%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC382+1 : TPTP v9.0.0. Released v2.4.0.
% 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 : n005.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 : Wed Apr 9 09:20:16 PM UTC 2025
% Result : Theorem 22.22s 8.85s
% Output : CNFRefutation 22.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 183 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 350 ( 130 equ)
% Maximal formula atoms : 17 ( 1 avg)
% Number of connectives : 303 ( 136 ~; 124 |; 12 &)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 67 ( 60 !; 7 ?; 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_1021,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) ) )
| ( singletonP(U)
& segmentP(V,U) ) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_769,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssItem(V)
& ( hd(U) = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
tff(f_311,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
tff(f_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_779,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssList(V)
& ( tl(U) = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_318,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
tff(f_327,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) != U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
tff(f_378,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( hd(cons(V,U)) = V ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
tff(f_96,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& ( cons(V,nil) = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
tff(f_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
tff(f_519,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
tff(f_834,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) = app(cons(V,nil),U) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
tff(f_803,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ( cons(hd(U),tl(U)) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_406,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_411,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).
tff(c_396,plain,
( ~ segmentP('#skF_49','#skF_48')
| ~ singletonP('#skF_48')
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_412,plain,
( ~ segmentP('#skF_51','#skF_48')
| ~ singletonP('#skF_48')
| ~ neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_396]) ).
tff(c_417,plain,
( ~ segmentP('#skF_51','#skF_48')
| ~ singletonP('#skF_48') ),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_412]) ).
tff(c_419,plain,
( ~ segmentP('#skF_51','#skF_50')
| ~ singletonP('#skF_50') ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_384,c_417]) ).
tff(c_429,plain,
~ singletonP('#skF_50'),
inference(splitLeft,[status(thm)],[c_419]) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_388,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_5025,plain,
! [U_1506] :
( ( hd(U_1506) = '#skF_46'(U_1506) )
| ( nil = U_1506 )
| ~ ssList(U_1506) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_5133,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_5025]) ).
tff(c_5135,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_5133]) ).
tff(c_5166,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_5135,c_411]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_5339,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_5166,c_164]) ).
tff(c_5344,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5339]) ).
tff(c_5345,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(splitRight,[status(thm)],[c_5133]) ).
tff(c_4467,plain,
! [U_1450] :
( ssItem(hd(U_1450))
| ( nil = U_1450 )
| ~ ssList(U_1450) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_1760,plain,
! [U_1333] :
( ( tl(U_1333) = '#skF_47'(U_1333) )
| ( nil = U_1333 )
| ~ ssList(U_1333) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_1868,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_1760]) ).
tff(c_1870,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_1868]) ).
tff(c_1903,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_1870,c_411]) ).
tff(c_2152,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_1903,c_164]) ).
tff(c_2157,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2152]) ).
tff(c_2159,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_1868]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_4303,plain,
! [U_1429,V_1430] :
( neq(U_1429,V_1430)
| ( V_1430 = U_1429 )
| ~ ssList(V_1430)
| ~ ssList(U_1429) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_774,plain,
! [U_1248] :
( ( hd(U_1248) = '#skF_46'(U_1248) )
| ( nil = U_1248 )
| ~ ssList(U_1248) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_878,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_774]) ).
tff(c_880,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_878]) ).
tff(c_910,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_880,c_411]) ).
tff(c_1067,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_910,c_164]) ).
tff(c_1072,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1067]) ).
tff(c_1074,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_878]) ).
tff(c_1073,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(splitRight,[status(thm)],[c_878]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_1079,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1073,c_184]) ).
tff(c_1083,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1079]) ).
tff(c_1084,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_1074,c_1083]) ).
tff(c_1378,plain,
! [V_1266,U_1267] :
( ssList(cons(V_1266,U_1267))
| ~ ssItem(V_1266)
| ~ ssList(U_1267) ),
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_1021]) ).
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_430,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitLeft,[status(thm)],[c_415]) ).
tff(c_1075,plain,
~ ssList(cons('#skF_46'('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_1073,c_430]) ).
tff(c_1384,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_1378,c_1075]) ).
tff(c_1398,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_1084,c_1384]) ).
tff(c_1399,plain,
( ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51')
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_415]) ).
tff(c_1413,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_1399]) ).
tff(c_4306,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_4303,c_1413]) ).
tff(c_4317,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_4306]) ).
tff(c_4319,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2159,c_4317]) ).
tff(c_4320,plain,
( ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_1399]) ).
tff(c_4323,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_4320]) ).
tff(c_4470,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_4467,c_4323]) ).
tff(c_4473,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4470]) ).
tff(c_4501,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_4473,c_411]) ).
tff(c_4521,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_4501,c_164]) ).
tff(c_4526,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4521]) ).
tff(c_4528,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_4320]) ).
tff(c_5459,plain,
ssItem('#skF_46'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_5345,c_4528]) ).
tff(c_5134,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_5025]) ).
tff(c_5470,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_5134]) ).
tff(c_4527,plain,
cons(hd('#skF_51'),nil) = '#skF_50',
inference(splitRight,[status(thm)],[c_4320]) ).
tff(c_5458,plain,
cons('#skF_46'('#skF_51'),nil) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_5345,c_4527]) ).
tff(c_5540,plain,
cons('#skF_46'('#skF_51'),'#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_5470,c_5458]) ).
tff(c_170,plain,
! [V_864,U_862] :
( ( cons(V_864,U_862) != U_862 )
| ~ ssItem(V_864)
| ~ ssList(U_862) ),
inference(cnfTransformation,[status(thm)],[f_327]) ).
tff(c_5543,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_5540,c_170]) ).
tff(c_5552,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_390,c_5459,c_5543]) ).
tff(c_5554,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_5134]) ).
tff(c_5553,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(splitRight,[status(thm)],[c_5134]) ).
tff(c_5560,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_5553,c_184]) ).
tff(c_5564,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_5560]) ).
tff(c_5565,plain,
ssItem('#skF_46'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_5554,c_5564]) ).
tff(c_5904,plain,
! [V_1524,U_1525] :
( ( hd(cons(V_1524,U_1525)) = V_1524 )
| ~ ssItem(V_1524)
| ~ ssList(U_1525) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_5916,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_51') )
| ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_5458,c_5904]) ).
tff(c_5920,plain,
'#skF_46'('#skF_51') = '#skF_46'('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_5459,c_5553,c_5916]) ).
tff(c_5921,plain,
cons('#skF_46'('#skF_50'),nil) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_5920,c_5458]) ).
tff(c_6910,plain,
! [V_1574] :
( singletonP(cons(V_1574,nil))
| ~ ssItem(V_1574)
| ~ ssList(cons(V_1574,nil)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_6916,plain,
( singletonP(cons('#skF_46'('#skF_50'),nil))
| ~ ssItem('#skF_46'('#skF_50'))
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_5921,c_6910]) ).
tff(c_6922,plain,
singletonP('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_5565,c_5921,c_6916]) ).
tff(c_6924,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_429,c_6922]) ).
tff(c_6925,plain,
~ segmentP('#skF_51','#skF_50'),
inference(splitRight,[status(thm)],[c_419]) ).
tff(c_9480,plain,
! [U_1835] :
( ( tl(U_1835) = '#skF_47'(U_1835) )
| ( nil = U_1835 )
| ~ ssList(U_1835) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_9584,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_9480]) ).
tff(c_9586,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_9584]) ).
tff(c_9618,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_9586,c_411]) ).
tff(c_9641,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_9618,c_164]) ).
tff(c_9648,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_9641]) ).
tff(c_9650,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_9584]) ).
tff(c_9649,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(splitRight,[status(thm)],[c_9584]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_9654,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_9649,c_188]) ).
tff(c_9658,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_9654]) ).
tff(c_9659,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_9650,c_9658]) ).
tff(c_6926,plain,
singletonP('#skF_50'),
inference(splitRight,[status(thm)],[c_419]) ).
tff(c_9585,plain,
( ( tl('#skF_50') = '#skF_47'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_9480]) ).
tff(c_9673,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_9585]) ).
tff(c_230,plain,
~ singletonP(nil),
inference(cnfTransformation,[status(thm)],[f_519]) ).
tff(c_9712,plain,
~ singletonP('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_9673,c_230]) ).
tff(c_9723,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6926,c_9712]) ).
tff(c_9725,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_9585]) ).
tff(c_9726,plain,
! [U_1838] :
( ( hd(U_1838) = '#skF_46'(U_1838) )
| ( nil = U_1838 )
| ~ ssList(U_1838) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_9837,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_9726]) ).
tff(c_9864,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_9725,c_9837]) ).
tff(c_9868,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_9864,c_184]) ).
tff(c_9872,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_9868]) ).
tff(c_9873,plain,
ssItem('#skF_46'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_9725,c_9872]) ).
tff(c_9804,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_9726]) ).
tff(c_9836,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_9650,c_9804]) ).
tff(c_9044,plain,
! [U_1780] :
( ssItem(hd(U_1780))
| ( nil = U_1780 )
| ~ ssList(U_1780) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_7819,plain,
! [U_1710] :
( ( tl(U_1710) = '#skF_47'(U_1710) )
| ( nil = U_1710 )
| ~ ssList(U_1710) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_7927,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_7819]) ).
tff(c_7929,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_7927]) ).
tff(c_7975,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_7929,c_411]) ).
tff(c_8014,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_7975,c_164]) ).
tff(c_8021,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_8014]) ).
tff(c_8023,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_7927]) ).
tff(c_8736,plain,
! [U_1735,V_1736] :
( neq(U_1735,V_1736)
| ( V_1736 = U_1735 )
| ~ ssList(V_1736)
| ~ ssList(U_1735) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_7380,plain,
! [V_1645,U_1646] :
( ssList(cons(V_1645,U_1646))
| ~ ssItem(V_1645)
| ~ ssList(U_1646) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_6929,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitLeft,[status(thm)],[c_415]) ).
tff(c_7392,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_7380,c_6929]) ).
tff(c_7398,plain,
~ ssItem(hd('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_7392]) ).
tff(c_7401,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_184,c_7398]) ).
tff(c_7404,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_7401]) ).
tff(c_7434,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_7404,c_411]) ).
tff(c_7452,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_7434,c_164]) ).
tff(c_7459,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_7452]) ).
tff(c_7460,plain,
( ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51')
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_415]) ).
tff(c_7470,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_7460]) ).
tff(c_8739,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_8736,c_7470]) ).
tff(c_8750,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_8739]) ).
tff(c_8752,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8023,c_8750]) ).
tff(c_8753,plain,
( ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_7460]) ).
tff(c_8757,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_8753]) ).
tff(c_9047,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_9044,c_8757]) ).
tff(c_9050,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_9047]) ).
tff(c_9081,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_9050,c_411]) ).
tff(c_9099,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_9081,c_164]) ).
tff(c_9106,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_9099]) ).
tff(c_9108,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_8753]) ).
tff(c_9876,plain,
ssItem('#skF_46'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_9836,c_9108]) ).
tff(c_9107,plain,
cons(hd('#skF_51'),nil) = '#skF_50',
inference(splitRight,[status(thm)],[c_8753]) ).
tff(c_9875,plain,
cons('#skF_46'('#skF_51'),nil) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_9836,c_9107]) ).
tff(c_10350,plain,
! [V_1858,U_1859] :
( ( hd(cons(V_1858,U_1859)) = V_1858 )
| ~ ssItem(V_1858)
| ~ ssList(U_1859) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_10362,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_51') )
| ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_9875,c_10350]) ).
tff(c_10366,plain,
'#skF_46'('#skF_51') = '#skF_46'('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_9876,c_9864,c_10362]) ).
tff(c_10367,plain,
cons('#skF_46'('#skF_50'),nil) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_10366,c_9875]) ).
tff(c_15295,plain,
! [V_2095,U_2096] :
( ( app(cons(V_2095,nil),U_2096) = cons(V_2095,U_2096) )
| ~ ssItem(V_2095)
| ~ ssList(U_2096) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_15317,plain,
! [U_2096] :
( ( cons('#skF_46'('#skF_50'),U_2096) = app('#skF_50',U_2096) )
| ~ ssItem('#skF_46'('#skF_50'))
| ~ ssList(U_2096) ),
inference(superposition,[status(thm),theory(equality)],[c_10367,c_15295]) ).
tff(c_15322,plain,
! [U_2097] :
( ( cons('#skF_46'('#skF_50'),U_2097) = app('#skF_50',U_2097) )
| ~ ssList(U_2097) ),
inference(demodulation,[status(thm),theory(equality)],[c_9873,c_15317]) ).
tff(c_10369,plain,
hd('#skF_51') = '#skF_46'('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_10366,c_9836]) ).
tff(c_12584,plain,
! [U_1966] :
( ( cons(hd(U_1966),tl(U_1966)) = U_1966 )
| ( nil = U_1966 )
| ~ ssList(U_1966) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_12630,plain,
( ( cons(hd('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_9649,c_12584]) ).
tff(c_12651,plain,
( ( cons('#skF_46'('#skF_50'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_10369,c_12630]) ).
tff(c_12652,plain,
cons('#skF_46'('#skF_50'),'#skF_47'('#skF_51')) = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_9650,c_12651]) ).
tff(c_15338,plain,
( ( app('#skF_50','#skF_47'('#skF_51')) = '#skF_51' )
| ~ ssList('#skF_47'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_15322,c_12652]) ).
tff(c_15407,plain,
app('#skF_50','#skF_47'('#skF_51')) = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_9659,c_15338]) ).
tff(c_9152,plain,
! [U_1785] :
( ( app(nil,U_1785) = U_1785 )
| ~ ssList(U_1785) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_9165,plain,
app(nil,'#skF_50') = '#skF_50',
inference(resolution,[status(thm)],[c_390,c_9152]) ).
tff(c_31100,plain,
! [W_2371,V_2372,X_2373] :
( segmentP(app(app(W_2371,V_2372),X_2373),V_2372)
| ~ ssList(X_2373)
| ~ ssList(W_2371)
| ~ ssList(V_2372)
| ~ ssList(app(app(W_2371,V_2372),X_2373)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_31393,plain,
! [X_2373] :
( segmentP(app('#skF_50',X_2373),'#skF_50')
| ~ ssList(X_2373)
| ~ ssList(nil)
| ~ ssList('#skF_50')
| ~ ssList(app(app(nil,'#skF_50'),X_2373)) ),
inference(superposition,[status(thm),theory(equality)],[c_9165,c_31100]) ).
tff(c_34218,plain,
! [X_2476] :
( segmentP(app('#skF_50',X_2476),'#skF_50')
| ~ ssList(X_2476)
| ~ ssList(app('#skF_50',X_2476)) ),
inference(demodulation,[status(thm),theory(equality)],[c_9165,c_390,c_168,c_31393]) ).
tff(c_34232,plain,
( segmentP('#skF_51','#skF_50')
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssList(app('#skF_50','#skF_47'('#skF_51'))) ),
inference(superposition,[status(thm),theory(equality)],[c_15407,c_34218]) ).
tff(c_34245,plain,
segmentP('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_15407,c_9659,c_34232]) ).
tff(c_34247,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6925,c_34245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC382+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.14 % 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
% 0.14/0.35 % Computer : n005.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 : Wed Apr 9 02:22:57 EDT 2025
% 0.14/0.36 % CPUTime :
% 22.22/8.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.22/8.86
% 22.22/8.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------