%------------------------------------------------------------------------------