TSTP Solution File: SET983+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET983+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 10:57:27 EDT 2023
% Result : Theorem 4.57s 2.26s
% Output : CNFRefutation 5.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 17
% Syntax : Number of formulae : 27 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 24 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 5 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 29 (; 29 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_intersection2 > cartesian_product2 > #nlpp > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_3 > #skF_2 > #skF_9 > #skF_8 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $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('#skF_2',type,
'#skF_2': ( $i * $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_4',type,
'#skF_4': $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_58,negated_conjecture,
~ ! [A,B,C,D,E] :
( ( in(A,cartesian_product2(B,C))
& in(A,cartesian_product2(D,E)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
tff(f_51,axiom,
! [A,B,C,D] : ( cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
tff(f_42,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(f_33,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(c_34,plain,
in('#skF_5',cartesian_product2('#skF_8','#skF_9')),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_36,plain,
in('#skF_5',cartesian_product2('#skF_6','#skF_7')),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_128,plain,
! [A_31,C_32,B_33,D_34] : ( set_intersection2(cartesian_product2(A_31,C_32),cartesian_product2(B_33,D_34)) = cartesian_product2(set_intersection2(A_31,B_33),set_intersection2(C_32,D_34)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_6,plain,
! [D_10,A_5,B_6] :
( in(D_10,set_intersection2(A_5,B_6))
| ~ in(D_10,B_6)
| ~ in(D_10,A_5) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_1516,plain,
! [A_134,B_133,D_130,C_132,D_131] :
( in(D_131,cartesian_product2(set_intersection2(A_134,B_133),set_intersection2(C_132,D_130)))
| ~ in(D_131,cartesian_product2(B_133,D_130))
| ~ in(D_131,cartesian_product2(A_134,C_132)) ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_6]) ).
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_32,plain,
~ in('#skF_5',cartesian_product2(set_intersection2('#skF_6','#skF_8'),set_intersection2('#skF_7','#skF_9'))),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_37,plain,
~ in('#skF_5',cartesian_product2(set_intersection2('#skF_8','#skF_6'),set_intersection2('#skF_9','#skF_7'))),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_32]) ).
tff(c_1560,plain,
( ~ in('#skF_5',cartesian_product2('#skF_6','#skF_7'))
| ~ in('#skF_5',cartesian_product2('#skF_8','#skF_9')) ),
inference(resolution,[status(thm)],[c_1516,c_37]) ).
tff(c_1631,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_36,c_1560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET983+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
% 0.13/0.34 % Computer : n021.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 16:38:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.57/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.57/2.26
% 4.57/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.02/2.29
% 5.02/2.29 Inference rules
% 5.02/2.29 ----------------------
% 5.02/2.29 #Ref : 0
% 5.02/2.29 #Sup : 407
% 5.02/2.29 #Fact : 0
% 5.02/2.29 #Define : 0
% 5.02/2.29 #Split : 0
% 5.02/2.29 #Chain : 0
% 5.02/2.29 #Close : 0
% 5.02/2.29
% 5.02/2.29 Ordering : KBO
% 5.02/2.29
% 5.02/2.29 Simplification rules
% 5.02/2.29 ----------------------
% 5.02/2.29 #Subsume : 106
% 5.02/2.29 #Demod : 45
% 5.02/2.29 #Tautology : 78
% 5.02/2.29 #SimpNegUnit : 0
% 5.02/2.29 #BackRed : 0
% 5.02/2.29
% 5.02/2.29 #Partial instantiations: 0
% 5.02/2.29 #Strategies tried : 1
% 5.02/2.29
% 5.02/2.29 Timing (in seconds)
% 5.02/2.29 ----------------------
% 5.02/2.29 Preprocessing : 0.49
% 5.02/2.29 Parsing : 0.24
% 5.02/2.29 CNF conversion : 0.03
% 5.02/2.29 Main loop : 0.69
% 5.02/2.29 Inferencing : 0.23
% 5.02/2.29 Reduction : 0.24
% 5.02/2.29 Demodulation : 0.20
% 5.02/2.29 BG Simplification : 0.03
% 5.02/2.29 Subsumption : 0.14
% 5.02/2.29 Abstraction : 0.04
% 5.02/2.29 MUC search : 0.00
% 5.02/2.29 Cooper : 0.00
% 5.02/2.29 Total : 1.22
% 5.02/2.29 Index Insertion : 0.00
% 5.02/2.29 Index Deletion : 0.00
% 5.02/2.29 Index Matching : 0.00
% 5.02/2.29 BG Taut test : 0.00
%------------------------------------------------------------------------------