TSTP Solution File: GEO222+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GEO222+2 : TPTP v8.1.2. 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 : n005.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 : Tue Aug 22 10:38:45 EDT 2023
% Result : Theorem 7.76s 2.78s
% Output : CNFRefutation 7.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 49 ( 15 unt; 11 typ; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 25 ~; 38 |; 3 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 9 >; 9 *; 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 : 69 (; 69 !; 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_63,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).
tff(f_197,axiom,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
tff(f_214,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
tff(f_81,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_234,negated_conjecture,
~ ! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
tff(f_128,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
tff(f_228,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_98,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_57,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
tff(f_210,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_6,plain,
! [X_3] : ~ convergent_lines(X_3,X_3),
inference(cnfTransformation,[status(thm)],[f_63]) ).
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_197]) ).
tff(c_46,plain,
! [L_44,A_43] : ~ unorthogonal_lines(orthogonal_through_point(L_44,A_43),L_44),
inference(cnfTransformation,[status(thm)],[f_214]) ).
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_80,plain,
! [Y_80,Z_81,X_82] :
( convergent_lines(Y_80,Z_81)
| convergent_lines(X_82,Z_81)
| ~ convergent_lines(X_82,Y_80) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
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_80]) ).
tff(c_95,plain,
! [M_83,A_85] : convergent_lines(M_83,orthogonal_through_point(M_83,A_85)),
inference(resolution,[status(thm)],[c_87,c_6]) ).
tff(c_52,plain,
convergent_lines('#skF_2',orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1')),
inference(cnfTransformation,[status(thm)],[f_234]) ).
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_128]) ).
tff(c_1050,plain,
! [M_231,N_232,L_233,A_234] :
( unorthogonal_lines(M_231,N_232)
| unorthogonal_lines(L_233,N_232)
| apart_point_and_line(A_234,M_231)
| apart_point_and_line(A_234,L_233)
| ~ distinct_lines(L_233,M_231) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_2240,plain,
! [Y_374,N_375,X_376,A_377] :
( unorthogonal_lines(Y_374,N_375)
| unorthogonal_lines(X_376,N_375)
| apart_point_and_line(A_377,Y_374)
| apart_point_and_line(A_377,X_376)
| ~ convergent_lines(X_376,Y_374) ),
inference(resolution,[status(thm)],[c_28,c_1050]) ).
tff(c_2426,plain,
! [N_375,A_377] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'),N_375)
| unorthogonal_lines('#skF_2',N_375)
| apart_point_and_line(A_377,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'))
| apart_point_and_line(A_377,'#skF_2') ),
inference(resolution,[status(thm)],[c_52,c_2240]) ).
tff(c_2457,plain,
! [A_387] :
( apart_point_and_line(A_387,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'))
| apart_point_and_line(A_387,'#skF_2') ),
inference(splitLeft,[status(thm)],[c_2426]) ).
tff(c_252,plain,
! [Z_114,Y_115,X_116] :
( ~ apart_point_and_line(Z_114,Y_115)
| distinct_points(Z_114,intersection_point(X_116,Y_115))
| ~ convergent_lines(X_116,Y_115) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_2,plain,
! [X_1] : ~ distinct_points(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_260,plain,
! [X_116,Y_115] :
( ~ apart_point_and_line(intersection_point(X_116,Y_115),Y_115)
| ~ convergent_lines(X_116,Y_115) ),
inference(resolution,[status(thm)],[c_252,c_2]) ).
tff(c_5780,plain,
! [X_506] :
( ~ convergent_lines(X_506,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'))
| apart_point_and_line(intersection_point(X_506,orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1')),'#skF_2') ),
inference(resolution,[status(thm)],[c_2457,c_260]) ).
tff(c_262,plain,
! [Z_119,X_120,Y_121] :
( ~ apart_point_and_line(Z_119,X_120)
| distinct_points(Z_119,intersection_point(X_120,Y_121))
| ~ convergent_lines(X_120,Y_121) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_270,plain,
! [X_120,Y_121] :
( ~ apart_point_and_line(intersection_point(X_120,Y_121),X_120)
| ~ convergent_lines(X_120,Y_121) ),
inference(resolution,[status(thm)],[c_262,c_2]) ).
tff(c_5792,plain,
~ convergent_lines('#skF_2',orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1')),
inference(resolution,[status(thm)],[c_5780,c_270]) ).
tff(c_5804,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_5792]) ).
tff(c_5806,plain,
! [N_507] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point('#skF_2','#skF_1'),'#skF_1'),N_507)
| unorthogonal_lines('#skF_2',N_507) ),
inference(splitRight,[status(thm)],[c_2426]) ).
tff(c_5823,plain,
unorthogonal_lines('#skF_2',orthogonal_through_point('#skF_2','#skF_1')),
inference(resolution,[status(thm)],[c_5806,c_46]) ).
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_210]) ).
tff(c_5827,plain,
! [N_42] :
( convergent_lines('#skF_2',N_42)
| unorthogonal_lines(orthogonal_through_point('#skF_2','#skF_1'),N_42)
| ~ convergent_lines('#skF_2',orthogonal_through_point('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_5823,c_40]) ).
tff(c_5844,plain,
! [N_508] :
( convergent_lines('#skF_2',N_508)
| unorthogonal_lines(orthogonal_through_point('#skF_2','#skF_1'),N_508) ),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_5827]) ).
tff(c_5856,plain,
convergent_lines('#skF_2','#skF_2'),
inference(resolution,[status(thm)],[c_5844,c_46]) ).
tff(c_5864,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_5856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO222+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % 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 : n005.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 : Fri Aug 4 00:31:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.76/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.76/2.79
% 7.76/2.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.76/2.82
% 7.76/2.82 Inference rules
% 7.76/2.82 ----------------------
% 7.76/2.82 #Ref : 0
% 7.76/2.82 #Sup : 1274
% 7.76/2.82 #Fact : 140
% 7.76/2.82 #Define : 0
% 7.76/2.82 #Split : 3
% 7.76/2.82 #Chain : 0
% 7.76/2.82 #Close : 0
% 7.76/2.82
% 7.76/2.82 Ordering : KBO
% 7.76/2.82
% 7.76/2.82 Simplification rules
% 7.76/2.82 ----------------------
% 7.76/2.82 #Subsume : 251
% 7.76/2.82 #Demod : 172
% 7.76/2.82 #Tautology : 172
% 7.76/2.82 #SimpNegUnit : 73
% 7.76/2.82 #BackRed : 0
% 7.76/2.82
% 7.76/2.82 #Partial instantiations: 0
% 7.76/2.82 #Strategies tried : 1
% 7.76/2.82
% 7.76/2.82 Timing (in seconds)
% 7.76/2.82 ----------------------
% 7.76/2.82 Preprocessing : 0.49
% 7.76/2.82 Parsing : 0.28
% 7.76/2.83 CNF conversion : 0.03
% 7.76/2.83 Main loop : 1.30
% 7.76/2.83 Inferencing : 0.45
% 7.76/2.83 Reduction : 0.36
% 7.76/2.83 Demodulation : 0.22
% 7.76/2.83 BG Simplification : 0.04
% 7.76/2.83 Subsumption : 0.35
% 7.76/2.83 Abstraction : 0.04
% 7.76/2.83 MUC search : 0.00
% 7.76/2.83 Cooper : 0.00
% 7.76/2.83 Total : 1.84
% 7.76/2.83 Index Insertion : 0.00
% 7.76/2.83 Index Deletion : 0.00
% 7.76/2.83 Index Matching : 0.00
% 7.76/2.83 BG Taut test : 0.00
%------------------------------------------------------------------------------