TSTP Solution File: SET880+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET880+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 : n021.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 10:57:16 EDT 2023
% Result : Theorem 2.68s 1.64s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 21 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 16 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 2 |; 0 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 11 (; 11 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > empty_set > #skF_5 > #skF_6 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $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('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_53,negated_conjecture,
~ ! [A,B] :
( ( set_difference(singleton(A),singleton(B)) = empty_set )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
tff(f_43,axiom,
! [A,B] :
( ( set_difference(singleton(A),B) = empty_set )
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
tff(f_38,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_26,plain,
'#skF_5' != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_28,plain,
set_difference(singleton('#skF_5'),singleton('#skF_6')) = empty_set,
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_45,plain,
! [A_16,B_17] :
( in(A_16,B_17)
| ( set_difference(singleton(A_16),B_17) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_49,plain,
in('#skF_5',singleton('#skF_6')),
inference(superposition,[status(thm),theory(equality)],[c_28,c_45]) ).
tff(c_4,plain,
! [C_7,A_3] :
( ( C_7 = A_3 )
| ~ in(C_7,singleton(A_3)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_52,plain,
'#skF_5' = '#skF_6',
inference(resolution,[status(thm)],[c_49,c_4]) ).
tff(c_58,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 16:22:06 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.68/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.68/1.64
% 2.68/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.68/1.66
% 2.68/1.66 Inference rules
% 2.68/1.66 ----------------------
% 2.68/1.66 #Ref : 0
% 2.68/1.66 #Sup : 7
% 2.68/1.66 #Fact : 0
% 2.68/1.66 #Define : 0
% 2.68/1.66 #Split : 0
% 2.68/1.66 #Chain : 0
% 2.68/1.66 #Close : 0
% 2.68/1.66
% 2.68/1.66 Ordering : KBO
% 2.68/1.66
% 2.68/1.66 Simplification rules
% 2.68/1.66 ----------------------
% 2.68/1.66 #Subsume : 0
% 2.68/1.66 #Demod : 0
% 2.68/1.66 #Tautology : 3
% 2.68/1.66 #SimpNegUnit : 1
% 2.68/1.66 #BackRed : 0
% 2.68/1.66
% 2.68/1.66 #Partial instantiations: 0
% 2.68/1.66 #Strategies tried : 1
% 2.68/1.66
% 2.68/1.66 Timing (in seconds)
% 2.68/1.66 ----------------------
% 2.68/1.67 Preprocessing : 0.47
% 2.68/1.67 Parsing : 0.23
% 2.68/1.67 CNF conversion : 0.03
% 2.68/1.67 Main loop : 0.14
% 2.68/1.67 Inferencing : 0.05
% 2.68/1.67 Reduction : 0.04
% 2.68/1.67 Demodulation : 0.03
% 2.68/1.67 BG Simplification : 0.01
% 2.68/1.67 Subsumption : 0.04
% 2.68/1.67 Abstraction : 0.01
% 2.68/1.67 MUC search : 0.00
% 2.68/1.67 Cooper : 0.00
% 2.68/1.67 Total : 0.65
% 2.68/1.67 Index Insertion : 0.00
% 2.68/1.67 Index Deletion : 0.00
% 2.68/1.67 Index Matching : 0.00
% 2.68/1.67 BG Taut test : 0.00
%------------------------------------------------------------------------------