TSTP Solution File: SEU319+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU319+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 : n018.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 10:58:24 EDT 2023
% Result : Theorem 4.27s 2.01s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 58 ( 17 unt; 17 typ; 0 def)
% Number of atoms : 83 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 34 ~; 30 |; 1 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 13 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 29 (; 29 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > open_subset > element > closed_subset > top_str > one_sorted_str > subset_difference > subset_complement > set_difference > #nlpp > the_carrier > powerset > cast_as_carrier_subset > #skF_5 > #skF_2 > #skF_1 > #skF_4 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(open_subset,type,
open_subset: ( $i * $i ) > $o ).
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_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
tff(closed_subset,type,
closed_subset: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(top_str,type,
top_str: $i > $o ).
tff(f_90,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
tff(f_54,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
tff(f_40,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
tff(f_71,axiom,
! [A,B,C] :
( ( element(B,powerset(A))
& element(C,powerset(A)) )
=> ( subset_difference(A,B,C) = set_difference(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
tff(f_80,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
tff(f_35,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
tff(c_40,plain,
top_str('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_55,plain,
! [A_28] :
( one_sorted_str(A_28)
| ~ top_str(A_28) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_63,plain,
one_sorted_str('#skF_4'),
inference(resolution,[status(thm)],[c_40,c_55]) ).
tff(c_8,plain,
! [A_4] :
( element(cast_as_carrier_subset(A_4),powerset(the_carrier(A_4)))
| ~ one_sorted_str(A_4) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_38,plain,
element('#skF_5',powerset(the_carrier('#skF_4'))),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_944,plain,
! [A_90,B_91,C_92] :
( ( subset_difference(A_90,B_91,C_92) = set_difference(B_91,C_92) )
| ~ element(C_92,powerset(A_90))
| ~ element(B_91,powerset(A_90)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_964,plain,
! [B_93] :
( ( subset_difference(the_carrier('#skF_4'),B_93,'#skF_5') = set_difference(B_93,'#skF_5') )
| ~ element(B_93,powerset(the_carrier('#skF_4'))) ),
inference(resolution,[status(thm)],[c_38,c_944]) ).
tff(c_976,plain,
( ( subset_difference(the_carrier('#skF_4'),cast_as_carrier_subset('#skF_4'),'#skF_5') = set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5') )
| ~ one_sorted_str('#skF_4') ),
inference(resolution,[status(thm)],[c_8,c_964]) ).
tff(c_992,plain,
subset_difference(the_carrier('#skF_4'),cast_as_carrier_subset('#skF_4'),'#skF_5') = set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_976]) ).
tff(c_1105,plain,
! [A_95,B_96] :
( ( subset_difference(the_carrier(A_95),cast_as_carrier_subset(A_95),B_96) = subset_complement(the_carrier(A_95),B_96) )
| ~ element(B_96,powerset(the_carrier(A_95)))
| ~ one_sorted_str(A_95) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_1120,plain,
( ( subset_difference(the_carrier('#skF_4'),cast_as_carrier_subset('#skF_4'),'#skF_5') = subset_complement(the_carrier('#skF_4'),'#skF_5') )
| ~ one_sorted_str('#skF_4') ),
inference(resolution,[status(thm)],[c_38,c_1105]) ).
tff(c_1133,plain,
subset_complement(the_carrier('#skF_4'),'#skF_5') = set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_992,c_1120]) ).
tff(c_48,plain,
( closed_subset('#skF_5','#skF_4')
| open_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_64,plain,
open_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4'),
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_42,plain,
( ~ open_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
| ~ closed_subset('#skF_5','#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_88,plain,
~ closed_subset('#skF_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_42]) ).
tff(c_313,plain,
! [A_54,B_55,C_56] :
( ( subset_difference(A_54,B_55,C_56) = set_difference(B_55,C_56) )
| ~ element(C_56,powerset(A_54))
| ~ element(B_55,powerset(A_54)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_333,plain,
! [B_57] :
( ( subset_difference(the_carrier('#skF_4'),B_57,'#skF_5') = set_difference(B_57,'#skF_5') )
| ~ element(B_57,powerset(the_carrier('#skF_4'))) ),
inference(resolution,[status(thm)],[c_38,c_313]) ).
tff(c_345,plain,
( ( subset_difference(the_carrier('#skF_4'),cast_as_carrier_subset('#skF_4'),'#skF_5') = set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5') )
| ~ one_sorted_str('#skF_4') ),
inference(resolution,[status(thm)],[c_8,c_333]) ).
tff(c_361,plain,
subset_difference(the_carrier('#skF_4'),cast_as_carrier_subset('#skF_4'),'#skF_5') = set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_345]) ).
tff(c_445,plain,
! [A_59,B_60] :
( ( subset_difference(the_carrier(A_59),cast_as_carrier_subset(A_59),B_60) = subset_complement(the_carrier(A_59),B_60) )
| ~ element(B_60,powerset(the_carrier(A_59)))
| ~ one_sorted_str(A_59) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_460,plain,
( ( subset_difference(the_carrier('#skF_4'),cast_as_carrier_subset('#skF_4'),'#skF_5') = subset_complement(the_carrier('#skF_4'),'#skF_5') )
| ~ one_sorted_str('#skF_4') ),
inference(resolution,[status(thm)],[c_38,c_445]) ).
tff(c_473,plain,
subset_complement(the_carrier('#skF_4'),'#skF_5') = set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_361,c_460]) ).
tff(c_476,plain,
open_subset(set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_473,c_64]) ).
tff(c_676,plain,
! [B_63,A_64] :
( closed_subset(B_63,A_64)
| ~ open_subset(subset_difference(the_carrier(A_64),cast_as_carrier_subset(A_64),B_63),A_64)
| ~ element(B_63,powerset(the_carrier(A_64)))
| ~ top_str(A_64) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_685,plain,
( closed_subset('#skF_5','#skF_4')
| ~ open_subset(set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),'#skF_4')
| ~ element('#skF_5',powerset(the_carrier('#skF_4')))
| ~ top_str('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_361,c_676]) ).
tff(c_691,plain,
closed_subset('#skF_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_38,c_476,c_685]) ).
tff(c_693,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_88,c_691]) ).
tff(c_695,plain,
~ open_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4'),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_1136,plain,
~ open_subset(set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1133,c_695]) ).
tff(c_694,plain,
closed_subset('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_1337,plain,
! [A_99,B_100] :
( open_subset(subset_difference(the_carrier(A_99),cast_as_carrier_subset(A_99),B_100),A_99)
| ~ closed_subset(B_100,A_99)
| ~ element(B_100,powerset(the_carrier(A_99)))
| ~ top_str(A_99) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_1346,plain,
( open_subset(set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),'#skF_4')
| ~ closed_subset('#skF_5','#skF_4')
| ~ element('#skF_5',powerset(the_carrier('#skF_4')))
| ~ top_str('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_992,c_1337]) ).
tff(c_1352,plain,
open_subset(set_difference(cast_as_carrier_subset('#skF_4'),'#skF_5'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_38,c_694,c_1346]) ).
tff(c_1354,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1136,c_1352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU319+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 12:18:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.27/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/2.02
% 4.27/2.02 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.27/2.05
% 4.27/2.05 Inference rules
% 4.27/2.05 ----------------------
% 4.27/2.05 #Ref : 0
% 4.27/2.05 #Sup : 305
% 4.27/2.05 #Fact : 0
% 4.27/2.05 #Define : 0
% 4.27/2.05 #Split : 5
% 4.27/2.05 #Chain : 0
% 4.27/2.05 #Close : 0
% 4.27/2.05
% 4.27/2.05 Ordering : KBO
% 4.27/2.05
% 4.27/2.05 Simplification rules
% 4.27/2.05 ----------------------
% 4.27/2.05 #Subsume : 13
% 4.27/2.05 #Demod : 163
% 4.27/2.05 #Tautology : 172
% 4.27/2.05 #SimpNegUnit : 4
% 4.27/2.05 #BackRed : 4
% 4.27/2.05
% 4.27/2.05 #Partial instantiations: 0
% 4.27/2.05 #Strategies tried : 1
% 4.27/2.05
% 4.27/2.05 Timing (in seconds)
% 4.27/2.05 ----------------------
% 4.63/2.05 Preprocessing : 0.47
% 4.63/2.05 Parsing : 0.25
% 4.63/2.05 CNF conversion : 0.03
% 4.63/2.05 Main loop : 0.53
% 4.63/2.05 Inferencing : 0.21
% 4.63/2.05 Reduction : 0.16
% 4.63/2.05 Demodulation : 0.11
% 4.63/2.05 BG Simplification : 0.02
% 4.63/2.05 Subsumption : 0.10
% 4.63/2.05 Abstraction : 0.03
% 4.63/2.05 MUC search : 0.00
% 4.63/2.05 Cooper : 0.00
% 4.63/2.05 Total : 1.05
% 4.63/2.05 Index Insertion : 0.00
% 4.63/2.05 Index Deletion : 0.00
% 4.63/2.05 Index Matching : 0.00
% 4.63/2.05 BG Taut test : 0.00
%------------------------------------------------------------------------------