TSTP Solution File: SEU310+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU310+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 : n024.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 10:58:23 EDT 2023
% Result : Theorem 13.86s 4.44s
% Output : CNFRefutation 13.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 37
% Syntax : Number of formulae : 188 ( 43 unt; 34 typ; 0 def)
% Number of atoms : 504 ( 87 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 654 ( 304 ~; 333 |; 10 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 31 >; 10 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 138 (; 135 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > closed_subset > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > topological_space > top_str > one_sorted_str > natural > empty > set_difference > #nlpp > the_carrier > powerset > cast_as_carrier_subset > #skF_13 > #skF_7 > #skF_11 > #skF_4 > #skF_8 > #skF_12 > #skF_5 > #skF_2 > #skF_10 > #skF_1 > #skF_3 > #skF_9 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(v1_int_1,type,
v1_int_1: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
tff(empty,type,
empty: $i > $o ).
tff(closed_subset,type,
closed_subset: ( $i * $i ) > $o ).
tff(v1_xreal_0,type,
v1_xreal_0: $i > $o ).
tff(v5_membered,type,
v5_membered: $i > $o ).
tff(v2_membered,type,
v2_membered: $i > $o ).
tff(v1_membered,type,
v1_membered: $i > $o ).
tff(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(v1_rat_1,type,
v1_rat_1: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(topological_space,type,
topological_space: $i > $o ).
tff(top_str,type,
top_str: $i > $o ).
tff(f_41,negated_conjecture,
~ ! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(powerset(the_carrier(A)))) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(D,powerset(the_carrier(A)))
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
tff(f_306,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(powerset(the_carrier(A)))) )
=> ( ! [C,D,E] :
( ( ( C = D )
& in(set_difference(cast_as_carrier_subset(A),D),B)
& ( C = E )
& in(set_difference(cast_as_carrier_subset(A),E),B) )
=> ( D = E ) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( in(E,powerset(the_carrier(A)))
& ( E = D )
& in(set_difference(cast_as_carrier_subset(A),D),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
tff(f_261,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
tff(c_18,plain,
! [C_4] :
( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| in('#skF_4'(C_4),C_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_14,plain,
! [C_4] :
( ~ in('#skF_3'(C_4),C_4)
| in('#skF_4'(C_4),C_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_6,plain,
topological_space('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_4,plain,
top_str('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_2,plain,
element('#skF_2',powerset(powerset(the_carrier('#skF_1')))),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1415,plain,
! [A_299,B_300,D_301] :
( ( '#skF_11'(A_299,B_300) = '#skF_9'(A_299,B_300) )
| in(set_difference(cast_as_carrier_subset(A_299),D_301),B_300)
| ~ in(D_301,'#skF_12'(A_299,B_300))
| ~ element(B_300,powerset(powerset(the_carrier(A_299))))
| ~ top_str(A_299)
| ~ topological_space(A_299) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_1423,plain,
! [D_301] :
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in(set_difference(cast_as_carrier_subset('#skF_1'),D_301),'#skF_2')
| ~ in(D_301,'#skF_12'('#skF_1','#skF_2'))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_1415]) ).
tff(c_1430,plain,
! [D_301] :
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in(set_difference(cast_as_carrier_subset('#skF_1'),D_301),'#skF_2')
| ~ in(D_301,'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_1423]) ).
tff(c_2228,plain,
'#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_1430]) ).
tff(c_1452,plain,
! [A_308,B_309,D_310] :
( ( '#skF_11'(A_308,B_309) != '#skF_10'(A_308,B_309) )
| in(set_difference(cast_as_carrier_subset(A_308),D_310),B_309)
| ~ in(D_310,'#skF_12'(A_308,B_309))
| ~ element(B_309,powerset(powerset(the_carrier(A_308))))
| ~ top_str(A_308)
| ~ topological_space(A_308) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_1460,plain,
! [D_310] :
( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
| in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
| ~ in(D_310,'#skF_12'('#skF_1','#skF_2'))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_1452]) ).
tff(c_1467,plain,
! [D_310] :
( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
| in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
| ~ in(D_310,'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_1460]) ).
tff(c_2243,plain,
! [D_310] :
( ( '#skF_10'('#skF_1','#skF_2') != '#skF_9'('#skF_1','#skF_2') )
| in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
| ~ in(D_310,'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_2228,c_1467]) ).
tff(c_2244,plain,
'#skF_10'('#skF_1','#skF_2') != '#skF_9'('#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_2243]) ).
tff(c_16,plain,
! [C_4] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
| in('#skF_4'(C_4),C_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_2699,plain,
! [A_438,B_439,E_440] :
( ( '#skF_10'(A_438,B_439) = '#skF_9'(A_438,B_439) )
| in(E_440,'#skF_12'(A_438,B_439))
| ~ in(set_difference(cast_as_carrier_subset(A_438),E_440),B_439)
| ~ in(E_440,powerset(the_carrier(A_438)))
| ~ element(B_439,powerset(powerset(the_carrier(A_438))))
| ~ top_str(A_438)
| ~ topological_space(A_438) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_2741,plain,
! [C_4] :
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| in('#skF_4'(C_4),C_4) ),
inference(resolution,[status(thm)],[c_16,c_2699]) ).
tff(c_2785,plain,
! [C_4] :
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| in('#skF_4'(C_4),C_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_2741]) ).
tff(c_2788,plain,
! [C_441] :
( in('#skF_3'(C_441),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_441),powerset(the_carrier('#skF_1')))
| in('#skF_4'(C_441),C_441) ),
inference(negUnitSimplification,[status(thm)],[c_2244,c_2785]) ).
tff(c_2807,plain,
! [C_442] :
( in('#skF_3'(C_442),'#skF_12'('#skF_1','#skF_2'))
| in('#skF_4'(C_442),C_442) ),
inference(resolution,[status(thm)],[c_18,c_2788]) ).
tff(c_190,plain,
! [A_63,B_64,D_84] :
( ( '#skF_10'(A_63,B_64) = '#skF_9'(A_63,B_64) )
| ( '#skF_13'(A_63,B_64,D_84) = D_84 )
| ~ in(D_84,'#skF_12'(A_63,B_64))
| ~ element(B_64,powerset(powerset(the_carrier(A_63))))
| ~ top_str(A_63)
| ~ topological_space(A_63) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_3675,plain,
! [A_521,B_522] :
( ( '#skF_10'(A_521,B_522) = '#skF_9'(A_521,B_522) )
| ( '#skF_13'(A_521,B_522,'#skF_4'('#skF_12'(A_521,B_522))) = '#skF_4'('#skF_12'(A_521,B_522)) )
| ~ element(B_522,powerset(powerset(the_carrier(A_521))))
| ~ top_str(A_521)
| ~ topological_space(A_521)
| in('#skF_3'('#skF_12'(A_521,B_522)),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_2807,c_190]) ).
tff(c_1271,plain,
! [A_266,B_267,D_268] :
( ( '#skF_10'(A_266,B_267) = '#skF_9'(A_266,B_267) )
| ( '#skF_13'(A_266,B_267,D_268) = D_268 )
| ~ in(D_268,'#skF_12'(A_266,B_267))
| ~ element(B_267,powerset(powerset(the_carrier(A_266))))
| ~ top_str(A_266)
| ~ topological_space(A_266) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_1283,plain,
! [A_266,B_267] :
( ( '#skF_10'(A_266,B_267) = '#skF_9'(A_266,B_267) )
| ( '#skF_13'(A_266,B_267,'#skF_4'('#skF_12'(A_266,B_267))) = '#skF_4'('#skF_12'(A_266,B_267)) )
| ~ element(B_267,powerset(powerset(the_carrier(A_266))))
| ~ top_str(A_266)
| ~ topological_space(A_266)
| ~ in('#skF_3'('#skF_12'(A_266,B_267)),'#skF_12'(A_266,B_267)) ),
inference(resolution,[status(thm)],[c_14,c_1271]) ).
tff(c_3740,plain,
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_3675,c_1283]) ).
tff(c_3800,plain,
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_3740]) ).
tff(c_3801,plain,
'#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_2244,c_3800]) ).
tff(c_2076,plain,
! [A_381,B_382,D_383] :
( ( '#skF_10'(A_381,B_382) = '#skF_9'(A_381,B_382) )
| in('#skF_13'(A_381,B_382,D_383),powerset(the_carrier(A_381)))
| ~ in(D_383,'#skF_12'(A_381,B_382))
| ~ element(B_382,powerset(powerset(the_carrier(A_381))))
| ~ top_str(A_381)
| ~ topological_space(A_381) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_154,plain,
! [B_58,A_57] :
( ~ in(B_58,A_57)
| ~ in(A_57,B_58) ),
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_2097,plain,
! [A_381,B_382,D_383] :
( ~ in(powerset(the_carrier(A_381)),'#skF_13'(A_381,B_382,D_383))
| ( '#skF_10'(A_381,B_382) = '#skF_9'(A_381,B_382) )
| ~ in(D_383,'#skF_12'(A_381,B_382))
| ~ element(B_382,powerset(powerset(the_carrier(A_381))))
| ~ top_str(A_381)
| ~ topological_space(A_381) ),
inference(resolution,[status(thm)],[c_2076,c_154]) ).
tff(c_3836,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_3801,c_2097]) ).
tff(c_3878,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_3836]) ).
tff(c_3879,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_2244,c_3878]) ).
tff(c_3896,plain,
~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_3879]) ).
tff(c_3929,plain,
~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_3896]) ).
tff(c_2806,plain,
! [C_4] :
( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| in('#skF_4'(C_4),C_4) ),
inference(resolution,[status(thm)],[c_18,c_2788]) ).
tff(c_3928,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_2806,c_3896]) ).
tff(c_3938,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3929,c_3928]) ).
tff(c_3940,plain,
in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_3879]) ).
tff(c_1493,plain,
! [A_314,B_315,D_316] :
( ( '#skF_10'(A_314,B_315) = '#skF_9'(A_314,B_315) )
| in(set_difference(cast_as_carrier_subset(A_314),D_316),B_315)
| ~ in(D_316,'#skF_12'(A_314,B_315))
| ~ element(B_315,powerset(powerset(the_carrier(A_314))))
| ~ top_str(A_314)
| ~ topological_space(A_314) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_1501,plain,
! [D_316] :
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in(set_difference(cast_as_carrier_subset('#skF_1'),D_316),'#skF_2')
| ~ in(D_316,'#skF_12'('#skF_1','#skF_2'))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_2,c_1493]) ).
tff(c_1508,plain,
! [D_316] :
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in(set_difference(cast_as_carrier_subset('#skF_1'),D_316),'#skF_2')
| ~ in(D_316,'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_1501]) ).
tff(c_2290,plain,
! [D_316] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),D_316),'#skF_2')
| ~ in(D_316,'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_2244,c_1508]) ).
tff(c_200,plain,
! [A_63,B_64,D_84] :
( ( '#skF_10'(A_63,B_64) = '#skF_9'(A_63,B_64) )
| in('#skF_13'(A_63,B_64,D_84),powerset(the_carrier(A_63)))
| ~ in(D_84,'#skF_12'(A_63,B_64))
| ~ element(B_64,powerset(powerset(the_carrier(A_63))))
| ~ top_str(A_63)
| ~ topological_space(A_63) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_3854,plain,
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_3801,c_200]) ).
tff(c_3891,plain,
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_3854]) ).
tff(c_3892,plain,
( in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_2244,c_3891]) ).
tff(c_4048,plain,
in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_3940,c_3892]) ).
tff(c_2291,plain,
! [D_406] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),D_406),'#skF_2')
| ~ in(D_406,'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_2244,c_1508]) ).
tff(c_12,plain,
! [C_4] :
( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'(C_4)),'#skF_2')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1'))) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_2301,plain,
! [C_4] :
( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_2291,c_12]) ).
tff(c_4057,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_4048,c_2301]) ).
tff(c_4068,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_3940,c_4057]) ).
tff(c_10,plain,
! [C_4] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
| ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'(C_4)),'#skF_2')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1'))) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_2300,plain,
! [C_4] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_2291,c_10]) ).
tff(c_2715,plain,
! [C_4] :
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_2300,c_2699]) ).
tff(c_2757,plain,
! [C_4] :
( ( '#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_2715]) ).
tff(c_2758,plain,
! [C_4] :
( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_2244,c_2757]) ).
tff(c_4051,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_4048,c_2758]) ).
tff(c_4062,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_3940,c_4051]) ).
tff(c_4093,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_4068,c_4062]) ).
tff(c_8,plain,
! [C_4] :
( ~ in('#skF_3'(C_4),C_4)
| ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'(C_4)),'#skF_2')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1'))) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_4117,plain,
( ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2')
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
inference(resolution,[status(thm)],[c_4093,c_8]) ).
tff(c_4149,plain,
~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_4048,c_4117]) ).
tff(c_4153,plain,
~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_2290,c_4149]) ).
tff(c_4163,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3940,c_4153]) ).
tff(c_4165,plain,
'#skF_10'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_2243]) ).
tff(c_4417,plain,
! [A_548,B_549,E_550] :
( ( '#skF_11'(A_548,B_549) != '#skF_10'(A_548,B_549) )
| in(E_550,'#skF_12'(A_548,B_549))
| ~ in(set_difference(cast_as_carrier_subset(A_548),E_550),B_549)
| ~ in(E_550,powerset(the_carrier(A_548)))
| ~ element(B_549,powerset(powerset(the_carrier(A_548))))
| ~ top_str(A_548)
| ~ topological_space(A_548) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_4455,plain,
! [C_4] :
( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| in('#skF_4'(C_4),C_4) ),
inference(resolution,[status(thm)],[c_16,c_4417]) ).
tff(c_4490,plain,
! [C_551] :
( in('#skF_3'(C_551),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_551),powerset(the_carrier('#skF_1')))
| in('#skF_4'(C_551),C_551) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_4455]) ).
tff(c_4509,plain,
! [C_552] :
( in('#skF_3'(C_552),'#skF_12'('#skF_1','#skF_2'))
| in('#skF_4'(C_552),C_552) ),
inference(resolution,[status(thm)],[c_18,c_4490]) ).
tff(c_182,plain,
! [A_63,B_64,D_84] :
( ( '#skF_11'(A_63,B_64) != '#skF_10'(A_63,B_64) )
| ( '#skF_13'(A_63,B_64,D_84) = D_84 )
| ~ in(D_84,'#skF_12'(A_63,B_64))
| ~ element(B_64,powerset(powerset(the_carrier(A_63))))
| ~ top_str(A_63)
| ~ topological_space(A_63) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_5648,plain,
! [A_651,B_652] :
( ( '#skF_11'(A_651,B_652) != '#skF_10'(A_651,B_652) )
| ( '#skF_13'(A_651,B_652,'#skF_4'('#skF_12'(A_651,B_652))) = '#skF_4'('#skF_12'(A_651,B_652)) )
| ~ element(B_652,powerset(powerset(the_carrier(A_651))))
| ~ top_str(A_651)
| ~ topological_space(A_651)
| in('#skF_3'('#skF_12'(A_651,B_652)),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_4509,c_182]) ).
tff(c_1309,plain,
! [A_274,B_275,D_276] :
( ( '#skF_11'(A_274,B_275) != '#skF_10'(A_274,B_275) )
| ( '#skF_13'(A_274,B_275,D_276) = D_276 )
| ~ in(D_276,'#skF_12'(A_274,B_275))
| ~ element(B_275,powerset(powerset(the_carrier(A_274))))
| ~ top_str(A_274)
| ~ topological_space(A_274) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_1321,plain,
! [A_274,B_275] :
( ( '#skF_11'(A_274,B_275) != '#skF_10'(A_274,B_275) )
| ( '#skF_13'(A_274,B_275,'#skF_4'('#skF_12'(A_274,B_275))) = '#skF_4'('#skF_12'(A_274,B_275)) )
| ~ element(B_275,powerset(powerset(the_carrier(A_274))))
| ~ top_str(A_274)
| ~ topological_space(A_274)
| ~ in('#skF_3'('#skF_12'(A_274,B_275)),'#skF_12'(A_274,B_275)) ),
inference(resolution,[status(thm)],[c_14,c_1309]) ).
tff(c_5709,plain,
( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
| ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_5648,c_1321]) ).
tff(c_5768,plain,
'#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_5709]) ).
tff(c_2162,plain,
! [A_394,B_395,D_396] :
( ( '#skF_11'(A_394,B_395) != '#skF_10'(A_394,B_395) )
| in('#skF_13'(A_394,B_395,D_396),powerset(the_carrier(A_394)))
| ~ in(D_396,'#skF_12'(A_394,B_395))
| ~ element(B_395,powerset(powerset(the_carrier(A_394))))
| ~ top_str(A_394)
| ~ topological_space(A_394) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_2183,plain,
! [A_394,B_395,D_396] :
( ~ in(powerset(the_carrier(A_394)),'#skF_13'(A_394,B_395,D_396))
| ( '#skF_11'(A_394,B_395) != '#skF_10'(A_394,B_395) )
| ~ in(D_396,'#skF_12'(A_394,B_395))
| ~ element(B_395,powerset(powerset(the_carrier(A_394))))
| ~ top_str(A_394)
| ~ topological_space(A_394) ),
inference(resolution,[status(thm)],[c_2162,c_154]) ).
tff(c_5803,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_5768,c_2183]) ).
tff(c_5845,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_5803]) ).
tff(c_5861,plain,
~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_5845]) ).
tff(c_5875,plain,
~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_5861]) ).
tff(c_4508,plain,
! [C_4] :
( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| in('#skF_4'(C_4),C_4) ),
inference(resolution,[status(thm)],[c_18,c_4490]) ).
tff(c_5874,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_4508,c_5861]) ).
tff(c_5960,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5875,c_5874]) ).
tff(c_5962,plain,
in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_5845]) ).
tff(c_4164,plain,
! [D_310] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),D_310),'#skF_2')
| ~ in(D_310,'#skF_12'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_2243]) ).
tff(c_192,plain,
! [A_63,B_64,D_84] :
( ( '#skF_11'(A_63,B_64) != '#skF_10'(A_63,B_64) )
| in('#skF_13'(A_63,B_64,D_84),powerset(the_carrier(A_63)))
| ~ in(D_84,'#skF_12'(A_63,B_64))
| ~ element(B_64,powerset(powerset(the_carrier(A_63))))
| ~ top_str(A_63)
| ~ topological_space(A_63) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_5818,plain,
( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
| in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_5768,c_192]) ).
tff(c_5855,plain,
( in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_5818]) ).
tff(c_6011,plain,
in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_5962,c_5855]) ).
tff(c_4231,plain,
! [D_534] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),D_534),'#skF_2')
| ~ in(D_534,'#skF_12'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_2243]) ).
tff(c_4241,plain,
! [C_4] :
( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_4231,c_12]) ).
tff(c_6020,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_6011,c_4241]) ).
tff(c_6031,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_5962,c_6020]) ).
tff(c_4240,plain,
! [C_4] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_4231,c_10]) ).
tff(c_4429,plain,
! [C_4] :
( ( '#skF_11'('#skF_1','#skF_2') != '#skF_10'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_4240,c_4417]) ).
tff(c_4465,plain,
! [C_4] :
( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_4165,c_2228,c_4429]) ).
tff(c_6014,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_6011,c_4465]) ).
tff(c_6025,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_5962,c_6014]) ).
tff(c_6114,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_6031,c_6025]) ).
tff(c_6138,plain,
( ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2')
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
inference(resolution,[status(thm)],[c_6114,c_8]) ).
tff(c_6168,plain,
~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_6011,c_6138]) ).
tff(c_6191,plain,
~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_4164,c_6168]) ).
tff(c_6201,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5962,c_6191]) ).
tff(c_6203,plain,
'#skF_11'('#skF_1','#skF_2') != '#skF_9'('#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_1430]) ).
tff(c_6899,plain,
! [A_717,B_718,E_719] :
( ( '#skF_11'(A_717,B_718) = '#skF_9'(A_717,B_718) )
| in(E_719,'#skF_12'(A_717,B_718))
| ~ in(set_difference(cast_as_carrier_subset(A_717),E_719),B_718)
| ~ in(E_719,powerset(the_carrier(A_717)))
| ~ element(B_718,powerset(powerset(the_carrier(A_717))))
| ~ top_str(A_717)
| ~ topological_space(A_717) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_6945,plain,
! [C_4] :
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| in('#skF_4'(C_4),C_4) ),
inference(resolution,[status(thm)],[c_16,c_6899]) ).
tff(c_6994,plain,
! [C_4] :
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| in('#skF_4'(C_4),C_4) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_6945]) ).
tff(c_6997,plain,
! [C_720] :
( in('#skF_3'(C_720),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_720),powerset(the_carrier('#skF_1')))
| in('#skF_4'(C_720),C_720) ),
inference(negUnitSimplification,[status(thm)],[c_6203,c_6994]) ).
tff(c_7015,plain,
! [C_4] :
( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| in('#skF_4'(C_4),C_4) ),
inference(resolution,[status(thm)],[c_18,c_6997]) ).
tff(c_7016,plain,
! [C_721] :
( in('#skF_3'(C_721),'#skF_12'('#skF_1','#skF_2'))
| in('#skF_4'(C_721),C_721) ),
inference(resolution,[status(thm)],[c_18,c_6997]) ).
tff(c_186,plain,
! [A_63,B_64,D_84] :
( ( '#skF_11'(A_63,B_64) = '#skF_9'(A_63,B_64) )
| ( '#skF_13'(A_63,B_64,D_84) = D_84 )
| ~ in(D_84,'#skF_12'(A_63,B_64))
| ~ element(B_64,powerset(powerset(the_carrier(A_63))))
| ~ top_str(A_63)
| ~ topological_space(A_63) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_7669,plain,
! [A_785,B_786] :
( ( '#skF_11'(A_785,B_786) = '#skF_9'(A_785,B_786) )
| ( '#skF_13'(A_785,B_786,'#skF_4'('#skF_12'(A_785,B_786))) = '#skF_4'('#skF_12'(A_785,B_786)) )
| ~ element(B_786,powerset(powerset(the_carrier(A_785))))
| ~ top_str(A_785)
| ~ topological_space(A_785)
| in('#skF_3'('#skF_12'(A_785,B_786)),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_7016,c_186]) ).
tff(c_1374,plain,
! [A_287,B_288,D_289] :
( ( '#skF_11'(A_287,B_288) = '#skF_9'(A_287,B_288) )
| ( '#skF_13'(A_287,B_288,D_289) = D_289 )
| ~ in(D_289,'#skF_12'(A_287,B_288))
| ~ element(B_288,powerset(powerset(the_carrier(A_287))))
| ~ top_str(A_287)
| ~ topological_space(A_287) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_1386,plain,
! [A_287,B_288] :
( ( '#skF_11'(A_287,B_288) = '#skF_9'(A_287,B_288) )
| ( '#skF_13'(A_287,B_288,'#skF_4'('#skF_12'(A_287,B_288))) = '#skF_4'('#skF_12'(A_287,B_288)) )
| ~ element(B_288,powerset(powerset(the_carrier(A_287))))
| ~ top_str(A_287)
| ~ topological_space(A_287)
| ~ in('#skF_3'('#skF_12'(A_287,B_288)),'#skF_12'(A_287,B_288)) ),
inference(resolution,[status(thm)],[c_14,c_1374]) ).
tff(c_7724,plain,
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_7669,c_1386]) ).
tff(c_7783,plain,
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ( '#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_7724]) ).
tff(c_7784,plain,
'#skF_13'('#skF_1','#skF_2','#skF_4'('#skF_12'('#skF_1','#skF_2'))) = '#skF_4'('#skF_12'('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_6203,c_7783]) ).
tff(c_1720,plain,
! [A_353,B_354,D_355] :
( ( '#skF_11'(A_353,B_354) = '#skF_9'(A_353,B_354) )
| in('#skF_13'(A_353,B_354,D_355),powerset(the_carrier(A_353)))
| ~ in(D_355,'#skF_12'(A_353,B_354))
| ~ element(B_354,powerset(powerset(the_carrier(A_353))))
| ~ top_str(A_353)
| ~ topological_space(A_353) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_1735,plain,
! [A_353,B_354,D_355] :
( ~ in(powerset(the_carrier(A_353)),'#skF_13'(A_353,B_354,D_355))
| ( '#skF_11'(A_353,B_354) = '#skF_9'(A_353,B_354) )
| ~ in(D_355,'#skF_12'(A_353,B_354))
| ~ element(B_354,powerset(powerset(the_carrier(A_353))))
| ~ top_str(A_353)
| ~ topological_space(A_353) ),
inference(resolution,[status(thm)],[c_1720,c_154]) ).
tff(c_7830,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_7784,c_1735]) ).
tff(c_7872,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_7830]) ).
tff(c_7873,plain,
( ~ in(powerset(the_carrier('#skF_1')),'#skF_4'('#skF_12'('#skF_1','#skF_2')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_6203,c_7872]) ).
tff(c_7890,plain,
~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_7873]) ).
tff(c_7903,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_7015,c_7890]) ).
tff(c_7904,plain,
~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_14,c_7890]) ).
tff(c_8038,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7903,c_7904]) ).
tff(c_8040,plain,
in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_7873]) ).
tff(c_6202,plain,
! [D_301] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),D_301),'#skF_2')
| ~ in(D_301,'#skF_12'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_1430]) ).
tff(c_196,plain,
! [A_63,B_64,D_84] :
( ( '#skF_11'(A_63,B_64) = '#skF_9'(A_63,B_64) )
| in('#skF_13'(A_63,B_64,D_84),powerset(the_carrier(A_63)))
| ~ in(D_84,'#skF_12'(A_63,B_64))
| ~ element(B_64,powerset(powerset(the_carrier(A_63))))
| ~ top_str(A_63)
| ~ topological_space(A_63) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_7853,plain,
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_7784,c_196]) ).
tff(c_7887,plain,
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_7853]) ).
tff(c_7888,plain,
( in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_6203,c_7887]) ).
tff(c_8090,plain,
in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_8040,c_7888]) ).
tff(c_6204,plain,
! [D_665] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),D_665),'#skF_2')
| ~ in(D_665,'#skF_12'('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_1430]) ).
tff(c_6214,plain,
! [C_4] :
( in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_6204,c_12]) ).
tff(c_8099,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_8090,c_6214]) ).
tff(c_8110,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_8040,c_8099]) ).
tff(c_6213,plain,
! [C_4] :
( in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_3'(C_4)),'#skF_2')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_6204,c_10]) ).
tff(c_6919,plain,
! [C_4] :
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ element('#skF_2',powerset(powerset(the_carrier('#skF_1'))))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_6213,c_6899]) ).
tff(c_6966,plain,
! [C_4] :
( ( '#skF_11'('#skF_1','#skF_2') = '#skF_9'('#skF_1','#skF_2') )
| in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_6919]) ).
tff(c_6967,plain,
! [C_4] :
( in('#skF_3'(C_4),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'(C_4),'#skF_12'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_6203,c_6966]) ).
tff(c_8093,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_8090,c_6967]) ).
tff(c_8104,plain,
( in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2'))
| ~ in('#skF_3'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_8040,c_8093]) ).
tff(c_8193,plain,
in('#skF_3'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_8110,c_8104]) ).
tff(c_8217,plain,
( ~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2')
| ~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
inference(resolution,[status(thm)],[c_8193,c_8]) ).
tff(c_8249,plain,
~ in(set_difference(cast_as_carrier_subset('#skF_1'),'#skF_4'('#skF_12'('#skF_1','#skF_2'))),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_8090,c_8217]) ).
tff(c_8272,plain,
~ in('#skF_4'('#skF_12'('#skF_1','#skF_2')),'#skF_12'('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_6202,c_8249]) ).
tff(c_8282,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8040,c_8272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 11:28:45 EDT 2023
% 0.15/0.35 % CPUTime :
% 13.86/4.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.86/4.45
% 13.86/4.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.99/4.50
% 13.99/4.50 Inference rules
% 13.99/4.50 ----------------------
% 13.99/4.50 #Ref : 0
% 13.99/4.50 #Sup : 1903
% 13.99/4.50 #Fact : 4
% 13.99/4.50 #Define : 0
% 13.99/4.50 #Split : 26
% 13.99/4.50 #Chain : 0
% 13.99/4.50 #Close : 0
% 13.99/4.50
% 13.99/4.50 Ordering : KBO
% 13.99/4.50
% 13.99/4.50 Simplification rules
% 13.99/4.50 ----------------------
% 13.99/4.50 #Subsume : 461
% 13.99/4.50 #Demod : 1264
% 13.99/4.50 #Tautology : 384
% 13.99/4.50 #SimpNegUnit : 51
% 13.99/4.50 #BackRed : 1
% 13.99/4.50
% 13.99/4.50 #Partial instantiations: 0
% 13.99/4.50 #Strategies tried : 1
% 13.99/4.50
% 13.99/4.50 Timing (in seconds)
% 13.99/4.50 ----------------------
% 13.99/4.51 Preprocessing : 0.69
% 13.99/4.51 Parsing : 0.33
% 13.99/4.51 CNF conversion : 0.06
% 13.99/4.51 Main loop : 2.70
% 13.99/4.51 Inferencing : 0.98
% 13.99/4.51 Reduction : 0.76
% 13.99/4.51 Demodulation : 0.47
% 13.99/4.51 BG Simplification : 0.10
% 13.99/4.51 Subsumption : 0.68
% 13.99/4.51 Abstraction : 0.11
% 13.99/4.51 MUC search : 0.00
% 13.99/4.51 Cooper : 0.00
% 13.99/4.51 Total : 3.47
% 13.99/4.51 Index Insertion : 0.00
% 13.99/4.51 Index Deletion : 0.00
% 13.99/4.51 Index Matching : 0.00
% 13.99/4.51 BG Taut test : 0.00
%------------------------------------------------------------------------------