%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET667+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n016.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 08:39:02 PM UTC 2025
% Result : Theorem 36.90s 23.07s
% Output : CNFRefutation 37.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 192 ( 81 ~; 73 |; 5 &)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 29 ( 29 usr; 7 con; 0-3 aty)
% Number of variables : 114 ( 114 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > range > domain > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > identity_relation_of > domain_of > set_type > binary_relation_type > #skF_15 > #skF_8 > #skF_3 > #skF_16 > #skF_14 > #skF_5 > #skF_13 > #skF_10 > #skF_11 > #skF_2 > #skF_12 > #skF_7 > #skF_1 > #skF_9 > #skF_6 > #skF_4
%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_15',type,
'#skF_15': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(identity_relation_of,type,
identity_relation_of: $i > $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(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_10',type,
'#skF_10': ( $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_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_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('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_352,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_30) ).
tff(f_333,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
tff(f_319,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/sandbox/benchmark/theBenchmark.p',p29) ).
tff(f_297,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/sandbox/benchmark/theBenchmark.p',p27) ).
tff(f_112,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/sandbox/benchmark/theBenchmark.p',p7) ).
tff(f_88,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/sandbox/benchmark/theBenchmark.p',p5) ).
tff(f_268,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/sandbox/benchmark/theBenchmark.p',p24) ).
tff(f_165,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
tff(f_67,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(ordered_pair(C,D),identity_relation_of(B))
<=> ( member(C,B)
& ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
tff(f_42,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/sandbox/benchmark/theBenchmark.p',p1) ).
tff(c_122,plain,
ilf_type('#skF_16',relation_type('#skF_13','#skF_14')),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_116,plain,
! [B_169] : ilf_type(B_169,set_type),
inference(cnfTransformation,[status(thm)],[f_333]) ).
tff(c_112,plain,
! [B_155,C_159,D_161] :
( ( range(B_155,C_159,D_161) = range_of(D_161) )
| ~ ilf_type(D_161,relation_type(B_155,C_159))
| ~ ilf_type(C_159,set_type)
| ~ ilf_type(B_155,set_type) ),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_50654,plain,
! [B_1492,C_1493,D_1494] :
( ( range(B_1492,C_1493,D_1494) = range_of(D_1494) )
| ~ ilf_type(D_1494,relation_type(B_1492,C_1493)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_112]) ).
tff(c_50674,plain,
range('#skF_13','#skF_14','#skF_16') = range_of('#skF_16'),
inference(resolution,[status(thm)],[c_122,c_50654]) ).
tff(c_108,plain,
! [B_141,C_145,D_147] :
( ( domain(B_141,C_145,D_147) = domain_of(D_147) )
| ~ ilf_type(D_147,relation_type(B_141,C_145))
| ~ ilf_type(C_145,set_type)
| ~ ilf_type(B_141,set_type) ),
inference(cnfTransformation,[status(thm)],[f_297]) ).
tff(c_685,plain,
! [B_284,C_285,D_286] :
( ( domain(B_284,C_285,D_286) = domain_of(D_286) )
| ~ ilf_type(D_286,relation_type(B_284,C_285)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_108]) ).
tff(c_705,plain,
domain('#skF_13','#skF_14','#skF_16') = domain_of('#skF_16'),
inference(resolution,[status(thm)],[c_122,c_685]) ).
tff(c_118,plain,
( ~ subset('#skF_15',range('#skF_13','#skF_14','#skF_16'))
| ~ subset('#skF_15',domain('#skF_13','#skF_14','#skF_16')) ),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_268,plain,
~ subset('#skF_15',domain('#skF_13','#skF_14','#skF_16')),
inference(splitLeft,[status(thm)],[c_118]) ).
tff(c_706,plain,
~ subset('#skF_15',domain_of('#skF_16')),
inference(demodulation,[status(thm),theory(equality)],[c_705,c_268]) ).
tff(c_28,plain,
! [B_36,C_42] :
( member('#skF_2'(B_36,C_42),B_36)
| subset(B_36,C_42)
| ~ ilf_type(C_42,set_type)
| ~ ilf_type(B_36,set_type) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_206,plain,
! [B_36,C_42] :
( member('#skF_2'(B_36,C_42),B_36)
| subset(B_36,C_42) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_28]) ).
tff(c_18,plain,
! [E_29,B_19,C_25] :
( ilf_type(E_29,subset_type(cross_product(B_19,C_25)))
| ~ ilf_type(E_29,relation_type(B_19,C_25))
| ~ ilf_type(C_25,set_type)
| ~ ilf_type(B_19,set_type) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_766,plain,
! [E_302,B_303,C_304] :
( ilf_type(E_302,subset_type(cross_product(B_303,C_304)))
| ~ ilf_type(E_302,relation_type(B_303,C_304)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_18]) ).
tff(c_98,plain,
! [D_135,B_129,C_133] :
( relation_like(D_135)
| ~ ilf_type(D_135,subset_type(cross_product(B_129,C_133)))
| ~ ilf_type(C_133,set_type)
| ~ ilf_type(B_129,set_type) ),
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_149,plain,
! [D_135,B_129,C_133] :
( relation_like(D_135)
| ~ ilf_type(D_135,subset_type(cross_product(B_129,C_133))) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_98]) ).
tff(c_780,plain,
! [E_305,B_306,C_307] :
( relation_like(E_305)
| ~ ilf_type(E_305,relation_type(B_306,C_307)) ),
inference(resolution,[status(thm)],[c_766,c_149]) ).
tff(c_807,plain,
relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_122,c_780]) ).
tff(c_50,plain,
! [B_79] :
( ilf_type(B_79,binary_relation_type)
| ~ relation_like(B_79)
| ~ ilf_type(B_79,set_type) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_192,plain,
! [B_79] :
( ilf_type(B_79,binary_relation_type)
| ~ relation_like(B_79) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_50]) ).
tff(c_120,plain,
subset(identity_relation_of('#skF_15'),'#skF_16'),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_10,plain,
! [D_17,B_11] :
( member(ordered_pair(D_17,D_17),identity_relation_of(B_11))
| ~ member(D_17,B_11)
| ~ ilf_type(D_17,set_type)
| ~ ilf_type(B_11,set_type) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_532,plain,
! [D_257,B_258] :
( member(ordered_pair(D_257,D_257),identity_relation_of(B_258))
| ~ member(D_257,B_258) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_10]) ).
tff(c_24,plain,
! [D_45,C_42,B_36] :
( member(D_45,C_42)
| ~ member(D_45,B_36)
| ~ ilf_type(D_45,set_type)
| ~ subset(B_36,C_42)
| ~ ilf_type(C_42,set_type)
| ~ ilf_type(B_36,set_type) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_210,plain,
! [D_45,C_42,B_36] :
( member(D_45,C_42)
| ~ member(D_45,B_36)
| ~ subset(B_36,C_42) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_116,c_24]) ).
tff(c_1767,plain,
! [D_417,C_418,B_419] :
( member(ordered_pair(D_417,D_417),C_418)
| ~ subset(identity_relation_of(B_419),C_418)
| ~ member(D_417,B_419) ),
inference(resolution,[status(thm)],[c_532,c_210]) ).
tff(c_1785,plain,
! [D_421] :
( member(ordered_pair(D_421,D_421),'#skF_16')
| ~ member(D_421,'#skF_15') ),
inference(resolution,[status(thm)],[c_120,c_1767]) ).
tff(c_4,plain,
! [B_1,D_7,C_5] :
( member(B_1,domain_of(D_7))
| ~ member(ordered_pair(B_1,C_5),D_7)
| ~ ilf_type(D_7,binary_relation_type)
| ~ ilf_type(C_5,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_230,plain,
! [B_1,D_7,C_5] :
( member(B_1,domain_of(D_7))
| ~ member(ordered_pair(B_1,C_5),D_7)
| ~ ilf_type(D_7,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_4]) ).
tff(c_1799,plain,
! [D_421] :
( member(D_421,domain_of('#skF_16'))
| ~ ilf_type('#skF_16',binary_relation_type)
| ~ member(D_421,'#skF_15') ),
inference(resolution,[status(thm)],[c_1785,c_230]) ).
tff(c_1963,plain,
~ ilf_type('#skF_16',binary_relation_type),
inference(splitLeft,[status(thm)],[c_1799]) ).
tff(c_1966,plain,
~ relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_192,c_1963]) ).
tff(c_1970,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_807,c_1966]) ).
tff(c_1978,plain,
! [D_438] :
( member(D_438,domain_of('#skF_16'))
| ~ member(D_438,'#skF_15') ),
inference(splitRight,[status(thm)],[c_1799]) ).
tff(c_26,plain,
! [B_36,C_42] :
( ~ member('#skF_2'(B_36,C_42),C_42)
| subset(B_36,C_42)
| ~ ilf_type(C_42,set_type)
| ~ ilf_type(B_36,set_type) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_208,plain,
! [B_36,C_42] :
( ~ member('#skF_2'(B_36,C_42),C_42)
| subset(B_36,C_42) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_26]) ).
tff(c_50190,plain,
! [B_1401] :
( subset(B_1401,domain_of('#skF_16'))
| ~ member('#skF_2'(B_1401,domain_of('#skF_16')),'#skF_15') ),
inference(resolution,[status(thm)],[c_1978,c_208]) ).
tff(c_50202,plain,
subset('#skF_15',domain_of('#skF_16')),
inference(resolution,[status(thm)],[c_206,c_50190]) ).
tff(c_50208,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_706,c_706,c_50202]) ).
tff(c_50209,plain,
~ subset('#skF_15',range('#skF_13','#skF_14','#skF_16')),
inference(splitRight,[status(thm)],[c_118]) ).
tff(c_50676,plain,
~ subset('#skF_15',range_of('#skF_16')),
inference(demodulation,[status(thm),theory(equality)],[c_50674,c_50209]) ).
tff(c_50552,plain,
! [E_1470,B_1471,C_1472] :
( ilf_type(E_1470,subset_type(cross_product(B_1471,C_1472)))
| ~ ilf_type(E_1470,relation_type(B_1471,C_1472)) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_18]) ).
tff(c_50562,plain,
! [E_1473,B_1474,C_1475] :
( relation_like(E_1473)
| ~ ilf_type(E_1473,relation_type(B_1474,C_1475)) ),
inference(resolution,[status(thm)],[c_50552,c_149]) ).
tff(c_50570,plain,
relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_122,c_50562]) ).
tff(c_224,plain,
! [D_17,B_11] :
( member(ordered_pair(D_17,D_17),identity_relation_of(B_11))
| ~ member(D_17,B_11) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_10]) ).
tff(c_50317,plain,
! [D_1437,C_1438,B_1439] :
( member(D_1437,C_1438)
| ~ member(D_1437,B_1439)
| ~ subset(B_1439,C_1438) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_116,c_24]) ).
tff(c_51750,plain,
! [D_1618,C_1619,B_1620] :
( member(ordered_pair(D_1618,D_1618),C_1619)
| ~ subset(identity_relation_of(B_1620),C_1619)
| ~ member(D_1618,B_1620) ),
inference(resolution,[status(thm)],[c_224,c_50317]) ).
tff(c_51768,plain,
! [D_1622] :
( member(ordered_pair(D_1622,D_1622),'#skF_16')
| ~ member(D_1622,'#skF_15') ),
inference(resolution,[status(thm)],[c_120,c_51750]) ).
tff(c_51783,plain,
! [D_1622] :
( member(D_1622,domain_of('#skF_16'))
| ~ ilf_type('#skF_16',binary_relation_type)
| ~ member(D_1622,'#skF_15') ),
inference(resolution,[status(thm)],[c_51768,c_230]) ).
tff(c_51963,plain,
~ ilf_type('#skF_16',binary_relation_type),
inference(splitLeft,[status(thm)],[c_51783]) ).
tff(c_51966,plain,
~ relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_192,c_51963]) ).
tff(c_51970,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50570,c_51966]) ).
tff(c_51972,plain,
ilf_type('#skF_16',binary_relation_type),
inference(splitRight,[status(thm)],[c_51783]) ).
tff(c_2,plain,
! [C_5,D_7,B_1] :
( member(C_5,range_of(D_7))
| ~ member(ordered_pair(B_1,C_5),D_7)
| ~ ilf_type(D_7,binary_relation_type)
| ~ ilf_type(C_5,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_232,plain,
! [C_5,D_7,B_1] :
( member(C_5,range_of(D_7))
| ~ member(ordered_pair(B_1,C_5),D_7)
| ~ ilf_type(D_7,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_116,c_2]) ).
tff(c_51782,plain,
! [D_1622] :
( member(D_1622,range_of('#skF_16'))
| ~ ilf_type('#skF_16',binary_relation_type)
| ~ member(D_1622,'#skF_15') ),
inference(resolution,[status(thm)],[c_51768,c_232]) ).
tff(c_52159,plain,
! [D_1645] :
( member(D_1645,range_of('#skF_16'))
| ~ member(D_1645,'#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_51972,c_51782]) ).
tff(c_101320,plain,
! [B_2629] :
( subset(B_2629,range_of('#skF_16'))
| ~ member('#skF_2'(B_2629,range_of('#skF_16')),'#skF_15') ),
inference(resolution,[status(thm)],[c_52159,c_208]) ).
tff(c_101332,plain,
subset('#skF_15',range_of('#skF_16')),
inference(resolution,[status(thm)],[c_206,c_101320]) ).
tff(c_101338,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50676,c_50676,c_101332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET667+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.32 % Computer : n016.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Apr 8 21:23:23 EDT 2025
% 0.13/0.32 % CPUTime :
% 36.90/23.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.90/23.08
% 36.90/23.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------