TSTP Solution File: SEU325+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU325+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 : n007.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 9.67s 3.21s
% Output : CNFRefutation 9.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 48
% Syntax : Number of formulae : 86 ( 23 unt; 36 typ; 0 def)
% Number of atoms : 100 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 39 ~; 26 |; 12 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 30 >; 10 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 53 (; 50 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > is_a_cover_of_carrier > in > element > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > one_sorted_str > natural > empty_carrier > empty > union_of_subsets > #nlpp > union > the_carrier > powerset > cast_as_carrier_subset > empty_set > #skF_9 > #skF_8 > #skF_4 > #skF_7 > #skF_3 > #skF_10 > #skF_5 > #skF_13 > #skF_11 > #skF_2 > #skF_1 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff(union,type,
union: $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_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $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(is_a_cover_of_carrier,type,
is_a_cover_of_carrier: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff(cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
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(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $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(natural,type,
natural: $i > $o ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_206,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_326,negated_conjecture,
~ ! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( is_a_cover_of_carrier(A,B)
& ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).
tff(f_173,axiom,
! [A] :
( one_sorted_str(A)
=> ( cast_as_carrier_subset(A) = the_carrier(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
tff(f_214,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
tff(f_295,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_263,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
tff(f_330,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_283,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_192,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( is_a_cover_of_carrier(A,B)
<=> ( cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
tff(f_183,axiom,
! [A,B] :
( ( B = union(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
tff(f_312,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
tff(f_236,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
tff(c_124,plain,
! [A_64] : element('#skF_6'(A_64),A_64),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_196,plain,
~ empty_carrier('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_194,plain,
one_sorted_str('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_312,plain,
! [A_120] :
( ( the_carrier(A_120) = cast_as_carrier_subset(A_120) )
| ~ one_sorted_str(A_120) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_324,plain,
the_carrier('#skF_12') = cast_as_carrier_subset('#skF_12'),
inference(resolution,[status(thm)],[c_194,c_312]) ).
tff(c_424,plain,
! [A_147] :
( ~ empty(the_carrier(A_147))
| ~ one_sorted_str(A_147)
| empty_carrier(A_147) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_427,plain,
( ~ empty(cast_as_carrier_subset('#skF_12'))
| ~ one_sorted_str('#skF_12')
| empty_carrier('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_324,c_424]) ).
tff(c_435,plain,
( ~ empty(cast_as_carrier_subset('#skF_12'))
| empty_carrier('#skF_12') ),
inference(demodulation,[status(thm),theory(equality)],[c_194,c_427]) ).
tff(c_436,plain,
~ empty(cast_as_carrier_subset('#skF_12')),
inference(negUnitSimplification,[status(thm)],[c_196,c_435]) ).
tff(c_178,plain,
! [A_81,B_82] :
( in(A_81,B_82)
| empty(B_82)
| ~ element(A_81,B_82) ),
inference(cnfTransformation,[status(thm)],[f_295]) ).
tff(c_190,plain,
is_a_cover_of_carrier('#skF_12','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_160,plain,
! [A_71] : empty('#skF_9'(A_71)),
inference(cnfTransformation,[status(thm)],[f_263]) ).
tff(c_188,plain,
empty_set = '#skF_13',
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_198,plain,
! [A_92] :
( ( empty_set = A_92 )
| ~ empty(A_92) ),
inference(cnfTransformation,[status(thm)],[f_330]) ).
tff(c_228,plain,
! [A_101] :
( ( A_101 = '#skF_13' )
| ~ empty(A_101) ),
inference(demodulation,[status(thm),theory(equality)],[c_188,c_198]) ).
tff(c_235,plain,
! [A_71] : ( '#skF_9'(A_71) = '#skF_13' ),
inference(resolution,[status(thm)],[c_160,c_228]) ).
tff(c_162,plain,
! [A_71] : element('#skF_9'(A_71),powerset(A_71)),
inference(cnfTransformation,[status(thm)],[f_263]) ).
tff(c_302,plain,
! [A_71] : element('#skF_13',powerset(A_71)),
inference(demodulation,[status(thm),theory(equality)],[c_235,c_162]) ).
tff(c_2210,plain,
! [A_297,B_298] :
( ( union_of_subsets(A_297,B_298) = union(B_298) )
| ~ element(B_298,powerset(powerset(A_297))) ),
inference(cnfTransformation,[status(thm)],[f_283]) ).
tff(c_2231,plain,
! [A_297] : ( union_of_subsets(A_297,'#skF_13') = union('#skF_13') ),
inference(resolution,[status(thm)],[c_302,c_2210]) ).
tff(c_7181,plain,
! [A_445,B_446] :
( ( union_of_subsets(the_carrier(A_445),B_446) = cast_as_carrier_subset(A_445) )
| ~ is_a_cover_of_carrier(A_445,B_446)
| ~ element(B_446,powerset(powerset(the_carrier(A_445))))
| ~ one_sorted_str(A_445) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_7200,plain,
! [B_446] :
( ( union_of_subsets(the_carrier('#skF_12'),B_446) = cast_as_carrier_subset('#skF_12') )
| ~ is_a_cover_of_carrier('#skF_12',B_446)
| ~ element(B_446,powerset(powerset(cast_as_carrier_subset('#skF_12'))))
| ~ one_sorted_str('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_324,c_7181]) ).
tff(c_7788,plain,
! [B_463] :
( ( union_of_subsets(cast_as_carrier_subset('#skF_12'),B_463) = cast_as_carrier_subset('#skF_12') )
| ~ is_a_cover_of_carrier('#skF_12',B_463)
| ~ element(B_463,powerset(powerset(cast_as_carrier_subset('#skF_12')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_194,c_324,c_7200]) ).
tff(c_7812,plain,
( ( union_of_subsets(cast_as_carrier_subset('#skF_12'),'#skF_13') = cast_as_carrier_subset('#skF_12') )
| ~ is_a_cover_of_carrier('#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_302,c_7788]) ).
tff(c_7827,plain,
union('#skF_13') = cast_as_carrier_subset('#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_190,c_2231,c_7812]) ).
tff(c_5725,plain,
! [A_394,C_395] :
( in('#skF_4'(A_394,union(A_394),C_395),A_394)
| ~ in(C_395,union(A_394)) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_2080,plain,
! [C_280,B_281,A_282] :
( ~ empty(C_280)
| ~ element(B_281,powerset(C_280))
| ~ in(A_282,B_281) ),
inference(cnfTransformation,[status(thm)],[f_312]) ).
tff(c_2104,plain,
! [A_71,A_282] :
( ~ empty(A_71)
| ~ in(A_282,'#skF_13') ),
inference(resolution,[status(thm)],[c_302,c_2080]) ).
tff(c_2106,plain,
! [A_282] : ~ in(A_282,'#skF_13'),
inference(splitLeft,[status(thm)],[c_2104]) ).
tff(c_5758,plain,
! [C_395] : ~ in(C_395,union('#skF_13')),
inference(resolution,[status(thm)],[c_5725,c_2106]) ).
tff(c_7874,plain,
! [C_464] : ~ in(C_464,cast_as_carrier_subset('#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_7827,c_5758]) ).
tff(c_7894,plain,
! [A_81] :
( empty(cast_as_carrier_subset('#skF_12'))
| ~ element(A_81,cast_as_carrier_subset('#skF_12')) ),
inference(resolution,[status(thm)],[c_178,c_7874]) ).
tff(c_8000,plain,
! [A_467] : ~ element(A_467,cast_as_carrier_subset('#skF_12')),
inference(negUnitSimplification,[status(thm)],[c_436,c_7894]) ).
tff(c_8005,plain,
$false,
inference(resolution,[status(thm)],[c_124,c_8000]) ).
tff(c_8006,plain,
! [A_71] : ~ empty(A_71),
inference(splitRight,[status(thm)],[c_2104]) ).
tff(c_142,plain,
empty(empty_set),
inference(cnfTransformation,[status(thm)],[f_236]) ).
tff(c_204,plain,
empty('#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_188,c_142]) ).
tff(c_8026,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8006,c_204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU325+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
% 0.16/0.35 % Computer : n007.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Aug 3 11:31:38 EDT 2023
% 0.16/0.35 % CPUTime :
% 9.67/3.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.67/3.21
% 9.67/3.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.67/3.24
% 9.67/3.24 Inference rules
% 9.67/3.24 ----------------------
% 9.67/3.24 #Ref : 0
% 9.67/3.24 #Sup : 1632
% 9.67/3.24 #Fact : 0
% 9.67/3.24 #Define : 0
% 9.67/3.24 #Split : 53
% 9.67/3.24 #Chain : 0
% 9.67/3.24 #Close : 0
% 9.67/3.24
% 9.67/3.24 Ordering : KBO
% 9.67/3.24
% 9.67/3.24 Simplification rules
% 9.67/3.24 ----------------------
% 9.67/3.24 #Subsume : 1163
% 9.67/3.24 #Demod : 598
% 9.67/3.24 #Tautology : 343
% 9.67/3.24 #SimpNegUnit : 244
% 9.67/3.24 #BackRed : 198
% 9.67/3.24
% 9.67/3.24 #Partial instantiations: 0
% 9.67/3.24 #Strategies tried : 1
% 9.67/3.24
% 9.67/3.24 Timing (in seconds)
% 9.67/3.24 ----------------------
% 9.67/3.25 Preprocessing : 0.65
% 9.67/3.25 Parsing : 0.33
% 9.67/3.25 CNF conversion : 0.06
% 9.67/3.25 Main loop : 1.52
% 9.67/3.25 Inferencing : 0.48
% 9.67/3.25 Reduction : 0.50
% 9.67/3.25 Demodulation : 0.32
% 9.67/3.25 BG Simplification : 0.05
% 9.67/3.25 Subsumption : 0.36
% 9.67/3.25 Abstraction : 0.04
% 9.67/3.25 MUC search : 0.00
% 9.67/3.25 Cooper : 0.00
% 9.67/3.25 Total : 2.23
% 9.67/3.25 Index Insertion : 0.00
% 9.67/3.25 Index Deletion : 0.00
% 9.67/3.25 Index Matching : 0.00
% 9.67/3.25 BG Taut test : 0.00
%------------------------------------------------------------------------------