%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC027+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 : 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 09:18:57 PM UTC 2025
% Result : Theorem 8.05s 2.68s
% Output : CNFRefutation 8.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 43 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 76 ( 34 ~; 29 |; 5 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 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 : 57 ( 57 usr; 8 con; 0-2 aty)
% Number of variables : 15 ( 14 !; 1 ?; 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_1029,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ! [Y] :
( ssItem(Y)
=> ( ( cons(Y,nil) != W )
| ~ memberP(X,Y)
| ? [Z] :
( ssItem(Z)
& ( Y != Z )
& memberP(X,Z)
& leq(Y,Z) ) ) )
& ( ( nil != X )
| ( nil != W ) ) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ( nil != U )
| ( nil = V ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_364,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( nil != cons(V,U) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
tff(f_517,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_402,plain,
( ( nil = '#skF_49' )
| ( nil = '#skF_48' ) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_420,plain,
( ( nil = '#skF_51' )
| ( nil = '#skF_48' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_402]) ).
tff(c_425,plain,
( ( nil = '#skF_51' )
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_420]) ).
tff(c_435,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_425]) ).
tff(c_396,plain,
( ( nil != '#skF_48' )
| ( nil != '#skF_49' ) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_421,plain,
( ( nil != '#skF_48' )
| ( nil != '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_396]) ).
tff(c_424,plain,
( ( nil != '#skF_50' )
| ( nil != '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_421]) ).
tff(c_452,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_435,c_435,c_424]) ).
tff(c_418,plain,
( ssItem('#skF_52')
| ( nil = '#skF_51' ) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_453,plain,
( ssItem('#skF_52')
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_435,c_418]) ).
tff(c_454,plain,
ssItem('#skF_52'),
inference(negUnitSimplification,[status(thm)],[c_452,c_453]) ).
tff(c_416,plain,
( ( cons('#skF_52',nil) = '#skF_50' )
| ( nil = '#skF_51' ) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_497,plain,
( ( cons('#skF_52','#skF_50') = '#skF_50' )
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_435,c_435,c_416]) ).
tff(c_498,plain,
cons('#skF_52','#skF_50') = '#skF_50',
inference(negUnitSimplification,[status(thm)],[c_452,c_497]) ).
tff(c_182,plain,
! [V_887,U_885] :
( ( cons(V_887,U_885) != nil )
| ~ ssItem(V_887)
| ~ ssList(U_885) ),
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_1267,plain,
! [V_1251,U_1252] :
( ( cons(V_1251,U_1252) != '#skF_50' )
| ~ ssItem(V_1251)
| ~ ssList(U_1252) ),
inference(demodulation,[status(thm),theory(equality)],[c_435,c_182]) ).
tff(c_1269,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_498,c_1267]) ).
tff(c_1273,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_390,c_454,c_1269]) ).
tff(c_1274,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_425]) ).
tff(c_1275,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_425]) ).
tff(c_1290,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1274,c_1275]) ).
tff(c_410,plain,
( ssItem('#skF_52')
| ( nil = '#skF_50' ) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_1291,plain,
( ssItem('#skF_52')
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1274,c_410]) ).
tff(c_1292,plain,
ssItem('#skF_52'),
inference(negUnitSimplification,[status(thm)],[c_1290,c_1291]) ).
tff(c_406,plain,
( memberP('#skF_51','#skF_52')
| ( nil = '#skF_50' ) ),
inference(cnfTransformation,[status(thm)],[f_1029]) ).
tff(c_1296,plain,
( memberP('#skF_51','#skF_52')
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1274,c_406]) ).
tff(c_1297,plain,
memberP('#skF_51','#skF_52'),
inference(negUnitSimplification,[status(thm)],[c_1290,c_1296]) ).
tff(c_228,plain,
! [U_948] :
( ~ memberP(nil,U_948)
| ~ ssItem(U_948) ),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_1320,plain,
! [U_1264] :
( ~ memberP('#skF_51',U_1264)
| ~ ssItem(U_1264) ),
inference(demodulation,[status(thm),theory(equality)],[c_1274,c_228]) ).
tff(c_1323,plain,
~ ssItem('#skF_52'),
inference(resolution,[status(thm)],[c_1297,c_1320]) ).
tff(c_1327,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1292,c_1323]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.10 % Problem : SWC027+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.11 % 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
% 0.12/0.32 % 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 01:19:29 EDT 2025
% 0.12/0.32 % CPUTime :
% 8.05/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.05/2.68
% 8.05/2.68 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------