TSTP Solution File: SET879+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET879+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 : 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 10:57:16 EDT 2023
% Result : Theorem 2.93s 1.74s
% Output : CNFRefutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 38 ( 16 unt; 12 typ; 0 def)
% Number of atoms : 37 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 7 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 14 (; 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > #skF_7 > #skF_5 > #skF_6 > #skF_3 > #skF_8 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $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_54,negated_conjecture,
~ ! [A,B] :
( ( set_difference(singleton(A),singleton(B)) = singleton(A) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
tff(f_43,axiom,
! [A,B] :
( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
tff(c_6,plain,
! [C_7] : in(C_7,singleton(C_7)),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_26,plain,
( ( '#skF_5' != '#skF_6' )
| ( '#skF_7' = '#skF_8' ) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_31,plain,
'#skF_5' != '#skF_6',
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_18,plain,
! [A_8,B_9] :
( ( set_difference(singleton(A_8),B_9) = singleton(A_8) )
| in(A_8,B_9) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_24,plain,
( ( set_difference(singleton('#skF_5'),singleton('#skF_6')) != singleton('#skF_5') )
| ( '#skF_7' = '#skF_8' ) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_53,plain,
set_difference(singleton('#skF_5'),singleton('#skF_6')) != singleton('#skF_5'),
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_57,plain,
in('#skF_5',singleton('#skF_6')),
inference(superposition,[status(thm),theory(equality)],[c_18,c_53]) ).
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_60,plain,
'#skF_5' = '#skF_6',
inference(resolution,[status(thm)],[c_57,c_4]) ).
tff(c_66,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31,c_60]) ).
tff(c_67,plain,
'#skF_7' = '#skF_8',
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_68,plain,
set_difference(singleton('#skF_5'),singleton('#skF_6')) = singleton('#skF_5'),
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_28,plain,
( ( set_difference(singleton('#skF_5'),singleton('#skF_6')) != singleton('#skF_5') )
| ( set_difference(singleton('#skF_7'),singleton('#skF_8')) = singleton('#skF_7') ) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_105,plain,
set_difference(singleton('#skF_8'),singleton('#skF_8')) = singleton('#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_67,c_67,c_68,c_28]) ).
tff(c_16,plain,
! [A_8,B_9] :
( ~ in(A_8,B_9)
| ( set_difference(singleton(A_8),B_9) != singleton(A_8) ) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_109,plain,
~ in('#skF_8',singleton('#skF_8')),
inference(superposition,[status(thm),theory(equality)],[c_105,c_16]) ).
tff(c_121,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_109]) ).
tff(c_122,plain,
'#skF_7' = '#skF_8',
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_123,plain,
'#skF_5' = '#skF_6',
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_30,plain,
( ( '#skF_5' != '#skF_6' )
| ( set_difference(singleton('#skF_7'),singleton('#skF_8')) = singleton('#skF_7') ) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_147,plain,
set_difference(singleton('#skF_8'),singleton('#skF_8')) = singleton('#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_122,c_123,c_30]) ).
tff(c_151,plain,
~ in('#skF_8',singleton('#skF_8')),
inference(superposition,[status(thm),theory(equality)],[c_147,c_16]) ).
tff(c_157,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % 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
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu Aug 3 16:38:11 EDT 2023
% 0.16/0.36 % CPUTime :
% 2.93/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.93/1.74
% 2.93/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.04/1.77
% 3.04/1.77 Inference rules
% 3.04/1.77 ----------------------
% 3.04/1.77 #Ref : 0
% 3.04/1.77 #Sup : 31
% 3.04/1.77 #Fact : 0
% 3.04/1.77 #Define : 0
% 3.04/1.77 #Split : 2
% 3.04/1.77 #Chain : 0
% 3.04/1.77 #Close : 0
% 3.04/1.77
% 3.04/1.77 Ordering : KBO
% 3.04/1.77
% 3.04/1.77 Simplification rules
% 3.04/1.77 ----------------------
% 3.04/1.77 #Subsume : 1
% 3.04/1.77 #Demod : 11
% 3.04/1.77 #Tautology : 18
% 3.04/1.77 #SimpNegUnit : 1
% 3.04/1.77 #BackRed : 0
% 3.04/1.77
% 3.04/1.77 #Partial instantiations: 0
% 3.04/1.77 #Strategies tried : 1
% 3.04/1.77
% 3.04/1.77 Timing (in seconds)
% 3.04/1.77 ----------------------
% 3.04/1.77 Preprocessing : 0.48
% 3.04/1.77 Parsing : 0.24
% 3.04/1.77 CNF conversion : 0.04
% 3.04/1.77 Main loop : 0.22
% 3.04/1.77 Inferencing : 0.08
% 3.04/1.77 Reduction : 0.06
% 3.04/1.77 Demodulation : 0.04
% 3.04/1.77 BG Simplification : 0.01
% 3.04/1.77 Subsumption : 0.05
% 3.04/1.77 Abstraction : 0.01
% 3.04/1.77 MUC search : 0.00
% 3.04/1.77 Cooper : 0.00
% 3.04/1.77 Total : 0.74
% 3.04/1.77 Index Insertion : 0.00
% 3.04/1.77 Index Deletion : 0.00
% 3.04/1.77 Index Matching : 0.00
% 3.04/1.77 BG Taut test : 0.00
%------------------------------------------------------------------------------