TSTP Solution File: SET987+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET987+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 : n003.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 10:57:28 EDT 2023
% Result : Theorem 2.89s 1.70s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of formulae : 19 ( 7 unt; 9 typ; 0 def)
% Number of atoms : 13 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 1 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 10 (; 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_union2 > set_difference > #nlpp > singleton > #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(in,type,
in: ( $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('#skF_4',type,
'#skF_4': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(f_58,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> ( set_difference(set_union2(B,singleton(A)),singleton(A)) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
tff(f_65,axiom,
! [A,B] :
( ( set_difference(A,singleton(B)) = A )
<=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
tff(f_60,axiom,
! [A,B] : ( set_difference(set_union2(A,B),B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
tff(c_18,plain,
~ in('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_113,plain,
! [A_28,B_29] :
( ( set_difference(A_28,singleton(B_29)) = A_28 )
| in(B_29,A_28) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_20,plain,
! [A_11,B_12] : ( set_difference(set_union2(A_11,B_12),B_12) = set_difference(A_11,B_12) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16,plain,
set_difference(set_union2('#skF_4',singleton('#skF_3')),singleton('#skF_3')) != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_25,plain,
set_difference('#skF_4',singleton('#skF_3')) != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_20,c_16]) ).
tff(c_126,plain,
in('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_113,c_25]) ).
tff(c_139,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET987+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % 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
% 0.13/0.35 % Computer : n003.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 16:36:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.89/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.89/1.70
% 2.89/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.89/1.73
% 2.89/1.73 Inference rules
% 2.89/1.73 ----------------------
% 2.89/1.73 #Ref : 0
% 2.89/1.73 #Sup : 28
% 2.89/1.73 #Fact : 0
% 2.89/1.73 #Define : 0
% 2.89/1.73 #Split : 0
% 2.89/1.73 #Chain : 0
% 2.89/1.73 #Close : 0
% 2.89/1.73
% 2.89/1.73 Ordering : KBO
% 2.89/1.73
% 2.89/1.73 Simplification rules
% 2.89/1.73 ----------------------
% 2.89/1.73 #Subsume : 4
% 2.89/1.73 #Demod : 1
% 2.89/1.73 #Tautology : 17
% 2.89/1.73 #SimpNegUnit : 1
% 2.89/1.73 #BackRed : 0
% 2.89/1.73
% 2.89/1.73 #Partial instantiations: 0
% 2.89/1.73 #Strategies tried : 1
% 2.89/1.73
% 2.89/1.73 Timing (in seconds)
% 2.89/1.73 ----------------------
% 2.89/1.73 Preprocessing : 0.46
% 2.89/1.73 Parsing : 0.25
% 2.89/1.73 CNF conversion : 0.03
% 2.89/1.73 Main loop : 0.22
% 2.89/1.73 Inferencing : 0.09
% 2.89/1.73 Reduction : 0.06
% 2.89/1.73 Demodulation : 0.04
% 2.89/1.73 BG Simplification : 0.01
% 2.89/1.73 Subsumption : 0.05
% 2.89/1.73 Abstraction : 0.01
% 2.89/1.73 MUC search : 0.00
% 2.89/1.73 Cooper : 0.00
% 2.89/1.73 Total : 0.72
% 2.89/1.73 Index Insertion : 0.00
% 2.89/1.73 Index Deletion : 0.00
% 2.89/1.73 Index Matching : 0.00
% 2.89/1.73 BG Taut test : 0.00
%------------------------------------------------------------------------------