%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET925+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 : n032.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 2.59s 1.65s
% Output : CNFRefutation 2.59s
% 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 : 23 ( 14 ~; 7 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > empty_set > #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(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_42,negated_conjecture,
~ ! [A,B] :
( ( set_difference(singleton(A),B) = empty_set )
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
tff(f_46,axiom,
! [A,B] :
( ( set_difference(singleton(A),B) = empty_set )
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
tff(c_12,plain,
( in('#skF_3','#skF_4')
| ~ in('#skF_5','#skF_6') ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_22,plain,
~ in('#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_16,plain,
( in('#skF_3','#skF_4')
| ( set_difference(singleton('#skF_5'),'#skF_6') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_23,plain,
set_difference(singleton('#skF_5'),'#skF_6') = empty_set,
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_44,plain,
! [A_9,B_10] :
( in(A_9,B_10)
| ( set_difference(singleton(A_9),B_10) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_50,plain,
in('#skF_5','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_23,c_44]) ).
tff(c_55,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_50]) ).
tff(c_56,plain,
in('#skF_3','#skF_4'),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_20,plain,
! [A_3,B_4] :
( ( set_difference(singleton(A_3),B_4) = empty_set )
| ~ in(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_57,plain,
set_difference(singleton('#skF_5'),'#skF_6') != empty_set,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_14,plain,
( ( set_difference(singleton('#skF_3'),'#skF_4') != empty_set )
| ( set_difference(singleton('#skF_5'),'#skF_6') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_79,plain,
set_difference(singleton('#skF_3'),'#skF_4') != empty_set,
inference(negUnitSimplification,[status(thm)],[c_57,c_14]) ).
tff(c_82,plain,
~ in('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_20,c_79]) ).
tff(c_86,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_82]) ).
tff(c_87,plain,
in('#skF_3','#skF_4'),
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_98,plain,
! [A_15,B_16] :
( ( set_difference(singleton(A_15),B_16) = empty_set )
| ~ in(A_15,B_16) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_88,plain,
in('#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_10,plain,
( ( set_difference(singleton('#skF_3'),'#skF_4') != empty_set )
| ~ in('#skF_5','#skF_6') ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_97,plain,
set_difference(singleton('#skF_3'),'#skF_4') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_88,c_10]) ).
tff(c_104,plain,
~ in('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_98,c_97]) ).
tff(c_112,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_87,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SET925+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.10 % 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
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Apr 8 21:50:45 EDT 2025
% 0.10/0.29 % CPUTime :
% 2.59/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/1.66
% 2.59/1.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------