TSTP Solution File: SEU315+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU315+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 : n011.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 39.47s 25.28s
% Output : CNFRefutation 39.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 44
% Syntax : Number of formulae : 165 ( 58 unt; 35 typ; 0 def)
% Number of atoms : 330 ( 20 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 369 ( 169 ~; 173 |; 15 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 29 >; 8 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 101 (; 95 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > 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 > #nlpp > the_carrier > powerset > empty_set > #skF_7 > #skF_4 > #skF_8 > #skF_12 > #skF_14 > #skF_5 > #skF_13 > #skF_2 > #skF_1 > #skF_3 > #skF_11 > #skF_9 > #skF_6 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $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_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff('#skF_1',type,
'#skF_1': $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(empty_set,type,
empty_set: $i ).
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('#skF_11',type,
'#skF_11': $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('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(topological_space,type,
topological_space: $i > $o ).
tff(top_str,type,
top_str: $i > $o ).
tff(f_286,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_293,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_204,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
tff(f_50,negated_conjecture,
~ ! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(the_carrier(A))) )
=> ? [C] :
( element(C,powerset(powerset(the_carrier(A))))
& ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> ? [E] :
( element(E,powerset(the_carrier(A)))
& ( E = D )
& closed_subset(E,A)
& subset(B,D) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
tff(f_298,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
tff(f_273,axiom,
! [A,B] :
( ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
tff(f_260,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(the_carrier(A))) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(D,powerset(the_carrier(A)))
& ? [E] :
( element(E,powerset(the_carrier(A)))
& ( E = D )
& closed_subset(E,A)
& subset(B,D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
tff(f_239,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
tff(f_284,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
tff(c_178,plain,
empty('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_286]) ).
tff(c_222,plain,
! [A_113] :
( ( empty_set = A_113 )
| ~ empty(A_113) ),
inference(cnfTransformation,[status(thm)],[f_293]) ).
tff(c_235,plain,
empty_set = '#skF_13',
inference(resolution,[status(thm)],[c_178,c_222]) ).
tff(c_116,plain,
! [A_57] : empty('#skF_7'(A_57)),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_232,plain,
! [A_57] : ( '#skF_7'(A_57) = empty_set ),
inference(resolution,[status(thm)],[c_116,c_222]) ).
tff(c_248,plain,
! [A_57] : ( '#skF_7'(A_57) = '#skF_13' ),
inference(demodulation,[status(thm),theory(equality)],[c_235,c_232]) ).
tff(c_118,plain,
! [A_57] : element('#skF_7'(A_57),powerset(A_57)),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_285,plain,
! [A_57] : element('#skF_13',powerset(A_57)),
inference(demodulation,[status(thm),theory(equality)],[c_248,c_118]) ).
tff(c_286,plain,
! [A_122] : element('#skF_13',powerset(A_122)),
inference(demodulation,[status(thm),theory(equality)],[c_248,c_118]) ).
tff(c_24,plain,
! [C_12] :
( in('#skF_3'(C_12),C_12)
| ( '#skF_4'(C_12) = '#skF_3'(C_12) )
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_290,plain,
( in('#skF_3'('#skF_13'),'#skF_13')
| ( '#skF_4'('#skF_13') = '#skF_3'('#skF_13') ) ),
inference(resolution,[status(thm)],[c_286,c_24]) ).
tff(c_1222,plain,
'#skF_4'('#skF_13') = '#skF_3'('#skF_13'),
inference(splitLeft,[status(thm)],[c_290]) ).
tff(c_293,plain,
! [C_127] :
( in('#skF_3'(C_127),C_127)
| closed_subset('#skF_4'(C_127),'#skF_1')
| ~ element(C_127,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_300,plain,
( in('#skF_3'('#skF_13'),'#skF_13')
| closed_subset('#skF_4'('#skF_13'),'#skF_1') ),
inference(resolution,[status(thm)],[c_285,c_293]) ).
tff(c_1123,plain,
closed_subset('#skF_4'('#skF_13'),'#skF_1'),
inference(splitLeft,[status(thm)],[c_300]) ).
tff(c_1223,plain,
closed_subset('#skF_3'('#skF_13'),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_1222,c_1123]) ).
tff(c_369,plain,
! [C_138] :
( in('#skF_3'(C_138),C_138)
| subset('#skF_2','#skF_3'(C_138))
| ~ element(C_138,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_382,plain,
( in('#skF_3'('#skF_13'),'#skF_13')
| subset('#skF_2','#skF_3'('#skF_13')) ),
inference(resolution,[status(thm)],[c_285,c_369]) ).
tff(c_1146,plain,
subset('#skF_2','#skF_3'('#skF_13')),
inference(splitLeft,[status(thm)],[c_382]) ).
tff(c_440,plain,
! [C_147] :
( in('#skF_3'(C_147),C_147)
| element('#skF_4'(C_147),powerset(the_carrier('#skF_1')))
| ~ element(C_147,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_184,plain,
! [B_99,A_98] :
( ~ empty(B_99)
| ~ in(A_98,B_99) ),
inference(cnfTransformation,[status(thm)],[f_298]) ).
tff(c_3349,plain,
! [C_340] :
( ~ empty(C_340)
| element('#skF_4'(C_340),powerset(the_carrier('#skF_1')))
| ~ element(C_340,powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_440,c_184]) ).
tff(c_3448,plain,
( ~ empty('#skF_13')
| element('#skF_3'('#skF_13'),powerset(the_carrier('#skF_1')))
| ~ element('#skF_13',powerset(powerset(the_carrier('#skF_1')))) ),
inference(superposition,[status(thm),theory(equality)],[c_1222,c_3349]) ).
tff(c_3481,plain,
element('#skF_3'('#skF_13'),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_285,c_178,c_3448]) ).
tff(c_10,plain,
! [C_12] :
( ~ subset('#skF_2','#skF_3'(C_12))
| ~ closed_subset('#skF_3'(C_12),'#skF_1')
| ~ element('#skF_3'(C_12),powerset(the_carrier('#skF_1')))
| ~ in('#skF_3'(C_12),C_12)
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_3534,plain,
( ~ subset('#skF_2','#skF_3'('#skF_13'))
| ~ closed_subset('#skF_3'('#skF_13'),'#skF_1')
| ~ in('#skF_3'('#skF_13'),'#skF_13')
| ~ element('#skF_13',powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_3481,c_10]) ).
tff(c_3602,plain,
~ in('#skF_3'('#skF_13'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_285,c_1223,c_1146,c_3534]) ).
tff(c_6,plain,
topological_space('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_4,plain,
top_str('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_2,plain,
element('#skF_2',powerset(the_carrier('#skF_1'))),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_162,plain,
! [B_91,A_90] :
( in(B_91,A_90)
| ~ element(B_91,A_90)
| empty(A_90) ),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_2849,plain,
! [B_285,D_286,A_287] :
( subset(B_285,D_286)
| ~ in(D_286,'#skF_9'(A_287,B_285))
| ~ element(B_285,powerset(the_carrier(A_287)))
| ~ top_str(A_287)
| ~ topological_space(A_287) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_65861,plain,
! [B_1473,B_1474,A_1475] :
( subset(B_1473,B_1474)
| ~ element(B_1473,powerset(the_carrier(A_1475)))
| ~ top_str(A_1475)
| ~ topological_space(A_1475)
| ~ element(B_1474,'#skF_9'(A_1475,B_1473))
| empty('#skF_9'(A_1475,B_1473)) ),
inference(resolution,[status(thm)],[c_162,c_2849]) ).
tff(c_65905,plain,
! [B_1474] :
( subset('#skF_2',B_1474)
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| ~ element(B_1474,'#skF_9'('#skF_1','#skF_2'))
| empty('#skF_9'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_2,c_65861]) ).
tff(c_65943,plain,
! [B_1474] :
( subset('#skF_2',B_1474)
| ~ element(B_1474,'#skF_9'('#skF_1','#skF_2'))
| empty('#skF_9'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_65905]) ).
tff(c_68950,plain,
empty('#skF_9'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_65943]) ).
tff(c_182,plain,
! [A_97] :
( ( empty_set = A_97 )
| ~ empty(A_97) ),
inference(cnfTransformation,[status(thm)],[f_293]) ).
tff(c_241,plain,
! [A_97] :
( ( A_97 = '#skF_13' )
| ~ empty(A_97) ),
inference(demodulation,[status(thm),theory(equality)],[c_235,c_182]) ).
tff(c_69011,plain,
'#skF_9'('#skF_1','#skF_2') = '#skF_13',
inference(resolution,[status(thm)],[c_68950,c_241]) ).
tff(c_146,plain,
! [A_67] : ~ empty(powerset(A_67)),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_3321,plain,
! [E_336,A_337,B_338] :
( in(E_336,'#skF_9'(A_337,B_338))
| ~ subset(B_338,E_336)
| ~ closed_subset(E_336,A_337)
| ~ element(E_336,powerset(the_carrier(A_337)))
| ~ in(E_336,powerset(the_carrier(A_337)))
| ~ element(B_338,powerset(the_carrier(A_337)))
| ~ top_str(A_337)
| ~ topological_space(A_337) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_3327,plain,
! [B_91,A_337,B_338] :
( in(B_91,'#skF_9'(A_337,B_338))
| ~ subset(B_338,B_91)
| ~ closed_subset(B_91,A_337)
| ~ element(B_338,powerset(the_carrier(A_337)))
| ~ top_str(A_337)
| ~ topological_space(A_337)
| ~ element(B_91,powerset(the_carrier(A_337)))
| empty(powerset(the_carrier(A_337))) ),
inference(resolution,[status(thm)],[c_162,c_3321]) ).
tff(c_73186,plain,
! [B_1712,A_1713,B_1714] :
( in(B_1712,'#skF_9'(A_1713,B_1714))
| ~ subset(B_1714,B_1712)
| ~ closed_subset(B_1712,A_1713)
| ~ element(B_1714,powerset(the_carrier(A_1713)))
| ~ top_str(A_1713)
| ~ topological_space(A_1713)
| ~ element(B_1712,powerset(the_carrier(A_1713))) ),
inference(negUnitSimplification,[status(thm)],[c_146,c_3327]) ).
tff(c_73274,plain,
! [B_1712] :
( in(B_1712,'#skF_9'('#skF_1','#skF_2'))
| ~ subset('#skF_2',B_1712)
| ~ closed_subset(B_1712,'#skF_1')
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| ~ element(B_1712,powerset(the_carrier('#skF_1'))) ),
inference(resolution,[status(thm)],[c_2,c_73186]) ).
tff(c_105682,plain,
! [B_2097] :
( in(B_2097,'#skF_13')
| ~ subset('#skF_2',B_2097)
| ~ closed_subset(B_2097,'#skF_1')
| ~ element(B_2097,powerset(the_carrier('#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_69011,c_73274]) ).
tff(c_105893,plain,
( in('#skF_3'('#skF_13'),'#skF_13')
| ~ subset('#skF_2','#skF_3'('#skF_13'))
| ~ closed_subset('#skF_3'('#skF_13'),'#skF_1') ),
inference(resolution,[status(thm)],[c_3481,c_105682]) ).
tff(c_106002,plain,
in('#skF_3'('#skF_13'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_1223,c_1146,c_105893]) ).
tff(c_106004,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3602,c_106002]) ).
tff(c_106006,plain,
~ empty('#skF_9'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_65943]) ).
tff(c_2214,plain,
! [A_270,B_271] :
( in('#skF_12'(A_270,B_271),A_270)
| element(A_270,powerset(B_271)) ),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_160,plain,
! [B_91,A_90] :
( element(B_91,A_90)
| ~ in(B_91,A_90)
| empty(A_90) ),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_2228,plain,
! [A_270,B_271] :
( element('#skF_12'(A_270,B_271),A_270)
| empty(A_270)
| element(A_270,powerset(B_271)) ),
inference(resolution,[status(thm)],[c_2214,c_160]) ).
tff(c_3003,plain,
! [D_306,A_307,B_308] :
( in(D_306,powerset(the_carrier(A_307)))
| ~ in(D_306,'#skF_9'(A_307,B_308))
| ~ element(B_308,powerset(the_carrier(A_307)))
| ~ top_str(A_307)
| ~ topological_space(A_307) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_108793,plain,
! [B_2222,A_2223,B_2224] :
( in(B_2222,powerset(the_carrier(A_2223)))
| ~ element(B_2224,powerset(the_carrier(A_2223)))
| ~ top_str(A_2223)
| ~ topological_space(A_2223)
| ~ element(B_2222,'#skF_9'(A_2223,B_2224))
| empty('#skF_9'(A_2223,B_2224)) ),
inference(resolution,[status(thm)],[c_162,c_3003]) ).
tff(c_108870,plain,
! [B_2222] :
( in(B_2222,powerset(the_carrier('#skF_1')))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| ~ element(B_2222,'#skF_9'('#skF_1','#skF_2'))
| empty('#skF_9'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_2,c_108793]) ).
tff(c_108919,plain,
! [B_2222] :
( in(B_2222,powerset(the_carrier('#skF_1')))
| ~ element(B_2222,'#skF_9'('#skF_1','#skF_2'))
| empty('#skF_9'('#skF_1','#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_108870]) ).
tff(c_109187,plain,
! [B_2234] :
( in(B_2234,powerset(the_carrier('#skF_1')))
| ~ element(B_2234,'#skF_9'('#skF_1','#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_106006,c_108919]) ).
tff(c_174,plain,
! [A_94,B_95] :
( ~ in('#skF_12'(A_94,B_95),B_95)
| element(A_94,powerset(B_95)) ),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_173320,plain,
! [A_2835] :
( element(A_2835,powerset(powerset(the_carrier('#skF_1'))))
| ~ element('#skF_12'(A_2835,powerset(the_carrier('#skF_1'))),'#skF_9'('#skF_1','#skF_2')) ),
inference(resolution,[status(thm)],[c_109187,c_174]) ).
tff(c_173330,plain,
( empty('#skF_9'('#skF_1','#skF_2'))
| element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_2228,c_173320]) ).
tff(c_173338,plain,
element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))),
inference(negUnitSimplification,[status(thm)],[c_106006,c_173330]) ).
tff(c_16,plain,
! [C_12] :
( in('#skF_3'(C_12),C_12)
| subset('#skF_2','#skF_3'(C_12))
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_173511,plain,
( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
| subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) ),
inference(resolution,[status(thm)],[c_173338,c_16]) ).
tff(c_173516,plain,
subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),
inference(splitLeft,[status(thm)],[c_173511]) ).
tff(c_173515,plain,
( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
| ( '#skF_4'('#skF_9'('#skF_1','#skF_2')) = '#skF_3'('#skF_9'('#skF_1','#skF_2')) ) ),
inference(resolution,[status(thm)],[c_173338,c_24]) ).
tff(c_173552,plain,
'#skF_4'('#skF_9'('#skF_1','#skF_2')) = '#skF_3'('#skF_9'('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_173515]) ).
tff(c_20,plain,
! [C_12] :
( in('#skF_3'(C_12),C_12)
| closed_subset('#skF_4'(C_12),'#skF_1')
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_173514,plain,
( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
| closed_subset('#skF_4'('#skF_9'('#skF_1','#skF_2')),'#skF_1') ),
inference(resolution,[status(thm)],[c_173338,c_20]) ).
tff(c_173546,plain,
closed_subset('#skF_4'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
inference(splitLeft,[status(thm)],[c_173514]) ).
tff(c_173553,plain,
closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_173552,c_173546]) ).
tff(c_28,plain,
! [C_12] :
( in('#skF_3'(C_12),C_12)
| element('#skF_4'(C_12),powerset(the_carrier('#skF_1')))
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_8,plain,
! [C_12] :
( element('#skF_3'(C_12),powerset(the_carrier('#skF_1')))
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_746,plain,
! [C_182] :
( ~ subset('#skF_2','#skF_3'(C_182))
| ~ closed_subset('#skF_3'(C_182),'#skF_1')
| ~ element('#skF_3'(C_182),powerset(the_carrier('#skF_1')))
| ~ in('#skF_3'(C_182),C_182)
| ~ element(C_182,powerset(powerset(the_carrier('#skF_1')))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_65665,plain,
! [C_1470] :
( ~ subset('#skF_2','#skF_3'(C_1470))
| ~ closed_subset('#skF_3'(C_1470),'#skF_1')
| ~ in('#skF_3'(C_1470),C_1470)
| ~ element(C_1470,powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_8,c_746]) ).
tff(c_65681,plain,
! [C_12] :
( ~ subset('#skF_2','#skF_3'(C_12))
| ~ closed_subset('#skF_3'(C_12),'#skF_1')
| element('#skF_4'(C_12),powerset(the_carrier('#skF_1')))
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_28,c_65665]) ).
tff(c_173619,plain,
( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
| ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
| element('#skF_3'('#skF_9'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1')))
| ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
inference(superposition,[status(thm),theory(equality)],[c_173552,c_65681]) ).
tff(c_173694,plain,
( ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
| element('#skF_3'('#skF_9'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173516,c_173619]) ).
tff(c_173704,plain,
element('#skF_3'('#skF_9'('#skF_1','#skF_2')),powerset(the_carrier('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_173553,c_173694]) ).
tff(c_109933,plain,
! [B_2252,A_2253,B_2254] :
( in(B_2252,'#skF_9'(A_2253,B_2254))
| ~ subset(B_2254,B_2252)
| ~ closed_subset(B_2252,A_2253)
| ~ element(B_2254,powerset(the_carrier(A_2253)))
| ~ top_str(A_2253)
| ~ topological_space(A_2253)
| ~ element(B_2252,powerset(the_carrier(A_2253))) ),
inference(negUnitSimplification,[status(thm)],[c_146,c_3327]) ).
tff(c_110015,plain,
! [B_2252] :
( in(B_2252,'#skF_9'('#skF_1','#skF_2'))
| ~ subset('#skF_2',B_2252)
| ~ closed_subset(B_2252,'#skF_1')
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1')
| ~ element(B_2252,powerset(the_carrier('#skF_1'))) ),
inference(resolution,[status(thm)],[c_2,c_109933]) ).
tff(c_110068,plain,
! [B_2252] :
( in(B_2252,'#skF_9'('#skF_1','#skF_2'))
| ~ subset('#skF_2',B_2252)
| ~ closed_subset(B_2252,'#skF_1')
| ~ element(B_2252,powerset(the_carrier('#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_110015]) ).
tff(c_173712,plain,
( in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2'))
| ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
| ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1') ),
inference(resolution,[status(thm)],[c_173704,c_110068]) ).
tff(c_173826,plain,
in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_173553,c_173516,c_173712]) ).
tff(c_749,plain,
! [C_12] :
( ~ subset('#skF_2','#skF_3'(C_12))
| ~ closed_subset('#skF_3'(C_12),'#skF_1')
| ~ in('#skF_3'(C_12),C_12)
| ~ element(C_12,powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_8,c_746]) ).
tff(c_173907,plain,
( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
| ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
| ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_173826,c_749]) ).
tff(c_173975,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173553,c_173516,c_173907]) ).
tff(c_173976,plain,
in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_173515]) ).
tff(c_174009,plain,
( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
| ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
| ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_173976,c_749]) ).
tff(c_174076,plain,
~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173516,c_174009]) ).
tff(c_154,plain,
! [A_68,B_69,D_86] :
( ( '#skF_10'(A_68,B_69,D_86) = D_86 )
| ~ in(D_86,'#skF_9'(A_68,B_69))
| ~ element(B_69,powerset(the_carrier(A_68)))
| ~ top_str(A_68)
| ~ topological_space(A_68) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_174018,plain,
( ( '#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(the_carrier('#skF_1')))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_173976,c_154]) ).
tff(c_174086,plain,
'#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_174018]) ).
tff(c_152,plain,
! [A_68,B_69,D_86] :
( closed_subset('#skF_10'(A_68,B_69,D_86),A_68)
| ~ in(D_86,'#skF_9'(A_68,B_69))
| ~ element(B_69,powerset(the_carrier(A_68)))
| ~ top_str(A_68)
| ~ topological_space(A_68) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_174011,plain,
( closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1')
| ~ element('#skF_2',powerset(the_carrier('#skF_1')))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_173976,c_152]) ).
tff(c_174079,plain,
closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_174011]) ).
tff(c_175454,plain,
closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_174086,c_174079]) ).
tff(c_175456,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_174076,c_175454]) ).
tff(c_175457,plain,
in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_173514]) ).
tff(c_177140,plain,
( ~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
| ~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1')
| ~ element('#skF_9'('#skF_1','#skF_2'),powerset(powerset(the_carrier('#skF_1')))) ),
inference(resolution,[status(thm)],[c_175457,c_749]) ).
tff(c_177207,plain,
~ closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_173338,c_173516,c_177140]) ).
tff(c_177149,plain,
( ( '#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')) )
| ~ element('#skF_2',powerset(the_carrier('#skF_1')))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_175457,c_154]) ).
tff(c_177217,plain,
'#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))) = '#skF_3'('#skF_9'('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_177149]) ).
tff(c_177142,plain,
( closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1')
| ~ element('#skF_2',powerset(the_carrier('#skF_1')))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_175457,c_152]) ).
tff(c_177210,plain,
closed_subset('#skF_10'('#skF_1','#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_177142]) ).
tff(c_178350,plain,
closed_subset('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_177217,c_177210]) ).
tff(c_178352,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_177207,c_178350]) ).
tff(c_178354,plain,
~ subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),
inference(splitRight,[status(thm)],[c_173511]) ).
tff(c_178353,plain,
in('#skF_3'('#skF_9'('#skF_1','#skF_2')),'#skF_9'('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_173511]) ).
tff(c_150,plain,
! [B_69,D_86,A_68] :
( subset(B_69,D_86)
| ~ in(D_86,'#skF_9'(A_68,B_69))
| ~ element(B_69,powerset(the_carrier(A_68)))
| ~ top_str(A_68)
| ~ topological_space(A_68) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_178402,plain,
( subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2')))
| ~ element('#skF_2',powerset(the_carrier('#skF_1')))
| ~ top_str('#skF_1')
| ~ topological_space('#skF_1') ),
inference(resolution,[status(thm)],[c_178353,c_150]) ).
tff(c_178471,plain,
subset('#skF_2','#skF_3'('#skF_9'('#skF_1','#skF_2'))),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_178402]) ).
tff(c_178473,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_178354,c_178471]) ).
tff(c_178474,plain,
in('#skF_3'('#skF_13'),'#skF_13'),
inference(splitRight,[status(thm)],[c_290]) ).
tff(c_178480,plain,
~ empty('#skF_13'),
inference(resolution,[status(thm)],[c_178474,c_184]) ).
tff(c_178485,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_178,c_178480]) ).
tff(c_178486,plain,
in('#skF_3'('#skF_13'),'#skF_13'),
inference(splitRight,[status(thm)],[c_382]) ).
tff(c_178528,plain,
~ empty('#skF_13'),
inference(resolution,[status(thm)],[c_178486,c_184]) ).
tff(c_178533,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_178,c_178528]) ).
tff(c_178534,plain,
in('#skF_3'('#skF_13'),'#skF_13'),
inference(splitRight,[status(thm)],[c_300]) ).
tff(c_178540,plain,
~ empty('#skF_13'),
inference(resolution,[status(thm)],[c_178534,c_184]) ).
tff(c_178545,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_178,c_178540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 11:39:36 EDT 2023
% 0.15/0.37 % CPUTime :
% 39.47/25.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.56/25.30
% 39.56/25.30 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.56/25.34
% 39.56/25.34 Inference rules
% 39.56/25.34 ----------------------
% 39.56/25.34 #Ref : 0
% 39.56/25.34 #Sup : 45082
% 39.56/25.34 #Fact : 0
% 39.56/25.34 #Define : 0
% 39.56/25.34 #Split : 125
% 39.56/25.34 #Chain : 0
% 39.56/25.34 #Close : 0
% 39.56/25.34
% 39.56/25.34 Ordering : KBO
% 39.56/25.34
% 39.56/25.34 Simplification rules
% 39.56/25.34 ----------------------
% 39.56/25.34 #Subsume : 25094
% 39.56/25.34 #Demod : 14962
% 39.56/25.34 #Tautology : 4254
% 39.56/25.34 #SimpNegUnit : 5172
% 39.56/25.34 #BackRed : 20
% 39.56/25.34
% 39.56/25.34 #Partial instantiations: 0
% 39.56/25.34 #Strategies tried : 1
% 39.56/25.34
% 39.56/25.34 Timing (in seconds)
% 39.56/25.34 ----------------------
% 39.56/25.34 Preprocessing : 0.63
% 39.56/25.34 Parsing : 0.31
% 39.56/25.34 CNF conversion : 0.06
% 39.56/25.34 Main loop : 23.62
% 39.56/25.34 Inferencing : 4.96
% 39.56/25.34 Reduction : 7.69
% 39.56/25.34 Demodulation : 5.33
% 39.56/25.34 BG Simplification : 0.19
% 39.56/25.34 Subsumption : 9.39
% 39.56/25.34 Abstraction : 0.35
% 39.56/25.34 MUC search : 0.00
% 39.56/25.34 Cooper : 0.00
% 39.56/25.34 Total : 24.32
% 39.56/25.34 Index Insertion : 0.00
% 39.56/25.34 Index Deletion : 0.00
% 39.56/25.34 Index Matching : 0.00
% 39.56/25.34 BG Taut test : 0.00
%------------------------------------------------------------------------------