TSTP Solution File: SET681+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET681+3 : TPTP v8.1.2. 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 : n032.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 10:56:52 EDT 2023
% Result : Theorem 12.23s 4.15s
% Output : CNFRefutation 12.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 45
% Syntax : Number of formulae : 138 ( 40 unt; 34 typ; 0 def)
% Number of atoms : 251 ( 8 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 271 ( 124 ~; 100 |; 9 &)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 26 >; 16 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 8 con; 0-3 aty)
% Number of variables : 136 (; 134 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ 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_4 > #skF_15 > #skF_16 > #skF_14 > #skF_5 > #skF_13 > #skF_10 > #skF_8 > #skF_3 > #skF_11 > #skF_2 > #skF_7 > #skF_1 > #skF_9 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $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_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('#skF_5',type,
'#skF_5': $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $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(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(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_11',type,
'#skF_11': $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_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_375,negated_conjecture,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,range(C,B,D))
<=> ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).
tff(f_349,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
tff(f_335,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( range(B,C,D) = range_of(D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
tff(f_258,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_119,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',p6) ).
tff(f_302,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',p26) ).
tff(f_209,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',p17) ).
tff(f_55,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',p2) ).
tff(f_40,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,range_of(C))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(D,B),C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(f_76,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(D,B)
& member(E,C) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
tff(f_141,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',p8) ).
tff(c_120,plain,
ilf_type('#skF_14',relation_type('#skF_13','#skF_12')),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_116,plain,
! [B_210] : ilf_type(B_210,set_type),
inference(cnfTransformation,[status(thm)],[f_349]) ).
tff(c_112,plain,
! [B_196,C_200,D_202] :
( ( range(B_196,C_200,D_202) = range_of(D_202) )
| ~ ilf_type(D_202,relation_type(B_196,C_200))
| ~ ilf_type(C_200,set_type)
| ~ ilf_type(B_196,set_type) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_8124,plain,
! [B_983,C_984,D_985] :
( ( range(B_983,C_984,D_985) = range_of(D_985) )
| ~ ilf_type(D_985,relation_type(B_983,C_984)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_112]) ).
tff(c_8132,plain,
range('#skF_13','#skF_12','#skF_14') = range_of('#skF_14'),
inference(resolution,[status(thm)],[c_120,c_8124]) ).
tff(c_1777,plain,
! [B_475,C_476,D_477] :
( ( range(B_475,C_476,D_477) = range_of(D_477) )
| ~ ilf_type(D_477,relation_type(B_475,C_476)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_112]) ).
tff(c_1785,plain,
range('#skF_13','#skF_12','#skF_14') = range_of('#skF_14'),
inference(resolution,[status(thm)],[c_120,c_1777]) ).
tff(c_84,plain,
! [B_137,C_143] :
( member('#skF_8'(B_137,C_143),B_137)
| member(B_137,power_set(C_143))
| ~ ilf_type(C_143,set_type)
| ~ ilf_type(B_137,set_type) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_174,plain,
! [B_137,C_143] :
( member('#skF_8'(B_137,C_143),B_137)
| member(B_137,power_set(C_143)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_84]) ).
tff(c_82,plain,
! [B_137,C_143] :
( ~ member('#skF_8'(B_137,C_143),C_143)
| member(B_137,power_set(C_143))
| ~ ilf_type(C_143,set_type)
| ~ ilf_type(B_137,set_type) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_409,plain,
! [B_294,C_295] :
( ~ member('#skF_8'(B_294,C_295),C_295)
| member(B_294,power_set(C_295)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_82]) ).
tff(c_423,plain,
! [B_137] : member(B_137,power_set(B_137)),
inference(resolution,[status(thm)],[c_174,c_409]) ).
tff(c_140,plain,
( member('#skF_15',range('#skF_13','#skF_12','#skF_14'))
| ilf_type('#skF_16',member_type('#skF_13')) ),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_304,plain,
ilf_type('#skF_16',member_type('#skF_13')),
inference(splitLeft,[status(thm)],[c_140]) ).
tff(c_136,plain,
( member('#skF_15',range('#skF_13','#skF_12','#skF_14'))
| member(ordered_pair('#skF_16','#skF_15'),'#skF_14') ),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_370,plain,
member(ordered_pair('#skF_16','#skF_15'),'#skF_14'),
inference(splitLeft,[status(thm)],[c_136]) ).
tff(c_80,plain,
! [D_146,C_143,B_137] :
( member(D_146,C_143)
| ~ member(D_146,B_137)
| ~ ilf_type(D_146,set_type)
| ~ member(B_137,power_set(C_143))
| ~ ilf_type(C_143,set_type)
| ~ ilf_type(B_137,set_type) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_487,plain,
! [D_304,C_305,B_306] :
( member(D_304,C_305)
| ~ member(D_304,B_306)
| ~ member(B_306,power_set(C_305)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_116,c_80]) ).
tff(c_512,plain,
! [C_305] :
( member(ordered_pair('#skF_16','#skF_15'),C_305)
| ~ member('#skF_14',power_set(C_305)) ),
inference(resolution,[status(thm)],[c_370,c_487]) ).
tff(c_22,plain,
! [E_93,B_83,C_89] :
( ilf_type(E_93,subset_type(cross_product(B_83,C_89)))
| ~ ilf_type(E_93,relation_type(B_83,C_89))
| ~ ilf_type(C_89,set_type)
| ~ ilf_type(B_83,set_type) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_931,plain,
! [E_361,B_362,C_363] :
( ilf_type(E_361,subset_type(cross_product(B_362,C_363)))
| ~ ilf_type(E_361,relation_type(B_362,C_363)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_22]) ).
tff(c_106,plain,
! [D_181,B_175,C_179] :
( relation_like(D_181)
| ~ ilf_type(D_181,subset_type(cross_product(B_175,C_179)))
| ~ ilf_type(C_179,set_type)
| ~ ilf_type(B_175,set_type) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_152,plain,
! [D_181,B_175,C_179] :
( relation_like(D_181)
| ~ ilf_type(D_181,subset_type(cross_product(B_175,C_179))) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_106]) ).
tff(c_964,plain,
! [E_364,B_365,C_366] :
( relation_like(E_364)
| ~ ilf_type(E_364,relation_type(B_365,C_366)) ),
inference(resolution,[status(thm)],[c_931,c_152]) ).
tff(c_986,plain,
relation_like('#skF_14'),
inference(resolution,[status(thm)],[c_120,c_964]) ).
tff(c_52,plain,
! [B_121] :
( ilf_type(B_121,binary_relation_type)
| ~ relation_like(B_121)
| ~ ilf_type(B_121,set_type) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_194,plain,
! [B_121] :
( ilf_type(B_121,binary_relation_type)
| ~ relation_like(B_121) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_52]) ).
tff(c_607,plain,
! [B_318,C_319,D_320] :
( ( range(B_318,C_319,D_320) = range_of(D_320) )
| ~ ilf_type(D_320,relation_type(B_318,C_319)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_112]) ).
tff(c_615,plain,
range('#skF_13','#skF_12','#skF_14') = range_of('#skF_14'),
inference(resolution,[status(thm)],[c_120,c_607]) ).
tff(c_130,plain,
! [F_252] :
( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
| ~ ilf_type(F_252,member_type('#skF_13'))
| ~ member('#skF_15',range('#skF_13','#skF_12','#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_671,plain,
! [F_252] :
( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
| ~ ilf_type(F_252,member_type('#skF_13'))
| ~ member('#skF_15',range_of('#skF_14')) ),
inference(demodulation,[status(thm),theory(equality)],[c_615,c_130]) ).
tff(c_672,plain,
~ member('#skF_15',range_of('#skF_14')),
inference(splitLeft,[status(thm)],[c_671]) ).
tff(c_8,plain,
! [C_15,D_17,B_11] :
( member(C_15,range_of(D_17))
| ~ member(ordered_pair(B_11,C_15),D_17)
| ~ ilf_type(D_17,binary_relation_type)
| ~ ilf_type(C_15,set_type)
| ~ ilf_type(B_11,set_type) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_1283,plain,
! [C_407,D_408,B_409] :
( member(C_407,range_of(D_408))
| ~ member(ordered_pair(B_409,C_407),D_408)
| ~ ilf_type(D_408,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_8]) ).
tff(c_1301,plain,
( member('#skF_15',range_of('#skF_14'))
| ~ ilf_type('#skF_14',binary_relation_type) ),
inference(resolution,[status(thm)],[c_370,c_1283]) ).
tff(c_1308,plain,
~ ilf_type('#skF_14',binary_relation_type),
inference(negUnitSimplification,[status(thm)],[c_672,c_1301]) ).
tff(c_1311,plain,
~ relation_like('#skF_14'),
inference(resolution,[status(thm)],[c_194,c_1308]) ).
tff(c_1315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_986,c_1311]) ).
tff(c_1436,plain,
! [F_425] :
( ~ member(ordered_pair(F_425,'#skF_15'),'#skF_14')
| ~ ilf_type(F_425,member_type('#skF_13')) ),
inference(splitRight,[status(thm)],[c_671]) ).
tff(c_1440,plain,
( ~ ilf_type('#skF_16',member_type('#skF_13'))
| ~ member('#skF_14',power_set('#skF_14')) ),
inference(resolution,[status(thm)],[c_512,c_1436]) ).
tff(c_1447,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_423,c_304,c_1440]) ).
tff(c_1448,plain,
member('#skF_15',range('#skF_13','#skF_12','#skF_14')),
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_1787,plain,
member('#skF_15',range_of('#skF_14')),
inference(demodulation,[status(thm),theory(equality)],[c_1785,c_1448]) ).
tff(c_1670,plain,
! [E_460,B_461,C_462] :
( ilf_type(E_460,subset_type(cross_product(B_461,C_462)))
| ~ ilf_type(E_460,relation_type(B_461,C_462)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_22]) ).
tff(c_1685,plain,
! [E_463,B_464,C_465] :
( relation_like(E_463)
| ~ ilf_type(E_463,relation_type(B_464,C_465)) ),
inference(resolution,[status(thm)],[c_1670,c_152]) ).
tff(c_1693,plain,
relation_like('#skF_14'),
inference(resolution,[status(thm)],[c_120,c_1685]) ).
tff(c_4,plain,
! [B_1,C_7] :
( member(ordered_pair('#skF_1'(B_1,C_7),B_1),C_7)
| ~ member(B_1,range_of(C_7))
| ~ ilf_type(C_7,binary_relation_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_3732,plain,
! [B_711,C_712] :
( member(ordered_pair('#skF_1'(B_711,C_712),B_711),C_712)
| ~ member(B_711,range_of(C_712))
| ~ ilf_type(C_712,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_4]) ).
tff(c_1449,plain,
~ member(ordered_pair('#skF_16','#skF_15'),'#skF_14'),
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_134,plain,
! [F_252] :
( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
| ~ ilf_type(F_252,member_type('#skF_13'))
| member(ordered_pair('#skF_16','#skF_15'),'#skF_14') ),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_1609,plain,
! [F_252] :
( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
| ~ ilf_type(F_252,member_type('#skF_13')) ),
inference(negUnitSimplification,[status(thm)],[c_1449,c_134]) ).
tff(c_3758,plain,
( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
| ~ member('#skF_15',range_of('#skF_14'))
| ~ ilf_type('#skF_14',binary_relation_type) ),
inference(resolution,[status(thm)],[c_3732,c_1609]) ).
tff(c_3777,plain,
( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
| ~ ilf_type('#skF_14',binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_1787,c_3758]) ).
tff(c_3802,plain,
~ ilf_type('#skF_14',binary_relation_type),
inference(splitLeft,[status(thm)],[c_3777]) ).
tff(c_3805,plain,
~ relation_like('#skF_14'),
inference(resolution,[status(thm)],[c_194,c_3802]) ).
tff(c_3809,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1693,c_3805]) ).
tff(c_3811,plain,
ilf_type('#skF_14',binary_relation_type),
inference(splitRight,[status(thm)],[c_3777]) ).
tff(c_14,plain,
! [C_34,E_46,F_48,D_42,B_18] :
( member(D_42,B_18)
| ~ member(ordered_pair(D_42,E_46),F_48)
| ~ ilf_type(F_48,relation_type(B_18,C_34))
| ~ ilf_type(E_46,set_type)
| ~ ilf_type(D_42,set_type)
| ~ ilf_type(C_34,set_type)
| ~ ilf_type(B_18,set_type) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_230,plain,
! [C_34,E_46,F_48,D_42,B_18] :
( member(D_42,B_18)
| ~ member(ordered_pair(D_42,E_46),F_48)
| ~ ilf_type(F_48,relation_type(B_18,C_34)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_116,c_116,c_14]) ).
tff(c_7763,plain,
! [B_928,C_929,B_930,C_931] :
( member('#skF_1'(B_928,C_929),B_930)
| ~ ilf_type(C_929,relation_type(B_930,C_931))
| ~ member(B_928,range_of(C_929))
| ~ ilf_type(C_929,binary_relation_type) ),
inference(resolution,[status(thm)],[c_3732,c_230]) ).
tff(c_7789,plain,
! [B_928] :
( member('#skF_1'(B_928,'#skF_14'),'#skF_13')
| ~ member(B_928,range_of('#skF_14'))
| ~ ilf_type('#skF_14',binary_relation_type) ),
inference(resolution,[status(thm)],[c_120,c_7763]) ).
tff(c_7817,plain,
! [B_935] :
( member('#skF_1'(B_935,'#skF_14'),'#skF_13')
| ~ member(B_935,range_of('#skF_14')) ),
inference(demodulation,[status(thm),theory(equality)],[c_3811,c_7789]) ).
tff(c_124,plain,
~ empty('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_28,plain,
! [B_100,C_102] :
( ilf_type(B_100,member_type(C_102))
| ~ member(B_100,C_102)
| ~ ilf_type(C_102,set_type)
| empty(C_102)
| ~ ilf_type(B_100,set_type) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_216,plain,
! [B_100,C_102] :
( ilf_type(B_100,member_type(C_102))
| ~ member(B_100,C_102)
| empty(C_102) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_28]) ).
tff(c_3810,plain,
~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13')),
inference(splitRight,[status(thm)],[c_3777]) ).
tff(c_3819,plain,
( ~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13')
| empty('#skF_13') ),
inference(resolution,[status(thm)],[c_216,c_3810]) ).
tff(c_3822,plain,
~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_124,c_3819]) ).
tff(c_7820,plain,
~ member('#skF_15',range_of('#skF_14')),
inference(resolution,[status(thm)],[c_7817,c_3822]) ).
tff(c_7826,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1787,c_7820]) ).
tff(c_7827,plain,
member('#skF_15',range('#skF_13','#skF_12','#skF_14')),
inference(splitRight,[status(thm)],[c_140]) ).
tff(c_8134,plain,
member('#skF_15',range_of('#skF_14')),
inference(demodulation,[status(thm),theory(equality)],[c_8132,c_7827]) ).
tff(c_8298,plain,
! [E_1015,B_1016,C_1017] :
( ilf_type(E_1015,subset_type(cross_product(B_1016,C_1017)))
| ~ ilf_type(E_1015,relation_type(B_1016,C_1017)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_22]) ).
tff(c_8322,plain,
! [E_1018,B_1019,C_1020] :
( relation_like(E_1018)
| ~ ilf_type(E_1018,relation_type(B_1019,C_1020)) ),
inference(resolution,[status(thm)],[c_8298,c_152]) ).
tff(c_8344,plain,
relation_like('#skF_14'),
inference(resolution,[status(thm)],[c_120,c_8322]) ).
tff(c_9652,plain,
! [B_1188,C_1189] :
( member(ordered_pair('#skF_1'(B_1188,C_1189),B_1188),C_1189)
| ~ member(B_1188,range_of(C_1189))
| ~ ilf_type(C_1189,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_4]) ).
tff(c_7828,plain,
~ ilf_type('#skF_16',member_type('#skF_13')),
inference(splitRight,[status(thm)],[c_140]) ).
tff(c_138,plain,
! [F_252] :
( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
| ~ ilf_type(F_252,member_type('#skF_13'))
| ilf_type('#skF_16',member_type('#skF_13')) ),
inference(cnfTransformation,[status(thm)],[f_375]) ).
tff(c_7945,plain,
! [F_252] :
( ~ member(ordered_pair(F_252,'#skF_15'),'#skF_14')
| ~ ilf_type(F_252,member_type('#skF_13')) ),
inference(negUnitSimplification,[status(thm)],[c_7828,c_138]) ).
tff(c_9680,plain,
( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
| ~ member('#skF_15',range_of('#skF_14'))
| ~ ilf_type('#skF_14',binary_relation_type) ),
inference(resolution,[status(thm)],[c_9652,c_7945]) ).
tff(c_9698,plain,
( ~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13'))
| ~ ilf_type('#skF_14',binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_8134,c_9680]) ).
tff(c_9701,plain,
~ ilf_type('#skF_14',binary_relation_type),
inference(splitLeft,[status(thm)],[c_9698]) ).
tff(c_9704,plain,
~ relation_like('#skF_14'),
inference(resolution,[status(thm)],[c_194,c_9701]) ).
tff(c_9708,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8344,c_9704]) ).
tff(c_9710,plain,
ilf_type('#skF_14',binary_relation_type),
inference(splitRight,[status(thm)],[c_9698]) ).
tff(c_13362,plain,
! [B_1401,C_1402,B_1403,C_1404] :
( member('#skF_1'(B_1401,C_1402),B_1403)
| ~ ilf_type(C_1402,relation_type(B_1403,C_1404))
| ~ member(B_1401,range_of(C_1402))
| ~ ilf_type(C_1402,binary_relation_type) ),
inference(resolution,[status(thm)],[c_9652,c_230]) ).
tff(c_13400,plain,
! [B_1401] :
( member('#skF_1'(B_1401,'#skF_14'),'#skF_13')
| ~ member(B_1401,range_of('#skF_14'))
| ~ ilf_type('#skF_14',binary_relation_type) ),
inference(resolution,[status(thm)],[c_120,c_13362]) ).
tff(c_13422,plain,
! [B_1405] :
( member('#skF_1'(B_1405,'#skF_14'),'#skF_13')
| ~ member(B_1405,range_of('#skF_14')) ),
inference(demodulation,[status(thm),theory(equality)],[c_9710,c_13400]) ).
tff(c_9709,plain,
~ ilf_type('#skF_1'('#skF_15','#skF_14'),member_type('#skF_13')),
inference(splitRight,[status(thm)],[c_9698]) ).
tff(c_9718,plain,
( ~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13')
| empty('#skF_13') ),
inference(resolution,[status(thm)],[c_216,c_9709]) ).
tff(c_9721,plain,
~ member('#skF_1'('#skF_15','#skF_14'),'#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_124,c_9718]) ).
tff(c_13425,plain,
~ member('#skF_15',range_of('#skF_14')),
inference(resolution,[status(thm)],[c_13422,c_9721]) ).
tff(c_13434,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8134,c_13425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET681+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % 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
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Aug 3 16:42:51 EDT 2023
% 0.11/0.31 % CPUTime :
% 12.23/4.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.23/4.17
% 12.23/4.17 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.23/4.21
% 12.23/4.21 Inference rules
% 12.23/4.21 ----------------------
% 12.23/4.21 #Ref : 2
% 12.23/4.21 #Sup : 3160
% 12.23/4.21 #Fact : 12
% 12.23/4.21 #Define : 0
% 12.23/4.21 #Split : 18
% 12.23/4.21 #Chain : 0
% 12.23/4.21 #Close : 0
% 12.23/4.21
% 12.23/4.21 Ordering : KBO
% 12.23/4.21
% 12.23/4.21 Simplification rules
% 12.23/4.21 ----------------------
% 12.23/4.21 #Subsume : 1081
% 12.23/4.21 #Demod : 309
% 12.23/4.21 #Tautology : 266
% 12.23/4.21 #SimpNegUnit : 192
% 12.23/4.21 #BackRed : 19
% 12.23/4.21
% 12.23/4.21 #Partial instantiations: 0
% 12.23/4.21 #Strategies tried : 1
% 12.23/4.21
% 12.23/4.21 Timing (in seconds)
% 12.23/4.21 ----------------------
% 12.23/4.21 Preprocessing : 0.67
% 12.23/4.21 Parsing : 0.34
% 12.23/4.21 CNF conversion : 0.06
% 12.23/4.21 Main loop : 2.42
% 12.23/4.21 Inferencing : 0.89
% 12.23/4.21 Reduction : 0.74
% 12.23/4.21 Demodulation : 0.52
% 12.23/4.21 BG Simplification : 0.07
% 12.23/4.21 Subsumption : 0.54
% 12.23/4.21 Abstraction : 0.08
% 12.23/4.21 MUC search : 0.00
% 12.23/4.21 Cooper : 0.00
% 12.23/4.21 Total : 3.16
% 12.23/4.21 Index Insertion : 0.00
% 12.23/4.21 Index Deletion : 0.00
% 12.23/4.21 Index Matching : 0.00
% 12.23/4.21 BG Taut test : 0.00
%------------------------------------------------------------------------------