%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU162+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/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 : n005.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 08:53:01 PM UTC 2025
% Result : Theorem 28.19s 14.90s
% Output : CNFRefutation 28.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 35 ~; 28 |; 2 &)
% ( 7 <=>; 2 =>; 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 : 44 ( 44 usr; 7 con; 0-4 aty)
% Number of variables : 61 ( 60 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > ordered_pair > cartesian_product2 > #nlpp > union > singleton > powerset > empty_set > #skF_13 > #skF_33 > #skF_24 > #skF_17 > #skF_6 > #skF_30 > #skF_31 > #skF_25 > #skF_18 > #skF_20 > #skF_22 > #skF_12 > #skF_15 > #skF_26 > #skF_23 > #skF_19 > #skF_11 > #skF_32 > #skF_7 > #skF_9 > #skF_28 > #skF_3 > #skF_2 > #skF_8 > #skF_29 > #skF_27 > #skF_14 > #skF_1 > #skF_16 > #skF_21 > #skF_5 > #skF_4 > #skF_10 > #skF_34
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff(union,type,
union: $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
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(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': $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_28',type,
'#skF_28': ( $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_29',type,
'#skF_29': ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $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('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff(f_220,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_387,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_174,lemma,
! [A] : ( singleton(A) != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
tff(f_381,negated_conjecture,
~ ! [A,B] :
( ( set_difference(A,singleton(B)) = A )
<=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
tff(f_225,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_202,lemma,
! [A,B,C] :
( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
tff(f_290,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
tff(f_48,axiom,
! [A,B] :
( ( A = B )
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
tff(f_61,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_55,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_134,axiom,
! [A,B,C] :
( ( C = set_difference(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
tff(c_244,plain,
empty('#skF_25'),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_92962,plain,
! [A_164232] :
( ( empty_set = A_164232 )
| ~ empty(A_164232) ),
inference(cnfTransformation,[status(thm)],[f_387]) ).
tff(c_92969,plain,
empty_set = '#skF_25',
inference(resolution,[status(thm)],[c_244,c_92962]) ).
tff(c_212,plain,
! [A_127] : ( singleton(A_127) != empty_set ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_92978,plain,
! [A_127] : ( singleton(A_127) != '#skF_25' ),
inference(demodulation,[status(thm),theory(equality)],[c_92969,c_212]) ).
tff(c_428,plain,
! [A_257] :
( ( empty_set = A_257 )
| ~ empty(A_257) ),
inference(cnfTransformation,[status(thm)],[f_387]) ).
tff(c_435,plain,
empty_set = '#skF_25',
inference(resolution,[status(thm)],[c_244,c_428]) ).
tff(c_443,plain,
! [A_127] : ( singleton(A_127) != '#skF_25' ),
inference(demodulation,[status(thm),theory(equality)],[c_435,c_212]) ).
tff(c_340,plain,
( ( set_difference('#skF_31',singleton('#skF_32')) != '#skF_31' )
| in('#skF_34','#skF_33') ),
inference(cnfTransformation,[status(thm)],[f_381]) ).
tff(c_451,plain,
set_difference('#skF_31',singleton('#skF_32')) != '#skF_31',
inference(splitLeft,[status(thm)],[c_340]) ).
tff(c_342,plain,
( ~ in('#skF_32','#skF_31')
| in('#skF_34','#skF_33') ),
inference(cnfTransformation,[status(thm)],[f_381]) ).
tff(c_390,plain,
~ in('#skF_32','#skF_31'),
inference(splitLeft,[status(thm)],[c_342]) ).
tff(c_248,plain,
! [A_149] : subset(A_149,A_149),
inference(cnfTransformation,[status(thm)],[f_225]) ).
tff(c_228,plain,
! [A_138,B_139,C_140] :
( subset(A_138,set_difference(B_139,singleton(C_140)))
| in(C_140,A_138)
| ~ subset(A_138,B_139) ),
inference(cnfTransformation,[status(thm)],[f_202]) ).
tff(c_288,plain,
! [A_185,B_186] : subset(set_difference(A_185,B_186),A_185),
inference(cnfTransformation,[status(thm)],[f_290]) ).
tff(c_4930,plain,
! [B_539,A_540] :
( ( B_539 = A_540 )
| ~ subset(B_539,A_540)
| ~ subset(A_540,B_539) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_64684,plain,
! [A_135730,B_135731] :
( ( set_difference(A_135730,B_135731) = A_135730 )
| ~ subset(A_135730,set_difference(A_135730,B_135731)) ),
inference(resolution,[status(thm)],[c_288,c_4930]) ).
tff(c_64775,plain,
! [B_139,C_140] :
( ( set_difference(B_139,singleton(C_140)) = B_139 )
| in(C_140,B_139)
| ~ subset(B_139,B_139) ),
inference(resolution,[status(thm)],[c_228,c_64684]) ).
tff(c_87417,plain,
! [B_163733,C_163734] :
( ( set_difference(B_163733,singleton(C_163734)) = B_163733 )
| in(C_163734,B_163733) ),
inference(demodulation,[status(thm),theory(equality)],[c_248,c_64775]) ).
tff(c_344,plain,
( ( set_difference('#skF_31',singleton('#skF_32')) != '#skF_31' )
| ( set_difference('#skF_33',singleton('#skF_34')) = '#skF_33' ) ),
inference(cnfTransformation,[status(thm)],[f_381]) ).
tff(c_584,plain,
set_difference('#skF_31',singleton('#skF_32')) != '#skF_31',
inference(splitLeft,[status(thm)],[c_344]) ).
tff(c_87686,plain,
in('#skF_32','#skF_31'),
inference(superposition,[status(thm),theory(equality)],[c_87417,c_584]) ).
tff(c_87798,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_390,c_87686]) ).
tff(c_87800,plain,
set_difference('#skF_31',singleton('#skF_32')) = '#skF_31',
inference(splitRight,[status(thm)],[c_344]) ).
tff(c_87882,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_451,c_87800]) ).
tff(c_87883,plain,
in('#skF_34','#skF_33'),
inference(splitRight,[status(thm)],[c_340]) ).
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_88239,plain,
! [A_18] :
( ( A_18 = '#skF_25' )
| in('#skF_3'(A_18),A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_435,c_32]) ).
tff(c_88399,plain,
! [C_163974,A_163975] :
( ( C_163974 = A_163975 )
| ~ in(C_163974,singleton(A_163975)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_88403,plain,
! [A_163975] :
( ( '#skF_3'(singleton(A_163975)) = A_163975 )
| ( singleton(A_163975) = '#skF_25' ) ),
inference(resolution,[status(thm)],[c_88239,c_88399]) ).
tff(c_88412,plain,
! [A_163975] : ( '#skF_3'(singleton(A_163975)) = A_163975 ),
inference(negUnitSimplification,[status(thm)],[c_443,c_88403]) ).
tff(c_87967,plain,
set_difference('#skF_31',singleton('#skF_32')) != '#skF_31',
inference(splitLeft,[status(thm)],[c_344]) ).
tff(c_87884,plain,
set_difference('#skF_31',singleton('#skF_32')) = '#skF_31',
inference(splitRight,[status(thm)],[c_340]) ).
tff(c_88092,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_87967,c_87884]) ).
tff(c_88093,plain,
set_difference('#skF_33',singleton('#skF_34')) = '#skF_33',
inference(splitRight,[status(thm)],[c_344]) ).
tff(c_92440,plain,
! [D_164212,B_164213,A_164214] :
( ~ in(D_164212,B_164213)
| ~ in(D_164212,set_difference(A_164214,B_164213)) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_92907,plain,
! [D_164229] :
( ~ in(D_164229,singleton('#skF_34'))
| ~ in(D_164229,'#skF_33') ),
inference(superposition,[status(thm),theory(equality)],[c_88093,c_92440]) ).
tff(c_92923,plain,
( ~ in('#skF_3'(singleton('#skF_34')),'#skF_33')
| ( singleton('#skF_34') = '#skF_25' ) ),
inference(resolution,[status(thm)],[c_88239,c_92907]) ).
tff(c_92933,plain,
singleton('#skF_34') = '#skF_25',
inference(demodulation,[status(thm),theory(equality)],[c_87883,c_88412,c_92923]) ).
tff(c_92935,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_443,c_92933]) ).
tff(c_92936,plain,
in('#skF_34','#skF_33'),
inference(splitRight,[status(thm)],[c_342]) ).
tff(c_93308,plain,
! [A_18] :
( ( A_18 = '#skF_25' )
| in('#skF_3'(A_18),A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_92969,c_32]) ).
tff(c_93333,plain,
! [C_164285,A_164286] :
( ( C_164285 = A_164286 )
| ~ in(C_164285,singleton(A_164286)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_93337,plain,
! [A_164286] :
( ( '#skF_3'(singleton(A_164286)) = A_164286 )
| ( singleton(A_164286) = '#skF_25' ) ),
inference(resolution,[status(thm)],[c_93308,c_93333]) ).
tff(c_93346,plain,
! [A_164286] : ( '#skF_3'(singleton(A_164286)) = A_164286 ),
inference(negUnitSimplification,[status(thm)],[c_92978,c_93337]) ).
tff(c_92937,plain,
in('#skF_32','#skF_31'),
inference(splitRight,[status(thm)],[c_342]) ).
tff(c_346,plain,
( ~ in('#skF_32','#skF_31')
| ( set_difference('#skF_33',singleton('#skF_34')) = '#skF_33' ) ),
inference(cnfTransformation,[status(thm)],[f_381]) ).
tff(c_93044,plain,
set_difference('#skF_33',singleton('#skF_34')) = '#skF_33',
inference(demodulation,[status(thm),theory(equality)],[c_92937,c_346]) ).
tff(c_97424,plain,
! [D_164512,B_164513,A_164514] :
( ~ in(D_164512,B_164513)
| ~ in(D_164512,set_difference(A_164514,B_164513)) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_97479,plain,
! [D_164516] :
( ~ in(D_164516,singleton('#skF_34'))
| ~ in(D_164516,'#skF_33') ),
inference(superposition,[status(thm),theory(equality)],[c_93044,c_97424]) ).
tff(c_97491,plain,
( ~ in('#skF_3'(singleton('#skF_34')),'#skF_33')
| ( singleton('#skF_34') = '#skF_25' ) ),
inference(resolution,[status(thm)],[c_93308,c_97479]) ).
tff(c_97500,plain,
singleton('#skF_34') = '#skF_25',
inference(demodulation,[status(thm),theory(equality)],[c_92936,c_93346,c_97491]) ).
tff(c_97502,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_92978,c_97500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU162+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 22:09:57 EDT 2025
% 0.14/0.35 % CPUTime :
% 28.19/14.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.19/14.91
% 28.19/14.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------