%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEO223+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 : n004.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 9.34s 3.25s
% Output : CNFRefutation 9.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 64 ( 22 ~; 36 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ unorthogonal_lines > distinct_points > distinct_lines > convergent_lines > apart_point_and_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(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('#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(f_157,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
tff(f_64,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).
tff(f_198,axiom,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
tff(f_215,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
tff(f_82,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_160,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
tff(f_235,negated_conjecture,
~ ! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
tff(f_229,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
tff(f_218,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
tff(f_211,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+3.ax',oac1) ).
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_6,plain,
! [X_3] : ~ convergent_lines(X_3,X_3),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_66,plain,
! [L_64,M_65] :
( unorthogonal_lines(L_64,M_65)
| convergent_lines(L_64,M_65) ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_46,plain,
! [L_44,A_43] : ~ unorthogonal_lines(orthogonal_through_point(L_44,A_43),L_44),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_71,plain,
! [M_65,A_43] : convergent_lines(orthogonal_through_point(M_65,A_43),M_65),
inference(resolution,[status(thm)],[c_66,c_46]) ).
tff(c_76,plain,
! [Y_77,Z_78,X_79] :
( convergent_lines(Y_77,Z_78)
| convergent_lines(X_79,Z_78)
| ~ convergent_lines(X_79,Y_77) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_87,plain,
! [M_83,Z_84,A_85] :
( convergent_lines(M_83,Z_84)
| convergent_lines(orthogonal_through_point(M_83,A_85),Z_84) ),
inference(resolution,[status(thm)],[c_71,c_76]) ).
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_233,plain,
! [Z_121,Z_122,M_123,A_124] :
( convergent_lines(Z_121,Z_122)
| convergent_lines(orthogonal_through_point(M_123,A_124),Z_122)
| convergent_lines(M_123,Z_121) ),
inference(resolution,[status(thm)],[c_87,c_12]) ).
tff(c_272,plain,
! [Z_121,M_123,A_124] :
( convergent_lines(Z_121,orthogonal_through_point(M_123,A_124))
| convergent_lines(M_123,Z_121) ),
inference(resolution,[status(thm)],[c_233,c_6]) ).
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_52,plain,
distinct_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_235]) ).
tff(c_1064,plain,
! [M_245,N_246,L_247,A_248] :
( unorthogonal_lines(M_245,N_246)
| unorthogonal_lines(L_247,N_246)
| apart_point_and_line(A_248,M_245)
| apart_point_and_line(A_248,L_247)
| ~ distinct_lines(L_247,M_245) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_1156,plain,
! [N_246,A_248] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'),N_246)
| unorthogonal_lines(parallel_through_point('#skF_2','#skF_1'),N_246)
| apart_point_and_line(A_248,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'))
| apart_point_and_line(A_248,parallel_through_point('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_52,c_1064]) ).
tff(c_1188,plain,
! [A_259] :
( apart_point_and_line(A_259,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'))
| apart_point_and_line(A_259,parallel_through_point('#skF_2','#skF_1')) ),
inference(splitLeft,[status(thm)],[c_1156]) ).
tff(c_48,plain,
! [A_45,L_46] : ~ apart_point_and_line(A_45,orthogonal_through_point(L_46,A_45)),
inference(cnfTransformation,[status(thm)],[f_218]) ).
tff(c_1204,plain,
apart_point_and_line('#skF_1',parallel_through_point('#skF_2','#skF_1')),
inference(resolution,[status(thm)],[c_1188,c_48]) ).
tff(c_1212,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_1204]) ).
tff(c_1214,plain,
! [N_260] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'),N_260)
| unorthogonal_lines(parallel_through_point('#skF_2','#skF_1'),N_260) ),
inference(splitRight,[status(thm)],[c_1156]) ).
tff(c_1231,plain,
unorthogonal_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point('#skF_2','#skF_1')),
inference(resolution,[status(thm)],[c_1214,c_46]) ).
tff(c_42,plain,
! [L_40,N_42,M_41] :
( unorthogonal_lines(L_40,N_42)
| convergent_lines(M_41,N_42)
| ~ unorthogonal_lines(L_40,M_41)
| ~ convergent_lines(L_40,M_41) ),
inference(cnfTransformation,[status(thm)],[f_211]) ).
tff(c_1243,plain,
! [N_42] :
( unorthogonal_lines(parallel_through_point('#skF_2','#skF_1'),N_42)
| convergent_lines(orthogonal_through_point('#skF_2','#skF_1'),N_42)
| ~ convergent_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_1231,c_42]) ).
tff(c_6782,plain,
~ convergent_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point('#skF_2','#skF_1')),
inference(splitLeft,[status(thm)],[c_1243]) ).
tff(c_6836,plain,
convergent_lines('#skF_2',parallel_through_point('#skF_2','#skF_1')),
inference(resolution,[status(thm)],[c_272,c_6782]) ).
tff(c_7074,plain,
! [Z_632] :
( convergent_lines(parallel_through_point('#skF_2','#skF_1'),Z_632)
| convergent_lines('#skF_2',Z_632) ),
inference(resolution,[status(thm)],[c_6836,c_12]) ).
tff(c_7091,plain,
convergent_lines('#skF_2','#skF_2'),
inference(resolution,[status(thm)],[c_7074,c_30]) ).
tff(c_7106,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_7091]) ).
tff(c_7108,plain,
convergent_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point('#skF_2','#skF_1')),
inference(splitRight,[status(thm)],[c_1243]) ).
tff(c_40,plain,
! [L_40,N_42,M_41] :
( convergent_lines(L_40,N_42)
| unorthogonal_lines(M_41,N_42)
| ~ unorthogonal_lines(L_40,M_41)
| ~ convergent_lines(L_40,M_41) ),
inference(cnfTransformation,[status(thm)],[f_211]) ).
tff(c_1241,plain,
! [N_42] :
( convergent_lines(parallel_through_point('#skF_2','#skF_1'),N_42)
| unorthogonal_lines(orthogonal_through_point('#skF_2','#skF_1'),N_42)
| ~ convergent_lines(parallel_through_point('#skF_2','#skF_1'),orthogonal_through_point('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_1231,c_40]) ).
tff(c_7157,plain,
! [N_635] :
( convergent_lines(parallel_through_point('#skF_2','#skF_1'),N_635)
| unorthogonal_lines(orthogonal_through_point('#skF_2','#skF_1'),N_635) ),
inference(demodulation,[status(thm),theory(equality)],[c_7108,c_1241]) ).
tff(c_7169,plain,
convergent_lines(parallel_through_point('#skF_2','#skF_1'),'#skF_2'),
inference(resolution,[status(thm)],[c_7157,c_46]) ).
tff(c_7177,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30,c_7169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GEO223+2 : TPTP v9.0.0. Released v3.3.0.
% 0.02/0.12 % 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
% 0.11/0.31 % Computer : n004.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Apr 7 19:59:23 EDT 2025
% 0.11/0.31 % CPUTime :
% 9.34/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.34/3.26
% 9.34/3.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------