TSTP Solution File: SET918+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET918+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 : n020.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 3.39s 2.03s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 20
% Syntax : Number of formulae : 31 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 31 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 26 ( 10 ~; 7 |; 3 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 11 >; 13 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 22 (; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_intersection2 > #nlpp > singleton > #skF_11 > #skF_6 > #skF_4 > #skF_7 > #skF_10 > #skF_5 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_76,negated_conjecture,
~ ! [A,B,C] :
~ ( ( set_intersection2(unordered_pair(A,B),C) = singleton(A) )
& in(B,C)
& ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
tff(f_51,axiom,
! [A,B,C] :
( ( C = unordered_pair(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
tff(f_60,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(f_42,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_62,plain,
'#skF_10' != '#skF_9',
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_64,plain,
in('#skF_10','#skF_11'),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_22,plain,
! [D_17,A_12] : in(D_17,unordered_pair(A_12,D_17)),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_66,plain,
set_intersection2(unordered_pair('#skF_9','#skF_10'),'#skF_11') = singleton('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_356,plain,
! [D_64,A_65,B_66] :
( in(D_64,set_intersection2(A_65,B_66))
| ~ in(D_64,B_66)
| ~ in(D_64,A_65) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_489,plain,
! [D_76] :
( in(D_76,singleton('#skF_9'))
| ~ in(D_76,'#skF_11')
| ~ in(D_76,unordered_pair('#skF_9','#skF_10')) ),
inference(superposition,[status(thm),theory(equality)],[c_66,c_356]) ).
tff(c_504,plain,
( in('#skF_10',singleton('#skF_9'))
| ~ in('#skF_10','#skF_11') ),
inference(resolution,[status(thm)],[c_22,c_489]) ).
tff(c_512,plain,
in('#skF_10',singleton('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_504]) ).
tff(c_8,plain,
! [C_11,A_7] :
( ( C_11 = A_7 )
| ~ in(C_11,singleton(A_7)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_541,plain,
'#skF_10' = '#skF_9',
inference(resolution,[status(thm)],[c_512,c_8]) ).
tff(c_548,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.37 % Computer : n020.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 3 16:47:07 EDT 2023
% 0.14/0.37 % CPUTime :
% 3.39/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/2.03
% 3.39/2.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.39/2.06
% 3.39/2.06 Inference rules
% 3.39/2.06 ----------------------
% 3.39/2.06 #Ref : 0
% 3.39/2.06 #Sup : 116
% 3.39/2.06 #Fact : 0
% 3.39/2.06 #Define : 0
% 3.39/2.06 #Split : 0
% 3.39/2.06 #Chain : 0
% 3.39/2.06 #Close : 0
% 3.39/2.06
% 3.39/2.06 Ordering : KBO
% 3.39/2.06
% 3.39/2.06 Simplification rules
% 3.39/2.06 ----------------------
% 3.39/2.06 #Subsume : 27
% 3.39/2.06 #Demod : 11
% 3.39/2.06 #Tautology : 42
% 3.39/2.06 #SimpNegUnit : 1
% 3.39/2.06 #BackRed : 0
% 3.39/2.06
% 3.39/2.06 #Partial instantiations: 0
% 3.39/2.06 #Strategies tried : 1
% 3.39/2.06
% 3.39/2.06 Timing (in seconds)
% 3.39/2.06 ----------------------
% 3.39/2.06 Preprocessing : 0.51
% 3.39/2.06 Parsing : 0.25
% 3.39/2.06 CNF conversion : 0.04
% 3.39/2.06 Main loop : 0.39
% 3.39/2.06 Inferencing : 0.13
% 3.39/2.06 Reduction : 0.12
% 3.39/2.06 Demodulation : 0.09
% 3.39/2.06 BG Simplification : 0.02
% 3.39/2.06 Subsumption : 0.09
% 3.39/2.06 Abstraction : 0.02
% 3.39/2.06 MUC search : 0.00
% 3.39/2.06 Cooper : 0.00
% 3.39/2.06 Total : 0.95
% 3.39/2.06 Index Insertion : 0.00
% 3.39/2.06 Index Deletion : 0.00
% 3.39/2.06 Index Matching : 0.00
% 3.39/2.06 BG Taut test : 0.00
%------------------------------------------------------------------------------