TSTP Solution File: SEU262+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU262+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 : n009.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 10:58:12 EDT 2023
% Result : Theorem 65.24s 50.34s
% Output : CNFRefutation 65.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 49
% Syntax : Number of formulae : 291 ( 79 unt; 32 typ; 0 def)
% Number of atoms : 549 ( 40 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 560 ( 270 ~; 267 |; 6 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 26 >; 23 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 395 (; 391 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > subset > in > element > relation > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > relation_rng > relation_dom > powerset > empty_set > #skF_6 > #skF_17 > #skF_15 > #skF_3 > #skF_16 > #skF_12 > #skF_14 > #skF_13 > #skF_5 > #skF_10 > #skF_8 > #skF_9 > #skF_11 > #skF_2 > #skF_7 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
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_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $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_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_110,negated_conjecture,
~ ! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_dom(C),A)
& subset(relation_rng(C),B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
tff(f_44,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_114,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
tff(f_146,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
tff(f_120,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
tff(f_73,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
tff(f_35,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
tff(f_55,axiom,
! [A] :
( relation(A)
=> ! [B] :
( ( B = relation_dom(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
tff(f_79,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_137,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
tff(f_88,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_141,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_124,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_66,axiom,
! [A] :
( relation(A)
=> ! [B] :
( ( B = relation_rng(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
tff(f_130,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
tff(f_103,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
tff(f_97,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(c_88,plain,
( ~ subset(relation_rng('#skF_17'),'#skF_16')
| ~ subset(relation_dom('#skF_17'),'#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_129,plain,
~ subset(relation_dom('#skF_17'),'#skF_15'),
inference(splitLeft,[status(thm)],[c_88]) ).
tff(c_248,plain,
! [A_181,B_182] :
( in('#skF_1'(A_181,B_182),A_181)
| subset(A_181,B_182) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_92,plain,
! [A_117,B_118] :
( element(A_117,B_118)
| ~ in(A_117,B_118) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_264,plain,
! [A_181,B_182] :
( element('#skF_1'(A_181,B_182),A_181)
| subset(A_181,B_182) ),
inference(resolution,[status(thm)],[c_248,c_92]) ).
tff(c_106,plain,
! [B_131,A_130] :
( ~ empty(B_131)
| ~ in(A_130,B_131) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_266,plain,
! [A_183,B_184] :
( ~ empty(A_183)
| subset(A_183,B_184) ),
inference(resolution,[status(thm)],[c_248,c_106]) ).
tff(c_275,plain,
~ empty(relation_dom('#skF_17')),
inference(resolution,[status(thm)],[c_266,c_129]) ).
tff(c_94,plain,
! [A_119,B_120] :
( in(A_119,B_120)
| empty(B_120)
| ~ element(A_119,B_120) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_90,plain,
relation_of2_as_subset('#skF_17','#skF_15','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_425,plain,
! [C_217,A_218,B_219] :
( element(C_217,powerset(cartesian_product2(A_218,B_219)))
| ~ relation_of2_as_subset(C_217,A_218,B_219) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_4,plain,
! [C_5,A_3,B_4] :
( relation(C_5)
| ~ element(C_5,powerset(cartesian_product2(A_3,B_4))) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_437,plain,
! [C_220,A_221,B_222] :
( relation(C_220)
| ~ relation_of2_as_subset(C_220,A_221,B_222) ),
inference(resolution,[status(thm)],[c_425,c_4]) ).
tff(c_449,plain,
relation('#skF_17'),
inference(resolution,[status(thm)],[c_90,c_437]) ).
tff(c_877,plain,
! [C_295,A_296] :
( in(ordered_pair(C_295,'#skF_5'(A_296,relation_dom(A_296),C_295)),A_296)
| ~ in(C_295,relation_dom(A_296))
| ~ relation(A_296) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_934,plain,
! [C_295,A_296] :
( element(ordered_pair(C_295,'#skF_5'(A_296,relation_dom(A_296),C_295)),A_296)
| ~ in(C_295,relation_dom(A_296))
| ~ relation(A_296) ),
inference(resolution,[status(thm)],[c_877,c_92]) ).
tff(c_12,plain,
! [A_8,B_9] :
( in('#skF_1'(A_8,B_9),A_8)
| subset(A_8,B_9) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1708,plain,
! [A_333,C_334] :
( ~ empty(A_333)
| ~ in(C_334,relation_dom(A_333))
| ~ relation(A_333) ),
inference(resolution,[status(thm)],[c_877,c_106]) ).
tff(c_1791,plain,
! [A_337,B_338] :
( ~ empty(A_337)
| ~ relation(A_337)
| subset(relation_dom(A_337),B_338) ),
inference(resolution,[status(thm)],[c_12,c_1708]) ).
tff(c_1810,plain,
( ~ empty('#skF_17')
| ~ relation('#skF_17') ),
inference(resolution,[status(thm)],[c_1791,c_129]) ).
tff(c_1822,plain,
~ empty('#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_449,c_1810]) ).
tff(c_64,plain,
! [A_101] : element('#skF_11'(A_101),A_101),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_343,plain,
! [C_197,B_198,A_199] :
( ~ empty(C_197)
| ~ element(B_198,powerset(C_197))
| ~ in(A_199,B_198) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_355,plain,
! [C_200,A_201] :
( ~ empty(C_200)
| ~ in(A_201,'#skF_11'(powerset(C_200))) ),
inference(resolution,[status(thm)],[c_64,c_343]) ).
tff(c_867,plain,
! [C_293,A_294] :
( ~ empty(C_293)
| empty('#skF_11'(powerset(C_293)))
| ~ element(A_294,'#skF_11'(powerset(C_293))) ),
inference(resolution,[status(thm)],[c_94,c_355]) ).
tff(c_936,plain,
! [C_297] :
( ~ empty(C_297)
| empty('#skF_11'(powerset(C_297))) ),
inference(resolution,[status(thm)],[c_64,c_867]) ).
tff(c_72,plain,
empty('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_111,plain,
! [A_137] :
( ( empty_set = A_137 )
| ~ empty(A_137) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_120,plain,
empty_set = '#skF_13',
inference(resolution,[status(thm)],[c_72,c_111]) ).
tff(c_104,plain,
! [A_129] :
( ( empty_set = A_129 )
| ~ empty(A_129) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_121,plain,
! [A_129] :
( ( A_129 = '#skF_13' )
| ~ empty(A_129) ),
inference(demodulation,[status(thm),theory(equality)],[c_120,c_104]) ).
tff(c_944,plain,
! [C_298] :
( ( '#skF_11'(powerset(C_298)) = '#skF_13' )
| ~ empty(C_298) ),
inference(resolution,[status(thm)],[c_936,c_121]) ).
tff(c_178,plain,
! [A_154,B_155] :
( subset(A_154,B_155)
| ~ element(A_154,powerset(B_155)) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_183,plain,
! [B_155] : subset('#skF_11'(powerset(B_155)),B_155),
inference(resolution,[status(thm)],[c_64,c_178]) ).
tff(c_995,plain,
! [C_299] :
( subset('#skF_13',C_299)
| ~ empty(C_299) ),
inference(superposition,[status(thm),theory(equality)],[c_944,c_183]) ).
tff(c_98,plain,
! [A_121,B_122] :
( element(A_121,powerset(B_122))
| ~ subset(A_121,B_122) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_378,plain,
! [B_209,A_210,A_211] :
( ~ empty(B_209)
| ~ in(A_210,A_211)
| ~ subset(A_211,B_209) ),
inference(resolution,[status(thm)],[c_98,c_343]) ).
tff(c_383,plain,
! [B_209,A_8,B_9] :
( ~ empty(B_209)
| ~ subset(A_8,B_209)
| subset(A_8,B_9) ),
inference(resolution,[status(thm)],[c_12,c_378]) ).
tff(c_1014,plain,
! [B_9,C_299] :
( subset('#skF_13',B_9)
| ~ empty(C_299) ),
inference(resolution,[status(thm)],[c_995,c_383]) ).
tff(c_1016,plain,
! [C_299] : ~ empty(C_299),
inference(splitLeft,[status(thm)],[c_1014]) ).
tff(c_1026,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1016,c_72]) ).
tff(c_1088,plain,
! [B_302] : subset('#skF_13',B_302),
inference(splitRight,[status(thm)],[c_1014]) ).
tff(c_205,plain,
! [C_167,A_168,B_169] :
( relation(C_167)
| ~ element(C_167,powerset(cartesian_product2(A_168,B_169))) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_214,plain,
! [A_121,A_168,B_169] :
( relation(A_121)
| ~ subset(A_121,cartesian_product2(A_168,B_169)) ),
inference(resolution,[status(thm)],[c_98,c_205]) ).
tff(c_1110,plain,
relation('#skF_13'),
inference(resolution,[status(thm)],[c_1088,c_214]) ).
tff(c_26,plain,
! [A_53,C_89] :
( in(ordered_pair('#skF_9'(A_53,relation_rng(A_53),C_89),C_89),A_53)
| ~ in(C_89,relation_rng(A_53))
| ~ relation(A_53) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_1117,plain,
! [C_306] :
( element('#skF_13',powerset(C_306))
| ~ empty(C_306) ),
inference(superposition,[status(thm),theory(equality)],[c_944,c_64]) ).
tff(c_102,plain,
! [C_128,B_127,A_126] :
( ~ empty(C_128)
| ~ element(B_127,powerset(C_128))
| ~ in(A_126,B_127) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_1134,plain,
! [A_126,C_306] :
( ~ in(A_126,'#skF_13')
| ~ empty(C_306) ),
inference(resolution,[status(thm)],[c_1117,c_102]) ).
tff(c_1139,plain,
! [C_306] : ~ empty(C_306),
inference(splitLeft,[status(thm)],[c_1134]) ).
tff(c_1149,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1139,c_72]) ).
tff(c_1151,plain,
! [A_307] : ~ in(A_307,'#skF_13'),
inference(splitRight,[status(thm)],[c_1134]) ).
tff(c_1155,plain,
! [C_89] :
( ~ in(C_89,relation_rng('#skF_13'))
| ~ relation('#skF_13') ),
inference(resolution,[status(thm)],[c_26,c_1151]) ).
tff(c_1183,plain,
! [C_308] : ~ in(C_308,relation_rng('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_1110,c_1155]) ).
tff(c_1208,plain,
! [A_119] :
( empty(relation_rng('#skF_13'))
| ~ element(A_119,relation_rng('#skF_13')) ),
inference(resolution,[status(thm)],[c_94,c_1183]) ).
tff(c_1536,plain,
! [A_325] : ~ element(A_325,relation_rng('#skF_13')),
inference(splitLeft,[status(thm)],[c_1208]) ).
tff(c_1547,plain,
$false,
inference(resolution,[status(thm)],[c_64,c_1536]) ).
tff(c_1548,plain,
empty(relation_rng('#skF_13')),
inference(splitRight,[status(thm)],[c_1208]) ).
tff(c_1555,plain,
relation_rng('#skF_13') = '#skF_13',
inference(resolution,[status(thm)],[c_1548,c_121]) ).
tff(c_1403,plain,
! [A_319,B_320] :
( in(ordered_pair('#skF_7'(A_319,B_320),'#skF_6'(A_319,B_320)),A_319)
| in('#skF_8'(A_319,B_320),B_320)
| ( relation_rng(A_319) = B_320 )
| ~ relation(A_319) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_1150,plain,
! [A_126] : ~ in(A_126,'#skF_13'),
inference(splitRight,[status(thm)],[c_1134]) ).
tff(c_1415,plain,
! [B_320] :
( in('#skF_8'('#skF_13',B_320),B_320)
| ( relation_rng('#skF_13') = B_320 )
| ~ relation('#skF_13') ),
inference(resolution,[status(thm)],[c_1403,c_1150]) ).
tff(c_1463,plain,
! [B_320] :
( in('#skF_8'('#skF_13',B_320),B_320)
| ( relation_rng('#skF_13') = B_320 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1110,c_1415]) ).
tff(c_2369,plain,
! [B_320] :
( in('#skF_8'('#skF_13',B_320),B_320)
| ( B_320 = '#skF_13' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1555,c_1463]) ).
tff(c_14,plain,
! [C_49,A_13] :
( in(ordered_pair(C_49,'#skF_5'(A_13,relation_dom(A_13),C_49)),A_13)
| ~ in(C_49,relation_dom(A_13))
| ~ relation(A_13) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_1159,plain,
! [C_49] :
( ~ in(C_49,relation_dom('#skF_13'))
| ~ relation('#skF_13') ),
inference(resolution,[status(thm)],[c_14,c_1151]) ).
tff(c_1214,plain,
! [C_312] : ~ in(C_312,relation_dom('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_1110,c_1159]) ).
tff(c_1239,plain,
! [A_119] :
( empty(relation_dom('#skF_13'))
| ~ element(A_119,relation_dom('#skF_13')) ),
inference(resolution,[status(thm)],[c_94,c_1214]) ).
tff(c_1666,plain,
! [A_332] : ~ element(A_332,relation_dom('#skF_13')),
inference(splitLeft,[status(thm)],[c_1239]) ).
tff(c_1677,plain,
$false,
inference(resolution,[status(thm)],[c_64,c_1666]) ).
tff(c_1678,plain,
empty(relation_dom('#skF_13')),
inference(splitRight,[status(thm)],[c_1239]) ).
tff(c_1685,plain,
relation_dom('#skF_13') = '#skF_13',
inference(resolution,[status(thm)],[c_1678,c_121]) ).
tff(c_60,plain,
! [C_97,A_95,B_96] :
( element(C_97,powerset(cartesian_product2(A_95,B_96)))
| ~ relation_of2_as_subset(C_97,A_95,B_96) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_467,plain,
! [A_230,C_231,B_232] :
( element(A_230,C_231)
| ~ element(B_232,powerset(C_231))
| ~ in(A_230,B_232) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_2125,plain,
! [A_353,A_354,B_355,C_356] :
( element(A_353,cartesian_product2(A_354,B_355))
| ~ in(A_353,C_356)
| ~ relation_of2_as_subset(C_356,A_354,B_355) ),
inference(resolution,[status(thm)],[c_60,c_467]) ).
tff(c_187049,plain,
! [A_2812,A_2813,B_2814,B_2815] :
( element(A_2812,cartesian_product2(A_2813,B_2814))
| ~ relation_of2_as_subset(B_2815,A_2813,B_2814)
| empty(B_2815)
| ~ element(A_2812,B_2815) ),
inference(resolution,[status(thm)],[c_94,c_2125]) ).
tff(c_187055,plain,
! [A_2812] :
( element(A_2812,cartesian_product2('#skF_15','#skF_16'))
| empty('#skF_17')
| ~ element(A_2812,'#skF_17') ),
inference(resolution,[status(thm)],[c_90,c_187049]) ).
tff(c_187061,plain,
! [A_2816] :
( element(A_2816,cartesian_product2('#skF_15','#skF_16'))
| ~ element(A_2816,'#skF_17') ),
inference(negUnitSimplification,[status(thm)],[c_1822,c_187055]) ).
tff(c_373,plain,
! [B_205,D_206,A_207,C_208] :
( in(B_205,D_206)
| ~ in(ordered_pair(A_207,B_205),cartesian_product2(C_208,D_206)) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_377,plain,
! [B_205,D_206,C_208,A_207] :
( in(B_205,D_206)
| empty(cartesian_product2(C_208,D_206))
| ~ element(ordered_pair(A_207,B_205),cartesian_product2(C_208,D_206)) ),
inference(resolution,[status(thm)],[c_94,c_373]) ).
tff(c_187102,plain,
! [B_205,A_207] :
( in(B_205,'#skF_16')
| empty(cartesian_product2('#skF_15','#skF_16'))
| ~ element(ordered_pair(A_207,B_205),'#skF_17') ),
inference(resolution,[status(thm)],[c_187061,c_377]) ).
tff(c_187112,plain,
empty(cartesian_product2('#skF_15','#skF_16')),
inference(splitLeft,[status(thm)],[c_187102]) ).
tff(c_187361,plain,
cartesian_product2('#skF_15','#skF_16') = '#skF_13',
inference(resolution,[status(thm)],[c_187112,c_121]) ).
tff(c_1261,plain,
! [A_314,B_315] :
( in(ordered_pair('#skF_2'(A_314,B_315),'#skF_3'(A_314,B_315)),A_314)
| in('#skF_4'(A_314,B_315),B_315)
| ( relation_dom(A_314) = B_315 )
| ~ relation(A_314) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_1273,plain,
! [B_315] :
( in('#skF_4'('#skF_13',B_315),B_315)
| ( relation_dom('#skF_13') = B_315 )
| ~ relation('#skF_13') ),
inference(resolution,[status(thm)],[c_1261,c_1150]) ).
tff(c_1319,plain,
! [B_315] :
( in('#skF_4'('#skF_13',B_315),B_315)
| ( relation_dom('#skF_13') = B_315 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1110,c_1273]) ).
tff(c_2012,plain,
! [B_315] :
( in('#skF_4'('#skF_13',B_315),B_315)
| ( B_315 = '#skF_13' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1685,c_1319]) ).
tff(c_80,plain,
! [A_111] : subset(A_111,A_111),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_235,plain,
! [A_176,A_177,B_178] :
( relation(A_176)
| ~ subset(A_176,cartesian_product2(A_177,B_178)) ),
inference(resolution,[status(thm)],[c_98,c_205]) ).
tff(c_246,plain,
! [A_177,B_178] : relation(cartesian_product2(A_177,B_178)),
inference(resolution,[status(thm)],[c_80,c_235]) ).
tff(c_668,plain,
! [A_259,B_260,C_261,D_262] :
( in(ordered_pair(A_259,B_260),cartesian_product2(C_261,D_262))
| ~ in(B_260,D_262)
| ~ in(A_259,C_261) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_16,plain,
! [C_49,A_13,D_52] :
( in(C_49,relation_dom(A_13))
| ~ in(ordered_pair(C_49,D_52),A_13)
| ~ relation(A_13) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_674,plain,
! [A_259,C_261,D_262,B_260] :
( in(A_259,relation_dom(cartesian_product2(C_261,D_262)))
| ~ relation(cartesian_product2(C_261,D_262))
| ~ in(B_260,D_262)
| ~ in(A_259,C_261) ),
inference(resolution,[status(thm)],[c_668,c_16]) ).
tff(c_126487,plain,
! [A_2187,C_2188,D_2189,B_2190] :
( in(A_2187,relation_dom(cartesian_product2(C_2188,D_2189)))
| ~ in(B_2190,D_2189)
| ~ in(A_2187,C_2188) ),
inference(demodulation,[status(thm),theory(equality)],[c_246,c_674]) ).
tff(c_126589,plain,
! [A_2187,C_2188,B_315] :
( in(A_2187,relation_dom(cartesian_product2(C_2188,B_315)))
| ~ in(A_2187,C_2188)
| ( B_315 = '#skF_13' ) ),
inference(resolution,[status(thm)],[c_2012,c_126487]) ).
tff(c_187487,plain,
! [A_2187] :
( in(A_2187,relation_dom('#skF_13'))
| ~ in(A_2187,'#skF_15')
| ( '#skF_16' = '#skF_13' ) ),
inference(superposition,[status(thm),theory(equality)],[c_187361,c_126589]) ).
tff(c_187639,plain,
! [A_2187] :
( in(A_2187,'#skF_13')
| ~ in(A_2187,'#skF_15')
| ( '#skF_16' = '#skF_13' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1685,c_187487]) ).
tff(c_187640,plain,
! [A_2187] :
( ~ in(A_2187,'#skF_15')
| ( '#skF_16' = '#skF_13' ) ),
inference(negUnitSimplification,[status(thm)],[c_1150,c_187639]) ).
tff(c_191145,plain,
! [A_2858] : ~ in(A_2858,'#skF_15'),
inference(splitLeft,[status(thm)],[c_187640]) ).
tff(c_191278,plain,
'#skF_15' = '#skF_13',
inference(resolution,[status(thm)],[c_2369,c_191145]) ).
tff(c_191430,plain,
relation_of2_as_subset('#skF_17','#skF_13','#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_191278,c_90]) ).
tff(c_96,plain,
! [A_121,B_122] :
( subset(A_121,B_122)
| ~ element(A_121,powerset(B_122)) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_436,plain,
! [C_217,A_218,B_219] :
( subset(C_217,cartesian_product2(A_218,B_219))
| ~ relation_of2_as_subset(C_217,A_218,B_219) ),
inference(resolution,[status(thm)],[c_425,c_96]) ).
tff(c_276,plain,
! [C_185,B_186,A_187] :
( in(C_185,B_186)
| ~ in(C_185,A_187)
| ~ subset(A_187,B_186) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_845,plain,
! [A_290,B_291,B_292] :
( in(A_290,B_291)
| ~ subset(B_292,B_291)
| empty(B_292)
| ~ element(A_290,B_292) ),
inference(resolution,[status(thm)],[c_94,c_276]) ).
tff(c_175284,plain,
! [A_2711,A_2712,B_2713,C_2714] :
( in(A_2711,cartesian_product2(A_2712,B_2713))
| empty(C_2714)
| ~ element(A_2711,C_2714)
| ~ relation_of2_as_subset(C_2714,A_2712,B_2713) ),
inference(resolution,[status(thm)],[c_436,c_845]) ).
tff(c_175548,plain,
! [A_2717,A_2718,B_2719] :
( in('#skF_11'(A_2717),cartesian_product2(A_2718,B_2719))
| empty(A_2717)
| ~ relation_of2_as_subset(A_2717,A_2718,B_2719) ),
inference(resolution,[status(thm)],[c_64,c_175284]) ).
tff(c_175671,plain,
! [A_2718,B_2719,A_2717] :
( ~ empty(cartesian_product2(A_2718,B_2719))
| empty(A_2717)
| ~ relation_of2_as_subset(A_2717,A_2718,B_2719) ),
inference(resolution,[status(thm)],[c_175548,c_106]) ).
tff(c_187297,plain,
! [A_2717] :
( empty(A_2717)
| ~ relation_of2_as_subset(A_2717,'#skF_15','#skF_16') ),
inference(resolution,[status(thm)],[c_187112,c_175671]) ).
tff(c_192343,plain,
! [A_2871] :
( empty(A_2871)
| ~ relation_of2_as_subset(A_2871,'#skF_13','#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_191278,c_187297]) ).
tff(c_192346,plain,
empty('#skF_17'),
inference(resolution,[status(thm)],[c_191430,c_192343]) ).
tff(c_192358,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1822,c_192346]) ).
tff(c_192359,plain,
'#skF_16' = '#skF_13',
inference(splitRight,[status(thm)],[c_187640]) ).
tff(c_192363,plain,
relation_of2_as_subset('#skF_17','#skF_15','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_192359,c_90]) ).
tff(c_192915,plain,
! [A_2878] :
( empty(A_2878)
| ~ relation_of2_as_subset(A_2878,'#skF_15','#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_192359,c_187297]) ).
tff(c_192918,plain,
empty('#skF_17'),
inference(resolution,[status(thm)],[c_192363,c_192915]) ).
tff(c_192930,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1822,c_192918]) ).
tff(c_192932,plain,
~ empty(cartesian_product2('#skF_15','#skF_16')),
inference(splitRight,[status(thm)],[c_187102]) ).
tff(c_495,plain,
! [A_235,C_236,B_237,D_238] :
( in(A_235,C_236)
| ~ in(ordered_pair(A_235,B_237),cartesian_product2(C_236,D_238)) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_499,plain,
! [A_235,C_236,D_238,B_237] :
( in(A_235,C_236)
| empty(cartesian_product2(C_236,D_238))
| ~ element(ordered_pair(A_235,B_237),cartesian_product2(C_236,D_238)) ),
inference(resolution,[status(thm)],[c_94,c_495]) ).
tff(c_187103,plain,
! [A_235,B_237] :
( in(A_235,'#skF_15')
| empty(cartesian_product2('#skF_15','#skF_16'))
| ~ element(ordered_pair(A_235,B_237),'#skF_17') ),
inference(resolution,[status(thm)],[c_187061,c_499]) ).
tff(c_193263,plain,
! [A_2884,B_2885] :
( in(A_2884,'#skF_15')
| ~ element(ordered_pair(A_2884,B_2885),'#skF_17') ),
inference(negUnitSimplification,[status(thm)],[c_192932,c_187103]) ).
tff(c_193285,plain,
! [C_295] :
( in(C_295,'#skF_15')
| ~ in(C_295,relation_dom('#skF_17'))
| ~ relation('#skF_17') ),
inference(resolution,[status(thm)],[c_934,c_193263]) ).
tff(c_193298,plain,
! [C_2886] :
( in(C_2886,'#skF_15')
| ~ in(C_2886,relation_dom('#skF_17')) ),
inference(demodulation,[status(thm),theory(equality)],[c_449,c_193285]) ).
tff(c_193432,plain,
! [A_119] :
( in(A_119,'#skF_15')
| empty(relation_dom('#skF_17'))
| ~ element(A_119,relation_dom('#skF_17')) ),
inference(resolution,[status(thm)],[c_94,c_193298]) ).
tff(c_193741,plain,
! [A_2893] :
( in(A_2893,'#skF_15')
| ~ element(A_2893,relation_dom('#skF_17')) ),
inference(negUnitSimplification,[status(thm)],[c_275,c_193432]) ).
tff(c_201561,plain,
! [B_2963] :
( in('#skF_1'(relation_dom('#skF_17'),B_2963),'#skF_15')
| subset(relation_dom('#skF_17'),B_2963) ),
inference(resolution,[status(thm)],[c_264,c_193741]) ).
tff(c_10,plain,
! [A_8,B_9] :
( ~ in('#skF_1'(A_8,B_9),B_9)
| subset(A_8,B_9) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_201582,plain,
subset(relation_dom('#skF_17'),'#skF_15'),
inference(resolution,[status(thm)],[c_201561,c_10]) ).
tff(c_201602,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_129,c_129,c_201582]) ).
tff(c_201603,plain,
~ subset(relation_rng('#skF_17'),'#skF_16'),
inference(splitRight,[status(thm)],[c_88]) ).
tff(c_201665,plain,
! [A_2984,B_2985] :
( in('#skF_1'(A_2984,B_2985),A_2984)
| subset(A_2984,B_2985) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_201675,plain,
! [A_2984,B_2985] :
( element('#skF_1'(A_2984,B_2985),A_2984)
| subset(A_2984,B_2985) ),
inference(resolution,[status(thm)],[c_201665,c_92]) ).
tff(c_201677,plain,
! [A_2986,B_2987] :
( ~ empty(A_2986)
| subset(A_2986,B_2987) ),
inference(resolution,[status(thm)],[c_201665,c_106]) ).
tff(c_201681,plain,
~ empty(relation_rng('#skF_17')),
inference(resolution,[status(thm)],[c_201677,c_201603]) ).
tff(c_202026,plain,
! [C_3050,A_3051,B_3052] :
( element(C_3050,powerset(cartesian_product2(A_3051,B_3052)))
| ~ relation_of2_as_subset(C_3050,A_3051,B_3052) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_202053,plain,
! [C_3056,A_3057,B_3058] :
( relation(C_3056)
| ~ relation_of2_as_subset(C_3056,A_3057,B_3058) ),
inference(resolution,[status(thm)],[c_202026,c_4]) ).
tff(c_202065,plain,
relation('#skF_17'),
inference(resolution,[status(thm)],[c_90,c_202053]) ).
tff(c_230617,plain,
! [A_4179,C_4180] :
( in(ordered_pair('#skF_9'(A_4179,relation_rng(A_4179),C_4180),C_4180),A_4179)
| ~ in(C_4180,relation_rng(A_4179))
| ~ relation(A_4179) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_230689,plain,
! [A_4179,C_4180] :
( element(ordered_pair('#skF_9'(A_4179,relation_rng(A_4179),C_4180),C_4180),A_4179)
| ~ in(C_4180,relation_rng(A_4179))
| ~ relation(A_4179) ),
inference(resolution,[status(thm)],[c_230617,c_92]) ).
tff(c_230691,plain,
! [A_4181,C_4182] :
( ~ empty(A_4181)
| ~ in(C_4182,relation_rng(A_4181))
| ~ relation(A_4181) ),
inference(resolution,[status(thm)],[c_230617,c_106]) ).
tff(c_230722,plain,
! [A_4183,B_4184] :
( ~ empty(A_4183)
| ~ relation(A_4183)
| subset(relation_rng(A_4183),B_4184) ),
inference(resolution,[status(thm)],[c_12,c_230691]) ).
tff(c_230737,plain,
( ~ empty('#skF_17')
| ~ relation('#skF_17') ),
inference(resolution,[status(thm)],[c_230722,c_201603]) ).
tff(c_230745,plain,
~ empty('#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_202065,c_230737]) ).
tff(c_201676,plain,
! [A_2984,B_2985] :
( ~ empty(A_2984)
| subset(A_2984,B_2985) ),
inference(resolution,[status(thm)],[c_201665,c_106]) ).
tff(c_201721,plain,
! [C_3000,A_3001,B_3002] :
( relation(C_3000)
| ~ element(C_3000,powerset(cartesian_product2(A_3001,B_3002))) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_201733,plain,
! [A_3005,A_3006,B_3007] :
( relation(A_3005)
| ~ subset(A_3005,cartesian_product2(A_3006,B_3007)) ),
inference(resolution,[status(thm)],[c_98,c_201721]) ).
tff(c_201746,plain,
! [A_2984] :
( relation(A_2984)
| ~ empty(A_2984) ),
inference(resolution,[status(thm)],[c_201676,c_201733]) ).
tff(c_230341,plain,
! [C_4151,A_4152] :
( in(ordered_pair(C_4151,'#skF_5'(A_4152,relation_dom(A_4152),C_4151)),A_4152)
| ~ in(C_4151,relation_dom(A_4152))
| ~ relation(A_4152) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_230405,plain,
! [A_4153,C_4154] :
( ~ empty(A_4153)
| ~ in(C_4154,relation_dom(A_4153))
| ~ relation(A_4153) ),
inference(resolution,[status(thm)],[c_230341,c_106]) ).
tff(c_231444,plain,
! [A_4240,A_4241] :
( ~ empty(A_4240)
| ~ relation(A_4240)
| empty(relation_dom(A_4240))
| ~ element(A_4241,relation_dom(A_4240)) ),
inference(resolution,[status(thm)],[c_94,c_230405]) ).
tff(c_231469,plain,
! [A_4242] :
( ~ empty(A_4242)
| ~ relation(A_4242)
| empty(relation_dom(A_4242)) ),
inference(resolution,[status(thm)],[c_64,c_231444]) ).
tff(c_231483,plain,
! [A_4243] :
( ( relation_dom(A_4243) = '#skF_13' )
| ~ empty(A_4243)
| ~ relation(A_4243) ),
inference(resolution,[status(thm)],[c_231469,c_121]) ).
tff(c_231582,plain,
! [A_4246] :
( ( relation_dom(A_4246) = '#skF_13' )
| ~ empty(A_4246) ),
inference(resolution,[status(thm)],[c_201746,c_231483]) ).
tff(c_231590,plain,
relation_dom('#skF_13') = '#skF_13',
inference(resolution,[status(thm)],[c_72,c_231582]) ).
tff(c_230425,plain,
! [A_4153,B_9] :
( ~ empty(A_4153)
| ~ relation(A_4153)
| subset(relation_dom(A_4153),B_9) ),
inference(resolution,[status(thm)],[c_12,c_230405]) ).
tff(c_231611,plain,
! [B_9] :
( ~ empty('#skF_13')
| ~ relation('#skF_13')
| subset('#skF_13',B_9) ),
inference(superposition,[status(thm),theory(equality)],[c_231590,c_230425]) ).
tff(c_231633,plain,
! [B_9] :
( ~ relation('#skF_13')
| subset('#skF_13',B_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_72,c_231611]) ).
tff(c_231643,plain,
~ relation('#skF_13'),
inference(splitLeft,[status(thm)],[c_231633]) ).
tff(c_231735,plain,
~ empty('#skF_13'),
inference(resolution,[status(thm)],[c_201746,c_231643]) ).
tff(c_231739,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_72,c_231735]) ).
tff(c_231741,plain,
relation('#skF_13'),
inference(splitRight,[status(thm)],[c_231633]) ).
tff(c_231961,plain,
! [A_4255,B_4256] :
( in(ordered_pair('#skF_2'(A_4255,B_4256),'#skF_3'(A_4255,B_4256)),A_4255)
| in('#skF_4'(A_4255,B_4256),B_4256)
| ( relation_dom(A_4255) = B_4256 )
| ~ relation(A_4255) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_230404,plain,
! [A_4152,C_4151] :
( ~ empty(A_4152)
| ~ in(C_4151,relation_dom(A_4152))
| ~ relation(A_4152) ),
inference(resolution,[status(thm)],[c_230341,c_106]) ).
tff(c_231614,plain,
! [C_4151] :
( ~ empty('#skF_13')
| ~ in(C_4151,'#skF_13')
| ~ relation('#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_231590,c_230404]) ).
tff(c_231635,plain,
! [C_4151] :
( ~ in(C_4151,'#skF_13')
| ~ relation('#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_72,c_231614]) ).
tff(c_231823,plain,
! [C_4151] : ~ in(C_4151,'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_231741,c_231635]) ).
tff(c_231969,plain,
! [B_4256] :
( in('#skF_4'('#skF_13',B_4256),B_4256)
| ( relation_dom('#skF_13') = B_4256 )
| ~ relation('#skF_13') ),
inference(resolution,[status(thm)],[c_231961,c_231823]) ).
tff(c_232038,plain,
! [B_4256] :
( in('#skF_4'('#skF_13',B_4256),B_4256)
| ( B_4256 = '#skF_13' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_231741,c_231590,c_231969]) ).
tff(c_202038,plain,
! [A_3053,C_3054,B_3055] :
( element(A_3053,C_3054)
| ~ element(B_3055,powerset(C_3054))
| ~ in(A_3053,B_3055) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_232965,plain,
! [A_4278,A_4279,B_4280,C_4281] :
( element(A_4278,cartesian_product2(A_4279,B_4280))
| ~ in(A_4278,C_4281)
| ~ relation_of2_as_subset(C_4281,A_4279,B_4280) ),
inference(resolution,[status(thm)],[c_60,c_202038]) ).
tff(c_404938,plain,
! [A_6732,A_6733,B_6734,B_6735] :
( element(A_6732,cartesian_product2(A_6733,B_6734))
| ~ relation_of2_as_subset(B_6735,A_6733,B_6734)
| empty(B_6735)
| ~ element(A_6732,B_6735) ),
inference(resolution,[status(thm)],[c_94,c_232965]) ).
tff(c_404944,plain,
! [A_6732] :
( element(A_6732,cartesian_product2('#skF_15','#skF_16'))
| empty('#skF_17')
| ~ element(A_6732,'#skF_17') ),
inference(resolution,[status(thm)],[c_90,c_404938]) ).
tff(c_404950,plain,
! [A_6736] :
( element(A_6736,cartesian_product2('#skF_15','#skF_16'))
| ~ element(A_6736,'#skF_17') ),
inference(negUnitSimplification,[status(thm)],[c_230745,c_404944]) ).
tff(c_202017,plain,
! [B_3046,D_3047,A_3048,C_3049] :
( in(B_3046,D_3047)
| ~ in(ordered_pair(A_3048,B_3046),cartesian_product2(C_3049,D_3047)) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_202021,plain,
! [B_3046,D_3047,C_3049,A_3048] :
( in(B_3046,D_3047)
| empty(cartesian_product2(C_3049,D_3047))
| ~ element(ordered_pair(A_3048,B_3046),cartesian_product2(C_3049,D_3047)) ),
inference(resolution,[status(thm)],[c_94,c_202017]) ).
tff(c_405001,plain,
! [B_3046,A_3048] :
( in(B_3046,'#skF_16')
| empty(cartesian_product2('#skF_15','#skF_16'))
| ~ element(ordered_pair(A_3048,B_3046),'#skF_17') ),
inference(resolution,[status(thm)],[c_404950,c_202021]) ).
tff(c_405339,plain,
empty(cartesian_product2('#skF_15','#skF_16')),
inference(splitLeft,[status(thm)],[c_405001]) ).
tff(c_201749,plain,
! [A_3006,B_3007] : relation(cartesian_product2(A_3006,B_3007)),
inference(resolution,[status(thm)],[c_80,c_201733]) ).
tff(c_202254,plain,
! [A_3101,C_3102] :
( in(ordered_pair('#skF_9'(A_3101,relation_rng(A_3101),C_3102),C_3102),A_3101)
| ~ in(C_3102,relation_rng(A_3101))
| ~ relation(A_3101) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_202339,plain,
! [A_3103,C_3104] :
( ~ empty(A_3103)
| ~ in(C_3104,relation_rng(A_3103))
| ~ relation(A_3103) ),
inference(resolution,[status(thm)],[c_202254,c_106]) ).
tff(c_220400,plain,
! [A_3807,A_3808] :
( ~ empty(A_3807)
| ~ relation(A_3807)
| empty(relation_rng(A_3807))
| ~ element(A_3808,relation_rng(A_3807)) ),
inference(resolution,[status(thm)],[c_94,c_202339]) ).
tff(c_220428,plain,
! [A_3811] :
( ~ empty(A_3811)
| ~ relation(A_3811)
| empty(relation_rng(A_3811)) ),
inference(resolution,[status(thm)],[c_64,c_220400]) ).
tff(c_220442,plain,
! [A_3812] :
( ( relation_rng(A_3812) = '#skF_13' )
| ~ empty(A_3812)
| ~ relation(A_3812) ),
inference(resolution,[status(thm)],[c_220428,c_121]) ).
tff(c_220483,plain,
! [A_3813] :
( ( relation_rng(A_3813) = '#skF_13' )
| ~ empty(A_3813) ),
inference(resolution,[status(thm)],[c_201746,c_220442]) ).
tff(c_220491,plain,
relation_rng('#skF_13') = '#skF_13',
inference(resolution,[status(thm)],[c_72,c_220483]) ).
tff(c_202354,plain,
! [A_3103,B_9] :
( ~ empty(A_3103)
| ~ relation(A_3103)
| subset(relation_rng(A_3103),B_9) ),
inference(resolution,[status(thm)],[c_12,c_202339]) ).
tff(c_220507,plain,
! [B_9] :
( ~ empty('#skF_13')
| ~ relation('#skF_13')
| subset('#skF_13',B_9) ),
inference(superposition,[status(thm),theory(equality)],[c_220491,c_202354]) ).
tff(c_220521,plain,
! [B_9] :
( ~ relation('#skF_13')
| subset('#skF_13',B_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_72,c_220507]) ).
tff(c_220526,plain,
~ relation('#skF_13'),
inference(splitLeft,[status(thm)],[c_220521]) ).
tff(c_220529,plain,
~ empty('#skF_13'),
inference(resolution,[status(thm)],[c_201746,c_220526]) ).
tff(c_220533,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_72,c_220529]) ).
tff(c_220535,plain,
relation('#skF_13'),
inference(splitRight,[status(thm)],[c_220521]) ).
tff(c_221454,plain,
! [A_3849,B_3850] :
( in(ordered_pair('#skF_7'(A_3849,B_3850),'#skF_6'(A_3849,B_3850)),A_3849)
| in('#skF_8'(A_3849,B_3850),B_3850)
| ( relation_rng(A_3849) = B_3850 )
| ~ relation(A_3849) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_202312,plain,
! [A_3101,C_3102] :
( ~ empty(A_3101)
| ~ in(C_3102,relation_rng(A_3101))
| ~ relation(A_3101) ),
inference(resolution,[status(thm)],[c_202254,c_106]) ).
tff(c_220510,plain,
! [C_3102] :
( ~ empty('#skF_13')
| ~ in(C_3102,'#skF_13')
| ~ relation('#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_220491,c_202312]) ).
tff(c_220523,plain,
! [C_3102] :
( ~ in(C_3102,'#skF_13')
| ~ relation('#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_72,c_220510]) ).
tff(c_220570,plain,
! [C_3102] : ~ in(C_3102,'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_220535,c_220523]) ).
tff(c_221458,plain,
! [B_3850] :
( in('#skF_8'('#skF_13',B_3850),B_3850)
| ( relation_rng('#skF_13') = B_3850 )
| ~ relation('#skF_13') ),
inference(resolution,[status(thm)],[c_221454,c_220570]) ).
tff(c_221520,plain,
! [B_3850] :
( in('#skF_8'('#skF_13',B_3850),B_3850)
| ( B_3850 = '#skF_13' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_220535,c_220491,c_221458]) ).
tff(c_201604,plain,
subset(relation_dom('#skF_17'),'#skF_15'),
inference(splitRight,[status(thm)],[c_88]) ).
tff(c_201833,plain,
! [C_3028,B_3029,A_3030] :
( in(C_3028,B_3029)
| ~ in(C_3028,A_3030)
| ~ subset(A_3030,B_3029) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_202231,plain,
! [A_3098,B_3099,B_3100] :
( in(A_3098,B_3099)
| ~ subset(B_3100,B_3099)
| empty(B_3100)
| ~ element(A_3098,B_3100) ),
inference(resolution,[status(thm)],[c_94,c_201833]) ).
tff(c_202251,plain,
! [A_3098] :
( in(A_3098,'#skF_15')
| empty(relation_dom('#skF_17'))
| ~ element(A_3098,relation_dom('#skF_17')) ),
inference(resolution,[status(thm)],[c_201604,c_202231]) ).
tff(c_202253,plain,
empty(relation_dom('#skF_17')),
inference(splitLeft,[status(thm)],[c_202251]) ).
tff(c_202319,plain,
relation_dom('#skF_17') = '#skF_13',
inference(resolution,[status(thm)],[c_202253,c_121]) ).
tff(c_229977,plain,
! [A_4136,C_4137] :
( in('#skF_9'(A_4136,relation_rng(A_4136),C_4137),relation_dom(A_4136))
| ~ in(C_4137,relation_rng(A_4136))
| ~ relation(A_4136) ),
inference(resolution,[status(thm)],[c_202254,c_16]) ).
tff(c_230039,plain,
! [C_4137] :
( in('#skF_9'('#skF_17',relation_rng('#skF_17'),C_4137),'#skF_13')
| ~ in(C_4137,relation_rng('#skF_17'))
| ~ relation('#skF_17') ),
inference(superposition,[status(thm),theory(equality)],[c_202319,c_229977]) ).
tff(c_230063,plain,
! [C_4137] :
( in('#skF_9'('#skF_17',relation_rng('#skF_17'),C_4137),'#skF_13')
| ~ in(C_4137,relation_rng('#skF_17')) ),
inference(demodulation,[status(thm),theory(equality)],[c_202065,c_230039]) ).
tff(c_230065,plain,
! [C_4138] : ~ in(C_4138,relation_rng('#skF_17')),
inference(negUnitSimplification,[status(thm)],[c_220570,c_230063]) ).
tff(c_230129,plain,
relation_rng('#skF_17') = '#skF_13',
inference(resolution,[status(thm)],[c_221520,c_230065]) ).
tff(c_230144,plain,
~ empty('#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_230129,c_201681]) ).
tff(c_230150,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_72,c_230144]) ).
tff(c_230153,plain,
! [A_4139] :
( in(A_4139,'#skF_15')
| ~ element(A_4139,relation_dom('#skF_17')) ),
inference(splitRight,[status(thm)],[c_202251]) ).
tff(c_230163,plain,
in('#skF_11'(relation_dom('#skF_17')),'#skF_15'),
inference(resolution,[status(thm)],[c_64,c_230153]) ).
tff(c_202169,plain,
! [A_3087,B_3088,C_3089,D_3090] :
( in(ordered_pair(A_3087,B_3088),cartesian_product2(C_3089,D_3090))
| ~ in(B_3088,D_3090)
| ~ in(A_3087,C_3089) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_28,plain,
! [C_89,A_53,D_92] :
( in(C_89,relation_rng(A_53))
| ~ in(ordered_pair(D_92,C_89),A_53)
| ~ relation(A_53) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_202172,plain,
! [B_3088,C_3089,D_3090,A_3087] :
( in(B_3088,relation_rng(cartesian_product2(C_3089,D_3090)))
| ~ relation(cartesian_product2(C_3089,D_3090))
| ~ in(B_3088,D_3090)
| ~ in(A_3087,C_3089) ),
inference(resolution,[status(thm)],[c_202169,c_28]) ).
tff(c_352197,plain,
! [B_5987,C_5988,D_5989,A_5990] :
( in(B_5987,relation_rng(cartesian_product2(C_5988,D_5989)))
| ~ in(B_5987,D_5989)
| ~ in(A_5990,C_5988) ),
inference(demodulation,[status(thm),theory(equality)],[c_201749,c_202172]) ).
tff(c_352330,plain,
! [B_5991,D_5992] :
( in(B_5991,relation_rng(cartesian_product2('#skF_15',D_5992)))
| ~ in(B_5991,D_5992) ),
inference(resolution,[status(thm)],[c_230163,c_352197]) ).
tff(c_230690,plain,
! [A_4179,C_4180] :
( ~ empty(A_4179)
| ~ in(C_4180,relation_rng(A_4179))
| ~ relation(A_4179) ),
inference(resolution,[status(thm)],[c_230617,c_106]) ).
tff(c_352364,plain,
! [D_5992,B_5991] :
( ~ empty(cartesian_product2('#skF_15',D_5992))
| ~ relation(cartesian_product2('#skF_15',D_5992))
| ~ in(B_5991,D_5992) ),
inference(resolution,[status(thm)],[c_352330,c_230690]) ).
tff(c_352419,plain,
! [D_5992,B_5991] :
( ~ empty(cartesian_product2('#skF_15',D_5992))
| ~ in(B_5991,D_5992) ),
inference(demodulation,[status(thm),theory(equality)],[c_201749,c_352364]) ).
tff(c_405520,plain,
! [B_6739] : ~ in(B_6739,'#skF_16'),
inference(resolution,[status(thm)],[c_405339,c_352419]) ).
tff(c_405679,plain,
'#skF_16' = '#skF_13',
inference(resolution,[status(thm)],[c_232038,c_405520]) ).
tff(c_405694,plain,
relation_of2_as_subset('#skF_17','#skF_15','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_405679,c_90]) ).
tff(c_202037,plain,
! [C_3050,A_3051,B_3052] :
( subset(C_3050,cartesian_product2(A_3051,B_3052))
| ~ relation_of2_as_subset(C_3050,A_3051,B_3052) ),
inference(resolution,[status(thm)],[c_202026,c_96]) ).
tff(c_386046,plain,
! [A_6586,A_6587,B_6588,C_6589] :
( in(A_6586,cartesian_product2(A_6587,B_6588))
| empty(C_6589)
| ~ element(A_6586,C_6589)
| ~ relation_of2_as_subset(C_6589,A_6587,B_6588) ),
inference(resolution,[status(thm)],[c_202037,c_202231]) ).
tff(c_386255,plain,
! [A_6590,A_6591,B_6592] :
( in('#skF_11'(A_6590),cartesian_product2(A_6591,B_6592))
| empty(A_6590)
| ~ relation_of2_as_subset(A_6590,A_6591,B_6592) ),
inference(resolution,[status(thm)],[c_64,c_386046]) ).
tff(c_386354,plain,
! [A_6591,B_6592,A_6590] :
( ~ empty(cartesian_product2(A_6591,B_6592))
| empty(A_6590)
| ~ relation_of2_as_subset(A_6590,A_6591,B_6592) ),
inference(resolution,[status(thm)],[c_386255,c_106]) ).
tff(c_405461,plain,
! [A_6590] :
( empty(A_6590)
| ~ relation_of2_as_subset(A_6590,'#skF_15','#skF_16') ),
inference(resolution,[status(thm)],[c_405339,c_386354]) ).
tff(c_406695,plain,
! [A_6746] :
( empty(A_6746)
| ~ relation_of2_as_subset(A_6746,'#skF_15','#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_405679,c_405461]) ).
tff(c_406698,plain,
empty('#skF_17'),
inference(resolution,[status(thm)],[c_405694,c_406695]) ).
tff(c_406710,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_230745,c_406698]) ).
tff(c_406713,plain,
! [B_6747,A_6748] :
( in(B_6747,'#skF_16')
| ~ element(ordered_pair(A_6748,B_6747),'#skF_17') ),
inference(splitRight,[status(thm)],[c_405001]) ).
tff(c_406735,plain,
! [C_4180] :
( in(C_4180,'#skF_16')
| ~ in(C_4180,relation_rng('#skF_17'))
| ~ relation('#skF_17') ),
inference(resolution,[status(thm)],[c_230689,c_406713]) ).
tff(c_406748,plain,
! [C_6749] :
( in(C_6749,'#skF_16')
| ~ in(C_6749,relation_rng('#skF_17')) ),
inference(demodulation,[status(thm),theory(equality)],[c_202065,c_406735]) ).
tff(c_406902,plain,
! [A_119] :
( in(A_119,'#skF_16')
| empty(relation_rng('#skF_17'))
| ~ element(A_119,relation_rng('#skF_17')) ),
inference(resolution,[status(thm)],[c_94,c_406748]) ).
tff(c_407121,plain,
! [A_6752] :
( in(A_6752,'#skF_16')
| ~ element(A_6752,relation_rng('#skF_17')) ),
inference(negUnitSimplification,[status(thm)],[c_201681,c_406902]) ).
tff(c_414544,plain,
! [B_6845] :
( in('#skF_1'(relation_rng('#skF_17'),B_6845),'#skF_16')
| subset(relation_rng('#skF_17'),B_6845) ),
inference(resolution,[status(thm)],[c_201675,c_407121]) ).
tff(c_414565,plain,
subset(relation_rng('#skF_17'),'#skF_16'),
inference(resolution,[status(thm)],[c_414544,c_10]) ).
tff(c_414585,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_201603,c_201603,c_414565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU262+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/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
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 12:08:08 EDT 2023
% 0.15/0.35 % CPUTime :
% 65.24/50.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 65.24/50.38
% 65.24/50.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 65.43/50.43
% 65.43/50.43 Inference rules
% 65.43/50.43 ----------------------
% 65.43/50.43 #Ref : 0
% 65.43/50.43 #Sup : 106082
% 65.43/50.43 #Fact : 0
% 65.43/50.43 #Define : 0
% 65.43/50.43 #Split : 162
% 65.43/50.43 #Chain : 0
% 65.43/50.43 #Close : 0
% 65.43/50.43
% 65.43/50.43 Ordering : KBO
% 65.43/50.43
% 65.43/50.43 Simplification rules
% 65.43/50.43 ----------------------
% 65.43/50.43 #Subsume : 39261
% 65.43/50.43 #Demod : 59264
% 65.43/50.43 #Tautology : 27790
% 65.43/50.43 #SimpNegUnit : 2634
% 65.43/50.43 #BackRed : 543
% 65.43/50.43
% 65.43/50.43 #Partial instantiations: 0
% 65.43/50.43 #Strategies tried : 1
% 65.43/50.43
% 65.43/50.43 Timing (in seconds)
% 65.43/50.43 ----------------------
% 65.43/50.44 Preprocessing : 0.57
% 65.43/50.44 Parsing : 0.30
% 65.43/50.44 CNF conversion : 0.05
% 65.43/50.44 Main loop : 48.74
% 65.43/50.44 Inferencing : 7.32
% 65.43/50.44 Reduction : 14.44
% 65.43/50.44 Demodulation : 10.36
% 65.43/50.44 BG Simplification : 0.40
% 65.43/50.44 Subsumption : 22.32
% 65.43/50.44 Abstraction : 0.69
% 65.43/50.44 MUC search : 0.00
% 65.43/50.44 Cooper : 0.00
% 65.43/50.44 Total : 49.42
% 65.43/50.44 Index Insertion : 0.00
% 65.43/50.44 Index Deletion : 0.00
% 65.43/50.44 Index Matching : 0.00
% 65.43/50.44 BG Taut test : 0.00
%------------------------------------------------------------------------------