%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET926+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/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 : n015.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 2.49s 1.57s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > empty_set > #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_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_41,axiom,
! [A,B] :
( ( set_difference(singleton(A),B) = empty_set )
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
tff(f_51,negated_conjecture,
~ ! [A,B] :
( ( set_difference(singleton(A),B) = empty_set )
| ( set_difference(singleton(A),B) = singleton(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
tff(f_37,axiom,
! [A,B] :
( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
tff(c_22,plain,
! [A_9,B_10] :
( ( set_difference(singleton(A_9),B_10) = empty_set )
| ~ in(A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_20,plain,
set_difference(singleton('#skF_3'),'#skF_4') != empty_set,
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_36,plain,
~ in('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_22,c_20]) ).
tff(c_43,plain,
! [A_13,B_14] :
( ( set_difference(singleton(A_13),B_14) = singleton(A_13) )
| in(A_13,B_14) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_18,plain,
set_difference(singleton('#skF_3'),'#skF_4') != singleton('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_55,plain,
in('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_43,c_18]) ).
tff(c_69,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET926+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % 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
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Apr 8 21:51:05 EDT 2025
% 0.14/0.34 % CPUTime :
% 2.49/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.49/1.57
% 2.49/1.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------