TSTP Solution File: SET979+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET979+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 : n010.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 2.38s 1.55s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 16
% Syntax : Number of formulae : 24 ( 7 unt; 13 typ; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 16 (; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ empty > unordered_pair > set_union2 > cartesian_product2 > #nlpp > singleton > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
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_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_60,axiom,
! [A,B] : ( unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
tff(f_53,axiom,
! [A,B,C] :
( ( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) )
& ( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
tff(f_58,negated_conjecture,
~ ! [A,B,C] :
( ( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) )
& ( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
tff(c_22,plain,
! [A_14,B_15] : ( set_union2(singleton(A_14),singleton(B_15)) = unordered_pair(A_14,B_15) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16,plain,
! [A_11,C_13,B_12] : ( set_union2(cartesian_product2(A_11,C_13),cartesian_product2(B_12,C_13)) = cartesian_product2(set_union2(A_11,B_12),C_13) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_18,plain,
! [C_13,A_11,B_12] : ( set_union2(cartesian_product2(C_13,A_11),cartesian_product2(C_13,B_12)) = cartesian_product2(C_13,set_union2(A_11,B_12)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_20,plain,
( ( set_union2(cartesian_product2(singleton('#skF_6'),'#skF_8'),cartesian_product2(singleton('#skF_7'),'#skF_8')) != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8') )
| ( set_union2(cartesian_product2('#skF_5',singleton('#skF_3')),cartesian_product2('#skF_5',singleton('#skF_4'))) != cartesian_product2('#skF_5',unordered_pair('#skF_3','#skF_4')) ) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_23,plain,
( ( set_union2(cartesian_product2(singleton('#skF_6'),'#skF_8'),cartesian_product2(singleton('#skF_7'),'#skF_8')) != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8') )
| ( cartesian_product2('#skF_5',set_union2(singleton('#skF_3'),singleton('#skF_4'))) != cartesian_product2('#skF_5',unordered_pair('#skF_3','#skF_4')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_20]) ).
tff(c_25,plain,
set_union2(cartesian_product2(singleton('#skF_6'),'#skF_8'),cartesian_product2(singleton('#skF_7'),'#skF_8')) != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_23]) ).
tff(c_26,plain,
cartesian_product2(set_union2(singleton('#skF_6'),singleton('#skF_7')),'#skF_8') != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_25]) ).
tff(c_28,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % 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
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 16:03:58 EDT 2023
% 0.15/0.35 % CPUTime :
% 2.38/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.38/1.55
% 2.38/1.55 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.38/1.58
% 2.38/1.58 Inference rules
% 2.38/1.58 ----------------------
% 2.38/1.58 #Ref : 0
% 2.38/1.58 #Sup : 0
% 2.38/1.58 #Fact : 0
% 2.38/1.58 #Define : 0
% 2.38/1.58 #Split : 0
% 2.38/1.58 #Chain : 0
% 2.38/1.58 #Close : 0
% 2.38/1.58
% 2.38/1.58 Ordering : KBO
% 2.38/1.58
% 2.38/1.58 Simplification rules
% 2.38/1.58 ----------------------
% 2.38/1.58 #Subsume : 10
% 2.38/1.58 #Demod : 4
% 2.38/1.58 #Tautology : 0
% 2.38/1.58 #SimpNegUnit : 0
% 2.38/1.58 #BackRed : 0
% 2.38/1.58
% 2.38/1.58 #Partial instantiations: 0
% 2.38/1.58 #Strategies tried : 1
% 2.38/1.58
% 2.38/1.58 Timing (in seconds)
% 2.38/1.58 ----------------------
% 2.38/1.58 Preprocessing : 0.45
% 2.38/1.58 Parsing : 0.25
% 2.38/1.59 CNF conversion : 0.03
% 2.38/1.59 Main loop : 0.06
% 2.38/1.59 Inferencing : 0.00
% 2.38/1.59 Reduction : 0.03
% 2.38/1.59 Demodulation : 0.02
% 2.38/1.59 BG Simplification : 0.01
% 2.38/1.59 Subsumption : 0.03
% 2.38/1.59 Abstraction : 0.01
% 2.38/1.59 MUC search : 0.00
% 2.38/1.59 Cooper : 0.00
% 2.38/1.59 Total : 0.57
% 2.38/1.59 Index Insertion : 0.00
% 2.38/1.59 Index Deletion : 0.00
% 2.38/1.59 Index Matching : 0.00
% 2.38/1.59 BG Taut test : 0.00
%------------------------------------------------------------------------------