%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU348+1 : 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 : n031.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 08:53:43 PM UTC 2025
% Result : Theorem 8.34s 2.73s
% Output : CNFRefutation 8.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 151 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 159 ( 63 ~; 74 |; 11 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 14 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ v1_partfun1 > relstr_element_smaller > relation_of2_as_subset > relation_of2 > latt_set_smaller > subset > in > element > transitive_relstr > transitive > strict_rel_str > relation > rel_str > reflexive_relstr > reflexive > one_sorted_str > meet_semilatt_str > meet_commutative > meet_associative > meet_absorbing > lattice > latt_str > join_semilatt_str > join_commutative > join_associative > join_absorbing > empty_carrier > empty > antisymmetric_relstr > antisymmetric > rel_str_of > cast_to_el_of_lattice > cast_to_el_of_LattPOSet > cartesian_product2 > #nlpp > the_carrier > the_InternalRel > relation_of_lattice > powerset > poset_of_lattice > k2_lattice3 > empty_set > #skF_7 > #skF_16 > #skF_6 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_14 > #skF_5 > #skF_10 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_9 > #skF_13 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(antisymmetric,type,
antisymmetric: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff(latt_set_smaller,type,
latt_set_smaller: ( $i * $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff(the_InternalRel,type,
the_InternalRel: $i > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(v1_partfun1,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(join_absorbing,type,
join_absorbing: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff(meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
tff(antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
tff(meet_associative,type,
meet_associative: $i > $o ).
tff(latt_str,type,
latt_str: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(strict_rel_str,type,
strict_rel_str: $i > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(reflexive_relstr,type,
reflexive_relstr: $i > $o ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(relation_of_lattice,type,
relation_of_lattice: $i > $i ).
tff(cast_to_el_of_lattice,type,
cast_to_el_of_lattice: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(transitive_relstr,type,
transitive_relstr: $i > $o ).
tff(rel_str_of,type,
rel_str_of: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(poset_of_lattice,type,
poset_of_lattice: $i > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(cast_to_el_of_LattPOSet,type,
cast_to_el_of_LattPOSet: ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff(join_semilatt_str,type,
join_semilatt_str: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(lattice,type,
lattice: $i > $o ).
tff(join_associative,type,
join_associative: $i > $o ).
tff(rel_str,type,
rel_str: $i > $o ).
tff(transitive,type,
transitive: $i > $o ).
tff(meet_absorbing,type,
meet_absorbing: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(reflexive,type,
reflexive: $i > $o ).
tff(relstr_element_smaller,type,
relstr_element_smaller: ( $i * $i * $i ) > $o ).
tff(meet_commutative,type,
meet_commutative: $i > $o ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(k2_lattice3,type,
k2_lattice3: $i > $i ).
tff(relation_of2_as_subset,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(join_commutative,type,
join_commutative: $i > $o ).
tff(f_429,negated_conjecture,
~ ! [A,B] :
( ( ~ empty_carrier(B)
& lattice(B)
& latt_str(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattice3) ).
tff(f_118,axiom,
! [A] :
( ( ~ empty_carrier(A)
& lattice(A)
& latt_str(A) )
=> ! [B] :
( element(B,the_carrier(poset_of_lattice(A)))
=> ( cast_to_el_of_lattice(A,B) = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
tff(f_181,axiom,
! [A,B] :
( ( ~ empty_carrier(A)
& lattice(A)
& latt_str(A)
& element(B,the_carrier(poset_of_lattice(A))) )
=> element(cast_to_el_of_lattice(A,B),the_carrier(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
tff(f_106,axiom,
! [A] :
( ( ~ empty_carrier(A)
& lattice(A)
& latt_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ( cast_to_el_of_LattPOSet(A,B) = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
tff(f_414,axiom,
! [A,B] :
( ( ~ empty_carrier(B)
& lattice(B)
& latt_str(B) )
=> ! [C] :
( element(C,the_carrier(B))
=> ( latt_set_smaller(B,C,A)
<=> relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice3) ).
tff(c_206,plain,
~ empty_carrier('#skF_18'),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_204,plain,
lattice('#skF_18'),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_202,plain,
latt_str('#skF_18'),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_200,plain,
element('#skF_19',the_carrier(poset_of_lattice('#skF_18'))),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_2801,plain,
! [A_599,B_600] :
( ( cast_to_el_of_lattice(A_599,B_600) = B_600 )
| ~ element(B_600,the_carrier(poset_of_lattice(A_599)))
| ~ latt_str(A_599)
| ~ lattice(A_599)
| empty_carrier(A_599) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_2812,plain,
( ( cast_to_el_of_lattice('#skF_18','#skF_19') = '#skF_19' )
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(resolution,[status(thm)],[c_200,c_2801]) ).
tff(c_2821,plain,
( ( cast_to_el_of_lattice('#skF_18','#skF_19') = '#skF_19' )
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_2812]) ).
tff(c_2822,plain,
cast_to_el_of_lattice('#skF_18','#skF_19') = '#skF_19',
inference(negUnitSimplification,[status(thm)],[c_206,c_2821]) ).
tff(c_1222,plain,
! [A_306,B_307] :
( ( cast_to_el_of_lattice(A_306,B_307) = B_307 )
| ~ element(B_307,the_carrier(poset_of_lattice(A_306)))
| ~ latt_str(A_306)
| ~ lattice(A_306)
| empty_carrier(A_306) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_1233,plain,
( ( cast_to_el_of_lattice('#skF_18','#skF_19') = '#skF_19' )
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(resolution,[status(thm)],[c_200,c_1222]) ).
tff(c_1242,plain,
( ( cast_to_el_of_lattice('#skF_18','#skF_19') = '#skF_19' )
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_1233]) ).
tff(c_1243,plain,
cast_to_el_of_lattice('#skF_18','#skF_19') = '#skF_19',
inference(negUnitSimplification,[status(thm)],[c_206,c_1242]) ).
tff(c_208,plain,
( ~ latt_set_smaller('#skF_18',cast_to_el_of_lattice('#skF_18','#skF_19'),'#skF_17')
| ~ relstr_element_smaller(poset_of_lattice('#skF_18'),'#skF_17','#skF_19') ),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_291,plain,
~ relstr_element_smaller(poset_of_lattice('#skF_18'),'#skF_17','#skF_19'),
inference(splitLeft,[status(thm)],[c_208]) ).
tff(c_214,plain,
( relstr_element_smaller(poset_of_lattice('#skF_18'),'#skF_17','#skF_19')
| latt_set_smaller('#skF_18',cast_to_el_of_lattice('#skF_18','#skF_19'),'#skF_17') ),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_309,plain,
latt_set_smaller('#skF_18',cast_to_el_of_lattice('#skF_18','#skF_19'),'#skF_17'),
inference(negUnitSimplification,[status(thm)],[c_291,c_214]) ).
tff(c_1245,plain,
latt_set_smaller('#skF_18','#skF_19','#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_1243,c_309]) ).
tff(c_1261,plain,
! [A_309,B_310] :
( element(cast_to_el_of_lattice(A_309,B_310),the_carrier(A_309))
| ~ element(B_310,the_carrier(poset_of_lattice(A_309)))
| ~ latt_str(A_309)
| ~ lattice(A_309)
| empty_carrier(A_309) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_1273,plain,
( element('#skF_19',the_carrier('#skF_18'))
| ~ element('#skF_19',the_carrier(poset_of_lattice('#skF_18')))
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(superposition,[status(thm),theory(equality)],[c_1243,c_1261]) ).
tff(c_1278,plain,
( element('#skF_19',the_carrier('#skF_18'))
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_200,c_1273]) ).
tff(c_1279,plain,
element('#skF_19',the_carrier('#skF_18')),
inference(negUnitSimplification,[status(thm)],[c_206,c_1278]) ).
tff(c_28,plain,
! [A_10,B_12] :
( ( cast_to_el_of_LattPOSet(A_10,B_12) = B_12 )
| ~ element(B_12,the_carrier(A_10))
| ~ latt_str(A_10)
| ~ lattice(A_10)
| empty_carrier(A_10) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_1282,plain,
( ( cast_to_el_of_LattPOSet('#skF_18','#skF_19') = '#skF_19' )
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(resolution,[status(thm)],[c_1279,c_28]) ).
tff(c_1287,plain,
( ( cast_to_el_of_LattPOSet('#skF_18','#skF_19') = '#skF_19' )
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_1282]) ).
tff(c_1288,plain,
cast_to_el_of_LattPOSet('#skF_18','#skF_19') = '#skF_19',
inference(negUnitSimplification,[status(thm)],[c_206,c_1287]) ).
tff(c_1826,plain,
! [B_379,A_380,C_381] :
( relstr_element_smaller(poset_of_lattice(B_379),A_380,cast_to_el_of_LattPOSet(B_379,C_381))
| ~ latt_set_smaller(B_379,C_381,A_380)
| ~ element(C_381,the_carrier(B_379))
| ~ latt_str(B_379)
| ~ lattice(B_379)
| empty_carrier(B_379) ),
inference(cnfTransformation,[status(thm)],[f_414]) ).
tff(c_1835,plain,
! [A_380] :
( relstr_element_smaller(poset_of_lattice('#skF_18'),A_380,'#skF_19')
| ~ latt_set_smaller('#skF_18','#skF_19',A_380)
| ~ element('#skF_19',the_carrier('#skF_18'))
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(superposition,[status(thm),theory(equality)],[c_1288,c_1826]) ).
tff(c_1840,plain,
! [A_380] :
( relstr_element_smaller(poset_of_lattice('#skF_18'),A_380,'#skF_19')
| ~ latt_set_smaller('#skF_18','#skF_19',A_380)
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_1279,c_1835]) ).
tff(c_1842,plain,
! [A_382] :
( relstr_element_smaller(poset_of_lattice('#skF_18'),A_382,'#skF_19')
| ~ latt_set_smaller('#skF_18','#skF_19',A_382) ),
inference(negUnitSimplification,[status(thm)],[c_206,c_1840]) ).
tff(c_1848,plain,
~ latt_set_smaller('#skF_18','#skF_19','#skF_17'),
inference(resolution,[status(thm)],[c_1842,c_291]) ).
tff(c_1853,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1245,c_1848]) ).
tff(c_1854,plain,
~ latt_set_smaller('#skF_18',cast_to_el_of_lattice('#skF_18','#skF_19'),'#skF_17'),
inference(splitRight,[status(thm)],[c_208]) ).
tff(c_1863,plain,
latt_set_smaller('#skF_18',cast_to_el_of_lattice('#skF_18','#skF_19'),'#skF_17'),
inference(splitLeft,[status(thm)],[c_214]) ).
tff(c_1875,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1854,c_1863]) ).
tff(c_1877,plain,
~ latt_set_smaller('#skF_18',cast_to_el_of_lattice('#skF_18','#skF_19'),'#skF_17'),
inference(splitRight,[status(thm)],[c_214]) ).
tff(c_2824,plain,
~ latt_set_smaller('#skF_18','#skF_19','#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_2822,c_1877]) ).
tff(c_1876,plain,
relstr_element_smaller(poset_of_lattice('#skF_18'),'#skF_17','#skF_19'),
inference(splitRight,[status(thm)],[c_214]) ).
tff(c_2840,plain,
! [A_602,B_603] :
( element(cast_to_el_of_lattice(A_602,B_603),the_carrier(A_602))
| ~ element(B_603,the_carrier(poset_of_lattice(A_602)))
| ~ latt_str(A_602)
| ~ lattice(A_602)
| empty_carrier(A_602) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_2852,plain,
( element('#skF_19',the_carrier('#skF_18'))
| ~ element('#skF_19',the_carrier(poset_of_lattice('#skF_18')))
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(superposition,[status(thm),theory(equality)],[c_2822,c_2840]) ).
tff(c_2857,plain,
( element('#skF_19',the_carrier('#skF_18'))
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_200,c_2852]) ).
tff(c_2858,plain,
element('#skF_19',the_carrier('#skF_18')),
inference(negUnitSimplification,[status(thm)],[c_206,c_2857]) ).
tff(c_2861,plain,
( ( cast_to_el_of_LattPOSet('#skF_18','#skF_19') = '#skF_19' )
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(resolution,[status(thm)],[c_2858,c_28]) ).
tff(c_2866,plain,
( ( cast_to_el_of_LattPOSet('#skF_18','#skF_19') = '#skF_19' )
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_2861]) ).
tff(c_2867,plain,
cast_to_el_of_LattPOSet('#skF_18','#skF_19') = '#skF_19',
inference(negUnitSimplification,[status(thm)],[c_206,c_2866]) ).
tff(c_3369,plain,
! [B_657,C_658,A_659] :
( latt_set_smaller(B_657,C_658,A_659)
| ~ relstr_element_smaller(poset_of_lattice(B_657),A_659,cast_to_el_of_LattPOSet(B_657,C_658))
| ~ element(C_658,the_carrier(B_657))
| ~ latt_str(B_657)
| ~ lattice(B_657)
| empty_carrier(B_657) ),
inference(cnfTransformation,[status(thm)],[f_414]) ).
tff(c_3378,plain,
! [A_659] :
( latt_set_smaller('#skF_18','#skF_19',A_659)
| ~ relstr_element_smaller(poset_of_lattice('#skF_18'),A_659,'#skF_19')
| ~ element('#skF_19',the_carrier('#skF_18'))
| ~ latt_str('#skF_18')
| ~ lattice('#skF_18')
| empty_carrier('#skF_18') ),
inference(superposition,[status(thm),theory(equality)],[c_2867,c_3369]) ).
tff(c_3383,plain,
! [A_659] :
( latt_set_smaller('#skF_18','#skF_19',A_659)
| ~ relstr_element_smaller(poset_of_lattice('#skF_18'),A_659,'#skF_19')
| empty_carrier('#skF_18') ),
inference(demodulation,[status(thm),theory(equality)],[c_204,c_202,c_2858,c_3378]) ).
tff(c_3385,plain,
! [A_660] :
( latt_set_smaller('#skF_18','#skF_19',A_660)
| ~ relstr_element_smaller(poset_of_lattice('#skF_18'),A_660,'#skF_19') ),
inference(negUnitSimplification,[status(thm)],[c_206,c_3383]) ).
tff(c_3391,plain,
latt_set_smaller('#skF_18','#skF_19','#skF_17'),
inference(resolution,[status(thm)],[c_1876,c_3385]) ).
tff(c_3396,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2824,c_3391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU348+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:54:37 EDT 2025
% 0.13/0.34 % CPUTime :
% 8.34/2.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.34/2.74
% 8.34/2.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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