%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU153+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 : n029.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 08:52:58 PM UTC 2025
% Result : Theorem 6.99s 2.46s
% Output : CNFRefutation 6.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 15 ~; 9 |; 2 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 5 con; 0-3 aty)
% Number of variables : 31 ( 30 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > #nlpp > singleton > powerset > empty_set > #skF_13 > #skF_22 > #skF_18 > #skF_17 > #skF_6 > #skF_15 > #skF_20 > #skF_12 > #skF_16 > #skF_19 > #skF_10 > #skF_11 > #skF_7 > #skF_9 > #skF_14 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_21 > #skF_5 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_179,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_314,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_147,lemma,
! [A] : ( singleton(A) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
tff(f_157,negated_conjecture,
~ ! [A,B] :
~ ( disjoint(singleton(A),B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
tff(f_61,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_55,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_329,lemma,
! [A,B] :
( disjoint(A,B)
<=> ( set_difference(A,B) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
tff(f_112,axiom,
! [A,B,C] :
( ( C = set_difference(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
tff(c_184,plain,
empty('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_309,plain,
! [A_172] :
( ( empty_set = A_172 )
| ~ empty(A_172) ),
inference(cnfTransformation,[status(thm)],[f_314]) ).
tff(c_318,plain,
empty_set = '#skF_17',
inference(resolution,[status(thm)],[c_184,c_309]) ).
tff(c_160,plain,
! [A_70] : ( singleton(A_70) != empty_set ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_329,plain,
! [A_70] : ( singleton(A_70) != '#skF_17' ),
inference(demodulation,[status(thm),theory(equality)],[c_318,c_160]) ).
tff(c_164,plain,
in('#skF_15','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_32,plain,
! [A_18] :
( ( empty_set = A_18 )
| in('#skF_3'(A_18),A_18) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_800,plain,
! [A_18] :
( ( A_18 = '#skF_17' )
| in('#skF_3'(A_18),A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_318,c_32]) ).
tff(c_812,plain,
! [C_227,A_228] :
( ( C_227 = A_228 )
| ~ in(C_227,singleton(A_228)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_816,plain,
! [A_228] :
( ( '#skF_3'(singleton(A_228)) = A_228 )
| ( singleton(A_228) = '#skF_17' ) ),
inference(resolution,[status(thm)],[c_800,c_812]) ).
tff(c_825,plain,
! [A_228] : ( '#skF_3'(singleton(A_228)) = A_228 ),
inference(negUnitSimplification,[status(thm)],[c_329,c_816]) ).
tff(c_166,plain,
disjoint(singleton('#skF_15'),'#skF_16'),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_1779,plain,
! [A_292,B_293] :
( ( set_difference(A_292,B_293) = A_292 )
| ~ disjoint(A_292,B_293) ),
inference(cnfTransformation,[status(thm)],[f_329]) ).
tff(c_1791,plain,
set_difference(singleton('#skF_15'),'#skF_16') = singleton('#skF_15'),
inference(resolution,[status(thm)],[c_166,c_1779]) ).
tff(c_3165,plain,
! [D_350,B_351,A_352] :
( ~ in(D_350,B_351)
| ~ in(D_350,set_difference(A_352,B_351)) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_3438,plain,
! [D_365] :
( ~ in(D_365,'#skF_16')
| ~ in(D_365,singleton('#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_1791,c_3165]) ).
tff(c_3446,plain,
( ~ in('#skF_3'(singleton('#skF_15')),'#skF_16')
| ( singleton('#skF_15') = '#skF_17' ) ),
inference(resolution,[status(thm)],[c_800,c_3438]) ).
tff(c_3454,plain,
singleton('#skF_15') = '#skF_17',
inference(demodulation,[status(thm),theory(equality)],[c_164,c_825,c_3446]) ).
tff(c_3456,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_329,c_3454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU153+2 : TPTP v9.0.0. Released v3.3.0.
% 0.09/0.12 % 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
% 0.12/0.31 % Computer : n029.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Apr 8 22:08:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 6.99/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.99/2.47
% 6.99/2.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------