TSTP Solution File: SET685+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET685+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 : n026.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 10:56:53 EDT 2023
% Result : Theorem 15.02s 5.32s
% Output : CNFRefutation 15.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 44
% Syntax : Number of formulae : 176 ( 49 unt; 33 typ; 0 def)
% Number of atoms : 367 ( 10 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 438 ( 214 ~; 173 |; 11 &)
% ( 6 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 24 >; 17 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 9 con; 0-4 aty)
% Number of variables : 213 (; 211 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > ilf_type > relation_like > empty > image4 > unordered_pair > relation_type > ordered_pair > image > cross_product > #nlpp > subset_type > singleton > power_set > member_type > set_type > binary_relation_type > #skF_1 > #skF_4 > #skF_17 > #skF_15 > #skF_16 > #skF_14 > #skF_5 > #skF_13 > #skF_10 > #skF_8 > #skF_3 > #skF_11 > #skF_2 > #skF_7 > #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_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $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(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(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(image4,type,
image4: ( $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_11',type,
'#skF_11': $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_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_354,negated_conjecture,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ( ~ empty(D)
& ilf_type(D,set_type) )
=> ! [E] :
( ilf_type(E,relation_type(D,B))
=> ! [F] :
( ilf_type(F,member_type(B))
=> ( member(F,image4(D,B,E,C))
<=> ? [G] :
( ilf_type(G,member_type(D))
& member(ordered_pair(G,F),E)
& member(G,C) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_52) ).
tff(f_320,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
tff(f_108,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',p5) ).
tff(f_289,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',p24) ).
tff(f_196,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_44,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(C,image(D,B))
<=> ? [E] :
( ilf_type(E,set_type)
& member(ordered_pair(E,C),D)
& member(E,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(f_303,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> ( image4(B,C,D,E) = image(D,E) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
tff(f_245,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',p20) ).
tff(f_150,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
tff(f_65,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',p2) ).
tff(f_130,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',p7) ).
tff(c_112,plain,
ilf_type('#skF_15',relation_type('#skF_14','#skF_12')),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_108,plain,
! [B_218] : ilf_type(B_218,set_type),
inference(cnfTransformation,[status(thm)],[f_320]) ).
tff(c_20,plain,
! [E_98,B_88,C_94] :
( ilf_type(E_98,subset_type(cross_product(B_88,C_94)))
| ~ ilf_type(E_98,relation_type(B_88,C_94))
| ~ ilf_type(C_94,set_type)
| ~ ilf_type(B_88,set_type) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_14858,plain,
! [E_1668,B_1669,C_1670] :
( ilf_type(E_1668,subset_type(cross_product(B_1669,C_1670)))
| ~ ilf_type(E_1668,relation_type(B_1669,C_1670)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_20]) ).
tff(c_102,plain,
! [D_187,B_181,C_185] :
( relation_like(D_187)
| ~ ilf_type(D_187,subset_type(cross_product(B_181,C_185)))
| ~ ilf_type(C_185,set_type)
| ~ ilf_type(B_181,set_type) ),
inference(cnfTransformation,[status(thm)],[f_289]) ).
tff(c_149,plain,
! [D_187,B_181,C_185] :
( relation_like(D_187)
| ~ ilf_type(D_187,subset_type(cross_product(B_181,C_185))) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_102]) ).
tff(c_14868,plain,
! [E_1671,B_1672,C_1673] :
( relation_like(E_1671)
| ~ ilf_type(E_1671,relation_type(B_1672,C_1673)) ),
inference(resolution,[status(thm)],[c_14858,c_149]) ).
tff(c_14876,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_14868]) ).
tff(c_48,plain,
! [B_127] :
( ilf_type(B_127,binary_relation_type)
| ~ relation_like(B_127)
| ~ ilf_type(B_127,set_type) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_191,plain,
! [B_127] :
( ilf_type(B_127,binary_relation_type)
| ~ relation_like(B_127) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_48]) ).
tff(c_6,plain,
! [B_1,C_13,D_19] :
( member(ordered_pair('#skF_1'(B_1,C_13,D_19),C_13),D_19)
| ~ member(C_13,image(D_19,B_1))
| ~ ilf_type(D_19,binary_relation_type)
| ~ ilf_type(C_13,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_16375,plain,
! [B_1823,C_1824,D_1825] :
( member(ordered_pair('#skF_1'(B_1823,C_1824,D_1825),C_1824),D_1825)
| ~ member(C_1824,image(D_1825,B_1823))
| ~ ilf_type(D_1825,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_6]) ).
tff(c_8490,plain,
! [E_1123,B_1124,C_1125] :
( ilf_type(E_1123,subset_type(cross_product(B_1124,C_1125)))
| ~ ilf_type(E_1123,relation_type(B_1124,C_1125)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_20]) ).
tff(c_8509,plain,
! [E_1126,B_1127,C_1128] :
( relation_like(E_1126)
| ~ ilf_type(E_1126,relation_type(B_1127,C_1128)) ),
inference(resolution,[status(thm)],[c_8490,c_149]) ).
tff(c_8531,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_8509]) ).
tff(c_104,plain,
! [B_188,C_196,D_200,E_202] :
( ( image4(B_188,C_196,D_200,E_202) = image(D_200,E_202) )
| ~ ilf_type(E_202,set_type)
| ~ ilf_type(D_200,relation_type(B_188,C_196))
| ~ ilf_type(C_196,set_type)
| ~ ilf_type(B_188,set_type) ),
inference(cnfTransformation,[status(thm)],[f_303]) ).
tff(c_9229,plain,
! [B_1215,C_1216,D_1217,E_1218] :
( ( image4(B_1215,C_1216,D_1217,E_1218) = image(D_1217,E_1218) )
| ~ ilf_type(D_1217,relation_type(B_1215,C_1216)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_9250,plain,
! [E_1218] : ( image4('#skF_14','#skF_12','#skF_15',E_1218) = image('#skF_15',E_1218) ),
inference(resolution,[status(thm)],[c_112,c_9229]) ).
tff(c_2236,plain,
! [E_568,B_569,C_570] :
( ilf_type(E_568,subset_type(cross_product(B_569,C_570)))
| ~ ilf_type(E_568,relation_type(B_569,C_570)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_20]) ).
tff(c_2261,plain,
! [E_571,B_572,C_573] :
( relation_like(E_571)
| ~ ilf_type(E_571,relation_type(B_572,C_573)) ),
inference(resolution,[status(thm)],[c_2236,c_149]) ).
tff(c_2269,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_2261]) ).
tff(c_3450,plain,
! [B_721,C_722,D_723] :
( member(ordered_pair('#skF_1'(B_721,C_722,D_723),C_722),D_723)
| ~ member(C_722,image(D_723,B_721))
| ~ ilf_type(D_723,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_6]) ).
tff(c_80,plain,
! [B_143,C_149] :
( member('#skF_8'(B_143,C_149),B_143)
| member(B_143,power_set(C_149))
| ~ ilf_type(C_149,set_type)
| ~ ilf_type(B_143,set_type) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_448,plain,
! [B_354,C_355] :
( member('#skF_8'(B_354,C_355),B_354)
| member(B_354,power_set(C_355)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_80]) ).
tff(c_78,plain,
! [B_143,C_149] :
( ~ member('#skF_8'(B_143,C_149),C_149)
| member(B_143,power_set(C_149))
| ~ ilf_type(C_149,set_type)
| ~ ilf_type(B_143,set_type) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_173,plain,
! [B_143,C_149] :
( ~ member('#skF_8'(B_143,C_149),C_149)
| member(B_143,power_set(C_149)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_78]) ).
tff(c_461,plain,
! [B_354] : member(B_354,power_set(B_354)),
inference(resolution,[status(thm)],[c_448,c_173]) ).
tff(c_140,plain,
( member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13'))
| ilf_type('#skF_17',member_type('#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_352,plain,
ilf_type('#skF_17',member_type('#skF_14')),
inference(splitLeft,[status(thm)],[c_140]) ).
tff(c_132,plain,
( member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13'))
| member('#skF_17','#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_298,plain,
member('#skF_17','#skF_13'),
inference(splitLeft,[status(thm)],[c_132]) ).
tff(c_136,plain,
( member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13'))
| member(ordered_pair('#skF_17','#skF_16'),'#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_436,plain,
member(ordered_pair('#skF_17','#skF_16'),'#skF_15'),
inference(splitLeft,[status(thm)],[c_136]) ).
tff(c_76,plain,
! [D_152,C_149,B_143] :
( member(D_152,C_149)
| ~ member(D_152,B_143)
| ~ ilf_type(D_152,set_type)
| ~ member(B_143,power_set(C_149))
| ~ ilf_type(C_149,set_type)
| ~ ilf_type(B_143,set_type) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_463,plain,
! [D_356,C_357,B_358] :
( member(D_356,C_357)
| ~ member(D_356,B_358)
| ~ member(B_358,power_set(C_357)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_76]) ).
tff(c_483,plain,
! [C_357] :
( member(ordered_pair('#skF_17','#skF_16'),C_357)
| ~ member('#skF_15',power_set(C_357)) ),
inference(resolution,[status(thm)],[c_436,c_463]) ).
tff(c_580,plain,
! [E_370,B_371,C_372] :
( ilf_type(E_370,subset_type(cross_product(B_371,C_372)))
| ~ ilf_type(E_370,relation_type(B_371,C_372)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_20]) ).
tff(c_590,plain,
! [E_373,B_374,C_375] :
( relation_like(E_373)
| ~ ilf_type(E_373,relation_type(B_374,C_375)) ),
inference(resolution,[status(thm)],[c_580,c_149]) ).
tff(c_598,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_590]) ).
tff(c_1215,plain,
! [B_440,C_441,D_442,E_443] :
( ( image4(B_440,C_441,D_442,E_443) = image(D_442,E_443) )
| ~ ilf_type(D_442,relation_type(B_440,C_441)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_1236,plain,
! [E_443] : ( image4('#skF_14','#skF_12','#skF_15',E_443) = image('#skF_15',E_443) ),
inference(resolution,[status(thm)],[c_112,c_1215]) ).
tff(c_126,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair(G_307,'#skF_16'),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| ~ member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13')) ),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_887,plain,
~ member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13')),
inference(splitLeft,[status(thm)],[c_126]) ).
tff(c_1251,plain,
~ member('#skF_16',image('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_1236,c_887]) ).
tff(c_2,plain,
! [C_13,D_19,B_1,E_22] :
( member(C_13,image(D_19,B_1))
| ~ member(E_22,B_1)
| ~ member(ordered_pair(E_22,C_13),D_19)
| ~ ilf_type(E_22,set_type)
| ~ ilf_type(D_19,binary_relation_type)
| ~ ilf_type(C_13,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1782,plain,
! [C_517,D_518,B_519,E_520] :
( member(C_517,image(D_518,B_519))
| ~ member(E_520,B_519)
| ~ member(ordered_pair(E_520,C_517),D_518)
| ~ ilf_type(D_518,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_2]) ).
tff(c_1867,plain,
! [C_527,D_528] :
( member(C_527,image(D_528,'#skF_13'))
| ~ member(ordered_pair('#skF_17',C_527),D_528)
| ~ ilf_type(D_528,binary_relation_type) ),
inference(resolution,[status(thm)],[c_298,c_1782]) ).
tff(c_1881,plain,
( member('#skF_16',image('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_436,c_1867]) ).
tff(c_1891,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(negUnitSimplification,[status(thm)],[c_1251,c_1881]) ).
tff(c_1895,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_1891]) ).
tff(c_1899,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_598,c_1895]) ).
tff(c_1962,plain,
! [G_538] :
( ~ member(G_538,'#skF_13')
| ~ member(ordered_pair(G_538,'#skF_16'),'#skF_15')
| ~ ilf_type(G_538,member_type('#skF_14')) ),
inference(splitRight,[status(thm)],[c_126]) ).
tff(c_1966,plain,
( ~ member('#skF_17','#skF_13')
| ~ ilf_type('#skF_17',member_type('#skF_14'))
| ~ member('#skF_15',power_set('#skF_15')) ),
inference(resolution,[status(thm)],[c_483,c_1962]) ).
tff(c_1973,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_461,c_352,c_298,c_1966]) ).
tff(c_1975,plain,
~ member(ordered_pair('#skF_17','#skF_16'),'#skF_15'),
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_134,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair(G_307,'#skF_16'),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| member(ordered_pair('#skF_17','#skF_16'),'#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_2271,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair(G_307,'#skF_16'),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14')) ),
inference(negUnitSimplification,[status(thm)],[c_1975,c_134]) ).
tff(c_3485,plain,
! [B_721] :
( ~ member('#skF_1'(B_721,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_721,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',image('#skF_15',B_721))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_3450,c_2271]) ).
tff(c_3560,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(splitLeft,[status(thm)],[c_3485]) ).
tff(c_3563,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_3560]) ).
tff(c_3567,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2269,c_3563]) ).
tff(c_3569,plain,
ilf_type('#skF_15',binary_relation_type),
inference(splitRight,[status(thm)],[c_3485]) ).
tff(c_3011,plain,
! [B_672,C_673,D_674,E_675] :
( ( image4(B_672,C_673,D_674,E_675) = image(D_674,E_675) )
| ~ ilf_type(D_674,relation_type(B_672,C_673)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_3032,plain,
! [E_675] : ( image4('#skF_14','#skF_12','#skF_15',E_675) = image('#skF_15',E_675) ),
inference(resolution,[status(thm)],[c_112,c_3011]) ).
tff(c_1974,plain,
member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13')),
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_3037,plain,
member('#skF_16',image('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_3032,c_1974]) ).
tff(c_32,plain,
! [C_113,B_110] :
( ~ member(C_113,B_110)
| ~ ilf_type(C_113,set_type)
| ~ empty(B_110)
| ~ ilf_type(B_110,set_type) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_207,plain,
! [C_113,B_110] :
( ~ member(C_113,B_110)
| ~ empty(B_110) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_32]) ).
tff(c_3489,plain,
! [D_724,C_725,B_726] :
( ~ empty(D_724)
| ~ member(C_725,image(D_724,B_726))
| ~ ilf_type(D_724,binary_relation_type) ),
inference(resolution,[status(thm)],[c_3450,c_207]) ).
tff(c_3547,plain,
( ~ empty('#skF_15')
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_3037,c_3489]) ).
tff(c_3559,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(splitLeft,[status(thm)],[c_3547]) ).
tff(c_3576,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3569,c_3559]) ).
tff(c_3578,plain,
ilf_type('#skF_15',binary_relation_type),
inference(splitRight,[status(thm)],[c_3547]) ).
tff(c_4,plain,
! [B_1,C_13,D_19] :
( member('#skF_1'(B_1,C_13,D_19),B_1)
| ~ member(C_13,image(D_19,B_1))
| ~ ilf_type(D_19,binary_relation_type)
| ~ ilf_type(C_13,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_235,plain,
! [B_1,C_13,D_19] :
( member('#skF_1'(B_1,C_13,D_19),B_1)
| ~ member(C_13,image(D_19,B_1))
| ~ ilf_type(D_19,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_4]) ).
tff(c_12,plain,
! [C_39,F_53,E_51,B_23,D_47] :
( member(D_47,B_23)
| ~ member(ordered_pair(D_47,E_51),F_53)
| ~ ilf_type(F_53,relation_type(B_23,C_39))
| ~ ilf_type(E_51,set_type)
| ~ ilf_type(D_47,set_type)
| ~ ilf_type(C_39,set_type)
| ~ ilf_type(B_23,set_type) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_227,plain,
! [C_39,F_53,E_51,B_23,D_47] :
( member(D_47,B_23)
| ~ member(ordered_pair(D_47,E_51),F_53)
| ~ ilf_type(F_53,relation_type(B_23,C_39)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_108,c_12]) ).
tff(c_8059,plain,
! [B_1050,B_1053,D_1049,C_1051,C_1052] :
( member('#skF_1'(B_1050,C_1052,D_1049),B_1053)
| ~ ilf_type(D_1049,relation_type(B_1053,C_1051))
| ~ member(C_1052,image(D_1049,B_1050))
| ~ ilf_type(D_1049,binary_relation_type) ),
inference(resolution,[status(thm)],[c_3450,c_227]) ).
tff(c_8075,plain,
! [B_1050,C_1052] :
( member('#skF_1'(B_1050,C_1052,'#skF_15'),'#skF_14')
| ~ member(C_1052,image('#skF_15',B_1050))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_112,c_8059]) ).
tff(c_8089,plain,
! [B_1058,C_1059] :
( member('#skF_1'(B_1058,C_1059,'#skF_15'),'#skF_14')
| ~ member(C_1059,image('#skF_15',B_1058)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3578,c_8075]) ).
tff(c_116,plain,
~ empty('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_26,plain,
! [B_105,C_107] :
( ilf_type(B_105,member_type(C_107))
| ~ member(B_105,C_107)
| ~ ilf_type(C_107,set_type)
| empty(C_107)
| ~ ilf_type(B_105,set_type) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_213,plain,
! [B_105,C_107] :
( ilf_type(B_105,member_type(C_107))
| ~ member(B_105,C_107)
| empty(C_107) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_26]) ).
tff(c_4449,plain,
! [B_805] :
( ~ member('#skF_1'(B_805,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_805,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',image('#skF_15',B_805)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3578,c_3485]) ).
tff(c_4452,plain,
! [B_805] :
( ~ member('#skF_1'(B_805,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_805))
| ~ member('#skF_1'(B_805,'#skF_16','#skF_15'),'#skF_14')
| empty('#skF_14') ),
inference(resolution,[status(thm)],[c_213,c_4449]) ).
tff(c_4455,plain,
! [B_805] :
( ~ member('#skF_1'(B_805,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_805))
| ~ member('#skF_1'(B_805,'#skF_16','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_116,c_4452]) ).
tff(c_8141,plain,
! [B_1075] :
( ~ member('#skF_1'(B_1075,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_1075)) ),
inference(resolution,[status(thm)],[c_8089,c_4455]) ).
tff(c_8149,plain,
( ~ member('#skF_16',image('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_235,c_8141]) ).
tff(c_8156,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3578,c_3037,c_8149]) ).
tff(c_8157,plain,
member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13')),
inference(splitRight,[status(thm)],[c_140]) ).
tff(c_9254,plain,
member('#skF_16',image('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_9250,c_8157]) ).
tff(c_9839,plain,
! [B_1279,C_1280,D_1281] :
( member(ordered_pair('#skF_1'(B_1279,C_1280,D_1281),C_1280),D_1281)
| ~ member(C_1280,image(D_1281,B_1279))
| ~ ilf_type(D_1281,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_6]) ).
tff(c_9886,plain,
! [D_1282,C_1283,B_1284] :
( ~ empty(D_1282)
| ~ member(C_1283,image(D_1282,B_1284))
| ~ ilf_type(D_1282,binary_relation_type) ),
inference(resolution,[status(thm)],[c_9839,c_207]) ).
tff(c_9945,plain,
( ~ empty('#skF_15')
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_9254,c_9886]) ).
tff(c_9956,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(splitLeft,[status(thm)],[c_9945]) ).
tff(c_9959,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_9956]) ).
tff(c_9963,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8531,c_9959]) ).
tff(c_9965,plain,
ilf_type('#skF_15',binary_relation_type),
inference(splitRight,[status(thm)],[c_9945]) ).
tff(c_14425,plain,
! [C_1602,B_1603,D_1605,C_1601,B_1604] :
( member('#skF_1'(B_1603,C_1602,D_1605),B_1604)
| ~ ilf_type(D_1605,relation_type(B_1604,C_1601))
| ~ member(C_1602,image(D_1605,B_1603))
| ~ ilf_type(D_1605,binary_relation_type) ),
inference(resolution,[status(thm)],[c_9839,c_227]) ).
tff(c_14441,plain,
! [B_1603,C_1602] :
( member('#skF_1'(B_1603,C_1602,'#skF_15'),'#skF_14')
| ~ member(C_1602,image('#skF_15',B_1603))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_112,c_14425]) ).
tff(c_14453,plain,
! [B_1608,C_1609] :
( member('#skF_1'(B_1608,C_1609,'#skF_15'),'#skF_14')
| ~ member(C_1609,image('#skF_15',B_1608)) ),
inference(demodulation,[status(thm),theory(equality)],[c_9965,c_14441]) ).
tff(c_8158,plain,
~ ilf_type('#skF_17',member_type('#skF_14')),
inference(splitRight,[status(thm)],[c_140]) ).
tff(c_138,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair(G_307,'#skF_16'),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| ilf_type('#skF_17',member_type('#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_8456,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair(G_307,'#skF_16'),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14')) ),
inference(negUnitSimplification,[status(thm)],[c_8158,c_138]) ).
tff(c_9882,plain,
! [B_1279] :
( ~ member('#skF_1'(B_1279,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1279,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',image('#skF_15',B_1279))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_9839,c_8456]) ).
tff(c_10107,plain,
! [B_1304] :
( ~ member('#skF_1'(B_1304,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1304,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',image('#skF_15',B_1304)) ),
inference(demodulation,[status(thm),theory(equality)],[c_9965,c_9882]) ).
tff(c_10110,plain,
! [B_1304] :
( ~ member('#skF_1'(B_1304,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_1304))
| ~ member('#skF_1'(B_1304,'#skF_16','#skF_15'),'#skF_14')
| empty('#skF_14') ),
inference(resolution,[status(thm)],[c_213,c_10107]) ).
tff(c_10113,plain,
! [B_1304] :
( ~ member('#skF_1'(B_1304,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_1304))
| ~ member('#skF_1'(B_1304,'#skF_16','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_116,c_10110]) ).
tff(c_14549,plain,
! [B_1619] :
( ~ member('#skF_1'(B_1619,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_1619)) ),
inference(resolution,[status(thm)],[c_14453,c_10113]) ).
tff(c_14557,plain,
( ~ member('#skF_16',image('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_235,c_14549]) ).
tff(c_14564,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9965,c_9254,c_14557]) ).
tff(c_14566,plain,
~ member('#skF_17','#skF_13'),
inference(splitRight,[status(thm)],[c_132]) ).
tff(c_130,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair(G_307,'#skF_16'),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| member('#skF_17','#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_354]) ).
tff(c_14792,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair(G_307,'#skF_16'),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14')) ),
inference(negUnitSimplification,[status(thm)],[c_14566,c_130]) ).
tff(c_16411,plain,
! [B_1823] :
( ~ member('#skF_1'(B_1823,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1823,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',image('#skF_15',B_1823))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_16375,c_14792]) ).
tff(c_16423,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(splitLeft,[status(thm)],[c_16411]) ).
tff(c_16426,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_16423]) ).
tff(c_16430,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14876,c_16426]) ).
tff(c_16432,plain,
ilf_type('#skF_15',binary_relation_type),
inference(splitRight,[status(thm)],[c_16411]) ).
tff(c_16126,plain,
! [B_1801,C_1802,D_1803,E_1804] :
( ( image4(B_1801,C_1802,D_1803,E_1804) = image(D_1803,E_1804) )
| ~ ilf_type(D_1803,relation_type(B_1801,C_1802)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_16147,plain,
! [E_1804] : ( image4('#skF_14','#skF_12','#skF_15',E_1804) = image('#skF_15',E_1804) ),
inference(resolution,[status(thm)],[c_112,c_16126]) ).
tff(c_14565,plain,
member('#skF_16',image4('#skF_14','#skF_12','#skF_15','#skF_13')),
inference(splitRight,[status(thm)],[c_132]) ).
tff(c_16198,plain,
member('#skF_16',image('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_16147,c_14565]) ).
tff(c_20990,plain,
! [D_2139,B_2143,C_2141,B_2140,C_2142] :
( member('#skF_1'(B_2140,C_2142,D_2139),B_2143)
| ~ ilf_type(D_2139,relation_type(B_2143,C_2141))
| ~ member(C_2142,image(D_2139,B_2140))
| ~ ilf_type(D_2139,binary_relation_type) ),
inference(resolution,[status(thm)],[c_16375,c_227]) ).
tff(c_21006,plain,
! [B_2140,C_2142] :
( member('#skF_1'(B_2140,C_2142,'#skF_15'),'#skF_14')
| ~ member(C_2142,image('#skF_15',B_2140))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_112,c_20990]) ).
tff(c_21020,plain,
! [B_2153,C_2154] :
( member('#skF_1'(B_2153,C_2154,'#skF_15'),'#skF_14')
| ~ member(C_2154,image('#skF_15',B_2153)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16432,c_21006]) ).
tff(c_18037,plain,
! [B_1947] :
( ~ member('#skF_1'(B_1947,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1947,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',image('#skF_15',B_1947)) ),
inference(splitRight,[status(thm)],[c_16411]) ).
tff(c_18040,plain,
! [B_1947] :
( ~ member('#skF_1'(B_1947,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_1947))
| ~ member('#skF_1'(B_1947,'#skF_16','#skF_15'),'#skF_14')
| empty('#skF_14') ),
inference(resolution,[status(thm)],[c_213,c_18037]) ).
tff(c_18043,plain,
! [B_1947] :
( ~ member('#skF_1'(B_1947,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_1947))
| ~ member('#skF_1'(B_1947,'#skF_16','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_116,c_18040]) ).
tff(c_21120,plain,
! [B_2170] :
( ~ member('#skF_1'(B_2170,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',image('#skF_15',B_2170)) ),
inference(resolution,[status(thm)],[c_21020,c_18043]) ).
tff(c_21128,plain,
( ~ member('#skF_16',image('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_235,c_21120]) ).
tff(c_21135,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16432,c_16198,c_21128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET685+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 3 16:33:47 EDT 2023
% 0.13/0.33 % CPUTime :
% 15.02/5.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.02/5.33
% 15.02/5.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.17/5.38
% 15.17/5.38 Inference rules
% 15.17/5.38 ----------------------
% 15.17/5.38 #Ref : 4
% 15.17/5.38 #Sup : 4940
% 15.17/5.38 #Fact : 20
% 15.17/5.38 #Define : 0
% 15.17/5.38 #Split : 25
% 15.17/5.38 #Chain : 0
% 15.17/5.38 #Close : 0
% 15.17/5.38
% 15.17/5.38 Ordering : KBO
% 15.17/5.38
% 15.17/5.38 Simplification rules
% 15.17/5.38 ----------------------
% 15.17/5.38 #Subsume : 1564
% 15.17/5.38 #Demod : 409
% 15.17/5.38 #Tautology : 353
% 15.17/5.38 #SimpNegUnit : 313
% 15.17/5.38 #BackRed : 55
% 15.17/5.38
% 15.17/5.38 #Partial instantiations: 0
% 15.17/5.38 #Strategies tried : 1
% 15.17/5.38
% 15.17/5.38 Timing (in seconds)
% 15.17/5.38 ----------------------
% 15.17/5.38 Preprocessing : 0.75
% 15.17/5.38 Parsing : 0.36
% 15.17/5.38 CNF conversion : 0.08
% 15.17/5.38 Main loop : 3.54
% 15.17/5.38 Inferencing : 1.22
% 15.17/5.38 Reduction : 1.15
% 15.17/5.38 Demodulation : 0.82
% 15.17/5.38 BG Simplification : 0.10
% 15.17/5.38 Subsumption : 0.80
% 15.17/5.38 Abstraction : 0.10
% 15.17/5.38 MUC search : 0.00
% 15.17/5.38 Cooper : 0.00
% 15.17/5.38 Total : 4.36
% 15.17/5.38 Index Insertion : 0.00
% 15.17/5.38 Index Deletion : 0.00
% 15.17/5.38 Index Matching : 0.00
% 15.17/5.38 BG Taut test : 0.00
%------------------------------------------------------------------------------