%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEO223+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 : Wed Apr 9 06:14:21 PM UTC 2025
% Result : Theorem 14.19s 4.79s
% Output : CNFRefutation 14.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 81 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 154 ( 63 ~; 77 |; 6 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 185 ( 185 !; 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_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_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_188,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
tff(f_292,axiom,
! [L,M] :
~ ( ~ convergent_lines(L,M)
& ~ unorthogonal_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',coipo1) ).
tff(f_246,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
tff(f_132,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( distinct_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
tff(f_58,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
tff(f_61,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
tff(f_160,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
tff(f_426,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a5) ).
tff(f_242,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/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
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/sandbox/benchmark/Axioms/GEO006+4.ax',cotno1) ).
tff(f_321,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
tff(f_411,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
tff(f_431,negated_conjecture,
~ ! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
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_125,plain,
! [L_105,M_106] :
( unorthogonal_lines(L_105,M_106)
| convergent_lines(L_105,M_106) ),
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_130,plain,
! [M_106,A_48] : convergent_lines(orthogonal_through_point(M_106,A_48),M_106),
inference(resolution,[status(thm)],[c_125,c_48]) ).
tff(c_291,plain,
! [Y_173,Z_174,X_175] :
( convergent_lines(Y_173,Z_174)
| convergent_lines(X_175,Z_174)
| ~ convergent_lines(X_175,Y_173) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_304,plain,
! [M_176,Z_177,A_178] :
( convergent_lines(M_176,Z_177)
| convergent_lines(orthogonal_through_point(M_176,A_178),Z_177) ),
inference(resolution,[status(thm)],[c_130,c_291]) ).
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_316,plain,
! [M_176,A_178,Z_33,Z_177] :
( convergent_lines(orthogonal_through_point(M_176,A_178),Z_33)
| distinct_lines(Z_177,Z_33)
| convergent_lines(M_176,Z_177) ),
inference(resolution,[status(thm)],[c_304,c_28]) ).
tff(c_196,plain,
! [X_147,Z_148,Y_149] :
( convergent_lines(X_147,Z_148)
| distinct_lines(Y_149,Z_148)
| ~ convergent_lines(X_147,Y_149) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_202,plain,
! [M_106,A_48,Z_148] :
( convergent_lines(orthogonal_through_point(M_106,A_48),Z_148)
| distinct_lines(M_106,Z_148) ),
inference(resolution,[status(thm)],[c_130,c_196]) ).
tff(c_1058,plain,
! [Z_317,Z_318,M_319,A_320] :
( convergent_lines(Z_317,Z_318)
| convergent_lines(orthogonal_through_point(M_319,A_320),Z_318)
| distinct_lines(M_319,Z_317) ),
inference(resolution,[status(thm)],[c_202,c_291]) ).
tff(c_1104,plain,
! [M_321,A_322,Z_323,X_324] :
( convergent_lines(orthogonal_through_point(M_321,A_322),Z_323)
| distinct_lines(M_321,parallel_through_point(Z_323,X_324)) ),
inference(resolution,[status(thm)],[c_1058,c_32]) ).
tff(c_4,plain,
! [X_2] : ~ distinct_lines(X_2,X_2),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_1132,plain,
! [Z_325,X_326,A_327] : convergent_lines(orthogonal_through_point(parallel_through_point(Z_325,X_326),A_327),Z_325),
inference(resolution,[status(thm)],[c_1104,c_4]) ).
tff(c_12,plain,
! [Y_11,Z_12,X_10] :
( convergent_lines(Y_11,Z_12)
| convergent_lines(X_10,Z_12)
| ~ convergent_lines(X_10,Y_11) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1240,plain,
! [Z_339,Z_340,X_341,A_342] :
( convergent_lines(Z_339,Z_340)
| convergent_lines(orthogonal_through_point(parallel_through_point(Z_339,X_341),A_342),Z_340) ),
inference(resolution,[status(thm)],[c_1132,c_12]) ).
tff(c_6,plain,
! [X_3] : ~ convergent_lines(X_3,X_3),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_1254,plain,
! [Z_339,X_341,A_342] : convergent_lines(Z_339,orthogonal_through_point(parallel_through_point(Z_339,X_341),A_342)),
inference(resolution,[status(thm)],[c_1240,c_6]) ).
tff(c_1131,plain,
! [Z_323,X_324,A_322] : convergent_lines(orthogonal_through_point(parallel_through_point(Z_323,X_324),A_322),Z_323),
inference(resolution,[status(thm)],[c_1104,c_4]) ).
tff(c_204,plain,
! [M_153,A_154,Z_155] :
( convergent_lines(orthogonal_through_point(M_153,A_154),Z_155)
| distinct_lines(M_153,Z_155) ),
inference(resolution,[status(thm)],[c_130,c_196]) ).
tff(c_216,plain,
! [M_156,A_157] : distinct_lines(M_156,orthogonal_through_point(M_156,A_157)),
inference(resolution,[status(thm)],[c_204,c_6]) ).
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_223,plain,
! [M_156,A_157] : convergent_lines(M_156,orthogonal_through_point(M_156,A_157)),
inference(resolution,[status(thm)],[c_216,c_30]) ).
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_351,plain,
! [L_196,N_197,M_198] :
( convergent_lines(L_196,N_197)
| unorthogonal_lines(M_198,N_197)
| ~ unorthogonal_lines(L_196,M_198)
| ~ convergent_lines(L_196,M_198) ),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_4530,plain,
! [X_587,N_588,Y_589] :
( convergent_lines(X_587,N_588)
| unorthogonal_lines(Y_589,N_588)
| ~ convergent_lines(X_587,Y_589)
| orthogonal_lines(X_587,Y_589) ),
inference(resolution,[status(thm)],[c_92,c_351]) ).
tff(c_4663,plain,
! [Y_590,N_591] :
( unorthogonal_lines(Y_590,N_591)
| ~ convergent_lines(N_591,Y_590)
| orthogonal_lines(N_591,Y_590) ),
inference(resolution,[status(thm)],[c_4530,c_6]) ).
tff(c_4684,plain,
! [N_591,A_48] :
( ~ convergent_lines(N_591,orthogonal_through_point(N_591,A_48))
| orthogonal_lines(N_591,orthogonal_through_point(N_591,A_48)) ),
inference(resolution,[status(thm)],[c_4663,c_48]) ).
tff(c_4695,plain,
! [N_591,A_48] : orthogonal_lines(N_591,orthogonal_through_point(N_591,A_48)),
inference(demodulation,[status(thm),theory(equality)],[c_223,c_4684]) ).
tff(c_1188,plain,
! [L_336,M_337,N_338] :
( unorthogonal_lines(L_336,M_337)
| convergent_lines(L_336,N_338)
| ~ unorthogonal_lines(M_337,N_338)
| ~ convergent_lines(M_337,N_338) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_4912,plain,
! [L_605,X_606,Y_607] :
( unorthogonal_lines(L_605,X_606)
| convergent_lines(L_605,Y_607)
| ~ convergent_lines(X_606,Y_607)
| orthogonal_lines(X_606,Y_607) ),
inference(resolution,[status(thm)],[c_92,c_1188]) ).
tff(c_6023,plain,
! [Y_666,X_667,X_668] :
( unorthogonal_lines(parallel_through_point(Y_666,X_667),X_668)
| ~ convergent_lines(X_668,Y_666)
| orthogonal_lines(X_668,Y_666) ),
inference(resolution,[status(thm)],[c_4912,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_6225,plain,
! [Y_680,X_681,X_682] :
( ~ orthogonal_lines(parallel_through_point(Y_680,X_681),X_682)
| ~ convergent_lines(X_682,Y_680)
| orthogonal_lines(X_682,Y_680) ),
inference(resolution,[status(thm)],[c_6023,c_90]) ).
tff(c_6245,plain,
! [Y_680,X_681,A_48] :
( ~ convergent_lines(orthogonal_through_point(parallel_through_point(Y_680,X_681),A_48),Y_680)
| orthogonal_lines(orthogonal_through_point(parallel_through_point(Y_680,X_681),A_48),Y_680) ),
inference(resolution,[status(thm)],[c_4695,c_6225]) ).
tff(c_6283,plain,
! [Y_683,X_684,A_685] : orthogonal_lines(orthogonal_through_point(parallel_through_point(Y_683,X_684),A_685),Y_683),
inference(demodulation,[status(thm),theory(equality)],[c_1131,c_6245]) ).
tff(c_4692,plain,
! [Y_590,N_591] :
( ~ orthogonal_lines(Y_590,N_591)
| ~ convergent_lines(N_591,Y_590)
| orthogonal_lines(N_591,Y_590) ),
inference(resolution,[status(thm)],[c_4663,c_90]) ).
tff(c_6291,plain,
! [Y_683,X_684,A_685] :
( ~ convergent_lines(Y_683,orthogonal_through_point(parallel_through_point(Y_683,X_684),A_685))
| orthogonal_lines(Y_683,orthogonal_through_point(parallel_through_point(Y_683,X_684),A_685)) ),
inference(resolution,[status(thm)],[c_6283,c_4692]) ).
tff(c_6394,plain,
! [Y_689,X_690,A_691] : orthogonal_lines(Y_689,orthogonal_through_point(parallel_through_point(Y_689,X_690),A_691)),
inference(demodulation,[status(thm),theory(equality)],[c_1254,c_6291]) ).
tff(c_174,plain,
! [M_138,N_139,L_140] :
( ~ convergent_lines(M_138,N_139)
| unorthogonal_lines(L_140,N_139)
| unorthogonal_lines(L_140,M_138) ),
inference(cnfTransformation,[status(thm)],[f_321]) ).
tff(c_181,plain,
! [L_141,M_142,A_143] :
( unorthogonal_lines(L_141,M_142)
| unorthogonal_lines(L_141,orthogonal_through_point(M_142,A_143)) ),
inference(resolution,[status(thm)],[c_130,c_174]) ).
tff(c_189,plain,
! [L_141,M_142,A_143] :
( ~ orthogonal_lines(L_141,orthogonal_through_point(M_142,A_143))
| unorthogonal_lines(L_141,M_142) ),
inference(resolution,[status(thm)],[c_181,c_90]) ).
tff(c_6472,plain,
! [Y_692,X_693] : unorthogonal_lines(Y_692,parallel_through_point(Y_692,X_693)),
inference(resolution,[status(thm)],[c_6394,c_189]) ).
tff(c_6497,plain,
! [Y_692,X_693] : ~ orthogonal_lines(Y_692,parallel_through_point(Y_692,X_693)),
inference(resolution,[status(thm)],[c_6472,c_90]) ).
tff(c_1676,plain,
! [L_396,M_397,N_398] :
( convergent_lines(L_396,M_397)
| convergent_lines(L_396,N_398)
| ~ unorthogonal_lines(M_397,N_398)
| ~ convergent_lines(M_397,N_398) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_3291,plain,
! [L_514,X_515,Y_516] :
( convergent_lines(L_514,X_515)
| convergent_lines(L_514,Y_516)
| ~ convergent_lines(X_515,Y_516)
| orthogonal_lines(X_515,Y_516) ),
inference(resolution,[status(thm)],[c_92,c_1676]) ).
tff(c_3481,plain,
! [X_519,X_520,Y_521] :
( convergent_lines(parallel_through_point(X_519,X_520),Y_521)
| ~ convergent_lines(X_519,Y_521)
| orthogonal_lines(X_519,Y_521) ),
inference(resolution,[status(thm)],[c_3291,c_32]) ).
tff(c_3500,plain,
! [X_519,X_520] :
( ~ convergent_lines(X_519,parallel_through_point(X_519,X_520))
| orthogonal_lines(X_519,parallel_through_point(X_519,X_520)) ),
inference(resolution,[status(thm)],[c_3481,c_6]) ).
tff(c_6599,plain,
! [X_698,X_699] : ~ convergent_lines(X_698,parallel_through_point(X_698,X_699)),
inference(negUnitSimplification,[status(thm)],[c_6497,c_3500]) ).
tff(c_7233,plain,
! [M_736,A_737,Z_738,X_739] :
( convergent_lines(orthogonal_through_point(M_736,A_737),Z_738)
| distinct_lines(parallel_through_point(M_736,X_739),Z_738) ),
inference(resolution,[status(thm)],[c_316,c_6599]) ).
tff(c_7271,plain,
! [M_736,A_737,X_739] : convergent_lines(orthogonal_through_point(M_736,A_737),parallel_through_point(M_736,X_739)),
inference(resolution,[status(thm)],[c_7233,c_4]) ).
tff(c_566,plain,
! [L_232,N_233,M_234] :
( unorthogonal_lines(L_232,N_233)
| convergent_lines(M_234,N_233)
| ~ unorthogonal_lines(L_232,M_234)
| ~ convergent_lines(L_232,M_234) ),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_5806,plain,
! [X_658,N_659,Y_660] :
( unorthogonal_lines(X_658,N_659)
| convergent_lines(Y_660,N_659)
| ~ convergent_lines(X_658,Y_660)
| orthogonal_lines(X_658,Y_660) ),
inference(resolution,[status(thm)],[c_92,c_566]) ).
tff(c_8088,plain,
! [Y_831,N_832,A_833] :
( convergent_lines(Y_831,N_832)
| ~ convergent_lines(orthogonal_through_point(N_832,A_833),Y_831)
| orthogonal_lines(orthogonal_through_point(N_832,A_833),Y_831) ),
inference(resolution,[status(thm)],[c_5806,c_48]) ).
tff(c_4696,plain,
! [N_592,A_593] : orthogonal_lines(N_592,orthogonal_through_point(N_592,A_593)),
inference(demodulation,[status(thm),theory(equality)],[c_223,c_4684]) ).
tff(c_110,plain,
! [X_99,Y_100] :
( equal_lines(X_99,Y_100)
| distinct_lines(X_99,Y_100) ),
inference(cnfTransformation,[status(thm)],[f_411]) ).
tff(c_94,plain,
~ equal_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1')),
inference(cnfTransformation,[status(thm)],[f_431]) ).
tff(c_114,plain,
distinct_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1')),
inference(resolution,[status(thm)],[c_110,c_94]) ).
tff(c_153,plain,
! [X_119,Y_120] :
( convergent_lines(X_119,Y_120)
| ~ distinct_lines(X_119,Y_120) ),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_157,plain,
convergent_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1')),
inference(resolution,[status(thm)],[c_114,c_153]) ).
tff(c_336,plain,
! [L_182] :
( unorthogonal_lines(L_182,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'))
| unorthogonal_lines(L_182,parallel_through_point('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_157,c_174]) ).
tff(c_344,plain,
! [L_182] :
( ~ orthogonal_lines(L_182,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'))
| unorthogonal_lines(L_182,parallel_through_point('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_336,c_90]) ).
tff(c_4737,plain,
unorthogonal_lines(orthogonal_through_point('#skF_2','#skF_1'),parallel_through_point('#skF_2','#skF_1')),
inference(resolution,[status(thm)],[c_4696,c_344]) ).
tff(c_5118,plain,
~ orthogonal_lines(orthogonal_through_point('#skF_2','#skF_1'),parallel_through_point('#skF_2','#skF_1')),
inference(resolution,[status(thm)],[c_4737,c_90]) ).
tff(c_8145,plain,
( convergent_lines(parallel_through_point('#skF_2','#skF_1'),'#skF_2')
| ~ convergent_lines(orthogonal_through_point('#skF_2','#skF_1'),parallel_through_point('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_8088,c_5118]) ).
tff(c_8237,plain,
convergent_lines(parallel_through_point('#skF_2','#skF_1'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_7271,c_8145]) ).
tff(c_8239,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_8237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GEO223+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.11 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 7 20:00:23 EDT 2025
% 0.10/0.31 % CPUTime :
% 14.19/4.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.19/4.81
% 14.19/4.81 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------