TSTP Solution File: SEU324+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU324+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 : n022.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 10:58:25 EDT 2023
% Result : Theorem 5.94s 2.45s
% Output : CNFRefutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 29
% Syntax : Number of formulae : 87 ( 33 unt; 22 typ; 0 def)
% Number of atoms : 134 ( 34 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 123 ( 54 ~; 45 |; 6 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 16 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 36 (; 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > open_subset > element > closed_subset > topological_space > top_str > one_sorted_str > topstr_closure > subset_complement > interior > #nlpp > the_carrier > powerset > #skF_5 > #skF_4 > #skF_7 > #skF_10 > #skF_2 > #skF_1 > #skF_9 > #skF_8 > #skF_3 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(topstr_closure,type,
topstr_closure: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(open_subset,type,
open_subset: ( $i * $i ) > $o ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(closed_subset,type,
closed_subset: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(interior,type,
interior: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $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_182,negated_conjecture,
~ ! [A] :
( ( topological_space(A)
& top_str(A) )
=> ! [B] :
( top_str(B)
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ! [D] :
( element(D,powerset(the_carrier(B)))
=> ( ( open_subset(D,B)
=> ( interior(B,D) = D ) )
& ( ( interior(A,C) = C )
=> open_subset(C,A) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).
tff(f_97,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(the_carrier(A))) )
=> open_subset(interior(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
tff(f_101,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,subset_complement(A,B)) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
tff(f_141,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
tff(f_44,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
tff(f_33,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
tff(f_160,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( ( closed_subset(B,A)
=> ( topstr_closure(A,B) = B ) )
& ( ( topological_space(A)
& ( topstr_closure(A,B) = B ) )
=> closed_subset(B,A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
tff(c_76,plain,
( open_subset('#skF_10','#skF_8')
| ~ open_subset('#skF_9','#skF_7') ),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_96,plain,
~ open_subset('#skF_9','#skF_7'),
inference(splitLeft,[status(thm)],[c_76]) ).
tff(c_72,plain,
topological_space('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_70,plain,
top_str('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_80,plain,
( open_subset('#skF_10','#skF_8')
| ( interior('#skF_7','#skF_9') = '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_97,plain,
interior('#skF_7','#skF_9') = '#skF_9',
inference(splitLeft,[status(thm)],[c_80]) ).
tff(c_66,plain,
element('#skF_9',powerset(the_carrier('#skF_7'))),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_298,plain,
! [A_78,B_79] :
( open_subset(interior(A_78,B_79),A_78)
| ~ element(B_79,powerset(the_carrier(A_78)))
| ~ top_str(A_78)
| ~ topological_space(A_78) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_317,plain,
( open_subset(interior('#skF_7','#skF_9'),'#skF_7')
| ~ top_str('#skF_7')
| ~ topological_space('#skF_7') ),
inference(resolution,[status(thm)],[c_66,c_298]) ).
tff(c_329,plain,
open_subset('#skF_9','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_72,c_70,c_97,c_317]) ).
tff(c_331,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_96,c_329]) ).
tff(c_333,plain,
interior('#skF_7','#skF_9') != '#skF_9',
inference(splitRight,[status(thm)],[c_80]) ).
tff(c_78,plain,
( ( interior('#skF_8','#skF_10') != '#skF_10' )
| ( interior('#skF_7','#skF_9') = '#skF_9' ) ),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_334,plain,
interior('#skF_8','#skF_10') != '#skF_10',
inference(negUnitSimplification,[status(thm)],[c_333,c_78]) ).
tff(c_68,plain,
top_str('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_64,plain,
element('#skF_10',powerset(the_carrier('#skF_8'))),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_371,plain,
! [A_95,B_96] :
( ( subset_complement(A_95,subset_complement(A_95,B_96)) = B_96 )
| ~ element(B_96,powerset(A_95)) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_388,plain,
subset_complement(the_carrier('#skF_8'),subset_complement(the_carrier('#skF_8'),'#skF_10')) = '#skF_10',
inference(resolution,[status(thm)],[c_64,c_371]) ).
tff(c_332,plain,
open_subset('#skF_10','#skF_8'),
inference(splitRight,[status(thm)],[c_80]) ).
tff(c_739,plain,
! [A_131,B_132] :
( closed_subset(subset_complement(the_carrier(A_131),B_132),A_131)
| ~ open_subset(B_132,A_131)
| ~ element(B_132,powerset(the_carrier(A_131)))
| ~ top_str(A_131) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_757,plain,
( closed_subset(subset_complement(the_carrier('#skF_8'),'#skF_10'),'#skF_8')
| ~ open_subset('#skF_10','#skF_8')
| ~ top_str('#skF_8') ),
inference(resolution,[status(thm)],[c_64,c_739]) ).
tff(c_772,plain,
closed_subset(subset_complement(the_carrier('#skF_8'),'#skF_10'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_332,c_757]) ).
tff(c_8,plain,
! [A_6,B_7] :
( element(subset_complement(A_6,B_7),powerset(A_6))
| ~ element(B_7,powerset(A_6)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1163,plain,
! [A_151,B_152] :
( ( subset_complement(the_carrier(A_151),topstr_closure(A_151,subset_complement(the_carrier(A_151),B_152))) = interior(A_151,B_152) )
| ~ element(B_152,powerset(the_carrier(A_151)))
| ~ top_str(A_151) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_1219,plain,
( ( subset_complement(the_carrier('#skF_8'),topstr_closure('#skF_8','#skF_10')) = interior('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) )
| ~ element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8')))
| ~ top_str('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_388,c_1163]) ).
tff(c_1225,plain,
( ( subset_complement(the_carrier('#skF_8'),topstr_closure('#skF_8','#skF_10')) = interior('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) )
| ~ element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_1219]) ).
tff(c_1449,plain,
~ element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8'))),
inference(splitLeft,[status(thm)],[c_1225]) ).
tff(c_1452,plain,
~ element('#skF_10',powerset(the_carrier('#skF_8'))),
inference(resolution,[status(thm)],[c_8,c_1449]) ).
tff(c_1459,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_1452]) ).
tff(c_1461,plain,
element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8'))),
inference(splitRight,[status(thm)],[c_1225]) ).
tff(c_62,plain,
! [A_36,B_38] :
( ( topstr_closure(A_36,B_38) = B_38 )
| ~ closed_subset(B_38,A_36)
| ~ element(B_38,powerset(the_carrier(A_36)))
| ~ top_str(A_36) ),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_1473,plain,
( ( topstr_closure('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) = subset_complement(the_carrier('#skF_8'),'#skF_10') )
| ~ closed_subset(subset_complement(the_carrier('#skF_8'),'#skF_10'),'#skF_8')
| ~ top_str('#skF_8') ),
inference(resolution,[status(thm)],[c_1461,c_62]) ).
tff(c_1494,plain,
topstr_closure('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) = subset_complement(the_carrier('#skF_8'),'#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_772,c_1473]) ).
tff(c_2,plain,
! [A_1,B_3] :
( ( subset_complement(the_carrier(A_1),topstr_closure(A_1,subset_complement(the_carrier(A_1),B_3))) = interior(A_1,B_3) )
| ~ element(B_3,powerset(the_carrier(A_1)))
| ~ top_str(A_1) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_1539,plain,
( ( subset_complement(the_carrier('#skF_8'),subset_complement(the_carrier('#skF_8'),'#skF_10')) = interior('#skF_8','#skF_10') )
| ~ element('#skF_10',powerset(the_carrier('#skF_8')))
| ~ top_str('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_1494,c_2]) ).
tff(c_1551,plain,
interior('#skF_8','#skF_10') = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_68,c_64,c_388,c_1539]) ).
tff(c_1553,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_334,c_1551]) ).
tff(c_1555,plain,
open_subset('#skF_9','#skF_7'),
inference(splitRight,[status(thm)],[c_76]) ).
tff(c_74,plain,
( ( interior('#skF_8','#skF_10') != '#skF_10' )
| ~ open_subset('#skF_9','#skF_7') ),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_1573,plain,
interior('#skF_8','#skF_10') != '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_1555,c_74]) ).
tff(c_1601,plain,
! [A_181,B_182] :
( ( subset_complement(A_181,subset_complement(A_181,B_182)) = B_182 )
| ~ element(B_182,powerset(A_181)) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_1621,plain,
subset_complement(the_carrier('#skF_8'),subset_complement(the_carrier('#skF_8'),'#skF_10')) = '#skF_10',
inference(resolution,[status(thm)],[c_64,c_1601]) ).
tff(c_1554,plain,
open_subset('#skF_10','#skF_8'),
inference(splitRight,[status(thm)],[c_76]) ).
tff(c_2199,plain,
! [A_229,B_230] :
( closed_subset(subset_complement(the_carrier(A_229),B_230),A_229)
| ~ open_subset(B_230,A_229)
| ~ element(B_230,powerset(the_carrier(A_229)))
| ~ top_str(A_229) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_2217,plain,
( closed_subset(subset_complement(the_carrier('#skF_8'),'#skF_10'),'#skF_8')
| ~ open_subset('#skF_10','#skF_8')
| ~ top_str('#skF_8') ),
inference(resolution,[status(thm)],[c_64,c_2199]) ).
tff(c_2232,plain,
closed_subset(subset_complement(the_carrier('#skF_8'),'#skF_10'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_1554,c_2217]) ).
tff(c_2379,plain,
! [A_239,B_240] :
( ( subset_complement(the_carrier(A_239),topstr_closure(A_239,subset_complement(the_carrier(A_239),B_240))) = interior(A_239,B_240) )
| ~ element(B_240,powerset(the_carrier(A_239)))
| ~ top_str(A_239) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_2432,plain,
( ( subset_complement(the_carrier('#skF_8'),topstr_closure('#skF_8','#skF_10')) = interior('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) )
| ~ element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8')))
| ~ top_str('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_1621,c_2379]) ).
tff(c_2438,plain,
( ( subset_complement(the_carrier('#skF_8'),topstr_closure('#skF_8','#skF_10')) = interior('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) )
| ~ element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_2432]) ).
tff(c_2688,plain,
~ element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8'))),
inference(splitLeft,[status(thm)],[c_2438]) ).
tff(c_2691,plain,
~ element('#skF_10',powerset(the_carrier('#skF_8'))),
inference(resolution,[status(thm)],[c_8,c_2688]) ).
tff(c_2698,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_2691]) ).
tff(c_2700,plain,
element(subset_complement(the_carrier('#skF_8'),'#skF_10'),powerset(the_carrier('#skF_8'))),
inference(splitRight,[status(thm)],[c_2438]) ).
tff(c_2710,plain,
( ( topstr_closure('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) = subset_complement(the_carrier('#skF_8'),'#skF_10') )
| ~ closed_subset(subset_complement(the_carrier('#skF_8'),'#skF_10'),'#skF_8')
| ~ top_str('#skF_8') ),
inference(resolution,[status(thm)],[c_2700,c_62]) ).
tff(c_2730,plain,
topstr_closure('#skF_8',subset_complement(the_carrier('#skF_8'),'#skF_10')) = subset_complement(the_carrier('#skF_8'),'#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_2232,c_2710]) ).
tff(c_2810,plain,
( ( subset_complement(the_carrier('#skF_8'),subset_complement(the_carrier('#skF_8'),'#skF_10')) = interior('#skF_8','#skF_10') )
| ~ element('#skF_10',powerset(the_carrier('#skF_8')))
| ~ top_str('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_2730,c_2]) ).
tff(c_2820,plain,
interior('#skF_8','#skF_10') = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_68,c_64,c_1621,c_2810]) ).
tff(c_2822,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1573,c_2820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU324+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.13 % 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
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 11:37:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.94/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.94/2.47
% 5.94/2.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.94/2.50
% 5.94/2.50 Inference rules
% 5.94/2.50 ----------------------
% 5.94/2.50 #Ref : 0
% 5.94/2.50 #Sup : 630
% 5.94/2.50 #Fact : 0
% 5.94/2.50 #Define : 0
% 5.94/2.50 #Split : 16
% 5.94/2.50 #Chain : 0
% 5.94/2.50 #Close : 0
% 5.94/2.50
% 5.94/2.50 Ordering : KBO
% 5.94/2.50
% 5.94/2.50 Simplification rules
% 5.94/2.50 ----------------------
% 5.94/2.50 #Subsume : 138
% 5.94/2.50 #Demod : 274
% 5.94/2.50 #Tautology : 210
% 5.94/2.50 #SimpNegUnit : 23
% 5.94/2.50 #BackRed : 2
% 5.94/2.50
% 5.94/2.50 #Partial instantiations: 0
% 5.94/2.50 #Strategies tried : 1
% 5.94/2.50
% 5.94/2.50 Timing (in seconds)
% 5.94/2.50 ----------------------
% 5.94/2.50 Preprocessing : 0.55
% 5.94/2.50 Parsing : 0.29
% 5.94/2.50 CNF conversion : 0.05
% 5.94/2.50 Main loop : 0.86
% 5.94/2.50 Inferencing : 0.34
% 5.94/2.50 Reduction : 0.26
% 5.94/2.50 Demodulation : 0.18
% 5.94/2.50 BG Simplification : 0.04
% 5.94/2.50 Subsumption : 0.15
% 5.94/2.50 Abstraction : 0.03
% 5.94/2.51 MUC search : 0.00
% 5.94/2.51 Cooper : 0.00
% 5.94/2.51 Total : 1.47
% 5.94/2.51 Index Insertion : 0.00
% 5.94/2.51 Index Deletion : 0.00
% 5.94/2.51 Index Matching : 0.00
% 5.94/2.51 BG Taut test : 0.00
%------------------------------------------------------------------------------