%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET924+1 : TPTP v9.0.0. 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 : n013.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 08:39:36 PM UTC 2025
% Result : Theorem 2.92s 1.74s
% Output : CNFRefutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 7 |; 0 &)
% ( 2 <=>; 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_42,negated_conjecture,
~ ! [A,B] :
( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
tff(f_47,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_10,plain,
( ~ in('#skF_3','#skF_4')
| in('#skF_5','#skF_6') ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_20,plain,
~ in('#skF_3','#skF_4'),
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_23,plain,
! [A_9,B_10] :
( ( set_difference(singleton(A_9),B_10) = singleton(A_9) )
| in(A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_8,plain,
( ( set_difference(singleton('#skF_3'),'#skF_4') != singleton('#skF_3') )
| in('#skF_5','#skF_6') ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_21,plain,
set_difference(singleton('#skF_3'),'#skF_4') != singleton('#skF_3'),
inference(splitLeft,[status(thm)],[c_8]) ).
tff(c_32,plain,
in('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_23,c_21]) ).
tff(c_41,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_32]) ).
tff(c_42,plain,
in('#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_8]) ).
tff(c_43,plain,
set_difference(singleton('#skF_3'),'#skF_4') = singleton('#skF_3'),
inference(splitRight,[status(thm)],[c_8]) ).
tff(c_12,plain,
( ( set_difference(singleton('#skF_3'),'#skF_4') != singleton('#skF_3') )
| ( set_difference(singleton('#skF_5'),'#skF_6') = singleton('#skF_5') ) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_80,plain,
set_difference(singleton('#skF_5'),'#skF_6') = singleton('#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_43,c_12]) ).
tff(c_16,plain,
! [A_3,B_4] :
( ~ in(A_3,B_4)
| ( set_difference(singleton(A_3),B_4) != singleton(A_3) ) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_87,plain,
~ in('#skF_5','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_80,c_16]) ).
tff(c_98,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42,c_87]) ).
tff(c_99,plain,
in('#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_100,plain,
in('#skF_3','#skF_4'),
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_14,plain,
( ~ in('#skF_3','#skF_4')
| ( set_difference(singleton('#skF_5'),'#skF_6') = singleton('#skF_5') ) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_108,plain,
set_difference(singleton('#skF_5'),'#skF_6') = singleton('#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_14]) ).
tff(c_114,plain,
! [A_15,B_16] :
( ~ in(A_15,B_16)
| ( set_difference(singleton(A_15),B_16) != singleton(A_15) ) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_117,plain,
~ in('#skF_5','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_108,c_114]) ).
tff(c_121,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_99,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET924+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % 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
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 21:50:32 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.92/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/1.74
% 2.92/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------