TSTP Solution File: SEU235+3 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU235+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 : 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 10:58:07 EDT 2023
% Result : Theorem 23.32s 11.02s
% Output : CNFRefutation 23.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 55
% Syntax : Number of formulae : 292 ( 74 unt; 34 typ; 0 def)
% Number of atoms : 670 ( 78 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 800 ( 388 ~; 365 |; 26 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 18 >; 5 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 16 con; 0-2 aty)
% Number of variables : 249 (; 246 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > ordinal_subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_5 > #skF_19 > #skF_6 > #skF_13 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
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_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(ordinal_subset,type,
ordinal_subset: ( $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_149,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
tff(f_278,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_135,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
tff(f_257,negated_conjecture,
~ ! [A,B] :
( ordinal(B)
=> ~ ( subset(A,B)
& ( A != empty_set )
& ! [C] :
( ordinal(C)
=> ~ ( in(C,A)
& ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
tff(f_89,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_71,axiom,
! [A] :
( empty(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
tff(f_196,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
tff(f_235,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_229,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& ( A != B )
& ~ in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
tff(f_274,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
tff(f_86,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_261,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_267,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
tff(f_214,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
tff(f_63,axiom,
! [A] :
( ( epsilon_transitive(A)
& epsilon_connected(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
tff(f_204,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_296,axiom,
! [A,B] :
~ ( in(A,B)
& ! [C] :
~ ( in(C,B)
& ! [D] :
~ ( in(D,B)
& in(D,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
tff(f_202,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ordinal_subset(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
tff(f_41,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
tff(f_208,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
tff(f_283,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
tff(c_92,plain,
empty('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_222,plain,
! [A_64] :
( ( empty_set = A_64 )
| ~ empty(A_64) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_243,plain,
empty_set = '#skF_8',
inference(resolution,[status(thm)],[c_92,c_222]) ).
tff(c_82,plain,
empty('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_238,plain,
empty_set = '#skF_7',
inference(resolution,[status(thm)],[c_82,c_222]) ).
tff(c_261,plain,
'#skF_7' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_243,c_238]) ).
tff(c_152,plain,
empty_set != '#skF_16',
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_250,plain,
'#skF_7' != '#skF_16',
inference(demodulation,[status(thm),theory(equality)],[c_238,c_152]) ).
tff(c_275,plain,
'#skF_16' != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_261,c_250]) ).
tff(c_34,plain,
! [A_15] : element('#skF_2'(A_15),A_15),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_20,plain,
! [A_8] :
( ordinal(A_8)
| ~ empty(A_8) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_156,plain,
ordinal('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_154,plain,
subset('#skF_16','#skF_17'),
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_590,plain,
! [A_117,B_118] :
( ordinal_subset(A_117,B_118)
| ~ subset(A_117,B_118)
| ~ ordinal(B_118)
| ~ ordinal(A_117) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_605,plain,
( ordinal_subset('#skF_16','#skF_17')
| ~ ordinal('#skF_17')
| ~ ordinal('#skF_16') ),
inference(resolution,[status(thm)],[c_154,c_590]) ).
tff(c_612,plain,
( ordinal_subset('#skF_16','#skF_17')
| ~ ordinal('#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_605]) ).
tff(c_613,plain,
~ ordinal('#skF_16'),
inference(splitLeft,[status(thm)],[c_612]) ).
tff(c_621,plain,
~ empty('#skF_16'),
inference(resolution,[status(thm)],[c_20,c_613]) ).
tff(c_150,plain,
! [A_30,B_31] :
( in(A_30,B_31)
| empty(B_31)
| ~ element(A_30,B_31) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_86,plain,
ordinal('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_162,plain,
! [C_35] :
( ordinal('#skF_18'(C_35))
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_148,plain,
! [B_29,A_27] :
( in(B_29,A_27)
| ( B_29 = A_27 )
| in(A_27,B_29)
| ~ ordinal(B_29)
| ~ ordinal(A_27) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_558,plain,
! [C_112,B_113,A_114] :
( ~ empty(C_112)
| ~ element(B_113,powerset(C_112))
| ~ in(A_114,B_113) ),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_574,plain,
! [C_115,A_116] :
( ~ empty(C_115)
| ~ in(A_116,'#skF_2'(powerset(C_115))) ),
inference(resolution,[status(thm)],[c_34,c_558]) ).
tff(c_59776,plain,
! [C_1422,A_1423] :
( ~ empty(C_1422)
| empty('#skF_2'(powerset(C_1422)))
| ~ element(A_1423,'#skF_2'(powerset(C_1422))) ),
inference(resolution,[status(thm)],[c_150,c_574]) ).
tff(c_59811,plain,
! [C_1424] :
( ~ empty(C_1424)
| empty('#skF_2'(powerset(C_1424))) ),
inference(resolution,[status(thm)],[c_34,c_59776]) ).
tff(c_172,plain,
! [A_45] :
( ( empty_set = A_45 )
| ~ empty(A_45) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_244,plain,
! [A_45] :
( ( A_45 = '#skF_7' )
| ~ empty(A_45) ),
inference(demodulation,[status(thm),theory(equality)],[c_238,c_172]) ).
tff(c_344,plain,
! [A_45] :
( ( A_45 = '#skF_8' )
| ~ empty(A_45) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_244]) ).
tff(c_59819,plain,
! [C_1425] :
( ( '#skF_2'(powerset(C_1425)) = '#skF_8' )
| ~ empty(C_1425) ),
inference(resolution,[status(thm)],[c_59811,c_344]) ).
tff(c_59888,plain,
! [C_1427] :
( element('#skF_8',powerset(C_1427))
| ~ empty(C_1427) ),
inference(superposition,[status(thm),theory(equality)],[c_59819,c_34]) ).
tff(c_170,plain,
! [C_44,B_43,A_42] :
( ~ empty(C_44)
| ~ element(B_43,powerset(C_44))
| ~ in(A_42,B_43) ),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_59906,plain,
! [A_42,C_1427] :
( ~ in(A_42,'#skF_8')
| ~ empty(C_1427) ),
inference(resolution,[status(thm)],[c_59888,c_170]) ).
tff(c_59986,plain,
! [C_1427] : ~ empty(C_1427),
inference(splitLeft,[status(thm)],[c_59906]) ).
tff(c_60000,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_59986,c_92]) ).
tff(c_60002,plain,
! [A_1430] : ~ in(A_1430,'#skF_8'),
inference(splitRight,[status(thm)],[c_59906]) ).
tff(c_60018,plain,
! [A_27] :
( in('#skF_8',A_27)
| ( A_27 = '#skF_8' )
| ~ ordinal('#skF_8')
| ~ ordinal(A_27) ),
inference(resolution,[status(thm)],[c_148,c_60002]) ).
tff(c_60042,plain,
! [A_27] :
( in('#skF_8',A_27)
| ( A_27 = '#skF_8' )
| ~ ordinal(A_27) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_60018]) ).
tff(c_28,plain,
! [B_14,A_11] :
( subset(B_14,A_11)
| ~ in(B_14,A_11)
| ~ epsilon_transitive(A_11) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_60173,plain,
! [B_1434,A_1435] :
( ordinal_subset(B_1434,A_1435)
| ~ ordinal(A_1435)
| ~ ordinal(B_1434)
| ~ in(B_1434,A_1435)
| ~ epsilon_transitive(A_1435) ),
inference(resolution,[status(thm)],[c_28,c_590]) ).
tff(c_158,plain,
! [C_35] :
( ~ ordinal_subset(C_35,'#skF_18'(C_35))
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_60186,plain,
! [B_1438] :
( ~ in(B_1438,'#skF_16')
| ~ ordinal('#skF_18'(B_1438))
| ~ ordinal(B_1438)
| ~ in(B_1438,'#skF_18'(B_1438))
| ~ epsilon_transitive('#skF_18'(B_1438)) ),
inference(resolution,[status(thm)],[c_60173,c_158]) ).
tff(c_60190,plain,
( ~ in('#skF_8','#skF_16')
| ~ ordinal('#skF_8')
| ~ epsilon_transitive('#skF_18'('#skF_8'))
| ( '#skF_18'('#skF_8') = '#skF_8' )
| ~ ordinal('#skF_18'('#skF_8')) ),
inference(resolution,[status(thm)],[c_60042,c_60186]) ).
tff(c_60209,plain,
( ~ in('#skF_8','#skF_16')
| ~ epsilon_transitive('#skF_18'('#skF_8'))
| ( '#skF_18'('#skF_8') = '#skF_8' )
| ~ ordinal('#skF_18'('#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_60190]) ).
tff(c_62297,plain,
~ ordinal('#skF_18'('#skF_8')),
inference(splitLeft,[status(thm)],[c_60209]) ).
tff(c_62306,plain,
( ~ in('#skF_8','#skF_16')
| ~ ordinal('#skF_8') ),
inference(resolution,[status(thm)],[c_162,c_62297]) ).
tff(c_62311,plain,
~ in('#skF_8','#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_62306]) ).
tff(c_62325,plain,
( empty('#skF_16')
| ~ element('#skF_8','#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_62311]) ).
tff(c_62338,plain,
~ element('#skF_8','#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_621,c_62325]) ).
tff(c_166,plain,
! [A_37,B_38] :
( element(A_37,powerset(B_38))
| ~ subset(A_37,B_38) ),
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_55859,plain,
! [B_1195,A_1196,A_1197] :
( ~ empty(B_1195)
| ~ in(A_1196,A_1197)
| ~ subset(A_1197,B_1195) ),
inference(resolution,[status(thm)],[c_166,c_558]) ).
tff(c_56116,plain,
! [B_1236,B_1237,A_1238] :
( ~ empty(B_1236)
| ~ subset(B_1237,B_1236)
| empty(B_1237)
| ~ element(A_1238,B_1237) ),
inference(resolution,[status(thm)],[c_150,c_55859]) ).
tff(c_56132,plain,
! [A_1238] :
( ~ empty('#skF_17')
| empty('#skF_16')
| ~ element(A_1238,'#skF_16') ),
inference(resolution,[status(thm)],[c_154,c_56116]) ).
tff(c_56142,plain,
! [A_1238] :
( ~ empty('#skF_17')
| ~ element(A_1238,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_621,c_56132]) ).
tff(c_56143,plain,
~ empty('#skF_17'),
inference(splitLeft,[status(thm)],[c_56142]) ).
tff(c_55842,plain,
! [A_1191,C_1192,B_1193] :
( element(A_1191,C_1192)
| ~ element(B_1193,powerset(C_1192))
| ~ in(A_1191,B_1193) ),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_55929,plain,
! [A_1204,B_1205,A_1206] :
( element(A_1204,B_1205)
| ~ in(A_1204,A_1206)
| ~ subset(A_1206,B_1205) ),
inference(resolution,[status(thm)],[c_166,c_55842]) ).
tff(c_60499,plain,
! [A_1453,B_1454,B_1455] :
( element(A_1453,B_1454)
| ~ subset(B_1455,B_1454)
| empty(B_1455)
| ~ element(A_1453,B_1455) ),
inference(resolution,[status(thm)],[c_150,c_55929]) ).
tff(c_60521,plain,
! [A_1453] :
( element(A_1453,'#skF_17')
| empty('#skF_16')
| ~ element(A_1453,'#skF_16') ),
inference(resolution,[status(thm)],[c_154,c_60499]) ).
tff(c_60562,plain,
! [A_1458] :
( element(A_1458,'#skF_17')
| ~ element(A_1458,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_621,c_60521]) ).
tff(c_480,plain,
! [A_98,B_99] :
( in(A_98,B_99)
| empty(B_99)
| ~ element(A_98,B_99) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_146,plain,
! [A_25,B_26] :
( ordinal(A_25)
| ~ in(A_25,B_26)
| ~ ordinal(B_26) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_500,plain,
! [A_98,B_99] :
( ordinal(A_98)
| ~ ordinal(B_99)
| empty(B_99)
| ~ element(A_98,B_99) ),
inference(resolution,[status(thm)],[c_480,c_146]) ).
tff(c_60567,plain,
! [A_1458] :
( ordinal(A_1458)
| ~ ordinal('#skF_17')
| empty('#skF_17')
| ~ element(A_1458,'#skF_16') ),
inference(resolution,[status(thm)],[c_60562,c_500]) ).
tff(c_60573,plain,
! [A_1458] :
( ordinal(A_1458)
| empty('#skF_17')
| ~ element(A_1458,'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_60567]) ).
tff(c_60575,plain,
! [A_1459] :
( ordinal(A_1459)
| ~ element(A_1459,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_56143,c_60573]) ).
tff(c_60624,plain,
ordinal('#skF_2'('#skF_16')),
inference(resolution,[status(thm)],[c_34,c_60575]) ).
tff(c_18,plain,
! [A_7] :
( ordinal(A_7)
| ~ epsilon_connected(A_7)
| ~ epsilon_transitive(A_7) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_620,plain,
( ~ epsilon_connected('#skF_16')
| ~ epsilon_transitive('#skF_16') ),
inference(resolution,[status(thm)],[c_18,c_613]) ).
tff(c_622,plain,
~ epsilon_transitive('#skF_16'),
inference(splitLeft,[status(thm)],[c_620]) ).
tff(c_32,plain,
! [A_11] :
( in('#skF_1'(A_11),A_11)
| epsilon_transitive(A_11) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_142,plain,
! [A_21] : subset(A_21,A_21),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_178,plain,
! [A_48,B_49] :
( in('#skF_19'(A_48,B_49),B_49)
| ~ in(A_48,B_49) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_664,plain,
! [A_125,C_126,B_127] :
( element(A_125,C_126)
| ~ element(B_127,powerset(C_126))
| ~ in(A_125,B_127) ),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_757,plain,
! [A_139,B_140,A_141] :
( element(A_139,B_140)
| ~ in(A_139,A_141)
| ~ subset(A_141,B_140) ),
inference(resolution,[status(thm)],[c_166,c_664]) ).
tff(c_766,plain,
! [A_48,B_49,B_140] :
( element('#skF_19'(A_48,B_49),B_140)
| ~ subset(B_49,B_140)
| ~ in(A_48,B_49) ),
inference(resolution,[status(thm)],[c_178,c_757]) ).
tff(c_628,plain,
! [B_120,A_121,A_122] :
( ~ empty(B_120)
| ~ in(A_121,A_122)
| ~ subset(A_122,B_120) ),
inference(resolution,[status(thm)],[c_166,c_558]) ).
tff(c_641,plain,
! [B_123,A_124] :
( ~ empty(B_123)
| ~ subset(A_124,B_123)
| epsilon_transitive(A_124) ),
inference(resolution,[status(thm)],[c_32,c_628]) ).
tff(c_656,plain,
( ~ empty('#skF_17')
| epsilon_transitive('#skF_16') ),
inference(resolution,[status(thm)],[c_154,c_641]) ).
tff(c_663,plain,
~ empty('#skF_17'),
inference(negUnitSimplification,[status(thm)],[c_622,c_656]) ).
tff(c_5116,plain,
! [A_368,B_369,B_370] :
( element(A_368,B_369)
| ~ subset(B_370,B_369)
| empty(B_370)
| ~ element(A_368,B_370) ),
inference(resolution,[status(thm)],[c_150,c_757]) ).
tff(c_5138,plain,
! [A_368] :
( element(A_368,'#skF_17')
| empty('#skF_16')
| ~ element(A_368,'#skF_16') ),
inference(resolution,[status(thm)],[c_154,c_5116]) ).
tff(c_5153,plain,
! [A_371] :
( element(A_371,'#skF_17')
| ~ element(A_371,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_621,c_5138]) ).
tff(c_5158,plain,
! [A_371] :
( ordinal(A_371)
| ~ ordinal('#skF_17')
| empty('#skF_17')
| ~ element(A_371,'#skF_16') ),
inference(resolution,[status(thm)],[c_5153,c_500]) ).
tff(c_5164,plain,
! [A_371] :
( ordinal(A_371)
| empty('#skF_17')
| ~ element(A_371,'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_5158]) ).
tff(c_5212,plain,
! [A_375] :
( ordinal(A_375)
| ~ element(A_375,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_663,c_5164]) ).
tff(c_5256,plain,
! [A_48,B_49] :
( ordinal('#skF_19'(A_48,B_49))
| ~ subset(B_49,'#skF_16')
| ~ in(A_48,B_49) ),
inference(resolution,[status(thm)],[c_766,c_5212]) ).
tff(c_140,plain,
! [A_19,B_20] :
( ordinal_subset(A_19,A_19)
| ~ ordinal(B_20)
| ~ ordinal(A_19) ),
inference(cnfTransformation,[status(thm)],[f_202]) ).
tff(c_392,plain,
! [B_20] : ~ ordinal(B_20),
inference(splitLeft,[status(thm)],[c_140]) ).
tff(c_400,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_392,c_86]) ).
tff(c_401,plain,
! [A_19] :
( ordinal_subset(A_19,A_19)
| ~ ordinal(A_19) ),
inference(splitRight,[status(thm)],[c_140]) ).
tff(c_311,plain,
! [A_69] :
( epsilon_transitive(A_69)
| ~ ordinal(A_69) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_331,plain,
! [C_35] :
( epsilon_transitive('#skF_18'(C_35))
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_162,c_311]) ).
tff(c_160,plain,
! [C_35] :
( in('#skF_18'(C_35),'#skF_16')
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_1056,plain,
! [B_177,A_178] :
( in(B_177,A_178)
| ( B_177 = A_178 )
| in(A_178,B_177)
| ~ ordinal(B_177)
| ~ ordinal(A_178) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_176,plain,
! [D_54,A_48,B_49] :
( ~ in(D_54,'#skF_19'(A_48,B_49))
| ~ in(D_54,B_49)
| ~ in(A_48,B_49) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_5417,plain,
! [A_387,B_388,A_389] :
( ~ in(A_387,B_388)
| ~ in(A_389,B_388)
| in('#skF_19'(A_389,B_388),A_387)
| ( A_387 = '#skF_19'(A_389,B_388) )
| ~ ordinal('#skF_19'(A_389,B_388))
| ~ ordinal(A_387) ),
inference(resolution,[status(thm)],[c_1056,c_176]) ).
tff(c_4564,plain,
! [B_338,A_339] :
( ordinal_subset(B_338,A_339)
| ~ ordinal(A_339)
| ~ ordinal(B_338)
| ~ in(B_338,A_339)
| ~ epsilon_transitive(A_339) ),
inference(resolution,[status(thm)],[c_28,c_590]) ).
tff(c_4569,plain,
! [B_338] :
( ~ in(B_338,'#skF_16')
| ~ ordinal('#skF_18'(B_338))
| ~ ordinal(B_338)
| ~ in(B_338,'#skF_18'(B_338))
| ~ epsilon_transitive('#skF_18'(B_338)) ),
inference(resolution,[status(thm)],[c_4564,c_158]) ).
tff(c_44057,plain,
! [A_1068,B_1069] :
( ~ in('#skF_19'(A_1068,B_1069),'#skF_16')
| ~ epsilon_transitive('#skF_18'('#skF_19'(A_1068,B_1069)))
| ~ in('#skF_18'('#skF_19'(A_1068,B_1069)),B_1069)
| ~ in(A_1068,B_1069)
| ( '#skF_18'('#skF_19'(A_1068,B_1069)) = '#skF_19'(A_1068,B_1069) )
| ~ ordinal('#skF_19'(A_1068,B_1069))
| ~ ordinal('#skF_18'('#skF_19'(A_1068,B_1069))) ),
inference(resolution,[status(thm)],[c_5417,c_4569]) ).
tff(c_44578,plain,
! [A_1075] :
( ~ epsilon_transitive('#skF_18'('#skF_19'(A_1075,'#skF_16')))
| ~ in(A_1075,'#skF_16')
| ( '#skF_18'('#skF_19'(A_1075,'#skF_16')) = '#skF_19'(A_1075,'#skF_16') )
| ~ ordinal('#skF_18'('#skF_19'(A_1075,'#skF_16')))
| ~ in('#skF_19'(A_1075,'#skF_16'),'#skF_16')
| ~ ordinal('#skF_19'(A_1075,'#skF_16')) ),
inference(resolution,[status(thm)],[c_160,c_44057]) ).
tff(c_44756,plain,
! [A_1079] :
( ~ epsilon_transitive('#skF_18'('#skF_19'(A_1079,'#skF_16')))
| ~ in(A_1079,'#skF_16')
| ( '#skF_18'('#skF_19'(A_1079,'#skF_16')) = '#skF_19'(A_1079,'#skF_16') )
| ~ in('#skF_19'(A_1079,'#skF_16'),'#skF_16')
| ~ ordinal('#skF_19'(A_1079,'#skF_16')) ),
inference(resolution,[status(thm)],[c_162,c_44578]) ).
tff(c_45391,plain,
! [A_1083] :
( ~ in(A_1083,'#skF_16')
| ( '#skF_18'('#skF_19'(A_1083,'#skF_16')) = '#skF_19'(A_1083,'#skF_16') )
| ~ in('#skF_19'(A_1083,'#skF_16'),'#skF_16')
| ~ ordinal('#skF_19'(A_1083,'#skF_16')) ),
inference(resolution,[status(thm)],[c_331,c_44756]) ).
tff(c_54822,plain,
! [A_1176] :
( ( '#skF_18'('#skF_19'(A_1176,'#skF_16')) = '#skF_19'(A_1176,'#skF_16') )
| ~ ordinal('#skF_19'(A_1176,'#skF_16'))
| ~ in(A_1176,'#skF_16') ),
inference(resolution,[status(thm)],[c_178,c_45391]) ).
tff(c_54830,plain,
! [A_48] :
( ( '#skF_18'('#skF_19'(A_48,'#skF_16')) = '#skF_19'(A_48,'#skF_16') )
| ~ subset('#skF_16','#skF_16')
| ~ in(A_48,'#skF_16') ),
inference(resolution,[status(thm)],[c_5256,c_54822]) ).
tff(c_54852,plain,
! [A_1177] :
( ( '#skF_18'('#skF_19'(A_1177,'#skF_16')) = '#skF_19'(A_1177,'#skF_16') )
| ~ in(A_1177,'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_54830]) ).
tff(c_55656,plain,
! [A_1187] :
( ~ ordinal_subset('#skF_19'(A_1187,'#skF_16'),'#skF_19'(A_1187,'#skF_16'))
| ~ in('#skF_19'(A_1187,'#skF_16'),'#skF_16')
| ~ ordinal('#skF_19'(A_1187,'#skF_16'))
| ~ in(A_1187,'#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_54852,c_158]) ).
tff(c_55679,plain,
! [A_1188] :
( ~ in('#skF_19'(A_1188,'#skF_16'),'#skF_16')
| ~ in(A_1188,'#skF_16')
| ~ ordinal('#skF_19'(A_1188,'#skF_16')) ),
inference(resolution,[status(thm)],[c_401,c_55656]) ).
tff(c_55712,plain,
! [A_1189] :
( ~ ordinal('#skF_19'(A_1189,'#skF_16'))
| ~ in(A_1189,'#skF_16') ),
inference(resolution,[status(thm)],[c_178,c_55679]) ).
tff(c_55720,plain,
! [A_48] :
( ~ subset('#skF_16','#skF_16')
| ~ in(A_48,'#skF_16') ),
inference(resolution,[status(thm)],[c_5256,c_55712]) ).
tff(c_55743,plain,
! [A_1190] : ~ in(A_1190,'#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_55720]) ).
tff(c_55811,plain,
epsilon_transitive('#skF_16'),
inference(resolution,[status(thm)],[c_32,c_55743]) ).
tff(c_55835,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_622,c_55811]) ).
tff(c_55837,plain,
epsilon_transitive('#skF_16'),
inference(splitRight,[status(thm)],[c_620]) ).
tff(c_60056,plain,
! [A_1432] :
( in('#skF_8',A_1432)
| ( A_1432 = '#skF_8' )
| ~ ordinal(A_1432) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_60018]) ).
tff(c_55855,plain,
! [A_1191,B_38,A_37] :
( element(A_1191,B_38)
| ~ in(A_1191,A_37)
| ~ subset(A_37,B_38) ),
inference(resolution,[status(thm)],[c_166,c_55842]) ).
tff(c_60441,plain,
! [B_1449,A_1450] :
( element('#skF_8',B_1449)
| ~ subset(A_1450,B_1449)
| ( A_1450 = '#skF_8' )
| ~ ordinal(A_1450) ),
inference(resolution,[status(thm)],[c_60056,c_55855]) ).
tff(c_62390,plain,
! [A_1543,B_1544] :
( element('#skF_8',A_1543)
| ( B_1544 = '#skF_8' )
| ~ ordinal(B_1544)
| ~ in(B_1544,A_1543)
| ~ epsilon_transitive(A_1543) ),
inference(resolution,[status(thm)],[c_28,c_60441]) ).
tff(c_62420,plain,
! [C_35] :
( element('#skF_8','#skF_16')
| ( '#skF_18'(C_35) = '#skF_8' )
| ~ ordinal('#skF_18'(C_35))
| ~ epsilon_transitive('#skF_16')
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_62390]) ).
tff(c_62434,plain,
! [C_35] :
( element('#skF_8','#skF_16')
| ( '#skF_18'(C_35) = '#skF_8' )
| ~ ordinal('#skF_18'(C_35))
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_55837,c_62420]) ).
tff(c_62436,plain,
! [C_1545] :
( ( '#skF_18'(C_1545) = '#skF_8' )
| ~ ordinal('#skF_18'(C_1545))
| ~ in(C_1545,'#skF_16')
| ~ ordinal(C_1545) ),
inference(negUnitSimplification,[status(thm)],[c_62338,c_62434]) ).
tff(c_62449,plain,
! [C_1546] :
( ( '#skF_18'(C_1546) = '#skF_8' )
| ~ in(C_1546,'#skF_16')
| ~ ordinal(C_1546) ),
inference(resolution,[status(thm)],[c_162,c_62436]) ).
tff(c_62481,plain,
! [A_30] :
( ( '#skF_18'(A_30) = '#skF_8' )
| ~ ordinal(A_30)
| empty('#skF_16')
| ~ element(A_30,'#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_62449]) ).
tff(c_62505,plain,
! [A_1547] :
( ( '#skF_18'(A_1547) = '#skF_8' )
| ~ ordinal(A_1547)
| ~ element(A_1547,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_621,c_62481]) ).
tff(c_62560,plain,
( ( '#skF_18'('#skF_2'('#skF_16')) = '#skF_8' )
| ~ ordinal('#skF_2'('#skF_16')) ),
inference(resolution,[status(thm)],[c_34,c_62505]) ).
tff(c_62585,plain,
'#skF_18'('#skF_2'('#skF_16')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_60624,c_62560]) ).
tff(c_372,plain,
! [A_78,B_79] :
( element(A_78,B_79)
| ~ in(A_78,B_79) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_380,plain,
! [C_35] :
( element('#skF_18'(C_35),'#skF_16')
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_372]) ).
tff(c_62612,plain,
( element('#skF_8','#skF_16')
| ~ in('#skF_2'('#skF_16'),'#skF_16')
| ~ ordinal('#skF_2'('#skF_16')) ),
inference(superposition,[status(thm),theory(equality)],[c_62585,c_380]) ).
tff(c_62647,plain,
( element('#skF_8','#skF_16')
| ~ in('#skF_2'('#skF_16'),'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_60624,c_62612]) ).
tff(c_62648,plain,
~ in('#skF_2'('#skF_16'),'#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_62338,c_62647]) ).
tff(c_62675,plain,
( empty('#skF_16')
| ~ element('#skF_2'('#skF_16'),'#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_62648]) ).
tff(c_62690,plain,
empty('#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_62675]) ).
tff(c_62692,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_621,c_62690]) ).
tff(c_62694,plain,
ordinal('#skF_18'('#skF_8')),
inference(splitRight,[status(thm)],[c_60209]) ).
tff(c_8,plain,
! [A_4] :
( epsilon_transitive(A_4)
| ~ ordinal(A_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_62701,plain,
epsilon_transitive('#skF_18'('#skF_8')),
inference(resolution,[status(thm)],[c_62694,c_8]) ).
tff(c_62693,plain,
( ~ epsilon_transitive('#skF_18'('#skF_8'))
| ~ in('#skF_8','#skF_16')
| ( '#skF_18'('#skF_8') = '#skF_8' ) ),
inference(splitRight,[status(thm)],[c_60209]) ).
tff(c_62730,plain,
( ~ in('#skF_8','#skF_16')
| ( '#skF_18'('#skF_8') = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_62701,c_62693]) ).
tff(c_62731,plain,
~ in('#skF_8','#skF_16'),
inference(splitLeft,[status(thm)],[c_62730]) ).
tff(c_62745,plain,
( empty('#skF_16')
| ~ element('#skF_8','#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_62731]) ).
tff(c_62758,plain,
~ element('#skF_8','#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_621,c_62745]) ).
tff(c_62810,plain,
! [A_1553,B_1554] :
( element('#skF_8',A_1553)
| ( B_1554 = '#skF_8' )
| ~ ordinal(B_1554)
| ~ in(B_1554,A_1553)
| ~ epsilon_transitive(A_1553) ),
inference(resolution,[status(thm)],[c_28,c_60441]) ).
tff(c_62840,plain,
! [C_35] :
( element('#skF_8','#skF_16')
| ( '#skF_18'(C_35) = '#skF_8' )
| ~ ordinal('#skF_18'(C_35))
| ~ epsilon_transitive('#skF_16')
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_62810]) ).
tff(c_62854,plain,
! [C_35] :
( element('#skF_8','#skF_16')
| ( '#skF_18'(C_35) = '#skF_8' )
| ~ ordinal('#skF_18'(C_35))
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_55837,c_62840]) ).
tff(c_62856,plain,
! [C_1555] :
( ( '#skF_18'(C_1555) = '#skF_8' )
| ~ ordinal('#skF_18'(C_1555))
| ~ in(C_1555,'#skF_16')
| ~ ordinal(C_1555) ),
inference(negUnitSimplification,[status(thm)],[c_62758,c_62854]) ).
tff(c_62925,plain,
! [C_1559] :
( ( '#skF_18'(C_1559) = '#skF_8' )
| ~ in(C_1559,'#skF_16')
| ~ ordinal(C_1559) ),
inference(resolution,[status(thm)],[c_162,c_62856]) ).
tff(c_62957,plain,
! [A_30] :
( ( '#skF_18'(A_30) = '#skF_8' )
| ~ ordinal(A_30)
| empty('#skF_16')
| ~ element(A_30,'#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_62925]) ).
tff(c_62981,plain,
! [A_1560] :
( ( '#skF_18'(A_1560) = '#skF_8' )
| ~ ordinal(A_1560)
| ~ element(A_1560,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_621,c_62957]) ).
tff(c_63036,plain,
( ( '#skF_18'('#skF_2'('#skF_16')) = '#skF_8' )
| ~ ordinal('#skF_2'('#skF_16')) ),
inference(resolution,[status(thm)],[c_34,c_62981]) ).
tff(c_63061,plain,
'#skF_18'('#skF_2'('#skF_16')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_60624,c_63036]) ).
tff(c_63100,plain,
( in('#skF_8','#skF_16')
| ~ in('#skF_2'('#skF_16'),'#skF_16')
| ~ ordinal('#skF_2'('#skF_16')) ),
inference(superposition,[status(thm),theory(equality)],[c_63061,c_160]) ).
tff(c_63132,plain,
( in('#skF_8','#skF_16')
| ~ in('#skF_2'('#skF_16'),'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_60624,c_63100]) ).
tff(c_63133,plain,
~ in('#skF_2'('#skF_16'),'#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_62731,c_63132]) ).
tff(c_63175,plain,
( empty('#skF_16')
| ~ element('#skF_2'('#skF_16'),'#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_63133]) ).
tff(c_63190,plain,
empty('#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_63175]) ).
tff(c_63192,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_621,c_63190]) ).
tff(c_63193,plain,
'#skF_18'('#skF_8') = '#skF_8',
inference(splitRight,[status(thm)],[c_62730]) ).
tff(c_416,plain,
! [A_92,B_93] :
( subset(A_92,B_93)
| ~ element(A_92,powerset(B_93)) ),
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_430,plain,
! [B_93] : subset('#skF_2'(powerset(B_93)),B_93),
inference(resolution,[status(thm)],[c_34,c_416]) ).
tff(c_59866,plain,
! [C_1426] :
( subset('#skF_8',C_1426)
| ~ empty(C_1426) ),
inference(superposition,[status(thm),theory(equality)],[c_59819,c_430]) ).
tff(c_136,plain,
! [A_17,B_18] :
( ordinal_subset(A_17,B_18)
| ~ subset(A_17,B_18)
| ~ ordinal(B_18)
| ~ ordinal(A_17) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_59878,plain,
! [C_1426] :
( ordinal_subset('#skF_8',C_1426)
| ~ ordinal(C_1426)
| ~ ordinal('#skF_8')
| ~ empty(C_1426) ),
inference(resolution,[status(thm)],[c_59866,c_136]) ).
tff(c_60048,plain,
! [C_1431] :
( ordinal_subset('#skF_8',C_1431)
| ~ ordinal(C_1431)
| ~ empty(C_1431) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_59878]) ).
tff(c_60052,plain,
( ~ in('#skF_8','#skF_16')
| ~ ordinal('#skF_8')
| ~ ordinal('#skF_18'('#skF_8'))
| ~ empty('#skF_18'('#skF_8')) ),
inference(resolution,[status(thm)],[c_60048,c_158]) ).
tff(c_60055,plain,
( ~ in('#skF_8','#skF_16')
| ~ ordinal('#skF_18'('#skF_8'))
| ~ empty('#skF_18'('#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_60052]) ).
tff(c_60213,plain,
~ empty('#skF_18'('#skF_8')),
inference(splitLeft,[status(thm)],[c_60055]) ).
tff(c_63198,plain,
~ empty('#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_63193,c_60213]) ).
tff(c_63204,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_63198]) ).
tff(c_63206,plain,
empty('#skF_18'('#skF_8')),
inference(splitRight,[status(thm)],[c_60055]) ).
tff(c_63216,plain,
'#skF_18'('#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_63206,c_344]) ).
tff(c_63205,plain,
( ~ ordinal('#skF_18'('#skF_8'))
| ~ in('#skF_8','#skF_16') ),
inference(splitRight,[status(thm)],[c_60055]) ).
tff(c_63284,plain,
~ in('#skF_8','#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_63216,c_63205]) ).
tff(c_63298,plain,
( empty('#skF_16')
| ~ element('#skF_8','#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_63284]) ).
tff(c_63311,plain,
~ element('#skF_8','#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_621,c_63298]) ).
tff(c_63748,plain,
! [A_1579,B_1580,B_1581] :
( element(A_1579,B_1580)
| ~ subset(B_1581,B_1580)
| empty(B_1581)
| ~ element(A_1579,B_1581) ),
inference(resolution,[status(thm)],[c_150,c_55929]) ).
tff(c_63770,plain,
! [A_1579] :
( element(A_1579,'#skF_17')
| empty('#skF_16')
| ~ element(A_1579,'#skF_16') ),
inference(resolution,[status(thm)],[c_154,c_63748]) ).
tff(c_63811,plain,
! [A_1585] :
( element(A_1585,'#skF_17')
| ~ element(A_1585,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_621,c_63770]) ).
tff(c_63816,plain,
! [A_1585] :
( ordinal(A_1585)
| ~ ordinal('#skF_17')
| empty('#skF_17')
| ~ element(A_1585,'#skF_16') ),
inference(resolution,[status(thm)],[c_63811,c_500]) ).
tff(c_63822,plain,
! [A_1585] :
( ordinal(A_1585)
| empty('#skF_17')
| ~ element(A_1585,'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_63816]) ).
tff(c_63824,plain,
! [A_1586] :
( ordinal(A_1586)
| ~ element(A_1586,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_56143,c_63822]) ).
tff(c_63873,plain,
ordinal('#skF_2'('#skF_16')),
inference(resolution,[status(thm)],[c_34,c_63824]) ).
tff(c_63699,plain,
! [B_1577,A_1578] :
( element('#skF_8',B_1577)
| ~ subset(A_1578,B_1577)
| ( A_1578 = '#skF_8' )
| ~ ordinal(A_1578) ),
inference(resolution,[status(thm)],[c_60056,c_55855]) ).
tff(c_65421,plain,
! [A_1663,B_1664] :
( element('#skF_8',A_1663)
| ( B_1664 = '#skF_8' )
| ~ ordinal(B_1664)
| ~ in(B_1664,A_1663)
| ~ epsilon_transitive(A_1663) ),
inference(resolution,[status(thm)],[c_28,c_63699]) ).
tff(c_65451,plain,
! [C_35] :
( element('#skF_8','#skF_16')
| ( '#skF_18'(C_35) = '#skF_8' )
| ~ ordinal('#skF_18'(C_35))
| ~ epsilon_transitive('#skF_16')
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_65421]) ).
tff(c_65465,plain,
! [C_35] :
( element('#skF_8','#skF_16')
| ( '#skF_18'(C_35) = '#skF_8' )
| ~ ordinal('#skF_18'(C_35))
| ~ in(C_35,'#skF_16')
| ~ ordinal(C_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_55837,c_65451]) ).
tff(c_65467,plain,
! [C_1665] :
( ( '#skF_18'(C_1665) = '#skF_8' )
| ~ ordinal('#skF_18'(C_1665))
| ~ in(C_1665,'#skF_16')
| ~ ordinal(C_1665) ),
inference(negUnitSimplification,[status(thm)],[c_63311,c_65465]) ).
tff(c_65485,plain,
! [C_1666] :
( ( '#skF_18'(C_1666) = '#skF_8' )
| ~ in(C_1666,'#skF_16')
| ~ ordinal(C_1666) ),
inference(resolution,[status(thm)],[c_162,c_65467]) ).
tff(c_65517,plain,
! [A_30] :
( ( '#skF_18'(A_30) = '#skF_8' )
| ~ ordinal(A_30)
| empty('#skF_16')
| ~ element(A_30,'#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_65485]) ).
tff(c_65591,plain,
! [A_1670] :
( ( '#skF_18'(A_1670) = '#skF_8' )
| ~ ordinal(A_1670)
| ~ element(A_1670,'#skF_16') ),
inference(negUnitSimplification,[status(thm)],[c_621,c_65517]) ).
tff(c_65646,plain,
( ( '#skF_18'('#skF_2'('#skF_16')) = '#skF_8' )
| ~ ordinal('#skF_2'('#skF_16')) ),
inference(resolution,[status(thm)],[c_34,c_65591]) ).
tff(c_65671,plain,
'#skF_18'('#skF_2'('#skF_16')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_63873,c_65646]) ).
tff(c_65698,plain,
( element('#skF_8','#skF_16')
| ~ in('#skF_2'('#skF_16'),'#skF_16')
| ~ ordinal('#skF_2'('#skF_16')) ),
inference(superposition,[status(thm),theory(equality)],[c_65671,c_380]) ).
tff(c_65733,plain,
( element('#skF_8','#skF_16')
| ~ in('#skF_2'('#skF_16'),'#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_63873,c_65698]) ).
tff(c_65734,plain,
~ in('#skF_2'('#skF_16'),'#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_63311,c_65733]) ).
tff(c_65761,plain,
( empty('#skF_16')
| ~ element('#skF_2'('#skF_16'),'#skF_16') ),
inference(resolution,[status(thm)],[c_150,c_65734]) ).
tff(c_65776,plain,
empty('#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_65761]) ).
tff(c_65778,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_621,c_65776]) ).
tff(c_65803,plain,
! [A_1671] : ~ element(A_1671,'#skF_16'),
inference(splitRight,[status(thm)],[c_56142]) ).
tff(c_65831,plain,
$false,
inference(resolution,[status(thm)],[c_34,c_65803]) ).
tff(c_65833,plain,
ordinal('#skF_16'),
inference(splitRight,[status(thm)],[c_612]) ).
tff(c_68373,plain,
! [C_1833,A_1834] :
( ~ empty(C_1833)
| empty('#skF_2'(powerset(C_1833)))
| ~ element(A_1834,'#skF_2'(powerset(C_1833))) ),
inference(resolution,[status(thm)],[c_150,c_574]) ).
tff(c_68485,plain,
! [C_1837] :
( ~ empty(C_1837)
| empty('#skF_2'(powerset(C_1837))) ),
inference(resolution,[status(thm)],[c_34,c_68373]) ).
tff(c_68493,plain,
! [C_1838] :
( ( '#skF_2'(powerset(C_1838)) = '#skF_8' )
| ~ empty(C_1838) ),
inference(resolution,[status(thm)],[c_68485,c_344]) ).
tff(c_68565,plain,
! [C_1840] :
( element('#skF_8',powerset(C_1840))
| ~ empty(C_1840) ),
inference(superposition,[status(thm),theory(equality)],[c_68493,c_34]) ).
tff(c_68583,plain,
! [A_42,C_1840] :
( ~ in(A_42,'#skF_8')
| ~ empty(C_1840) ),
inference(resolution,[status(thm)],[c_68565,c_170]) ).
tff(c_68585,plain,
! [C_1840] : ~ empty(C_1840),
inference(splitLeft,[status(thm)],[c_68583]) ).
tff(c_68600,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_68585,c_92]) ).
tff(c_68602,plain,
! [A_1841] : ~ in(A_1841,'#skF_8'),
inference(splitRight,[status(thm)],[c_68583]) ).
tff(c_68618,plain,
! [A_27] :
( in('#skF_8',A_27)
| ( A_27 = '#skF_8' )
| ~ ordinal('#skF_8')
| ~ ordinal(A_27) ),
inference(resolution,[status(thm)],[c_148,c_68602]) ).
tff(c_68642,plain,
! [A_27] :
( in('#skF_8',A_27)
| ( A_27 = '#skF_8' )
| ~ ordinal(A_27) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_68618]) ).
tff(c_66179,plain,
! [B_1721,A_1722] :
( in(B_1721,A_1722)
| ( B_1721 = A_1722 )
| in(A_1722,B_1721)
| ~ ordinal(B_1721)
| ~ ordinal(A_1722) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_174,plain,
! [B_47,A_46] :
( ~ empty(B_47)
| ~ in(A_46,B_47) ),
inference(cnfTransformation,[status(thm)],[f_283]) ).
tff(c_66269,plain,
! [B_1721,A_1722] :
( ~ empty(B_1721)
| in(B_1721,A_1722)
| ( B_1721 = A_1722 )
| ~ ordinal(B_1721)
| ~ ordinal(A_1722) ),
inference(resolution,[status(thm)],[c_66179,c_174]) ).
tff(c_68781,plain,
! [B_1847,A_1848] :
( ordinal_subset(B_1847,A_1848)
| ~ ordinal(A_1848)
| ~ ordinal(B_1847)
| ~ in(B_1847,A_1848)
| ~ epsilon_transitive(A_1848) ),
inference(resolution,[status(thm)],[c_28,c_590]) ).
tff(c_68849,plain,
! [B_1852] :
( ~ in(B_1852,'#skF_16')
| ~ ordinal('#skF_18'(B_1852))
| ~ ordinal(B_1852)
| ~ in(B_1852,'#skF_18'(B_1852))
| ~ epsilon_transitive('#skF_18'(B_1852)) ),
inference(resolution,[status(thm)],[c_68781,c_158]) ).
tff(c_69168,plain,
! [B_1865] :
( ~ in(B_1865,'#skF_16')
| ~ epsilon_transitive('#skF_18'(B_1865))
| ~ empty(B_1865)
| ( '#skF_18'(B_1865) = B_1865 )
| ~ ordinal(B_1865)
| ~ ordinal('#skF_18'(B_1865)) ),
inference(resolution,[status(thm)],[c_66269,c_68849]) ).
tff(c_69332,plain,
! [C_1874] :
( ~ epsilon_transitive('#skF_18'(C_1874))
| ~ empty(C_1874)
| ( '#skF_18'(C_1874) = C_1874 )
| ~ in(C_1874,'#skF_16')
| ~ ordinal(C_1874) ),
inference(resolution,[status(thm)],[c_162,c_69168]) ).
tff(c_69426,plain,
! [C_1884] :
( ~ empty(C_1884)
| ( '#skF_18'(C_1884) = C_1884 )
| ~ in(C_1884,'#skF_16')
| ~ ordinal(C_1884) ),
inference(resolution,[status(thm)],[c_331,c_69332]) ).
tff(c_69430,plain,
( ~ empty('#skF_8')
| ( '#skF_18'('#skF_8') = '#skF_8' )
| ~ ordinal('#skF_8')
| ( '#skF_16' = '#skF_8' )
| ~ ordinal('#skF_16') ),
inference(resolution,[status(thm)],[c_68642,c_69426]) ).
tff(c_69464,plain,
( ( '#skF_18'('#skF_8') = '#skF_8' )
| ( '#skF_16' = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_65833,c_86,c_92,c_69430]) ).
tff(c_69465,plain,
'#skF_18'('#skF_8') = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_275,c_69464]) ).
tff(c_68543,plain,
! [C_1839] :
( subset('#skF_8',C_1839)
| ~ empty(C_1839) ),
inference(superposition,[status(thm),theory(equality)],[c_68493,c_430]) ).
tff(c_68555,plain,
! [C_1839] :
( ordinal_subset('#skF_8',C_1839)
| ~ ordinal(C_1839)
| ~ ordinal('#skF_8')
| ~ empty(C_1839) ),
inference(resolution,[status(thm)],[c_68543,c_136]) ).
tff(c_68648,plain,
! [C_1842] :
( ordinal_subset('#skF_8',C_1842)
| ~ ordinal(C_1842)
| ~ empty(C_1842) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_68555]) ).
tff(c_68652,plain,
( ~ in('#skF_8','#skF_16')
| ~ ordinal('#skF_8')
| ~ ordinal('#skF_18'('#skF_8'))
| ~ empty('#skF_18'('#skF_8')) ),
inference(resolution,[status(thm)],[c_68648,c_158]) ).
tff(c_68655,plain,
( ~ in('#skF_8','#skF_16')
| ~ ordinal('#skF_18'('#skF_8'))
| ~ empty('#skF_18'('#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_68652]) ).
tff(c_68738,plain,
~ empty('#skF_18'('#skF_8')),
inference(splitLeft,[status(thm)],[c_68655]) ).
tff(c_69485,plain,
~ empty('#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_69465,c_68738]) ).
tff(c_69488,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_69485]) ).
tff(c_69490,plain,
empty('#skF_18'('#skF_8')),
inference(splitRight,[status(thm)],[c_68655]) ).
tff(c_69497,plain,
'#skF_18'('#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_69490,c_344]) ).
tff(c_69489,plain,
( ~ ordinal('#skF_18'('#skF_8'))
| ~ in('#skF_8','#skF_16') ),
inference(splitRight,[status(thm)],[c_68655]) ).
tff(c_69560,plain,
~ in('#skF_8','#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_69497,c_69489]) ).
tff(c_69563,plain,
( ( '#skF_16' = '#skF_8' )
| ~ ordinal('#skF_16') ),
inference(resolution,[status(thm)],[c_68642,c_69560]) ).
tff(c_69577,plain,
'#skF_16' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_65833,c_69563]) ).
tff(c_69579,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_275,c_69577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU235+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
% 0.13/0.36 % Computer : n002.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 3 11:48:46 EDT 2023
% 0.13/0.36 % CPUTime :
% 23.32/11.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.32/11.06
% 23.32/11.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.69/11.11
% 23.69/11.11 Inference rules
% 23.69/11.11 ----------------------
% 23.69/11.11 #Ref : 0
% 23.69/11.11 #Sup : 14509
% 23.69/11.11 #Fact : 20
% 23.69/11.11 #Define : 0
% 23.69/11.11 #Split : 113
% 23.69/11.11 #Chain : 0
% 23.69/11.11 #Close : 0
% 23.69/11.11
% 23.69/11.11 Ordering : KBO
% 23.69/11.11
% 23.69/11.11 Simplification rules
% 23.69/11.11 ----------------------
% 23.69/11.11 #Subsume : 6088
% 23.69/11.11 #Demod : 10737
% 23.69/11.11 #Tautology : 3063
% 23.69/11.11 #SimpNegUnit : 1850
% 23.69/11.11 #BackRed : 532
% 23.69/11.11
% 23.69/11.11 #Partial instantiations: 0
% 23.69/11.11 #Strategies tried : 1
% 23.69/11.11
% 23.69/11.11 Timing (in seconds)
% 23.69/11.11 ----------------------
% 23.69/11.11 Preprocessing : 0.60
% 23.69/11.11 Parsing : 0.31
% 23.69/11.11 CNF conversion : 0.05
% 23.69/11.11 Main loop : 9.39
% 23.69/11.11 Inferencing : 2.18
% 23.69/11.11 Reduction : 3.43
% 23.69/11.11 Demodulation : 2.46
% 23.69/11.11 BG Simplification : 0.12
% 23.69/11.11 Subsumption : 3.05
% 23.69/11.11 Abstraction : 0.17
% 23.69/11.11 MUC search : 0.00
% 23.69/11.11 Cooper : 0.00
% 23.69/11.11 Total : 10.09
% 23.69/11.11 Index Insertion : 0.00
% 23.69/11.11 Index Deletion : 0.00
% 23.69/11.11 Index Matching : 0.00
% 23.69/11.11 BG Taut test : 0.00
%------------------------------------------------------------------------------