TSTP Solution File: SET663+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET663+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/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 10:56:50 EDT 2023
% Result : Theorem 4.50s 2.16s
% Output : CNFRefutation 4.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 42
% Syntax : Number of formulae : 64 ( 9 unt; 34 typ; 0 def)
% Number of atoms : 78 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 74 ( 26 ~; 25 |; 3 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 27 >; 18 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 7 con; 0-3 aty)
% Number of variables : 45 (; 45 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ type > subset > member > ilf_type > relation_like > empty > range > domain > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > domain_of > set_type > empty_set > binary_relation_type > #skF_9 > #skF_7 > #skF_5 > #skF_11 > #skF_6 > #skF_15 > #skF_3 > #skF_14 > #skF_13 > #skF_10 > #skF_8 > #skF_4 > #skF_2 > #skF_12 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(type,type,
type: ( $i * $i ) > $o ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(binary_relation_type,type,
binary_relation_type: $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_350,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ilf_type(D,relation_type(empty_set,C))
=> ( D = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_26) ).
tff(f_336,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
tff(f_55,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
tff(f_33,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( subset(B,empty_set)
=> ( B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(f_81,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
tff(f_289,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).
tff(f_143,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
tff(f_42,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ( ( ( domain_of(B) = empty_set )
| ( range_of(B) = empty_set ) )
=> ( B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(c_128,plain,
empty_set != '#skF_15',
inference(cnfTransformation,[status(thm)],[f_350]) ).
tff(c_130,plain,
ilf_type('#skF_15',relation_type(empty_set,'#skF_14')),
inference(cnfTransformation,[status(thm)],[f_350]) ).
tff(c_126,plain,
! [B_164] : ilf_type(B_164,set_type),
inference(cnfTransformation,[status(thm)],[f_336]) ).
tff(c_10,plain,
! [D_9,B_3,C_7] :
( subset(domain_of(D_9),B_3)
| ~ ilf_type(D_9,relation_type(B_3,C_7))
| ~ ilf_type(C_7,set_type)
| ~ ilf_type(B_3,set_type) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_383,plain,
! [D_208,B_209,C_210] :
( subset(domain_of(D_208),B_209)
| ~ ilf_type(D_208,relation_type(B_209,C_210)) ),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_126,c_10]) ).
tff(c_391,plain,
subset(domain_of('#skF_15'),empty_set),
inference(resolution,[status(thm)],[c_130,c_383]) ).
tff(c_2,plain,
! [B_1] :
( ( empty_set = B_1 )
| ~ subset(B_1,empty_set)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_228,plain,
! [B_1] :
( ( empty_set = B_1 )
| ~ subset(B_1,empty_set) ),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_2]) ).
tff(c_396,plain,
domain_of('#skF_15') = empty_set,
inference(resolution,[status(thm)],[c_391,c_228]) ).
tff(c_18,plain,
! [E_21,B_11,C_17] :
( ilf_type(E_21,subset_type(cross_product(B_11,C_17)))
| ~ ilf_type(E_21,relation_type(B_11,C_17))
| ~ ilf_type(C_17,set_type)
| ~ ilf_type(B_11,set_type) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_895,plain,
! [E_277,B_278,C_279] :
( ilf_type(E_277,subset_type(cross_product(B_278,C_279)))
| ~ ilf_type(E_277,relation_type(B_278,C_279)) ),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_126,c_18]) ).
tff(c_116,plain,
! [D_135,B_129,C_133] :
( relation_like(D_135)
| ~ ilf_type(D_135,subset_type(cross_product(B_129,C_133)))
| ~ ilf_type(C_133,set_type)
| ~ ilf_type(B_129,set_type) ),
inference(cnfTransformation,[status(thm)],[f_289]) ).
tff(c_148,plain,
! [D_135,B_129,C_133] :
( relation_like(D_135)
| ~ ilf_type(D_135,subset_type(cross_product(B_129,C_133))) ),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_126,c_116]) ).
tff(c_905,plain,
! [E_280,B_281,C_282] :
( relation_like(E_280)
| ~ ilf_type(E_280,relation_type(B_281,C_282)) ),
inference(resolution,[status(thm)],[c_895,c_148]) ).
tff(c_916,plain,
relation_like('#skF_15'),
inference(resolution,[status(thm)],[c_130,c_905]) ).
tff(c_48,plain,
! [B_61] :
( ilf_type(B_61,binary_relation_type)
| ~ relation_like(B_61)
| ~ ilf_type(B_61,set_type) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_206,plain,
! [B_61] :
( ilf_type(B_61,binary_relation_type)
| ~ relation_like(B_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_48]) ).
tff(c_263,plain,
! [B_181] :
( ( domain_of(B_181) != empty_set )
| ( empty_set = B_181 )
| ~ ilf_type(B_181,binary_relation_type) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_270,plain,
! [B_61] :
( ( domain_of(B_61) != empty_set )
| ( empty_set = B_61 )
| ~ relation_like(B_61) ),
inference(resolution,[status(thm)],[c_206,c_263]) ).
tff(c_923,plain,
( ( domain_of('#skF_15') != empty_set )
| ( empty_set = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_916,c_270]) ).
tff(c_929,plain,
empty_set = '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_923]) ).
tff(c_931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_128,c_929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET663+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 16:51:38 EDT 2023
% 0.15/0.37 % CPUTime :
% 4.50/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.88/2.17
% 4.88/2.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.88/2.20
% 4.88/2.20 Inference rules
% 4.88/2.20 ----------------------
% 4.88/2.20 #Ref : 0
% 4.88/2.20 #Sup : 147
% 4.88/2.20 #Fact : 2
% 4.88/2.20 #Define : 0
% 4.88/2.20 #Split : 2
% 4.88/2.20 #Chain : 0
% 4.88/2.20 #Close : 0
% 4.88/2.20
% 4.88/2.20 Ordering : KBO
% 4.88/2.20
% 4.88/2.20 Simplification rules
% 4.88/2.20 ----------------------
% 4.88/2.20 #Subsume : 15
% 4.88/2.20 #Demod : 110
% 4.88/2.20 #Tautology : 66
% 4.88/2.20 #SimpNegUnit : 7
% 4.88/2.20 #BackRed : 1
% 4.88/2.20
% 4.88/2.20 #Partial instantiations: 0
% 4.88/2.20 #Strategies tried : 1
% 4.88/2.20
% 4.88/2.20 Timing (in seconds)
% 4.88/2.20 ----------------------
% 4.88/2.20 Preprocessing : 0.66
% 4.88/2.20 Parsing : 0.33
% 4.88/2.20 CNF conversion : 0.06
% 4.88/2.20 Main loop : 0.46
% 4.88/2.20 Inferencing : 0.16
% 4.88/2.20 Reduction : 0.15
% 4.88/2.20 Demodulation : 0.11
% 4.88/2.20 BG Simplification : 0.04
% 4.88/2.20 Subsumption : 0.08
% 4.88/2.20 Abstraction : 0.02
% 4.88/2.20 MUC search : 0.00
% 4.88/2.20 Cooper : 0.00
% 4.88/2.20 Total : 1.17
% 4.88/2.20 Index Insertion : 0.00
% 4.88/2.20 Index Deletion : 0.00
% 4.88/2.20 Index Matching : 0.00
% 4.88/2.20 BG Taut test : 0.00
%------------------------------------------------------------------------------