%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEO209+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 : n012.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 06:14:15 PM UTC 2025
% Result : Theorem 4.05s 2.06s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 31 ( 12 ~; 12 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 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 > #skF_4
%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('#skF_4',type,
'#skF_4': $i ).
tff(f_189,negated_conjecture,
~ ! [A,L,M,N] :
( ( apart_point_and_line(A,L)
& ~ apart_point_and_line(A,M)
& ~ apart_point_and_line(A,N)
& ~ convergent_lines(M,L)
& ~ convergent_lines(N,L) )
=> ~ distinct_lines(M,N) ),
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(c_42,plain,
~ apart_point_and_line('#skF_1','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_38,plain,
~ convergent_lines('#skF_4','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_36,plain,
distinct_lines('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_874,plain,
! [Y_117,Z_118,X_119] :
( convergent_lines(Y_117,Z_118)
| apart_point_and_line(X_119,Z_118)
| apart_point_and_line(X_119,Y_117)
| ~ distinct_lines(Y_117,Z_118) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_982,plain,
! [X_119] :
( convergent_lines('#skF_3','#skF_4')
| apart_point_and_line(X_119,'#skF_4')
| apart_point_and_line(X_119,'#skF_3') ),
inference(resolution,[status(thm)],[c_36,c_874]) ).
tff(c_983,plain,
convergent_lines('#skF_3','#skF_4'),
inference(splitLeft,[status(thm)],[c_982]) ).
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_990,plain,
! [Z_120] :
( convergent_lines('#skF_4',Z_120)
| convergent_lines('#skF_3',Z_120) ),
inference(resolution,[status(thm)],[c_983,c_12]) ).
tff(c_40,plain,
~ convergent_lines('#skF_3','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_1001,plain,
convergent_lines('#skF_4','#skF_2'),
inference(resolution,[status(thm)],[c_990,c_40]) ).
tff(c_1008,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_1001]) ).
tff(c_1011,plain,
! [X_121] :
( apart_point_and_line(X_121,'#skF_4')
| apart_point_and_line(X_121,'#skF_3') ),
inference(splitRight,[status(thm)],[c_982]) ).
tff(c_44,plain,
~ apart_point_and_line('#skF_1','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_1026,plain,
apart_point_and_line('#skF_1','#skF_4'),
inference(resolution,[status(thm)],[c_1011,c_44]) ).
tff(c_1034,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_1026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO209+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n012.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 19:58:00 EDT 2025
% 0.20/0.34 % CPUTime :
% 4.05/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.05/2.06
% 4.05/2.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------