TSTP Solution File: SET679+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET679+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/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 : n001.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 10:56:52 EDT 2023
% Result : Theorem 4.02s 1.97s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 51 ( 9 unt; 25 typ; 0 def)
% Number of atoms : 63 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 24 ~; 20 |; 4 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 20 >; 10 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-2 aty)
% Number of variables : 32 (; 31 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ type > not_equal > member > ilf_type > relation_like > empty > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > identity_relation_of > set_type > empty_set > binary_relation_type > #skF_9 > #skF_7 > #skF_2 > #skF_10 > #skF_3 > #skF_8 > #skF_1 > #skF_5 > #skF_6 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(identity_relation_of,type,
identity_relation_of: $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(set_type,type,
set_type: $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
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(type,type,
type: ( $i * $i ) > $o ).
tff(subset_type,type,
subset_type: $i > $i ).
tff(not_equal,type,
not_equal: ( $i * $i ) > $o ).
tff(binary_relation_type,type,
binary_relation_type: $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_239,negated_conjecture,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_46) ).
tff(f_230,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
tff(f_227,axiom,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ? [C] : ilf_type(C,member_type(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
tff(f_218,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
tff(f_41,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
tff(f_91,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( not_equal(B,C)
<=> ( B != C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
tff(f_60,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(ordered_pair(C,D),identity_relation_of(B))
<=> ( member(C,B)
& ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
tff(c_102,plain,
~ empty('#skF_10'),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_96,plain,
! [B_92] : ilf_type(B_92,set_type),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_94,plain,
! [B_90] :
( ilf_type('#skF_9'(B_90),member_type(B_90))
| ~ ilf_type(B_90,set_type)
| empty(B_90) ),
inference(cnfTransformation,[status(thm)],[f_227]) ).
tff(c_105,plain,
! [B_90] :
( ilf_type('#skF_9'(B_90),member_type(B_90))
| empty(B_90) ),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_94]) ).
tff(c_92,plain,
! [B_87,C_89] :
( member(B_87,C_89)
| ~ ilf_type(B_87,member_type(C_89))
| ~ ilf_type(C_89,set_type)
| empty(C_89)
| ~ ilf_type(B_87,set_type) ),
inference(cnfTransformation,[status(thm)],[f_218]) ).
tff(c_388,plain,
! [B_150,C_151] :
( member(B_150,C_151)
| ~ ilf_type(B_150,member_type(C_151))
| empty(C_151) ),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_96,c_92]) ).
tff(c_402,plain,
! [B_90] :
( member('#skF_9'(B_90),B_90)
| empty(B_90) ),
inference(resolution,[status(thm)],[c_105,c_388]) ).
tff(c_6,plain,
! [B_4] :
( ~ member(B_4,empty_set)
| ~ ilf_type(B_4,set_type) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_177,plain,
! [B_4] : ~ member(B_4,empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_6]) ).
tff(c_34,plain,
! [B_23,C_25] :
( not_equal(B_23,C_25)
| ( C_25 = B_23 )
| ~ ilf_type(C_25,set_type)
| ~ ilf_type(B_23,set_type) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_199,plain,
! [B_102,C_103] :
( not_equal(B_102,C_103)
| ( C_103 = B_102 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_96,c_34]) ).
tff(c_98,plain,
~ not_equal(identity_relation_of('#skF_10'),empty_set),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_207,plain,
identity_relation_of('#skF_10') = empty_set,
inference(resolution,[status(thm)],[c_199,c_98]) ).
tff(c_12,plain,
! [D_11,B_5] :
( member(ordered_pair(D_11,D_11),identity_relation_of(B_5))
| ~ member(D_11,B_5)
| ~ ilf_type(D_11,set_type)
| ~ ilf_type(B_5,set_type) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_436,plain,
! [D_157,B_158] :
( member(ordered_pair(D_157,D_157),identity_relation_of(B_158))
| ~ member(D_157,B_158) ),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_96,c_12]) ).
tff(c_448,plain,
! [D_157] :
( member(ordered_pair(D_157,D_157),empty_set)
| ~ member(D_157,'#skF_10') ),
inference(superposition,[status(thm),theory(equality)],[c_207,c_436]) ).
tff(c_454,plain,
! [D_159] : ~ member(D_159,'#skF_10'),
inference(negUnitSimplification,[status(thm)],[c_177,c_448]) ).
tff(c_458,plain,
empty('#skF_10'),
inference(resolution,[status(thm)],[c_402,c_454]) ).
tff(c_474,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_102,c_458]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET679+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/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 : n001.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 17:10:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.02/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.02/1.98
% 4.02/1.98 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.14/2.00
% 4.14/2.00 Inference rules
% 4.14/2.00 ----------------------
% 4.14/2.00 #Ref : 0
% 4.14/2.00 #Sup : 55
% 4.14/2.00 #Fact : 0
% 4.14/2.00 #Define : 0
% 4.14/2.00 #Split : 0
% 4.14/2.00 #Chain : 0
% 4.14/2.00 #Close : 0
% 4.14/2.00
% 4.14/2.00 Ordering : KBO
% 4.14/2.00
% 4.14/2.01 Simplification rules
% 4.14/2.01 ----------------------
% 4.14/2.01 #Subsume : 11
% 4.14/2.01 #Demod : 85
% 4.14/2.01 #Tautology : 32
% 4.14/2.01 #SimpNegUnit : 7
% 4.14/2.01 #BackRed : 1
% 4.14/2.01
% 4.14/2.01 #Partial instantiations: 0
% 4.14/2.01 #Strategies tried : 1
% 4.14/2.01
% 4.14/2.01 Timing (in seconds)
% 4.14/2.01 ----------------------
% 4.14/2.01 Preprocessing : 0.59
% 4.14/2.01 Parsing : 0.30
% 4.14/2.01 CNF conversion : 0.05
% 4.14/2.01 Main loop : 0.34
% 4.14/2.01 Inferencing : 0.13
% 4.14/2.01 Reduction : 0.11
% 4.14/2.01 Demodulation : 0.07
% 4.14/2.01 BG Simplification : 0.03
% 4.14/2.01 Subsumption : 0.06
% 4.14/2.01 Abstraction : 0.01
% 4.14/2.01 MUC search : 0.00
% 4.14/2.01 Cooper : 0.00
% 4.14/2.01 Total : 0.98
% 4.14/2.01 Index Insertion : 0.00
% 4.14/2.01 Index Deletion : 0.00
% 4.14/2.01 Index Matching : 0.00
% 4.14/2.01 BG Taut test : 0.00
%------------------------------------------------------------------------------