TSTP Solution File: SEU344+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU344+1 : TPTP v8.1.2. 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 : n023.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 : Tue Aug 22 10:58:28 EDT 2023
% Result : Theorem 12.01s 3.86s
% Output : CNFRefutation 12.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 60
% Syntax : Number of formulae : 98 ( 22 unt; 52 typ; 0 def)
% Number of atoms : 98 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 36 ~; 36 |; 5 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 39 >; 32 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 13 con; 0-6 aty)
% Number of variables : 43 (; 43 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > below > subset > in > element > strict_latt_str > relation > one_sorted_str > meet_semilatt_str > latt_str > join_semilatt_str > function > empty_carrier > empty > apply_binary_as_element > meet > latt_str_of > join > apply_binary > unordered_pair > set_union2 > set_intersection2 > ordered_pair > cartesian_product2 > apply > #nlpp > the_carrier > the_L_meet > the_L_join > singleton > powerset > boole_lattice > empty_set > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_8 > #skF_16 > #skF_10 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_4 > #skF_14 > #skF_7 > #skF_5 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(quasi_total,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(join,type,
join: ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(function,type,
function: $i > $o ).
tff(meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
tff(apply_binary,type,
apply_binary: ( $i * $i * $i ) > $i ).
tff(the_L_join,type,
the_L_join: $i > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(latt_str,type,
latt_str: $i > $o ).
tff(in,type,
in: ( $i * $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('#skF_13',type,
'#skF_13': $i ).
tff(latt_str_of,type,
latt_str_of: ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(strict_latt_str,type,
strict_latt_str: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(meet,type,
meet: ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(the_L_meet,type,
the_L_meet: $i > $i ).
tff(join_semilatt_str,type,
join_semilatt_str: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(below,type,
below: ( $i * $i * $i ) > $o ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(boole_lattice,type,
boole_lattice: $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(apply_binary_as_element,type,
apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(relation_of2_as_subset,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_399,negated_conjecture,
~ ! [A,B] :
( element(B,the_carrier(boole_lattice(A)))
=> ! [C] :
( element(C,the_carrier(boole_lattice(A)))
=> ( below(boole_lattice(A),B,C)
<=> subset(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
tff(f_372,axiom,
! [A,B] :
( subset(A,B)
=> ( set_union2(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
tff(f_383,axiom,
! [A,B] :
( element(B,the_carrier(boole_lattice(A)))
=> ! [C] :
( element(C,the_carrier(boole_lattice(A)))
=> ( ( join(boole_lattice(A),B,C) = set_union2(B,C) )
& ( meet(boole_lattice(A),B,C) = set_intersection2(B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
tff(f_214,axiom,
! [A] :
( ~ empty_carrier(boole_lattice(A))
& strict_latt_str(boole_lattice(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
tff(f_118,axiom,
! [A] :
( strict_latt_str(boole_lattice(A))
& latt_str(boole_lattice(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
tff(f_172,axiom,
! [A] :
( latt_str(A)
=> ( meet_semilatt_str(A)
& join_semilatt_str(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
tff(f_95,axiom,
! [A] :
( ( ~ empty_carrier(A)
& join_semilatt_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below(A,B,C)
<=> ( join(A,B,C) = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
tff(f_433,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(c_198,plain,
( below(boole_lattice('#skF_16'),'#skF_17','#skF_18')
| subset('#skF_17','#skF_18') ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_259,plain,
subset('#skF_17','#skF_18'),
inference(splitLeft,[status(thm)],[c_198]) ).
tff(c_192,plain,
( ~ subset('#skF_17','#skF_18')
| ~ below(boole_lattice('#skF_16'),'#skF_17','#skF_18') ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_290,plain,
~ below(boole_lattice('#skF_16'),'#skF_17','#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_259,c_192]) ).
tff(c_662,plain,
! [A_204,B_205] :
( ( set_union2(A_204,B_205) = B_205 )
| ~ subset(A_204,B_205) ),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_682,plain,
set_union2('#skF_17','#skF_18') = '#skF_18',
inference(resolution,[status(thm)],[c_259,c_662]) ).
tff(c_190,plain,
element('#skF_17',the_carrier(boole_lattice('#skF_16'))),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_188,plain,
element('#skF_18',the_carrier(boole_lattice('#skF_16'))),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_2241,plain,
! [A_319,B_320,C_321] :
( ( join(boole_lattice(A_319),B_320,C_321) = set_union2(B_320,C_321) )
| ~ element(C_321,the_carrier(boole_lattice(A_319)))
| ~ element(B_320,the_carrier(boole_lattice(A_319))) ),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_2476,plain,
! [B_342] :
( ( join(boole_lattice('#skF_16'),B_342,'#skF_18') = set_union2(B_342,'#skF_18') )
| ~ element(B_342,the_carrier(boole_lattice('#skF_16'))) ),
inference(resolution,[status(thm)],[c_188,c_2241]) ).
tff(c_2487,plain,
join(boole_lattice('#skF_16'),'#skF_17','#skF_18') = set_union2('#skF_17','#skF_18'),
inference(resolution,[status(thm)],[c_190,c_2476]) ).
tff(c_2498,plain,
join(boole_lattice('#skF_16'),'#skF_17','#skF_18') = '#skF_18',
inference(demodulation,[status(thm),theory(equality)],[c_682,c_2487]) ).
tff(c_104,plain,
! [A_73] : ~ empty_carrier(boole_lattice(A_73)),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_36,plain,
! [A_44] : latt_str(boole_lattice(A_44)),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_260,plain,
! [A_158] :
( join_semilatt_str(A_158)
| ~ latt_str(A_158) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_273,plain,
! [A_44] : join_semilatt_str(boole_lattice(A_44)),
inference(resolution,[status(thm)],[c_36,c_260]) ).
tff(c_3432,plain,
! [A_363,B_364,C_365] :
( below(A_363,B_364,C_365)
| ( join(A_363,B_364,C_365) != C_365 )
| ~ element(C_365,the_carrier(A_363))
| ~ element(B_364,the_carrier(A_363))
| ~ join_semilatt_str(A_363)
| empty_carrier(A_363) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_3445,plain,
! [B_364] :
( below(boole_lattice('#skF_16'),B_364,'#skF_18')
| ( join(boole_lattice('#skF_16'),B_364,'#skF_18') != '#skF_18' )
| ~ element(B_364,the_carrier(boole_lattice('#skF_16')))
| ~ join_semilatt_str(boole_lattice('#skF_16'))
| empty_carrier(boole_lattice('#skF_16')) ),
inference(resolution,[status(thm)],[c_188,c_3432]) ).
tff(c_3459,plain,
! [B_364] :
( below(boole_lattice('#skF_16'),B_364,'#skF_18')
| ( join(boole_lattice('#skF_16'),B_364,'#skF_18') != '#skF_18' )
| ~ element(B_364,the_carrier(boole_lattice('#skF_16')))
| empty_carrier(boole_lattice('#skF_16')) ),
inference(demodulation,[status(thm),theory(equality)],[c_273,c_3445]) ).
tff(c_8374,plain,
! [B_580] :
( below(boole_lattice('#skF_16'),B_580,'#skF_18')
| ( join(boole_lattice('#skF_16'),B_580,'#skF_18') != '#skF_18' )
| ~ element(B_580,the_carrier(boole_lattice('#skF_16'))) ),
inference(negUnitSimplification,[status(thm)],[c_104,c_3459]) ).
tff(c_8424,plain,
( below(boole_lattice('#skF_16'),'#skF_17','#skF_18')
| ( join(boole_lattice('#skF_16'),'#skF_17','#skF_18') != '#skF_18' ) ),
inference(resolution,[status(thm)],[c_190,c_8374]) ).
tff(c_8455,plain,
below(boole_lattice('#skF_16'),'#skF_17','#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_2498,c_8424]) ).
tff(c_8457,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_290,c_8455]) ).
tff(c_8459,plain,
~ subset('#skF_17','#skF_18'),
inference(splitRight,[status(thm)],[c_198]) ).
tff(c_8460,plain,
! [A_581] :
( join_semilatt_str(A_581)
| ~ latt_str(A_581) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_8473,plain,
! [A_44] : join_semilatt_str(boole_lattice(A_44)),
inference(resolution,[status(thm)],[c_36,c_8460]) ).
tff(c_8458,plain,
below(boole_lattice('#skF_16'),'#skF_17','#skF_18'),
inference(splitRight,[status(thm)],[c_198]) ).
tff(c_11650,plain,
! [A_787,B_788,C_789] :
( ( join(A_787,B_788,C_789) = C_789 )
| ~ below(A_787,B_788,C_789)
| ~ element(C_789,the_carrier(A_787))
| ~ element(B_788,the_carrier(A_787))
| ~ join_semilatt_str(A_787)
| empty_carrier(A_787) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_11652,plain,
( ( join(boole_lattice('#skF_16'),'#skF_17','#skF_18') = '#skF_18' )
| ~ element('#skF_18',the_carrier(boole_lattice('#skF_16')))
| ~ element('#skF_17',the_carrier(boole_lattice('#skF_16')))
| ~ join_semilatt_str(boole_lattice('#skF_16'))
| empty_carrier(boole_lattice('#skF_16')) ),
inference(resolution,[status(thm)],[c_8458,c_11650]) ).
tff(c_11655,plain,
( ( join(boole_lattice('#skF_16'),'#skF_17','#skF_18') = '#skF_18' )
| empty_carrier(boole_lattice('#skF_16')) ),
inference(demodulation,[status(thm),theory(equality)],[c_8473,c_190,c_188,c_11652]) ).
tff(c_11656,plain,
join(boole_lattice('#skF_16'),'#skF_17','#skF_18') = '#skF_18',
inference(negUnitSimplification,[status(thm)],[c_104,c_11655]) ).
tff(c_10726,plain,
! [A_746,B_747,C_748] :
( ( join(boole_lattice(A_746),B_747,C_748) = set_union2(B_747,C_748) )
| ~ element(C_748,the_carrier(boole_lattice(A_746)))
| ~ element(B_747,the_carrier(boole_lattice(A_746))) ),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_12048,plain,
! [B_796] :
( ( join(boole_lattice('#skF_16'),B_796,'#skF_18') = set_union2(B_796,'#skF_18') )
| ~ element(B_796,the_carrier(boole_lattice('#skF_16'))) ),
inference(resolution,[status(thm)],[c_188,c_10726]) ).
tff(c_12069,plain,
join(boole_lattice('#skF_16'),'#skF_17','#skF_18') = set_union2('#skF_17','#skF_18'),
inference(resolution,[status(thm)],[c_190,c_12048]) ).
tff(c_12088,plain,
set_union2('#skF_17','#skF_18') = '#skF_18',
inference(demodulation,[status(thm),theory(equality)],[c_11656,c_12069]) ).
tff(c_214,plain,
! [A_142,B_143] : subset(A_142,set_union2(A_142,B_143)),
inference(cnfTransformation,[status(thm)],[f_433]) ).
tff(c_12157,plain,
subset('#skF_17','#skF_18'),
inference(superposition,[status(thm),theory(equality)],[c_12088,c_214]) ).
tff(c_12179,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8459,c_12157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU344+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % 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
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 12:27:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 12.01/3.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.01/3.87
% 12.01/3.87 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.14/3.90
% 12.14/3.90 Inference rules
% 12.14/3.90 ----------------------
% 12.14/3.90 #Ref : 6
% 12.14/3.90 #Sup : 2868
% 12.14/3.90 #Fact : 0
% 12.14/3.90 #Define : 0
% 12.14/3.90 #Split : 17
% 12.14/3.90 #Chain : 0
% 12.14/3.90 #Close : 0
% 12.14/3.90
% 12.14/3.90 Ordering : KBO
% 12.14/3.90
% 12.14/3.90 Simplification rules
% 12.14/3.90 ----------------------
% 12.14/3.90 #Subsume : 644
% 12.14/3.90 #Demod : 2441
% 12.14/3.90 #Tautology : 1454
% 12.14/3.90 #SimpNegUnit : 214
% 12.14/3.90 #BackRed : 30
% 12.14/3.90
% 12.14/3.90 #Partial instantiations: 0
% 12.14/3.90 #Strategies tried : 1
% 12.14/3.90
% 12.14/3.90 Timing (in seconds)
% 12.14/3.90 ----------------------
% 12.14/3.91 Preprocessing : 0.68
% 12.14/3.91 Parsing : 0.35
% 12.14/3.91 CNF conversion : 0.06
% 12.14/3.91 Main loop : 2.15
% 12.14/3.91 Inferencing : 0.66
% 12.14/3.91 Reduction : 0.91
% 12.14/3.91 Demodulation : 0.70
% 12.14/3.91 BG Simplification : 0.07
% 12.14/3.91 Subsumption : 0.39
% 12.14/3.91 Abstraction : 0.08
% 12.14/3.91 MUC search : 0.00
% 12.14/3.91 Cooper : 0.00
% 12.14/3.91 Total : 2.88
% 12.14/3.91 Index Insertion : 0.00
% 12.14/3.91 Index Deletion : 0.00
% 12.14/3.91 Index Matching : 0.00
% 12.14/3.91 BG Taut test : 0.00
%------------------------------------------------------------------------------