TSTP Solution File: SEU216+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU216+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : n018.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 10:58:02 EDT 2023
% Result : Theorem 18.50s 7.61s
% Output : CNFRefutation 18.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 44
% Syntax : Number of formulae : 246 ( 84 unt; 32 typ; 0 def)
% Number of atoms : 520 ( 208 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 515 ( 209 ~; 277 |; 11 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 22 >; 10 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-2 aty)
% Number of variables : 127 (; 126 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > unordered_pair > ordered_pair > apply > #nlpp > singleton > relation_rng > relation_dom > powerset > identity_relation > empty_set > #skF_5 > #skF_15 > #skF_8 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_11 > #skF_2 > #skF_1 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(identity_relation,type,
identity_relation: $i > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_192,negated_conjecture,
~ ! [A,B] :
( ( relation(B)
& function(B) )
=> ( ( B = identity_relation(A) )
<=> ( ( relation_dom(B) = A )
& ! [C] :
( in(C,A)
=> ( apply(B,C) = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
tff(f_149,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_213,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_70,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B,C] :
( ( in(B,relation_dom(A))
=> ( ( C = apply(A,B) )
<=> in(ordered_pair(B,C),A) ) )
& ( ~ in(B,relation_dom(A))
=> ( ( C = apply(A,B) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
tff(f_124,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
tff(f_52,axiom,
! [A,B] :
( relation(B)
=> ( ( B = identity_relation(A) )
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( in(C,A)
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
tff(f_240,axiom,
! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( in(A,relation_dom(C))
& ( B = apply(C,A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
tff(f_172,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
tff(f_178,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_93,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
tff(f_217,axiom,
! [A] :
( ( relation_dom(identity_relation(A)) = A )
& ( relation_rng(identity_relation(A)) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
tff(f_118,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
tff(c_128,plain,
( ( identity_relation('#skF_14') = '#skF_15' )
| ( relation_dom('#skF_15') = '#skF_14' ) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_167,plain,
relation_dom('#skF_15') = '#skF_14',
inference(splitLeft,[status(thm)],[c_128]) ).
tff(c_124,plain,
! [C_48] :
( ( apply('#skF_15','#skF_16') != '#skF_16' )
| ( relation_dom('#skF_15') != '#skF_14' )
| ( apply('#skF_15',C_48) = C_48 )
| ~ in(C_48,'#skF_14') ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_46339,plain,
! [C_48] :
( ( apply('#skF_15','#skF_16') != '#skF_16' )
| ( apply('#skF_15',C_48) = C_48 )
| ~ in(C_48,'#skF_14') ),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_124]) ).
tff(c_46340,plain,
apply('#skF_15','#skF_16') != '#skF_16',
inference(splitLeft,[status(thm)],[c_46339]) ).
tff(c_126,plain,
! [C_48] :
( in('#skF_16','#skF_14')
| ( relation_dom('#skF_15') != '#skF_14' )
| ( apply('#skF_15',C_48) = C_48 )
| ~ in(C_48,'#skF_14') ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_46302,plain,
! [C_48] :
( in('#skF_16','#skF_14')
| ( apply('#skF_15',C_48) = C_48 )
| ~ in(C_48,'#skF_14') ),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_126]) ).
tff(c_46303,plain,
in('#skF_16','#skF_14'),
inference(splitLeft,[status(thm)],[c_46302]) ).
tff(c_114,plain,
relation('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_112,plain,
function('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_90,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_194,plain,
! [A_78] :
( ( empty_set = A_78 )
| ~ empty(A_78) ),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_210,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_90,c_194]) ).
tff(c_34,plain,
! [A_15,B_18] :
( ( apply(A_15,B_18) = empty_set )
| in(B_18,relation_dom(A_15))
| ~ function(A_15)
| ~ relation(A_15) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_1309,plain,
! [A_179,B_180] :
( ( apply(A_179,B_180) = '#skF_9' )
| in(B_180,relation_dom(A_179))
| ~ function(A_179)
| ~ relation(A_179) ),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_34]) ).
tff(c_1340,plain,
! [B_180] :
( ( apply('#skF_15',B_180) = '#skF_9' )
| in(B_180,'#skF_14')
| ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_1309]) ).
tff(c_1404,plain,
! [B_187] :
( ( apply('#skF_15',B_187) = '#skF_9' )
| in(B_187,'#skF_14') ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_1340]) ).
tff(c_120,plain,
( in('#skF_16','#skF_14')
| ( relation_dom('#skF_15') != '#skF_14' )
| ( identity_relation('#skF_14') != '#skF_15' ) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_171,plain,
identity_relation('#skF_14') != '#skF_15',
inference(splitLeft,[status(thm)],[c_120]) ).
tff(c_122,plain,
! [C_48] :
( ( identity_relation('#skF_14') = '#skF_15' )
| ( apply('#skF_15',C_48) = C_48 )
| ~ in(C_48,'#skF_14') ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_249,plain,
! [C_48] :
( ( apply('#skF_15',C_48) = C_48 )
| ~ in(C_48,'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_171,c_122]) ).
tff(c_1431,plain,
! [B_187] :
( ( apply('#skF_15',B_187) = B_187 )
| ( apply('#skF_15',B_187) = '#skF_9' ) ),
inference(resolution,[status(thm)],[c_1404,c_249]) ).
tff(c_1460,plain,
! [B_187] :
( ( apply('#skF_15',B_187) = B_187 )
| ( B_187 != '#skF_9' ) ),
inference(factorization,[status(thm),theory(equality)],[c_1431]) ).
tff(c_263,plain,
! [A_88] :
( empty(relation_dom(A_88))
| ~ empty(A_88) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_272,plain,
( empty('#skF_14')
| ~ empty('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_263]) ).
tff(c_282,plain,
~ empty('#skF_15'),
inference(splitLeft,[status(thm)],[c_272]) ).
tff(c_1992,plain,
! [A_218,B_219] :
( in('#skF_1'(A_218,B_219),A_218)
| in(ordered_pair('#skF_3'(A_218,B_219),'#skF_4'(A_218,B_219)),B_219)
| ( identity_relation(A_218) = B_219 )
| ~ relation(B_219) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_156,plain,
! [A_63,C_65,B_64] :
( in(A_63,relation_dom(C_65))
| ~ in(ordered_pair(A_63,B_64),C_65)
| ~ function(C_65)
| ~ relation(C_65) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_11080,plain,
! [A_407,B_408] :
( in('#skF_3'(A_407,B_408),relation_dom(B_408))
| ~ function(B_408)
| in('#skF_1'(A_407,B_408),A_407)
| ( identity_relation(A_407) = B_408 )
| ~ relation(B_408) ),
inference(resolution,[status(thm)],[c_1992,c_156]) ).
tff(c_11209,plain,
! [A_407] :
( in('#skF_3'(A_407,'#skF_15'),'#skF_14')
| ~ function('#skF_15')
| in('#skF_1'(A_407,'#skF_15'),A_407)
| ( identity_relation(A_407) = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_11080]) ).
tff(c_12569,plain,
! [A_415] :
( in('#skF_3'(A_415,'#skF_15'),'#skF_14')
| in('#skF_1'(A_415,'#skF_15'),A_415)
| ( identity_relation(A_415) = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_11209]) ).
tff(c_14,plain,
! [A_7,B_8] :
( in('#skF_1'(A_7,B_8),A_7)
| ( '#skF_3'(A_7,B_8) != '#skF_4'(A_7,B_8) )
| ~ in('#skF_3'(A_7,B_8),A_7)
| ( identity_relation(A_7) = B_8 )
| ~ relation(B_8) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_12580,plain,
( ( '#skF_3'('#skF_14','#skF_15') != '#skF_4'('#skF_14','#skF_15') )
| ~ relation('#skF_15')
| in('#skF_1'('#skF_14','#skF_15'),'#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_12569,c_14]) ).
tff(c_12653,plain,
( ( '#skF_3'('#skF_14','#skF_15') != '#skF_4'('#skF_14','#skF_15') )
| in('#skF_1'('#skF_14','#skF_15'),'#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_12580]) ).
tff(c_12654,plain,
( ( '#skF_3'('#skF_14','#skF_15') != '#skF_4'('#skF_14','#skF_15') )
| in('#skF_1'('#skF_14','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_171,c_12653]) ).
tff(c_14382,plain,
'#skF_3'('#skF_14','#skF_15') != '#skF_4'('#skF_14','#skF_15'),
inference(splitLeft,[status(thm)],[c_12654]) ).
tff(c_15856,plain,
! [A_456] :
( ( apply('#skF_15','#skF_3'(A_456,'#skF_15')) = '#skF_3'(A_456,'#skF_15') )
| in('#skF_1'(A_456,'#skF_15'),A_456)
| ( identity_relation(A_456) = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_12569,c_249]) ).
tff(c_15906,plain,
( ( apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_1'('#skF_14','#skF_15') )
| ( apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_3'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_15856,c_249]) ).
tff(c_15924,plain,
( ( apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_1'('#skF_14','#skF_15') )
| ( apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_3'('#skF_14','#skF_15') ) ),
inference(negUnitSimplification,[status(thm)],[c_171,c_15906]) ).
tff(c_16648,plain,
apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_3'('#skF_14','#skF_15'),
inference(splitLeft,[status(thm)],[c_15924]) ).
tff(c_154,plain,
! [C_65,A_63,B_64] :
( ( apply(C_65,A_63) = B_64 )
| ~ in(ordered_pair(A_63,B_64),C_65)
| ~ function(C_65)
| ~ relation(C_65) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_2056,plain,
! [B_219,A_218] :
( ( apply(B_219,'#skF_3'(A_218,B_219)) = '#skF_4'(A_218,B_219) )
| ~ function(B_219)
| in('#skF_1'(A_218,B_219),A_218)
| ( identity_relation(A_218) = B_219 )
| ~ relation(B_219) ),
inference(resolution,[status(thm)],[c_1992,c_154]) ).
tff(c_19074,plain,
! [B_483,A_484] :
( ( apply(B_483,'#skF_3'(A_484,B_483)) = '#skF_4'(A_484,B_483) )
| ~ function(B_483)
| in('#skF_1'(A_484,B_483),A_484)
| ( identity_relation(A_484) = B_483 )
| ~ relation(B_483) ),
inference(resolution,[status(thm)],[c_1992,c_154]) ).
tff(c_19693,plain,
! [B_506] :
( ( apply('#skF_15','#skF_1'('#skF_14',B_506)) = '#skF_1'('#skF_14',B_506) )
| ( apply(B_506,'#skF_3'('#skF_14',B_506)) = '#skF_4'('#skF_14',B_506) )
| ~ function(B_506)
| ( identity_relation('#skF_14') = B_506 )
| ~ relation(B_506) ),
inference(resolution,[status(thm)],[c_19074,c_249]) ).
tff(c_19731,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15') )
| ( apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_1'('#skF_14','#skF_15') )
| ~ function('#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_19693,c_16648]) ).
tff(c_19854,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15') )
| ( apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_1'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_19731]) ).
tff(c_19855,plain,
apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_1'('#skF_14','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_171,c_14382,c_19854]) ).
tff(c_1824,plain,
! [A_214,C_215] :
( in(ordered_pair(A_214,apply(C_215,A_214)),C_215)
| ~ in(A_214,relation_dom(C_215))
| ~ function(C_215)
| ~ relation(C_215) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_1896,plain,
! [B_187] :
( in(ordered_pair(B_187,B_187),'#skF_15')
| ~ in(B_187,relation_dom('#skF_15'))
| ~ function('#skF_15')
| ~ relation('#skF_15')
| ( apply('#skF_15',B_187) = '#skF_9' ) ),
inference(superposition,[status(thm),theory(equality)],[c_1431,c_1824]) ).
tff(c_1946,plain,
! [B_187] :
( in(ordered_pair(B_187,B_187),'#skF_15')
| ~ in(B_187,'#skF_14')
| ( apply('#skF_15',B_187) = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_167,c_1896]) ).
tff(c_2384,plain,
! [A_225,B_226] :
( ( '#skF_2'(A_225,B_226) = '#skF_1'(A_225,B_226) )
| in(ordered_pair('#skF_3'(A_225,B_226),'#skF_4'(A_225,B_226)),B_226)
| ( identity_relation(A_225) = B_226 )
| ~ relation(B_226) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_21748,plain,
! [B_525,A_526] :
( ( apply(B_525,'#skF_3'(A_526,B_525)) = '#skF_4'(A_526,B_525) )
| ~ function(B_525)
| ( '#skF_2'(A_526,B_525) = '#skF_1'(A_526,B_525) )
| ( identity_relation(A_526) = B_525 )
| ~ relation(B_525) ),
inference(resolution,[status(thm)],[c_2384,c_154]) ).
tff(c_21761,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15') )
| ~ function('#skF_15')
| ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_21748,c_16648]) ).
tff(c_21862,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15') )
| ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_21761]) ).
tff(c_21863,plain,
'#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_171,c_14382,c_21862]) ).
tff(c_2929,plain,
! [A_260,B_261] :
( ~ in(ordered_pair('#skF_1'(A_260,B_261),'#skF_2'(A_260,B_261)),B_261)
| in(ordered_pair('#skF_3'(A_260,B_261),'#skF_4'(A_260,B_261)),B_261)
| ( identity_relation(A_260) = B_261 )
| ~ relation(B_261) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_23747,plain,
! [A_549,B_550] :
( in('#skF_3'(A_549,B_550),relation_dom(B_550))
| ~ function(B_550)
| ~ in(ordered_pair('#skF_1'(A_549,B_550),'#skF_2'(A_549,B_550)),B_550)
| ( identity_relation(A_549) = B_550 )
| ~ relation(B_550) ),
inference(resolution,[status(thm)],[c_2929,c_156]) ).
tff(c_23750,plain,
( in('#skF_3'('#skF_14','#skF_15'),relation_dom('#skF_15'))
| ~ function('#skF_15')
| ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_21863,c_23747]) ).
tff(c_23788,plain,
( in('#skF_3'('#skF_14','#skF_15'),'#skF_14')
| ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_167,c_23750]) ).
tff(c_23789,plain,
( in('#skF_3'('#skF_14','#skF_15'),'#skF_14')
| ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_171,c_23788]) ).
tff(c_25348,plain,
~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15'),
inference(splitLeft,[status(thm)],[c_23789]) ).
tff(c_25354,plain,
( ~ in('#skF_1'('#skF_14','#skF_15'),'#skF_14')
| ( apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_9' ) ),
inference(resolution,[status(thm)],[c_1946,c_25348]) ).
tff(c_25363,plain,
( ~ in('#skF_1'('#skF_14','#skF_15'),'#skF_14')
| ( '#skF_1'('#skF_14','#skF_15') = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_19855,c_25354]) ).
tff(c_25372,plain,
~ in('#skF_1'('#skF_14','#skF_15'),'#skF_14'),
inference(splitLeft,[status(thm)],[c_25363]) ).
tff(c_25375,plain,
( ( apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_4'('#skF_14','#skF_15') )
| ~ function('#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(resolution,[status(thm)],[c_2056,c_25372]) ).
tff(c_25395,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_16648,c_25375]) ).
tff(c_25397,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_171,c_14382,c_25395]) ).
tff(c_25398,plain,
'#skF_1'('#skF_14','#skF_15') = '#skF_9',
inference(splitRight,[status(thm)],[c_25363]) ).
tff(c_25415,plain,
( ( apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_4'('#skF_14','#skF_15') )
| ~ function('#skF_15')
| in('#skF_9','#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_25398,c_2056]) ).
tff(c_25454,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15') )
| in('#skF_9','#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_16648,c_25415]) ).
tff(c_25455,plain,
in('#skF_9','#skF_14'),
inference(negUnitSimplification,[status(thm)],[c_171,c_14382,c_25454]) ).
tff(c_1893,plain,
! [B_187] :
( in(ordered_pair(B_187,B_187),'#skF_15')
| ~ in(B_187,relation_dom('#skF_15'))
| ~ function('#skF_15')
| ~ relation('#skF_15')
| ( B_187 != '#skF_9' ) ),
inference(superposition,[status(thm),theory(equality)],[c_1460,c_1824]) ).
tff(c_27948,plain,
! [B_635] :
( in(ordered_pair(B_635,B_635),'#skF_15')
| ~ in(B_635,'#skF_14')
| ( B_635 != '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_167,c_1893]) ).
tff(c_25401,plain,
~ in(ordered_pair('#skF_9','#skF_9'),'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_25398,c_25398,c_25348]) ).
tff(c_27951,plain,
~ in('#skF_9','#skF_14'),
inference(resolution,[status(thm)],[c_27948,c_25401]) ).
tff(c_27979,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25455,c_27951]) ).
tff(c_27981,plain,
in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15'),
inference(splitRight,[status(thm)],[c_23789]) ).
tff(c_108,plain,
! [A_42,B_43] :
( element(A_42,B_43)
| ~ in(A_42,B_43) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_28278,plain,
! [A_641,B_642] :
( element(ordered_pair('#skF_3'(A_641,B_642),'#skF_4'(A_641,B_642)),B_642)
| ~ in(ordered_pair('#skF_1'(A_641,B_642),'#skF_2'(A_641,B_642)),B_642)
| ( identity_relation(A_641) = B_642 )
| ~ relation(B_642) ),
inference(resolution,[status(thm)],[c_2929,c_108]) ).
tff(c_28281,plain,
( element(ordered_pair('#skF_3'('#skF_14','#skF_15'),'#skF_4'('#skF_14','#skF_15')),'#skF_15')
| ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_21863,c_28278]) ).
tff(c_28319,plain,
( element(ordered_pair('#skF_3'('#skF_14','#skF_15'),'#skF_4'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_27981,c_28281]) ).
tff(c_28320,plain,
element(ordered_pair('#skF_3'('#skF_14','#skF_15'),'#skF_4'('#skF_14','#skF_15')),'#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_171,c_28319]) ).
tff(c_110,plain,
! [A_44,B_45] :
( in(A_44,B_45)
| empty(B_45)
| ~ element(A_44,B_45) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_1630,plain,
! [C_197,A_198,B_199] :
( ( apply(C_197,A_198) = B_199 )
| ~ in(ordered_pair(A_198,B_199),C_197)
| ~ function(C_197)
| ~ relation(C_197) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_1651,plain,
! [B_45,A_198,B_199] :
( ( apply(B_45,A_198) = B_199 )
| ~ function(B_45)
| ~ relation(B_45)
| empty(B_45)
| ~ element(ordered_pair(A_198,B_199),B_45) ),
inference(resolution,[status(thm)],[c_110,c_1630]) ).
tff(c_28343,plain,
( ( apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_4'('#skF_14','#skF_15') )
| ~ function('#skF_15')
| ~ relation('#skF_15')
| empty('#skF_15') ),
inference(resolution,[status(thm)],[c_28320,c_1651]) ).
tff(c_28350,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15') )
| empty('#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_16648,c_28343]) ).
tff(c_28352,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_282,c_14382,c_28350]) ).
tff(c_28354,plain,
apply('#skF_15','#skF_3'('#skF_14','#skF_15')) != '#skF_3'('#skF_14','#skF_15'),
inference(splitRight,[status(thm)],[c_15924]) ).
tff(c_28433,plain,
'#skF_3'('#skF_14','#skF_15') != '#skF_9',
inference(superposition,[status(thm),theory(equality)],[c_1460,c_28354]) ).
tff(c_28434,plain,
apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_9',
inference(superposition,[status(thm),theory(equality)],[c_1431,c_28354]) ).
tff(c_12661,plain,
! [A_415] :
( ( apply('#skF_15','#skF_3'(A_415,'#skF_15')) = '#skF_3'(A_415,'#skF_15') )
| in('#skF_1'(A_415,'#skF_15'),A_415)
| ( identity_relation(A_415) = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_12569,c_249]) ).
tff(c_28353,plain,
apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_1'('#skF_14','#skF_15'),
inference(splitRight,[status(thm)],[c_15924]) ).
tff(c_14485,plain,
! [A_437,B_438] :
( in('#skF_3'(A_437,B_438),relation_dom(B_438))
| ~ function(B_438)
| ( '#skF_2'(A_437,B_438) = '#skF_1'(A_437,B_438) )
| ( identity_relation(A_437) = B_438 )
| ~ relation(B_438) ),
inference(resolution,[status(thm)],[c_2384,c_156]) ).
tff(c_14583,plain,
! [A_437] :
( in('#skF_3'(A_437,'#skF_15'),'#skF_14')
| ~ function('#skF_15')
| ( '#skF_2'(A_437,'#skF_15') = '#skF_1'(A_437,'#skF_15') )
| ( identity_relation(A_437) = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_14485]) ).
tff(c_32708,plain,
! [A_683] :
( in('#skF_3'(A_683,'#skF_15'),'#skF_14')
| ( '#skF_2'(A_683,'#skF_15') = '#skF_1'(A_683,'#skF_15') )
| ( identity_relation(A_683) = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_14583]) ).
tff(c_34012,plain,
! [A_694] :
( ( apply('#skF_15','#skF_3'(A_694,'#skF_15')) = '#skF_3'(A_694,'#skF_15') )
| ( '#skF_2'(A_694,'#skF_15') = '#skF_1'(A_694,'#skF_15') )
| ( identity_relation(A_694) = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_32708,c_249]) ).
tff(c_34023,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_9' )
| ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(superposition,[status(thm),theory(equality)],[c_34012,c_28434]) ).
tff(c_34089,plain,
'#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_171,c_28433,c_34023]) ).
tff(c_35826,plain,
! [A_718,B_719] :
( in('#skF_3'(A_718,B_719),relation_dom(B_719))
| ~ function(B_719)
| ~ in(ordered_pair('#skF_1'(A_718,B_719),'#skF_2'(A_718,B_719)),B_719)
| ( identity_relation(A_718) = B_719 )
| ~ relation(B_719) ),
inference(resolution,[status(thm)],[c_2929,c_156]) ).
tff(c_35829,plain,
( in('#skF_3'('#skF_14','#skF_15'),relation_dom('#skF_15'))
| ~ function('#skF_15')
| ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_34089,c_35826]) ).
tff(c_35867,plain,
( in('#skF_3'('#skF_14','#skF_15'),'#skF_14')
| ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_167,c_35829]) ).
tff(c_35868,plain,
( in('#skF_3'('#skF_14','#skF_15'),'#skF_14')
| ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_171,c_35867]) ).
tff(c_36081,plain,
~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15'),
inference(splitLeft,[status(thm)],[c_35868]) ).
tff(c_36087,plain,
( ~ in('#skF_1'('#skF_14','#skF_15'),'#skF_14')
| ( apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_9' ) ),
inference(resolution,[status(thm)],[c_1946,c_36081]) ).
tff(c_36096,plain,
( ~ in('#skF_1'('#skF_14','#skF_15'),'#skF_14')
| ( '#skF_1'('#skF_14','#skF_15') = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_28353,c_36087]) ).
tff(c_36105,plain,
~ in('#skF_1'('#skF_14','#skF_15'),'#skF_14'),
inference(splitLeft,[status(thm)],[c_36096]) ).
tff(c_36111,plain,
( ( apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_3'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_12661,c_36105]) ).
tff(c_36131,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_9' )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_28434,c_36111]) ).
tff(c_36133,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_171,c_28433,c_36131]) ).
tff(c_36134,plain,
'#skF_1'('#skF_14','#skF_15') = '#skF_9',
inference(splitRight,[status(thm)],[c_36096]) ).
tff(c_36151,plain,
( ( apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_3'('#skF_14','#skF_15') )
| in('#skF_9','#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(superposition,[status(thm),theory(equality)],[c_36134,c_12661]) ).
tff(c_36186,plain,
( ( '#skF_3'('#skF_14','#skF_15') = '#skF_9' )
| in('#skF_9','#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_28434,c_36151]) ).
tff(c_36187,plain,
in('#skF_9','#skF_14'),
inference(negUnitSimplification,[status(thm)],[c_171,c_28433,c_36186]) ).
tff(c_1455,plain,
! [B_187] :
( ( apply('#skF_15',B_187) = '#skF_9' )
| ( B_187 != '#skF_9' ) ),
inference(factorization,[status(thm),theory(equality)],[c_1431]) ).
tff(c_6406,plain,
! [A_368,C_369] :
( element(ordered_pair(A_368,apply(C_369,A_368)),C_369)
| ~ in(A_368,relation_dom(C_369))
| ~ function(C_369)
| ~ relation(C_369) ),
inference(resolution,[status(thm)],[c_1824,c_108]) ).
tff(c_6453,plain,
! [B_187] :
( element(ordered_pair(B_187,'#skF_9'),'#skF_15')
| ~ in(B_187,relation_dom('#skF_15'))
| ~ function('#skF_15')
| ~ relation('#skF_15')
| ( B_187 != '#skF_9' ) ),
inference(superposition,[status(thm),theory(equality)],[c_1455,c_6406]) ).
tff(c_40446,plain,
! [B_822] :
( element(ordered_pair(B_822,'#skF_9'),'#skF_15')
| ~ in(B_822,'#skF_14')
| ( B_822 != '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_167,c_6453]) ).
tff(c_36090,plain,
( empty('#skF_15')
| ~ element(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15') ),
inference(resolution,[status(thm)],[c_110,c_36081]) ).
tff(c_36099,plain,
~ element(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_282,c_36090]) ).
tff(c_36136,plain,
~ element(ordered_pair('#skF_9','#skF_9'),'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_36134,c_36134,c_36099]) ).
tff(c_40449,plain,
~ in('#skF_9','#skF_14'),
inference(resolution,[status(thm)],[c_40446,c_36136]) ).
tff(c_40460,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36187,c_40449]) ).
tff(c_40461,plain,
in('#skF_3'('#skF_14','#skF_15'),'#skF_14'),
inference(splitRight,[status(thm)],[c_35868]) ).
tff(c_40489,plain,
apply('#skF_15','#skF_3'('#skF_14','#skF_15')) = '#skF_3'('#skF_14','#skF_15'),
inference(resolution,[status(thm)],[c_40461,c_249]) ).
tff(c_40507,plain,
'#skF_3'('#skF_14','#skF_15') = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_28434,c_40489]) ).
tff(c_40509,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28433,c_40507]) ).
tff(c_40510,plain,
in('#skF_1'('#skF_14','#skF_15'),'#skF_14'),
inference(splitRight,[status(thm)],[c_12654]) ).
tff(c_40541,plain,
apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_1'('#skF_14','#skF_15'),
inference(resolution,[status(thm)],[c_40510,c_249]) ).
tff(c_40511,plain,
'#skF_3'('#skF_14','#skF_15') = '#skF_4'('#skF_14','#skF_15'),
inference(splitRight,[status(thm)],[c_12654]) ).
tff(c_12,plain,
! [A_7,B_8] :
( ( '#skF_2'(A_7,B_8) = '#skF_1'(A_7,B_8) )
| ( '#skF_3'(A_7,B_8) != '#skF_4'(A_7,B_8) )
| ~ in('#skF_3'(A_7,B_8),A_7)
| ( identity_relation(A_7) = B_8 )
| ~ relation(B_8) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_40579,plain,
( ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ( '#skF_3'('#skF_14','#skF_15') != '#skF_4'('#skF_14','#skF_15') )
| ~ in('#skF_4'('#skF_14','#skF_15'),'#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_40511,c_12]) ).
tff(c_40606,plain,
( ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ~ in('#skF_4'('#skF_14','#skF_15'),'#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_40511,c_40579]) ).
tff(c_40607,plain,
( ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ~ in('#skF_4'('#skF_14','#skF_15'),'#skF_14') ),
inference(negUnitSimplification,[status(thm)],[c_171,c_40606]) ).
tff(c_40832,plain,
~ in('#skF_4'('#skF_14','#skF_15'),'#skF_14'),
inference(splitLeft,[status(thm)],[c_40607]) ).
tff(c_152,plain,
! [A_63,C_65] :
( in(ordered_pair(A_63,apply(C_65,A_63)),C_65)
| ~ in(A_63,relation_dom(C_65))
| ~ function(C_65)
| ~ relation(C_65) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_40785,plain,
( in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ~ in('#skF_1'('#skF_14','#skF_15'),relation_dom('#skF_15'))
| ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_40541,c_152]) ).
tff(c_40819,plain,
in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_40510,c_167,c_40785]) ).
tff(c_40647,plain,
! [A_824,B_825] :
( in('#skF_3'(A_824,B_825),relation_dom(B_825))
| ~ function(B_825)
| ( '#skF_2'(A_824,B_825) = '#skF_1'(A_824,B_825) )
| ( identity_relation(A_824) = B_825 )
| ~ relation(B_825) ),
inference(resolution,[status(thm)],[c_2384,c_156]) ).
tff(c_40679,plain,
( in('#skF_4'('#skF_14','#skF_15'),relation_dom('#skF_15'))
| ~ function('#skF_15')
| ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_40511,c_40647]) ).
tff(c_40760,plain,
( in('#skF_4'('#skF_14','#skF_15'),'#skF_14')
| ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') )
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_167,c_40679]) ).
tff(c_40761,plain,
( in('#skF_4'('#skF_14','#skF_15'),'#skF_14')
| ( '#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15') ) ),
inference(negUnitSimplification,[status(thm)],[c_171,c_40760]) ).
tff(c_40914,plain,
'#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_40832,c_40761]) ).
tff(c_16,plain,
! [A_7,B_8] :
( ~ in(ordered_pair('#skF_1'(A_7,B_8),'#skF_2'(A_7,B_8)),B_8)
| in(ordered_pair('#skF_3'(A_7,B_8),'#skF_4'(A_7,B_8)),B_8)
| ( identity_relation(A_7) = B_8 )
| ~ relation(B_8) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_40576,plain,
( ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_2'('#skF_14','#skF_15')),'#skF_15')
| in(ordered_pair('#skF_4'('#skF_14','#skF_15'),'#skF_4'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_40511,c_16]) ).
tff(c_40603,plain,
( ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_2'('#skF_14','#skF_15')),'#skF_15')
| in(ordered_pair('#skF_4'('#skF_14','#skF_15'),'#skF_4'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_40576]) ).
tff(c_40604,plain,
( ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_2'('#skF_14','#skF_15')),'#skF_15')
| in(ordered_pair('#skF_4'('#skF_14','#skF_15'),'#skF_4'('#skF_14','#skF_15')),'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_171,c_40603]) ).
tff(c_45346,plain,
in(ordered_pair('#skF_4'('#skF_14','#skF_15'),'#skF_4'('#skF_14','#skF_15')),'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_40819,c_40914,c_40604]) ).
tff(c_45357,plain,
( in('#skF_4'('#skF_14','#skF_15'),relation_dom('#skF_15'))
| ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(resolution,[status(thm)],[c_45346,c_156]) ).
tff(c_45379,plain,
in('#skF_4'('#skF_14','#skF_15'),'#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_167,c_45357]) ).
tff(c_45381,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40832,c_45379]) ).
tff(c_45383,plain,
in('#skF_4'('#skF_14','#skF_15'),'#skF_14'),
inference(splitRight,[status(thm)],[c_40607]) ).
tff(c_45382,plain,
'#skF_2'('#skF_14','#skF_15') = '#skF_1'('#skF_14','#skF_15'),
inference(splitRight,[status(thm)],[c_40607]) ).
tff(c_10,plain,
! [A_7,B_8] :
( ~ in(ordered_pair('#skF_1'(A_7,B_8),'#skF_2'(A_7,B_8)),B_8)
| ( '#skF_3'(A_7,B_8) != '#skF_4'(A_7,B_8) )
| ~ in('#skF_3'(A_7,B_8),A_7)
| ( identity_relation(A_7) = B_8 )
| ~ relation(B_8) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_45430,plain,
( ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ( '#skF_3'('#skF_14','#skF_15') != '#skF_4'('#skF_14','#skF_15') )
| ~ in('#skF_3'('#skF_14','#skF_15'),'#skF_14')
| ( identity_relation('#skF_14') = '#skF_15' )
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_45382,c_10]) ).
tff(c_45434,plain,
( ~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15')
| ( identity_relation('#skF_14') = '#skF_15' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_45383,c_40511,c_40511,c_45430]) ).
tff(c_45435,plain,
~ in(ordered_pair('#skF_1'('#skF_14','#skF_15'),'#skF_1'('#skF_14','#skF_15')),'#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_171,c_45434]) ).
tff(c_45569,plain,
( ~ in('#skF_1'('#skF_14','#skF_15'),'#skF_14')
| ( apply('#skF_15','#skF_1'('#skF_14','#skF_15')) = '#skF_9' ) ),
inference(resolution,[status(thm)],[c_1946,c_45435]) ).
tff(c_45579,plain,
'#skF_1'('#skF_14','#skF_15') = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_40541,c_40510,c_45569]) ).
tff(c_45583,plain,
~ in(ordered_pair('#skF_9','#skF_9'),'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_45579,c_45579,c_45435]) ).
tff(c_45765,plain,
in(ordered_pair('#skF_9','#skF_9'),'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_45579,c_45579,c_40819]) ).
tff(c_45766,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_45583,c_45765]) ).
tff(c_45768,plain,
empty('#skF_15'),
inference(splitRight,[status(thm)],[c_272]) ).
tff(c_142,plain,
! [A_57] :
( ( empty_set = A_57 )
| ~ empty(A_57) ),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_212,plain,
! [A_57] :
( ( A_57 = '#skF_9' )
| ~ empty(A_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_142]) ).
tff(c_45776,plain,
'#skF_15' = '#skF_9',
inference(resolution,[status(thm)],[c_45768,c_212]) ).
tff(c_45767,plain,
empty('#skF_14'),
inference(splitRight,[status(thm)],[c_272]) ).
tff(c_45772,plain,
'#skF_14' = '#skF_9',
inference(resolution,[status(thm)],[c_45767,c_212]) ).
tff(c_45779,plain,
identity_relation('#skF_9') != '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_45772,c_171]) ).
tff(c_45806,plain,
identity_relation('#skF_9') != '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_45776,c_45779]) ).
tff(c_54,plain,
! [A_28] : relation(identity_relation(A_28)),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_146,plain,
! [A_58] : ( relation_rng(identity_relation(A_58)) = A_58 ),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_46092,plain,
! [A_928] :
( ~ empty(relation_rng(A_928))
| ~ relation(A_928)
| empty(A_928) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_46107,plain,
! [A_58] :
( ~ empty(A_58)
| ~ relation(identity_relation(A_58))
| empty(identity_relation(A_58)) ),
inference(superposition,[status(thm),theory(equality)],[c_146,c_46092]) ).
tff(c_46117,plain,
! [A_929] :
( ~ empty(A_929)
| empty(identity_relation(A_929)) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_46107]) ).
tff(c_46176,plain,
! [A_931] :
( ( identity_relation(A_931) = '#skF_9' )
| ~ empty(A_931) ),
inference(resolution,[status(thm)],[c_46117,c_212]) ).
tff(c_46188,plain,
identity_relation('#skF_9') = '#skF_9',
inference(resolution,[status(thm)],[c_90,c_46176]) ).
tff(c_46195,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_45806,c_46188]) ).
tff(c_46197,plain,
identity_relation('#skF_14') = '#skF_15',
inference(splitRight,[status(thm)],[c_120]) ).
tff(c_22,plain,
! [D_14,A_7] :
( in(ordered_pair(D_14,D_14),identity_relation(A_7))
| ~ in(D_14,A_7)
| ~ relation(identity_relation(A_7)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_47116,plain,
! [D_1000,A_1001] :
( in(ordered_pair(D_1000,D_1000),identity_relation(A_1001))
| ~ in(D_1000,A_1001) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_22]) ).
tff(c_47142,plain,
! [D_1000] :
( in(ordered_pair(D_1000,D_1000),'#skF_15')
| ~ in(D_1000,'#skF_14') ),
inference(superposition,[status(thm),theory(equality)],[c_46197,c_47116]) ).
tff(c_47782,plain,
! [C_1073,A_1074,B_1075] :
( ( apply(C_1073,A_1074) = B_1075 )
| ~ in(ordered_pair(A_1074,B_1075),C_1073)
| ~ function(C_1073)
| ~ relation(C_1073) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_47793,plain,
! [D_1000] :
( ( apply('#skF_15',D_1000) = D_1000 )
| ~ function('#skF_15')
| ~ relation('#skF_15')
| ~ in(D_1000,'#skF_14') ),
inference(resolution,[status(thm)],[c_47142,c_47782]) ).
tff(c_47810,plain,
! [D_1076] :
( ( apply('#skF_15',D_1076) = D_1076 )
| ~ in(D_1076,'#skF_14') ),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_112,c_47793]) ).
tff(c_47820,plain,
apply('#skF_15','#skF_16') = '#skF_16',
inference(resolution,[status(thm)],[c_46303,c_47810]) ).
tff(c_47828,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46340,c_47820]) ).
tff(c_47830,plain,
apply('#skF_15','#skF_16') = '#skF_16',
inference(splitRight,[status(thm)],[c_46339]) ).
tff(c_118,plain,
( ( apply('#skF_15','#skF_16') != '#skF_16' )
| ( relation_dom('#skF_15') != '#skF_14' )
| ( identity_relation('#skF_14') != '#skF_15' ) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_46200,plain,
identity_relation('#skF_14') != '#skF_15',
inference(splitLeft,[status(thm)],[c_118]) ).
tff(c_46217,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46197,c_46200]) ).
tff(c_46218,plain,
( ( relation_dom('#skF_15') != '#skF_14' )
| ( apply('#skF_15','#skF_16') != '#skF_16' ) ),
inference(splitRight,[status(thm)],[c_118]) ).
tff(c_47875,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_47830,c_167,c_46218]) ).
tff(c_47877,plain,
~ in('#skF_16','#skF_14'),
inference(splitRight,[status(thm)],[c_46302]) ).
tff(c_46196,plain,
( ( relation_dom('#skF_15') != '#skF_14' )
| in('#skF_16','#skF_14') ),
inference(splitRight,[status(thm)],[c_120]) ).
tff(c_47949,plain,
in('#skF_16','#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_46196]) ).
tff(c_47950,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_47877,c_47949]) ).
tff(c_47952,plain,
relation_dom('#skF_15') != '#skF_14',
inference(splitRight,[status(thm)],[c_128]) ).
tff(c_47951,plain,
identity_relation('#skF_14') = '#skF_15',
inference(splitRight,[status(thm)],[c_128]) ).
tff(c_47974,plain,
! [A_1107] : ( relation_dom(identity_relation(A_1107)) = A_1107 ),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_47983,plain,
relation_dom('#skF_15') = '#skF_14',
inference(superposition,[status(thm),theory(equality)],[c_47951,c_47974]) ).
tff(c_47987,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_47952,c_47983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU216+3 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.36 % Computer : n018.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 11:59:35 EDT 2023
% 0.14/0.36 % CPUTime :
% 18.50/7.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.50/7.63
% 18.50/7.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.62/7.68
% 18.62/7.68 Inference rules
% 18.62/7.68 ----------------------
% 18.62/7.68 #Ref : 0
% 18.62/7.68 #Sup : 13122
% 18.62/7.68 #Fact : 2
% 18.62/7.68 #Define : 0
% 18.62/7.68 #Split : 42
% 18.62/7.68 #Chain : 0
% 18.62/7.68 #Close : 0
% 18.62/7.68
% 18.62/7.68 Ordering : KBO
% 18.62/7.68
% 18.62/7.68 Simplification rules
% 18.62/7.68 ----------------------
% 18.62/7.68 #Subsume : 6666
% 18.62/7.68 #Demod : 6525
% 18.62/7.68 #Tautology : 2449
% 18.62/7.68 #SimpNegUnit : 632
% 18.62/7.68 #BackRed : 260
% 18.62/7.68
% 18.62/7.68 #Partial instantiations: 0
% 18.62/7.68 #Strategies tried : 1
% 18.62/7.68
% 18.62/7.68 Timing (in seconds)
% 18.62/7.68 ----------------------
% 18.62/7.69 Preprocessing : 0.60
% 18.62/7.69 Parsing : 0.30
% 18.62/7.69 CNF conversion : 0.05
% 18.62/7.69 Main loop : 5.98
% 18.62/7.69 Inferencing : 1.29
% 18.62/7.69 Reduction : 2.05
% 18.62/7.69 Demodulation : 1.52
% 18.62/7.69 BG Simplification : 0.11
% 18.62/7.69 Subsumption : 2.17
% 18.62/7.69 Abstraction : 0.15
% 18.62/7.69 MUC search : 0.00
% 18.62/7.69 Cooper : 0.00
% 18.62/7.69 Total : 6.67
% 18.62/7.69 Index Insertion : 0.00
% 18.62/7.69 Index Deletion : 0.00
% 18.62/7.69 Index Matching : 0.00
% 18.62/7.69 BG Taut test : 0.00
%------------------------------------------------------------------------------