%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC153+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 : n003.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 09:19:27 PM UTC 2025
% Result : Theorem 10.17s 3.38s
% Output : CNFRefutation 10.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 36 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 14 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 191 ( 88 ~; 82 |; 11 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 6 ( 2 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 : 62 ( 62 usr; 13 con; 0-2 aty)
% Number of variables : 49 ( 43 !; 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_57 > #skF_52 > #skF_44 > #skF_21 > #skF_16 > #skF_6 > #skF_49 > #skF_18 > #skF_24 > #skF_35 > #skF_19 > #skF_31 > #skF_55 > #skF_22 > #skF_37 > #skF_56 > #skF_54 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_53 > #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_57',type,
'#skF_57': $i ).
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_55',type,
'#skF_55': $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('#skF_56',type,
'#skF_56': $i ).
tff(totalorderP,type,
totalorderP: $i > $o ).
tff(ssItem,type,
ssItem: $i > $o ).
tff('#skF_54',type,
'#skF_54': $i ).
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_53',type,
'#skF_53': $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_1060,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( X != V )
| ( W != U )
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssItem(Z)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = W )
& leq(Z,Y)
& ( ~ leq(Y,Z)
| ? [X4] :
( ssItem(X4)
& memberP(X2,X4)
& ( ~ leq(Y,X4)
| ~ leq(X4,Z) ) ) ) ) ) ) ) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != U )
| ~ leq(X6,X5)
| ( ! [X10] :
( ssItem(X10)
=> ( ~ memberP(X8,X10)
| ( leq(X10,X6)
& leq(X5,X10) ) ) )
& leq(X5,X6) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(c_414,plain,
( ssItem('#skF_57')
| ~ leq('#skF_52','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_441,plain,
~ leq('#skF_52','#skF_53'),
inference(splitLeft,[status(thm)],[c_414]) ).
tff(c_396,plain,
ssItem('#skF_52'),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_394,plain,
ssItem('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_392,plain,
ssList('#skF_54'),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_390,plain,
ssList('#skF_55'),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_388,plain,
ssList('#skF_56'),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_384,plain,
leq('#skF_53','#skF_52'),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_398,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_386,plain,
app(app(app(app('#skF_54',cons('#skF_52',nil)),'#skF_55'),cons('#skF_53',nil)),'#skF_56') = '#skF_48',
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_425,plain,
app(app(app(app('#skF_54',cons('#skF_52',nil)),'#skF_55'),cons('#skF_53',nil)),'#skF_56') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_398,c_386]) ).
tff(c_416,plain,
! [Y_3023,X3_3083,Z_3055,X2_3079,X1_3071] :
( leq(Y_3023,Z_3055)
| ~ leq(Z_3055,Y_3023)
| ( app(app(app(app(X1_3071,cons(Y_3023,nil)),X2_3079),cons(Z_3055,nil)),X3_3083) != '#skF_50' )
| ~ ssList(X3_3083)
| ~ ssList(X2_3079)
| ~ ssList(X1_3071)
| ~ ssItem(Z_3055)
| ~ ssItem(Y_3023) ),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_705,plain,
( leq('#skF_52','#skF_53')
| ~ leq('#skF_53','#skF_52')
| ~ ssList('#skF_56')
| ~ ssList('#skF_55')
| ~ ssList('#skF_54')
| ~ ssItem('#skF_53')
| ~ ssItem('#skF_52') ),
inference(superposition,[status(thm),theory(equality)],[c_425,c_416]) ).
tff(c_712,plain,
leq('#skF_52','#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_394,c_392,c_390,c_388,c_384,c_705]) ).
tff(c_714,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_441,c_712]) ).
tff(c_716,plain,
leq('#skF_52','#skF_53'),
inference(splitRight,[status(thm)],[c_414]) ).
tff(c_410,plain,
( ~ leq('#skF_52','#skF_57')
| ~ leq('#skF_57','#skF_53')
| ~ leq('#skF_52','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_796,plain,
( ~ leq('#skF_52','#skF_57')
| ~ leq('#skF_57','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_716,c_410]) ).
tff(c_797,plain,
~ leq('#skF_57','#skF_53'),
inference(splitLeft,[status(thm)],[c_796]) ).
tff(c_715,plain,
ssItem('#skF_57'),
inference(splitRight,[status(thm)],[c_414]) ).
tff(c_412,plain,
( memberP('#skF_55','#skF_57')
| ~ leq('#skF_52','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_725,plain,
memberP('#skF_55','#skF_57'),
inference(demodulation,[status(thm),theory(equality)],[c_716,c_412]) ).
tff(c_932,plain,
! [X4_3254,Z_3249,X1_3250,Y_3252,X2_3251,X3_3253] :
( leq(X4_3254,Z_3249)
| ~ memberP(X2_3251,X4_3254)
| ~ ssItem(X4_3254)
| ~ leq(Z_3249,Y_3252)
| ( app(app(app(app(X1_3250,cons(Y_3252,nil)),X2_3251),cons(Z_3249,nil)),X3_3253) != '#skF_50' )
| ~ ssList(X3_3253)
| ~ ssList(X2_3251)
| ~ ssList(X1_3250)
| ~ ssItem(Z_3249)
| ~ ssItem(Y_3252) ),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_934,plain,
! [Z_3249,Y_3252,X1_3250,X3_3253] :
( leq('#skF_57',Z_3249)
| ~ ssItem('#skF_57')
| ~ leq(Z_3249,Y_3252)
| ( app(app(app(app(X1_3250,cons(Y_3252,nil)),'#skF_55'),cons(Z_3249,nil)),X3_3253) != '#skF_50' )
| ~ ssList(X3_3253)
| ~ ssList('#skF_55')
| ~ ssList(X1_3250)
| ~ ssItem(Z_3249)
| ~ ssItem(Y_3252) ),
inference(resolution,[status(thm)],[c_725,c_932]) ).
tff(c_1133,plain,
! [Z_3282,Y_3283,X1_3284,X3_3285] :
( leq('#skF_57',Z_3282)
| ~ leq(Z_3282,Y_3283)
| ( app(app(app(app(X1_3284,cons(Y_3283,nil)),'#skF_55'),cons(Z_3282,nil)),X3_3285) != '#skF_50' )
| ~ ssList(X3_3285)
| ~ ssList(X1_3284)
| ~ ssItem(Z_3282)
| ~ ssItem(Y_3283) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_715,c_934]) ).
tff(c_1136,plain,
( leq('#skF_57','#skF_53')
| ~ leq('#skF_53','#skF_52')
| ~ ssList('#skF_56')
| ~ ssList('#skF_54')
| ~ ssItem('#skF_53')
| ~ ssItem('#skF_52') ),
inference(superposition,[status(thm),theory(equality)],[c_425,c_1133]) ).
tff(c_1139,plain,
leq('#skF_57','#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_394,c_392,c_388,c_384,c_1136]) ).
tff(c_1141,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_797,c_1139]) ).
tff(c_1142,plain,
~ leq('#skF_52','#skF_57'),
inference(splitRight,[status(thm)],[c_796]) ).
tff(c_1277,plain,
! [X1_3315,Y_3317,Z_3314,X4_3319,X2_3316,X3_3318] :
( leq(Y_3317,X4_3319)
| ~ memberP(X2_3316,X4_3319)
| ~ ssItem(X4_3319)
| ~ leq(Z_3314,Y_3317)
| ( app(app(app(app(X1_3315,cons(Y_3317,nil)),X2_3316),cons(Z_3314,nil)),X3_3318) != '#skF_50' )
| ~ ssList(X3_3318)
| ~ ssList(X2_3316)
| ~ ssList(X1_3315)
| ~ ssItem(Z_3314)
| ~ ssItem(Y_3317) ),
inference(cnfTransformation,[status(thm)],[f_1060]) ).
tff(c_1279,plain,
! [Y_3317,Z_3314,X1_3315,X3_3318] :
( leq(Y_3317,'#skF_57')
| ~ ssItem('#skF_57')
| ~ leq(Z_3314,Y_3317)
| ( app(app(app(app(X1_3315,cons(Y_3317,nil)),'#skF_55'),cons(Z_3314,nil)),X3_3318) != '#skF_50' )
| ~ ssList(X3_3318)
| ~ ssList('#skF_55')
| ~ ssList(X1_3315)
| ~ ssItem(Z_3314)
| ~ ssItem(Y_3317) ),
inference(resolution,[status(thm)],[c_725,c_1277]) ).
tff(c_1462,plain,
! [Y_3347,Z_3348,X1_3349,X3_3350] :
( leq(Y_3347,'#skF_57')
| ~ leq(Z_3348,Y_3347)
| ( app(app(app(app(X1_3349,cons(Y_3347,nil)),'#skF_55'),cons(Z_3348,nil)),X3_3350) != '#skF_50' )
| ~ ssList(X3_3350)
| ~ ssList(X1_3349)
| ~ ssItem(Z_3348)
| ~ ssItem(Y_3347) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_715,c_1279]) ).
tff(c_1465,plain,
( leq('#skF_52','#skF_57')
| ~ leq('#skF_53','#skF_52')
| ~ ssList('#skF_56')
| ~ ssList('#skF_54')
| ~ ssItem('#skF_53')
| ~ ssItem('#skF_52') ),
inference(superposition,[status(thm),theory(equality)],[c_425,c_1462]) ).
tff(c_1468,plain,
leq('#skF_52','#skF_57'),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_394,c_392,c_388,c_384,c_1465]) ).
tff(c_1470,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1142,c_1468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SWC153+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.10 % 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
% 0.09/0.30 % Computer : n003.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Wed Apr 9 01:38:48 EDT 2025
% 0.09/0.30 % CPUTime :
% 10.17/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.17/3.39
% 10.17/3.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------