TSTP Solution File: GEO076-4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO076-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n003.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  : 300s
% DateTime : Tue Aug 22 10:38:06 EDT 2023

% Result   : Unsatisfiable 11.09s 3.63s
% Output   : CNFRefutation 11.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  101 (  23 unt;  16 typ;   0 def)
%            Number of atoms       :  300 (  92 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  391 ( 176   ~; 215   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  14   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-3 aty)
%            Number of variables   :   88 (;  88   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ collinear > on > point > plane > line > plane_for_points > line_through_3_points > common_point_on_planes > line_from_to > #nlpp > point_on_plane > point_not_on_plane > point_not_on_line > point_2_on_line > point_1_on_line > at_least_one_line > a_point

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(at_least_one_line,type,
    at_least_one_line: $i ).

tff(point_on_plane,type,
    point_on_plane: $i > $i ).

tff(point_1_on_line,type,
    point_1_on_line: $i > $i ).

tff(point_2_on_line,type,
    point_2_on_line: $i > $i ).

tff(point,type,
    point: $i > $o ).

tff(on,type,
    on: ( $i * $i ) > $o ).

tff(line,type,
    line: $i > $o ).

tff(plane,type,
    plane: $i > $o ).

tff(a_point,type,
    a_point: $i ).

tff(collinear,type,
    collinear: ( $i * $i * $i ) > $o ).

tff(point_not_on_line,type,
    point_not_on_line: $i > $i ).

tff(plane_for_points,type,
    plane_for_points: ( $i * $i * $i ) > $i ).

tff(point_not_on_plane,type,
    point_not_on_plane: $i > $i ).

tff(line_from_to,type,
    line_from_to: ( $i * $i ) > $i ).

tff(common_point_on_planes,type,
    common_point_on_planes: ( $i * $i * $i ) > $i ).

tff(line_through_3_points,type,
    line_through_3_points: ( $i * $i * $i ) > $i ).

tff(f_143,axiom,
    line(at_least_one_line),
    file(unknown,unknown) ).

tff(f_113,axiom,
    ! [Y1] :
      ( on(point_2_on_line(Y1),Y1)
      | ~ line(Y1) ),
    file(unknown,unknown) ).

tff(f_141,axiom,
    ! [Y1] :
      ( point(point_not_on_line(Y1))
      | ~ line(Y1) ),
    file(unknown,unknown) ).

tff(f_123,axiom,
    ! [Y1] :
      ( point(point_2_on_line(Y1))
      | ~ line(Y1) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ! [Z1,Z2] :
      ( line(line_from_to(Z1,Z2))
      | ( Z1 = Z2 )
      | ~ point(Z1)
      | ~ point(Z2) ),
    file(unknown,unknown) ).

tff(f_515,axiom,
    ! [Line] :
      ( ~ line(Line)
      | on(a_point,Line) ),
    file(unknown,unknown) ).

tff(f_64,axiom,
    ! [Z2,Z1] :
      ( on(Z2,line_from_to(Z1,Z2))
      | ( Z1 = Z2 )
      | ~ point(Z1)
      | ~ point(Z2) ),
    file(unknown,unknown) ).

tff(f_510,axiom,
    point(a_point),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [Z1,Y3,Z2,Y4] :
      ( ~ on(Z1,Y3)
      | ( Z1 = Z2 )
      | ~ on(Z2,Y3)
      | ( Y3 = Y4 )
      | ~ on(Z1,Y4)
      | ~ on(Z2,Y4)
      | ~ point(Z1)
      | ~ point(Z2)
      | ~ line(Y3)
      | ~ line(Y4) ),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [Z1,Z2] :
      ( on(Z1,line_from_to(Z1,Z2))
      | ( Z1 = Z2 )
      | ~ point(Z1)
      | ~ point(Z2) ),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [Y1] :
      ( ~ on(point_not_on_line(Y1),Y1)
      | ~ line(Y1) ),
    file(unknown,unknown) ).

tff(f_129,axiom,
    ! [Y1] :
      ( ( point_1_on_line(Y1) != point_2_on_line(Y1) )
      | ~ line(Y1) ),
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [Y1] :
      ( point(point_1_on_line(Y1))
      | ~ line(Y1) ),
    file(unknown,unknown) ).

tff(f_108,axiom,
    ! [Y1] :
      ( on(point_1_on_line(Y1),Y1)
      | ~ line(Y1) ),
    file(unknown,unknown) ).

tff(c_24,plain,
    line(at_least_one_line),
    inference(cnfTransformation,[status(thm)],[f_143]) ).

tff(c_12,plain,
    ! [Y1_12] :
      ( ~ line(Y1_12)
      | on(point_2_on_line(Y1_12),Y1_12) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_22,plain,
    ! [Y1_17] :
      ( ~ line(Y1_17)
      | point(point_not_on_line(Y1_17)) ),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_16,plain,
    ! [Y1_14] :
      ( ~ line(Y1_14)
      | point(point_2_on_line(Y1_14)) ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_6,plain,
    ! [Z2_6,Z1_5] :
      ( ~ point(Z2_6)
      | ~ point(Z1_5)
      | ( Z2_6 = Z1_5 )
      | line(line_from_to(Z1_5,Z2_6)) ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_66,plain,
    ! [Line_71] :
      ( on(a_point,Line_71)
      | ~ line(Line_71) ),
    inference(cnfTransformation,[status(thm)],[f_515]) ).

tff(c_4,plain,
    ! [Z2_3,Z1_4] :
      ( ~ point(Z2_3)
      | ~ point(Z1_4)
      | ( Z2_3 = Z1_4 )
      | on(Z2_3,line_from_to(Z1_4,Z2_3)) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_64,plain,
    point(a_point),
    inference(cnfTransformation,[status(thm)],[f_510]) ).

tff(c_107,plain,
    ! [Y4_128,Y3_129,Z2_130,Z1_131] :
      ( ~ line(Y4_128)
      | ~ line(Y3_129)
      | ~ point(Z2_130)
      | ~ point(Z1_131)
      | ~ on(Z2_130,Y4_128)
      | ~ on(Z1_131,Y4_128)
      | ( Y4_128 = Y3_129 )
      | ~ on(Z2_130,Y3_129)
      | ( Z2_130 = Z1_131 )
      | ~ on(Z1_131,Y3_129) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_135,plain,
    ! [Y3_129,Z1_131,Line_71] :
      ( ~ line(Y3_129)
      | ~ point(a_point)
      | ~ point(Z1_131)
      | ~ on(Z1_131,Line_71)
      | ( Y3_129 = Line_71 )
      | ~ on(a_point,Y3_129)
      | ( a_point = Z1_131 )
      | ~ on(Z1_131,Y3_129)
      | ~ line(Line_71) ),
    inference(resolution,[status(thm)],[c_66,c_107]) ).

tff(c_152,plain,
    ! [Y3_132,Z1_133,Line_134] :
      ( ~ line(Y3_132)
      | ~ point(Z1_133)
      | ~ on(Z1_133,Line_134)
      | ( Y3_132 = Line_134 )
      | ~ on(a_point,Y3_132)
      | ( a_point = Z1_133 )
      | ~ on(Z1_133,Y3_132)
      | ~ line(Line_134) ),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_135]) ).

tff(c_3706,plain,
    ! [Y3_331,Z1_332,Z2_333] :
      ( ~ line(Y3_331)
      | ( line_from_to(Z1_332,Z2_333) = Y3_331 )
      | ~ on(a_point,Y3_331)
      | ( a_point = Z2_333 )
      | ~ on(Z2_333,Y3_331)
      | ~ line(line_from_to(Z1_332,Z2_333))
      | ~ point(Z2_333)
      | ~ point(Z1_332)
      | ( Z2_333 = Z1_332 ) ),
    inference(resolution,[status(thm)],[c_4,c_152]) ).

tff(c_3794,plain,
    ! [Z1_334,Z2_335,Line_336] :
      ( ( line_from_to(Z1_334,Z2_335) = Line_336 )
      | ( a_point = Z2_335 )
      | ~ on(Z2_335,Line_336)
      | ~ line(line_from_to(Z1_334,Z2_335))
      | ~ point(Z2_335)
      | ~ point(Z1_334)
      | ( Z2_335 = Z1_334 )
      | ~ line(Line_336) ),
    inference(resolution,[status(thm)],[c_66,c_3706]) ).

tff(c_3867,plain,
    ! [Z1_337,Y1_338] :
      ( ( line_from_to(Z1_337,point_2_on_line(Y1_338)) = Y1_338 )
      | ( point_2_on_line(Y1_338) = a_point )
      | ~ line(line_from_to(Z1_337,point_2_on_line(Y1_338)))
      | ~ point(point_2_on_line(Y1_338))
      | ~ point(Z1_337)
      | ( point_2_on_line(Y1_338) = Z1_337 )
      | ~ line(Y1_338) ),
    inference(resolution,[status(thm)],[c_12,c_3794]) ).

tff(c_3882,plain,
    ! [Z1_339,Y1_340] :
      ( ( line_from_to(Z1_339,point_2_on_line(Y1_340)) = Y1_340 )
      | ( point_2_on_line(Y1_340) = a_point )
      | ~ line(Y1_340)
      | ~ point(point_2_on_line(Y1_340))
      | ~ point(Z1_339)
      | ( point_2_on_line(Y1_340) = Z1_339 ) ),
    inference(resolution,[status(thm)],[c_6,c_3867]) ).

tff(c_3888,plain,
    ! [Z1_341,Y1_342] :
      ( ( line_from_to(Z1_341,point_2_on_line(Y1_342)) = Y1_342 )
      | ( point_2_on_line(Y1_342) = a_point )
      | ~ point(Z1_341)
      | ( point_2_on_line(Y1_342) = Z1_341 )
      | ~ line(Y1_342) ),
    inference(resolution,[status(thm)],[c_16,c_3882]) ).

tff(c_2,plain,
    ! [Z2_2,Z1_1] :
      ( ~ point(Z2_2)
      | ~ point(Z1_1)
      | ( Z2_2 = Z1_1 )
      | on(Z1_1,line_from_to(Z1_1,Z2_2)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_4005,plain,
    ! [Y1_347,Z1_348] :
      ( ~ point(point_2_on_line(Y1_347))
      | ~ point(Z1_348)
      | ( point_2_on_line(Y1_347) = Z1_348 )
      | on(Z1_348,Y1_347)
      | ( point_2_on_line(Y1_347) = a_point )
      | ~ point(Z1_348)
      | ( point_2_on_line(Y1_347) = Z1_348 )
      | ~ line(Y1_347) ),
    inference(superposition,[status(thm),theory(equality)],[c_3888,c_2]) ).

tff(c_4009,plain,
    ! [Z1_349,Y1_350] :
      ( on(Z1_349,Y1_350)
      | ( point_2_on_line(Y1_350) = a_point )
      | ~ point(Z1_349)
      | ( point_2_on_line(Y1_350) = Z1_349 )
      | ~ line(Y1_350) ),
    inference(resolution,[status(thm)],[c_16,c_4005]) ).

tff(c_20,plain,
    ! [Y1_16] :
      ( ~ line(Y1_16)
      | ~ on(point_not_on_line(Y1_16),Y1_16) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_4122,plain,
    ! [Y1_351] :
      ( ( point_2_on_line(Y1_351) = a_point )
      | ~ point(point_not_on_line(Y1_351))
      | ( point_not_on_line(Y1_351) = point_2_on_line(Y1_351) )
      | ~ line(Y1_351) ),
    inference(resolution,[status(thm)],[c_4009,c_20]) ).

tff(c_4127,plain,
    ! [Y1_352] :
      ( ( point_2_on_line(Y1_352) = a_point )
      | ( point_not_on_line(Y1_352) = point_2_on_line(Y1_352) )
      | ~ line(Y1_352) ),
    inference(resolution,[status(thm)],[c_22,c_4122]) ).

tff(c_4139,plain,
    ( ( point_2_on_line(at_least_one_line) = a_point )
    | ( point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line) ) ),
    inference(resolution,[status(thm)],[c_24,c_4127]) ).

tff(c_4140,plain,
    point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line),
    inference(splitLeft,[status(thm)],[c_4139]) ).

tff(c_4162,plain,
    ( ~ line(at_least_one_line)
    | ~ on(point_2_on_line(at_least_one_line),at_least_one_line) ),
    inference(superposition,[status(thm),theory(equality)],[c_4140,c_20]) ).

tff(c_4181,plain,
    ~ on(point_2_on_line(at_least_one_line),at_least_one_line),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4162]) ).

tff(c_4220,plain,
    ~ line(at_least_one_line),
    inference(resolution,[status(thm)],[c_12,c_4181]) ).

tff(c_4228,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4220]) ).

tff(c_4229,plain,
    point_2_on_line(at_least_one_line) = a_point,
    inference(splitRight,[status(thm)],[c_4139]) ).

tff(c_78,plain,
    ! [Y1_83] :
      ( ~ line(Y1_83)
      | ( point_2_on_line(Y1_83) != point_1_on_line(Y1_83) ) ),
    inference(cnfTransformation,[status(thm)],[f_129]) ).

tff(c_82,plain,
    point_2_on_line(at_least_one_line) != point_1_on_line(at_least_one_line),
    inference(resolution,[status(thm)],[c_24,c_78]) ).

tff(c_4231,plain,
    point_1_on_line(at_least_one_line) != a_point,
    inference(demodulation,[status(thm),theory(equality)],[c_4229,c_82]) ).

tff(c_14,plain,
    ! [Y1_13] :
      ( ~ line(Y1_13)
      | point(point_1_on_line(Y1_13)) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_4289,plain,
    ( ~ line(at_least_one_line)
    | on(a_point,at_least_one_line) ),
    inference(superposition,[status(thm),theory(equality)],[c_4229,c_12]) ).

tff(c_4332,plain,
    on(a_point,at_least_one_line),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4289]) ).

tff(c_10,plain,
    ! [Y1_11] :
      ( ~ line(Y1_11)
      | on(point_1_on_line(Y1_11),Y1_11) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_148,plain,
    ! [Y3_129,Y1_11,Z1_131] :
      ( ~ line(Y3_129)
      | ~ point(point_1_on_line(Y1_11))
      | ~ point(Z1_131)
      | ~ on(Z1_131,Y1_11)
      | ( Y3_129 = Y1_11 )
      | ~ on(point_1_on_line(Y1_11),Y3_129)
      | ( point_1_on_line(Y1_11) = Z1_131 )
      | ~ on(Z1_131,Y3_129)
      | ~ line(Y1_11) ),
    inference(resolution,[status(thm)],[c_10,c_107]) ).

tff(c_4438,plain,
    ! [Y3_129] :
      ( ~ line(Y3_129)
      | ~ point(point_1_on_line(at_least_one_line))
      | ~ point(a_point)
      | ( at_least_one_line = Y3_129 )
      | ~ on(point_1_on_line(at_least_one_line),Y3_129)
      | ( point_1_on_line(at_least_one_line) = a_point )
      | ~ on(a_point,Y3_129)
      | ~ line(at_least_one_line) ),
    inference(resolution,[status(thm)],[c_4332,c_148]) ).

tff(c_4492,plain,
    ! [Y3_129] :
      ( ~ line(Y3_129)
      | ~ point(point_1_on_line(at_least_one_line))
      | ( at_least_one_line = Y3_129 )
      | ~ on(point_1_on_line(at_least_one_line),Y3_129)
      | ( point_1_on_line(at_least_one_line) = a_point )
      | ~ on(a_point,Y3_129) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_64,c_4438]) ).

tff(c_4493,plain,
    ! [Y3_129] :
      ( ~ line(Y3_129)
      | ~ point(point_1_on_line(at_least_one_line))
      | ( at_least_one_line = Y3_129 )
      | ~ on(point_1_on_line(at_least_one_line),Y3_129)
      | ~ on(a_point,Y3_129) ),
    inference(negUnitSimplification,[status(thm)],[c_4231,c_4492]) ).

tff(c_4538,plain,
    ~ point(point_1_on_line(at_least_one_line)),
    inference(splitLeft,[status(thm)],[c_4493]) ).

tff(c_4541,plain,
    ~ line(at_least_one_line),
    inference(resolution,[status(thm)],[c_14,c_4538]) ).

tff(c_4545,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4541]) ).

tff(c_4547,plain,
    point(point_1_on_line(at_least_one_line)),
    inference(splitRight,[status(thm)],[c_4493]) ).

tff(c_4336,plain,
    ! [Z1_353,Z2_354,Y3_355,Z1_356] :
      ( ~ line(line_from_to(Z1_353,Z2_354))
      | ~ line(Y3_355)
      | ~ point(Z1_356)
      | ~ on(Z1_356,line_from_to(Z1_353,Z2_354))
      | ( line_from_to(Z1_353,Z2_354) = Y3_355 )
      | ~ on(Z2_354,Y3_355)
      | ( Z2_354 = Z1_356 )
      | ~ on(Z1_356,Y3_355)
      | ~ point(Z2_354)
      | ~ point(Z1_353)
      | ( Z2_354 = Z1_353 ) ),
    inference(resolution,[status(thm)],[c_4,c_107]) ).

tff(c_6478,plain,
    ! [Z1_392,Z2_393,Y3_394] :
      ( ~ line(line_from_to(Z1_392,Z2_393))
      | ~ line(Y3_394)
      | ( line_from_to(Z1_392,Z2_393) = Y3_394 )
      | ~ on(Z2_393,Y3_394)
      | ~ on(Z1_392,Y3_394)
      | ~ point(Z2_393)
      | ~ point(Z1_392)
      | ( Z2_393 = Z1_392 ) ),
    inference(resolution,[status(thm)],[c_2,c_4336]) ).

tff(c_6526,plain,
    ! [Y3_395,Z1_396,Z2_397] :
      ( ~ line(Y3_395)
      | ( line_from_to(Z1_396,Z2_397) = Y3_395 )
      | ~ on(Z2_397,Y3_395)
      | ~ on(Z1_396,Y3_395)
      | ~ point(Z2_397)
      | ~ point(Z1_396)
      | ( Z2_397 = Z1_396 ) ),
    inference(resolution,[status(thm)],[c_6,c_6478]) ).

tff(c_6534,plain,
    ! [Z1_396] :
      ( ~ line(at_least_one_line)
      | ( line_from_to(Z1_396,a_point) = at_least_one_line )
      | ~ on(Z1_396,at_least_one_line)
      | ~ point(a_point)
      | ~ point(Z1_396)
      | ( a_point = Z1_396 ) ),
    inference(resolution,[status(thm)],[c_4332,c_6526]) ).

tff(c_6621,plain,
    ! [Z1_398] :
      ( ( line_from_to(Z1_398,a_point) = at_least_one_line )
      | ~ on(Z1_398,at_least_one_line)
      | ~ point(Z1_398)
      | ( a_point = Z1_398 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_24,c_6534]) ).

tff(c_6672,plain,
    ( ( line_from_to(point_1_on_line(at_least_one_line),a_point) = at_least_one_line )
    | ~ point(point_1_on_line(at_least_one_line))
    | ( point_1_on_line(at_least_one_line) = a_point )
    | ~ line(at_least_one_line) ),
    inference(resolution,[status(thm)],[c_10,c_6621]) ).

tff(c_6714,plain,
    ( ( line_from_to(point_1_on_line(at_least_one_line),a_point) = at_least_one_line )
    | ( point_1_on_line(at_least_one_line) = a_point ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4547,c_6672]) ).

tff(c_6715,plain,
    line_from_to(point_1_on_line(at_least_one_line),a_point) = at_least_one_line,
    inference(negUnitSimplification,[status(thm)],[c_4231,c_6714]) ).

tff(c_6744,plain,
    ( ~ point(a_point)
    | ~ point(point_1_on_line(at_least_one_line))
    | ( point_1_on_line(at_least_one_line) = a_point )
    | on(point_1_on_line(at_least_one_line),at_least_one_line) ),
    inference(superposition,[status(thm),theory(equality)],[c_6715,c_2]) ).

tff(c_6781,plain,
    ( ( point_1_on_line(at_least_one_line) = a_point )
    | on(point_1_on_line(at_least_one_line),at_least_one_line) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4547,c_64,c_6744]) ).

tff(c_6782,plain,
    on(point_1_on_line(at_least_one_line),at_least_one_line),
    inference(negUnitSimplification,[status(thm)],[c_4231,c_6781]) ).

tff(c_3793,plain,
    ! [Z1_332,Z2_333,Line_71] :
      ( ( line_from_to(Z1_332,Z2_333) = Line_71 )
      | ( a_point = Z2_333 )
      | ~ on(Z2_333,Line_71)
      | ~ line(line_from_to(Z1_332,Z2_333))
      | ~ point(Z2_333)
      | ~ point(Z1_332)
      | ( Z2_333 = Z1_332 )
      | ~ line(Line_71) ),
    inference(resolution,[status(thm)],[c_66,c_3706]) ).

tff(c_6801,plain,
    ! [Z1_332] :
      ( ( line_from_to(Z1_332,point_1_on_line(at_least_one_line)) = at_least_one_line )
      | ( point_1_on_line(at_least_one_line) = a_point )
      | ~ line(line_from_to(Z1_332,point_1_on_line(at_least_one_line)))
      | ~ point(point_1_on_line(at_least_one_line))
      | ~ point(Z1_332)
      | ( point_1_on_line(at_least_one_line) = Z1_332 )
      | ~ line(at_least_one_line) ),
    inference(resolution,[status(thm)],[c_6782,c_3793]) ).

tff(c_6866,plain,
    ! [Z1_332] :
      ( ( line_from_to(Z1_332,point_1_on_line(at_least_one_line)) = at_least_one_line )
      | ( point_1_on_line(at_least_one_line) = a_point )
      | ~ line(line_from_to(Z1_332,point_1_on_line(at_least_one_line)))
      | ~ point(Z1_332)
      | ( point_1_on_line(at_least_one_line) = Z1_332 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4547,c_6801]) ).

tff(c_7575,plain,
    ! [Z1_415] :
      ( ( line_from_to(Z1_415,point_1_on_line(at_least_one_line)) = at_least_one_line )
      | ~ line(line_from_to(Z1_415,point_1_on_line(at_least_one_line)))
      | ~ point(Z1_415)
      | ( point_1_on_line(at_least_one_line) = Z1_415 ) ),
    inference(negUnitSimplification,[status(thm)],[c_4231,c_6866]) ).

tff(c_7603,plain,
    ! [Z1_5] :
      ( ( line_from_to(Z1_5,point_1_on_line(at_least_one_line)) = at_least_one_line )
      | ~ point(point_1_on_line(at_least_one_line))
      | ~ point(Z1_5)
      | ( point_1_on_line(at_least_one_line) = Z1_5 ) ),
    inference(resolution,[status(thm)],[c_6,c_7575]) ).

tff(c_7616,plain,
    ! [Z1_416] :
      ( ( line_from_to(Z1_416,point_1_on_line(at_least_one_line)) = at_least_one_line )
      | ~ point(Z1_416)
      | ( point_1_on_line(at_least_one_line) = Z1_416 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4547,c_7603]) ).

tff(c_7664,plain,
    ! [Z1_416] :
      ( ~ point(point_1_on_line(at_least_one_line))
      | ~ point(Z1_416)
      | ( point_1_on_line(at_least_one_line) = Z1_416 )
      | on(Z1_416,at_least_one_line)
      | ~ point(Z1_416)
      | ( point_1_on_line(at_least_one_line) = Z1_416 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_7616,c_2]) ).

tff(c_7743,plain,
    ! [Z1_419] :
      ( on(Z1_419,at_least_one_line)
      | ~ point(Z1_419)
      | ( point_1_on_line(at_least_one_line) = Z1_419 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4547,c_7664]) ).

tff(c_7835,plain,
    ( ~ line(at_least_one_line)
    | ~ point(point_not_on_line(at_least_one_line))
    | ( point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line) ) ),
    inference(resolution,[status(thm)],[c_7743,c_20]) ).

tff(c_7930,plain,
    ( ~ point(point_not_on_line(at_least_one_line))
    | ( point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_7835]) ).

tff(c_7932,plain,
    ~ point(point_not_on_line(at_least_one_line)),
    inference(splitLeft,[status(thm)],[c_7930]) ).

tff(c_7935,plain,
    ~ line(at_least_one_line),
    inference(resolution,[status(thm)],[c_22,c_7932]) ).

tff(c_7939,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_7935]) ).

tff(c_7940,plain,
    point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line),
    inference(splitRight,[status(thm)],[c_7930]) ).

tff(c_8014,plain,
    ( ~ line(at_least_one_line)
    | ~ on(point_1_on_line(at_least_one_line),at_least_one_line) ),
    inference(superposition,[status(thm),theory(equality)],[c_7940,c_20]) ).

tff(c_8037,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6782,c_24,c_8014]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : GEO076-4 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Aug  4 00:40:08 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 11.09/3.63  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.09/3.64  
% 11.09/3.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.38/3.68  
% 11.38/3.68  Inference rules
% 11.38/3.68  ----------------------
% 11.38/3.68  #Ref     : 0
% 11.38/3.68  #Sup     : 1883
% 11.38/3.68  #Fact    : 1
% 11.38/3.68  #Define  : 0
% 11.38/3.68  #Split   : 6
% 11.38/3.68  #Chain   : 0
% 11.38/3.68  #Close   : 0
% 11.38/3.68  
% 11.38/3.68  Ordering : KBO
% 11.38/3.68  
% 11.38/3.68  Simplification rules
% 11.38/3.68  ----------------------
% 11.38/3.68  #Subsume      : 338
% 11.38/3.68  #Demod        : 825
% 11.38/3.68  #Tautology    : 217
% 11.38/3.68  #SimpNegUnit  : 110
% 11.38/3.68  #BackRed      : 3
% 11.38/3.68  
% 11.38/3.68  #Partial instantiations: 0
% 11.38/3.68  #Strategies tried      : 1
% 11.38/3.68  
% 11.38/3.68  Timing (in seconds)
% 11.38/3.68  ----------------------
% 11.38/3.68  Preprocessing        : 0.57
% 11.38/3.68  Parsing              : 0.30
% 11.38/3.68  CNF conversion       : 0.03
% 11.38/3.68  Main loop            : 1.93
% 11.38/3.68  Inferencing          : 0.50
% 11.38/3.68  Reduction            : 0.39
% 11.38/3.68  Demodulation         : 0.25
% 11.38/3.68  BG Simplification    : 0.08
% 11.38/3.68  Subsumption          : 0.85
% 11.38/3.68  Abstraction          : 0.08
% 11.38/3.68  MUC search           : 0.00
% 11.38/3.68  Cooper               : 0.00
% 11.38/3.68  Total                : 2.57
% 11.38/3.68  Index Insertion      : 0.00
% 11.38/3.68  Index Deletion       : 0.00
% 11.38/3.68  Index Matching       : 0.00
% 11.38/3.68  BG Taut test         : 0.00
%------------------------------------------------------------------------------