TSTP Solution File: GEO202+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GEO202+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : n017.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 10:38:38 EDT 2023
% Result : Theorem 9.71s 3.49s
% Output : CNFRefutation 10.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 36
% Syntax : Number of formulae : 116 ( 41 unt; 19 typ; 0 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 179 ( 67 ~; 95 |; 6 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 16 >; 14 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 177 (; 177 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ unorthogonal_lines > parallel_lines > orthogonal_lines > incident_point_and_line > equal_points > equal_lines > distinct_points > distinct_lines > convergent_lines > apart_point_and_line > point > line > parallel_through_point > orthogonal_through_point > line_connecting > intersection_point > #nlpp > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(line_connecting,type,
line_connecting: ( $i * $i ) > $i ).
tff(equal_lines,type,
equal_lines: ( $i * $i ) > $o ).
tff(equal_points,type,
equal_points: ( $i * $i ) > $o ).
tff(incident_point_and_line,type,
incident_point_and_line: ( $i * $i ) > $o ).
tff(distinct_points,type,
distinct_points: ( $i * $i ) > $o ).
tff(intersection_point,type,
intersection_point: ( $i * $i ) > $i ).
tff(parallel_through_point,type,
parallel_through_point: ( $i * $i ) > $i ).
tff(apart_point_and_line,type,
apart_point_and_line: ( $i * $i ) > $o ).
tff(convergent_lines,type,
convergent_lines: ( $i * $i ) > $o ).
tff(orthogonal_through_point,type,
orthogonal_through_point: ( $i * $i ) > $i ).
tff(point,type,
point: $i > $o ).
tff(line,type,
line: $i > $o ).
tff(parallel_lines,type,
parallel_lines: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(unorthogonal_lines,type,
unorthogonal_lines: ( $i * $i ) > $o ).
tff(distinct_lines,type,
distinct_lines: ( $i * $i ) > $o ).
tff(orthogonal_lines,type,
orthogonal_lines: ( $i * $i ) > $o ).
tff(f_437,negated_conjecture,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
tff(f_132,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
tff(f_113,axiom,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_lines(U,V) )
=> ( apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
tff(f_85,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
tff(f_90,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
tff(f_61,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
tff(f_126,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
tff(f_160,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
tff(f_188,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
tff(f_426,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a5) ).
tff(f_311,axiom,
! [L,M,N] :
( ( ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M) )
& ( ~ convergent_lines(L,N)
| ~ unorthogonal_lines(L,N) ) )
=> ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',cotno1) ).
tff(f_292,axiom,
! [L,M] :
~ ( ~ convergent_lines(L,M)
& ~ unorthogonal_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
tff(f_246,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
tff(f_79,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
tff(f_58,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
tff(f_321,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
tff(f_191,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
tff(c_100,plain,
distinct_points('#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_98,plain,
distinct_points('#skF_1','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_96,plain,
convergent_lines(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_172,plain,
! [X_135,Z_136,Y_137] :
( convergent_lines(X_135,Z_136)
| distinct_lines(Y_137,Z_136)
| ~ convergent_lines(X_135,Y_137) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_178,plain,
! [Z_136] :
( convergent_lines(line_connecting('#skF_1','#skF_2'),Z_136)
| distinct_lines(line_connecting('#skF_1','#skF_3'),Z_136) ),
inference(resolution,[status(thm)],[c_96,c_172]) ).
tff(c_2944,plain,
! [Y_443,V_444,U_445,X_446] :
( apart_point_and_line(Y_443,V_444)
| apart_point_and_line(Y_443,U_445)
| apart_point_and_line(X_446,V_444)
| apart_point_and_line(X_446,U_445)
| ~ distinct_lines(U_445,V_444)
| ~ distinct_points(X_446,Y_443) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_6172,plain,
! [Y_612,Z_613,X_614] :
( apart_point_and_line(Y_612,Z_613)
| apart_point_and_line(Y_612,line_connecting('#skF_1','#skF_3'))
| apart_point_and_line(X_614,Z_613)
| apart_point_and_line(X_614,line_connecting('#skF_1','#skF_3'))
| ~ distinct_points(X_614,Y_612)
| convergent_lines(line_connecting('#skF_1','#skF_2'),Z_613) ),
inference(resolution,[status(thm)],[c_178,c_2944]) ).
tff(c_6300,plain,
! [Z_613] :
( apart_point_and_line('#skF_3',Z_613)
| apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_3'))
| apart_point_and_line('#skF_1',Z_613)
| apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3'))
| convergent_lines(line_connecting('#skF_1','#skF_2'),Z_613) ),
inference(resolution,[status(thm)],[c_98,c_6172]) ).
tff(c_6730,plain,
apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3')),
inference(splitLeft,[status(thm)],[c_6300]) ).
tff(c_14,plain,
! [X_13,Y_14] :
( ~ apart_point_and_line(X_13,line_connecting(X_13,Y_14))
| ~ distinct_points(X_13,Y_14) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_6737,plain,
~ distinct_points('#skF_1','#skF_3'),
inference(resolution,[status(thm)],[c_6730,c_14]) ).
tff(c_6743,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_6737]) ).
tff(c_6744,plain,
! [Z_613] :
( apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_3'))
| apart_point_and_line('#skF_3',Z_613)
| apart_point_and_line('#skF_1',Z_613)
| convergent_lines(line_connecting('#skF_1','#skF_2'),Z_613) ),
inference(splitRight,[status(thm)],[c_6300]) ).
tff(c_7068,plain,
apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_3')),
inference(splitLeft,[status(thm)],[c_6744]) ).
tff(c_16,plain,
! [Y_16,X_15] :
( ~ apart_point_and_line(Y_16,line_connecting(X_15,Y_16))
| ~ distinct_points(X_15,Y_16) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_7077,plain,
~ distinct_points('#skF_1','#skF_3'),
inference(resolution,[status(thm)],[c_7068,c_16]) ).
tff(c_7083,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_7077]) ).
tff(c_8649,plain,
! [Z_811] :
( apart_point_and_line('#skF_3',Z_811)
| apart_point_and_line('#skF_1',Z_811)
| convergent_lines(line_connecting('#skF_1','#skF_2'),Z_811) ),
inference(splitRight,[status(thm)],[c_6744]) ).
tff(c_6,plain,
! [X_3] : ~ convergent_lines(X_3,X_3),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_8673,plain,
( apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_2'))
| apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_8649,c_6]) ).
tff(c_8674,plain,
apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_8673]) ).
tff(c_8681,plain,
~ distinct_points('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_8674,c_14]) ).
tff(c_8687,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_100,c_8681]) ).
tff(c_8689,plain,
~ apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_8673]) ).
tff(c_6745,plain,
~ apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3')),
inference(splitRight,[status(thm)],[c_6300]) ).
tff(c_6301,plain,
! [Z_613] :
( apart_point_and_line('#skF_2',Z_613)
| apart_point_and_line('#skF_2',line_connecting('#skF_1','#skF_3'))
| apart_point_and_line('#skF_1',Z_613)
| apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3'))
| convergent_lines(line_connecting('#skF_1','#skF_2'),Z_613) ),
inference(resolution,[status(thm)],[c_100,c_6172]) ).
tff(c_6918,plain,
! [Z_613] :
( apart_point_and_line('#skF_2',Z_613)
| apart_point_and_line('#skF_2',line_connecting('#skF_1','#skF_3'))
| apart_point_and_line('#skF_1',Z_613)
| convergent_lines(line_connecting('#skF_1','#skF_2'),Z_613) ),
inference(negUnitSimplification,[status(thm)],[c_6745,c_6301]) ).
tff(c_6919,plain,
apart_point_and_line('#skF_2',line_connecting('#skF_1','#skF_3')),
inference(splitLeft,[status(thm)],[c_6918]) ).
tff(c_26,plain,
! [X_28,Z_30,Y_29] :
( apart_point_and_line(X_28,Z_30)
| distinct_lines(Y_29,Z_30)
| ~ apart_point_and_line(X_28,Y_29) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_6926,plain,
! [Z_665] :
( apart_point_and_line('#skF_2',Z_665)
| distinct_lines(line_connecting('#skF_1','#skF_3'),Z_665) ),
inference(resolution,[status(thm)],[c_6919,c_26]) ).
tff(c_30,plain,
! [X_34,Y_35] :
( convergent_lines(X_34,Y_35)
| ~ distinct_lines(X_34,Y_35) ),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_7033,plain,
! [Z_671] :
( convergent_lines(line_connecting('#skF_1','#skF_3'),Z_671)
| apart_point_and_line('#skF_2',Z_671) ),
inference(resolution,[status(thm)],[c_6926,c_30]) ).
tff(c_32,plain,
! [Y_37,X_36] : ~ convergent_lines(parallel_through_point(Y_37,X_36),Y_37),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_92,plain,
! [X_80,Y_81] :
( orthogonal_lines(X_80,Y_81)
| unorthogonal_lines(X_80,Y_81) ),
inference(cnfTransformation,[status(thm)],[f_426]) ).
tff(c_1088,plain,
! [L_231,M_232,N_233] :
( convergent_lines(L_231,M_232)
| convergent_lines(L_231,N_233)
| ~ unorthogonal_lines(M_232,N_233)
| ~ convergent_lines(M_232,N_233) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_5161,plain,
! [L_573,X_574,Y_575] :
( convergent_lines(L_573,X_574)
| convergent_lines(L_573,Y_575)
| ~ convergent_lines(X_574,Y_575)
| orthogonal_lines(X_574,Y_575) ),
inference(resolution,[status(thm)],[c_92,c_1088]) ).
tff(c_5306,plain,
! [Y_576,X_577] :
( convergent_lines(Y_576,X_577)
| ~ convergent_lines(X_577,Y_576)
| orthogonal_lines(X_577,Y_576) ),
inference(resolution,[status(thm)],[c_5161,c_6]) ).
tff(c_116,plain,
! [L_101,M_102] :
( unorthogonal_lines(L_101,M_102)
| convergent_lines(L_101,M_102) ),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_48,plain,
! [L_49,A_48] : ~ unorthogonal_lines(orthogonal_through_point(L_49,A_48),L_49),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_121,plain,
! [M_102,A_48] : convergent_lines(orthogonal_through_point(M_102,A_48),M_102),
inference(resolution,[status(thm)],[c_116,c_48]) ).
tff(c_177,plain,
! [M_102,A_48,Z_136] :
( convergent_lines(orthogonal_through_point(M_102,A_48),Z_136)
| distinct_lines(M_102,Z_136) ),
inference(resolution,[status(thm)],[c_121,c_172]) ).
tff(c_344,plain,
! [Y_185,Z_186,X_187] :
( convergent_lines(Y_185,Z_186)
| convergent_lines(X_187,Z_186)
| ~ convergent_lines(X_187,Y_185) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1689,plain,
! [Z_316,Z_317,M_318,A_319] :
( convergent_lines(Z_316,Z_317)
| convergent_lines(orthogonal_through_point(M_318,A_319),Z_317)
| distinct_lines(M_318,Z_316) ),
inference(resolution,[status(thm)],[c_177,c_344]) ).
tff(c_1775,plain,
! [M_323,A_324,Z_325,X_326] :
( convergent_lines(orthogonal_through_point(M_323,A_324),Z_325)
| distinct_lines(M_323,parallel_through_point(Z_325,X_326)) ),
inference(resolution,[status(thm)],[c_1689,c_32]) ).
tff(c_4,plain,
! [X_2] : ~ distinct_lines(X_2,X_2),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_1803,plain,
! [Z_327,X_328,A_329] : convergent_lines(orthogonal_through_point(parallel_through_point(Z_327,X_328),A_329),Z_327),
inference(resolution,[status(thm)],[c_1775,c_4]) ).
tff(c_28,plain,
! [X_31,Z_33,Y_32] :
( convergent_lines(X_31,Z_33)
| distinct_lines(Y_32,Z_33)
| ~ convergent_lines(X_31,Y_32) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_1938,plain,
! [Z_340,X_341,A_342,Z_343] :
( convergent_lines(orthogonal_through_point(parallel_through_point(Z_340,X_341),A_342),Z_343)
| distinct_lines(Z_340,Z_343) ),
inference(resolution,[status(thm)],[c_1803,c_28]) ).
tff(c_1953,plain,
! [Z_344,X_345,A_346] : distinct_lines(Z_344,orthogonal_through_point(parallel_through_point(Z_344,X_345),A_346)),
inference(resolution,[status(thm)],[c_1938,c_6]) ).
tff(c_1960,plain,
! [Z_344,X_345,A_346] : convergent_lines(Z_344,orthogonal_through_point(parallel_through_point(Z_344,X_345),A_346)),
inference(resolution,[status(thm)],[c_1953,c_30]) ).
tff(c_179,plain,
! [M_138,A_139,Z_140] :
( convergent_lines(orthogonal_through_point(M_138,A_139),Z_140)
| distinct_lines(M_138,Z_140) ),
inference(resolution,[status(thm)],[c_121,c_172]) ).
tff(c_189,plain,
! [M_144,A_145] : distinct_lines(M_144,orthogonal_through_point(M_144,A_145)),
inference(resolution,[status(thm)],[c_179,c_6]) ).
tff(c_196,plain,
! [M_144,A_145] : convergent_lines(M_144,orthogonal_through_point(M_144,A_145)),
inference(resolution,[status(thm)],[c_189,c_30]) ).
tff(c_764,plain,
! [L_216,M_217,N_218] :
( unorthogonal_lines(L_216,M_217)
| convergent_lines(L_216,N_218)
| ~ unorthogonal_lines(M_217,N_218)
| ~ convergent_lines(M_217,N_218) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_3889,plain,
! [L_507,X_508,Y_509] :
( unorthogonal_lines(L_507,X_508)
| convergent_lines(L_507,Y_509)
| ~ convergent_lines(X_508,Y_509)
| orthogonal_lines(X_508,Y_509) ),
inference(resolution,[status(thm)],[c_92,c_764]) ).
tff(c_4038,plain,
! [Y_513,X_514] :
( unorthogonal_lines(Y_513,X_514)
| ~ convergent_lines(X_514,Y_513)
| orthogonal_lines(X_514,Y_513) ),
inference(resolution,[status(thm)],[c_3889,c_6]) ).
tff(c_4059,plain,
! [X_514,A_48] :
( ~ convergent_lines(X_514,orthogonal_through_point(X_514,A_48))
| orthogonal_lines(X_514,orthogonal_through_point(X_514,A_48)) ),
inference(resolution,[status(thm)],[c_4038,c_48]) ).
tff(c_4071,plain,
! [X_515,A_516] : orthogonal_lines(X_515,orthogonal_through_point(X_515,A_516)),
inference(demodulation,[status(thm),theory(equality)],[c_196,c_4059]) ).
tff(c_1735,plain,
! [L_320,M_321,N_322] :
( convergent_lines(L_320,M_321)
| unorthogonal_lines(L_320,N_322)
| ~ unorthogonal_lines(M_321,N_322)
| ~ convergent_lines(M_321,N_322) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_3462,plain,
! [L_481,X_482,Y_483] :
( convergent_lines(L_481,X_482)
| unorthogonal_lines(L_481,Y_483)
| ~ convergent_lines(X_482,Y_483)
| orthogonal_lines(X_482,Y_483) ),
inference(resolution,[status(thm)],[c_92,c_1735]) ).
tff(c_3591,plain,
! [X_484,X_485,Y_486] :
( unorthogonal_lines(parallel_through_point(X_484,X_485),Y_486)
| ~ convergent_lines(X_484,Y_486)
| orthogonal_lines(X_484,Y_486) ),
inference(resolution,[status(thm)],[c_3462,c_32]) ).
tff(c_90,plain,
! [X_80,Y_81] :
( ~ unorthogonal_lines(X_80,Y_81)
| ~ orthogonal_lines(X_80,Y_81) ),
inference(cnfTransformation,[status(thm)],[f_426]) ).
tff(c_3616,plain,
! [X_484,X_485,Y_486] :
( ~ orthogonal_lines(parallel_through_point(X_484,X_485),Y_486)
| ~ convergent_lines(X_484,Y_486)
| orthogonal_lines(X_484,Y_486) ),
inference(resolution,[status(thm)],[c_3591,c_90]) ).
tff(c_4075,plain,
! [X_484,X_485,A_516] :
( ~ convergent_lines(X_484,orthogonal_through_point(parallel_through_point(X_484,X_485),A_516))
| orthogonal_lines(X_484,orthogonal_through_point(parallel_through_point(X_484,X_485),A_516)) ),
inference(resolution,[status(thm)],[c_4071,c_3616]) ).
tff(c_4505,plain,
! [X_534,X_535,A_536] : orthogonal_lines(X_534,orthogonal_through_point(parallel_through_point(X_534,X_535),A_536)),
inference(demodulation,[status(thm),theory(equality)],[c_1960,c_4075]) ).
tff(c_283,plain,
! [M_163,N_164,L_165] :
( ~ convergent_lines(M_163,N_164)
| unorthogonal_lines(L_165,N_164)
| unorthogonal_lines(L_165,M_163) ),
inference(cnfTransformation,[status(thm)],[f_321]) ).
tff(c_299,plain,
! [L_166,M_167,A_168] :
( unorthogonal_lines(L_166,M_167)
| unorthogonal_lines(L_166,orthogonal_through_point(M_167,A_168)) ),
inference(resolution,[status(thm)],[c_121,c_283]) ).
tff(c_307,plain,
! [L_166,M_167,A_168] :
( ~ orthogonal_lines(L_166,orthogonal_through_point(M_167,A_168))
| unorthogonal_lines(L_166,M_167) ),
inference(resolution,[status(thm)],[c_299,c_90]) ).
tff(c_4642,plain,
! [X_539,X_540] : unorthogonal_lines(X_539,parallel_through_point(X_539,X_540)),
inference(resolution,[status(thm)],[c_4505,c_307]) ).
tff(c_4667,plain,
! [X_539,X_540] : ~ orthogonal_lines(X_539,parallel_through_point(X_539,X_540)),
inference(resolution,[status(thm)],[c_4642,c_90]) ).
tff(c_5312,plain,
! [X_577,X_540] :
( convergent_lines(parallel_through_point(X_577,X_540),X_577)
| ~ convergent_lines(X_577,parallel_through_point(X_577,X_540)) ),
inference(resolution,[status(thm)],[c_5306,c_4667]) ).
tff(c_5392,plain,
! [X_577,X_540] : ~ convergent_lines(X_577,parallel_through_point(X_577,X_540)),
inference(negUnitSimplification,[status(thm)],[c_32,c_5312]) ).
tff(c_7054,plain,
! [X_672] : apart_point_and_line('#skF_2',parallel_through_point(line_connecting('#skF_1','#skF_3'),X_672)),
inference(resolution,[status(thm)],[c_7033,c_5392]) ).
tff(c_34,plain,
! [X_38,Y_39] : ~ apart_point_and_line(X_38,parallel_through_point(Y_39,X_38)),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_7065,plain,
$false,
inference(resolution,[status(thm)],[c_7054,c_34]) ).
tff(c_8824,plain,
! [Z_818] :
( apart_point_and_line('#skF_2',Z_818)
| apart_point_and_line('#skF_1',Z_818)
| convergent_lines(line_connecting('#skF_1','#skF_2'),Z_818) ),
inference(splitRight,[status(thm)],[c_6918]) ).
tff(c_8842,plain,
( apart_point_and_line('#skF_2',line_connecting('#skF_1','#skF_2'))
| apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_8824,c_6]) ).
tff(c_8850,plain,
apart_point_and_line('#skF_2',line_connecting('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_8689,c_8842]) ).
tff(c_8857,plain,
~ distinct_points('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_8850,c_16]) ).
tff(c_8863,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_100,c_8857]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GEO202+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % 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 : n017.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 : Thu Aug 3 23:41:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 9.71/3.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.71/3.51
% 9.71/3.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.17/3.55
% 10.17/3.55 Inference rules
% 10.17/3.55 ----------------------
% 10.17/3.55 #Ref : 0
% 10.17/3.55 #Sup : 1998
% 10.17/3.55 #Fact : 94
% 10.17/3.55 #Define : 0
% 10.17/3.55 #Split : 5
% 10.17/3.55 #Chain : 0
% 10.17/3.55 #Close : 0
% 10.17/3.55
% 10.17/3.55 Ordering : KBO
% 10.17/3.55
% 10.17/3.55 Simplification rules
% 10.17/3.55 ----------------------
% 10.17/3.55 #Subsume : 194
% 10.17/3.55 #Demod : 257
% 10.17/3.55 #Tautology : 253
% 10.17/3.55 #SimpNegUnit : 29
% 10.17/3.55 #BackRed : 0
% 10.17/3.55
% 10.17/3.55 #Partial instantiations: 0
% 10.17/3.55 #Strategies tried : 1
% 10.17/3.55
% 10.17/3.55 Timing (in seconds)
% 10.17/3.55 ----------------------
% 10.17/3.55 Preprocessing : 0.56
% 10.17/3.55 Parsing : 0.32
% 10.17/3.55 CNF conversion : 0.04
% 10.17/3.55 Main loop : 1.86
% 10.17/3.55 Inferencing : 0.64
% 10.17/3.55 Reduction : 0.53
% 10.17/3.55 Demodulation : 0.34
% 10.17/3.55 BG Simplification : 0.05
% 10.17/3.55 Subsumption : 0.48
% 10.17/3.55 Abstraction : 0.05
% 10.17/3.55 MUC search : 0.00
% 10.17/3.55 Cooper : 0.00
% 10.17/3.55 Total : 2.49
% 10.17/3.55 Index Insertion : 0.00
% 10.17/3.55 Index Deletion : 0.00
% 10.17/3.55 Index Matching : 0.00
% 10.17/3.55 BG Taut test : 0.00
%------------------------------------------------------------------------------