%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEO206+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/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 : n029.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 4.21s 2.25s
% Output : CNFRefutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 12 ~; 12 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ distinct_points > distinct_lines > convergent_lines > apart_point_and_line > parallel_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(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('#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_181,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
tff(f_169,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
tff(f_82,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
tff(f_157,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
tff(f_160,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
tff(c_40,plain,
~ apart_point_and_line('#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_38,plain,
~ convergent_lines('#skF_2','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_36,plain,
distinct_lines('#skF_2',parallel_through_point('#skF_3','#skF_1')),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_186,plain,
! [Y_87,Z_88,X_89] :
( convergent_lines(Y_87,Z_88)
| apart_point_and_line(X_89,Z_88)
| apart_point_and_line(X_89,Y_87)
| ~ distinct_lines(Y_87,Z_88) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_207,plain,
! [X_89] :
( convergent_lines('#skF_2',parallel_through_point('#skF_3','#skF_1'))
| apart_point_and_line(X_89,parallel_through_point('#skF_3','#skF_1'))
| apart_point_and_line(X_89,'#skF_2') ),
inference(resolution,[status(thm)],[c_36,c_186]) ).
tff(c_208,plain,
convergent_lines('#skF_2',parallel_through_point('#skF_3','#skF_1')),
inference(splitLeft,[status(thm)],[c_207]) ).
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_82]) ).
tff(c_215,plain,
! [Z_90] :
( convergent_lines(parallel_through_point('#skF_3','#skF_1'),Z_90)
| convergent_lines('#skF_2',Z_90) ),
inference(resolution,[status(thm)],[c_208,c_12]) ).
tff(c_30,plain,
! [Y_32,X_31] : ~ convergent_lines(parallel_through_point(Y_32,X_31),Y_32),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_223,plain,
convergent_lines('#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_215,c_30]) ).
tff(c_233,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_223]) ).
tff(c_236,plain,
! [X_91] :
( apart_point_and_line(X_91,parallel_through_point('#skF_3','#skF_1'))
| apart_point_and_line(X_91,'#skF_2') ),
inference(splitRight,[status(thm)],[c_207]) ).
tff(c_32,plain,
! [X_33,Y_34] : ~ apart_point_and_line(X_33,parallel_through_point(Y_34,X_33)),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_252,plain,
apart_point_and_line('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_236,c_32]) ).
tff(c_260,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : GEO206+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.09 % 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
% 0.09/0.29 % Computer : n029.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 7 19:58:04 EDT 2025
% 0.09/0.30 % CPUTime :
% 4.21/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.21/2.26
% 4.21/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------