%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC229+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 : n016.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 09:19:42 PM UTC 2025
% Result : Theorem 11.58s 3.61s
% Output : CNFRefutation 11.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 160 ( 44 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 201 ( 95 ~; 82 |; 7 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 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; 7 con; 0-3 aty)
% Number of variables : 54 ( 49 !; 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_52 > #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_52',type,
'#skF_52': ( $i * $i * $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_1029,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ~ segmentP(X,W)
| ( nil = U )
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& ( app(app(Z,cons(Y,nil)),X1) = U )
& ! [X2] :
( ssItem(X2)
=> ( ~ memberP(Z,X2)
| ~ memberP(X1,X2)
| ~ leq(Y,X2)
| leq(X2,Y) ) ) ) ) )
| ( ~ singletonP(W)
& 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_692,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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_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_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_517,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
tff(c_396,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_394,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_925,plain,
! [U_1459] :
( ( hd(U_1459) = '#skF_46'(U_1459) )
| ( nil = U_1459 )
| ~ ssList(U_1459) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_1033,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_394,c_925]) ).
tff(c_1064,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_1033]) ).
tff(c_390,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_386,plain,
nil != '#skF_48',
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_420,plain,
nil != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_386]) ).
tff(c_1103,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1064,c_420]) ).
tff(c_388,plain,
segmentP('#skF_51','#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_278,plain,
! [U_1031] :
( ( nil = U_1031 )
| ~ segmentP(nil,U_1031)
| ~ ssList(U_1031) ),
inference(cnfTransformation,[status(thm)],[f_692]) ).
tff(c_1605,plain,
! [U_1492] :
( ( U_1492 = '#skF_51' )
| ~ segmentP('#skF_51',U_1492)
| ~ ssList(U_1492) ),
inference(demodulation,[status(thm),theory(equality)],[c_1064,c_1064,c_278]) ).
tff(c_1616,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_388,c_1605]) ).
tff(c_1627,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_1616]) ).
tff(c_1629,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1103,c_1627]) ).
tff(c_1631,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_1033]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_2028,plain,
! [U_1505,V_1506] :
( neq(U_1505,V_1506)
| ( V_1506 = U_1505 )
| ~ ssList(V_1506)
| ~ ssList(U_1505) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_384,plain,
( ~ neq('#skF_51',nil)
| singletonP('#skF_50') ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_430,plain,
~ neq('#skF_51',nil),
inference(splitLeft,[status(thm)],[c_384]) ).
tff(c_2039,plain,
( ( nil = '#skF_51' )
| ~ ssList(nil)
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_2028,c_430]) ).
tff(c_2046,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_394,c_168,c_2039]) ).
tff(c_2048,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1631,c_2046]) ).
tff(c_2049,plain,
singletonP('#skF_50'),
inference(splitRight,[status(thm)],[c_384]) ).
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_2091,plain,
! [U_1525] :
( ( app(U_1525,nil) = U_1525 )
| ~ ssList(U_1525) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_2104,plain,
app('#skF_50',nil) = '#skF_50',
inference(resolution,[status(thm)],[c_396,c_2091]) ).
tff(c_2066,plain,
! [U_1524] :
( ( app(nil,U_1524) = U_1524 )
| ~ ssList(U_1524) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_2078,plain,
app(nil,'#skF_50') = '#skF_50',
inference(resolution,[status(thm)],[c_396,c_2066]) ).
tff(c_3194,plain,
! [U_1618] :
( ( cons('#skF_5'(U_1618),nil) = U_1618 )
| ~ singletonP(U_1618)
| ~ ssList(U_1618) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_410,plain,
! [Y_1358,Z_1366,X1_1370] :
( ssItem('#skF_52'(Y_1358,Z_1366,X1_1370))
| ( app(app(Z_1366,cons(Y_1358,nil)),X1_1370) != '#skF_48' )
| ~ ssList(X1_1370)
| ~ ssList(Z_1366)
| ~ ssItem(Y_1358) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_415,plain,
! [Y_1358,Z_1366,X1_1370] :
( ssItem('#skF_52'(Y_1358,Z_1366,X1_1370))
| ( app(app(Z_1366,cons(Y_1358,nil)),X1_1370) != '#skF_50' )
| ~ ssList(X1_1370)
| ~ ssList(Z_1366)
| ~ ssItem(Y_1358) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_410]) ).
tff(c_3243,plain,
! [U_1618,Z_1366,X1_1370] :
( ssItem('#skF_52'('#skF_5'(U_1618),Z_1366,X1_1370))
| ( app(app(Z_1366,U_1618),X1_1370) != '#skF_50' )
| ~ ssList(X1_1370)
| ~ ssList(Z_1366)
| ~ ssItem('#skF_5'(U_1618))
| ~ singletonP(U_1618)
| ~ ssList(U_1618) ),
inference(superposition,[status(thm),theory(equality)],[c_3194,c_415]) ).
tff(c_406,plain,
! [X1_1370,Y_1358,Z_1366] :
( memberP(X1_1370,'#skF_52'(Y_1358,Z_1366,X1_1370))
| ( app(app(Z_1366,cons(Y_1358,nil)),X1_1370) != '#skF_48' )
| ~ ssList(X1_1370)
| ~ ssList(Z_1366)
| ~ ssItem(Y_1358) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_414,plain,
! [X1_1370,Y_1358,Z_1366] :
( memberP(X1_1370,'#skF_52'(Y_1358,Z_1366,X1_1370))
| ( app(app(Z_1366,cons(Y_1358,nil)),X1_1370) != '#skF_50' )
| ~ ssList(X1_1370)
| ~ ssList(Z_1366)
| ~ ssItem(Y_1358) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_406]) ).
tff(c_3865,plain,
! [X1_1643,U_1644,Z_1645] :
( memberP(X1_1643,'#skF_52'('#skF_5'(U_1644),Z_1645,X1_1643))
| ( app(app(Z_1645,U_1644),X1_1643) != '#skF_50' )
| ~ ssList(X1_1643)
| ~ ssList(Z_1645)
| ~ ssItem('#skF_5'(U_1644))
| ~ singletonP(U_1644)
| ~ ssList(U_1644) ),
inference(superposition,[status(thm),theory(equality)],[c_3194,c_414]) ).
tff(c_228,plain,
! [U_948] :
( ~ memberP(nil,U_948)
| ~ ssItem(U_948) ),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_3869,plain,
! [U_1644,Z_1645] :
( ~ ssItem('#skF_52'('#skF_5'(U_1644),Z_1645,nil))
| ( app(app(Z_1645,U_1644),nil) != '#skF_50' )
| ~ ssList(nil)
| ~ ssList(Z_1645)
| ~ ssItem('#skF_5'(U_1644))
| ~ singletonP(U_1644)
| ~ ssList(U_1644) ),
inference(resolution,[status(thm)],[c_3865,c_228]) ).
tff(c_6156,plain,
! [U_1784,Z_1785] :
( ~ ssItem('#skF_52'('#skF_5'(U_1784),Z_1785,nil))
| ( app(app(Z_1785,U_1784),nil) != '#skF_50' )
| ~ ssList(Z_1785)
| ~ ssItem('#skF_5'(U_1784))
| ~ singletonP(U_1784)
| ~ ssList(U_1784) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_3869]) ).
tff(c_6160,plain,
! [Z_1366,U_1618] :
( ( app(app(Z_1366,U_1618),nil) != '#skF_50' )
| ~ ssList(nil)
| ~ ssList(Z_1366)
| ~ ssItem('#skF_5'(U_1618))
| ~ singletonP(U_1618)
| ~ ssList(U_1618) ),
inference(resolution,[status(thm)],[c_3243,c_6156]) ).
tff(c_6203,plain,
! [Z_1796,U_1797] :
( ( app(app(Z_1796,U_1797),nil) != '#skF_50' )
| ~ ssList(Z_1796)
| ~ ssItem('#skF_5'(U_1797))
| ~ singletonP(U_1797)
| ~ ssList(U_1797) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_6160]) ).
tff(c_6309,plain,
( ( app('#skF_50',nil) != '#skF_50' )
| ~ ssList(nil)
| ~ ssItem('#skF_5'('#skF_50'))
| ~ singletonP('#skF_50')
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_2078,c_6203]) ).
tff(c_6419,plain,
~ ssItem('#skF_5'('#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_2049,c_168,c_2104,c_6309]) ).
tff(c_6426,plain,
( ~ singletonP('#skF_50')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_24,c_6419]) ).
tff(c_6430,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_396,c_2049,c_6426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC229+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % 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
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Apr 9 01:55:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 11.58/3.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.58/3.62
% 11.58/3.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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