TSTP Solution File: SEU291+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU291+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/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 : Tue Aug 22 10:58:17 EDT 2023
% Result : Theorem 8.01s 2.83s
% Output : CNFRefutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 52
% Syntax : Number of formulae : 183 ( 80 unt; 37 typ; 0 def)
% Number of atoms : 251 ( 78 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 189 ( 84 ~; 75 |; 11 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 22 >; 16 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 15 con; 0-3 aty)
% Number of variables : 153 (; 150 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_dom_as_subset > cartesian_product2 > #nlpp > relation_dom > powerset > empty_set > #skF_11 > #skF_20 > #skF_2 > #skF_18 > #skF_17 > #skF_15 > #skF_8 > #skF_19 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_21 > #skF_9 > #skF_13 > #skF_4 > #skF_1 > #skF_5 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(quasi_total,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(relation_dom_as_subset,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $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_12',type,
'#skF_12': $i ).
tff(f_162,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_288,negated_conjecture,
~ ! [A,B,C,D] :
( ( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B) )
=> ( subset(B,C)
=> ( ( ( B = empty_set )
& ( A != empty_set ) )
| ( function(D)
& quasi_total(D,A,C)
& relation_of2_as_subset(D,A,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
tff(f_220,axiom,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
tff(f_255,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_147,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
tff(f_212,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
tff(f_208,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> ( relation_dom_as_subset(A,B,C) = relation_dom(C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
tff(f_73,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( quasi_total(C,A,B)
<=> ( A = relation_dom_as_subset(A,B,C) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( quasi_total(C,A,B)
<=> ( C = empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
tff(f_238,axiom,
! [A] :
( subset(A,empty_set)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
tff(f_185,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
tff(f_234,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_82,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
tff(f_43,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
tff(f_78,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_dom_as_subset(A,B,C),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
tff(f_120,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
tff(c_100,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_176,plain,
relation_of2_as_subset('#skF_21','#skF_18','#skF_19'),
inference(cnfTransformation,[status(thm)],[f_288]) ).
tff(c_174,plain,
subset('#skF_19','#skF_20'),
inference(cnfTransformation,[status(thm)],[f_288]) ).
tff(c_2548,plain,
! [D_411,C_412,B_413,A_414] :
( relation_of2_as_subset(D_411,C_412,B_413)
| ~ subset(A_414,B_413)
| ~ relation_of2_as_subset(D_411,C_412,A_414) ),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_2567,plain,
! [D_415,C_416] :
( relation_of2_as_subset(D_415,C_416,'#skF_20')
| ~ relation_of2_as_subset(D_415,C_416,'#skF_19') ),
inference(resolution,[status(thm)],[c_174,c_2548]) ).
tff(c_180,plain,
function('#skF_21'),
inference(cnfTransformation,[status(thm)],[f_288]) ).
tff(c_170,plain,
( ~ relation_of2_as_subset('#skF_21','#skF_18','#skF_20')
| ~ quasi_total('#skF_21','#skF_18','#skF_20')
| ~ function('#skF_21') ),
inference(cnfTransformation,[status(thm)],[f_288]) ).
tff(c_182,plain,
( ~ relation_of2_as_subset('#skF_21','#skF_18','#skF_20')
| ~ quasi_total('#skF_21','#skF_18','#skF_20') ),
inference(demodulation,[status(thm),theory(equality)],[c_180,c_170]) ).
tff(c_268,plain,
~ quasi_total('#skF_21','#skF_18','#skF_20'),
inference(splitLeft,[status(thm)],[c_182]) ).
tff(c_191,plain,
! [A_76] :
( ( empty_set = A_76 )
| ~ empty(A_76) ),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_215,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_100,c_191]) ).
tff(c_84,plain,
empty('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_213,plain,
empty_set = '#skF_6',
inference(resolution,[status(thm)],[c_84,c_191]) ).
tff(c_237,plain,
'#skF_6' = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_215,c_213]) ).
tff(c_172,plain,
( ( empty_set = '#skF_18' )
| ( empty_set != '#skF_19' ) ),
inference(cnfTransformation,[status(thm)],[f_288]) ).
tff(c_186,plain,
empty_set != '#skF_19',
inference(splitLeft,[status(thm)],[c_172]) ).
tff(c_218,plain,
'#skF_19' != '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_213,c_186]) ).
tff(c_270,plain,
'#skF_19' != '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_237,c_218]) ).
tff(c_178,plain,
quasi_total('#skF_21','#skF_18','#skF_19'),
inference(cnfTransformation,[status(thm)],[f_288]) ).
tff(c_574,plain,
! [C_140,A_141,B_142] :
( relation_of2(C_140,A_141,B_142)
| ~ relation_of2_as_subset(C_140,A_141,B_142) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_586,plain,
relation_of2('#skF_21','#skF_18','#skF_19'),
inference(resolution,[status(thm)],[c_176,c_574]) ).
tff(c_684,plain,
! [A_178,B_179,C_180] :
( ( relation_dom_as_subset(A_178,B_179,C_180) = relation_dom(C_180) )
| ~ relation_of2(C_180,A_178,B_179) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_701,plain,
relation_dom_as_subset('#skF_18','#skF_19','#skF_21') = relation_dom('#skF_21'),
inference(resolution,[status(thm)],[c_586,c_684]) ).
tff(c_26,plain,
! [B_10,A_9,C_11] :
( ( empty_set = B_10 )
| ( relation_dom_as_subset(A_9,B_10,C_11) = A_9 )
| ~ quasi_total(C_11,A_9,B_10)
| ~ relation_of2_as_subset(C_11,A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1500,plain,
! [B_257,A_258,C_259] :
( ( B_257 = '#skF_9' )
| ( relation_dom_as_subset(A_258,B_257,C_259) = A_258 )
| ~ quasi_total(C_259,A_258,B_257)
| ~ relation_of2_as_subset(C_259,A_258,B_257) ),
inference(demodulation,[status(thm),theory(equality)],[c_215,c_26]) ).
tff(c_1524,plain,
( ( '#skF_19' = '#skF_9' )
| ( relation_dom_as_subset('#skF_18','#skF_19','#skF_21') = '#skF_18' )
| ~ quasi_total('#skF_21','#skF_18','#skF_19') ),
inference(resolution,[status(thm)],[c_176,c_1500]) ).
tff(c_1539,plain,
( ( '#skF_19' = '#skF_9' )
| ( relation_dom('#skF_21') = '#skF_18' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_178,c_701,c_1524]) ).
tff(c_1540,plain,
relation_dom('#skF_21') = '#skF_18',
inference(negUnitSimplification,[status(thm)],[c_270,c_1539]) ).
tff(c_745,plain,
! [D_189,C_190,B_191,A_192] :
( relation_of2_as_subset(D_189,C_190,B_191)
| ~ subset(A_192,B_191)
| ~ relation_of2_as_subset(D_189,C_190,A_192) ),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_788,plain,
! [D_200,C_201] :
( relation_of2_as_subset(D_200,C_201,'#skF_20')
| ~ relation_of2_as_subset(D_200,C_201,'#skF_19') ),
inference(resolution,[status(thm)],[c_174,c_745]) ).
tff(c_142,plain,
! [C_46,A_44,B_45] :
( relation_of2(C_46,A_44,B_45)
| ~ relation_of2_as_subset(C_46,A_44,B_45) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_797,plain,
! [D_202,C_203] :
( relation_of2(D_202,C_203,'#skF_20')
| ~ relation_of2_as_subset(D_202,C_203,'#skF_19') ),
inference(resolution,[status(thm)],[c_788,c_142]) ).
tff(c_811,plain,
relation_of2('#skF_21','#skF_18','#skF_20'),
inference(resolution,[status(thm)],[c_176,c_797]) ).
tff(c_140,plain,
! [A_41,B_42,C_43] :
( ( relation_dom_as_subset(A_41,B_42,C_43) = relation_dom(C_43) )
| ~ relation_of2(C_43,A_41,B_42) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_820,plain,
relation_dom_as_subset('#skF_18','#skF_20','#skF_21') = relation_dom('#skF_21'),
inference(resolution,[status(thm)],[c_811,c_140]) ).
tff(c_1546,plain,
relation_dom_as_subset('#skF_18','#skF_20','#skF_21') = '#skF_18',
inference(demodulation,[status(thm),theory(equality)],[c_1540,c_820]) ).
tff(c_760,plain,
! [D_189,C_190] :
( relation_of2_as_subset(D_189,C_190,'#skF_20')
| ~ relation_of2_as_subset(D_189,C_190,'#skF_19') ),
inference(resolution,[status(thm)],[c_174,c_745]) ).
tff(c_22,plain,
! [B_10,C_11,A_9] :
( ( empty_set = B_10 )
| quasi_total(C_11,A_9,B_10)
| ( relation_dom_as_subset(A_9,B_10,C_11) != A_9 )
| ~ relation_of2_as_subset(C_11,A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1369,plain,
! [B_246,C_247,A_248] :
( ( B_246 = '#skF_9' )
| quasi_total(C_247,A_248,B_246)
| ( relation_dom_as_subset(A_248,B_246,C_247) != A_248 )
| ~ relation_of2_as_subset(C_247,A_248,B_246) ),
inference(demodulation,[status(thm),theory(equality)],[c_215,c_22]) ).
tff(c_1397,plain,
! [D_189,C_190] :
( ( '#skF_20' = '#skF_9' )
| quasi_total(D_189,C_190,'#skF_20')
| ( relation_dom_as_subset(C_190,'#skF_20',D_189) != C_190 )
| ~ relation_of2_as_subset(D_189,C_190,'#skF_19') ),
inference(resolution,[status(thm)],[c_760,c_1369]) ).
tff(c_1422,plain,
'#skF_20' = '#skF_9',
inference(splitLeft,[status(thm)],[c_1397]) ).
tff(c_1436,plain,
subset('#skF_19','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1422,c_174]) ).
tff(c_158,plain,
! [A_59] :
( ( empty_set = A_59 )
| ~ subset(A_59,empty_set) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_300,plain,
! [A_59] :
( ( A_59 = '#skF_9' )
| ~ subset(A_59,'#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_215,c_215,c_158]) ).
tff(c_1445,plain,
'#skF_19' = '#skF_9',
inference(resolution,[status(thm)],[c_1436,c_300]) ).
tff(c_1450,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_270,c_1445]) ).
tff(c_2006,plain,
! [D_291,C_292] :
( quasi_total(D_291,C_292,'#skF_20')
| ( relation_dom_as_subset(C_292,'#skF_20',D_291) != C_292 )
| ~ relation_of2_as_subset(D_291,C_292,'#skF_19') ),
inference(splitRight,[status(thm)],[c_1397]) ).
tff(c_2028,plain,
( quasi_total('#skF_21','#skF_18','#skF_20')
| ( relation_dom_as_subset('#skF_18','#skF_20','#skF_21') != '#skF_18' ) ),
inference(resolution,[status(thm)],[c_176,c_2006]) ).
tff(c_2039,plain,
quasi_total('#skF_21','#skF_18','#skF_20'),
inference(demodulation,[status(thm),theory(equality)],[c_1546,c_2028]) ).
tff(c_2041,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_268,c_2039]) ).
tff(c_2042,plain,
~ relation_of2_as_subset('#skF_21','#skF_18','#skF_20'),
inference(splitRight,[status(thm)],[c_182]) ).
tff(c_2576,plain,
~ relation_of2_as_subset('#skF_21','#skF_18','#skF_19'),
inference(resolution,[status(thm)],[c_2567,c_2042]) ).
tff(c_2582,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_176,c_2576]) ).
tff(c_2584,plain,
empty_set = '#skF_19',
inference(splitRight,[status(thm)],[c_172]) ).
tff(c_164,plain,
! [A_66] :
( ( empty_set = A_66 )
| ~ empty(A_66) ),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_3525,plain,
! [A_565] :
( ( A_565 = '#skF_19' )
| ~ empty(A_565) ),
inference(demodulation,[status(thm),theory(equality)],[c_2584,c_164]) ).
tff(c_3549,plain,
'#skF_19' = '#skF_9',
inference(resolution,[status(thm)],[c_100,c_3525]) ).
tff(c_3547,plain,
'#skF_19' = '#skF_6',
inference(resolution,[status(thm)],[c_84,c_3525]) ).
tff(c_3578,plain,
'#skF_6' = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_3549,c_3547]) ).
tff(c_2583,plain,
empty_set = '#skF_18',
inference(splitRight,[status(thm)],[c_172]) ).
tff(c_2592,plain,
'#skF_18' = '#skF_19',
inference(demodulation,[status(thm),theory(equality)],[c_2584,c_2583]) ).
tff(c_2600,plain,
relation_of2_as_subset('#skF_21','#skF_19','#skF_19'),
inference(demodulation,[status(thm),theory(equality)],[c_2592,c_176]) ).
tff(c_3553,plain,
relation_of2_as_subset('#skF_21','#skF_6','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_3547,c_3547,c_2600]) ).
tff(c_3644,plain,
relation_of2_as_subset('#skF_21','#skF_9','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3578,c_3578,c_3553]) ).
tff(c_118,plain,
! [A_39] : empty('#skF_13'(A_39)),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_3544,plain,
! [A_39] : ( '#skF_13'(A_39) = '#skF_19' ),
inference(resolution,[status(thm)],[c_118,c_3525]) ).
tff(c_3624,plain,
! [A_39] : ( '#skF_13'(A_39) = '#skF_9' ),
inference(demodulation,[status(thm),theory(equality)],[c_3549,c_3544]) ).
tff(c_120,plain,
! [A_39] : element('#skF_13'(A_39),powerset(A_39)),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_3650,plain,
! [A_39] : element('#skF_9',powerset(A_39)),
inference(demodulation,[status(thm),theory(equality)],[c_3624,c_120]) ).
tff(c_3746,plain,
! [A_599,B_600] :
( subset(A_599,B_600)
| ~ element(A_599,powerset(B_600)) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_3758,plain,
! [A_39] : subset('#skF_9',A_39),
inference(resolution,[status(thm)],[c_3650,c_3746]) ).
tff(c_4107,plain,
! [D_676,C_677,B_678,A_679] :
( relation_of2_as_subset(D_676,C_677,B_678)
| ~ subset(A_679,B_678)
| ~ relation_of2_as_subset(D_676,C_677,A_679) ),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_4120,plain,
! [D_680,C_681,A_682] :
( relation_of2_as_subset(D_680,C_681,A_682)
| ~ relation_of2_as_subset(D_680,C_681,'#skF_9') ),
inference(resolution,[status(thm)],[c_3758,c_4107]) ).
tff(c_4131,plain,
! [A_682] : relation_of2_as_subset('#skF_21','#skF_9',A_682),
inference(resolution,[status(thm)],[c_3644,c_4120]) ).
tff(c_2617,plain,
! [A_427] :
( ( A_427 = '#skF_19' )
| ~ empty(A_427) ),
inference(demodulation,[status(thm),theory(equality)],[c_2584,c_164]) ).
tff(c_2641,plain,
'#skF_19' = '#skF_9',
inference(resolution,[status(thm)],[c_100,c_2617]) ).
tff(c_2639,plain,
'#skF_19' = '#skF_6',
inference(resolution,[status(thm)],[c_84,c_2617]) ).
tff(c_2667,plain,
'#skF_6' = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_2641,c_2639]) ).
tff(c_2644,plain,
relation_of2_as_subset('#skF_21','#skF_6','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_2639,c_2639,c_2600]) ).
tff(c_2723,plain,
relation_of2_as_subset('#skF_21','#skF_9','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_2667,c_2667,c_2644]) ).
tff(c_3107,plain,
! [C_513,A_514,B_515] :
( element(C_513,powerset(cartesian_product2(A_514,B_515)))
| ~ relation_of2_as_subset(C_513,A_514,B_515) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_8,plain,
! [C_7,A_5,B_6] :
( relation(C_7)
| ~ element(C_7,powerset(cartesian_product2(A_5,B_6))) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_3119,plain,
! [C_516,A_517,B_518] :
( relation(C_516)
| ~ relation_of2_as_subset(C_516,A_517,B_518) ),
inference(resolution,[status(thm)],[c_3107,c_8]) ).
tff(c_3131,plain,
relation('#skF_21'),
inference(resolution,[status(thm)],[c_2723,c_3119]) ).
tff(c_2636,plain,
! [A_39] : ( '#skF_13'(A_39) = '#skF_19' ),
inference(resolution,[status(thm)],[c_118,c_2617]) ).
tff(c_2712,plain,
! [A_39] : ( '#skF_13'(A_39) = '#skF_9' ),
inference(demodulation,[status(thm),theory(equality)],[c_2641,c_2636]) ).
tff(c_2738,plain,
! [A_39] : element('#skF_9',powerset(A_39)),
inference(demodulation,[status(thm),theory(equality)],[c_2712,c_120]) ).
tff(c_2832,plain,
! [A_462,B_463] :
( subset(A_462,B_463)
| ~ element(A_462,powerset(B_463)) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_2844,plain,
! [A_39] : subset('#skF_9',A_39),
inference(resolution,[status(thm)],[c_2738,c_2832]) ).
tff(c_3194,plain,
! [D_535,C_536,B_537,A_538] :
( relation_of2_as_subset(D_535,C_536,B_537)
| ~ subset(A_538,B_537)
| ~ relation_of2_as_subset(D_535,C_536,A_538) ),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_3207,plain,
! [D_539,C_540,A_541] :
( relation_of2_as_subset(D_539,C_540,A_541)
| ~ relation_of2_as_subset(D_539,C_540,'#skF_9') ),
inference(resolution,[status(thm)],[c_2844,c_3194]) ).
tff(c_3220,plain,
! [A_542] : relation_of2_as_subset('#skF_21','#skF_9',A_542),
inference(resolution,[status(thm)],[c_2723,c_3207]) ).
tff(c_3234,plain,
! [A_542] : relation_of2('#skF_21','#skF_9',A_542),
inference(resolution,[status(thm)],[c_3220,c_142]) ).
tff(c_2928,plain,
! [C_482,A_483,B_484] :
( relation_of2(C_482,A_483,B_484)
| ~ relation_of2_as_subset(C_482,A_483,B_484) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_2940,plain,
relation_of2('#skF_21','#skF_9','#skF_9'),
inference(resolution,[status(thm)],[c_2723,c_2928]) ).
tff(c_3052,plain,
! [A_497,B_498,C_499] :
( ( relation_dom_as_subset(A_497,B_498,C_499) = relation_dom(C_499) )
| ~ relation_of2(C_499,A_497,B_498) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_3069,plain,
relation_dom_as_subset('#skF_9','#skF_9','#skF_21') = relation_dom('#skF_21'),
inference(resolution,[status(thm)],[c_2940,c_3052]) ).
tff(c_3271,plain,
! [A_548,B_549,C_550] :
( element(relation_dom_as_subset(A_548,B_549,C_550),powerset(A_548))
| ~ relation_of2(C_550,A_548,B_549) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_3285,plain,
( element(relation_dom('#skF_21'),powerset('#skF_9'))
| ~ relation_of2('#skF_21','#skF_9','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_3069,c_3271]) ).
tff(c_3291,plain,
element(relation_dom('#skF_21'),powerset('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_3234,c_3285]) ).
tff(c_154,plain,
! [A_57,B_58] :
( subset(A_57,B_58)
| ~ element(A_57,powerset(B_58)) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_3303,plain,
subset(relation_dom('#skF_21'),'#skF_9'),
inference(resolution,[status(thm)],[c_3291,c_154]) ).
tff(c_2650,plain,
empty_set = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_2639,c_2584]) ).
tff(c_2692,plain,
empty_set = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_2667,c_2650]) ).
tff(c_2740,plain,
! [A_59] :
( ( A_59 = '#skF_9' )
| ~ subset(A_59,'#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_2692,c_2692,c_158]) ).
tff(c_3316,plain,
relation_dom('#skF_21') = '#skF_9',
inference(resolution,[status(thm)],[c_3303,c_2740]) ).
tff(c_66,plain,
! [A_29] :
( ~ empty(relation_dom(A_29))
| ~ relation(A_29)
| empty(A_29) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_3339,plain,
( ~ empty('#skF_9')
| ~ relation('#skF_21')
| empty('#skF_21') ),
inference(superposition,[status(thm),theory(equality)],[c_3316,c_66]) ).
tff(c_3352,plain,
empty('#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_3131,c_100,c_3339]) ).
tff(c_2616,plain,
! [A_66] :
( ( A_66 = '#skF_19' )
| ~ empty(A_66) ),
inference(demodulation,[status(thm),theory(equality)],[c_2584,c_164]) ).
tff(c_2643,plain,
! [A_66] :
( ( A_66 = '#skF_6' )
| ~ empty(A_66) ),
inference(demodulation,[status(thm),theory(equality)],[c_2639,c_2616]) ).
tff(c_2724,plain,
! [A_66] :
( ( A_66 = '#skF_9' )
| ~ empty(A_66) ),
inference(demodulation,[status(thm),theory(equality)],[c_2667,c_2643]) ).
tff(c_3375,plain,
'#skF_21' = '#skF_9',
inference(resolution,[status(thm)],[c_3352,c_2724]) ).
tff(c_3236,plain,
! [A_543] : relation_of2('#skF_21','#skF_9',A_543),
inference(resolution,[status(thm)],[c_3220,c_142]) ).
tff(c_3245,plain,
! [A_543] : ( relation_dom_as_subset('#skF_9',A_543,'#skF_21') = relation_dom('#skF_21') ),
inference(resolution,[status(thm)],[c_3236,c_140]) ).
tff(c_3330,plain,
! [A_543] : ( relation_dom_as_subset('#skF_9',A_543,'#skF_21') = '#skF_9' ),
inference(demodulation,[status(thm),theory(equality)],[c_3316,c_3245]) ).
tff(c_3449,plain,
! [A_543] : ( relation_dom_as_subset('#skF_9',A_543,'#skF_9') = '#skF_9' ),
inference(demodulation,[status(thm),theory(equality)],[c_3375,c_3330]) ).
tff(c_3218,plain,
! [A_541] : relation_of2_as_subset('#skF_21','#skF_9',A_541),
inference(resolution,[status(thm)],[c_2723,c_3207]) ).
tff(c_3379,plain,
! [A_541] : relation_of2_as_subset('#skF_9','#skF_9',A_541),
inference(demodulation,[status(thm),theory(equality)],[c_3375,c_3218]) ).
tff(c_20,plain,
! [C_11,B_10] :
( quasi_total(C_11,empty_set,B_10)
| ( relation_dom_as_subset(empty_set,B_10,C_11) != empty_set )
| ~ relation_of2_as_subset(C_11,empty_set,B_10) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_3490,plain,
! [C_561,B_562] :
( quasi_total(C_561,'#skF_9',B_562)
| ( relation_dom_as_subset('#skF_9',B_562,C_561) != '#skF_9' )
| ~ relation_of2_as_subset(C_561,'#skF_9',B_562) ),
inference(demodulation,[status(thm),theory(equality)],[c_2692,c_2692,c_2692,c_2692,c_20]) ).
tff(c_3497,plain,
! [A_541] :
( quasi_total('#skF_9','#skF_9',A_541)
| ( relation_dom_as_subset('#skF_9',A_541,'#skF_9') != '#skF_9' ) ),
inference(resolution,[status(thm)],[c_3379,c_3490]) ).
tff(c_3513,plain,
! [A_541] : quasi_total('#skF_9','#skF_9',A_541),
inference(demodulation,[status(thm),theory(equality)],[c_3449,c_3497]) ).
tff(c_2613,plain,
( ~ relation_of2_as_subset('#skF_21','#skF_19','#skF_20')
| ~ quasi_total('#skF_21','#skF_19','#skF_20') ),
inference(demodulation,[status(thm),theory(equality)],[c_2592,c_2592,c_182]) ).
tff(c_2614,plain,
~ quasi_total('#skF_21','#skF_19','#skF_20'),
inference(splitLeft,[status(thm)],[c_2613]) ).
tff(c_2722,plain,
~ quasi_total('#skF_21','#skF_9','#skF_20'),
inference(demodulation,[status(thm),theory(equality)],[c_2641,c_2614]) ).
tff(c_3381,plain,
~ quasi_total('#skF_9','#skF_9','#skF_20'),
inference(demodulation,[status(thm),theory(equality)],[c_3375,c_2722]) ).
tff(c_3520,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3513,c_3381]) ).
tff(c_3521,plain,
~ relation_of2_as_subset('#skF_21','#skF_19','#skF_20'),
inference(splitRight,[status(thm)],[c_2613]) ).
tff(c_3619,plain,
~ relation_of2_as_subset('#skF_21','#skF_9','#skF_20'),
inference(demodulation,[status(thm),theory(equality)],[c_3549,c_3521]) ).
tff(c_4135,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4131,c_3619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % 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
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 3 12:16:22 EDT 2023
% 0.13/0.36 % CPUTime :
% 8.01/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.01/2.85
% 8.01/2.85 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.01/2.89
% 8.01/2.89 Inference rules
% 8.01/2.89 ----------------------
% 8.01/2.89 #Ref : 0
% 8.01/2.89 #Sup : 833
% 8.01/2.89 #Fact : 0
% 8.01/2.89 #Define : 0
% 8.01/2.89 #Split : 18
% 8.01/2.89 #Chain : 0
% 8.01/2.89 #Close : 0
% 8.01/2.89
% 8.01/2.89 Ordering : KBO
% 8.01/2.89
% 8.01/2.89 Simplification rules
% 8.01/2.89 ----------------------
% 8.01/2.89 #Subsume : 79
% 8.01/2.89 #Demod : 599
% 8.01/2.89 #Tautology : 427
% 8.01/2.89 #SimpNegUnit : 8
% 8.01/2.89 #BackRed : 111
% 8.01/2.89
% 8.01/2.89 #Partial instantiations: 0
% 8.01/2.89 #Strategies tried : 1
% 8.01/2.89
% 8.01/2.89 Timing (in seconds)
% 8.01/2.89 ----------------------
% 8.01/2.90 Preprocessing : 0.62
% 8.01/2.90 Parsing : 0.31
% 8.01/2.90 CNF conversion : 0.05
% 8.01/2.90 Main loop : 1.17
% 8.01/2.90 Inferencing : 0.42
% 8.01/2.90 Reduction : 0.38
% 8.01/2.90 Demodulation : 0.27
% 8.01/2.90 BG Simplification : 0.04
% 8.01/2.90 Subsumption : 0.21
% 8.01/2.90 Abstraction : 0.04
% 8.01/2.90 MUC search : 0.00
% 8.01/2.90 Cooper : 0.00
% 8.01/2.90 Total : 1.87
% 8.01/2.90 Index Insertion : 0.00
% 8.01/2.90 Index Deletion : 0.00
% 8.01/2.90 Index Matching : 0.00
% 8.01/2.90 BG Taut test : 0.00
%------------------------------------------------------------------------------