TSTP Solution File: SET686+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET686+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 : n002.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 13.86s 4.66s
% Output : CNFRefutation 13.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 44
% Syntax : Number of formulae : 173 ( 46 unt; 33 typ; 0 def)
% Number of atoms : 364 ( 10 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 437 ( 213 ~; 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 > inverse4 > unordered_pair > relation_type > ordered_pair > inverse2 > 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(inverse4,type,
inverse4: ( $i * $i * $i * $i ) > $i ).
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(inverse2,type,
inverse2: ( $i * $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(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $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_353,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(B,D))
=> ! [F] :
( ilf_type(F,member_type(B))
=> ( member(F,inverse4(B,D,E,C))
<=> ? [G] :
( ilf_type(G,member_type(D))
& member(ordered_pair(F,G),E)
& member(G,C) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_53) ).
tff(f_319,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
tff(f_109,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_288,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_195,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_45,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(C,inverse2(D,B))
<=> ? [E] :
( ilf_type(E,set_type)
& member(ordered_pair(C,E),D)
& member(E,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(f_302,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)
=> ( inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
tff(f_244,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_151,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_66,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_131,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_12','#skF_14')),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_108,plain,
! [B_218] : ilf_type(B_218,set_type),
inference(cnfTransformation,[status(thm)],[f_319]) ).
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_109]) ).
tff(c_14912,plain,
! [E_1667,B_1668,C_1669] :
( ilf_type(E_1667,subset_type(cross_product(B_1668,C_1669)))
| ~ ilf_type(E_1667,relation_type(B_1668,C_1669)) ),
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_288]) ).
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_14935,plain,
! [E_1670,B_1671,C_1672] :
( relation_like(E_1670)
| ~ ilf_type(E_1670,relation_type(B_1671,C_1672)) ),
inference(resolution,[status(thm)],[c_14912,c_149]) ).
tff(c_14957,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_14935]) ).
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_195]) ).
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,
! [C_13,B_1,D_19] :
( member(ordered_pair(C_13,'#skF_1'(B_1,C_13,D_19)),D_19)
| ~ member(C_13,inverse2(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_45]) ).
tff(c_16086,plain,
! [C_1805,B_1806,D_1807] :
( member(ordered_pair(C_1805,'#skF_1'(B_1806,C_1805,D_1807)),D_1807)
| ~ member(C_1805,inverse2(D_1807,B_1806))
| ~ ilf_type(D_1807,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_6]) ).
tff(c_8634,plain,
! [E_1130,B_1131,C_1132] :
( ilf_type(E_1130,subset_type(cross_product(B_1131,C_1132)))
| ~ ilf_type(E_1130,relation_type(B_1131,C_1132)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_20]) ).
tff(c_8658,plain,
! [E_1133,B_1134,C_1135] :
( relation_like(E_1133)
| ~ ilf_type(E_1133,relation_type(B_1134,C_1135)) ),
inference(resolution,[status(thm)],[c_8634,c_149]) ).
tff(c_8690,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_8658]) ).
tff(c_104,plain,
! [B_188,C_196,D_200,E_202] :
( ( inverse4(B_188,C_196,D_200,E_202) = inverse2(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_302]) ).
tff(c_9194,plain,
! [B_1190,C_1191,D_1192,E_1193] :
( ( inverse4(B_1190,C_1191,D_1192,E_1193) = inverse2(D_1192,E_1193) )
| ~ ilf_type(D_1192,relation_type(B_1190,C_1191)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_9215,plain,
! [E_1193] : ( inverse4('#skF_12','#skF_14','#skF_15',E_1193) = inverse2('#skF_15',E_1193) ),
inference(resolution,[status(thm)],[c_112,c_9194]) ).
tff(c_2485,plain,
! [E_592,B_593,C_594] :
( ilf_type(E_592,subset_type(cross_product(B_593,C_594)))
| ~ ilf_type(E_592,relation_type(B_593,C_594)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_20]) ).
tff(c_2514,plain,
! [E_595,B_596,C_597] :
( relation_like(E_595)
| ~ ilf_type(E_595,relation_type(B_596,C_597)) ),
inference(resolution,[status(thm)],[c_2485,c_149]) ).
tff(c_2536,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_2514]) ).
tff(c_2907,plain,
! [B_638,C_639,D_640,E_641] :
( ( inverse4(B_638,C_639,D_640,E_641) = inverse2(D_640,E_641) )
| ~ ilf_type(D_640,relation_type(B_638,C_639)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_2928,plain,
! [E_641] : ( inverse4('#skF_12','#skF_14','#skF_15',E_641) = inverse2('#skF_15',E_641) ),
inference(resolution,[status(thm)],[c_112,c_2907]) ).
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_244]) ).
tff(c_409,plain,
! [B_352,C_353] :
( member('#skF_8'(B_352,C_353),B_352)
| member(B_352,power_set(C_353)) ),
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_244]) ).
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_422,plain,
! [B_352] : member(B_352,power_set(B_352)),
inference(resolution,[status(thm)],[c_409,c_173]) ).
tff(c_140,plain,
( member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13'))
| ilf_type('#skF_17',member_type('#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_325,plain,
ilf_type('#skF_17',member_type('#skF_14')),
inference(splitLeft,[status(thm)],[c_140]) ).
tff(c_132,plain,
( member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13'))
| member('#skF_17','#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_266,plain,
member('#skF_17','#skF_13'),
inference(splitLeft,[status(thm)],[c_132]) ).
tff(c_136,plain,
( member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13'))
| member(ordered_pair('#skF_16','#skF_17'),'#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_403,plain,
member(ordered_pair('#skF_16','#skF_17'),'#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_244]) ).
tff(c_433,plain,
! [D_355,C_356,B_357] :
( member(D_355,C_356)
| ~ member(D_355,B_357)
| ~ member(B_357,power_set(C_356)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_76]) ).
tff(c_456,plain,
! [C_356] :
( member(ordered_pair('#skF_16','#skF_17'),C_356)
| ~ member('#skF_15',power_set(C_356)) ),
inference(resolution,[status(thm)],[c_403,c_433]) ).
tff(c_558,plain,
! [E_369,B_370,C_371] :
( ilf_type(E_369,subset_type(cross_product(B_370,C_371)))
| ~ ilf_type(E_369,relation_type(B_370,C_371)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_20]) ).
tff(c_568,plain,
! [E_372,B_373,C_374] :
( relation_like(E_372)
| ~ ilf_type(E_372,relation_type(B_373,C_374)) ),
inference(resolution,[status(thm)],[c_558,c_149]) ).
tff(c_576,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_112,c_568]) ).
tff(c_1384,plain,
! [B_481,C_482,D_483,E_484] :
( ( inverse4(B_481,C_482,D_483,E_484) = inverse2(D_483,E_484) )
| ~ ilf_type(D_483,relation_type(B_481,C_482)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_1405,plain,
! [E_484] : ( inverse4('#skF_12','#skF_14','#skF_15',E_484) = inverse2('#skF_15',E_484) ),
inference(resolution,[status(thm)],[c_112,c_1384]) ).
tff(c_126,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair('#skF_16',G_307),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| ~ member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13')) ),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_795,plain,
~ member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13')),
inference(splitLeft,[status(thm)],[c_126]) ).
tff(c_1406,plain,
~ member('#skF_16',inverse2('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_1405,c_795]) ).
tff(c_2,plain,
! [C_13,D_19,B_1,E_22] :
( member(C_13,inverse2(D_19,B_1))
| ~ member(E_22,B_1)
| ~ member(ordered_pair(C_13,E_22),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_45]) ).
tff(c_1957,plain,
! [C_536,D_537,B_538,E_539] :
( member(C_536,inverse2(D_537,B_538))
| ~ member(E_539,B_538)
| ~ member(ordered_pair(C_536,E_539),D_537)
| ~ ilf_type(D_537,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_2]) ).
tff(c_2053,plain,
! [C_545,D_546] :
( member(C_545,inverse2(D_546,'#skF_13'))
| ~ member(ordered_pair(C_545,'#skF_17'),D_546)
| ~ ilf_type(D_546,binary_relation_type) ),
inference(resolution,[status(thm)],[c_266,c_1957]) ).
tff(c_2071,plain,
( member('#skF_16',inverse2('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_403,c_2053]) ).
tff(c_2082,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(negUnitSimplification,[status(thm)],[c_1406,c_2071]) ).
tff(c_2086,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_2082]) ).
tff(c_2090,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_576,c_2086]) ).
tff(c_2234,plain,
! [G_556] :
( ~ member(G_556,'#skF_13')
| ~ member(ordered_pair('#skF_16',G_556),'#skF_15')
| ~ ilf_type(G_556,member_type('#skF_14')) ),
inference(splitRight,[status(thm)],[c_126]) ).
tff(c_2238,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_456,c_2234]) ).
tff(c_2245,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_422,c_325,c_266,c_2238]) ).
tff(c_2246,plain,
member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13')),
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_2931,plain,
member('#skF_16',inverse2('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_2928,c_2246]) ).
tff(c_3815,plain,
! [C_744,B_745,D_746] :
( member(ordered_pair(C_744,'#skF_1'(B_745,C_744,D_746)),D_746)
| ~ member(C_744,inverse2(D_746,B_745))
| ~ ilf_type(D_746,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_6]) ).
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_151]) ).
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_3862,plain,
! [D_747,C_748,B_749] :
( ~ empty(D_747)
| ~ member(C_748,inverse2(D_747,B_749))
| ~ ilf_type(D_747,binary_relation_type) ),
inference(resolution,[status(thm)],[c_3815,c_207]) ).
tff(c_3922,plain,
( ~ empty('#skF_15')
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_2931,c_3862]) ).
tff(c_3932,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(splitLeft,[status(thm)],[c_3922]) ).
tff(c_3935,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_3932]) ).
tff(c_3939,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2536,c_3935]) ).
tff(c_3941,plain,
ilf_type('#skF_15',binary_relation_type),
inference(splitRight,[status(thm)],[c_3922]) ).
tff(c_4,plain,
! [B_1,C_13,D_19] :
( member('#skF_1'(B_1,C_13,D_19),B_1)
| ~ member(C_13,inverse2(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_45]) ).
tff(c_235,plain,
! [B_1,C_13,D_19] :
( member('#skF_1'(B_1,C_13,D_19),B_1)
| ~ member(C_13,inverse2(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_10,plain,
! [C_39,F_53,E_51,B_23,D_47] :
( member(E_51,C_39)
| ~ 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_66]) ).
tff(c_229,plain,
! [C_39,F_53,E_51,B_23,D_47] :
( member(E_51,C_39)
| ~ 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_10]) ).
tff(c_8244,plain,
! [D_1056,C_1058,C_1057,B_1055,B_1059] :
( member('#skF_1'(B_1055,C_1057,D_1056),C_1058)
| ~ ilf_type(D_1056,relation_type(B_1059,C_1058))
| ~ member(C_1057,inverse2(D_1056,B_1055))
| ~ ilf_type(D_1056,binary_relation_type) ),
inference(resolution,[status(thm)],[c_3815,c_229]) ).
tff(c_8260,plain,
! [B_1055,C_1057] :
( member('#skF_1'(B_1055,C_1057,'#skF_15'),'#skF_14')
| ~ member(C_1057,inverse2('#skF_15',B_1055))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_112,c_8244]) ).
tff(c_8274,plain,
! [B_1063,C_1064] :
( member('#skF_1'(B_1063,C_1064,'#skF_15'),'#skF_14')
| ~ member(C_1064,inverse2('#skF_15',B_1063)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3941,c_8260]) ).
tff(c_116,plain,
~ empty('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_353]) ).
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_131]) ).
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_2247,plain,
~ member(ordered_pair('#skF_16','#skF_17'),'#skF_15'),
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_134,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair('#skF_16',G_307),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| member(ordered_pair('#skF_16','#skF_17'),'#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_2538,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair('#skF_16',G_307),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14')) ),
inference(negUnitSimplification,[status(thm)],[c_2247,c_134]) ).
tff(c_3858,plain,
! [B_745] :
( ~ member('#skF_1'(B_745,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_745,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',inverse2('#skF_15',B_745))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_3815,c_2538]) ).
tff(c_4320,plain,
! [B_794] :
( ~ member('#skF_1'(B_794,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_794,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',inverse2('#skF_15',B_794)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3941,c_3858]) ).
tff(c_4323,plain,
! [B_794] :
( ~ member('#skF_1'(B_794,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_794))
| ~ member('#skF_1'(B_794,'#skF_16','#skF_15'),'#skF_14')
| empty('#skF_14') ),
inference(resolution,[status(thm)],[c_213,c_4320]) ).
tff(c_4326,plain,
! [B_794] :
( ~ member('#skF_1'(B_794,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_794))
| ~ member('#skF_1'(B_794,'#skF_16','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_116,c_4323]) ).
tff(c_8323,plain,
! [B_1078] :
( ~ member('#skF_1'(B_1078,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_1078)) ),
inference(resolution,[status(thm)],[c_8274,c_4326]) ).
tff(c_8331,plain,
( ~ member('#skF_16',inverse2('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_235,c_8323]) ).
tff(c_8338,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3941,c_2931,c_8331]) ).
tff(c_8339,plain,
member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13')),
inference(splitRight,[status(thm)],[c_140]) ).
tff(c_9219,plain,
member('#skF_16',inverse2('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_9215,c_8339]) ).
tff(c_10136,plain,
! [C_1285,B_1286,D_1287] :
( member(ordered_pair(C_1285,'#skF_1'(B_1286,C_1285,D_1287)),D_1287)
| ~ member(C_1285,inverse2(D_1287,B_1286))
| ~ ilf_type(D_1287,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_6]) ).
tff(c_10183,plain,
! [D_1288,C_1289,B_1290] :
( ~ empty(D_1288)
| ~ member(C_1289,inverse2(D_1288,B_1290))
| ~ ilf_type(D_1288,binary_relation_type) ),
inference(resolution,[status(thm)],[c_10136,c_207]) ).
tff(c_10241,plain,
( ~ empty('#skF_15')
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_9219,c_10183]) ).
tff(c_10253,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(splitLeft,[status(thm)],[c_10241]) ).
tff(c_10256,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_10253]) ).
tff(c_10260,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8690,c_10256]) ).
tff(c_10262,plain,
ilf_type('#skF_15',binary_relation_type),
inference(splitRight,[status(thm)],[c_10241]) ).
tff(c_14370,plain,
! [D_1571,B_1572,C_1569,B_1573,C_1570] :
( member('#skF_1'(B_1573,C_1569,D_1571),C_1570)
| ~ ilf_type(D_1571,relation_type(B_1572,C_1570))
| ~ member(C_1569,inverse2(D_1571,B_1573))
| ~ ilf_type(D_1571,binary_relation_type) ),
inference(resolution,[status(thm)],[c_10136,c_229]) ).
tff(c_14386,plain,
! [B_1573,C_1569] :
( member('#skF_1'(B_1573,C_1569,'#skF_15'),'#skF_14')
| ~ member(C_1569,inverse2('#skF_15',B_1573))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_112,c_14370]) ).
tff(c_14436,plain,
! [B_1577,C_1578] :
( member('#skF_1'(B_1577,C_1578,'#skF_15'),'#skF_14')
| ~ member(C_1578,inverse2('#skF_15',B_1577)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10262,c_14386]) ).
tff(c_8340,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('#skF_16',G_307),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| ilf_type('#skF_17',member_type('#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_8600,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair('#skF_16',G_307),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14')) ),
inference(negUnitSimplification,[status(thm)],[c_8340,c_138]) ).
tff(c_10179,plain,
! [B_1286] :
( ~ member('#skF_1'(B_1286,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1286,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',inverse2('#skF_15',B_1286))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_10136,c_8600]) ).
tff(c_10404,plain,
! [B_1310] :
( ~ member('#skF_1'(B_1310,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1310,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',inverse2('#skF_15',B_1310)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10262,c_10179]) ).
tff(c_10407,plain,
! [B_1310] :
( ~ member('#skF_1'(B_1310,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_1310))
| ~ member('#skF_1'(B_1310,'#skF_16','#skF_15'),'#skF_14')
| empty('#skF_14') ),
inference(resolution,[status(thm)],[c_213,c_10404]) ).
tff(c_10410,plain,
! [B_1310] :
( ~ member('#skF_1'(B_1310,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_1310))
| ~ member('#skF_1'(B_1310,'#skF_16','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_116,c_10407]) ).
tff(c_14504,plain,
! [B_1598] :
( ~ member('#skF_1'(B_1598,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_1598)) ),
inference(resolution,[status(thm)],[c_14436,c_10410]) ).
tff(c_14512,plain,
( ~ member('#skF_16',inverse2('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_235,c_14504]) ).
tff(c_14519,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10262,c_9219,c_14512]) ).
tff(c_14521,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('#skF_16',G_307),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14'))
| member('#skF_17','#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_14746,plain,
! [G_307] :
( ~ member(G_307,'#skF_13')
| ~ member(ordered_pair('#skF_16',G_307),'#skF_15')
| ~ ilf_type(G_307,member_type('#skF_14')) ),
inference(negUnitSimplification,[status(thm)],[c_14521,c_130]) ).
tff(c_16126,plain,
! [B_1806] :
( ~ member('#skF_1'(B_1806,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1806,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',inverse2('#skF_15',B_1806))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_16086,c_14746]) ).
tff(c_16210,plain,
~ ilf_type('#skF_15',binary_relation_type),
inference(splitLeft,[status(thm)],[c_16126]) ).
tff(c_16213,plain,
~ relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_191,c_16210]) ).
tff(c_16217,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14957,c_16213]) ).
tff(c_16219,plain,
ilf_type('#skF_15',binary_relation_type),
inference(splitRight,[status(thm)],[c_16126]) ).
tff(c_15792,plain,
! [B_1778,C_1779,D_1780,E_1781] :
( ( inverse4(B_1778,C_1779,D_1780,E_1781) = inverse2(D_1780,E_1781) )
| ~ ilf_type(D_1780,relation_type(B_1778,C_1779)) ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_108,c_104]) ).
tff(c_15816,plain,
! [E_1781] : ( inverse4('#skF_12','#skF_14','#skF_15',E_1781) = inverse2('#skF_15',E_1781) ),
inference(resolution,[status(thm)],[c_112,c_15792]) ).
tff(c_14520,plain,
member('#skF_16',inverse4('#skF_12','#skF_14','#skF_15','#skF_13')),
inference(splitRight,[status(thm)],[c_132]) ).
tff(c_15821,plain,
member('#skF_16',inverse2('#skF_15','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_15816,c_14520]) ).
tff(c_20686,plain,
! [D_2117,C_2114,B_2118,B_2115,C_2116] :
( member('#skF_1'(B_2115,C_2114,D_2117),C_2116)
| ~ ilf_type(D_2117,relation_type(B_2118,C_2116))
| ~ member(C_2114,inverse2(D_2117,B_2115))
| ~ ilf_type(D_2117,binary_relation_type) ),
inference(resolution,[status(thm)],[c_16086,c_229]) ).
tff(c_20702,plain,
! [B_2115,C_2114] :
( member('#skF_1'(B_2115,C_2114,'#skF_15'),'#skF_14')
| ~ member(C_2114,inverse2('#skF_15',B_2115))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_112,c_20686]) ).
tff(c_20716,plain,
! [B_2122,C_2123] :
( member('#skF_1'(B_2122,C_2123,'#skF_15'),'#skF_14')
| ~ member(C_2123,inverse2('#skF_15',B_2122)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16219,c_20702]) ).
tff(c_17951,plain,
! [B_1922] :
( ~ member('#skF_1'(B_1922,'#skF_16','#skF_15'),'#skF_13')
| ~ ilf_type('#skF_1'(B_1922,'#skF_16','#skF_15'),member_type('#skF_14'))
| ~ member('#skF_16',inverse2('#skF_15',B_1922)) ),
inference(splitRight,[status(thm)],[c_16126]) ).
tff(c_17954,plain,
! [B_1922] :
( ~ member('#skF_1'(B_1922,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_1922))
| ~ member('#skF_1'(B_1922,'#skF_16','#skF_15'),'#skF_14')
| empty('#skF_14') ),
inference(resolution,[status(thm)],[c_213,c_17951]) ).
tff(c_17957,plain,
! [B_1922] :
( ~ member('#skF_1'(B_1922,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_1922))
| ~ member('#skF_1'(B_1922,'#skF_16','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_116,c_17954]) ).
tff(c_20764,plain,
! [B_2134] :
( ~ member('#skF_1'(B_2134,'#skF_16','#skF_15'),'#skF_13')
| ~ member('#skF_16',inverse2('#skF_15',B_2134)) ),
inference(resolution,[status(thm)],[c_20716,c_17957]) ).
tff(c_20772,plain,
( ~ member('#skF_16',inverse2('#skF_15','#skF_13'))
| ~ ilf_type('#skF_15',binary_relation_type) ),
inference(resolution,[status(thm)],[c_235,c_20764]) ).
tff(c_20779,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16219,c_15821,c_20772]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 16:37:31 EDT 2023
% 0.14/0.34 % CPUTime :
% 13.86/4.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.86/4.68
% 13.86/4.68 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.86/4.72
% 13.86/4.72 Inference rules
% 13.86/4.72 ----------------------
% 13.86/4.72 #Ref : 4
% 13.86/4.72 #Sup : 4826
% 13.86/4.72 #Fact : 22
% 13.86/4.72 #Define : 0
% 13.86/4.72 #Split : 25
% 13.86/4.72 #Chain : 0
% 13.86/4.72 #Close : 0
% 13.86/4.72
% 13.86/4.72 Ordering : KBO
% 13.86/4.72
% 13.86/4.72 Simplification rules
% 13.86/4.72 ----------------------
% 13.86/4.72 #Subsume : 1510
% 13.86/4.72 #Demod : 393
% 13.86/4.72 #Tautology : 314
% 13.86/4.72 #SimpNegUnit : 298
% 13.86/4.72 #BackRed : 49
% 13.86/4.72
% 13.86/4.72 #Partial instantiations: 0
% 13.86/4.72 #Strategies tried : 1
% 13.86/4.72
% 13.86/4.72 Timing (in seconds)
% 13.86/4.72 ----------------------
% 14.17/4.72 Preprocessing : 0.66
% 14.17/4.72 Parsing : 0.33
% 14.17/4.72 CNF conversion : 0.07
% 14.17/4.72 Main loop : 2.97
% 14.17/4.72 Inferencing : 1.03
% 14.17/4.72 Reduction : 0.96
% 14.17/4.72 Demodulation : 0.66
% 14.17/4.73 BG Simplification : 0.08
% 14.17/4.73 Subsumption : 0.66
% 14.17/4.73 Abstraction : 0.09
% 14.17/4.73 MUC search : 0.00
% 14.17/4.73 Cooper : 0.00
% 14.17/4.73 Total : 3.71
% 14.17/4.73 Index Insertion : 0.00
% 14.17/4.73 Index Deletion : 0.00
% 14.17/4.73 Index Matching : 0.00
% 14.17/4.73 BG Taut test : 0.00
%------------------------------------------------------------------------------