TSTP Solution File: SET921+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n024.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 10:57:20 EDT 2023
% Result : Theorem 3.34s 1.87s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 81 ( 40 unt; 16 typ; 0 def)
% Number of atoms : 99 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 38 ~; 27 |; 2 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 8 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 31 (; 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > #skF_11 > #skF_4 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_38,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_61,negated_conjecture,
~ ! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( in(A,B)
& ( A != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
tff(f_48,axiom,
! [A,B,C] :
( ( C = set_difference(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
tff(c_6,plain,
! [C_7] : in(C_7,singleton(C_7)),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_40,plain,
( ( '#skF_7' != '#skF_9' )
| ( '#skF_10' = '#skF_12' )
| ~ in('#skF_10','#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_60,plain,
~ in('#skF_10','#skF_11'),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_46,plain,
( ( '#skF_7' != '#skF_9' )
| in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_62,plain,
'#skF_7' != '#skF_9',
inference(splitLeft,[status(thm)],[c_46]) ).
tff(c_48,plain,
( in('#skF_7','#skF_8')
| in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_65,plain,
in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_20,plain,
! [D_13,A_8,B_9] :
( in(D_13,A_8)
| ~ in(D_13,set_difference(A_8,B_9)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_68,plain,
in('#skF_10','#skF_11'),
inference(resolution,[status(thm)],[c_65,c_20]) ).
tff(c_77,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_68]) ).
tff(c_78,plain,
in('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_16,plain,
! [D_13,A_8,B_9] :
( in(D_13,set_difference(A_8,B_9))
| in(D_13,B_9)
| ~ in(D_13,A_8) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_79,plain,
~ in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_44,plain,
( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
| in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_116,plain,
~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9'))),
inference(negUnitSimplification,[status(thm)],[c_79,c_44]) ).
tff(c_119,plain,
( in('#skF_7',singleton('#skF_9'))
| ~ in('#skF_7','#skF_8') ),
inference(resolution,[status(thm)],[c_16,c_116]) ).
tff(c_122,plain,
in('#skF_7',singleton('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_119]) ).
tff(c_4,plain,
! [C_7,A_3] :
( ( C_7 = A_3 )
| ~ in(C_7,singleton(A_3)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_127,plain,
'#skF_7' = '#skF_9',
inference(resolution,[status(thm)],[c_122,c_4]) ).
tff(c_132,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_127]) ).
tff(c_133,plain,
in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_149,plain,
! [D_37,A_38,B_39] :
( in(D_37,A_38)
| ~ in(D_37,set_difference(A_38,B_39)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_152,plain,
in('#skF_10','#skF_11'),
inference(resolution,[status(thm)],[c_133,c_149]) ).
tff(c_156,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_152]) ).
tff(c_157,plain,
( ( '#skF_7' != '#skF_9' )
| ( '#skF_10' = '#skF_12' ) ),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_162,plain,
'#skF_7' != '#skF_9',
inference(splitLeft,[status(thm)],[c_157]) ).
tff(c_158,plain,
in('#skF_10','#skF_11'),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_42,plain,
( in('#skF_7','#skF_8')
| ( '#skF_10' = '#skF_12' )
| ~ in('#skF_10','#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_165,plain,
( in('#skF_7','#skF_8')
| ( '#skF_10' = '#skF_12' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_158,c_42]) ).
tff(c_166,plain,
'#skF_10' = '#skF_12',
inference(splitLeft,[status(thm)],[c_165]) ).
tff(c_179,plain,
( in('#skF_7','#skF_8')
| in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_166,c_48]) ).
tff(c_180,plain,
in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_179]) ).
tff(c_18,plain,
! [D_13,B_9,A_8] :
( ~ in(D_13,B_9)
| ~ in(D_13,set_difference(A_8,B_9)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_186,plain,
~ in('#skF_12',singleton('#skF_12')),
inference(resolution,[status(thm)],[c_180,c_18]) ).
tff(c_194,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_186]) ).
tff(c_195,plain,
in('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_179]) ).
tff(c_196,plain,
~ in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_179]) ).
tff(c_243,plain,
( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
| in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_166,c_44]) ).
tff(c_244,plain,
~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9'))),
inference(negUnitSimplification,[status(thm)],[c_196,c_243]) ).
tff(c_247,plain,
( in('#skF_7',singleton('#skF_9'))
| ~ in('#skF_7','#skF_8') ),
inference(resolution,[status(thm)],[c_16,c_244]) ).
tff(c_250,plain,
in('#skF_7',singleton('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_195,c_247]) ).
tff(c_255,plain,
'#skF_7' = '#skF_9',
inference(resolution,[status(thm)],[c_250,c_4]) ).
tff(c_260,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_162,c_255]) ).
tff(c_261,plain,
in('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_165]) ).
tff(c_273,plain,
! [D_65,A_66,B_67] :
( in(D_65,set_difference(A_66,B_67))
| in(D_65,B_67)
| ~ in(D_65,A_66) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_262,plain,
'#skF_10' != '#skF_12',
inference(splitRight,[status(thm)],[c_165]) ).
tff(c_38,plain,
( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
| ( '#skF_10' = '#skF_12' )
| ~ in('#skF_10','#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_270,plain,
( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
| ( '#skF_10' = '#skF_12' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_158,c_38]) ).
tff(c_271,plain,
~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9'))),
inference(negUnitSimplification,[status(thm)],[c_262,c_270]) ).
tff(c_276,plain,
( in('#skF_7',singleton('#skF_9'))
| ~ in('#skF_7','#skF_8') ),
inference(resolution,[status(thm)],[c_273,c_271]) ).
tff(c_291,plain,
in('#skF_7',singleton('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_276]) ).
tff(c_300,plain,
'#skF_7' = '#skF_9',
inference(resolution,[status(thm)],[c_291,c_4]) ).
tff(c_305,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_162,c_300]) ).
tff(c_307,plain,
'#skF_7' = '#skF_9',
inference(splitRight,[status(thm)],[c_157]) ).
tff(c_306,plain,
'#skF_10' = '#skF_12',
inference(splitRight,[status(thm)],[c_157]) ).
tff(c_314,plain,
( ( '#skF_7' != '#skF_9' )
| in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_306,c_46]) ).
tff(c_315,plain,
'#skF_7' != '#skF_9',
inference(splitLeft,[status(thm)],[c_314]) ).
tff(c_321,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_307,c_315]) ).
tff(c_322,plain,
in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_314]) ).
tff(c_338,plain,
! [D_69,B_70,A_71] :
( ~ in(D_69,B_70)
| ~ in(D_69,set_difference(A_71,B_70)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_341,plain,
~ in('#skF_12',singleton('#skF_12')),
inference(resolution,[status(thm)],[c_322,c_338]) ).
tff(c_345,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15 % 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
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 16:45:00 EDT 2023
% 0.15/0.36 % CPUTime :
% 3.34/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.34/1.88
% 3.34/1.88 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.34/1.91
% 3.34/1.91 Inference rules
% 3.34/1.91 ----------------------
% 3.34/1.91 #Ref : 0
% 3.34/1.91 #Sup : 57
% 3.34/1.91 #Fact : 0
% 3.34/1.91 #Define : 0
% 3.34/1.91 #Split : 7
% 3.34/1.91 #Chain : 0
% 3.34/1.91 #Close : 0
% 3.34/1.91
% 3.34/1.91 Ordering : KBO
% 3.34/1.91
% 3.34/1.91 Simplification rules
% 3.34/1.91 ----------------------
% 3.34/1.91 #Subsume : 8
% 3.34/1.91 #Demod : 31
% 3.34/1.91 #Tautology : 24
% 3.34/1.91 #SimpNegUnit : 8
% 3.34/1.91 #BackRed : 4
% 3.34/1.91
% 3.34/1.91 #Partial instantiations: 0
% 3.34/1.91 #Strategies tried : 1
% 3.34/1.91
% 3.34/1.91 Timing (in seconds)
% 3.34/1.91 ----------------------
% 3.34/1.92 Preprocessing : 0.50
% 3.34/1.92 Parsing : 0.24
% 3.34/1.92 CNF conversion : 0.04
% 3.34/1.92 Main loop : 0.35
% 3.34/1.92 Inferencing : 0.12
% 3.34/1.92 Reduction : 0.10
% 3.34/1.92 Demodulation : 0.06
% 3.34/1.92 BG Simplification : 0.02
% 3.34/1.92 Subsumption : 0.09
% 3.34/1.92 Abstraction : 0.01
% 3.34/1.92 MUC search : 0.00
% 3.34/1.92 Cooper : 0.00
% 3.34/1.92 Total : 0.91
% 3.34/1.92 Index Insertion : 0.00
% 3.34/1.92 Index Deletion : 0.00
% 3.34/1.92 Index Matching : 0.00
% 3.34/1.92 BG Taut test : 0.00
%------------------------------------------------------------------------------