TSTP Solution File: SET877+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET877+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 : n019.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 2.79s 1.70s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 23 ( 8 unt; 10 typ; 0 def)
% Number of atoms : 19 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 2 |; 0 &)
% ( 2 <=>; 2 =>; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 15 (; 15 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_intersection2 > #nlpp > singleton > #skF_5 > #skF_6 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
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_56,negated_conjecture,
~ ! [A,B] :
( ( set_intersection2(singleton(A),singleton(B)) = singleton(A) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
tff(f_33,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_46,axiom,
! [A,B] :
( ( set_intersection2(A,singleton(B)) = singleton(B) )
=> in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).
tff(f_40,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_26,plain,
'#skF_5' != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_28,plain,
set_intersection2(singleton('#skF_5'),singleton('#skF_6')) = singleton('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_4,plain,
! [B_4,A_3] : ( set_intersection2(B_4,A_3) = set_intersection2(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_86,plain,
set_intersection2(singleton('#skF_6'),singleton('#skF_5')) = singleton('#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_28,c_4]) ).
tff(c_106,plain,
! [B_23,A_24] :
( in(B_23,A_24)
| ( set_intersection2(A_24,singleton(B_23)) != singleton(B_23) ) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_125,plain,
in('#skF_5',singleton('#skF_6')),
inference(superposition,[status(thm),theory(equality)],[c_86,c_106]) ).
tff(c_6,plain,
! [C_9,A_5] :
( ( C_9 = A_5 )
| ~ in(C_9,singleton(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_133,plain,
'#skF_5' = '#skF_6',
inference(resolution,[status(thm)],[c_125,c_6]) ).
tff(c_138,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET877+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/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
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 16:45:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.79/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.79/1.70
% 2.79/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.79/1.73
% 2.79/1.73 Inference rules
% 2.79/1.73 ----------------------
% 2.79/1.73 #Ref : 0
% 2.79/1.73 #Sup : 27
% 2.79/1.73 #Fact : 0
% 2.79/1.73 #Define : 0
% 2.79/1.73 #Split : 0
% 2.79/1.73 #Chain : 0
% 2.79/1.73 #Close : 0
% 2.79/1.73
% 2.79/1.73 Ordering : KBO
% 2.79/1.73
% 2.79/1.73 Simplification rules
% 2.79/1.73 ----------------------
% 2.79/1.73 #Subsume : 0
% 2.79/1.73 #Demod : 4
% 2.79/1.73 #Tautology : 19
% 2.79/1.73 #SimpNegUnit : 1
% 2.79/1.73 #BackRed : 0
% 2.79/1.73
% 2.79/1.73 #Partial instantiations: 0
% 2.79/1.73 #Strategies tried : 1
% 2.79/1.73
% 2.79/1.73 Timing (in seconds)
% 2.79/1.73 ----------------------
% 2.79/1.73 Preprocessing : 0.47
% 2.79/1.73 Parsing : 0.24
% 2.79/1.73 CNF conversion : 0.03
% 2.79/1.73 Main loop : 0.19
% 2.79/1.73 Inferencing : 0.06
% 2.79/1.73 Reduction : 0.06
% 2.79/1.73 Demodulation : 0.05
% 2.79/1.73 BG Simplification : 0.01
% 2.79/1.73 Subsumption : 0.05
% 2.79/1.73 Abstraction : 0.01
% 2.79/1.73 MUC search : 0.00
% 2.79/1.73 Cooper : 0.00
% 2.79/1.73 Total : 0.71
% 2.79/1.73 Index Insertion : 0.00
% 2.79/1.73 Index Deletion : 0.00
% 2.79/1.73 Index Matching : 0.00
% 2.79/1.73 BG Taut test : 0.00
%------------------------------------------------------------------------------