TSTP Solution File: GEO223+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 06:23:39 EDT 2022

% Result   : Theorem 3.18s 3.39s
% Output   : Refutation 3.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   39 (  16 unt;  20 nHn;  39 RR)
%            Number of literals    :   80 (   0 equ;  16 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ convergent_lines(u,u),
    file('GEO223+2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ convergent_lines(parallel_through_point(u,v),u),
    file('GEO223+2.p',unknown),
    [] ).

cnf(5,axiom,
    ~ apart_point_and_line(u,parallel_through_point(v,u)),
    file('GEO223+2.p',unknown),
    [] ).

cnf(6,axiom,
    ( unorthogonal_lines(u,v)
    | convergent_lines(u,v) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(7,axiom,
    ~ unorthogonal_lines(orthogonal_through_point(u,v),u),
    file('GEO223+2.p',unknown),
    [] ).

cnf(8,axiom,
    ~ apart_point_and_line(u,orthogonal_through_point(v,u)),
    file('GEO223+2.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ skP0(u,v)
    | convergent_lines(v,u) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ skP0(u,v)
    | unorthogonal_lines(v,u) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(12,axiom,
    distinct_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),
    file('GEO223+2.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ convergent_lines(u,v)
    | convergent_lines(v,w)
    | convergent_lines(u,w) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ skP0(u,v)
    | skP0(w,u)
    | skP0(w,v) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ unorthogonal_lines(u,v)
    | ~ convergent_lines(u,v)
    | skP0(v,u) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ distinct_lines(u,v)
    | convergent_lines(u,v)
    | apart_point_and_line(w,v)
    | apart_point_and_line(w,u) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ distinct_lines(u,v)
    | unorthogonal_lines(v,w)
    | unorthogonal_lines(u,w)
    | apart_point_and_line(x,v)
    | apart_point_and_line(x,u) ),
    file('GEO223+2.p',unknown),
    [] ).

cnf(27,plain,
    ( apart_point_and_line(u,parallel_through_point(skc2,skc3))
    | apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3))
    | unorthogonal_lines(parallel_through_point(skc2,skc3),v)
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3),v) ),
    inference(res,[status(thm),theory(equality)],[12,25]),
    [iquote('0:Res:12.0,25.0')] ).

cnf(28,plain,
    ( apart_point_and_line(u,parallel_through_point(skc2,skc3))
    | apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3))
    | convergent_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)) ),
    inference(res,[status(thm),theory(equality)],[12,24]),
    [iquote('0:Res:12.0,24.0')] ).

cnf(31,plain,
    ( apart_point_and_line(u,parallel_through_point(skc2,skc3))
    | apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)) ),
    inference(spt,[spt(split,[position(s1)])],[28]),
    [iquote('1:Spt:28.0,28.1')] ).

cnf(32,plain,
    apart_point_and_line(skc3,parallel_through_point(skc2,skc3)),
    inference(res,[status(thm),theory(equality)],[31,8]),
    [iquote('1:Res:31.1,8.0')] ).

cnf(33,plain,
    $false,
    inference(mrr,[status(thm)],[32,5]),
    [iquote('1:MRR:32.0,5.0')] ).

cnf(34,plain,
    convergent_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)),
    inference(spt,[spt(split,[position(s2)])],[28]),
    [iquote('1:Spt:33.0,28.2')] ).

cnf(35,plain,
    convergent_lines(orthogonal_through_point(u,v),u),
    inference(res,[status(thm),theory(equality)],[6,7]),
    [iquote('0:Res:6.0,7.0')] ).

cnf(43,plain,
    ( convergent_lines(u,v)
    | convergent_lines(orthogonal_through_point(u,w),v) ),
    inference(res,[status(thm),theory(equality)],[35,15]),
    [iquote('0:Res:35.0,15.0')] ).

cnf(46,plain,
    ( convergent_lines(u,v)
    | convergent_lines(v,w)
    | convergent_lines(orthogonal_through_point(u,x),w) ),
    inference(res,[status(thm),theory(equality)],[43,15]),
    [iquote('0:Res:43.1,15.0')] ).

cnf(52,plain,
    ( ~ unorthogonal_lines(u,v)
    | ~ convergent_lines(u,v)
    | skP0(w,v)
    | skP0(w,u) ),
    inference(res,[status(thm),theory(equality)],[19,18]),
    [iquote('0:Res:19.2,18.0')] ).

cnf(67,plain,
    ( convergent_lines(u,v)
    | convergent_lines(orthogonal_through_point(w,x),v)
    | convergent_lines(u,y)
    | convergent_lines(w,y) ),
    inference(res,[status(thm),theory(equality)],[46,15]),
    [iquote('0:Res:46.0,15.0')] ).

cnf(438,plain,
    ( unorthogonal_lines(parallel_through_point(skc2,skc3),u)
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3),u) ),
    inference(spt,[spt(split,[position(s2s1)])],[27]),
    [iquote('2:Spt:27.2,27.3')] ).

cnf(439,plain,
    unorthogonal_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(skc2,skc3)),
    inference(res,[status(thm),theory(equality)],[438,7]),
    [iquote('2:Res:438.1,7.0')] ).

cnf(441,plain,
    ( ~ convergent_lines(parallel_through_point(skc2,skc3),orthogonal_through_point(skc2,skc3))
    | skP0(u,orthogonal_through_point(skc2,skc3))
    | skP0(u,parallel_through_point(skc2,skc3)) ),
    inference(res,[status(thm),theory(equality)],[439,52]),
    [iquote('2:Res:439.0,52.0')] ).

cnf(3112,plain,
    ( convergent_lines(u,v)
    | convergent_lines(orthogonal_through_point(w,x),v)
    | convergent_lines(u,w) ),
    inference(res,[status(thm),theory(equality)],[67,3]),
    [iquote('0:Res:67.3,3.0')] ).

cnf(3776,plain,
    ( convergent_lines(parallel_through_point(u,v),w)
    | convergent_lines(orthogonal_through_point(u,x),w) ),
    inference(res,[status(thm),theory(equality)],[3112,4]),
    [iquote('0:Res:3112.2,4.0')] ).

cnf(3799,plain,
    convergent_lines(parallel_through_point(u,v),orthogonal_through_point(u,w)),
    inference(res,[status(thm),theory(equality)],[3776,3]),
    [iquote('0:Res:3776.1,3.0')] ).

cnf(3808,plain,
    ( skP0(u,orthogonal_through_point(skc2,skc3))
    | skP0(u,parallel_through_point(skc2,skc3)) ),
    inference(mrr,[status(thm)],[441,3799]),
    [iquote('2:MRR:441.0,3799.0')] ).

cnf(3881,plain,
    ( skP0(u,orthogonal_through_point(skc2,skc3))
    | convergent_lines(parallel_through_point(skc2,skc3),u) ),
    inference(res,[status(thm),theory(equality)],[3808,10]),
    [iquote('2:Res:3808.1,10.0')] ).

cnf(3885,plain,
    ( convergent_lines(parallel_through_point(skc2,skc3),u)
    | unorthogonal_lines(orthogonal_through_point(skc2,skc3),u) ),
    inference(res,[status(thm),theory(equality)],[3881,11]),
    [iquote('2:Res:3881.0,11.0')] ).

cnf(3935,plain,
    convergent_lines(parallel_through_point(skc2,skc3),skc2),
    inference(res,[status(thm),theory(equality)],[3885,7]),
    [iquote('2:Res:3885.1,7.0')] ).

cnf(3937,plain,
    $false,
    inference(mrr,[status(thm)],[3935,4]),
    [iquote('2:MRR:3935.0,4.0')] ).

cnf(3938,plain,
    ( apart_point_and_line(u,parallel_through_point(skc2,skc3))
    | apart_point_and_line(u,orthogonal_through_point(orthogonal_through_point(skc2,skc3),skc3)) ),
    inference(spt,[spt(split,[position(s2s2)])],[27]),
    [iquote('2:Spt:3937.0,27.0,27.1')] ).

cnf(3942,plain,
    apart_point_and_line(skc3,parallel_through_point(skc2,skc3)),
    inference(res,[status(thm),theory(equality)],[3938,8]),
    [iquote('2:Res:3938.1,8.0')] ).

cnf(3953,plain,
    $false,
    inference(mrr,[status(thm)],[3942,5]),
    [iquote('2:MRR:3942.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 06:33:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 3.18/3.39  
% 3.18/3.39  SPASS V 3.9 
% 3.18/3.39  SPASS beiseite: Proof found.
% 3.18/3.39  % SZS status Theorem
% 3.18/3.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 3.18/3.39  SPASS derived 3831 clauses, backtracked 13 clauses, performed 3 splits and kept 2734 clauses.
% 3.18/3.39  SPASS allocated 88916 KBytes.
% 3.18/3.39  SPASS spent	0:00:03.02 on the problem.
% 3.18/3.39  		0:00:00.04 for the input.
% 3.18/3.39  		0:00:00.03 for the FLOTTER CNF translation.
% 3.18/3.39  		0:00:00.09 for inferences.
% 3.18/3.39  		0:00:00.01 for the backtracking.
% 3.18/3.39  		0:00:02.81 for the reduction.
% 3.18/3.39  
% 3.18/3.39  
% 3.18/3.39  Here is a proof with depth 7, length 39 :
% 3.18/3.39  % SZS output start Refutation
% See solution above
% 3.18/3.39  Formulae used in the proof : apart3 cp1 cp2 occu1 ooc1 ooc2 oac1 con apart6 cup1 ouo1
% 3.18/3.39  
%------------------------------------------------------------------------------