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