TSTP Solution File: SET792+4 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET792+4 : 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 : n009.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 10:57:01 EDT 2023
% Result : Theorem 20.13s 9.61s
% Output : CNFRefutation 20.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 35
% Syntax : Number of formulae : 55 ( 7 unt; 31 typ; 0 def)
% Number of atoms : 85 ( 11 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 97 ( 36 ~; 39 |; 11 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 77 ( 28 >; 49 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-4 aty)
% Number of variables : 58 (; 58 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ least_upper_bound > greatest_lower_bound > upper_bound > min > max > lower_bound > least > greatest > apply > total_order > order > member > #nlpp > #skF_13 > #skF_6 > #skF_18 > #skF_17 > #skF_12 > #skF_19 > #skF_3 > #skF_15 > #skF_16 > #skF_8 > #skF_11 > #skF_9 > #skF_14 > #skF_2 > #skF_7 > #skF_1 > #skF_5 > #skF_4 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(upper_bound,type,
upper_bound: ( $i * $i * $i ) > $o ).
tff(greatest_lower_bound,type,
greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(apply,type,
apply: ( $i * $i * $i ) > $o ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(least_upper_bound,type,
least_upper_bound: ( $i * $i * $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': $i ).
tff(total_order,type,
total_order: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff(greatest,type,
greatest: ( $i * $i * $i ) > $o ).
tff(lower_bound,type,
lower_bound: ( $i * $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff(min,type,
min: ( $i * $i * $i ) > $o ).
tff(least,type,
least: ( $i * $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(order,type,
order: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(max,type,
max: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_182,negated_conjecture,
~ ! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> min(M,R,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV4) ).
tff(f_125,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least) ).
tff(f_147,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> ( M = X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',min) ).
tff(f_80,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> ( X = Y ) ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).
tff(c_214,plain,
least('#skF_19','#skF_17','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_220,plain,
! [M_87,E_88,R_89] :
( member(M_87,E_88)
| ~ least(M_87,R_89,E_88) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_224,plain,
member('#skF_19','#skF_18'),
inference(resolution,[status(thm)],[c_214,c_220]) ).
tff(c_325,plain,
! [R_153,E_154,M_155] :
( ( '#skF_14'(R_153,E_154,M_155) != M_155 )
| min(M_155,R_153,E_154)
| ~ member(M_155,E_154) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_212,plain,
~ min('#skF_19','#skF_17','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_331,plain,
( ( '#skF_14'('#skF_17','#skF_18','#skF_19') != '#skF_19' )
| ~ member('#skF_19','#skF_18') ),
inference(resolution,[status(thm)],[c_325,c_212]) ).
tff(c_335,plain,
'#skF_14'('#skF_17','#skF_18','#skF_19') != '#skF_19',
inference(demodulation,[status(thm),theory(equality)],[c_224,c_331]) ).
tff(c_216,plain,
order('#skF_17','#skF_18'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_186,plain,
! [R_59,E_60,M_61] :
( member('#skF_14'(R_59,E_60,M_61),E_60)
| min(M_61,R_59,E_60)
| ~ member(M_61,E_60) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_341,plain,
! [R_159,E_160,M_161] :
( member('#skF_14'(R_159,E_160,M_161),E_160)
| min(M_161,R_159,E_160)
| ~ member(M_161,E_160) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_160,plain,
! [R_47,M_49,X_52,E_48] :
( apply(R_47,M_49,X_52)
| ~ member(X_52,E_48)
| ~ least(M_49,R_47,E_48) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_352,plain,
! [R_47,R_159,M_161,M_49,E_160] :
( apply(R_47,M_49,'#skF_14'(R_159,E_160,M_161))
| ~ least(M_49,R_47,E_160)
| min(M_161,R_159,E_160)
| ~ member(M_161,E_160) ),
inference(resolution,[status(thm)],[c_341,c_160]) ).
tff(c_184,plain,
! [R_59,E_60,M_61] :
( apply(R_59,'#skF_14'(R_59,E_60,M_61),M_61)
| min(M_61,R_59,E_60)
| ~ member(M_61,E_60) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_1745,plain,
! [Y_469,X_470,R_471,E_472] :
( ( Y_469 = X_470 )
| ~ apply(R_471,Y_469,X_470)
| ~ apply(R_471,X_470,Y_469)
| ~ member(Y_469,E_472)
| ~ member(X_470,E_472)
| ~ order(R_471,E_472) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_39029,plain,
! [R_2907,E_2908,M_2909,E_2910] :
( ( '#skF_14'(R_2907,E_2908,M_2909) = M_2909 )
| ~ apply(R_2907,M_2909,'#skF_14'(R_2907,E_2908,M_2909))
| ~ member('#skF_14'(R_2907,E_2908,M_2909),E_2910)
| ~ member(M_2909,E_2910)
| ~ order(R_2907,E_2910)
| min(M_2909,R_2907,E_2908)
| ~ member(M_2909,E_2908) ),
inference(resolution,[status(thm)],[c_184,c_1745]) ).
tff(c_40472,plain,
! [R_2932,E_2933,M_2934,E_2935] :
( ( '#skF_14'(R_2932,E_2933,M_2934) = M_2934 )
| ~ member('#skF_14'(R_2932,E_2933,M_2934),E_2935)
| ~ member(M_2934,E_2935)
| ~ order(R_2932,E_2935)
| ~ least(M_2934,R_2932,E_2933)
| min(M_2934,R_2932,E_2933)
| ~ member(M_2934,E_2933) ),
inference(resolution,[status(thm)],[c_352,c_39029]) ).
tff(c_40477,plain,
! [R_2936,E_2937,M_2938] :
( ( '#skF_14'(R_2936,E_2937,M_2938) = M_2938 )
| ~ order(R_2936,E_2937)
| ~ least(M_2938,R_2936,E_2937)
| min(M_2938,R_2936,E_2937)
| ~ member(M_2938,E_2937) ),
inference(resolution,[status(thm)],[c_186,c_40472]) ).
tff(c_40622,plain,
( ( '#skF_14'('#skF_17','#skF_18','#skF_19') = '#skF_19' )
| ~ order('#skF_17','#skF_18')
| ~ least('#skF_19','#skF_17','#skF_18')
| ~ member('#skF_19','#skF_18') ),
inference(resolution,[status(thm)],[c_40477,c_212]) ).
tff(c_40670,plain,
'#skF_14'('#skF_17','#skF_18','#skF_19') = '#skF_19',
inference(demodulation,[status(thm),theory(equality)],[c_224,c_214,c_216,c_40622]) ).
tff(c_40672,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_335,c_40670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET792+4 : 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
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 16:18:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.13/9.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.36/9.61
% 20.36/9.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.46/9.64
% 20.46/9.64 Inference rules
% 20.46/9.64 ----------------------
% 20.46/9.64 #Ref : 0
% 20.46/9.64 #Sup : 11346
% 20.46/9.64 #Fact : 94
% 20.46/9.64 #Define : 0
% 20.46/9.64 #Split : 2
% 20.46/9.64 #Chain : 0
% 20.46/9.64 #Close : 0
% 20.46/9.64
% 20.46/9.64 Ordering : KBO
% 20.46/9.64
% 20.46/9.64 Simplification rules
% 20.46/9.64 ----------------------
% 20.46/9.64 #Subsume : 708
% 20.46/9.64 #Demod : 77
% 20.46/9.64 #Tautology : 228
% 20.46/9.64 #SimpNegUnit : 1
% 20.46/9.64 #BackRed : 0
% 20.46/9.64
% 20.46/9.64 #Partial instantiations: 0
% 20.46/9.64 #Strategies tried : 1
% 20.46/9.64
% 20.46/9.64 Timing (in seconds)
% 20.46/9.64 ----------------------
% 20.46/9.65 Preprocessing : 0.59
% 20.46/9.65 Parsing : 0.28
% 20.46/9.65 CNF conversion : 0.06
% 20.46/9.65 Main loop : 7.98
% 20.46/9.65 Inferencing : 2.29
% 20.46/9.65 Reduction : 1.26
% 20.46/9.65 Demodulation : 0.75
% 20.46/9.65 BG Simplification : 0.19
% 20.46/9.65 Subsumption : 3.68
% 20.46/9.65 Abstraction : 0.29
% 20.46/9.65 MUC search : 0.00
% 20.46/9.65 Cooper : 0.00
% 20.46/9.65 Total : 8.63
% 20.46/9.65 Index Insertion : 0.00
% 20.46/9.65 Index Deletion : 0.00
% 20.46/9.65 Index Matching : 0.00
% 20.46/9.65 BG Taut test : 0.00
%------------------------------------------------------------------------------