%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC379+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 : n024.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 09:20:15 PM UTC 2025
% Result : Theorem 10.68s 3.54s
% Output : CNFRefutation 10.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 55 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 170 ( 27 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 211 ( 96 ~; 95 |; 13 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 2 ( 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 : 59 ( 59 usr; 9 con; 0-2 aty)
% Number of variables : 22 ( 19 !; 3 ?; 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_54 > #skF_40 > #skF_48 > #skF_3 > #skF_52 > #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_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_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_52',type,
'#skF_52': $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_1062,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ? [Y] :
( ssItem(Y)
& ( ( ~ memberP(W,Y)
& ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| ~ leq(Z,Y)
| ( Y = Z ) ) )
& memberP(X,Y) )
| ( memberP(W,Y)
& ( ~ memberP(X,Y)
| ? [Z] :
( ssItem(Z)
& ( Y != Z )
& memberP(X,Z)
& leq(Z,Y) ) ) ) ) )
| ! [X1] :
( ssItem(X1)
=> ( ( ~ memberP(U,X1)
& ( ~ memberP(V,X1)
| ? [X2] :
( ssItem(X2)
& ( X1 != X2 )
& memberP(V,X2)
& leq(X2,X1) ) ) )
| ( ! [X2] :
( ssItem(X2)
=> ( ~ memberP(V,X2)
| ~ leq(X2,X1)
| ( X1 = X2 ) ) )
& memberP(V,X1)
& memberP(U,X1) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(c_384,plain,
ssItem('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_386,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_388,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_408,plain,
( memberP('#skF_49','#skF_53')
| memberP('#skF_48','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_426,plain,
( memberP('#skF_51','#skF_53')
| memberP('#skF_48','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_408]) ).
tff(c_430,plain,
( memberP('#skF_51','#skF_53')
| memberP('#skF_50','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_426]) ).
tff(c_459,plain,
memberP('#skF_50','#skF_53'),
inference(splitLeft,[status(thm)],[c_430]) ).
tff(c_412,plain,
! [Y_1283] :
( memberP('#skF_51',Y_1283)
| ~ memberP('#skF_50',Y_1283)
| ~ ssItem(Y_1283) ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_398,plain,
( ( '#skF_54' != '#skF_53' )
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_49','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_425,plain,
( ( '#skF_54' != '#skF_53' )
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_398]) ).
tff(c_435,plain,
( ( '#skF_54' != '#skF_53' )
| ~ memberP('#skF_50','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_425]) ).
tff(c_780,plain,
( ( '#skF_54' != '#skF_53' )
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_459,c_435]) ).
tff(c_781,plain,
~ memberP('#skF_51','#skF_53'),
inference(splitLeft,[status(thm)],[c_780]) ).
tff(c_784,plain,
( ~ memberP('#skF_50','#skF_53')
| ~ ssItem('#skF_53') ),
inference(resolution,[status(thm)],[c_412,c_781]) ).
tff(c_788,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_459,c_784]) ).
tff(c_789,plain,
'#skF_54' != '#skF_53',
inference(splitRight,[status(thm)],[c_780]) ).
tff(c_790,plain,
memberP('#skF_51','#skF_53'),
inference(splitRight,[status(thm)],[c_780]) ).
tff(c_404,plain,
( ssItem('#skF_54')
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_49','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_422,plain,
( ssItem('#skF_54')
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_404]) ).
tff(c_433,plain,
( ssItem('#skF_54')
| ~ memberP('#skF_50','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_422]) ).
tff(c_820,plain,
ssItem('#skF_54'),
inference(demodulation,[status(thm),theory(equality)],[c_790,c_459,c_433]) ).
tff(c_400,plain,
( leq('#skF_54','#skF_53')
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_49','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_424,plain,
( leq('#skF_54','#skF_53')
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_400]) ).
tff(c_434,plain,
( leq('#skF_54','#skF_53')
| ~ memberP('#skF_50','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_424]) ).
tff(c_1330,plain,
leq('#skF_54','#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_790,c_459,c_434]) ).
tff(c_410,plain,
! [Z_1286,Y_1283] :
( ~ leq(Z_1286,Y_1283)
| ~ memberP('#skF_51',Z_1286)
| ( Z_1286 = Y_1283 )
| ~ ssItem(Z_1286)
| ~ memberP('#skF_50',Y_1283)
| ~ ssItem(Y_1283) ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_1332,plain,
( ~ memberP('#skF_51','#skF_54')
| ( '#skF_54' = '#skF_53' )
| ~ ssItem('#skF_54')
| ~ memberP('#skF_50','#skF_53')
| ~ ssItem('#skF_53') ),
inference(resolution,[status(thm)],[c_1330,c_410]) ).
tff(c_1335,plain,
( ~ memberP('#skF_51','#skF_54')
| ( '#skF_54' = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_459,c_820,c_1332]) ).
tff(c_1336,plain,
~ memberP('#skF_51','#skF_54'),
inference(negUnitSimplification,[status(thm)],[c_789,c_1335]) ).
tff(c_402,plain,
( memberP('#skF_49','#skF_54')
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_49','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_423,plain,
( memberP('#skF_51','#skF_54')
| ~ memberP('#skF_48','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_388,c_402]) ).
tff(c_431,plain,
( memberP('#skF_51','#skF_54')
| ~ memberP('#skF_50','#skF_53')
| ~ memberP('#skF_51','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_423]) ).
tff(c_1431,plain,
memberP('#skF_51','#skF_54'),
inference(demodulation,[status(thm),theory(equality)],[c_790,c_459,c_431]) ).
tff(c_1432,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1336,c_1431]) ).
tff(c_1434,plain,
~ memberP('#skF_50','#skF_53'),
inference(splitRight,[status(thm)],[c_430]) ).
tff(c_1433,plain,
memberP('#skF_51','#skF_53'),
inference(splitRight,[status(thm)],[c_430]) ).
tff(c_420,plain,
! [Y_1283] :
( ssItem('#skF_52'(Y_1283))
| ~ memberP('#skF_51',Y_1283)
| memberP('#skF_50',Y_1283)
| ~ ssItem(Y_1283) ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_1454,plain,
! [Y_1385] :
( ( '#skF_52'(Y_1385) != Y_1385 )
| ~ memberP('#skF_51',Y_1385)
| memberP('#skF_50',Y_1385)
| ~ ssItem(Y_1385) ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_1457,plain,
( ( '#skF_52'('#skF_53') != '#skF_53' )
| memberP('#skF_50','#skF_53')
| ~ ssItem('#skF_53') ),
inference(resolution,[status(thm)],[c_1433,c_1454]) ).
tff(c_1463,plain,
( ( '#skF_52'('#skF_53') != '#skF_53' )
| memberP('#skF_50','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_1457]) ).
tff(c_1464,plain,
'#skF_52'('#skF_53') != '#skF_53',
inference(negUnitSimplification,[status(thm)],[c_1434,c_1463]) ).
tff(c_416,plain,
! [Y_1283] :
( leq('#skF_52'(Y_1283),Y_1283)
| ~ memberP('#skF_51',Y_1283)
| memberP('#skF_50',Y_1283)
| ~ ssItem(Y_1283) ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_418,plain,
! [Y_1283] :
( memberP('#skF_51','#skF_52'(Y_1283))
| ~ memberP('#skF_51',Y_1283)
| memberP('#skF_50',Y_1283)
| ~ ssItem(Y_1283) ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_406,plain,
! [X2_1289] :
( ~ leq(X2_1289,'#skF_53')
| ~ memberP('#skF_49',X2_1289)
| ( X2_1289 = '#skF_53' )
| ~ ssItem(X2_1289)
| memberP('#skF_48','#skF_53') ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_427,plain,
! [X2_1289] :
( ~ leq(X2_1289,'#skF_53')
| ~ memberP('#skF_51',X2_1289)
| ( X2_1289 = '#skF_53' )
| ~ ssItem(X2_1289)
| memberP('#skF_48','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_406]) ).
tff(c_432,plain,
! [X2_1289] :
( ~ leq(X2_1289,'#skF_53')
| ~ memberP('#skF_51',X2_1289)
| ( X2_1289 = '#skF_53' )
| ~ ssItem(X2_1289)
| memberP('#skF_50','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_427]) ).
tff(c_2655,plain,
! [X2_1469] :
( ~ leq(X2_1469,'#skF_53')
| ~ memberP('#skF_51',X2_1469)
| ( X2_1469 = '#skF_53' )
| ~ ssItem(X2_1469) ),
inference(negUnitSimplification,[status(thm)],[c_1434,c_432]) ).
tff(c_2832,plain,
! [Y_1479] :
( ~ leq('#skF_52'(Y_1479),'#skF_53')
| ( '#skF_52'(Y_1479) = '#skF_53' )
| ~ ssItem('#skF_52'(Y_1479))
| ~ memberP('#skF_51',Y_1479)
| memberP('#skF_50',Y_1479)
| ~ ssItem(Y_1479) ),
inference(resolution,[status(thm)],[c_418,c_2655]) ).
tff(c_2836,plain,
( ( '#skF_52'('#skF_53') = '#skF_53' )
| ~ ssItem('#skF_52'('#skF_53'))
| ~ memberP('#skF_51','#skF_53')
| memberP('#skF_50','#skF_53')
| ~ ssItem('#skF_53') ),
inference(resolution,[status(thm)],[c_416,c_2832]) ).
tff(c_2839,plain,
( ( '#skF_52'('#skF_53') = '#skF_53' )
| ~ ssItem('#skF_52'('#skF_53'))
| memberP('#skF_50','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_1433,c_2836]) ).
tff(c_2840,plain,
~ ssItem('#skF_52'('#skF_53')),
inference(negUnitSimplification,[status(thm)],[c_1434,c_1464,c_2839]) ).
tff(c_2843,plain,
( ~ memberP('#skF_51','#skF_53')
| memberP('#skF_50','#skF_53')
| ~ ssItem('#skF_53') ),
inference(resolution,[status(thm)],[c_420,c_2840]) ).
tff(c_2846,plain,
memberP('#skF_50','#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_1433,c_2843]) ).
tff(c_2848,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1434,c_2846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SWC379+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.09 % 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
% 0.09/0.29 % Computer : n024.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Apr 9 02:22:06 EDT 2025
% 0.09/0.29 % CPUTime :
% 10.68/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.68/3.55
% 10.68/3.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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