%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET987+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 : 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 08:39:43 PM UTC 2025
% Result : Theorem 2.46s 1.55s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 1 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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; 4 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_union2 > set_difference > #nlpp > singleton > #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('#skF_4',type,
'#skF_4': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(f_58,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> ( set_difference(set_union2(B,singleton(A)),singleton(A)) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
tff(f_65,axiom,
! [A,B] :
( ( set_difference(A,singleton(B)) = A )
<=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
tff(f_60,axiom,
! [A,B] : ( set_difference(set_union2(A,B),B) = set_difference(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
tff(c_18,plain,
~ in('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_113,plain,
! [A_28,B_29] :
( ( set_difference(A_28,singleton(B_29)) = A_28 )
| in(B_29,A_28) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_20,plain,
! [A_11,B_12] : ( set_difference(set_union2(A_11,B_12),B_12) = set_difference(A_11,B_12) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16,plain,
set_difference(set_union2('#skF_4',singleton('#skF_3')),singleton('#skF_3')) != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_25,plain,
set_difference('#skF_4',singleton('#skF_3')) != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_20,c_16]) ).
tff(c_126,plain,
in('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_113,c_25]) ).
tff(c_139,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET987+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.08 % 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
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Tue Apr 8 21:53:31 EDT 2025
% 0.09/0.27 % CPUTime :
% 2.46/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.46/1.56
% 2.46/1.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------