TSTP Solution File: SWC355+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC355+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 : n004.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 11:02:16 EDT 2023
% Result : Theorem 27.98s 13.45s
% Output : CNFRefutation 27.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 86
% Syntax : Number of formulae : 138 ( 29 unt; 76 typ; 0 def)
% Number of atoms : 134 ( 43 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 124 ( 52 ~; 45 |; 5 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 57 ( 57 usr; 8 con; 0-2 aty)
% Number of variables : 36 (; 32 !; 4 ?; 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_52 > #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_52',type,
'#skF_52': $i ).
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_1010,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ! [Y] :
( ssItem(Y)
=> ( app(W,cons(Y,nil)) != X ) )
| segmentP(V,U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(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_686,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
tff(f_769,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssItem(V)
& ( hd(U) = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
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_869,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil != U )
=> ( hd(app(U,V)) = hd(U) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_135,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& ( app(app(W,V),X) = U ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_410,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_416,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_410]) ).
tff(c_396,plain,
( ~ segmentP('#skF_49','#skF_48')
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_417,plain,
( ~ segmentP('#skF_51','#skF_48')
| ~ neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_396]) ).
tff(c_424,plain,
~ segmentP('#skF_51','#skF_48'),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_417]) ).
tff(c_426,plain,
~ segmentP('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_424]) ).
tff(c_388,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_398,plain,
( ( app('#skF_50',cons('#skF_52',nil)) = '#skF_51' )
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_420,plain,
app('#skF_50',cons('#skF_52',nil)) = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_416,c_398]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_400,plain,
( ssItem('#skF_52')
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_422,plain,
ssItem('#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_400]) ).
tff(c_166,plain,
! [V_861,U_859] :
( ssList(cons(V_861,U_859))
| ~ ssItem(V_861)
| ~ ssList(U_859) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1010]) ).
tff(c_782,plain,
! [U_1213] :
( ( tl(U_1213) = '#skF_47'(U_1213) )
| ( nil = U_1213 )
| ~ ssList(U_1213) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_884,plain,
( ( tl('#skF_50') = '#skF_47'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_782]) ).
tff(c_888,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_884]) ).
tff(c_274,plain,
! [U_1030] :
( segmentP(U_1030,nil)
| ~ ssList(U_1030) ),
inference(cnfTransformation,[status(thm)],[f_686]) ).
tff(c_1247,plain,
! [U_1218] :
( segmentP(U_1218,'#skF_50')
| ~ ssList(U_1218) ),
inference(demodulation,[status(thm),theory(equality)],[c_888,c_274]) ).
tff(c_1250,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_1247,c_426]) ).
tff(c_1254,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1250]) ).
tff(c_1256,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_884]) ).
tff(c_1703,plain,
! [U_1231] :
( ( hd(U_1231) = '#skF_46'(U_1231) )
| ( nil = U_1231 )
| ~ ssList(U_1231) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_1787,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_1703]) ).
tff(c_1823,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_1256,c_1787]) ).
tff(c_887,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_782]) ).
tff(c_1280,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_887]) ).
tff(c_1312,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_1280,c_416]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_1330,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_1312,c_164]) ).
tff(c_1337,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1330]) ).
tff(c_1339,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_887]) ).
tff(c_1793,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_1703]) ).
tff(c_1828,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_1339,c_1793]) ).
tff(c_45326,plain,
! [U_2284,V_2285] :
( ( hd(app(U_2284,V_2285)) = hd(U_2284) )
| ( nil = U_2284 )
| ~ ssList(V_2285)
| ~ ssList(U_2284) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_45524,plain,
( ( hd('#skF_51') = hd('#skF_50') )
| ( nil = '#skF_50' )
| ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_420,c_45326]) ).
tff(c_45708,plain,
( ( '#skF_46'('#skF_51') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' )
| ~ ssList(cons('#skF_52',nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_1823,c_1828,c_45524]) ).
tff(c_45709,plain,
( ( '#skF_46'('#skF_51') = '#skF_46'('#skF_50') )
| ~ ssList(cons('#skF_52',nil)) ),
inference(negUnitSimplification,[status(thm)],[c_1256,c_45708]) ).
tff(c_45710,plain,
~ ssList(cons('#skF_52',nil)),
inference(splitLeft,[status(thm)],[c_45709]) ).
tff(c_45713,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_45710]) ).
tff(c_45717,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_422,c_45713]) ).
tff(c_45719,plain,
ssList(cons('#skF_52',nil)),
inference(splitRight,[status(thm)],[c_45709]) ).
tff(c_480,plain,
! [U_1164] :
( ( app(nil,U_1164) = U_1164 )
| ~ ssList(U_1164) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_490,plain,
app(nil,'#skF_50') = '#skF_50',
inference(resolution,[status(thm)],[c_390,c_480]) ).
tff(c_60207,plain,
! [W_2557,V_2558,X_2559] :
( segmentP(app(app(W_2557,V_2558),X_2559),V_2558)
| ~ ssList(X_2559)
| ~ ssList(W_2557)
| ~ ssList(V_2558)
| ~ ssList(app(app(W_2557,V_2558),X_2559)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_60479,plain,
! [X_2559] :
( segmentP(app('#skF_50',X_2559),'#skF_50')
| ~ ssList(X_2559)
| ~ ssList(nil)
| ~ ssList('#skF_50')
| ~ ssList(app(app(nil,'#skF_50'),X_2559)) ),
inference(superposition,[status(thm),theory(equality)],[c_490,c_60207]) ).
tff(c_60856,plain,
! [X_2563] :
( segmentP(app('#skF_50',X_2563),'#skF_50')
| ~ ssList(X_2563)
| ~ ssList(app('#skF_50',X_2563)) ),
inference(demodulation,[status(thm),theory(equality)],[c_490,c_390,c_168,c_60479]) ).
tff(c_60873,plain,
( segmentP('#skF_51','#skF_50')
| ~ ssList(cons('#skF_52',nil))
| ~ ssList(app('#skF_50',cons('#skF_52',nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_420,c_60856]) ).
tff(c_60885,plain,
segmentP('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_420,c_45719,c_60873]) ).
tff(c_60887,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_426,c_60885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC355+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n004.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 21:21:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 27.98/13.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.98/13.46
% 27.98/13.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.98/13.49
% 27.98/13.49 Inference rules
% 27.98/13.49 ----------------------
% 27.98/13.49 #Ref : 10
% 27.98/13.49 #Sup : 13285
% 27.98/13.49 #Fact : 0
% 27.98/13.49 #Define : 0
% 27.98/13.49 #Split : 97
% 27.98/13.49 #Chain : 0
% 27.98/13.49 #Close : 0
% 27.98/13.49
% 27.98/13.49 Ordering : KBO
% 27.98/13.49
% 27.98/13.49 Simplification rules
% 27.98/13.49 ----------------------
% 27.98/13.49 #Subsume : 1966
% 27.98/13.49 #Demod : 11603
% 27.98/13.49 #Tautology : 3782
% 27.98/13.49 #SimpNegUnit : 1282
% 27.98/13.49 #BackRed : 269
% 27.98/13.49
% 27.98/13.49 #Partial instantiations: 0
% 27.98/13.49 #Strategies tried : 1
% 27.98/13.49
% 27.98/13.49 Timing (in seconds)
% 27.98/13.49 ----------------------
% 27.98/13.49 Preprocessing : 0.93
% 27.98/13.49 Parsing : 0.43
% 27.98/13.49 CNF conversion : 0.12
% 27.98/13.49 Main loop : 11.46
% 27.98/13.49 Inferencing : 2.72
% 27.98/13.49 Reduction : 4.85
% 27.98/13.49 Demodulation : 3.47
% 27.98/13.49 BG Simplification : 0.16
% 27.98/13.49 Subsumption : 2.95
% 27.98/13.49 Abstraction : 0.18
% 27.98/13.49 MUC search : 0.00
% 27.98/13.49 Cooper : 0.00
% 27.98/13.49 Total : 12.44
% 27.98/13.49 Index Insertion : 0.00
% 27.98/13.49 Index Deletion : 0.00
% 27.98/13.49 Index Matching : 0.00
% 27.98/13.49 BG Taut test : 0.00
%------------------------------------------------------------------------------