%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU134+2 : TPTP v9.0.0. Released v3.3.0.
% 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 : n016.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 08:52:52 PM UTC 2025
% Result : Theorem 5.39s 2.24s
% Output : CNFRefutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 12 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 17 ( 16 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > disjoint > empty > set_union2 > set_intersection2 > set_difference > #nlpp > empty_set > #skF_11 > #skF_6 > #skF_15 > #skF_1 > #skF_17 > #skF_10 > #skF_16 > #skF_12 > #skF_14 > #skF_18 > #skF_13 > #skF_5 > #skF_2 > #skF_9 > #skF_7 > #skF_3 > #skF_8 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_110,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_213,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_169,negated_conjecture,
~ ! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
tff(f_108,lemma,
! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
tff(c_104,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_189,plain,
! [A_105] :
( ( empty_set = A_105 )
| ~ empty(A_105) ),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_198,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_104,c_189]) ).
tff(c_148,plain,
( subset('#skF_13','#skF_14')
| ( set_difference('#skF_15','#skF_16') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_282,plain,
( subset('#skF_13','#skF_14')
| ( set_difference('#skF_15','#skF_16') = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_148]) ).
tff(c_283,plain,
set_difference('#skF_15','#skF_16') = '#skF_9',
inference(splitLeft,[status(thm)],[c_282]) ).
tff(c_100,plain,
! [A_46,B_47] :
( subset(A_46,B_47)
| ( set_difference(A_46,B_47) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_1031,plain,
! [A_161,B_162] :
( subset(A_161,B_162)
| ( set_difference(A_161,B_162) != '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_100]) ).
tff(c_144,plain,
( subset('#skF_13','#skF_14')
| ~ subset('#skF_15','#skF_16') ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_209,plain,
~ subset('#skF_15','#skF_16'),
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_1044,plain,
set_difference('#skF_15','#skF_16') != '#skF_9',
inference(resolution,[status(thm)],[c_1031,c_209]) ).
tff(c_1052,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_283,c_1044]) ).
tff(c_1054,plain,
set_difference('#skF_15','#skF_16') != '#skF_9',
inference(splitRight,[status(thm)],[c_282]) ).
tff(c_146,plain,
( ( set_difference('#skF_13','#skF_14') != empty_set )
| ( set_difference('#skF_15','#skF_16') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_1174,plain,
( ( set_difference('#skF_13','#skF_14') != '#skF_9' )
| ( set_difference('#skF_15','#skF_16') = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_198,c_146]) ).
tff(c_1175,plain,
set_difference('#skF_13','#skF_14') != '#skF_9',
inference(negUnitSimplification,[status(thm)],[c_1054,c_1174]) ).
tff(c_1053,plain,
subset('#skF_13','#skF_14'),
inference(splitRight,[status(thm)],[c_282]) ).
tff(c_102,plain,
! [A_46,B_47] :
( ( set_difference(A_46,B_47) = empty_set )
| ~ subset(A_46,B_47) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_1599,plain,
! [A_203,B_204] :
( ( set_difference(A_203,B_204) = '#skF_9' )
| ~ subset(A_203,B_204) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_102]) ).
tff(c_1617,plain,
set_difference('#skF_13','#skF_14') = '#skF_9',
inference(resolution,[status(thm)],[c_1053,c_1599]) ).
tff(c_1632,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1175,c_1617]) ).
tff(c_1634,plain,
subset('#skF_15','#skF_16'),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_142,plain,
( ( set_difference('#skF_13','#skF_14') != empty_set )
| ~ subset('#skF_15','#skF_16') ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_1811,plain,
set_difference('#skF_13','#skF_14') != '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_1634,c_198,c_142]) ).
tff(c_1633,plain,
subset('#skF_13','#skF_14'),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_2376,plain,
! [A_255,B_256] :
( ( set_difference(A_255,B_256) = '#skF_9' )
| ~ subset(A_255,B_256) ),
inference(demodulation,[status(thm),theory(equality)],[c_198,c_102]) ).
tff(c_2403,plain,
set_difference('#skF_13','#skF_14') = '#skF_9',
inference(resolution,[status(thm)],[c_1633,c_2376]) ).
tff(c_2419,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1811,c_2403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU134+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % 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
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Apr 8 22:06:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 5.39/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.39/2.25
% 5.39/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------