%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC416+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/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 : Wed Apr 9 09:20:24 PM UTC 2025
% Result : Theorem 23.49s 8.00s
% Output : CNFRefutation 23.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 112 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 81 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 262 ( 127 ~; 97 |; 11 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Maximal term depth : 4 ( 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 : 57 ( 57 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 49 !; 6 ?; 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_319,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_1027,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& ( V = Y )
& ? [Z] :
( ssList(Z)
& ( app(Z,U) = Y )
& ? [X1] :
( ssItem(X1)
& ( cons(X1,nil) = Z )
& ( hd(V) = X1 )
& neq(nil,V) ) ) )
| ! [X2] :
( ssItem(X2)
=> ( app(cons(X2,nil),W) != X ) ) )
& ( ~ 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_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_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_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_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_327,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) != U ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
tff(f_378,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( hd(cons(V,U)) = V ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
tff(f_399,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_388,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_410,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_416,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_410]) ).
tff(c_396,plain,
( ( app(cons('#skF_52',nil),'#skF_50') = '#skF_51' )
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_422,plain,
app(cons('#skF_52',nil),'#skF_50') = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_416,c_396]) ).
tff(c_398,plain,
( ssItem('#skF_52')
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_420,plain,
ssItem('#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_398]) ).
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_24672,plain,
! [V_2305] :
( singletonP(cons(V_2305,nil))
| ~ ssItem(V_2305)
| ~ ssList(cons(V_2305,nil)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_24679,plain,
! [V_861] :
( singletonP(cons(V_861,nil))
| ~ ssItem(V_861)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_24672]) ).
tff(c_24682,plain,
! [V_861] :
( singletonP(cons(V_861,nil))
| ~ ssItem(V_861) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_24679]) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_4941,plain,
! [U_1545] :
( ( tl(U_1545) = '#skF_47'(U_1545) )
| ( nil = U_1545 )
| ~ ssList(U_1545) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_5054,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_4941]) ).
tff(c_17893,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_5054]) ).
tff(c_17929,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_17893,c_416]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_17950,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_17929,c_164]) ).
tff(c_17955,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_17950]) ).
tff(c_17957,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_5054]) ).
tff(c_17996,plain,
! [U_2072] :
( ( hd(U_2072) = '#skF_46'(U_2072) )
| ( nil = U_2072 )
| ~ ssList(U_2072) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_18086,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_17996]) ).
tff(c_18121,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_17957,c_18086]) ).
tff(c_26857,plain,
! [U_2416,V_2417] :
( ( hd(app(U_2416,V_2417)) = hd(U_2416) )
| ( nil = U_2416 )
| ~ ssList(V_2417)
| ~ ssList(U_2416) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_27061,plain,
( ( hd(cons('#skF_52',nil)) = hd('#skF_51') )
| ( cons('#skF_52',nil) = nil )
| ~ ssList('#skF_50')
| ~ ssList(cons('#skF_52',nil)) ),
inference(superposition,[status(thm),theory(equality)],[c_422,c_26857]) ).
tff(c_27252,plain,
( ( hd(cons('#skF_52',nil)) = '#skF_46'('#skF_51') )
| ( cons('#skF_52',nil) = nil )
| ~ ssList(cons('#skF_52',nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_18121,c_27061]) ).
tff(c_27256,plain,
~ ssList(cons('#skF_52',nil)),
inference(splitLeft,[status(thm)],[c_27252]) ).
tff(c_27259,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_27256]) ).
tff(c_27263,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_420,c_27259]) ).
tff(c_27265,plain,
ssList(cons('#skF_52',nil)),
inference(splitRight,[status(thm)],[c_27252]) ).
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_18272,plain,
! [U_2083] :
( ( cons('#skF_5'(U_2083),nil) = U_2083 )
| ~ singletonP(U_2083)
| ~ ssList(U_2083) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
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_18279,plain,
! [U_2083] :
( ( nil != U_2083 )
| ~ ssItem('#skF_5'(U_2083))
| ~ ssList(nil)
| ~ singletonP(U_2083)
| ~ ssList(U_2083) ),
inference(superposition,[status(thm),theory(equality)],[c_18272,c_170]) ).
tff(c_24050,plain,
! [U_2287] :
( ( nil != U_2287 )
| ~ ssItem('#skF_5'(U_2287))
| ~ singletonP(U_2287)
| ~ ssList(U_2287) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_18279]) ).
tff(c_24054,plain,
! [U_30] :
( ( nil != U_30 )
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(resolution,[status(thm)],[c_24,c_24050]) ).
tff(c_27301,plain,
( ( cons('#skF_52',nil) != nil )
| ~ singletonP(cons('#skF_52',nil)) ),
inference(resolution,[status(thm)],[c_27265,c_24054]) ).
tff(c_27358,plain,
~ singletonP(cons('#skF_52',nil)),
inference(splitLeft,[status(thm)],[c_27301]) ).
tff(c_27407,plain,
~ ssItem('#skF_52'),
inference(resolution,[status(thm)],[c_24682,c_27358]) ).
tff(c_27411,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_420,c_27407]) ).
tff(c_27412,plain,
cons('#skF_52',nil) != nil,
inference(splitRight,[status(thm)],[c_27301]) ).
tff(c_27264,plain,
( ( cons('#skF_52',nil) = nil )
| ( hd(cons('#skF_52',nil)) = '#skF_46'('#skF_51') ) ),
inference(splitRight,[status(thm)],[c_27252]) ).
tff(c_27414,plain,
hd(cons('#skF_52',nil)) = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_27412,c_27264]) ).
tff(c_186,plain,
! [V_891,U_889] :
( ( hd(cons(V_891,U_889)) = V_891 )
| ~ ssItem(V_891)
| ~ ssList(U_889) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_27421,plain,
( ( '#skF_46'('#skF_51') = '#skF_52' )
| ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_27414,c_186]) ).
tff(c_27434,plain,
'#skF_46'('#skF_51') = '#skF_52',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_420,c_27421]) ).
tff(c_2395,plain,
! [U_1414] :
( ( tl(U_1414) = '#skF_47'(U_1414) )
| ( nil = U_1414 )
| ~ ssList(U_1414) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_2504,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_2395]) ).
tff(c_3680,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_2504]) ).
tff(c_3715,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_3680,c_416]) ).
tff(c_3833,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_3715,c_164]) ).
tff(c_3838,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_3833]) ).
tff(c_3840,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_2504]) ).
tff(c_4396,plain,
! [U_1494,V_1495] :
( neq(U_1494,V_1495)
| ( V_1495 = U_1494 )
| ~ ssList(V_1495)
| ~ ssList(U_1494) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_783,plain,
! [U_1325] :
( ( tl(U_1325) = '#skF_47'(U_1325) )
| ( nil = U_1325 )
| ~ ssList(U_1325) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_888,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_783]) ).
tff(c_1708,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_888]) ).
tff(c_1740,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_1708,c_416]) ).
tff(c_1764,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_1740,c_164]) ).
tff(c_1769,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1764]) ).
tff(c_1771,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_888]) ).
tff(c_1953,plain,
! [U_1357,V_1358] :
( ssList(app(U_1357,V_1358))
| ~ ssList(V_1358)
| ~ ssList(U_1357) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_400,plain,
( ~ neq(nil,'#skF_49')
| ~ ssItem(hd('#skF_49'))
| ~ ssList(cons(hd('#skF_49'),nil))
| ( app(cons(hd('#skF_49'),nil),'#skF_48') != '#skF_49' )
| ~ ssList(app(cons(hd('#skF_49'),nil),'#skF_48'))
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_417,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ( app(cons(hd('#skF_51'),nil),'#skF_48') != '#skF_51' )
| ~ ssList(app(cons(hd('#skF_51'),nil),'#skF_48'))
| ~ neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_386,c_386,c_386,c_386,c_386,c_400]) ).
tff(c_424,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ( app(cons(hd('#skF_51'),nil),'#skF_48') != '#skF_51' )
| ~ ssList(app(cons(hd('#skF_51'),nil),'#skF_48')) ),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_417]) ).
tff(c_426,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ( app(cons(hd('#skF_51'),nil),'#skF_50') != '#skF_51' )
| ~ ssList(app(cons(hd('#skF_51'),nil),'#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_384,c_424]) ).
tff(c_450,plain,
~ ssList(app(cons(hd('#skF_51'),nil),'#skF_50')),
inference(splitLeft,[status(thm)],[c_426]) ).
tff(c_1968,plain,
( ~ ssList('#skF_50')
| ~ ssList(cons(hd('#skF_51'),nil)) ),
inference(resolution,[status(thm)],[c_1953,c_450]) ).
tff(c_2008,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_1968]) ).
tff(c_2032,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_2008]) ).
tff(c_2035,plain,
~ ssItem(hd('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_2032]) ).
tff(c_2038,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_184,c_2035]) ).
tff(c_2041,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2038]) ).
tff(c_2043,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1771,c_2041]) ).
tff(c_2044,plain,
( ( app(cons(hd('#skF_51'),nil),'#skF_50') != '#skF_51' )
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51') ),
inference(splitRight,[status(thm)],[c_426]) ).
tff(c_2109,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_2044]) ).
tff(c_4399,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_4396,c_2109]) ).
tff(c_4410,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_4399]) ).
tff(c_4412,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3840,c_4410]) ).
tff(c_4413,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ( app(cons(hd('#skF_51'),nil),'#skF_50') != '#skF_51' ) ),
inference(splitRight,[status(thm)],[c_2044]) ).
tff(c_4555,plain,
app(cons(hd('#skF_51'),nil),'#skF_50') != '#skF_51',
inference(splitLeft,[status(thm)],[c_4413]) ).
tff(c_18122,plain,
app(cons('#skF_46'('#skF_51'),nil),'#skF_50') != '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_18121,c_4555]) ).
tff(c_27451,plain,
app(cons('#skF_52',nil),'#skF_50') != '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_27434,c_18122]) ).
tff(c_27464,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_422,c_27451]) ).
tff(c_27465,plain,
( ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssItem(hd('#skF_51')) ),
inference(splitRight,[status(thm)],[c_4413]) ).
tff(c_27516,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_27465]) ).
tff(c_27519,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_184,c_27516]) ).
tff(c_27522,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_27519]) ).
tff(c_27551,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_27522,c_416]) ).
tff(c_27572,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_27551,c_164]) ).
tff(c_27577,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_27572]) ).
tff(c_27579,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_27465]) ).
tff(c_28501,plain,
! [V_2462,U_2463] :
( ssList(cons(V_2462,U_2463))
| ~ ssItem(V_2462)
| ~ ssList(U_2463) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_27578,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitRight,[status(thm)],[c_27465]) ).
tff(c_28510,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_28501,c_27578]) ).
tff(c_28522,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_27579,c_28510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC416+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % 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
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Apr 9 02:28:14 EDT 2025
% 0.12/0.32 % CPUTime :
% 23.49/8.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.64/8.01
% 23.64/8.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------