TSTP Solution File: SET977+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET977+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n017.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 10:57:27 EDT 2023
% Result : Theorem 3.49s 2.01s
% Output : CNFRefutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 32 ( 10 unt; 12 typ; 0 def)
% Number of atoms : 33 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 6 |; 3 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 24 (; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > empty_set > #skF_1 > #skF_5 > #skF_2 > #skF_3 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_72,negated_conjecture,
~ ! [A,B] :
( ( A != empty_set )
=> ( ( cartesian_product2(singleton(B),A) != empty_set )
& ( cartesian_product2(A,singleton(B)) != empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
tff(f_39,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_56,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( ( A = C )
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
tff(f_62,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( in(A,C)
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
tff(c_34,plain,
empty_set != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_8,plain,
! [A_5] :
( ( empty_set = A_5 )
| in('#skF_1'(A_5),A_5) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_6,plain,
! [B_8] : ~ in(B_8,empty_set),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_32,plain,
( ( cartesian_product2('#skF_4',singleton('#skF_5')) = empty_set )
| ( cartesian_product2(singleton('#skF_5'),'#skF_4') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_81,plain,
cartesian_product2(singleton('#skF_5'),'#skF_4') = empty_set,
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_267,plain,
! [C_46,B_47,D_48] :
( in(ordered_pair(C_46,B_47),cartesian_product2(singleton(C_46),D_48))
| ~ in(B_47,D_48) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_279,plain,
! [B_47] :
( in(ordered_pair('#skF_5',B_47),empty_set)
| ~ in(B_47,'#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_267]) ).
tff(c_285,plain,
! [B_49] : ~ in(B_49,'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_6,c_279]) ).
tff(c_289,plain,
empty_set = '#skF_4',
inference(resolution,[status(thm)],[c_8,c_285]) ).
tff(c_293,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_289]) ).
tff(c_294,plain,
cartesian_product2('#skF_4',singleton('#skF_5')) = empty_set,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_484,plain,
! [A_71,D_72,C_73] :
( in(ordered_pair(A_71,D_72),cartesian_product2(C_73,singleton(D_72)))
| ~ in(A_71,C_73) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_500,plain,
! [A_71] :
( in(ordered_pair(A_71,'#skF_5'),empty_set)
| ~ in(A_71,'#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_294,c_484]) ).
tff(c_507,plain,
! [A_74] : ~ in(A_74,'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_6,c_500]) ).
tff(c_511,plain,
empty_set = '#skF_4',
inference(resolution,[status(thm)],[c_8,c_507]) ).
tff(c_515,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET977+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 15:42:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.49/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.49/2.01
% 3.49/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.49/2.03
% 3.49/2.03 Inference rules
% 3.49/2.03 ----------------------
% 3.49/2.03 #Ref : 0
% 3.49/2.03 #Sup : 123
% 3.49/2.03 #Fact : 0
% 3.49/2.03 #Define : 0
% 3.49/2.03 #Split : 1
% 3.49/2.03 #Chain : 0
% 3.49/2.03 #Close : 0
% 3.49/2.03
% 3.49/2.03 Ordering : KBO
% 3.49/2.03
% 3.49/2.03 Simplification rules
% 3.49/2.03 ----------------------
% 3.49/2.03 #Subsume : 2
% 3.49/2.03 #Demod : 24
% 3.49/2.03 #Tautology : 63
% 3.49/2.03 #SimpNegUnit : 4
% 3.49/2.03 #BackRed : 0
% 3.49/2.03
% 3.49/2.03 #Partial instantiations: 0
% 3.49/2.03 #Strategies tried : 1
% 3.49/2.03
% 3.49/2.03 Timing (in seconds)
% 3.49/2.03 ----------------------
% 3.49/2.04 Preprocessing : 0.48
% 3.49/2.04 Parsing : 0.26
% 3.49/2.04 CNF conversion : 0.03
% 3.49/2.04 Main loop : 0.36
% 3.49/2.04 Inferencing : 0.13
% 3.49/2.04 Reduction : 0.11
% 3.49/2.04 Demodulation : 0.08
% 3.49/2.04 BG Simplification : 0.02
% 3.49/2.04 Subsumption : 0.07
% 3.49/2.04 Abstraction : 0.02
% 3.49/2.04 MUC search : 0.00
% 3.49/2.04 Cooper : 0.00
% 3.49/2.04 Total : 0.89
% 3.49/2.04 Index Insertion : 0.00
% 3.49/2.04 Index Deletion : 0.00
% 3.49/2.04 Index Matching : 0.00
% 3.49/2.04 BG Taut test : 0.00
%------------------------------------------------------------------------------