%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEO205+2 : TPTP v9.0.0. Released v3.3.0.
% 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 : n015.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 06:14:14 PM UTC 2025
% Result : Theorem 6.24s 2.57s
% Output : CNFRefutation 6.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 39 ~; 68 |; 3 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ distinct_points > distinct_lines > convergent_lines > apart_point_and_line > 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(distinct_points,type,
distinct_points: ( $i * $i ) > $o ).
tff(intersection_point,type,
intersection_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('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(distinct_lines,type,
distinct_lines: ( $i * $i ) > $o ).
tff(f_143,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& ~ distinct_lines(Y,Z) )
=> ( convergent_lines(X,Z)
& ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
tff(f_83,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).
tff(f_130,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
tff(f_77,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart5) ).
tff(f_62,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).
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/GEO008+0.ax',cu1) ).
tff(f_100,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,X)
| apart_point_and_line(Z,Y) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con2) ).
tff(f_59,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
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/GEO008+0.ax',ceq2) ).
tff(c_30,plain,
( distinct_points(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3'))
| ~ convergent_lines('#skF_1','#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_66,plain,
~ convergent_lines('#skF_1','#skF_3'),
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_34,plain,
convergent_lines('#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_48,plain,
! [Y_36,Z_37,X_38] :
( convergent_lines(Y_36,Z_37)
| convergent_lines(X_38,Z_37)
| ~ convergent_lines(X_38,Y_36) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_52,plain,
! [Z_39] :
( convergent_lines('#skF_2',Z_39)
| convergent_lines('#skF_1',Z_39) ),
inference(resolution,[status(thm)],[c_34,c_48]) ).
tff(c_38,plain,
! [X_34,Y_35] :
( distinct_lines(X_34,Y_35)
| ~ convergent_lines(X_34,Y_35) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_32,plain,
~ distinct_lines('#skF_2','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_47,plain,
~ convergent_lines('#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_38,c_32]) ).
tff(c_63,plain,
convergent_lines('#skF_1','#skF_3'),
inference(resolution,[status(thm)],[c_52,c_47]) ).
tff(c_67,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66,c_63]) ).
tff(c_69,plain,
convergent_lines('#skF_1','#skF_3'),
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_68,plain,
distinct_points(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')),
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_28,plain,
! [X_29,Y_30] :
( distinct_lines(X_29,Y_30)
| ~ convergent_lines(X_29,Y_30) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_88,plain,
! [Y_44,Z_45,X_46] :
( distinct_lines(Y_44,Z_45)
| distinct_lines(X_46,Z_45)
| ~ distinct_lines(X_46,Y_44) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_174,plain,
! [Y_57,Z_58,X_59] :
( distinct_lines(Y_57,Z_58)
| distinct_lines(X_59,Z_58)
| ~ convergent_lines(X_59,Y_57) ),
inference(resolution,[status(thm)],[c_28,c_88]) ).
tff(c_208,plain,
! [Z_60] :
( distinct_lines('#skF_3',Z_60)
| distinct_lines('#skF_1',Z_60) ),
inference(resolution,[status(thm)],[c_69,c_174]) ).
tff(c_10,plain,
! [Y_8,Z_9,X_7] :
( distinct_lines(Y_8,Z_9)
| distinct_lines(X_7,Z_9)
| ~ distinct_lines(X_7,Y_8) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_439,plain,
! [Z_78,Z_79] :
( distinct_lines(Z_78,Z_79)
| distinct_lines('#skF_3',Z_79)
| distinct_lines('#skF_1',Z_78) ),
inference(resolution,[status(thm)],[c_208,c_10]) ).
tff(c_4,plain,
! [X_2] : ~ distinct_lines(X_2,X_2),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_467,plain,
! [Z_80] :
( distinct_lines(Z_80,'#skF_3')
| distinct_lines('#skF_1',Z_80) ),
inference(resolution,[status(thm)],[c_439,c_4]) ).
tff(c_1291,plain,
! [Z_123,Z_124] :
( distinct_lines(Z_123,Z_124)
| distinct_lines('#skF_1',Z_124)
| distinct_lines(Z_123,'#skF_3') ),
inference(resolution,[status(thm)],[c_467,c_10]) ).
tff(c_1330,plain,
! [Z_125] :
( distinct_lines(Z_125,'#skF_1')
| distinct_lines(Z_125,'#skF_3') ),
inference(resolution,[status(thm)],[c_1291,c_4]) ).
tff(c_1345,plain,
distinct_lines('#skF_2','#skF_1'),
inference(resolution,[status(thm)],[c_1330,c_32]) ).
tff(c_22,plain,
! [Y_20,V_22,U_21,X_19] :
( apart_point_and_line(Y_20,V_22)
| apart_point_and_line(Y_20,U_21)
| apart_point_and_line(X_19,V_22)
| apart_point_and_line(X_19,U_21)
| ~ distinct_lines(U_21,V_22)
| ~ distinct_points(X_19,Y_20) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_1630,plain,
! [Y_141,X_142] :
( apart_point_and_line(Y_141,'#skF_1')
| apart_point_and_line(Y_141,'#skF_2')
| apart_point_and_line(X_142,'#skF_1')
| apart_point_and_line(X_142,'#skF_2')
| ~ distinct_points(X_142,Y_141) ),
inference(resolution,[status(thm)],[c_1345,c_22]) ).
tff(c_1650,plain,
( apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1')
| apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2')
| apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1')
| apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2') ),
inference(resolution,[status(thm)],[c_68,c_1630]) ).
tff(c_2796,plain,
apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
inference(splitLeft,[status(thm)],[c_1650]) ).
tff(c_912,plain,
! [Z_105,Y_106,X_107] :
( ~ apart_point_and_line(Z_105,Y_106)
| distinct_points(Z_105,intersection_point(X_107,Y_106))
| ~ convergent_lines(X_107,Y_106) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_2,plain,
! [X_1] : ~ distinct_points(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_920,plain,
! [X_107,Y_106] :
( ~ apart_point_and_line(intersection_point(X_107,Y_106),Y_106)
| ~ convergent_lines(X_107,Y_106) ),
inference(resolution,[status(thm)],[c_912,c_2]) ).
tff(c_2803,plain,
~ convergent_lines('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_2796,c_920]) ).
tff(c_2813,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_2803]) ).
tff(c_2815,plain,
~ apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
inference(splitRight,[status(thm)],[c_1650]) ).
tff(c_1094,plain,
! [Y_117,V_118,U_119,X_120] :
( apart_point_and_line(Y_117,V_118)
| apart_point_and_line(Y_117,U_119)
| apart_point_and_line(X_120,V_118)
| apart_point_and_line(X_120,U_119)
| ~ distinct_lines(U_119,V_118)
| ~ distinct_points(X_120,Y_117) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_2264,plain,
! [Y_170,Y_171,X_172,X_173] :
( apart_point_and_line(Y_170,Y_171)
| apart_point_and_line(Y_170,X_172)
| apart_point_and_line(X_173,Y_171)
| apart_point_and_line(X_173,X_172)
| ~ distinct_points(X_173,Y_170)
| ~ convergent_lines(X_172,Y_171) ),
inference(resolution,[status(thm)],[c_28,c_1094]) ).
tff(c_2899,plain,
! [Y_201,X_202] :
( apart_point_and_line(intersection_point('#skF_1','#skF_3'),Y_201)
| apart_point_and_line(intersection_point('#skF_1','#skF_3'),X_202)
| apart_point_and_line(intersection_point('#skF_1','#skF_2'),Y_201)
| apart_point_and_line(intersection_point('#skF_1','#skF_2'),X_202)
| ~ convergent_lines(X_202,Y_201) ),
inference(resolution,[status(thm)],[c_68,c_2264]) ).
tff(c_2979,plain,
( apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2')
| apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1')
| apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
| apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1') ),
inference(resolution,[status(thm)],[c_34,c_2899]) ).
tff(c_3039,plain,
( apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2')
| apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1')
| apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_2815,c_2979]) ).
tff(c_3293,plain,
apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1'),
inference(splitLeft,[status(thm)],[c_3039]) ).
tff(c_662,plain,
! [Z_87,X_88,Y_89] :
( ~ apart_point_and_line(Z_87,X_88)
| distinct_points(Z_87,intersection_point(X_88,Y_89))
| ~ convergent_lines(X_88,Y_89) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_670,plain,
! [X_88,Y_89] :
( ~ apart_point_and_line(intersection_point(X_88,Y_89),X_88)
| ~ convergent_lines(X_88,Y_89) ),
inference(resolution,[status(thm)],[c_662,c_2]) ).
tff(c_3300,plain,
~ convergent_lines('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_3293,c_670]) ).
tff(c_3310,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_3300]) ).
tff(c_3311,plain,
( apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1')
| apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2') ),
inference(splitRight,[status(thm)],[c_3039]) ).
tff(c_3390,plain,
apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2'),
inference(splitLeft,[status(thm)],[c_3311]) ).
tff(c_26,plain,
! [X_26,Z_28,Y_27] :
( apart_point_and_line(X_26,Z_28)
| distinct_lines(Y_27,Z_28)
| ~ apart_point_and_line(X_26,Y_27) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_3622,plain,
! [Z_217] :
( apart_point_and_line(intersection_point('#skF_1','#skF_3'),Z_217)
| distinct_lines('#skF_2',Z_217) ),
inference(resolution,[status(thm)],[c_3390,c_26]) ).
tff(c_3630,plain,
( ~ convergent_lines('#skF_1','#skF_3')
| distinct_lines('#skF_2','#skF_3') ),
inference(resolution,[status(thm)],[c_3622,c_920]) ).
tff(c_3651,plain,
distinct_lines('#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_69,c_3630]) ).
tff(c_3653,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_3651]) ).
tff(c_3654,plain,
apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1'),
inference(splitRight,[status(thm)],[c_3311]) ).
tff(c_3662,plain,
~ convergent_lines('#skF_1','#skF_3'),
inference(resolution,[status(thm)],[c_3654,c_670]) ).
tff(c_3672,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_69,c_3662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO205+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n015.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 : 300
% 0.13/0.34 % DateTime : Mon Apr 7 19:58:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.24/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.59/2.58
% 6.59/2.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------