%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC024+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 : n020.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 09:18:56 PM UTC 2025
% Result : Theorem 13.09s 4.30s
% Output : CNFRefutation 13.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 23 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 108 ( 48 ~; 39 |; 9 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 3 ( 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 : 26 ( 21 !; 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_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_1033,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& neq(Y,nil)
& frontsegP(V,Y)
& frontsegP(U,Y) )
| ! [Z] :
( ssList(Z)
=> ( ( app(W,Z) != X )
| ~ equalelemsP(W)
| ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssList(X2)
& ( app(cons(X1,nil),X2) = Z )
& ? [X3] :
( ssList(X3)
& ( app(X3,cons(X1,nil)) = W ) ) ) ) ) )
| ( ( nil != X )
& ( nil = W ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_548,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
tff(f_108,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& ( app(V,W) = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(c_404,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_8658,plain,
! [U_1762] :
( frontsegP(U_1762,U_1762)
| ~ ssList(U_1762) ),
inference(cnfTransformation,[status(thm)],[f_548]) ).
tff(c_236,plain,
! [U_959] :
( frontsegP(U_959,U_959)
| ~ ssList(U_959) ),
inference(cnfTransformation,[status(thm)],[f_548]) ).
tff(c_384,plain,
( ( nil != '#skF_50' )
| ( nil = '#skF_51' ) ),
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_427,plain,
nil != '#skF_50',
inference(splitLeft,[status(thm)],[c_384]) ).
tff(c_402,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_390,plain,
app('#skF_50','#skF_52') = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_392,plain,
ssList('#skF_52'),
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_8224,plain,
! [V_1754,W_1755] :
( frontsegP(app(V_1754,W_1755),V_1754)
| ~ ssList(W_1755)
| ~ ssList(V_1754)
| ~ ssList(app(V_1754,W_1755)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_8427,plain,
( frontsegP('#skF_51','#skF_50')
| ~ ssList('#skF_52')
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_50','#skF_52')) ),
inference(superposition,[status(thm),theory(equality)],[c_390,c_8224]) ).
tff(c_8560,plain,
frontsegP('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_390,c_404,c_392,c_8427]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_1904,plain,
! [U_1483,V_1484] :
( neq(U_1483,V_1484)
| ( V_1484 = U_1483 )
| ~ ssList(V_1484)
| ~ ssList(U_1483) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_400,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_398,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_394,plain,
! [Y_1373] :
( ~ frontsegP('#skF_48',Y_1373)
| ~ frontsegP('#skF_49',Y_1373)
| ~ neq(Y_1373,nil)
| ~ ssList(Y_1373) ),
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_414,plain,
! [Y_1373] :
( ~ frontsegP('#skF_50',Y_1373)
| ~ frontsegP('#skF_51',Y_1373)
| ~ neq(Y_1373,nil)
| ~ ssList(Y_1373) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_398,c_394]) ).
tff(c_1908,plain,
! [U_1483] :
( ~ frontsegP('#skF_50',U_1483)
| ~ frontsegP('#skF_51',U_1483)
| ( nil = U_1483 )
| ~ ssList(nil)
| ~ ssList(U_1483) ),
inference(resolution,[status(thm)],[c_1904,c_414]) ).
tff(c_1919,plain,
! [U_1483] :
( ~ frontsegP('#skF_50',U_1483)
| ~ frontsegP('#skF_51',U_1483)
| ( nil = U_1483 )
| ~ ssList(U_1483) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_1908]) ).
tff(c_8565,plain,
( ~ frontsegP('#skF_50','#skF_50')
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_8560,c_1919]) ).
tff(c_8571,plain,
( ~ frontsegP('#skF_50','#skF_50')
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_404,c_8565]) ).
tff(c_8572,plain,
~ frontsegP('#skF_50','#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_427,c_8571]) ).
tff(c_8594,plain,
~ ssList('#skF_50'),
inference(resolution,[status(thm)],[c_236,c_8572]) ).
tff(c_8598,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_404,c_8594]) ).
tff(c_8600,plain,
nil = '#skF_50',
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_8599,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_8616,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_8600,c_8599]) ).
tff(c_396,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1033]) ).
tff(c_413,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_396]) ).
tff(c_8601,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_8599,c_413]) ).
tff(c_8643,plain,
neq('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_8616,c_8616,c_8601]) ).
tff(c_8649,plain,
! [Y_1759] :
( ~ frontsegP('#skF_50',Y_1759)
| ~ frontsegP('#skF_50',Y_1759)
| ~ neq(Y_1759,'#skF_50')
| ~ ssList(Y_1759) ),
inference(demodulation,[status(thm),theory(equality)],[c_8600,c_8616,c_414]) ).
tff(c_8652,plain,
( ~ frontsegP('#skF_50','#skF_50')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_8643,c_8649]) ).
tff(c_8655,plain,
~ frontsegP('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_404,c_8652]) ).
tff(c_8661,plain,
~ ssList('#skF_50'),
inference(resolution,[status(thm)],[c_8658,c_8655]) ).
tff(c_8665,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_404,c_8661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC024+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 01:19:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 13.09/4.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.09/4.31
% 13.09/4.31 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------