TSTP Solution File: SET923+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET923+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/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 10:57:20 EDT 2023
% Result : Theorem 2.86s 1.74s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of formulae : 20 ( 4 unt; 9 typ; 0 def)
% Number of atoms : 22 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 20 ( 9 ~; 7 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 12 (; 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > set_difference > #nlpp > singleton > empty_set > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_54,negated_conjecture,
~ ! [A,B] :
~ ( ( set_difference(A,singleton(B)) = empty_set )
& ( A != empty_set )
& ( A != singleton(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
tff(f_44,axiom,
! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
tff(f_33,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( ( A = empty_set )
| ( A = singleton(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
tff(c_22,plain,
empty_set != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_20,plain,
singleton('#skF_4') != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_24,plain,
set_difference('#skF_3',singleton('#skF_4')) = empty_set,
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_16,plain,
! [A_5,B_6] :
( subset(A_5,B_6)
| ( set_difference(A_5,B_6) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_60,plain,
! [B_15,A_16] :
( ( singleton(B_15) = A_16 )
| ( empty_set = A_16 )
| ~ subset(A_16,singleton(B_15)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_77,plain,
! [B_17,A_18] :
( ( singleton(B_17) = A_18 )
| ( empty_set = A_18 )
| ( set_difference(A_18,singleton(B_17)) != empty_set ) ),
inference(resolution,[status(thm)],[c_16,c_60]) ).
tff(c_87,plain,
( ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_77]) ).
tff(c_95,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_20,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET923+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/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
% 0.18/0.35 % Computer : n007.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 16:51:53 EDT 2023
% 0.18/0.35 % CPUTime :
% 2.86/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/1.74
% 2.86/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.86/1.77
% 2.86/1.77 Inference rules
% 2.86/1.77 ----------------------
% 2.86/1.77 #Ref : 0
% 2.86/1.77 #Sup : 15
% 2.86/1.77 #Fact : 0
% 2.86/1.77 #Define : 0
% 2.86/1.77 #Split : 0
% 2.86/1.77 #Chain : 0
% 2.86/1.77 #Close : 0
% 2.86/1.77
% 2.86/1.77 Ordering : KBO
% 2.86/1.77
% 2.86/1.77 Simplification rules
% 2.86/1.77 ----------------------
% 2.86/1.77 #Subsume : 0
% 2.86/1.77 #Demod : 1
% 2.86/1.77 #Tautology : 12
% 2.86/1.77 #SimpNegUnit : 1
% 2.86/1.77 #BackRed : 0
% 2.86/1.77
% 2.86/1.77 #Partial instantiations: 0
% 2.86/1.77 #Strategies tried : 1
% 2.86/1.77
% 2.86/1.77 Timing (in seconds)
% 2.86/1.77 ----------------------
% 2.86/1.77 Preprocessing : 0.46
% 2.86/1.77 Parsing : 0.23
% 2.86/1.77 CNF conversion : 0.03
% 2.86/1.77 Main loop : 0.17
% 2.86/1.77 Inferencing : 0.06
% 2.86/1.77 Reduction : 0.04
% 2.86/1.77 Demodulation : 0.03
% 2.86/1.77 BG Simplification : 0.01
% 2.86/1.77 Subsumption : 0.04
% 2.86/1.77 Abstraction : 0.01
% 2.86/1.77 MUC search : 0.00
% 2.86/1.77 Cooper : 0.00
% 2.86/1.77 Total : 0.67
% 2.86/1.77 Index Insertion : 0.00
% 2.86/1.77 Index Deletion : 0.00
% 2.86/1.77 Index Matching : 0.00
% 2.86/1.77 BG Taut test : 0.00
%------------------------------------------------------------------------------