%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET659+3 : TPTP v9.0.0. Released v2.2.0.
% 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 08:39:01 PM UTC 2025
% Result : Theorem 8.85s 3.05s
% Output : CNFRefutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 245 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 260 ( 106 ~; 98 |; 8 &)
% ( 8 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 7 con; 0-3 aty)
% Number of variables : 143 ( 141 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > range > domain > unordered_pair > relation_type > ordered_pair > cross_product > #nlpp > subset_type > singleton > range_of > power_set > member_type > domain_of > set_type > binary_relation_type > #skF_9 > #skF_5 > #skF_11 > #skF_6 > #skF_18 > #skF_15 > #skF_3 > #skF_16 > #skF_14 > #skF_10 > #skF_8 > #skF_13 > #skF_4 > #skF_17 > #skF_2 > #skF_12 > #skF_7 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
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(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
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(range,type,
range: ( $i * $i * $i ) > $i ).
tff(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(binary_relation_type,type,
binary_relation_type: $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_396,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) )
<=> ( domain(C,B,D) = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_22) ).
tff(f_374,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
tff(f_117,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
tff(f_309,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
tff(f_181,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
tff(f_338,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( domain(B,C,D) = domain_of(D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p30) ).
tff(f_230,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
tff(f_59,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(ordered_pair(B,C),D)
=> ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
tff(f_138,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
tff(f_349,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
tff(f_258,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
tff(f_194,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
tff(f_271,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
tff(f_250,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
tff(f_39,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,domain_of(B))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(c_140,plain,
ilf_type('#skF_16',relation_type('#skF_15','#skF_14')),
inference(cnfTransformation,[status(thm)],[f_396]) ).
tff(c_138,plain,
! [B_199] : ilf_type(B_199,set_type),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_30,plain,
! [E_69,B_59,C_65] :
( ilf_type(E_69,subset_type(cross_product(B_59,C_65)))
| ~ ilf_type(E_69,relation_type(B_59,C_65))
| ~ ilf_type(C_65,set_type)
| ~ ilf_type(B_59,set_type) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_4389,plain,
! [E_665,B_666,C_667] :
( ilf_type(E_665,subset_type(cross_product(B_666,C_667)))
| ~ ilf_type(E_665,relation_type(B_666,C_667)) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_30]) ).
tff(c_120,plain,
! [D_165,B_159,C_163] :
( relation_like(D_165)
| ~ ilf_type(D_165,subset_type(cross_product(B_159,C_163)))
| ~ ilf_type(C_163,set_type)
| ~ ilf_type(B_159,set_type) ),
inference(cnfTransformation,[status(thm)],[f_309]) ).
tff(c_207,plain,
! [D_165,B_159,C_163] :
( relation_like(D_165)
| ~ ilf_type(D_165,subset_type(cross_product(B_159,C_163))) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_120]) ).
tff(c_4399,plain,
! [E_668,B_669,C_670] :
( relation_like(E_668)
| ~ ilf_type(E_668,relation_type(B_669,C_670)) ),
inference(resolution,[status(thm)],[c_4389,c_207]) ).
tff(c_4407,plain,
relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_140,c_4399]) ).
tff(c_52,plain,
! [B_90] :
( ilf_type(B_90,binary_relation_type)
| ~ relation_like(B_90)
| ~ ilf_type(B_90,set_type) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_263,plain,
! [B_90] :
( ilf_type(B_90,binary_relation_type)
| ~ relation_like(B_90) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_52]) ).
tff(c_130,plain,
! [B_171,C_175,D_177] :
( ( domain(B_171,C_175,D_177) = domain_of(D_177) )
| ~ ilf_type(D_177,relation_type(B_171,C_175))
| ~ ilf_type(C_175,set_type)
| ~ ilf_type(B_171,set_type) ),
inference(cnfTransformation,[status(thm)],[f_338]) ).
tff(c_1084,plain,
! [B_390,C_391,D_392] :
( ( domain(B_390,C_391,D_392) = domain_of(D_392) )
| ~ ilf_type(D_392,relation_type(B_390,C_391)) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_130]) ).
tff(c_1112,plain,
domain('#skF_15','#skF_14','#skF_16') = domain_of('#skF_16'),
inference(resolution,[status(thm)],[c_140,c_1084]) ).
tff(c_152,plain,
( ( domain('#skF_15','#skF_14','#skF_16') != '#skF_15' )
| member('#skF_18','#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_396]) ).
tff(c_315,plain,
domain('#skF_15','#skF_14','#skF_16') != '#skF_15',
inference(splitLeft,[status(thm)],[c_152]) ).
tff(c_1113,plain,
domain_of('#skF_16') != '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_1112,c_315]) ).
tff(c_84,plain,
! [B_106,C_112] :
( member('#skF_7'(B_106,C_112),B_106)
| subset(B_106,C_112)
| ~ ilf_type(C_112,set_type)
| ~ ilf_type(B_106,set_type) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_243,plain,
! [B_106,C_112] :
( member('#skF_7'(B_106,C_112),B_106)
| subset(B_106,C_112) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_84]) ).
tff(c_871,plain,
! [E_358,B_359,C_360] :
( ilf_type(E_358,subset_type(cross_product(B_359,C_360)))
| ~ ilf_type(E_358,relation_type(B_359,C_360)) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_30]) ).
tff(c_890,plain,
! [E_361,B_362,C_363] :
( relation_like(E_361)
| ~ ilf_type(E_361,relation_type(B_362,C_363)) ),
inference(resolution,[status(thm)],[c_871,c_207]) ).
tff(c_912,plain,
relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_140,c_890]) ).
tff(c_166,plain,
! [E_246] :
( member(ordered_pair(E_246,'#skF_17'(E_246)),'#skF_16')
| ~ member(E_246,'#skF_15')
| ~ ilf_type(E_246,set_type)
| ( domain('#skF_15','#skF_14','#skF_16') = '#skF_15' ) ),
inference(cnfTransformation,[status(thm)],[f_396]) ).
tff(c_177,plain,
! [E_246] :
( member(ordered_pair(E_246,'#skF_17'(E_246)),'#skF_16')
| ~ member(E_246,'#skF_15')
| ( domain('#skF_15','#skF_14','#skF_16') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_166]) ).
tff(c_504,plain,
! [E_246] :
( member(ordered_pair(E_246,'#skF_17'(E_246)),'#skF_16')
| ~ member(E_246,'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_315,c_177]) ).
tff(c_10,plain,
! [C_16,D_18,B_12] :
( member(C_16,range_of(D_18))
| ~ member(ordered_pair(B_12,C_16),D_18)
| ~ ilf_type(D_18,binary_relation_type)
| ~ ilf_type(C_16,set_type)
| ~ ilf_type(B_12,set_type) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_1789,plain,
! [C_450,D_451,B_452] :
( member(C_450,range_of(D_451))
| ~ member(ordered_pair(B_452,C_450),D_451)
| ~ ilf_type(D_451,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_10]) ).
tff(c_1814,plain,
! [E_246] :
( member('#skF_17'(E_246),range_of('#skF_16'))
| ~ ilf_type('#skF_16',binary_relation_type)
| ~ member(E_246,'#skF_15') ),
inference(resolution,[status(thm)],[c_504,c_1789]) ).
tff(c_1856,plain,
~ ilf_type('#skF_16',binary_relation_type),
inference(splitLeft,[status(thm)],[c_1814]) ).
tff(c_1859,plain,
~ relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_263,c_1856]) ).
tff(c_1863,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_912,c_1859]) ).
tff(c_1865,plain,
ilf_type('#skF_16',binary_relation_type),
inference(splitRight,[status(thm)],[c_1814]) ).
tff(c_12,plain,
! [B_12,D_18,C_16] :
( member(B_12,domain_of(D_18))
| ~ member(ordered_pair(B_12,C_16),D_18)
| ~ ilf_type(D_18,binary_relation_type)
| ~ ilf_type(C_16,set_type)
| ~ ilf_type(B_12,set_type) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_2035,plain,
! [B_474,D_475,C_476] :
( member(B_474,domain_of(D_475))
| ~ member(ordered_pair(B_474,C_476),D_475)
| ~ ilf_type(D_475,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_12]) ).
tff(c_2052,plain,
! [E_246] :
( member(E_246,domain_of('#skF_16'))
| ~ ilf_type('#skF_16',binary_relation_type)
| ~ member(E_246,'#skF_15') ),
inference(resolution,[status(thm)],[c_504,c_2035]) ).
tff(c_2070,plain,
! [E_477] :
( member(E_477,domain_of('#skF_16'))
| ~ member(E_477,'#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_1865,c_2052]) ).
tff(c_82,plain,
! [B_106,C_112] :
( ~ member('#skF_7'(B_106,C_112),C_112)
| subset(B_106,C_112)
| ~ ilf_type(C_112,set_type)
| ~ ilf_type(B_106,set_type) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_245,plain,
! [B_106,C_112] :
( ~ member('#skF_7'(B_106,C_112),C_112)
| subset(B_106,C_112) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_82]) ).
tff(c_2111,plain,
! [B_479] :
( subset(B_479,domain_of('#skF_16'))
| ~ member('#skF_7'(B_479,domain_of('#skF_16')),'#skF_15') ),
inference(resolution,[status(thm)],[c_2070,c_245]) ).
tff(c_2116,plain,
subset('#skF_15',domain_of('#skF_16')),
inference(resolution,[status(thm)],[c_243,c_2111]) ).
tff(c_36,plain,
! [C_78,B_76] :
( ( C_78 = B_76 )
| ~ subset(C_78,B_76)
| ~ subset(B_76,C_78)
| ~ ilf_type(C_78,set_type)
| ~ ilf_type(B_76,set_type) ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_278,plain,
! [C_78,B_76] :
( ( C_78 = B_76 )
| ~ subset(C_78,B_76)
| ~ subset(B_76,C_78) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_36]) ).
tff(c_2132,plain,
( ( domain_of('#skF_16') = '#skF_15' )
| ~ subset(domain_of('#skF_16'),'#skF_15') ),
inference(resolution,[status(thm)],[c_2116,c_278]) ).
tff(c_2142,plain,
~ subset(domain_of('#skF_16'),'#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_1113,c_2132]) ).
tff(c_132,plain,
! [B_178,C_182,D_184] :
( ilf_type(domain(B_178,C_182,D_184),subset_type(B_178))
| ~ ilf_type(D_184,relation_type(B_178,C_182))
| ~ ilf_type(C_182,set_type)
| ~ ilf_type(B_178,set_type) ),
inference(cnfTransformation,[status(thm)],[f_349]) ).
tff(c_2169,plain,
! [B_481,C_482,D_483] :
( ilf_type(domain(B_481,C_482,D_483),subset_type(B_481))
| ~ ilf_type(D_483,relation_type(B_481,C_482)) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_132]) ).
tff(c_2189,plain,
( ilf_type(domain_of('#skF_16'),subset_type('#skF_15'))
| ~ ilf_type('#skF_16',relation_type('#skF_15','#skF_14')) ),
inference(superposition,[status(thm),theory(equality)],[c_1112,c_2169]) ).
tff(c_2197,plain,
ilf_type(domain_of('#skF_16'),subset_type('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_2189]) ).
tff(c_100,plain,
! [B_127] :
( ~ empty(power_set(B_127))
| ~ ilf_type(B_127,set_type) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_227,plain,
! [B_127] : ~ empty(power_set(B_127)),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_100]) ).
tff(c_62,plain,
! [C_93,B_91] :
( ilf_type(C_93,member_type(power_set(B_91)))
| ~ ilf_type(C_93,subset_type(B_91))
| ~ ilf_type(C_93,set_type)
| ~ ilf_type(B_91,set_type) ),
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_257,plain,
! [C_93,B_91] :
( ilf_type(C_93,member_type(power_set(B_91)))
| ~ ilf_type(C_93,subset_type(B_91)) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_62]) ).
tff(c_104,plain,
! [B_128,C_130] :
( member(B_128,C_130)
| ~ ilf_type(B_128,member_type(C_130))
| ~ ilf_type(C_130,set_type)
| empty(C_130)
| ~ ilf_type(B_128,set_type) ),
inference(cnfTransformation,[status(thm)],[f_271]) ).
tff(c_544,plain,
! [B_307,C_308] :
( member(B_307,C_308)
| ~ ilf_type(B_307,member_type(C_308))
| empty(C_308) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_104]) ).
tff(c_547,plain,
! [C_93,B_91] :
( member(C_93,power_set(B_91))
| empty(power_set(B_91))
| ~ ilf_type(C_93,subset_type(B_91)) ),
inference(resolution,[status(thm)],[c_257,c_544]) ).
tff(c_553,plain,
! [C_93,B_91] :
( member(C_93,power_set(B_91))
| ~ ilf_type(C_93,subset_type(B_91)) ),
inference(negUnitSimplification,[status(thm)],[c_227,c_547]) ).
tff(c_90,plain,
! [D_126,C_123,B_117] :
( member(D_126,C_123)
| ~ member(D_126,B_117)
| ~ ilf_type(D_126,set_type)
| ~ member(B_117,power_set(C_123))
| ~ ilf_type(C_123,set_type)
| ~ ilf_type(B_117,set_type) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_649,plain,
! [D_323,C_324,B_325] :
( member(D_323,C_324)
| ~ member(D_323,B_325)
| ~ member(B_325,power_set(C_324)) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_138,c_90]) ).
tff(c_3307,plain,
! [B_563,C_564,C_565] :
( member('#skF_7'(B_563,C_564),C_565)
| ~ member(B_563,power_set(C_565))
| subset(B_563,C_564) ),
inference(resolution,[status(thm)],[c_243,c_649]) ).
tff(c_3357,plain,
! [B_566,C_567] :
( ~ member(B_566,power_set(C_567))
| subset(B_566,C_567) ),
inference(resolution,[status(thm)],[c_3307,c_245]) ).
tff(c_3911,plain,
! [C_586,B_587] :
( subset(C_586,B_587)
| ~ ilf_type(C_586,subset_type(B_587)) ),
inference(resolution,[status(thm)],[c_553,c_3357]) ).
tff(c_3929,plain,
subset(domain_of('#skF_16'),'#skF_15'),
inference(resolution,[status(thm)],[c_2197,c_3911]) ).
tff(c_3966,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2142,c_3929]) ).
tff(c_3967,plain,
member('#skF_18','#skF_15'),
inference(splitRight,[status(thm)],[c_152]) ).
tff(c_3968,plain,
domain('#skF_15','#skF_14','#skF_16') = '#skF_15',
inference(splitRight,[status(thm)],[c_152]) ).
tff(c_4443,plain,
! [B_677,C_678,D_679] :
( ( domain(B_677,C_678,D_679) = domain_of(D_679) )
| ~ ilf_type(D_679,relation_type(B_677,C_678)) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_130]) ).
tff(c_4449,plain,
domain('#skF_15','#skF_14','#skF_16') = domain_of('#skF_16'),
inference(resolution,[status(thm)],[c_140,c_4443]) ).
tff(c_4452,plain,
domain_of('#skF_16') = '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_3968,c_4449]) ).
tff(c_4,plain,
! [C_7,B_1] :
( member(ordered_pair(C_7,'#skF_1'(B_1,C_7)),B_1)
| ~ member(C_7,domain_of(B_1))
| ~ ilf_type(C_7,set_type)
| ~ ilf_type(B_1,binary_relation_type) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_5869,plain,
! [C_853,B_854] :
( member(ordered_pair(C_853,'#skF_1'(B_854,C_853)),B_854)
| ~ member(C_853,domain_of(B_854))
| ~ ilf_type(B_854,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_4]) ).
tff(c_146,plain,
! [F_249] :
( ( domain('#skF_15','#skF_14','#skF_16') != '#skF_15' )
| ~ member(ordered_pair('#skF_18',F_249),'#skF_16')
| ~ ilf_type(F_249,set_type) ),
inference(cnfTransformation,[status(thm)],[f_396]) ).
tff(c_174,plain,
! [F_249] :
( ( domain('#skF_15','#skF_14','#skF_16') != '#skF_15' )
| ~ member(ordered_pair('#skF_18',F_249),'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_146]) ).
tff(c_4032,plain,
! [F_249] : ~ member(ordered_pair('#skF_18',F_249),'#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_3968,c_174]) ).
tff(c_5895,plain,
( ~ member('#skF_18',domain_of('#skF_16'))
| ~ ilf_type('#skF_16',binary_relation_type) ),
inference(resolution,[status(thm)],[c_5869,c_4032]) ).
tff(c_5908,plain,
~ ilf_type('#skF_16',binary_relation_type),
inference(demodulation,[status(thm),theory(equality)],[c_3967,c_4452,c_5895]) ).
tff(c_5912,plain,
~ relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_263,c_5908]) ).
tff(c_5916,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4407,c_5912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET659+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.14 % 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
% 0.15/0.35 % Computer : n005.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 : Tue Apr 8 21:22:12 EDT 2025
% 0.15/0.35 % CPUTime :
% 8.85/3.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.85/3.07
% 8.85/3.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------