TSTP Solution File: SEU327+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:58:26 EDT 2023
% Result : Theorem 24.47s 12.40s
% Output : CNFRefutation 24.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 77 ( 21 unt; 31 typ; 0 def)
% Number of atoms : 78 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 24 ~; 20 |; 1 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 27 >; 10 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 52 (; 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > natural > empty > subset_difference > union_of_subsets > subset_complement > set_difference > meet_of_subsets > complements_of_subsets > #nlpp > union > set_meet > powerset > cast_to_subset > empty_set > #skF_4 > #skF_1 > #skF_5 > #skF_6 > #skF_2 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(complements_of_subsets,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(cast_to_subset,type,
cast_to_subset: $i > $i ).
tff(union,type,
union: $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(v1_int_1,type,
v1_int_1: $i > $o ).
tff(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff(empty,type,
empty: $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(set_meet,type,
set_meet: $i > $i ).
tff(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(v1_rat_1,type,
v1_rat_1: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(natural,type,
natural: $i > $o ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff(f_316,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ( B != empty_set )
=> ( meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).
tff(f_200,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
tff(f_300,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( meet_of_subsets(A,B) = set_meet(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
tff(f_296,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( union_of_subsets(A,B) = union(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
tff(f_186,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
tff(f_175,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,B) = set_difference(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
tff(f_171,axiom,
! [A] : ( cast_to_subset(A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
tff(f_339,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ( B != empty_set )
=> ( subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
tff(f_332,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_178,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
tff(f_306,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(c_192,plain,
element('#skF_6',powerset(powerset('#skF_5'))),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_4353,plain,
! [A_376,B_377] :
( element(complements_of_subsets(A_376,B_377),powerset(powerset(A_376)))
| ~ element(B_377,powerset(powerset(A_376))) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_182,plain,
! [A_76,B_77] :
( ( meet_of_subsets(A_76,B_77) = set_meet(B_77) )
| ~ element(B_77,powerset(powerset(A_76))) ),
inference(cnfTransformation,[status(thm)],[f_300]) ).
tff(c_21072,plain,
! [A_773,B_774] :
( ( meet_of_subsets(A_773,complements_of_subsets(A_773,B_774)) = set_meet(complements_of_subsets(A_773,B_774)) )
| ~ element(B_774,powerset(powerset(A_773))) ),
inference(resolution,[status(thm)],[c_4353,c_182]) ).
tff(c_21146,plain,
meet_of_subsets('#skF_5',complements_of_subsets('#skF_5','#skF_6')) = set_meet(complements_of_subsets('#skF_5','#skF_6')),
inference(resolution,[status(thm)],[c_192,c_21072]) ).
tff(c_2464,plain,
! [A_348,B_349] :
( ( union_of_subsets(A_348,B_349) = union(B_349) )
| ~ element(B_349,powerset(powerset(A_348))) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_2495,plain,
union_of_subsets('#skF_5','#skF_6') = union('#skF_6'),
inference(resolution,[status(thm)],[c_192,c_2464]) ).
tff(c_3530,plain,
! [A_367,B_368] :
( element(union_of_subsets(A_367,B_368),powerset(A_367))
| ~ element(B_368,powerset(powerset(A_367))) ),
inference(cnfTransformation,[status(thm)],[f_186]) ).
tff(c_3652,plain,
( element(union('#skF_6'),powerset('#skF_5'))
| ~ element('#skF_6',powerset(powerset('#skF_5'))) ),
inference(superposition,[status(thm),theory(equality)],[c_2495,c_3530]) ).
tff(c_3696,plain,
element(union('#skF_6'),powerset('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_192,c_3652]) ).
tff(c_84,plain,
! [A_39,B_40] :
( ( subset_complement(A_39,B_40) = set_difference(A_39,B_40) )
| ~ element(B_40,powerset(A_39)) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_3799,plain,
subset_complement('#skF_5',union('#skF_6')) = set_difference('#skF_5',union('#skF_6')),
inference(resolution,[status(thm)],[c_3696,c_84]) ).
tff(c_188,plain,
subset_complement('#skF_5',union_of_subsets('#skF_5','#skF_6')) != meet_of_subsets('#skF_5',complements_of_subsets('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_2496,plain,
subset_complement('#skF_5',union('#skF_6')) != meet_of_subsets('#skF_5',complements_of_subsets('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_2495,c_188]) ).
tff(c_18890,plain,
set_difference('#skF_5',union('#skF_6')) != meet_of_subsets('#skF_5',complements_of_subsets('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_3799,c_2496]) ).
tff(c_21148,plain,
set_difference('#skF_5',union('#skF_6')) != set_meet(complements_of_subsets('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_21146,c_18890]) ).
tff(c_190,plain,
empty_set != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_82,plain,
! [A_38] : ( cast_to_subset(A_38) = A_38 ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_204,plain,
! [A_90,B_91] :
( ( subset_difference(A_90,cast_to_subset(A_90),union_of_subsets(A_90,B_91)) = meet_of_subsets(A_90,complements_of_subsets(A_90,B_91)) )
| ( empty_set = B_91 )
| ~ element(B_91,powerset(powerset(A_90))) ),
inference(cnfTransformation,[status(thm)],[f_339]) ).
tff(c_5032,plain,
! [A_385,B_386] :
( ( subset_difference(A_385,A_385,union_of_subsets(A_385,B_386)) = meet_of_subsets(A_385,complements_of_subsets(A_385,B_386)) )
| ( empty_set = B_386 )
| ~ element(B_386,powerset(powerset(A_385))) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_204]) ).
tff(c_5069,plain,
( ( subset_difference('#skF_5','#skF_5',union_of_subsets('#skF_5','#skF_6')) = meet_of_subsets('#skF_5',complements_of_subsets('#skF_5','#skF_6')) )
| ( empty_set = '#skF_6' ) ),
inference(resolution,[status(thm)],[c_192,c_5032]) ).
tff(c_5088,plain,
( ( subset_difference('#skF_5','#skF_5',union('#skF_6')) = meet_of_subsets('#skF_5',complements_of_subsets('#skF_5','#skF_6')) )
| ( empty_set = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2495,c_5069]) ).
tff(c_5089,plain,
subset_difference('#skF_5','#skF_5',union('#skF_6')) = meet_of_subsets('#skF_5',complements_of_subsets('#skF_5','#skF_6')),
inference(negUnitSimplification,[status(thm)],[c_190,c_5088]) ).
tff(c_21151,plain,
subset_difference('#skF_5','#skF_5',union('#skF_6')) = set_meet(complements_of_subsets('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_21146,c_5089]) ).
tff(c_200,plain,
! [A_88,B_89] :
( subset(A_88,B_89)
| ~ element(A_88,powerset(B_89)) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_3819,plain,
subset(union('#skF_6'),'#skF_5'),
inference(resolution,[status(thm)],[c_3696,c_200]) ).
tff(c_92,plain,
! [A_41] : element(cast_to_subset(A_41),powerset(A_41)),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_217,plain,
! [A_41] : element(A_41,powerset(A_41)),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_92]) ).
tff(c_202,plain,
! [A_88,B_89] :
( element(A_88,powerset(B_89))
| ~ subset(A_88,B_89) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_4706,plain,
! [A_378,B_379,C_380] :
( ( subset_difference(A_378,B_379,C_380) = set_difference(B_379,C_380) )
| ~ element(C_380,powerset(A_378))
| ~ element(B_379,powerset(A_378)) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_22345,plain,
! [B_787,B_788,A_789] :
( ( subset_difference(B_787,B_788,A_789) = set_difference(B_788,A_789) )
| ~ element(B_788,powerset(B_787))
| ~ subset(A_789,B_787) ),
inference(resolution,[status(thm)],[c_202,c_4706]) ).
tff(c_56979,plain,
! [A_1288,A_1289] :
( ( subset_difference(A_1288,A_1288,A_1289) = set_difference(A_1288,A_1289) )
| ~ subset(A_1289,A_1288) ),
inference(resolution,[status(thm)],[c_217,c_22345]) ).
tff(c_57077,plain,
subset_difference('#skF_5','#skF_5',union('#skF_6')) = set_difference('#skF_5',union('#skF_6')),
inference(resolution,[status(thm)],[c_3819,c_56979]) ).
tff(c_57146,plain,
set_difference('#skF_5',union('#skF_6')) = set_meet(complements_of_subsets('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_21151,c_57077]) ).
tff(c_57148,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21148,c_57146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.18/0.35 % Computer : n014.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 11:39:48 EDT 2023
% 0.18/0.35 % CPUTime :
% 24.47/12.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.47/12.40
% 24.47/12.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.54/12.43
% 24.54/12.43 Inference rules
% 24.54/12.43 ----------------------
% 24.54/12.43 #Ref : 0
% 24.54/12.43 #Sup : 12887
% 24.54/12.43 #Fact : 0
% 24.54/12.43 #Define : 0
% 24.54/12.43 #Split : 49
% 24.54/12.43 #Chain : 0
% 24.54/12.43 #Close : 0
% 24.54/12.43
% 24.54/12.43 Ordering : KBO
% 24.54/12.43
% 24.54/12.43 Simplification rules
% 24.54/12.43 ----------------------
% 24.54/12.43 #Subsume : 6528
% 24.54/12.43 #Demod : 7685
% 24.54/12.43 #Tautology : 2278
% 24.54/12.43 #SimpNegUnit : 849
% 24.54/12.43 #BackRed : 538
% 24.54/12.43
% 24.54/12.43 #Partial instantiations: 0
% 24.54/12.43 #Strategies tried : 1
% 24.54/12.43
% 24.54/12.43 Timing (in seconds)
% 24.54/12.43 ----------------------
% 24.54/12.44 Preprocessing : 0.65
% 24.54/12.44 Parsing : 0.34
% 24.54/12.44 CNF conversion : 0.05
% 24.54/12.44 Main loop : 10.72
% 24.54/12.44 Inferencing : 2.28
% 24.54/12.44 Reduction : 4.50
% 24.54/12.44 Demodulation : 3.50
% 24.54/12.44 BG Simplification : 0.13
% 24.54/12.44 Subsumption : 3.20
% 24.54/12.44 Abstraction : 0.18
% 24.54/12.44 MUC search : 0.00
% 24.54/12.44 Cooper : 0.00
% 24.54/12.44 Total : 11.43
% 24.54/12.44 Index Insertion : 0.00
% 24.54/12.44 Index Deletion : 0.00
% 24.54/12.44 Index Matching : 0.00
% 24.54/12.44 BG Taut test : 0.00
%------------------------------------------------------------------------------