TSTP Solution File: SET678+3 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET678+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/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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:56:52 EDT 2023
% Result : Theorem 8.21s 3.11s
% Output : CNFRefutation 9.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 54
% Syntax : Number of formulae : 140 ( 28 unt; 37 typ; 0 def)
% Number of atoms : 258 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 263 ( 108 ~; 101 |; 5 &)
% ( 6 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 32 >; 25 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 5 con; 0-5 aty)
% Number of variables : 167 (; 167 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > compose5 > range > domain > relation_type > ordered_pair > cross_product > compose > #nlpp > subset_type > range_of > power_set > member_type > identity_relation_of_type > identity_relation_of > domain_of > set_type > binary_relation_type > #skF_6 > #skF_2 > #skF_15 > #skF_8 > #skF_3 > #skF_16 > #skF_12 > #skF_5 > #skF_10 > #skF_13 > #skF_11 > #skF_14 > #skF_7 > #skF_1 > #skF_9 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(identity_relation_of_type,type,
identity_relation_of_type: $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(compose5,type,
compose5: ( $i * $i * $i * $i * $i ) > $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('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $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_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('#skF_13',type,
'#skF_13': $i > $i ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(subset_type,type,
subset_type: $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 * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_427,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( ( compose(C,identity_relation_of(B)) = C )
& ( compose(identity_relation_of(B),C) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_45) ).
tff(f_416,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38) ).
tff(f_105,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
tff(f_175,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',p15) ).
tff(f_272,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',p25) ).
tff(f_156,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_346,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',p32) ).
tff(f_357,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
tff(f_368,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',p34) ).
tff(f_379,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p35) ).
tff(f_295,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
tff(f_237,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
tff(f_308,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/sandbox/benchmark/theBenchmark.p',p28) ).
tff(f_214,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',p19) ).
tff(f_287,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/sandbox/benchmark/theBenchmark.p',p26) ).
tff(f_46,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(range_of(C),B)
=> ( compose(C,identity_relation_of(B)) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(f_36,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ( compose(identity_relation_of(B),C) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(c_146,plain,
ilf_type('#skF_16',identity_relation_of_type('#skF_15')),
inference(cnfTransformation,[status(thm)],[f_427]) ).
tff(c_142,plain,
! [B_284] : ilf_type(B_284,set_type),
inference(cnfTransformation,[status(thm)],[f_416]) ).
tff(c_26,plain,
! [C_66,B_64] :
( ilf_type(C_66,relation_type(B_64,B_64))
| ~ ilf_type(C_66,identity_relation_of_type(B_64))
| ~ ilf_type(C_66,set_type)
| ~ ilf_type(B_64,set_type) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_239,plain,
! [C_66,B_64] :
( ilf_type(C_66,relation_type(B_64,B_64))
| ~ ilf_type(C_66,identity_relation_of_type(B_64)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_26]) ).
tff(c_60,plain,
! [E_110,B_100,C_106] :
( ilf_type(E_110,subset_type(cross_product(B_100,C_106)))
| ~ ilf_type(E_110,relation_type(B_100,C_106))
| ~ ilf_type(C_106,set_type)
| ~ ilf_type(B_100,set_type) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_3668,plain,
! [E_740,B_741,C_742] :
( ilf_type(E_740,subset_type(cross_product(B_741,C_742)))
| ~ ilf_type(E_740,relation_type(B_741,C_742)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_60]) ).
tff(c_102,plain,
! [D_172,B_166,C_170] :
( relation_like(D_172)
| ~ ilf_type(D_172,subset_type(cross_product(B_166,C_170)))
| ~ ilf_type(C_170,set_type)
| ~ ilf_type(B_166,set_type) ),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_189,plain,
! [D_172,B_166,C_170] :
( relation_like(D_172)
| ~ ilf_type(D_172,subset_type(cross_product(B_166,C_170))) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_102]) ).
tff(c_3689,plain,
! [E_744,B_745,C_746] :
( relation_like(E_744)
| ~ ilf_type(E_744,relation_type(B_745,C_746)) ),
inference(resolution,[status(thm)],[c_3668,c_189]) ).
tff(c_3708,plain,
! [C_749,B_750] :
( relation_like(C_749)
| ~ ilf_type(C_749,identity_relation_of_type(B_750)) ),
inference(resolution,[status(thm)],[c_239,c_3689]) ).
tff(c_3730,plain,
relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_146,c_3708]) ).
tff(c_52,plain,
! [B_99] :
( ilf_type(B_99,binary_relation_type)
| ~ relation_like(B_99)
| ~ ilf_type(B_99,set_type) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_229,plain,
! [B_99] :
( ilf_type(B_99,binary_relation_type)
| ~ relation_like(B_99) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_52]) ).
tff(c_761,plain,
! [E_393,B_394,C_395] :
( ilf_type(E_393,subset_type(cross_product(B_394,C_395)))
| ~ ilf_type(E_393,relation_type(B_394,C_395)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_60]) ).
tff(c_771,plain,
! [E_396,B_397,C_398] :
( relation_like(E_396)
| ~ ilf_type(E_396,relation_type(B_397,C_398)) ),
inference(resolution,[status(thm)],[c_761,c_189]) ).
tff(c_781,plain,
! [C_401,B_402] :
( relation_like(C_401)
| ~ ilf_type(C_401,identity_relation_of_type(B_402)) ),
inference(resolution,[status(thm)],[c_239,c_771]) ).
tff(c_794,plain,
relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_146,c_781]) ).
tff(c_144,plain,
( ( compose(identity_relation_of('#skF_15'),'#skF_16') != '#skF_16' )
| ( compose('#skF_16',identity_relation_of('#skF_15')) != '#skF_16' ) ),
inference(cnfTransformation,[status(thm)],[f_427]) ).
tff(c_269,plain,
compose('#skF_16',identity_relation_of('#skF_15')) != '#skF_16',
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_130,plain,
! [B_194,C_198,D_200] :
( ( domain(B_194,C_198,D_200) = domain_of(D_200) )
| ~ ilf_type(D_200,relation_type(B_194,C_198))
| ~ ilf_type(C_198,set_type)
| ~ ilf_type(B_194,set_type) ),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_986,plain,
! [B_430,C_431,D_432] :
( ( domain(B_430,C_431,D_432) = domain_of(D_432) )
| ~ ilf_type(D_432,relation_type(B_430,C_431)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_130]) ).
tff(c_1180,plain,
! [B_458,C_459] :
( ( domain(B_458,B_458,C_459) = domain_of(C_459) )
| ~ ilf_type(C_459,identity_relation_of_type(B_458)) ),
inference(resolution,[status(thm)],[c_239,c_986]) ).
tff(c_1204,plain,
domain('#skF_15','#skF_15','#skF_16') = domain_of('#skF_16'),
inference(resolution,[status(thm)],[c_146,c_1180]) ).
tff(c_132,plain,
! [B_201,C_205,D_207] :
( ilf_type(domain(B_201,C_205,D_207),subset_type(B_201))
| ~ ilf_type(D_207,relation_type(B_201,C_205))
| ~ ilf_type(C_205,set_type)
| ~ ilf_type(B_201,set_type) ),
inference(cnfTransformation,[status(thm)],[f_357]) ).
tff(c_159,plain,
! [B_201,C_205,D_207] :
( ilf_type(domain(B_201,C_205,D_207),subset_type(B_201))
| ~ ilf_type(D_207,relation_type(B_201,C_205)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_132]) ).
tff(c_1208,plain,
( ilf_type(domain_of('#skF_16'),subset_type('#skF_15'))
| ~ ilf_type('#skF_16',relation_type('#skF_15','#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_1204,c_159]) ).
tff(c_1376,plain,
~ ilf_type('#skF_16',relation_type('#skF_15','#skF_15')),
inference(splitLeft,[status(thm)],[c_1208]) ).
tff(c_1382,plain,
~ ilf_type('#skF_16',identity_relation_of_type('#skF_15')),
inference(resolution,[status(thm)],[c_239,c_1376]) ).
tff(c_1387,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_146,c_1382]) ).
tff(c_1389,plain,
ilf_type('#skF_16',relation_type('#skF_15','#skF_15')),
inference(splitRight,[status(thm)],[c_1208]) ).
tff(c_134,plain,
! [B_208,C_212,D_214] :
( ( range(B_208,C_212,D_214) = range_of(D_214) )
| ~ ilf_type(D_214,relation_type(B_208,C_212))
| ~ ilf_type(C_212,set_type)
| ~ ilf_type(B_208,set_type) ),
inference(cnfTransformation,[status(thm)],[f_368]) ).
tff(c_157,plain,
! [B_208,C_212,D_214] :
( ( range(B_208,C_212,D_214) = range_of(D_214) )
| ~ ilf_type(D_214,relation_type(B_208,C_212)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_134]) ).
tff(c_1410,plain,
range('#skF_15','#skF_15','#skF_16') = range_of('#skF_16'),
inference(resolution,[status(thm)],[c_1389,c_157]) ).
tff(c_136,plain,
! [B_215,C_219,D_221] :
( ilf_type(range(B_215,C_219,D_221),subset_type(C_219))
| ~ ilf_type(D_221,relation_type(B_215,C_219))
| ~ ilf_type(C_219,set_type)
| ~ ilf_type(B_215,set_type) ),
inference(cnfTransformation,[status(thm)],[f_379]) ).
tff(c_155,plain,
! [B_215,C_219,D_221] :
( ilf_type(range(B_215,C_219,D_221),subset_type(C_219))
| ~ ilf_type(D_221,relation_type(B_215,C_219)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_136]) ).
tff(c_1433,plain,
( ilf_type(range_of('#skF_16'),subset_type('#skF_15'))
| ~ ilf_type('#skF_16',relation_type('#skF_15','#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_1410,c_155]) ).
tff(c_1437,plain,
ilf_type(range_of('#skF_16'),subset_type('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_1389,c_1433]) ).
tff(c_114,plain,
! [B_183] :
( ~ empty(power_set(B_183))
| ~ ilf_type(B_183,set_type) ),
inference(cnfTransformation,[status(thm)],[f_295]) ).
tff(c_177,plain,
! [B_183] : ~ empty(power_set(B_183)),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_114]) ).
tff(c_86,plain,
! [C_137,B_135] :
( ilf_type(C_137,member_type(power_set(B_135)))
| ~ ilf_type(C_137,subset_type(B_135))
| ~ ilf_type(C_137,set_type)
| ~ ilf_type(B_135,set_type) ),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_514,plain,
! [C_353,B_354] :
( ilf_type(C_353,member_type(power_set(B_354)))
| ~ ilf_type(C_353,subset_type(B_354)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_86]) ).
tff(c_118,plain,
! [B_184,C_186] :
( member(B_184,C_186)
| ~ ilf_type(B_184,member_type(C_186))
| ~ ilf_type(C_186,set_type)
| empty(C_186)
| ~ ilf_type(B_184,set_type) ),
inference(cnfTransformation,[status(thm)],[f_308]) ).
tff(c_173,plain,
! [B_184,C_186] :
( member(B_184,C_186)
| ~ ilf_type(B_184,member_type(C_186))
| empty(C_186) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_118]) ).
tff(c_520,plain,
! [C_353,B_354] :
( member(C_353,power_set(B_354))
| empty(power_set(B_354))
| ~ ilf_type(C_353,subset_type(B_354)) ),
inference(resolution,[status(thm)],[c_514,c_173]) ).
tff(c_524,plain,
! [C_353,B_354] :
( member(C_353,power_set(B_354))
| ~ ilf_type(C_353,subset_type(B_354)) ),
inference(negUnitSimplification,[status(thm)],[c_177,c_520]) ).
tff(c_76,plain,
! [B_121,C_127] :
( member('#skF_7'(B_121,C_127),B_121)
| subset(B_121,C_127)
| ~ ilf_type(C_127,set_type)
| ~ ilf_type(B_121,set_type) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_215,plain,
! [B_121,C_127] :
( member('#skF_7'(B_121,C_127),B_121)
| subset(B_121,C_127) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_76]) ).
tff(c_104,plain,
! [D_182,C_179,B_173] :
( member(D_182,C_179)
| ~ member(D_182,B_173)
| ~ ilf_type(D_182,set_type)
| ~ member(B_173,power_set(C_179))
| ~ ilf_type(C_179,set_type)
| ~ ilf_type(B_173,set_type) ),
inference(cnfTransformation,[status(thm)],[f_287]) ).
tff(c_666,plain,
! [D_380,C_381,B_382] :
( member(D_380,C_381)
| ~ member(D_380,B_382)
| ~ member(B_382,power_set(C_381)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_142,c_104]) ).
tff(c_2616,plain,
! [B_597,C_598,C_599] :
( member('#skF_7'(B_597,C_598),C_599)
| ~ member(B_597,power_set(C_599))
| subset(B_597,C_598) ),
inference(resolution,[status(thm)],[c_215,c_666]) ).
tff(c_74,plain,
! [B_121,C_127] :
( ~ member('#skF_7'(B_121,C_127),C_127)
| subset(B_121,C_127)
| ~ ilf_type(C_127,set_type)
| ~ ilf_type(B_121,set_type) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_217,plain,
! [B_121,C_127] :
( ~ member('#skF_7'(B_121,C_127),C_127)
| subset(B_121,C_127) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_74]) ).
tff(c_2652,plain,
! [B_600,C_601] :
( ~ member(B_600,power_set(C_601))
| subset(B_600,C_601) ),
inference(resolution,[status(thm)],[c_2616,c_217]) ).
tff(c_2854,plain,
! [C_605,B_606] :
( subset(C_605,B_606)
| ~ ilf_type(C_605,subset_type(B_606)) ),
inference(resolution,[status(thm)],[c_524,c_2652]) ).
tff(c_2906,plain,
subset(range_of('#skF_16'),'#skF_15'),
inference(resolution,[status(thm)],[c_1437,c_2854]) ).
tff(c_4,plain,
! [C_6,B_4] :
( ( compose(C_6,identity_relation_of(B_4)) = C_6 )
| ~ subset(range_of(C_6),B_4)
| ~ ilf_type(C_6,binary_relation_type)
| ~ ilf_type(B_4,set_type) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_259,plain,
! [C_6,B_4] :
( ( compose(C_6,identity_relation_of(B_4)) = C_6 )
| ~ subset(range_of(C_6),B_4)
| ~ ilf_type(C_6,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_4]) ).
tff(c_2975,plain,
( ( compose('#skF_16',identity_relation_of('#skF_15')) = '#skF_16' )
| ~ ilf_type('#skF_16',binary_relation_type) ),
inference(resolution,[status(thm)],[c_2906,c_259]) ).
tff(c_2987,plain,
~ ilf_type('#skF_16',binary_relation_type),
inference(negUnitSimplification,[status(thm)],[c_269,c_2975]) ).
tff(c_3001,plain,
~ relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_229,c_2987]) ).
tff(c_3005,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_794,c_3001]) ).
tff(c_3006,plain,
compose(identity_relation_of('#skF_15'),'#skF_16') != '#skF_16',
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_3412,plain,
! [B_694,C_695,D_696] :
( ( domain(B_694,C_695,D_696) = domain_of(D_696) )
| ~ ilf_type(D_696,relation_type(B_694,C_695)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_130]) ).
tff(c_3547,plain,
! [B_722,C_723] :
( ( domain(B_722,B_722,C_723) = domain_of(C_723) )
| ~ ilf_type(C_723,identity_relation_of_type(B_722)) ),
inference(resolution,[status(thm)],[c_239,c_3412]) ).
tff(c_3556,plain,
domain('#skF_15','#skF_15','#skF_16') = domain_of('#skF_16'),
inference(resolution,[status(thm)],[c_146,c_3547]) ).
tff(c_3774,plain,
! [B_757,C_758,D_759] :
( ilf_type(domain(B_757,C_758,D_759),subset_type(B_757))
| ~ ilf_type(D_759,relation_type(B_757,C_758)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_132]) ).
tff(c_3788,plain,
( ilf_type(domain_of('#skF_16'),subset_type('#skF_15'))
| ~ ilf_type('#skF_16',relation_type('#skF_15','#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_3556,c_3774]) ).
tff(c_3873,plain,
~ ilf_type('#skF_16',relation_type('#skF_15','#skF_15')),
inference(splitLeft,[status(thm)],[c_3788]) ).
tff(c_3879,plain,
~ ilf_type('#skF_16',identity_relation_of_type('#skF_15')),
inference(resolution,[status(thm)],[c_239,c_3873]) ).
tff(c_3884,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_146,c_3879]) ).
tff(c_3885,plain,
ilf_type(domain_of('#skF_16'),subset_type('#skF_15')),
inference(splitRight,[status(thm)],[c_3788]) ).
tff(c_205,plain,
! [C_137,B_135] :
( ilf_type(C_137,member_type(power_set(B_135)))
| ~ ilf_type(C_137,subset_type(B_135)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_86]) ).
tff(c_3110,plain,
! [B_653,C_654] :
( member(B_653,C_654)
| ~ ilf_type(B_653,member_type(C_654))
| empty(C_654) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_118]) ).
tff(c_3113,plain,
! [C_137,B_135] :
( member(C_137,power_set(B_135))
| empty(power_set(B_135))
| ~ ilf_type(C_137,subset_type(B_135)) ),
inference(resolution,[status(thm)],[c_205,c_3110]) ).
tff(c_3119,plain,
! [C_137,B_135] :
( member(C_137,power_set(B_135))
| ~ ilf_type(C_137,subset_type(B_135)) ),
inference(negUnitSimplification,[status(thm)],[c_177,c_3113]) ).
tff(c_3358,plain,
! [D_683,C_684,B_685] :
( member(D_683,C_684)
| ~ member(D_683,B_685)
| ~ member(B_685,power_set(C_684)) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_142,c_142,c_104]) ).
tff(c_5402,plain,
! [B_912,C_913,C_914] :
( member('#skF_7'(B_912,C_913),C_914)
| ~ member(B_912,power_set(C_914))
| subset(B_912,C_913) ),
inference(resolution,[status(thm)],[c_215,c_3358]) ).
tff(c_5438,plain,
! [B_915,C_916] :
( ~ member(B_915,power_set(C_916))
| subset(B_915,C_916) ),
inference(resolution,[status(thm)],[c_5402,c_217]) ).
tff(c_5645,plain,
! [C_921,B_922] :
( subset(C_921,B_922)
| ~ ilf_type(C_921,subset_type(B_922)) ),
inference(resolution,[status(thm)],[c_3119,c_5438]) ).
tff(c_5695,plain,
subset(domain_of('#skF_16'),'#skF_15'),
inference(resolution,[status(thm)],[c_3885,c_5645]) ).
tff(c_2,plain,
! [B_1,C_3] :
( ( compose(identity_relation_of(B_1),C_3) = C_3 )
| ~ subset(domain_of(C_3),B_1)
| ~ ilf_type(C_3,binary_relation_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_261,plain,
! [B_1,C_3] :
( ( compose(identity_relation_of(B_1),C_3) = C_3 )
| ~ subset(domain_of(C_3),B_1)
| ~ ilf_type(C_3,binary_relation_type) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_2]) ).
tff(c_5738,plain,
( ( compose(identity_relation_of('#skF_15'),'#skF_16') = '#skF_16' )
| ~ ilf_type('#skF_16',binary_relation_type) ),
inference(resolution,[status(thm)],[c_5695,c_261]) ).
tff(c_5750,plain,
~ ilf_type('#skF_16',binary_relation_type),
inference(negUnitSimplification,[status(thm)],[c_3006,c_5738]) ).
tff(c_5755,plain,
~ relation_like('#skF_16'),
inference(resolution,[status(thm)],[c_229,c_5750]) ).
tff(c_5759,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3730,c_5755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SET678+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.15 % 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
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 16:54:26 EDT 2023
% 0.14/0.36 % CPUTime :
% 8.21/3.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.98/3.12
% 8.98/3.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.08/3.16
% 9.08/3.16 Inference rules
% 9.08/3.16 ----------------------
% 9.08/3.16 #Ref : 2
% 9.08/3.16 #Sup : 1205
% 9.08/3.16 #Fact : 4
% 9.08/3.16 #Define : 0
% 9.08/3.16 #Split : 9
% 9.08/3.16 #Chain : 0
% 9.08/3.16 #Close : 0
% 9.08/3.16
% 9.08/3.16 Ordering : KBO
% 9.08/3.16
% 9.08/3.16 Simplification rules
% 9.08/3.16 ----------------------
% 9.08/3.16 #Subsume : 198
% 9.08/3.16 #Demod : 246
% 9.08/3.16 #Tautology : 208
% 9.08/3.16 #SimpNegUnit : 38
% 9.08/3.16 #BackRed : 5
% 9.08/3.16
% 9.08/3.16 #Partial instantiations: 0
% 9.08/3.16 #Strategies tried : 1
% 9.08/3.16
% 9.08/3.16 Timing (in seconds)
% 9.08/3.16 ----------------------
% 9.08/3.17 Preprocessing : 0.72
% 9.08/3.17 Parsing : 0.36
% 9.08/3.17 CNF conversion : 0.07
% 9.08/3.17 Main loop : 1.35
% 9.08/3.17 Inferencing : 0.56
% 9.08/3.17 Reduction : 0.39
% 9.08/3.17 Demodulation : 0.27
% 9.08/3.17 BG Simplification : 0.06
% 9.08/3.17 Subsumption : 0.24
% 9.08/3.17 Abstraction : 0.06
% 9.08/3.17 MUC search : 0.00
% 9.08/3.17 Cooper : 0.00
% 9.08/3.17 Total : 2.14
% 9.08/3.17 Index Insertion : 0.00
% 9.08/3.17 Index Deletion : 0.00
% 9.08/3.17 Index Matching : 0.00
% 9.08/3.17 BG Taut test : 0.00
%------------------------------------------------------------------------------