TSTP Solution File: SEU298+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU298+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n014.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 10:58:19 EDT 2023
% Result : Theorem 29.76s 15.46s
% Output : CNFRefutation 30.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 48
% Syntax : Number of formulae : 576 ( 204 unt; 44 typ; 0 def)
% Number of atoms : 1413 ( 378 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1653 ( 772 ~; 861 |; 12 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 30 >; 13 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 14 con; 0-3 aty)
% Number of variables : 326 (; 319 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > relation > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > set_difference > #nlpp > succ > singleton > powerset > #skF_5 > #skF_22 > #skF_20 > #skF_4 > #skF_18 > #skF_17 > #skF_26 > #skF_11 > #skF_19 > #skF_7 > #skF_10 > #skF_29 > #skF_16 > #skF_15 > #skF_14 > #skF_13 > #skF_2 > #skF_1 > #skF_21 > #skF_9 > #skF_24 > #skF_8 > #skF_23 > #skF_3 > #skF_25 > #skF_27 > #skF_28 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $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('#skF_10',type,
'#skF_10': $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(succ,type,
succ: $i > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_42,negated_conjecture,
~ ! [A,B] :
( ( ordinal(A)
& element(B,powerset(powerset(succ(A)))) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(D,powerset(A))
& ? [E] :
( in(E,B)
& ( D = set_difference(E,singleton(A)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
tff(f_328,axiom,
! [A,B] :
( ( ordinal(A)
& element(B,powerset(powerset(succ(A)))) )
=> ( ! [C,D,E] :
( ( ( C = D )
& ? [F] :
( in(F,B)
& ( D = set_difference(F,singleton(A)) ) )
& ( C = E )
& ? [G] :
( in(G,B)
& ( E = set_difference(G,singleton(A)) ) ) )
=> ( D = E ) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( in(E,powerset(A))
& ( E = D )
& ? [H] :
( in(H,B)
& ( D = set_difference(H,singleton(A)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
tff(f_177,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
tff(f_250,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
tff(c_4,plain,
ordinal('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_2,plain,
element('#skF_2',powerset(powerset(succ('#skF_1')))),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_996,plain,
! [A_237,B_238,D_239] :
( ( '#skF_22'(A_237,B_238) = '#skF_23'(A_237,B_238) )
| in('#skF_29'(A_237,B_238,D_239),B_238)
| ~ in(D_239,'#skF_27'(A_237,B_238))
| ~ element(B_238,powerset(powerset(succ(A_237))))
| ~ ordinal(A_237) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1010,plain,
! [D_239] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| in('#skF_29'('#skF_1','#skF_2',D_239),'#skF_2')
| ~ in(D_239,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_996]) ).
tff(c_1021,plain,
! [D_239] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| in('#skF_29'('#skF_1','#skF_2',D_239),'#skF_2')
| ~ in(D_239,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1010]) ).
tff(c_1022,plain,
'#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_1021]) ).
tff(c_1053,plain,
! [A_243,B_244,D_245] :
( ( '#skF_22'(A_243,B_244) = '#skF_24'(A_243,B_244) )
| in('#skF_29'(A_243,B_244,D_245),B_244)
| ~ in(D_245,'#skF_27'(A_243,B_244))
| ~ element(B_244,powerset(powerset(succ(A_243))))
| ~ ordinal(A_243) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1067,plain,
! [D_245] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| in('#skF_29'('#skF_1','#skF_2',D_245),'#skF_2')
| ~ in(D_245,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_1053]) ).
tff(c_1078,plain,
! [D_245] :
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| in('#skF_29'('#skF_1','#skF_2',D_245),'#skF_2')
| ~ in(D_245,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1022,c_1067]) ).
tff(c_1079,plain,
'#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_1078]) ).
tff(c_1110,plain,
! [A_248,B_249,D_250] :
( ( '#skF_24'(A_248,B_249) != '#skF_23'(A_248,B_249) )
| in('#skF_29'(A_248,B_249,D_250),B_249)
| ~ in(D_250,'#skF_27'(A_248,B_249))
| ~ element(B_249,powerset(powerset(succ(A_248))))
| ~ ordinal(A_248) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1124,plain,
! [D_250] :
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| in('#skF_29'('#skF_1','#skF_2',D_250),'#skF_2')
| ~ in(D_250,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_1110]) ).
tff(c_1135,plain,
! [D_250] :
( in('#skF_29'('#skF_1','#skF_2',D_250),'#skF_2')
| ~ in(D_250,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1079,c_1124]) ).
tff(c_1396,plain,
! [A_284,B_285,D_286] :
( ( '#skF_24'(A_284,B_285) != '#skF_23'(A_284,B_285) )
| ( set_difference('#skF_29'(A_284,B_285,D_286),singleton(A_284)) = D_286 )
| ~ in(D_286,'#skF_27'(A_284,B_285))
| ~ element(B_285,powerset(powerset(succ(A_284))))
| ~ ordinal(A_284) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1410,plain,
! [D_286] :
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_286),singleton('#skF_1')) = D_286 )
| ~ in(D_286,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_1396]) ).
tff(c_1421,plain,
! [D_286] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_286),singleton('#skF_1')) = D_286 )
| ~ in(D_286,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1079,c_1410]) ).
tff(c_18,plain,
! [C_12] :
( in('#skF_4'(C_12),'#skF_2')
| in('#skF_5'(C_12),C_12) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_975,plain,
! [A_234,B_235,D_236] :
( ( '#skF_24'(A_234,B_235) != '#skF_23'(A_234,B_235) )
| ( '#skF_28'(A_234,B_235,D_236) = D_236 )
| ~ in(D_236,'#skF_27'(A_234,B_235))
| ~ element(B_235,powerset(powerset(succ(A_234))))
| ~ ordinal(A_234) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1767,plain,
! [A_322,B_323] :
( ( '#skF_24'(A_322,B_323) != '#skF_23'(A_322,B_323) )
| ( '#skF_28'(A_322,B_323,'#skF_5'('#skF_27'(A_322,B_323))) = '#skF_5'('#skF_27'(A_322,B_323)) )
| ~ element(B_323,powerset(powerset(succ(A_322))))
| ~ ordinal(A_322)
| in('#skF_4'('#skF_27'(A_322,B_323)),'#skF_2') ),
inference(resolution,[status(thm)],[c_18,c_975]) ).
tff(c_1781,plain,
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(resolution,[status(thm)],[c_2,c_1767]) ).
tff(c_1792,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1079,c_1781]) ).
tff(c_1793,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitLeft,[status(thm)],[c_1792]) ).
tff(c_16,plain,
! [C_12] :
( ( set_difference('#skF_4'(C_12),singleton('#skF_1')) = '#skF_3'(C_12) )
| in('#skF_5'(C_12),C_12) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_10073,plain,
! [A_757,B_758] :
( ( '#skF_24'(A_757,B_758) != '#skF_23'(A_757,B_758) )
| ( '#skF_28'(A_757,B_758,'#skF_5'('#skF_27'(A_757,B_758))) = '#skF_5'('#skF_27'(A_757,B_758)) )
| ~ element(B_758,powerset(powerset(succ(A_757))))
| ~ ordinal(A_757)
| ( set_difference('#skF_4'('#skF_27'(A_757,B_758)),singleton('#skF_1')) = '#skF_3'('#skF_27'(A_757,B_758)) ) ),
inference(resolution,[status(thm)],[c_16,c_975]) ).
tff(c_10087,plain,
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(resolution,[status(thm)],[c_2,c_10073]) ).
tff(c_10098,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1079,c_10087]) ).
tff(c_10099,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_10098]) ).
tff(c_1815,plain,
! [A_330,B_331,H_332] :
( ( '#skF_24'(A_330,B_331) != '#skF_23'(A_330,B_331) )
| in(set_difference(H_332,singleton(A_330)),'#skF_27'(A_330,B_331))
| ~ in(H_332,B_331)
| ~ in(set_difference(H_332,singleton(A_330)),powerset(A_330))
| ~ element(B_331,powerset(powerset(succ(A_330))))
| ~ ordinal(A_330) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1819,plain,
! [B_331,C_12] :
( ( '#skF_24'('#skF_1',B_331) != '#skF_23'('#skF_1',B_331) )
| in(set_difference('#skF_4'(C_12),singleton('#skF_1')),'#skF_27'('#skF_1',B_331))
| ~ in('#skF_4'(C_12),B_331)
| ~ in('#skF_3'(C_12),powerset('#skF_1'))
| ~ element(B_331,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1')
| in('#skF_5'(C_12),C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1815]) ).
tff(c_6646,plain,
! [B_627,C_628] :
( ( '#skF_24'('#skF_1',B_627) != '#skF_23'('#skF_1',B_627) )
| in(set_difference('#skF_4'(C_628),singleton('#skF_1')),'#skF_27'('#skF_1',B_627))
| ~ in('#skF_4'(C_628),B_627)
| ~ in('#skF_3'(C_628),powerset('#skF_1'))
| ~ element(B_627,powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_628),C_628) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1819]) ).
tff(c_1422,plain,
! [D_287] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_287),singleton('#skF_1')) = D_287 )
| ~ in(D_287,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1079,c_1410]) ).
tff(c_122,plain,
! [A_33,B_34] :
( finite(set_difference(A_33,B_34))
| ~ finite(A_33) ),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_1433,plain,
! [D_287] :
( finite(D_287)
| ~ finite('#skF_29'('#skF_1','#skF_2',D_287))
| ~ in(D_287,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1422,c_122]) ).
tff(c_6722,plain,
! [C_628] :
( finite(set_difference('#skF_4'(C_628),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_628),singleton('#skF_1'))))
| ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_628),'#skF_2')
| ~ in('#skF_3'(C_628),powerset('#skF_1'))
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_628),C_628) ),
inference(resolution,[status(thm)],[c_6646,c_1433]) ).
tff(c_6907,plain,
! [C_628] :
( finite(set_difference('#skF_4'(C_628),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_628),singleton('#skF_1'))))
| ~ in('#skF_4'(C_628),'#skF_2')
| ~ in('#skF_3'(C_628),powerset('#skF_1'))
| in('#skF_5'(C_628),C_628) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1079,c_6722]) ).
tff(c_10120,plain,
( finite(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_10099,c_6907]) ).
tff(c_10167,plain,
( finite('#skF_3'('#skF_27'('#skF_1','#skF_2')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_1793,c_10099,c_10120]) ).
tff(c_10502,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitLeft,[status(thm)],[c_10167]) ).
tff(c_20,plain,
! [C_12] :
( in('#skF_3'(C_12),powerset('#skF_1'))
| in('#skF_5'(C_12),C_12) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_993,plain,
! [A_234,B_235] :
( ( '#skF_24'(A_234,B_235) != '#skF_23'(A_234,B_235) )
| ( '#skF_28'(A_234,B_235,'#skF_5'('#skF_27'(A_234,B_235))) = '#skF_5'('#skF_27'(A_234,B_235)) )
| ~ element(B_235,powerset(powerset(succ(A_234))))
| ~ ordinal(A_234)
| in('#skF_3'('#skF_27'(A_234,B_235)),powerset('#skF_1')) ),
inference(resolution,[status(thm)],[c_20,c_975]) ).
tff(c_10572,plain,
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_993,c_10502]) ).
tff(c_10597,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_1079,c_10572]) ).
tff(c_1271,plain,
! [A_268,B_269,D_270] :
( ( '#skF_24'(A_268,B_269) != '#skF_23'(A_268,B_269) )
| in('#skF_28'(A_268,B_269,D_270),powerset(A_268))
| ~ in(D_270,'#skF_27'(A_268,B_269))
| ~ element(B_269,powerset(powerset(succ(A_268))))
| ~ ordinal(A_268) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1285,plain,
! [D_270] :
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| in('#skF_28'('#skF_1','#skF_2',D_270),powerset('#skF_1'))
| ~ in(D_270,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_1271]) ).
tff(c_1323,plain,
! [D_273] :
( in('#skF_28'('#skF_1','#skF_2',D_273),powerset('#skF_1'))
| ~ in(D_273,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1079,c_1285]) ).
tff(c_170,plain,
! [B_45,A_44] :
( ~ in(B_45,A_44)
| ~ in(A_44,B_45) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_1326,plain,
! [D_273] :
( ~ in(powerset('#skF_1'),'#skF_28'('#skF_1','#skF_2',D_273))
| ~ in(D_273,'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_1323,c_170]) ).
tff(c_10615,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_10597,c_1326]) ).
tff(c_10630,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_10615]) ).
tff(c_10682,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(resolution,[status(thm)],[c_20,c_10630]) ).
tff(c_10701,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10502,c_10682]) ).
tff(c_10703,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_10615]) ).
tff(c_1296,plain,
! [D_270] :
( in('#skF_28'('#skF_1','#skF_2',D_270),powerset('#skF_1'))
| ~ in(D_270,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1079,c_1285]) ).
tff(c_10618,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_10597,c_1296]) ).
tff(c_10747,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_10703,c_10618]) ).
tff(c_12,plain,
! [C_12,E_20] :
( in('#skF_3'(C_12),powerset('#skF_1'))
| ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'(C_12) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_1435,plain,
! [C_12,D_287] :
( in('#skF_3'(C_12),powerset('#skF_1'))
| ( D_287 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_287),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_287,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1422,c_12]) ).
tff(c_1570,plain,
! [C_301] :
( in('#skF_3'(C_301),powerset('#skF_1'))
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_301)),'#skF_2')
| ~ in('#skF_5'(C_301),powerset('#skF_1'))
| ~ in('#skF_5'(C_301),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_1435]) ).
tff(c_1574,plain,
! [C_301] :
( in('#skF_3'(C_301),powerset('#skF_1'))
| ~ in('#skF_5'(C_301),powerset('#skF_1'))
| ~ in('#skF_5'(C_301),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_1135,c_1570]) ).
tff(c_10762,plain,
( in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_10747,c_1574]) ).
tff(c_10780,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_10703,c_10762]) ).
tff(c_10782,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10502,c_10780]) ).
tff(c_10784,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_10167]) ).
tff(c_266,plain,
! [A_55,B_56,H_115] :
( ( '#skF_24'(A_55,B_56) != '#skF_23'(A_55,B_56) )
| in(set_difference(H_115,singleton(A_55)),'#skF_27'(A_55,B_56))
| ~ in(H_115,B_56)
| ~ in(set_difference(H_115,singleton(A_55)),powerset(A_55))
| ~ element(B_56,powerset(powerset(succ(A_55))))
| ~ ordinal(A_55) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_10139,plain,
! [B_56] :
( ( '#skF_24'('#skF_1',B_56) != '#skF_23'('#skF_1',B_56) )
| in(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_10099,c_266]) ).
tff(c_10177,plain,
! [B_56] :
( ( '#skF_24'('#skF_1',B_56) != '#skF_23'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10099,c_10139]) ).
tff(c_14288,plain,
! [B_56] :
( ( '#skF_24'('#skF_1',B_56) != '#skF_23'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_10784,c_10177]) ).
tff(c_14,plain,
! [C_12] :
( ~ in('#skF_3'(C_12),C_12)
| in('#skF_5'(C_12),C_12) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_14289,plain,
! [B_848] :
( ( '#skF_24'('#skF_1',B_848) != '#skF_23'('#skF_1',B_848) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_848))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_848)
| ~ element(B_848,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_10784,c_10177]) ).
tff(c_995,plain,
! [A_234,B_235] :
( ( '#skF_24'(A_234,B_235) != '#skF_23'(A_234,B_235) )
| ( '#skF_28'(A_234,B_235,'#skF_5'('#skF_27'(A_234,B_235))) = '#skF_5'('#skF_27'(A_234,B_235)) )
| ~ element(B_235,powerset(powerset(succ(A_234))))
| ~ ordinal(A_234)
| ~ in('#skF_3'('#skF_27'(A_234,B_235)),'#skF_27'(A_234,B_235)) ),
inference(resolution,[status(thm)],[c_14,c_975]) ).
tff(c_14364,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_14289,c_995]) ).
tff(c_14485,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1793,c_1079,c_4,c_14364]) ).
tff(c_14558,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_14485,c_1326]) ).
tff(c_14573,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_14558]) ).
tff(c_14619,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_14573]) ).
tff(c_14622,plain,
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_14288,c_14619]) ).
tff(c_14639,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1793,c_1079,c_14622]) ).
tff(c_14641,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_14558]) ).
tff(c_14561,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_14485,c_1296]) ).
tff(c_14840,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_14641,c_14561]) ).
tff(c_6,plain,
! [C_12,E_20] :
( ~ in('#skF_3'(C_12),C_12)
| ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'(C_12) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_14424,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_14289,c_6]) ).
tff(c_14546,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1793,c_1079,c_14424]) ).
tff(c_14879,plain,
! [E_851] :
( ( set_difference(E_851,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_851,'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_14840,c_14546]) ).
tff(c_15274,plain,
! [D_854] :
( ( D_854 != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_854),'#skF_2')
| ~ in(D_854,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1421,c_14879]) ).
tff(c_15279,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_1135,c_15274]) ).
tff(c_15281,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15279,c_14641]) ).
tff(c_15283,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) != '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_10098]) ).
tff(c_15282,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_10098]) ).
tff(c_15298,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15282,c_1296]) ).
tff(c_15363,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_15298]) ).
tff(c_15386,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_16,c_15363]) ).
tff(c_15406,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15283,c_15386]) ).
tff(c_15408,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_15298]) ).
tff(c_15407,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_15298]) ).
tff(c_8,plain,
! [C_12,E_20] :
( ( set_difference('#skF_4'(C_12),singleton('#skF_1')) = '#skF_3'(C_12) )
| ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'(C_12) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_1430,plain,
! [C_12,D_287] :
( ( set_difference('#skF_4'(C_12),singleton('#skF_1')) = '#skF_3'(C_12) )
| ( D_287 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_287),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_287,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1422,c_8]) ).
tff(c_1606,plain,
! [C_305] :
( ( set_difference('#skF_4'(C_305),singleton('#skF_1')) = '#skF_3'(C_305) )
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_305)),'#skF_2')
| ~ in('#skF_5'(C_305),powerset('#skF_1'))
| ~ in('#skF_5'(C_305),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_1430]) ).
tff(c_1610,plain,
! [C_305] :
( ( set_difference('#skF_4'(C_305),singleton('#skF_1')) = '#skF_3'(C_305) )
| ~ in('#skF_5'(C_305),powerset('#skF_1'))
| ~ in('#skF_5'(C_305),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_1135,c_1606]) ).
tff(c_15438,plain,
( ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_15407,c_1610]) ).
tff(c_15449,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_15283,c_15438]) ).
tff(c_15497,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15408,c_15449]) ).
tff(c_15499,plain,
~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitRight,[status(thm)],[c_1792]) ).
tff(c_15498,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_1792]) ).
tff(c_15512,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15498,c_1326]) ).
tff(c_15519,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_15512]) ).
tff(c_15558,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(resolution,[status(thm)],[c_18,c_15519]) ).
tff(c_15568,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15499,c_15558]) ).
tff(c_15570,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_15512]) ).
tff(c_15515,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15498,c_1296]) ).
tff(c_15614,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_15570,c_15515]) ).
tff(c_10,plain,
! [C_12,E_20] :
( in('#skF_4'(C_12),'#skF_2')
| ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'(C_12) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_1437,plain,
! [C_12,D_287] :
( in('#skF_4'(C_12),'#skF_2')
| ( D_287 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_287),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_287,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1422,c_10]) ).
tff(c_1506,plain,
! [C_294] :
( in('#skF_4'(C_294),'#skF_2')
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_294)),'#skF_2')
| ~ in('#skF_5'(C_294),powerset('#skF_1'))
| ~ in('#skF_5'(C_294),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_1437]) ).
tff(c_1510,plain,
! [C_294] :
( in('#skF_4'(C_294),'#skF_2')
| ~ in('#skF_5'(C_294),powerset('#skF_1'))
| ~ in('#skF_5'(C_294),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_1135,c_1506]) ).
tff(c_15623,plain,
( in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_15614,c_1510]) ).
tff(c_15634,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_15570,c_15623]) ).
tff(c_15636,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15499,c_15634]) ).
tff(c_15637,plain,
! [D_245] :
( in('#skF_29'('#skF_1','#skF_2',D_245),'#skF_2')
| ~ in(D_245,'#skF_27'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_1078]) ).
tff(c_15638,plain,
'#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_1078]) ).
tff(c_15910,plain,
! [A_896,B_897,D_898] :
( ( '#skF_22'(A_896,B_897) = '#skF_24'(A_896,B_897) )
| ( set_difference('#skF_29'(A_896,B_897,D_898),singleton(A_896)) = D_898 )
| ~ in(D_898,'#skF_27'(A_896,B_897))
| ~ element(B_897,powerset(powerset(succ(A_896))))
| ~ ordinal(A_896) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_15924,plain,
! [D_898] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_898),singleton('#skF_1')) = D_898 )
| ~ in(D_898,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_15910]) ).
tff(c_15935,plain,
! [D_898] :
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_898),singleton('#skF_1')) = D_898 )
| ~ in(D_898,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1022,c_15924]) ).
tff(c_15936,plain,
! [D_898] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_898),singleton('#skF_1')) = D_898 )
| ~ in(D_898,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_15935]) ).
tff(c_954,plain,
! [A_231,B_232,D_233] :
( ( '#skF_22'(A_231,B_232) = '#skF_24'(A_231,B_232) )
| ( '#skF_28'(A_231,B_232,D_233) = D_233 )
| ~ in(D_233,'#skF_27'(A_231,B_232))
| ~ element(B_232,powerset(powerset(succ(A_231))))
| ~ ordinal(A_231) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_16485,plain,
! [A_960,B_961] :
( ( '#skF_22'(A_960,B_961) = '#skF_24'(A_960,B_961) )
| ( '#skF_28'(A_960,B_961,'#skF_5'('#skF_27'(A_960,B_961))) = '#skF_5'('#skF_27'(A_960,B_961)) )
| ~ element(B_961,powerset(powerset(succ(A_960))))
| ~ ordinal(A_960)
| in('#skF_4'('#skF_27'(A_960,B_961)),'#skF_2') ),
inference(resolution,[status(thm)],[c_18,c_954]) ).
tff(c_16499,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(resolution,[status(thm)],[c_2,c_16485]) ).
tff(c_16510,plain,
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1022,c_16499]) ).
tff(c_16511,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_16510]) ).
tff(c_16512,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitLeft,[status(thm)],[c_16511]) ).
tff(c_23675,plain,
! [A_1295,B_1296] :
( ( '#skF_22'(A_1295,B_1296) = '#skF_24'(A_1295,B_1296) )
| ( '#skF_28'(A_1295,B_1296,'#skF_5'('#skF_27'(A_1295,B_1296))) = '#skF_5'('#skF_27'(A_1295,B_1296)) )
| ~ element(B_1296,powerset(powerset(succ(A_1295))))
| ~ ordinal(A_1295)
| ( set_difference('#skF_4'('#skF_27'(A_1295,B_1296)),singleton('#skF_1')) = '#skF_3'('#skF_27'(A_1295,B_1296)) ) ),
inference(resolution,[status(thm)],[c_16,c_954]) ).
tff(c_23689,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(resolution,[status(thm)],[c_2,c_23675]) ).
tff(c_23700,plain,
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1022,c_23689]) ).
tff(c_23701,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_23700]) ).
tff(c_23703,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_23701]) ).
tff(c_16513,plain,
! [A_962,B_963,H_964] :
( ( '#skF_22'(A_962,B_963) = '#skF_24'(A_962,B_963) )
| in(set_difference(H_964,singleton(A_962)),'#skF_27'(A_962,B_963))
| ~ in(H_964,B_963)
| ~ in(set_difference(H_964,singleton(A_962)),powerset(A_962))
| ~ element(B_963,powerset(powerset(succ(A_962))))
| ~ ordinal(A_962) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_16517,plain,
! [B_963,C_12] :
( ( '#skF_22'('#skF_1',B_963) = '#skF_24'('#skF_1',B_963) )
| in(set_difference('#skF_4'(C_12),singleton('#skF_1')),'#skF_27'('#skF_1',B_963))
| ~ in('#skF_4'(C_12),B_963)
| ~ in('#skF_3'(C_12),powerset('#skF_1'))
| ~ element(B_963,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1')
| in('#skF_5'(C_12),C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_16513]) ).
tff(c_21563,plain,
! [B_1247,C_1248] :
( ( '#skF_22'('#skF_1',B_1247) = '#skF_24'('#skF_1',B_1247) )
| in(set_difference('#skF_4'(C_1248),singleton('#skF_1')),'#skF_27'('#skF_1',B_1247))
| ~ in('#skF_4'(C_1248),B_1247)
| ~ in('#skF_3'(C_1248),powerset('#skF_1'))
| ~ element(B_1247,powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_1248),C_1248) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16517]) ).
tff(c_15937,plain,
! [D_899] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_899),singleton('#skF_1')) = D_899 )
| ~ in(D_899,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_15935]) ).
tff(c_15948,plain,
! [D_899] :
( finite(D_899)
| ~ finite('#skF_29'('#skF_1','#skF_2',D_899))
| ~ in(D_899,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15937,c_122]) ).
tff(c_21643,plain,
! [C_1248] :
( finite(set_difference('#skF_4'(C_1248),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_1248),singleton('#skF_1'))))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_1248),'#skF_2')
| ~ in('#skF_3'(C_1248),powerset('#skF_1'))
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_1248),C_1248) ),
inference(resolution,[status(thm)],[c_21563,c_15948]) ).
tff(c_21830,plain,
! [C_1248] :
( finite(set_difference('#skF_4'(C_1248),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_1248),singleton('#skF_1'))))
| ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_1248),'#skF_2')
| ~ in('#skF_3'(C_1248),powerset('#skF_1'))
| in('#skF_5'(C_1248),C_1248) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1022,c_21643]) ).
tff(c_21831,plain,
! [C_1248] :
( finite(set_difference('#skF_4'(C_1248),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_1248),singleton('#skF_1'))))
| ~ in('#skF_4'(C_1248),'#skF_2')
| ~ in('#skF_3'(C_1248),powerset('#skF_1'))
| in('#skF_5'(C_1248),C_1248) ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_21830]) ).
tff(c_23717,plain,
( finite(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_23703,c_21831]) ).
tff(c_23767,plain,
( finite('#skF_3'('#skF_27'('#skF_1','#skF_2')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_16512,c_23703,c_23717]) ).
tff(c_23979,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitLeft,[status(thm)],[c_23767]) ).
tff(c_972,plain,
! [A_231,B_232] :
( ( '#skF_22'(A_231,B_232) = '#skF_24'(A_231,B_232) )
| ( '#skF_28'(A_231,B_232,'#skF_5'('#skF_27'(A_231,B_232))) = '#skF_5'('#skF_27'(A_231,B_232)) )
| ~ element(B_232,powerset(powerset(succ(A_231))))
| ~ ordinal(A_231)
| in('#skF_3'('#skF_27'(A_231,B_232)),powerset('#skF_1')) ),
inference(resolution,[status(thm)],[c_20,c_954]) ).
tff(c_23994,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_972,c_23979]) ).
tff(c_24016,plain,
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_1022,c_23994]) ).
tff(c_24017,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_15638,c_24016]) ).
tff(c_15774,plain,
! [A_880,B_881,D_882] :
( ( '#skF_22'(A_880,B_881) = '#skF_24'(A_880,B_881) )
| in('#skF_28'(A_880,B_881,D_882),powerset(A_880))
| ~ in(D_882,'#skF_27'(A_880,B_881))
| ~ element(B_881,powerset(powerset(succ(A_880))))
| ~ ordinal(A_880) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_15788,plain,
! [D_882] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| in('#skF_28'('#skF_1','#skF_2',D_882),powerset('#skF_1'))
| ~ in(D_882,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_15774]) ).
tff(c_15799,plain,
! [D_882] :
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| in('#skF_28'('#skF_1','#skF_2',D_882),powerset('#skF_1'))
| ~ in(D_882,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1022,c_15788]) ).
tff(c_15801,plain,
! [D_883] :
( in('#skF_28'('#skF_1','#skF_2',D_883),powerset('#skF_1'))
| ~ in(D_883,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_15799]) ).
tff(c_15804,plain,
! [D_883] :
( ~ in(powerset('#skF_1'),'#skF_28'('#skF_1','#skF_2',D_883))
| ~ in(D_883,'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_15801,c_170]) ).
tff(c_24034,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_24017,c_15804]) ).
tff(c_24048,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_24034]) ).
tff(c_24076,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(resolution,[status(thm)],[c_20,c_24048]) ).
tff(c_24095,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23979,c_24076]) ).
tff(c_24097,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_24034]) ).
tff(c_15800,plain,
! [D_882] :
( in('#skF_28'('#skF_1','#skF_2',D_882),powerset('#skF_1'))
| ~ in(D_882,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_15799]) ).
tff(c_24037,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_24017,c_15800]) ).
tff(c_24168,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_24097,c_24037]) ).
tff(c_15950,plain,
! [C_12,D_899] :
( in('#skF_3'(C_12),powerset('#skF_1'))
| ( D_899 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_899),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_899,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15937,c_12]) ).
tff(c_16078,plain,
! [C_913] :
( in('#skF_3'(C_913),powerset('#skF_1'))
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_913)),'#skF_2')
| ~ in('#skF_5'(C_913),powerset('#skF_1'))
| ~ in('#skF_5'(C_913),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_15950]) ).
tff(c_16082,plain,
! [C_913] :
( in('#skF_3'(C_913),powerset('#skF_1'))
| ~ in('#skF_5'(C_913),powerset('#skF_1'))
| ~ in('#skF_5'(C_913),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_15637,c_16078]) ).
tff(c_24183,plain,
( in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_24168,c_16082]) ).
tff(c_24201,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_24097,c_24183]) ).
tff(c_24203,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23979,c_24201]) ).
tff(c_24205,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_23767]) ).
tff(c_272,plain,
! [A_55,B_56,H_115] :
( ( '#skF_22'(A_55,B_56) = '#skF_24'(A_55,B_56) )
| in(set_difference(H_115,singleton(A_55)),'#skF_27'(A_55,B_56))
| ~ in(H_115,B_56)
| ~ in(set_difference(H_115,singleton(A_55)),powerset(A_55))
| ~ element(B_56,powerset(powerset(succ(A_55))))
| ~ ordinal(A_55) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_23739,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_23703,c_272]) ).
tff(c_23777,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23703,c_23739]) ).
tff(c_27201,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_24205,c_23777]) ).
tff(c_27202,plain,
! [B_1432] :
( ( '#skF_22'('#skF_1',B_1432) = '#skF_24'('#skF_1',B_1432) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_1432))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_1432)
| ~ element(B_1432,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_24205,c_23777]) ).
tff(c_974,plain,
! [A_231,B_232] :
( ( '#skF_22'(A_231,B_232) = '#skF_24'(A_231,B_232) )
| ( '#skF_28'(A_231,B_232,'#skF_5'('#skF_27'(A_231,B_232))) = '#skF_5'('#skF_27'(A_231,B_232)) )
| ~ element(B_232,powerset(powerset(succ(A_231))))
| ~ ordinal(A_231)
| ~ in('#skF_3'('#skF_27'(A_231,B_232)),'#skF_27'(A_231,B_232)) ),
inference(resolution,[status(thm)],[c_14,c_954]) ).
tff(c_27283,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_27202,c_974]) ).
tff(c_27411,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16512,c_1022,c_4,c_27283]) ).
tff(c_27412,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_15638,c_27411]) ).
tff(c_27517,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_15804]) ).
tff(c_27531,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_27517]) ).
tff(c_27577,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_27531]) ).
tff(c_27580,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_27201,c_27577]) ).
tff(c_27593,plain,
'#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16512,c_1022,c_27580]) ).
tff(c_27595,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15638,c_27593]) ).
tff(c_27597,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_27517]) ).
tff(c_27520,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_15800]) ).
tff(c_27642,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_27597,c_27520]) ).
tff(c_27337,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_27202,c_6]) ).
tff(c_27473,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16512,c_1022,c_27337]) ).
tff(c_27474,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_15638,c_27473]) ).
tff(c_27681,plain,
! [E_1435] :
( ( set_difference(E_1435,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_1435,'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_27642,c_27474]) ).
tff(c_28036,plain,
! [D_1440] :
( ( D_1440 != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_1440),'#skF_2')
| ~ in(D_1440,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15936,c_27681]) ).
tff(c_28041,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_15637,c_28036]) ).
tff(c_28043,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28041,c_27597]) ).
tff(c_28045,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) != '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_23701]) ).
tff(c_28044,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_23701]) ).
tff(c_28056,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28044,c_15804]) ).
tff(c_28071,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_28056]) ).
tff(c_28092,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_16,c_28071]) ).
tff(c_28112,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28045,c_28092]) ).
tff(c_28114,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_28056]) ).
tff(c_28059,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28044,c_15800]) ).
tff(c_28170,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_28114,c_28059]) ).
tff(c_15945,plain,
! [C_12,D_899] :
( ( set_difference('#skF_4'(C_12),singleton('#skF_1')) = '#skF_3'(C_12) )
| ( D_899 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_899),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_899,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15937,c_8]) ).
tff(c_16135,plain,
! [C_920] :
( ( set_difference('#skF_4'(C_920),singleton('#skF_1')) = '#skF_3'(C_920) )
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_920)),'#skF_2')
| ~ in('#skF_5'(C_920),powerset('#skF_1'))
| ~ in('#skF_5'(C_920),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_15945]) ).
tff(c_16139,plain,
! [C_920] :
( ( set_difference('#skF_4'(C_920),singleton('#skF_1')) = '#skF_3'(C_920) )
| ~ in('#skF_5'(C_920),powerset('#skF_1'))
| ~ in('#skF_5'(C_920),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_15637,c_16135]) ).
tff(c_28173,plain,
( ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28170,c_16139]) ).
tff(c_28184,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_28114,c_28173]) ).
tff(c_28186,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28045,c_28184]) ).
tff(c_28188,plain,
~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitRight,[status(thm)],[c_16511]) ).
tff(c_28187,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_16511]) ).
tff(c_28194,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28187,c_15804]) ).
tff(c_28203,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_28194]) ).
tff(c_28215,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(resolution,[status(thm)],[c_18,c_28203]) ).
tff(c_28225,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28188,c_28215]) ).
tff(c_28227,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_28194]) ).
tff(c_28197,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28187,c_15800]) ).
tff(c_28282,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_28227,c_28197]) ).
tff(c_15952,plain,
! [C_12,D_899] :
( in('#skF_4'(C_12),'#skF_2')
| ( D_899 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_899),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_899,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_15937,c_10]) ).
tff(c_16020,plain,
! [C_906] :
( in('#skF_4'(C_906),'#skF_2')
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_906)),'#skF_2')
| ~ in('#skF_5'(C_906),powerset('#skF_1'))
| ~ in('#skF_5'(C_906),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_15952]) ).
tff(c_16024,plain,
! [C_906] :
( in('#skF_4'(C_906),'#skF_2')
| ~ in('#skF_5'(C_906),powerset('#skF_1'))
| ~ in('#skF_5'(C_906),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_15637,c_16020]) ).
tff(c_28291,plain,
( in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28282,c_16024]) ).
tff(c_28302,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_28227,c_28291]) ).
tff(c_28304,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28188,c_28302]) ).
tff(c_28305,plain,
! [D_239] :
( in('#skF_29'('#skF_1','#skF_2',D_239),'#skF_2')
| ~ in(D_239,'#skF_27'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_1021]) ).
tff(c_28306,plain,
'#skF_22'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_1021]) ).
tff(c_28468,plain,
! [A_1469,B_1470,D_1471] :
( ( '#skF_24'(A_1469,B_1470) != '#skF_23'(A_1469,B_1470) )
| in('#skF_28'(A_1469,B_1470,D_1471),powerset(A_1469))
| ~ in(D_1471,'#skF_27'(A_1469,B_1470))
| ~ element(B_1470,powerset(powerset(succ(A_1469))))
| ~ ordinal(A_1469) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_28482,plain,
! [D_1471] :
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| in('#skF_28'('#skF_1','#skF_2',D_1471),powerset('#skF_1'))
| ~ in(D_1471,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_28468]) ).
tff(c_28493,plain,
! [D_1471] :
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| in('#skF_28'('#skF_1','#skF_2',D_1471),powerset('#skF_1'))
| ~ in(D_1471,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_28482]) ).
tff(c_28494,plain,
'#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_28493]) ).
tff(c_28605,plain,
! [A_1485,B_1486,D_1487] :
( ( '#skF_22'(A_1485,B_1486) = '#skF_24'(A_1485,B_1486) )
| ( set_difference('#skF_29'(A_1485,B_1486,D_1487),singleton(A_1485)) = D_1487 )
| ~ in(D_1487,'#skF_27'(A_1485,B_1486))
| ~ element(B_1486,powerset(powerset(succ(A_1485))))
| ~ ordinal(A_1485) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_28619,plain,
! [D_1487] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_1487),singleton('#skF_1')) = D_1487 )
| ~ in(D_1487,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_28605]) ).
tff(c_28630,plain,
! [D_1487] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_1487),singleton('#skF_1')) = D_1487 )
| ~ in(D_1487,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_28619]) ).
tff(c_28631,plain,
'#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_28630]) ).
tff(c_28637,plain,
! [A_1488,B_1489,D_1490] :
( ( '#skF_22'(A_1488,B_1489) = '#skF_23'(A_1488,B_1489) )
| ( set_difference('#skF_29'(A_1488,B_1489,D_1490),singleton(A_1488)) = D_1490 )
| ~ in(D_1490,'#skF_27'(A_1488,B_1489))
| ~ element(B_1489,powerset(powerset(succ(A_1488))))
| ~ ordinal(A_1488) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_28651,plain,
! [D_1490] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_1490),singleton('#skF_1')) = D_1490 )
| ~ in(D_1490,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_28637]) ).
tff(c_28662,plain,
! [D_1490] :
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_1490),singleton('#skF_1')) = D_1490 )
| ~ in(D_1490,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_28631,c_28651]) ).
tff(c_28663,plain,
! [D_1490] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_1490),singleton('#skF_1')) = D_1490 )
| ~ in(D_1490,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_28494,c_28662]) ).
tff(c_931,plain,
! [A_224,B_225,D_226] :
( ( '#skF_22'(A_224,B_225) = '#skF_23'(A_224,B_225) )
| ( '#skF_28'(A_224,B_225,D_226) = D_226 )
| ~ in(D_226,'#skF_27'(A_224,B_225))
| ~ element(B_225,powerset(powerset(succ(A_224))))
| ~ ordinal(A_224) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_29119,plain,
! [A_1542,B_1543] :
( ( '#skF_22'(A_1542,B_1543) = '#skF_23'(A_1542,B_1543) )
| ( '#skF_28'(A_1542,B_1543,'#skF_5'('#skF_27'(A_1542,B_1543))) = '#skF_5'('#skF_27'(A_1542,B_1543)) )
| ~ element(B_1543,powerset(powerset(succ(A_1542))))
| ~ ordinal(A_1542)
| in('#skF_4'('#skF_27'(A_1542,B_1543)),'#skF_2') ),
inference(resolution,[status(thm)],[c_18,c_931]) ).
tff(c_29133,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(resolution,[status(thm)],[c_2,c_29119]) ).
tff(c_29144,plain,
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_28631,c_29133]) ).
tff(c_29145,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_28494,c_29144]) ).
tff(c_29146,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitLeft,[status(thm)],[c_29145]) ).
tff(c_36664,plain,
! [A_1919,B_1920] :
( ( '#skF_22'(A_1919,B_1920) = '#skF_23'(A_1919,B_1920) )
| ( '#skF_28'(A_1919,B_1920,'#skF_5'('#skF_27'(A_1919,B_1920))) = '#skF_5'('#skF_27'(A_1919,B_1920)) )
| ~ element(B_1920,powerset(powerset(succ(A_1919))))
| ~ ordinal(A_1919)
| ( set_difference('#skF_4'('#skF_27'(A_1919,B_1920)),singleton('#skF_1')) = '#skF_3'('#skF_27'(A_1919,B_1920)) ) ),
inference(resolution,[status(thm)],[c_16,c_931]) ).
tff(c_36678,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(resolution,[status(thm)],[c_2,c_36664]) ).
tff(c_36689,plain,
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_28631,c_36678]) ).
tff(c_36690,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(negUnitSimplification,[status(thm)],[c_28494,c_36689]) ).
tff(c_36700,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_36690]) ).
tff(c_29150,plain,
! [A_1544,B_1545,H_1546] :
( ( '#skF_22'(A_1544,B_1545) = '#skF_23'(A_1544,B_1545) )
| in(set_difference(H_1546,singleton(A_1544)),'#skF_27'(A_1544,B_1545))
| ~ in(H_1546,B_1545)
| ~ in(set_difference(H_1546,singleton(A_1544)),powerset(A_1544))
| ~ element(B_1545,powerset(powerset(succ(A_1544))))
| ~ ordinal(A_1544) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_29154,plain,
! [B_1545,C_12] :
( ( '#skF_22'('#skF_1',B_1545) = '#skF_23'('#skF_1',B_1545) )
| in(set_difference('#skF_4'(C_12),singleton('#skF_1')),'#skF_27'('#skF_1',B_1545))
| ~ in('#skF_4'(C_12),B_1545)
| ~ in('#skF_3'(C_12),powerset('#skF_1'))
| ~ element(B_1545,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1')
| in('#skF_5'(C_12),C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_29150]) ).
tff(c_33893,plain,
! [B_1821,C_1822] :
( ( '#skF_22'('#skF_1',B_1821) = '#skF_23'('#skF_1',B_1821) )
| in(set_difference('#skF_4'(C_1822),singleton('#skF_1')),'#skF_27'('#skF_1',B_1821))
| ~ in('#skF_4'(C_1822),B_1821)
| ~ in('#skF_3'(C_1822),powerset('#skF_1'))
| ~ element(B_1821,powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_1822),C_1822) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_29154]) ).
tff(c_28664,plain,
! [D_1491] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_1491),singleton('#skF_1')) = D_1491 )
| ~ in(D_1491,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_28494,c_28662]) ).
tff(c_28675,plain,
! [D_1491] :
( finite(D_1491)
| ~ finite('#skF_29'('#skF_1','#skF_2',D_1491))
| ~ in(D_1491,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28664,c_122]) ).
tff(c_33971,plain,
! [C_1822] :
( finite(set_difference('#skF_4'(C_1822),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_1822),singleton('#skF_1'))))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_1822),'#skF_2')
| ~ in('#skF_3'(C_1822),powerset('#skF_1'))
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_1822),C_1822) ),
inference(resolution,[status(thm)],[c_33893,c_28675]) ).
tff(c_34157,plain,
! [C_1822] :
( finite(set_difference('#skF_4'(C_1822),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_1822),singleton('#skF_1'))))
| ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_1822),'#skF_2')
| ~ in('#skF_3'(C_1822),powerset('#skF_1'))
| in('#skF_5'(C_1822),C_1822) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_28631,c_33971]) ).
tff(c_34158,plain,
! [C_1822] :
( finite(set_difference('#skF_4'(C_1822),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_1822),singleton('#skF_1'))))
| ~ in('#skF_4'(C_1822),'#skF_2')
| ~ in('#skF_3'(C_1822),powerset('#skF_1'))
| in('#skF_5'(C_1822),C_1822) ),
inference(negUnitSimplification,[status(thm)],[c_28494,c_34157]) ).
tff(c_36721,plain,
( finite(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_36700,c_34158]) ).
tff(c_36768,plain,
( finite('#skF_3'('#skF_27'('#skF_1','#skF_2')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_29146,c_36700,c_36721]) ).
tff(c_37025,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitLeft,[status(thm)],[c_36768]) ).
tff(c_949,plain,
! [A_224,B_225] :
( ( '#skF_22'(A_224,B_225) = '#skF_23'(A_224,B_225) )
| ( '#skF_28'(A_224,B_225,'#skF_5'('#skF_27'(A_224,B_225))) = '#skF_5'('#skF_27'(A_224,B_225)) )
| ~ element(B_225,powerset(powerset(succ(A_224))))
| ~ ordinal(A_224)
| in('#skF_3'('#skF_27'(A_224,B_225)),powerset('#skF_1')) ),
inference(resolution,[status(thm)],[c_20,c_931]) ).
tff(c_37034,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_949,c_37025]) ).
tff(c_37056,plain,
( ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_28631,c_37034]) ).
tff(c_37057,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_28494,c_37056]) ).
tff(c_28547,plain,
! [A_1478,B_1479,D_1480] :
( ( '#skF_22'(A_1478,B_1479) = '#skF_23'(A_1478,B_1479) )
| in('#skF_28'(A_1478,B_1479,D_1480),powerset(A_1478))
| ~ in(D_1480,'#skF_27'(A_1478,B_1479))
| ~ element(B_1479,powerset(powerset(succ(A_1478))))
| ~ ordinal(A_1478) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_28561,plain,
! [D_1480] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| in('#skF_28'('#skF_1','#skF_2',D_1480),powerset('#skF_1'))
| ~ in(D_1480,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_28547]) ).
tff(c_28572,plain,
! [D_1480] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| in('#skF_28'('#skF_1','#skF_2',D_1480),powerset('#skF_1'))
| ~ in(D_1480,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_28561]) ).
tff(c_28574,plain,
! [D_1481] :
( in('#skF_28'('#skF_1','#skF_2',D_1481),powerset('#skF_1'))
| ~ in(D_1481,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_28572]) ).
tff(c_28577,plain,
! [D_1481] :
( ~ in(powerset('#skF_1'),'#skF_28'('#skF_1','#skF_2',D_1481))
| ~ in(D_1481,'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28574,c_170]) ).
tff(c_37080,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_37057,c_28577]) ).
tff(c_37094,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_37080]) ).
tff(c_37119,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(resolution,[status(thm)],[c_20,c_37094]) ).
tff(c_37138,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_37025,c_37119]) ).
tff(c_37140,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_37080]) ).
tff(c_28573,plain,
! [D_1480] :
( in('#skF_28'('#skF_1','#skF_2',D_1480),powerset('#skF_1'))
| ~ in(D_1480,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_28572]) ).
tff(c_37083,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_37057,c_28573]) ).
tff(c_37198,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_37140,c_37083]) ).
tff(c_28677,plain,
! [C_12,D_1491] :
( in('#skF_3'(C_12),powerset('#skF_1'))
| ( D_1491 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_1491),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_1491,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28664,c_12]) ).
tff(c_28805,plain,
! [C_1505] :
( in('#skF_3'(C_1505),powerset('#skF_1'))
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_1505)),'#skF_2')
| ~ in('#skF_5'(C_1505),powerset('#skF_1'))
| ~ in('#skF_5'(C_1505),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_28677]) ).
tff(c_28809,plain,
! [C_1505] :
( in('#skF_3'(C_1505),powerset('#skF_1'))
| ~ in('#skF_5'(C_1505),powerset('#skF_1'))
| ~ in('#skF_5'(C_1505),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_28805]) ).
tff(c_37213,plain,
( in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_37198,c_28809]) ).
tff(c_37231,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_37140,c_37213]) ).
tff(c_37233,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_37025,c_37231]) ).
tff(c_37235,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_36768]) ).
tff(c_278,plain,
! [A_55,B_56,H_115] :
( ( '#skF_22'(A_55,B_56) = '#skF_23'(A_55,B_56) )
| in(set_difference(H_115,singleton(A_55)),'#skF_27'(A_55,B_56))
| ~ in(H_115,B_56)
| ~ in(set_difference(H_115,singleton(A_55)),powerset(A_55))
| ~ element(B_56,powerset(powerset(succ(A_55))))
| ~ ordinal(A_55) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_36740,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_23'('#skF_1',B_56) )
| in(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_36700,c_278]) ).
tff(c_36778,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_23'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_36700,c_36740]) ).
tff(c_40259,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_23'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_37235,c_36778]) ).
tff(c_40260,plain,
! [B_2031] :
( ( '#skF_22'('#skF_1',B_2031) = '#skF_23'('#skF_1',B_2031) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_2031))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_2031)
| ~ element(B_2031,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_37235,c_36778]) ).
tff(c_951,plain,
! [A_224,B_225] :
( ( '#skF_22'(A_224,B_225) = '#skF_23'(A_224,B_225) )
| ( '#skF_28'(A_224,B_225,'#skF_5'('#skF_27'(A_224,B_225))) = '#skF_5'('#skF_27'(A_224,B_225)) )
| ~ element(B_225,powerset(powerset(succ(A_224))))
| ~ ordinal(A_224)
| ~ in('#skF_3'('#skF_27'(A_224,B_225)),'#skF_27'(A_224,B_225)) ),
inference(resolution,[status(thm)],[c_14,c_931]) ).
tff(c_40342,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_40260,c_951]) ).
tff(c_40465,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_29146,c_28631,c_4,c_40342]) ).
tff(c_40466,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_28494,c_40465]) ).
tff(c_40571,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_40466,c_28577]) ).
tff(c_40585,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_40571]) ).
tff(c_40631,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_40585]) ).
tff(c_40634,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_40259,c_40631]) ).
tff(c_40650,plain,
'#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_29146,c_28631,c_40634]) ).
tff(c_40652,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28494,c_40650]) ).
tff(c_40654,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_40571]) ).
tff(c_40574,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_40466,c_28573]) ).
tff(c_40699,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_40654,c_40574]) ).
tff(c_40395,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_40260,c_6]) ).
tff(c_40527,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_29146,c_28631,c_40395]) ).
tff(c_40528,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_28494,c_40527]) ).
tff(c_40738,plain,
! [E_2034] :
( ( set_difference(E_2034,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_2034,'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_40699,c_40528]) ).
tff(c_41204,plain,
! [D_2039] :
( ( D_2039 != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2039),'#skF_2')
| ~ in(D_2039,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28663,c_40738]) ).
tff(c_41245,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_28305,c_41204]) ).
tff(c_41247,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41245,c_40654]) ).
tff(c_41249,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) != '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_36690]) ).
tff(c_41248,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_36690]) ).
tff(c_41260,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41248,c_28577]) ).
tff(c_41275,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_41260]) ).
tff(c_41297,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_16,c_41275]) ).
tff(c_41317,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41249,c_41297]) ).
tff(c_41319,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_41260]) ).
tff(c_41263,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41248,c_28573]) ).
tff(c_41377,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_41319,c_41263]) ).
tff(c_28672,plain,
! [C_12,D_1491] :
( ( set_difference('#skF_4'(C_12),singleton('#skF_1')) = '#skF_3'(C_12) )
| ( D_1491 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_1491),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_1491,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28664,c_8]) ).
tff(c_28888,plain,
! [C_1514] :
( ( set_difference('#skF_4'(C_1514),singleton('#skF_1')) = '#skF_3'(C_1514) )
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_1514)),'#skF_2')
| ~ in('#skF_5'(C_1514),powerset('#skF_1'))
| ~ in('#skF_5'(C_1514),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_28672]) ).
tff(c_28892,plain,
! [C_1514] :
( ( set_difference('#skF_4'(C_1514),singleton('#skF_1')) = '#skF_3'(C_1514) )
| ~ in('#skF_5'(C_1514),powerset('#skF_1'))
| ~ in('#skF_5'(C_1514),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_28888]) ).
tff(c_41380,plain,
( ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_41377,c_28892]) ).
tff(c_41391,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_41319,c_41380]) ).
tff(c_41393,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41249,c_41391]) ).
tff(c_41395,plain,
~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitRight,[status(thm)],[c_29145]) ).
tff(c_41394,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_29145]) ).
tff(c_41399,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41394,c_28577]) ).
tff(c_41406,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_41399]) ).
tff(c_41418,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(resolution,[status(thm)],[c_18,c_41406]) ).
tff(c_41428,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41395,c_41418]) ).
tff(c_41430,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_41399]) ).
tff(c_41402,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41394,c_28573]) ).
tff(c_41502,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_41430,c_41402]) ).
tff(c_28679,plain,
! [C_12,D_1491] :
( in('#skF_4'(C_12),'#skF_2')
| ( D_1491 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_1491),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_1491,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_28664,c_10]) ).
tff(c_28742,plain,
! [C_1498] :
( in('#skF_4'(C_1498),'#skF_2')
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_1498)),'#skF_2')
| ~ in('#skF_5'(C_1498),powerset('#skF_1'))
| ~ in('#skF_5'(C_1498),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_28679]) ).
tff(c_28746,plain,
! [C_1498] :
( in('#skF_4'(C_1498),'#skF_2')
| ~ in('#skF_5'(C_1498),powerset('#skF_1'))
| ~ in('#skF_5'(C_1498),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_28742]) ).
tff(c_41511,plain,
( in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_41502,c_28746]) ).
tff(c_41522,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_41430,c_41511]) ).
tff(c_41524,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41395,c_41522]) ).
tff(c_41525,plain,
! [D_1487] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_1487),singleton('#skF_1')) = D_1487 )
| ~ in(D_1487,'#skF_27'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_28630]) ).
tff(c_41526,plain,
'#skF_22'('#skF_1','#skF_2') != '#skF_24'('#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_28630]) ).
tff(c_42010,plain,
! [A_2107,B_2108] :
( ( '#skF_22'(A_2107,B_2108) = '#skF_23'(A_2107,B_2108) )
| ( '#skF_28'(A_2107,B_2108,'#skF_5'('#skF_27'(A_2107,B_2108))) = '#skF_5'('#skF_27'(A_2107,B_2108)) )
| ~ element(B_2108,powerset(powerset(succ(A_2107))))
| ~ ordinal(A_2107)
| in('#skF_4'('#skF_27'(A_2107,B_2108)),'#skF_2') ),
inference(resolution,[status(thm)],[c_18,c_931]) ).
tff(c_42024,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(resolution,[status(thm)],[c_2,c_42010]) ).
tff(c_42035,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_42024]) ).
tff(c_42036,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_42035]) ).
tff(c_42037,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitLeft,[status(thm)],[c_42036]) ).
tff(c_48436,plain,
! [A_2429,B_2430] :
( ( '#skF_22'(A_2429,B_2430) = '#skF_23'(A_2429,B_2430) )
| ( '#skF_28'(A_2429,B_2430,'#skF_5'('#skF_27'(A_2429,B_2430))) = '#skF_5'('#skF_27'(A_2429,B_2430)) )
| ~ element(B_2430,powerset(powerset(succ(A_2429))))
| ~ ordinal(A_2429)
| ( set_difference('#skF_4'('#skF_27'(A_2429,B_2430)),singleton('#skF_1')) = '#skF_3'('#skF_27'(A_2429,B_2430)) ) ),
inference(resolution,[status(thm)],[c_16,c_931]) ).
tff(c_48450,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(resolution,[status(thm)],[c_2,c_48436]) ).
tff(c_48461,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_48450]) ).
tff(c_48462,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_48461]) ).
tff(c_48463,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_48462]) ).
tff(c_42226,plain,
! [A_2130,B_2131,H_2132] :
( ( '#skF_22'(A_2130,B_2131) = '#skF_24'(A_2130,B_2131) )
| in(set_difference(H_2132,singleton(A_2130)),'#skF_27'(A_2130,B_2131))
| ~ in(H_2132,B_2131)
| ~ in(set_difference(H_2132,singleton(A_2130)),powerset(A_2130))
| ~ element(B_2131,powerset(powerset(succ(A_2130))))
| ~ ordinal(A_2130) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_42230,plain,
! [B_2131,C_12] :
( ( '#skF_22'('#skF_1',B_2131) = '#skF_24'('#skF_1',B_2131) )
| in(set_difference('#skF_4'(C_12),singleton('#skF_1')),'#skF_27'('#skF_1',B_2131))
| ~ in('#skF_4'(C_12),B_2131)
| ~ in('#skF_3'(C_12),powerset('#skF_1'))
| ~ element(B_2131,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1')
| in('#skF_5'(C_12),C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_42226]) ).
tff(c_46785,plain,
! [B_2386,C_2387] :
( ( '#skF_22'('#skF_1',B_2386) = '#skF_24'('#skF_1',B_2386) )
| in(set_difference('#skF_4'(C_2387),singleton('#skF_1')),'#skF_27'('#skF_1',B_2386))
| ~ in('#skF_4'(C_2387),B_2386)
| ~ in('#skF_3'(C_2387),powerset('#skF_1'))
| ~ element(B_2386,powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_2387),C_2387) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_42230]) ).
tff(c_41527,plain,
! [D_2051] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_2051),singleton('#skF_1')) = D_2051 )
| ~ in(D_2051,'#skF_27'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_28630]) ).
tff(c_41538,plain,
! [D_2051] :
( finite(D_2051)
| ~ finite('#skF_29'('#skF_1','#skF_2',D_2051))
| ~ in(D_2051,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41527,c_122]) ).
tff(c_46865,plain,
! [C_2387] :
( finite(set_difference('#skF_4'(C_2387),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_2387),singleton('#skF_1'))))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_2387),'#skF_2')
| ~ in('#skF_3'(C_2387),powerset('#skF_1'))
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_2387),C_2387) ),
inference(resolution,[status(thm)],[c_46785,c_41538]) ).
tff(c_47052,plain,
! [C_2387] :
( finite(set_difference('#skF_4'(C_2387),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_2387),singleton('#skF_1'))))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_2387),'#skF_2')
| ~ in('#skF_3'(C_2387),powerset('#skF_1'))
| in('#skF_5'(C_2387),C_2387) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_46865]) ).
tff(c_47053,plain,
! [C_2387] :
( finite(set_difference('#skF_4'(C_2387),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_2387),singleton('#skF_1'))))
| ~ in('#skF_4'(C_2387),'#skF_2')
| ~ in('#skF_3'(C_2387),powerset('#skF_1'))
| in('#skF_5'(C_2387),C_2387) ),
inference(negUnitSimplification,[status(thm)],[c_41526,c_47052]) ).
tff(c_48477,plain,
( finite(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_48463,c_47053]) ).
tff(c_48524,plain,
( finite('#skF_3'('#skF_27'('#skF_1','#skF_2')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_42037,c_48463,c_48477]) ).
tff(c_48704,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitLeft,[status(thm)],[c_48524]) ).
tff(c_48722,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_949,c_48704]) ).
tff(c_48745,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_48722]) ).
tff(c_48746,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_28306,c_48745]) ).
tff(c_48763,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_48746,c_28577]) ).
tff(c_48778,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_48763]) ).
tff(c_48799,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(resolution,[status(thm)],[c_20,c_48778]) ).
tff(c_48818,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48704,c_48799]) ).
tff(c_48820,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_48763]) ).
tff(c_48766,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_48746,c_28573]) ).
tff(c_48896,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_48820,c_48766]) ).
tff(c_41540,plain,
! [C_12,D_2051] :
( in('#skF_3'(C_12),powerset('#skF_1'))
| ( D_2051 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2051),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_2051,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41527,c_12]) ).
tff(c_41674,plain,
! [C_2065] :
( in('#skF_3'(C_2065),powerset('#skF_1'))
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_2065)),'#skF_2')
| ~ in('#skF_5'(C_2065),powerset('#skF_1'))
| ~ in('#skF_5'(C_2065),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_41540]) ).
tff(c_41678,plain,
! [C_2065] :
( in('#skF_3'(C_2065),powerset('#skF_1'))
| ~ in('#skF_5'(C_2065),powerset('#skF_1'))
| ~ in('#skF_5'(C_2065),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_41674]) ).
tff(c_48911,plain,
( in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_48896,c_41678]) ).
tff(c_48929,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_48820,c_48911]) ).
tff(c_48931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48704,c_48929]) ).
tff(c_48933,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_48524]) ).
tff(c_48494,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_48463,c_272]) ).
tff(c_48532,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_48463,c_48494]) ).
tff(c_52830,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_48933,c_48532]) ).
tff(c_52831,plain,
! [B_2589] :
( ( '#skF_22'('#skF_1',B_2589) = '#skF_24'('#skF_1',B_2589) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_2589))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_2589)
| ~ element(B_2589,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_48933,c_48532]) ).
tff(c_52913,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_52831,c_974]) ).
tff(c_53044,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_42037,c_4,c_52913]) ).
tff(c_53045,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_41526,c_53044]) ).
tff(c_53118,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_53045,c_28577]) ).
tff(c_53133,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_53118]) ).
tff(c_53179,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_53133]) ).
tff(c_53214,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_52830,c_53179]) ).
tff(c_53227,plain,
'#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_42037,c_53214]) ).
tff(c_53229,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41526,c_53227]) ).
tff(c_53231,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_53118]) ).
tff(c_53121,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_53045,c_28573]) ).
tff(c_53313,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_53231,c_53121]) ).
tff(c_52966,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_52831,c_6]) ).
tff(c_53106,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_42037,c_52966]) ).
tff(c_53107,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_41526,c_53106]) ).
tff(c_53352,plain,
! [E_2594] :
( ( set_difference(E_2594,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_2594,'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_53313,c_53107]) ).
tff(c_53707,plain,
! [D_2599] :
( ( D_2599 != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2599),'#skF_2')
| ~ in(D_2599,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41525,c_53352]) ).
tff(c_53712,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_28305,c_53707]) ).
tff(c_53714,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_53712,c_53231]) ).
tff(c_53716,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) != '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_48462]) ).
tff(c_53715,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_48462]) ).
tff(c_53730,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_53715,c_28573]) ).
tff(c_53745,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_53730]) ).
tff(c_53763,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_16,c_53745]) ).
tff(c_53783,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_53716,c_53763]) ).
tff(c_53785,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_53730]) ).
tff(c_53784,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_53730]) ).
tff(c_41535,plain,
! [C_12,D_2051] :
( ( set_difference('#skF_4'(C_12),singleton('#skF_1')) = '#skF_3'(C_12) )
| ( D_2051 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2051),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_2051,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41527,c_8]) ).
tff(c_41731,plain,
! [C_2072] :
( ( set_difference('#skF_4'(C_2072),singleton('#skF_1')) = '#skF_3'(C_2072) )
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_2072)),'#skF_2')
| ~ in('#skF_5'(C_2072),powerset('#skF_1'))
| ~ in('#skF_5'(C_2072),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_41535]) ).
tff(c_41735,plain,
! [C_2072] :
( ( set_difference('#skF_4'(C_2072),singleton('#skF_1')) = '#skF_3'(C_2072) )
| ~ in('#skF_5'(C_2072),powerset('#skF_1'))
| ~ in('#skF_5'(C_2072),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_41731]) ).
tff(c_53788,plain,
( ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_53784,c_41735]) ).
tff(c_53799,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_53716,c_53788]) ).
tff(c_53853,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_53785,c_53799]) ).
tff(c_53855,plain,
~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitRight,[status(thm)],[c_42036]) ).
tff(c_53854,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_42036]) ).
tff(c_53889,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_53854,c_28577]) ).
tff(c_53898,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_53889]) ).
tff(c_53910,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(resolution,[status(thm)],[c_18,c_53898]) ).
tff(c_53920,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_53855,c_53910]) ).
tff(c_53922,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_53889]) ).
tff(c_53892,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_53854,c_28573]) ).
tff(c_53977,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_53922,c_53892]) ).
tff(c_41542,plain,
! [C_12,D_2051] :
( in('#skF_4'(C_12),'#skF_2')
| ( D_2051 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2051),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_2051,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_41527,c_10]) ).
tff(c_41610,plain,
! [C_2058] :
( in('#skF_4'(C_2058),'#skF_2')
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_2058)),'#skF_2')
| ~ in('#skF_5'(C_2058),powerset('#skF_1'))
| ~ in('#skF_5'(C_2058),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_41542]) ).
tff(c_41614,plain,
! [C_2058] :
( in('#skF_4'(C_2058),'#skF_2')
| ~ in('#skF_5'(C_2058),powerset('#skF_1'))
| ~ in('#skF_5'(C_2058),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_41610]) ).
tff(c_53986,plain,
( in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_53977,c_41614]) ).
tff(c_53997,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_53922,c_53986]) ).
tff(c_53999,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_53855,c_53997]) ).
tff(c_54001,plain,
'#skF_24'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_28493]) ).
tff(c_54117,plain,
! [A_2622,B_2623,D_2624] :
( ( '#skF_22'(A_2622,B_2623) = '#skF_24'(A_2622,B_2623) )
| ( set_difference('#skF_29'(A_2622,B_2623,D_2624),singleton(A_2622)) = D_2624 )
| ~ in(D_2624,'#skF_27'(A_2622,B_2623))
| ~ element(B_2623,powerset(powerset(succ(A_2622))))
| ~ ordinal(A_2622) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_54131,plain,
! [D_2624] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_2624),singleton('#skF_1')) = D_2624 )
| ~ in(D_2624,'#skF_27'('#skF_1','#skF_2'))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_54117]) ).
tff(c_54142,plain,
! [D_2624] :
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( set_difference('#skF_29'('#skF_1','#skF_2',D_2624),singleton('#skF_1')) = D_2624 )
| ~ in(D_2624,'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_54001,c_54131]) ).
tff(c_54143,plain,
! [D_2624] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_2624),singleton('#skF_1')) = D_2624 )
| ~ in(D_2624,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_54142]) ).
tff(c_54677,plain,
! [A_2688,B_2689] :
( ( '#skF_24'(A_2688,B_2689) != '#skF_23'(A_2688,B_2689) )
| ( '#skF_28'(A_2688,B_2689,'#skF_5'('#skF_27'(A_2688,B_2689))) = '#skF_5'('#skF_27'(A_2688,B_2689)) )
| ~ element(B_2689,powerset(powerset(succ(A_2688))))
| ~ ordinal(A_2688)
| in('#skF_4'('#skF_27'(A_2688,B_2689)),'#skF_2') ),
inference(resolution,[status(thm)],[c_18,c_975]) ).
tff(c_54691,plain,
( ( '#skF_24'('#skF_1','#skF_2') != '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(resolution,[status(thm)],[c_2,c_54677]) ).
tff(c_54702,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_54001,c_54691]) ).
tff(c_54703,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitLeft,[status(thm)],[c_54702]) ).
tff(c_61700,plain,
! [A_3059,B_3060] :
( ( '#skF_22'(A_3059,B_3060) = '#skF_24'(A_3059,B_3060) )
| ( '#skF_28'(A_3059,B_3060,'#skF_5'('#skF_27'(A_3059,B_3060))) = '#skF_5'('#skF_27'(A_3059,B_3060)) )
| ~ element(B_3060,powerset(powerset(succ(A_3059))))
| ~ ordinal(A_3059)
| ( set_difference('#skF_4'('#skF_27'(A_3059,B_3060)),singleton('#skF_1')) = '#skF_3'('#skF_27'(A_3059,B_3060)) ) ),
inference(resolution,[status(thm)],[c_16,c_954]) ).
tff(c_61714,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(resolution,[status(thm)],[c_2,c_61700]) ).
tff(c_61725,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_54001,c_61714]) ).
tff(c_61726,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_61725]) ).
tff(c_61729,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_61726]) ).
tff(c_54734,plain,
! [A_2692,B_2693,H_2694] :
( ( '#skF_22'(A_2692,B_2693) = '#skF_24'(A_2692,B_2693) )
| in(set_difference(H_2694,singleton(A_2692)),'#skF_27'(A_2692,B_2693))
| ~ in(H_2694,B_2693)
| ~ in(set_difference(H_2694,singleton(A_2692)),powerset(A_2692))
| ~ element(B_2693,powerset(powerset(succ(A_2692))))
| ~ ordinal(A_2692) ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_54738,plain,
! [B_2693,C_12] :
( ( '#skF_22'('#skF_1',B_2693) = '#skF_24'('#skF_1',B_2693) )
| in(set_difference('#skF_4'(C_12),singleton('#skF_1')),'#skF_27'('#skF_1',B_2693))
| ~ in('#skF_4'(C_12),B_2693)
| ~ in('#skF_3'(C_12),powerset('#skF_1'))
| ~ element(B_2693,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1')
| in('#skF_5'(C_12),C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_54734]) ).
tff(c_59412,plain,
! [B_2968,C_2969] :
( ( '#skF_22'('#skF_1',B_2968) = '#skF_24'('#skF_1',B_2968) )
| in(set_difference('#skF_4'(C_2969),singleton('#skF_1')),'#skF_27'('#skF_1',B_2968))
| ~ in('#skF_4'(C_2969),B_2968)
| ~ in('#skF_3'(C_2969),powerset('#skF_1'))
| ~ element(B_2968,powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_2969),C_2969) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_54738]) ).
tff(c_54144,plain,
! [D_2625] :
( ( set_difference('#skF_29'('#skF_1','#skF_2',D_2625),singleton('#skF_1')) = D_2625 )
| ~ in(D_2625,'#skF_27'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_54142]) ).
tff(c_54155,plain,
! [D_2625] :
( finite(D_2625)
| ~ finite('#skF_29'('#skF_1','#skF_2',D_2625))
| ~ in(D_2625,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_54144,c_122]) ).
tff(c_59492,plain,
! [C_2969] :
( finite(set_difference('#skF_4'(C_2969),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_2969),singleton('#skF_1'))))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_2969),'#skF_2')
| ~ in('#skF_3'(C_2969),powerset('#skF_1'))
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| in('#skF_5'(C_2969),C_2969) ),
inference(resolution,[status(thm)],[c_59412,c_54155]) ).
tff(c_59679,plain,
! [C_2969] :
( finite(set_difference('#skF_4'(C_2969),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_2969),singleton('#skF_1'))))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ~ in('#skF_4'(C_2969),'#skF_2')
| ~ in('#skF_3'(C_2969),powerset('#skF_1'))
| in('#skF_5'(C_2969),C_2969) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_54001,c_59492]) ).
tff(c_59680,plain,
! [C_2969] :
( finite(set_difference('#skF_4'(C_2969),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2',set_difference('#skF_4'(C_2969),singleton('#skF_1'))))
| ~ in('#skF_4'(C_2969),'#skF_2')
| ~ in('#skF_3'(C_2969),powerset('#skF_1'))
| in('#skF_5'(C_2969),C_2969) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_59679]) ).
tff(c_61748,plain,
( finite(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_61729,c_59680]) ).
tff(c_61797,plain,
( finite('#skF_3'('#skF_27'('#skF_1','#skF_2')))
| ~ finite('#skF_29'('#skF_1','#skF_2','#skF_3'('#skF_27'('#skF_1','#skF_2'))))
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_54703,c_61729,c_61748]) ).
tff(c_62021,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitLeft,[status(thm)],[c_61797]) ).
tff(c_62030,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(resolution,[status(thm)],[c_949,c_62021]) ).
tff(c_62052,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') )
| ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_62030]) ).
tff(c_62053,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_28306,c_62052]) ).
tff(c_54000,plain,
! [D_1471] :
( in('#skF_28'('#skF_1','#skF_2',D_1471),powerset('#skF_1'))
| ~ in(D_1471,'#skF_27'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_28493]) ).
tff(c_62080,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_62053,c_54000]) ).
tff(c_62097,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_62080]) ).
tff(c_62120,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(resolution,[status(thm)],[c_20,c_62097]) ).
tff(c_62139,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62021,c_62120]) ).
tff(c_62141,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_62080]) ).
tff(c_62140,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_62080]) ).
tff(c_54157,plain,
! [C_12,D_2625] :
( in('#skF_3'(C_12),powerset('#skF_1'))
| ( D_2625 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2625),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_2625,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_54144,c_12]) ).
tff(c_54281,plain,
! [C_2639] :
( in('#skF_3'(C_2639),powerset('#skF_1'))
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_2639)),'#skF_2')
| ~ in('#skF_5'(C_2639),powerset('#skF_1'))
| ~ in('#skF_5'(C_2639),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_54157]) ).
tff(c_54285,plain,
! [C_2639] :
( in('#skF_3'(C_2639),powerset('#skF_1'))
| ~ in('#skF_5'(C_2639),powerset('#skF_1'))
| ~ in('#skF_5'(C_2639),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_54281]) ).
tff(c_62161,plain,
( in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_62140,c_54285]) ).
tff(c_62178,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_62021,c_62161]) ).
tff(c_62227,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_62141,c_62178]) ).
tff(c_62229,plain,
in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_61797]) ).
tff(c_61767,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in(set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1'))))
| ~ ordinal('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_61729,c_272]) ).
tff(c_61805,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_61729,c_61767]) ).
tff(c_65172,plain,
! [B_56] :
( ( '#skF_22'('#skF_1',B_56) = '#skF_24'('#skF_1',B_56) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_56))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_56)
| ~ element(B_56,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_62229,c_61805]) ).
tff(c_65173,plain,
! [B_3162] :
( ( '#skF_22'('#skF_1',B_3162) = '#skF_24'('#skF_1',B_3162) )
| in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1',B_3162))
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),B_3162)
| ~ element(B_3162,powerset(powerset(succ('#skF_1')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_62229,c_61805]) ).
tff(c_65241,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ ordinal('#skF_1')
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_65173,c_974]) ).
tff(c_65369,plain,
( ( '#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_54703,c_54001,c_4,c_65241]) ).
tff(c_65370,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_28306,c_65369]) ).
tff(c_65462,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_65370,c_54000]) ).
tff(c_65561,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_65462]) ).
tff(c_65607,plain,
~ in('#skF_3'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_65561]) ).
tff(c_65610,plain,
( ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_65172,c_65607]) ).
tff(c_65620,plain,
'#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_54703,c_54001,c_65610]) ).
tff(c_65622,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28306,c_65620]) ).
tff(c_65623,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(splitRight,[status(thm)],[c_65462]) ).
tff(c_65308,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_24'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ element('#skF_2',powerset(powerset(succ('#skF_1')))) ),
inference(resolution,[status(thm)],[c_65173,c_6]) ).
tff(c_65447,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ( '#skF_22'('#skF_1','#skF_2') = '#skF_23'('#skF_1','#skF_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_54703,c_54001,c_65308]) ).
tff(c_65448,plain,
! [E_20] :
( ( set_difference(E_20,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_20,'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_28306,c_65447]) ).
tff(c_65848,plain,
! [E_3167] :
( ( set_difference(E_3167,singleton('#skF_1')) != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in(E_3167,'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_65623,c_65448]) ).
tff(c_66189,plain,
! [D_3170] :
( ( D_3170 != '#skF_5'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_3170),'#skF_2')
| ~ in(D_3170,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_54143,c_65848]) ).
tff(c_66194,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_28305,c_66189]) ).
tff(c_65624,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_65462]) ).
tff(c_66196,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66194,c_65624]) ).
tff(c_66198,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) != '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_61726]) ).
tff(c_66197,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_61726]) ).
tff(c_54032,plain,
! [D_2611] :
( in('#skF_28'('#skF_1','#skF_2',D_2611),powerset('#skF_1'))
| ~ in(D_2611,'#skF_27'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_28493]) ).
tff(c_54035,plain,
! [D_2611] :
( ~ in(powerset('#skF_1'),'#skF_28'('#skF_1','#skF_2',D_2611))
| ~ in(D_2611,'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_54032,c_170]) ).
tff(c_66209,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_66197,c_54035]) ).
tff(c_66228,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_66209]) ).
tff(c_66248,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_16,c_66228]) ).
tff(c_66268,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66198,c_66248]) ).
tff(c_66270,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_66209]) ).
tff(c_66212,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_66197,c_54000]) ).
tff(c_66343,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_66270,c_66212]) ).
tff(c_54152,plain,
! [C_12,D_2625] :
( ( set_difference('#skF_4'(C_12),singleton('#skF_1')) = '#skF_3'(C_12) )
| ( D_2625 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2625),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_2625,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_54144,c_8]) ).
tff(c_54317,plain,
! [C_2643] :
( ( set_difference('#skF_4'(C_2643),singleton('#skF_1')) = '#skF_3'(C_2643) )
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_2643)),'#skF_2')
| ~ in('#skF_5'(C_2643),powerset('#skF_1'))
| ~ in('#skF_5'(C_2643),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_54152]) ).
tff(c_54321,plain,
! [C_2643] :
( ( set_difference('#skF_4'(C_2643),singleton('#skF_1')) = '#skF_3'(C_2643) )
| ~ in('#skF_5'(C_2643),powerset('#skF_1'))
| ~ in('#skF_5'(C_2643),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_54317]) ).
tff(c_66346,plain,
( ( set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')) )
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_66343,c_54321]) ).
tff(c_66357,plain,
set_difference('#skF_4'('#skF_27'('#skF_1','#skF_2')),singleton('#skF_1')) = '#skF_3'('#skF_27'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_66270,c_66346]) ).
tff(c_66359,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66198,c_66357]) ).
tff(c_66361,plain,
~ in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(splitRight,[status(thm)],[c_54702]) ).
tff(c_66360,plain,
'#skF_28'('#skF_1','#skF_2','#skF_5'('#skF_27'('#skF_1','#skF_2'))) = '#skF_5'('#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_54702]) ).
tff(c_66367,plain,
( ~ in(powerset('#skF_1'),'#skF_5'('#skF_27'('#skF_1','#skF_2')))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_66360,c_54035]) ).
tff(c_66385,plain,
~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_66367]) ).
tff(c_66397,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(resolution,[status(thm)],[c_18,c_66385]) ).
tff(c_66407,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66361,c_66397]) ).
tff(c_66409,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_66367]) ).
tff(c_66370,plain,
( in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1'))
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_66360,c_54000]) ).
tff(c_66482,plain,
in('#skF_5'('#skF_27'('#skF_1','#skF_2')),powerset('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_66409,c_66370]) ).
tff(c_54159,plain,
! [C_12,D_2625] :
( in('#skF_4'(C_12),'#skF_2')
| ( D_2625 != '#skF_5'(C_12) )
| ~ in('#skF_29'('#skF_1','#skF_2',D_2625),'#skF_2')
| ~ in('#skF_5'(C_12),powerset('#skF_1'))
| ~ in(D_2625,'#skF_27'('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_54144,c_10]) ).
tff(c_54222,plain,
! [C_2632] :
( in('#skF_4'(C_2632),'#skF_2')
| ~ in('#skF_29'('#skF_1','#skF_2','#skF_5'(C_2632)),'#skF_2')
| ~ in('#skF_5'(C_2632),powerset('#skF_1'))
| ~ in('#skF_5'(C_2632),'#skF_27'('#skF_1','#skF_2')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_54159]) ).
tff(c_54226,plain,
! [C_2632] :
( in('#skF_4'(C_2632),'#skF_2')
| ~ in('#skF_5'(C_2632),powerset('#skF_1'))
| ~ in('#skF_5'(C_2632),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_28305,c_54222]) ).
tff(c_66491,plain,
( in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2')
| ~ in('#skF_5'('#skF_27'('#skF_1','#skF_2')),'#skF_27'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_66482,c_54226]) ).
tff(c_66502,plain,
in('#skF_4'('#skF_27'('#skF_1','#skF_2')),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_66409,c_66491]) ).
tff(c_66504,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66361,c_66502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU298+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 11:54:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 29.76/15.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.89/15.50
% 29.89/15.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.11/15.58
% 30.11/15.58 Inference rules
% 30.11/15.58 ----------------------
% 30.11/15.58 #Ref : 46
% 30.11/15.58 #Sup : 13445
% 30.11/15.58 #Fact : 20
% 30.11/15.58 #Define : 0
% 30.11/15.58 #Split : 195
% 30.11/15.58 #Chain : 0
% 30.11/15.58 #Close : 0
% 30.11/15.58
% 30.11/15.58 Ordering : KBO
% 30.11/15.58
% 30.11/15.58 Simplification rules
% 30.11/15.58 ----------------------
% 30.11/15.58 #Subsume : 1119
% 30.11/15.58 #Demod : 7913
% 30.11/15.58 #Tautology : 2678
% 30.11/15.58 #SimpNegUnit : 819
% 30.11/15.58 #BackRed : 9
% 30.11/15.58
% 30.11/15.58 #Partial instantiations: 0
% 30.11/15.58 #Strategies tried : 1
% 30.11/15.58
% 30.11/15.58 Timing (in seconds)
% 30.11/15.58 ----------------------
% 30.11/15.58 Preprocessing : 0.66
% 30.11/15.58 Parsing : 0.31
% 30.11/15.58 CNF conversion : 0.07
% 30.11/15.58 Main loop : 13.75
% 30.11/15.58 Inferencing : 4.06
% 30.11/15.58 Reduction : 5.60
% 30.11/15.58 Demodulation : 4.23
% 30.11/15.58 BG Simplification : 0.26
% 30.11/15.58 Subsumption : 3.04
% 30.11/15.58 Abstraction : 0.44
% 30.11/15.58 MUC search : 0.00
% 30.11/15.58 Cooper : 0.00
% 30.11/15.58 Total : 14.55
% 30.11/15.58 Index Insertion : 0.00
% 30.11/15.58 Index Deletion : 0.00
% 30.11/15.58 Index Matching : 0.00
% 30.11/15.58 BG Taut test : 0.00
%------------------------------------------------------------------------------