TSTP Solution File: SWC013+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC013+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n027.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 11:00:44 EDT 2023
% Result : Theorem 9.80s 3.17s
% Output : CNFRefutation 9.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 81
% Syntax : Number of formulae : 135 ( 34 unt; 75 typ; 0 def)
% Number of atoms : 135 ( 44 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 137 ( 62 ~; 50 |; 12 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 68 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 56 ( 56 usr; 7 con; 0-2 aty)
% Number of variables : 24 (; 19 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > cons > app > #nlpp > tl > hd > nil > #skF_36 > #skF_25 > #skF_5 > #skF_44 > #skF_21 > #skF_16 > #skF_6 > #skF_49 > #skF_18 > #skF_24 > #skF_35 > #skF_19 > #skF_31 > #skF_22 > #skF_37 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_51 > #skF_28 > #skF_10 > #skF_41 > #skF_2 > #skF_38 > #skF_43 > #skF_1 > #skF_8 > #skF_39 > #skF_23 > #skF_33 > #skF_26 > #skF_50 > #skF_13 > #skF_17 > #skF_11 > #skF_14 > #skF_27 > #skF_12 > #skF_7 > #skF_46 > #skF_42 > #skF_45 > #skF_9 > #skF_30 > #skF_4 > #skF_20 > #skF_47
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_36',type,
'#skF_36': $i > $i ).
tff(segmentP,type,
segmentP: ( $i * $i ) > $o ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff(totalorderedP,type,
totalorderedP: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(equalelemsP,type,
equalelemsP: $i > $o ).
tff('#skF_44',type,
'#skF_44': $i > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_24',type,
'#skF_24': $i > $i ).
tff('#skF_35',type,
'#skF_35': $i > $i ).
tff(singletonP,type,
singletonP: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_31',type,
'#skF_31': $i > $i ).
tff('#skF_22',type,
'#skF_22': $i > $i ).
tff(frontsegP,type,
frontsegP: ( $i * $i ) > $o ).
tff('#skF_37',type,
'#skF_37': $i > $i ).
tff(totalorderP,type,
totalorderP: $i > $o ).
tff(ssItem,type,
ssItem: $i > $o ).
tff('#skF_40',type,
'#skF_40': $i > $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': $i > $i ).
tff('#skF_29',type,
'#skF_29': $i > $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff('#skF_32',type,
'#skF_32': $i > $i ).
tff('#skF_51',type,
'#skF_51': $i ).
tff('#skF_28',type,
'#skF_28': $i > $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_41',type,
'#skF_41': $i > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_38',type,
'#skF_38': $i > $i ).
tff('#skF_43',type,
'#skF_43': $i > $i ).
tff(hd,type,
hd: $i > $i ).
tff(app,type,
app: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(duplicatefreeP,type,
duplicatefreeP: $i > $o ).
tff(gt,type,
gt: ( $i * $i ) > $o ).
tff('#skF_39',type,
'#skF_39': $i > $i ).
tff('#skF_23',type,
'#skF_23': $i > $i ).
tff(rearsegP,type,
rearsegP: ( $i * $i ) > $o ).
tff('#skF_33',type,
'#skF_33': $i > $i ).
tff(memberP,type,
memberP: ( $i * $i ) > $o ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff(ssList,type,
ssList: $i > $o ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(strictorderP,type,
strictorderP: $i > $o ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff(geq,type,
geq: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(lt,type,
lt: ( $i * $i ) > $o ).
tff(tl,type,
tl: $i > $i ).
tff(neq,type,
neq: ( $i * $i ) > $o ).
tff('#skF_27',type,
'#skF_27': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': $i > $i ).
tff(nil,type,
nil: $i ).
tff('#skF_42',type,
'#skF_42': $i > $i ).
tff('#skF_45',type,
'#skF_45': $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(strictorderedP,type,
strictorderedP: $i > $o ).
tff('#skF_30',type,
'#skF_30': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff(cyclefreeP,type,
cyclefreeP: $i > $o ).
tff('#skF_47',type,
'#skF_47': $i > $i ).
tff(f_1031,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& ( W != Y )
& ? [Z] :
( ssItem(Z)
& ( cons(Z,nil) = Y )
& ( hd(X) = Z )
& neq(nil,X) ) )
| ? [X1] :
( ssList(X1)
& ( U = X1 )
& ? [X2] :
( ssItem(X2)
& ( cons(X2,nil) = X1 )
& ( hd(V) = X2 )
& neq(nil,V) ) ) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_779,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssList(V)
& ( tl(U) = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
tff(f_311,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_318,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1031]) ).
tff(c_388,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1031]) ).
tff(c_4805,plain,
! [U_1489] :
( ssItem(hd(U_1489))
| ( nil = U_1489 )
| ~ ssList(U_1489) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_2329,plain,
! [U_1393] :
( ( tl(U_1393) = '#skF_47'(U_1393) )
| ( nil = U_1393 )
| ~ ssList(U_1393) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_2437,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_2329]) ).
tff(c_2439,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_2437]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1031]) ).
tff(c_406,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1031]) ).
tff(c_411,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).
tff(c_2472,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_2439,c_411]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_2625,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_2472,c_164]) ).
tff(c_2630,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2625]) ).
tff(c_2632,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_2437]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_4649,plain,
! [U_1468,V_1469] :
( neq(U_1468,V_1469)
| ( V_1469 = U_1468 )
| ~ ssList(V_1469)
| ~ ssList(U_1468) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_807,plain,
! [U_1298] :
( ( tl(U_1298) = '#skF_47'(U_1298) )
| ( nil = U_1298 )
| ~ ssList(U_1298) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_915,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_807]) ).
tff(c_917,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_915]) ).
tff(c_948,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_917,c_411]) ).
tff(c_1199,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_948,c_164]) ).
tff(c_1204,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1199]) ).
tff(c_1206,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_915]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_1941,plain,
! [V_1328,U_1329] :
( ssList(cons(V_1328,U_1329))
| ~ ssItem(V_1328)
| ~ ssList(U_1329) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_398,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' )
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1031]) ).
tff(c_415,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' )
| ~ ssList(cons(hd('#skF_51'),nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_398]) ).
tff(c_431,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitLeft,[status(thm)],[c_415]) ).
tff(c_1953,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_1941,c_431]) ).
tff(c_1959,plain,
~ ssItem(hd('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_1953]) ).
tff(c_1962,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_184,c_1959]) ).
tff(c_1965,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1962]) ).
tff(c_1967,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1206,c_1965]) ).
tff(c_1968,plain,
( ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51')
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_415]) ).
tff(c_1981,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_1968]) ).
tff(c_4652,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_4649,c_1981]) ).
tff(c_4663,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_4652]) ).
tff(c_4665,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2632,c_4663]) ).
tff(c_4666,plain,
( ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_1968]) ).
tff(c_4793,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_4666]) ).
tff(c_4808,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_4805,c_4793]) ).
tff(c_4811,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4808]) ).
tff(c_4837,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_4811,c_411]) ).
tff(c_4857,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_4837,c_164]) ).
tff(c_4862,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4857]) ).
tff(c_4863,plain,
cons(hd('#skF_51'),nil) = '#skF_50',
inference(splitRight,[status(thm)],[c_4666]) ).
tff(c_4864,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_4666]) ).
tff(c_4667,plain,
neq(nil,'#skF_51'),
inference(splitRight,[status(thm)],[c_1968]) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1031]) ).
tff(c_396,plain,
( ~ neq(nil,'#skF_49')
| ~ ssItem(hd('#skF_49'))
| ( cons(hd('#skF_49'),nil) != '#skF_48' )
| ~ ssList(cons(hd('#skF_49'),nil))
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1031]) ).
tff(c_412,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) != '#skF_48' )
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_386,c_386,c_386,c_396]) ).
tff(c_417,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) != '#skF_48' )
| ~ ssList(cons(hd('#skF_51'),nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_412]) ).
tff(c_419,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) != '#skF_50' )
| ~ ssList(cons(hd('#skF_51'),nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_417]) ).
tff(c_5023,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_390,c_4863,c_4863,c_4864,c_4667,c_419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC013+1 : TPTP v8.1.2. Released v2.4.0.
% 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
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 21:59:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 9.80/3.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.80/3.18
% 9.80/3.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.80/3.21
% 9.80/3.21 Inference rules
% 9.80/3.21 ----------------------
% 9.80/3.21 #Ref : 0
% 9.80/3.21 #Sup : 999
% 9.80/3.21 #Fact : 0
% 9.80/3.21 #Define : 0
% 9.80/3.21 #Split : 22
% 9.80/3.21 #Chain : 0
% 9.80/3.21 #Close : 0
% 9.80/3.21
% 9.80/3.21 Ordering : KBO
% 9.80/3.21
% 9.80/3.21 Simplification rules
% 9.80/3.21 ----------------------
% 9.80/3.21 #Subsume : 19
% 9.80/3.21 #Demod : 547
% 9.80/3.21 #Tautology : 248
% 9.80/3.21 #SimpNegUnit : 21
% 9.80/3.21 #BackRed : 234
% 9.80/3.21
% 9.80/3.21 #Partial instantiations: 0
% 9.80/3.21 #Strategies tried : 1
% 9.80/3.21
% 9.80/3.21 Timing (in seconds)
% 9.80/3.21 ----------------------
% 9.80/3.21 Preprocessing : 0.89
% 9.80/3.21 Parsing : 0.41
% 9.80/3.21 CNF conversion : 0.11
% 9.80/3.21 Main loop : 1.27
% 9.80/3.21 Inferencing : 0.42
% 9.80/3.21 Reduction : 0.37
% 9.80/3.21 Demodulation : 0.25
% 9.80/3.21 BG Simplification : 0.09
% 9.80/3.21 Subsumption : 0.26
% 9.80/3.21 Abstraction : 0.05
% 9.80/3.21 MUC search : 0.00
% 9.80/3.21 Cooper : 0.00
% 9.80/3.21 Total : 2.21
% 9.80/3.21 Index Insertion : 0.00
% 9.80/3.21 Index Deletion : 0.00
% 9.80/3.21 Index Matching : 0.00
% 9.80/3.21 BG Taut test : 0.00
%------------------------------------------------------------------------------