TSTP Solution File: SWC099+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC099+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 : n012.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 11:01:09 EDT 2023
% Result : Theorem 35.89s 21.82s
% Output : CNFRefutation 36.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 95
% Syntax : Number of formulae : 227 ( 53 unt; 75 typ; 0 def)
% Number of atoms : 372 ( 113 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 398 ( 178 ~; 168 |; 11 &)
% ( 5 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 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 : 101 (; 96 !; 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_1023,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ~ frontsegP(X,W)
| ~ equalelemsP(W)
| ? [Y] :
( ssList(Y)
& neq(W,Y)
& frontsegP(X,Y)
& segmentP(Y,W)
& equalelemsP(Y) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ~ neq(V,nil)
| ( neq(U,nil)
& frontsegP(V,U) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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_667,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
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_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_758,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax73) ).
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_96,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& ( cons(V,nil) = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
tff(f_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
tff(f_409,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ( cons(W,app(V,U)) = app(cons(W,V),U) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
tff(f_364,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( nil != cons(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
tff(f_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_108,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& ( app(V,W) = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
tff(f_803,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ( cons(hd(U),tl(U)) = U ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
tff(f_577,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( ( U = V )
& frontsegP(W,X) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
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_686,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_587,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
tff(c_396,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_1061,plain,
! [U_1223] :
( ( tl(U_1223) = '#skF_47'(U_1223) )
| ( nil = U_1223 )
| ~ ssList(U_1223) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_1173,plain,
( ( tl('#skF_50') = '#skF_47'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_396,c_1061]) ).
tff(c_1175,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_1173]) ).
tff(c_388,plain,
frontsegP('#skF_51','#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_386,plain,
equalelemsP('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_435,plain,
! [U_1151] :
( segmentP(U_1151,U_1151)
| ~ ssList(U_1151) ),
inference(cnfTransformation,[status(thm)],[f_667]) ).
tff(c_384,plain,
! [Y_1148] :
( ~ equalelemsP(Y_1148)
| ~ segmentP(Y_1148,'#skF_50')
| ~ frontsegP('#skF_51',Y_1148)
| ~ neq('#skF_50',Y_1148)
| ~ ssList(Y_1148) ),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_439,plain,
( ~ equalelemsP('#skF_50')
| ~ frontsegP('#skF_51','#skF_50')
| ~ neq('#skF_50','#skF_50')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_435,c_384]) ).
tff(c_442,plain,
~ neq('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_388,c_386,c_439]) ).
tff(c_394,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_1174,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_394,c_1061]) ).
tff(c_1176,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_1174]) ).
tff(c_1224,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_1176]) ).
tff(c_392,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_408,plain,
( ( nil = '#skF_49' )
| neq('#skF_49',nil) ),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_410,plain,
( ( nil = '#skF_51' )
| neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_392,c_408]) ).
tff(c_445,plain,
neq('#skF_51',nil),
inference(splitLeft,[status(thm)],[c_410]) ).
tff(c_1205,plain,
neq('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_445]) ).
tff(c_1242,plain,
neq('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_1224,c_1205]) ).
tff(c_1243,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_442,c_1242]) ).
tff(c_1245,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_1174]) ).
tff(c_1397,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_1245]) ).
tff(c_1393,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_1245]) ).
tff(c_330,plain,
! [U_1045] :
( ( hd(U_1045) = '#skF_46'(U_1045) )
| ( nil = U_1045 )
| ~ ssList(U_1045) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_1294,plain,
! [U_1226] :
( ( hd(U_1226) = '#skF_46'(U_1226) )
| ( U_1226 = '#skF_50' )
| ~ ssList(U_1226) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_330]) ).
tff(c_1391,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( '#skF_51' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_394,c_1294]) ).
tff(c_1392,plain,
'#skF_51' = '#skF_50',
inference(splitLeft,[status(thm)],[c_1391]) ).
tff(c_1394,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1393,c_1392]) ).
tff(c_1395,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(splitRight,[status(thm)],[c_1391]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_1808,plain,
! [U_1254] :
( ssItem(hd(U_1254))
| ( U_1254 = '#skF_50' )
| ~ ssList(U_1254) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_184]) ).
tff(c_1811,plain,
( ssItem('#skF_46'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1395,c_1808]) ).
tff(c_1813,plain,
( ssItem('#skF_46'('#skF_51'))
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1811]) ).
tff(c_1814,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_1397,c_1813]) ).
tff(c_326,plain,
! [U_1044] :
( equalelemsP(cons(U_1044,nil))
| ~ ssItem(U_1044) ),
inference(cnfTransformation,[status(thm)],[f_758]) ).
tff(c_1264,plain,
! [U_1044] :
( equalelemsP(cons(U_1044,'#skF_50'))
| ~ ssItem(U_1044) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_326]) ).
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_20,plain,
! [V_33] :
( singletonP(cons(V_33,nil))
| ~ ssItem(V_33)
| ~ ssList(cons(V_33,nil)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_3675,plain,
! [V_1336] :
( singletonP(cons(V_1336,'#skF_50'))
| ~ ssItem(V_1336)
| ~ ssList(cons(V_1336,'#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_1175,c_20]) ).
tff(c_3682,plain,
! [V_861] :
( singletonP(cons(V_861,'#skF_50'))
| ~ ssItem(V_861)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_3675]) ).
tff(c_3685,plain,
! [V_861] :
( singletonP(cons(V_861,'#skF_50'))
| ~ ssItem(V_861) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_3682]) ).
tff(c_484,plain,
! [U_1167] :
( ( app(U_1167,nil) = U_1167 )
| ~ ssList(U_1167) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_496,plain,
app('#skF_50',nil) = '#skF_50',
inference(resolution,[status(thm)],[c_396,c_484]) ).
tff(c_1261,plain,
app('#skF_50','#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_496]) ).
tff(c_13317,plain,
! [W_1698,V_1699,U_1700] :
( ( cons(W_1698,app(V_1699,U_1700)) = app(cons(W_1698,V_1699),U_1700) )
| ~ ssItem(W_1698)
| ~ ssList(V_1699)
| ~ ssList(U_1700) ),
inference(cnfTransformation,[status(thm)],[f_409]) ).
tff(c_13555,plain,
! [W_1698] :
( ( app(cons(W_1698,'#skF_50'),'#skF_50') = cons(W_1698,'#skF_50') )
| ~ ssItem(W_1698)
| ~ ssList('#skF_50')
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_1261,c_13317]) ).
tff(c_13673,plain,
! [W_1698] :
( ( app(cons(W_1698,'#skF_50'),'#skF_50') = cons(W_1698,'#skF_50') )
| ~ ssItem(W_1698) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_396,c_13555]) ).
tff(c_70020,plain,
! [W_2482,V_2483,U_2484] :
( ssList(app(cons(W_2482,V_2483),U_2484))
| ~ ssItem(W_2482)
| ~ ssList(app(V_2483,U_2484))
| ~ ssItem(W_2482)
| ~ ssList(V_2483)
| ~ ssList(U_2484) ),
inference(superposition,[status(thm),theory(equality)],[c_13317,c_166]) ).
tff(c_70163,plain,
! [W_1698] :
( ssList(cons(W_1698,'#skF_50'))
| ~ ssItem(W_1698)
| ~ ssList(app('#skF_50','#skF_50'))
| ~ ssItem(W_1698)
| ~ ssList('#skF_50')
| ~ ssList('#skF_50')
| ~ ssItem(W_1698) ),
inference(superposition,[status(thm),theory(equality)],[c_13673,c_70020]) ).
tff(c_70417,plain,
! [W_2486] :
( ssList(cons(W_2486,'#skF_50'))
| ~ ssItem(W_2486) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_396,c_396,c_1261,c_70163]) ).
tff(c_24,plain,
! [U_30] :
( ssItem('#skF_5'(U_30))
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_22,plain,
! [U_30] :
( ( cons('#skF_5'(U_30),nil) = U_30 )
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_2440,plain,
! [U_1286] :
( ( cons('#skF_5'(U_1286),'#skF_50') = U_1286 )
| ~ singletonP(U_1286)
| ~ ssList(U_1286) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_22]) ).
tff(c_182,plain,
! [V_887,U_885] :
( ( cons(V_887,U_885) != nil )
| ~ ssItem(V_887)
| ~ ssList(U_885) ),
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_1247,plain,
! [V_887,U_885] :
( ( cons(V_887,U_885) != '#skF_50' )
| ~ ssItem(V_887)
| ~ ssList(U_885) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_182]) ).
tff(c_2448,plain,
! [U_1286] :
( ( U_1286 != '#skF_50' )
| ~ ssItem('#skF_5'(U_1286))
| ~ ssList('#skF_50')
| ~ singletonP(U_1286)
| ~ ssList(U_1286) ),
inference(superposition,[status(thm),theory(equality)],[c_2440,c_1247]) ).
tff(c_2499,plain,
! [U_1287] :
( ( U_1287 != '#skF_50' )
| ~ ssItem('#skF_5'(U_1287))
| ~ singletonP(U_1287)
| ~ ssList(U_1287) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_2448]) ).
tff(c_2503,plain,
! [U_30] :
( ( U_30 != '#skF_50' )
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(resolution,[status(thm)],[c_24,c_2499]) ).
tff(c_72157,plain,
! [W_2514] :
( ( cons(W_2514,'#skF_50') != '#skF_50' )
| ~ singletonP(cons(W_2514,'#skF_50'))
| ~ ssItem(W_2514) ),
inference(resolution,[status(thm)],[c_70417,c_2503]) ).
tff(c_72346,plain,
! [V_2516] :
( ( cons(V_2516,'#skF_50') != '#skF_50' )
| ~ ssItem(V_2516) ),
inference(resolution,[status(thm)],[c_3685,c_72157]) ).
tff(c_72427,plain,
cons('#skF_46'('#skF_51'),'#skF_50') != '#skF_50',
inference(resolution,[status(thm)],[c_1814,c_72346]) ).
tff(c_1244,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(splitRight,[status(thm)],[c_1174]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_1680,plain,
! [U_1249] :
( ssList(tl(U_1249))
| ( U_1249 = '#skF_50' )
| ~ ssList(U_1249) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_188]) ).
tff(c_1698,plain,
( ssList('#skF_47'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1244,c_1680]) ).
tff(c_1705,plain,
( ssList('#skF_47'('#skF_51'))
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1698]) ).
tff(c_1706,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_1397,c_1705]) ).
tff(c_196,plain,
! [U_906] :
( ( app(nil,U_906) = U_906 )
| ~ ssList(U_906) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_1268,plain,
! [U_906] :
( ( app('#skF_50',U_906) = U_906 )
| ~ ssList(U_906) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_196]) ).
tff(c_1722,plain,
app('#skF_50','#skF_47'('#skF_51')) = '#skF_47'('#skF_51'),
inference(resolution,[status(thm)],[c_1706,c_1268]) ).
tff(c_6573,plain,
! [V_1455,W_1456] :
( frontsegP(app(V_1455,W_1456),V_1455)
| ~ ssList(W_1456)
| ~ ssList(V_1455)
| ~ ssList(app(V_1455,W_1456)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_6740,plain,
( frontsegP('#skF_47'('#skF_51'),'#skF_50')
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_50','#skF_47'('#skF_51'))) ),
inference(superposition,[status(thm),theory(equality)],[c_1722,c_6573]) ).
tff(c_6854,plain,
frontsegP('#skF_47'('#skF_51'),'#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_1706,c_1722,c_396,c_1706,c_6740]) ).
tff(c_340,plain,
! [U_1052] :
( ( cons(hd(U_1052),tl(U_1052)) = U_1052 )
| ( nil = U_1052 )
| ~ ssList(U_1052) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_3479,plain,
! [U_1328] :
( ( cons(hd(U_1328),tl(U_1328)) = U_1328 )
| ( U_1328 = '#skF_50' )
| ~ ssList(U_1328) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_340]) ).
tff(c_3522,plain,
( ( cons(hd('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1244,c_3479]) ).
tff(c_3540,plain,
( ( cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1395,c_3522]) ).
tff(c_3541,plain,
cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_1397,c_3540]) ).
tff(c_13144,plain,
! [V_1689,W_1690,X_1691] :
( frontsegP(cons(V_1689,W_1690),cons(V_1689,X_1691))
| ~ frontsegP(W_1690,X_1691)
| ~ ssList(X_1691)
| ~ ssList(W_1690)
| ~ ssItem(V_1689) ),
inference(cnfTransformation,[status(thm)],[f_577]) ).
tff(c_13163,plain,
! [X_1691] :
( frontsegP('#skF_51',cons('#skF_46'('#skF_51'),X_1691))
| ~ frontsegP('#skF_47'('#skF_51'),X_1691)
| ~ ssList(X_1691)
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssItem('#skF_46'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_3541,c_13144]) ).
tff(c_26899,plain,
! [X_2040] :
( frontsegP('#skF_51',cons('#skF_46'('#skF_51'),X_2040))
| ~ frontsegP('#skF_47'('#skF_51'),X_2040)
| ~ ssList(X_2040) ),
inference(demodulation,[status(thm),theory(equality)],[c_1814,c_1706,c_13163]) ).
tff(c_1650,plain,
! [U_1244,V_1245] :
( neq(U_1244,V_1245)
| ( V_1245 = U_1244 )
| ~ ssList(V_1245)
| ~ ssList(U_1244) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_274,plain,
! [U_1030] :
( segmentP(U_1030,nil)
| ~ ssList(U_1030) ),
inference(cnfTransformation,[status(thm)],[f_686]) ).
tff(c_1437,plain,
! [U_1230] :
( segmentP(U_1230,'#skF_50')
| ~ ssList(U_1230) ),
inference(demodulation,[status(thm),theory(equality)],[c_1175,c_274]) ).
tff(c_1441,plain,
! [U_1230] :
( ~ equalelemsP(U_1230)
| ~ frontsegP('#skF_51',U_1230)
| ~ neq('#skF_50',U_1230)
| ~ ssList(U_1230) ),
inference(resolution,[status(thm)],[c_1437,c_384]) ).
tff(c_1654,plain,
! [V_1245] :
( ~ equalelemsP(V_1245)
| ~ frontsegP('#skF_51',V_1245)
| ( V_1245 = '#skF_50' )
| ~ ssList(V_1245)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_1650,c_1441]) ).
tff(c_1668,plain,
! [V_1245] :
( ~ equalelemsP(V_1245)
| ~ frontsegP('#skF_51',V_1245)
| ( V_1245 = '#skF_50' )
| ~ ssList(V_1245) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_1654]) ).
tff(c_26923,plain,
! [X_2040] :
( ~ equalelemsP(cons('#skF_46'('#skF_51'),X_2040))
| ( cons('#skF_46'('#skF_51'),X_2040) = '#skF_50' )
| ~ ssList(cons('#skF_46'('#skF_51'),X_2040))
| ~ frontsegP('#skF_47'('#skF_51'),X_2040)
| ~ ssList(X_2040) ),
inference(resolution,[status(thm)],[c_26899,c_1668]) ).
tff(c_70451,plain,
( ~ equalelemsP(cons('#skF_46'('#skF_51'),'#skF_50'))
| ( cons('#skF_46'('#skF_51'),'#skF_50') = '#skF_50' )
| ~ frontsegP('#skF_47'('#skF_51'),'#skF_50')
| ~ ssList('#skF_50')
| ~ ssItem('#skF_46'('#skF_51')) ),
inference(resolution,[status(thm)],[c_70417,c_26923]) ).
tff(c_70542,plain,
( ~ equalelemsP(cons('#skF_46'('#skF_51'),'#skF_50'))
| ( cons('#skF_46'('#skF_51'),'#skF_50') = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1814,c_396,c_6854,c_70451]) ).
tff(c_76362,plain,
~ equalelemsP(cons('#skF_46'('#skF_51'),'#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_72427,c_70542]) ).
tff(c_76368,plain,
~ ssItem('#skF_46'('#skF_51')),
inference(resolution,[status(thm)],[c_1264,c_76362]) ).
tff(c_76375,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1814,c_76368]) ).
tff(c_76377,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_1173]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_76838,plain,
! [U_2586,V_2587] :
( neq(U_2586,V_2587)
| ( V_2587 = U_2586 )
| ~ ssList(V_2587)
| ~ ssList(U_2586) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_390,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_404,plain,
( ( nil = '#skF_49' )
| ~ frontsegP('#skF_49','#skF_48')
| ~ neq('#skF_48',nil) ),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_412,plain,
( ( nil = '#skF_51' )
| ~ frontsegP('#skF_51','#skF_48')
| ~ neq('#skF_48',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_392,c_404]) ).
tff(c_417,plain,
( ( nil = '#skF_51' )
| ~ frontsegP('#skF_51','#skF_50')
| ~ neq('#skF_50',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_390,c_412]) ).
tff(c_421,plain,
( ( nil = '#skF_51' )
| ~ neq('#skF_50',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_417]) ).
tff(c_434,plain,
~ neq('#skF_50',nil),
inference(splitLeft,[status(thm)],[c_421]) ).
tff(c_76852,plain,
( ( nil = '#skF_50' )
| ~ ssList(nil)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_76838,c_434]) ).
tff(c_76863,plain,
nil = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_168,c_76852]) ).
tff(c_76865,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_76377,c_76863]) ).
tff(c_76866,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_410]) ).
tff(c_76867,plain,
~ neq('#skF_51',nil),
inference(splitRight,[status(thm)],[c_410]) ).
tff(c_76884,plain,
~ neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_76866,c_76867]) ).
tff(c_406,plain,
( ( nil != '#skF_48' )
| neq('#skF_49',nil) ),
inference(cnfTransformation,[status(thm)],[f_1023]) ).
tff(c_411,plain,
( ( nil != '#skF_48' )
| neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_406]) ).
tff(c_416,plain,
( ( nil != '#skF_50' )
| neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_411]) ).
tff(c_76885,plain,
( ( '#skF_51' != '#skF_50' )
| neq('#skF_51','#skF_51') ),
inference(demodulation,[status(thm),theory(equality)],[c_76866,c_76866,c_416]) ).
tff(c_76886,plain,
'#skF_51' != '#skF_50',
inference(negUnitSimplification,[status(thm)],[c_76884,c_76885]) ).
tff(c_250,plain,
! [U_983] :
( ( nil = U_983 )
| ~ frontsegP(nil,U_983)
| ~ ssList(U_983) ),
inference(cnfTransformation,[status(thm)],[f_587]) ).
tff(c_77089,plain,
! [U_2628] :
( ( U_2628 = '#skF_51' )
| ~ frontsegP('#skF_51',U_2628)
| ~ ssList(U_2628) ),
inference(demodulation,[status(thm),theory(equality)],[c_76866,c_76866,c_250]) ).
tff(c_77100,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_388,c_77089]) ).
tff(c_77111,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_77100]) ).
tff(c_77113,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_76886,c_77111]) ).
tff(c_77114,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_421]) ).
tff(c_77137,plain,
( ( '#skF_51' != '#skF_50' )
| neq('#skF_51','#skF_51') ),
inference(demodulation,[status(thm),theory(equality)],[c_77114,c_77114,c_416]) ).
tff(c_77138,plain,
'#skF_51' != '#skF_50',
inference(splitLeft,[status(thm)],[c_77137]) ).
tff(c_77310,plain,
! [U_2668] :
( ( U_2668 = '#skF_51' )
| ~ frontsegP('#skF_51',U_2668)
| ~ ssList(U_2668) ),
inference(demodulation,[status(thm),theory(equality)],[c_77114,c_77114,c_250]) ).
tff(c_77321,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_388,c_77310]) ).
tff(c_77332,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_77321]) ).
tff(c_77334,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_77138,c_77332]) ).
tff(c_77336,plain,
'#skF_51' = '#skF_50',
inference(splitRight,[status(thm)],[c_77137]) ).
tff(c_77335,plain,
neq('#skF_51','#skF_51'),
inference(splitRight,[status(thm)],[c_77137]) ).
tff(c_77366,plain,
neq('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_77336,c_77336,c_77335]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_77369,plain,
~ ssList('#skF_50'),
inference(resolution,[status(thm)],[c_77366,c_164]) ).
tff(c_77373,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_396,c_77369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC099+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
% 0.18/0.35 % Computer : n012.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 21:38:07 EDT 2023
% 0.18/0.35 % CPUTime :
% 35.89/21.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.89/21.84
% 35.89/21.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.07/21.88
% 36.07/21.88 Inference rules
% 36.07/21.88 ----------------------
% 36.07/21.88 #Ref : 5
% 36.07/21.88 #Sup : 17122
% 36.07/21.88 #Fact : 0
% 36.07/21.88 #Define : 0
% 36.07/21.88 #Split : 58
% 36.07/21.88 #Chain : 0
% 36.07/21.88 #Close : 0
% 36.07/21.88
% 36.07/21.88 Ordering : KBO
% 36.07/21.88
% 36.07/21.88 Simplification rules
% 36.07/21.88 ----------------------
% 36.07/21.88 #Subsume : 3827
% 36.07/21.88 #Demod : 14586
% 36.07/21.88 #Tautology : 2998
% 36.07/21.88 #SimpNegUnit : 1401
% 36.07/21.88 #BackRed : 257
% 36.07/21.88
% 36.07/21.88 #Partial instantiations: 0
% 36.07/21.88 #Strategies tried : 1
% 36.07/21.88
% 36.07/21.88 Timing (in seconds)
% 36.07/21.88 ----------------------
% 36.07/21.89 Preprocessing : 0.88
% 36.07/21.89 Parsing : 0.41
% 36.07/21.89 CNF conversion : 0.11
% 36.07/21.89 Main loop : 19.93
% 36.07/21.89 Inferencing : 3.60
% 36.07/21.89 Reduction : 7.81
% 36.07/21.89 Demodulation : 5.45
% 36.07/21.89 BG Simplification : 0.18
% 36.07/21.89 Subsumption : 6.62
% 36.07/21.89 Abstraction : 0.23
% 36.07/21.89 MUC search : 0.00
% 36.07/21.89 Cooper : 0.00
% 36.07/21.89 Total : 20.88
% 36.07/21.89 Index Insertion : 0.00
% 36.07/21.89 Index Deletion : 0.00
% 36.07/21.89 Index Matching : 0.00
% 36.07/21.89 BG Taut test : 0.00
%------------------------------------------------------------------------------