TSTP Solution File: SWC015+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC015+1 : TPTP v8.1.2. 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 : n013.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 : Tue Aug 22 11:00:45 EDT 2023
% Result : Theorem 16.54s 5.23s
% Output : CNFRefutation 16.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 88
% Syntax : Number of formulae : 201 ( 60 unt; 75 typ; 0 def)
% Number of atoms : 277 ( 130 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 265 ( 114 ~; 111 |; 11 &)
% ( 1 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 68 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 56 ( 56 usr; 7 con; 0-2 aty)
% Number of variables : 65 (; 59 !; 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_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_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_1027,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& ( X != Y )
& ? [Z] :
( ssList(Z)
& ( tl(X) = Z )
& ( app(W,Z) = Y )
& neq(nil,X) ) )
| ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssList(X2)
& ( cons(X1,nil) = U )
& ( app(cons(X1,nil),X2) = V ) ) ) )
& ( ~ neq(V,nil)
| 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_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_779,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssList(V)
& ( tl(U) = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
tff(f_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_399,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
tff(f_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_803,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ( cons(hd(U),tl(U)) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
tff(f_327,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) != U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
tff(f_879,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil != U )
=> ( tl(app(U,V)) = app(tl(U),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
tff(f_815,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( app(W,V) = app(U,V) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
tff(c_388,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_4023,plain,
! [U_1532] :
( ( hd(U_1532) = '#skF_46'(U_1532) )
| ( nil = U_1532 )
| ~ ssList(U_1532) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_4139,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_4023]) ).
tff(c_4141,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_4139]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_406,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_411,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).
tff(c_4175,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_4141,c_411]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_4373,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_4175,c_164]) ).
tff(c_4378,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4373]) ).
tff(c_4380,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_4139]) ).
tff(c_5827,plain,
! [U_1617] :
( ( tl(U_1617) = '#skF_47'(U_1617) )
| ( nil = U_1617 )
| ~ ssList(U_1617) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_5911,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_5827]) ).
tff(c_5945,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_4380,c_5911]) ).
tff(c_3297,plain,
! [U_1464] :
( ssList(tl(U_1464))
| ( nil = U_1464 )
| ~ ssList(U_1464) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_1789,plain,
! [U_1370] :
( ( tl(U_1370) = '#skF_47'(U_1370) )
| ( nil = U_1370 )
| ~ ssList(U_1370) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_1901,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_1789]) ).
tff(c_1905,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_1901]) ).
tff(c_1938,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_1905,c_411]) ).
tff(c_2005,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_1938,c_164]) ).
tff(c_2010,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2005]) ).
tff(c_2012,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_1901]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_3059,plain,
! [U_1420,V_1421] :
( neq(U_1420,V_1421)
| ( V_1421 = U_1420 )
| ~ ssList(V_1421)
| ~ ssList(U_1420) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_773,plain,
! [U_1296,V_1297] :
( ssList(app(U_1296,V_1297))
| ~ ssList(V_1297)
| ~ ssList(U_1296) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_398,plain,
( ~ neq(nil,'#skF_51')
| ~ ssList(tl('#skF_51'))
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' )
| ~ ssList(app('#skF_50',tl('#skF_51')))
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_415,plain,
( ~ neq(nil,'#skF_51')
| ~ ssList(tl('#skF_51'))
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' )
| ~ ssList(app('#skF_50',tl('#skF_51'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_398]) ).
tff(c_431,plain,
~ ssList(app('#skF_50',tl('#skF_51'))),
inference(splitLeft,[status(thm)],[c_415]) ).
tff(c_782,plain,
( ~ ssList(tl('#skF_51'))
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_773,c_431]) ).
tff(c_802,plain,
~ ssList(tl('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_782]) ).
tff(c_815,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_188,c_802]) ).
tff(c_818,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_815]) ).
tff(c_847,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_818,c_411]) ).
tff(c_1184,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_847,c_164]) ).
tff(c_1189,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1184]) ).
tff(c_1190,plain,
( ~ ssList(tl('#skF_51'))
| ~ neq(nil,'#skF_51')
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' ) ),
inference(splitRight,[status(thm)],[c_415]) ).
tff(c_1196,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_1190]) ).
tff(c_3070,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_3059,c_1196]) ).
tff(c_3077,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_3070]) ).
tff(c_3079,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2012,c_3077]) ).
tff(c_3080,plain,
( ~ ssList(tl('#skF_51'))
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' ) ),
inference(splitRight,[status(thm)],[c_1190]) ).
tff(c_3086,plain,
~ ssList(tl('#skF_51')),
inference(splitLeft,[status(thm)],[c_3080]) ).
tff(c_3306,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_3297,c_3086]) ).
tff(c_3311,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_3306]) ).
tff(c_3339,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_3311,c_411]) ).
tff(c_3359,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_3339,c_164]) ).
tff(c_3364,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_3359]) ).
tff(c_3365,plain,
app('#skF_50',tl('#skF_51')) = '#skF_51',
inference(splitRight,[status(thm)],[c_3080]) ).
tff(c_5995,plain,
app('#skF_50','#skF_47'('#skF_51')) = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_5945,c_3365]) ).
tff(c_3366,plain,
ssList(tl('#skF_51')),
inference(splitRight,[status(thm)],[c_3080]) ).
tff(c_5996,plain,
ssList('#skF_47'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_5945,c_3366]) ).
tff(c_4379,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(splitRight,[status(thm)],[c_4139]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_4384,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_4379,c_184]) ).
tff(c_4388,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4384]) ).
tff(c_4389,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_4380,c_4388]) ).
tff(c_4140,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_4023]) ).
tff(c_4391,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_4140]) ).
tff(c_4392,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_4391,c_4380]) ).
tff(c_3411,plain,
! [U_1476] :
( ( app(nil,U_1476) = U_1476 )
| ~ ssList(U_1476) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_3424,plain,
app(nil,tl('#skF_51')) = tl('#skF_51'),
inference(resolution,[status(thm)],[c_3366,c_3411]) ).
tff(c_4404,plain,
app('#skF_50',tl('#skF_51')) = tl('#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_4391,c_3424]) ).
tff(c_4436,plain,
tl('#skF_51') = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_3365,c_4404]) ).
tff(c_340,plain,
! [U_1052] :
( ( cons(hd(U_1052),tl(U_1052)) = U_1052 )
| ( nil = U_1052 )
| ~ ssList(U_1052) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_5749,plain,
! [U_1616] :
( ( cons(hd(U_1616),tl(U_1616)) = U_1616 )
| ( U_1616 = '#skF_50' )
| ~ ssList(U_1616) ),
inference(demodulation,[status(thm),theory(equality)],[c_4391,c_340]) ).
tff(c_5780,plain,
( ( cons(hd('#skF_51'),'#skF_51') = '#skF_51' )
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_4436,c_5749]) ).
tff(c_5789,plain,
( ( cons('#skF_46'('#skF_51'),'#skF_51') = '#skF_51' )
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4379,c_5780]) ).
tff(c_5790,plain,
cons('#skF_46'('#skF_51'),'#skF_51') = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_4392,c_5789]) ).
tff(c_170,plain,
! [V_864,U_862] :
( ( cons(V_864,U_862) != U_862 )
| ~ ssItem(V_864)
| ~ ssList(U_862) ),
inference(cnfTransformation,[status(thm)],[f_327]) ).
tff(c_5807,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_5790,c_170]) ).
tff(c_5824,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4389,c_5807]) ).
tff(c_5826,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_4140]) ).
tff(c_5825,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(splitRight,[status(thm)],[c_4140]) ).
tff(c_5950,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_5825,c_184]) ).
tff(c_5954,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_5950]) ).
tff(c_5955,plain,
ssItem('#skF_46'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_5826,c_5954]) ).
tff(c_5946,plain,
( ( tl('#skF_50') = '#skF_47'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_5827]) ).
tff(c_5957,plain,
tl('#skF_50') = '#skF_47'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_5826,c_5946]) ).
tff(c_5961,plain,
( ssList('#skF_47'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_5957,c_188]) ).
tff(c_5965,plain,
( ssList('#skF_47'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_5961]) ).
tff(c_5966,plain,
ssList('#skF_47'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_5826,c_5965]) ).
tff(c_334,plain,
! [U_1047] :
( ( tl(U_1047) = '#skF_47'(U_1047) )
| ( nil = U_1047 )
| ~ ssList(U_1047) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_5986,plain,
( ( tl('#skF_47'('#skF_50')) = '#skF_47'('#skF_47'('#skF_50')) )
| ( '#skF_47'('#skF_50') = nil ) ),
inference(resolution,[status(thm)],[c_5966,c_334]) ).
tff(c_6205,plain,
'#skF_47'('#skF_50') = nil,
inference(splitLeft,[status(thm)],[c_5986]) ).
tff(c_6210,plain,
tl('#skF_50') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_6205,c_5957]) ).
tff(c_6983,plain,
! [U_1654] :
( ( cons(hd(U_1654),tl(U_1654)) = U_1654 )
| ( nil = U_1654 )
| ~ ssList(U_1654) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_7023,plain,
( ( cons('#skF_46'('#skF_50'),tl('#skF_50')) = '#skF_50' )
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_5825,c_6983]) ).
tff(c_7041,plain,
( ( cons('#skF_46'('#skF_50'),nil) = '#skF_50' )
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_6210,c_7023]) ).
tff(c_7042,plain,
cons('#skF_46'('#skF_50'),nil) = '#skF_50',
inference(negUnitSimplification,[status(thm)],[c_5826,c_7041]) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_396,plain,
! [X1_1226,X2_1228] :
( ( app(cons(X1_1226,nil),X2_1228) != '#skF_49' )
| ( cons(X1_1226,nil) != '#skF_48' )
| ~ ssList(X2_1228)
| ~ ssItem(X1_1226)
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_412,plain,
! [X1_1226,X2_1228] :
( ( app(cons(X1_1226,nil),X2_1228) != '#skF_51' )
| ( cons(X1_1226,nil) != '#skF_48' )
| ~ ssList(X2_1228)
| ~ ssItem(X1_1226)
| ~ neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_396]) ).
tff(c_417,plain,
! [X1_1226,X2_1228] :
( ( app(cons(X1_1226,nil),X2_1228) != '#skF_51' )
| ( cons(X1_1226,nil) != '#skF_48' )
| ~ ssList(X2_1228)
| ~ ssItem(X1_1226) ),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_412]) ).
tff(c_419,plain,
! [X1_1226,X2_1228] :
( ( app(cons(X1_1226,nil),X2_1228) != '#skF_51' )
| ( cons(X1_1226,nil) != '#skF_50' )
| ~ ssList(X2_1228)
| ~ ssItem(X1_1226) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_417]) ).
tff(c_7083,plain,
! [X2_1228] :
( ( app('#skF_50',X2_1228) != '#skF_51' )
| ( cons('#skF_46'('#skF_50'),nil) != '#skF_50' )
| ~ ssList(X2_1228)
| ~ ssItem('#skF_46'('#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_7042,c_419]) ).
tff(c_7165,plain,
! [X2_1657] :
( ( app('#skF_50',X2_1657) != '#skF_51' )
| ~ ssList(X2_1657) ),
inference(demodulation,[status(thm),theory(equality)],[c_5955,c_7042,c_7083]) ).
tff(c_7168,plain,
app('#skF_50','#skF_47'('#skF_51')) != '#skF_51',
inference(resolution,[status(thm)],[c_5996,c_7165]) ).
tff(c_7256,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5995,c_7168]) ).
tff(c_7258,plain,
'#skF_47'('#skF_50') != nil,
inference(splitRight,[status(thm)],[c_5986]) ).
tff(c_16327,plain,
! [U_1930,V_1931] :
( ( app(tl(U_1930),V_1931) = tl(app(U_1930,V_1931)) )
| ( nil = U_1930 )
| ~ ssList(V_1931)
| ~ ssList(U_1930) ),
inference(cnfTransformation,[status(thm)],[f_879]) ).
tff(c_16406,plain,
! [V_1931] :
( ( app('#skF_47'('#skF_50'),V_1931) = tl(app('#skF_50',V_1931)) )
| ( nil = '#skF_50' )
| ~ ssList(V_1931)
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_5957,c_16327]) ).
tff(c_16427,plain,
! [V_1931] :
( ( app('#skF_47'('#skF_50'),V_1931) = tl(app('#skF_50',V_1931)) )
| ( nil = '#skF_50' )
| ~ ssList(V_1931) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_16406]) ).
tff(c_17570,plain,
! [V_1952] :
( ( app('#skF_47'('#skF_50'),V_1952) = tl(app('#skF_50',V_1952)) )
| ~ ssList(V_1952) ),
inference(negUnitSimplification,[status(thm)],[c_5826,c_16427]) ).
tff(c_5993,plain,
app(nil,'#skF_47'('#skF_51')) = '#skF_47'('#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_5945,c_5945,c_3424]) ).
tff(c_12717,plain,
! [W_1891,U_1892,V_1893] :
( ( W_1891 = U_1892 )
| ( app(W_1891,V_1893) != app(U_1892,V_1893) )
| ~ ssList(W_1891)
| ~ ssList(V_1893)
| ~ ssList(U_1892) ),
inference(cnfTransformation,[status(thm)],[f_815]) ).
tff(c_12941,plain,
! [W_1891] :
( ( nil = W_1891 )
| ( app(W_1891,'#skF_47'('#skF_51')) != '#skF_47'('#skF_51') )
| ~ ssList(W_1891)
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_5993,c_12717]) ).
tff(c_13181,plain,
! [W_1891] :
( ( nil = W_1891 )
| ( app(W_1891,'#skF_47'('#skF_51')) != '#skF_47'('#skF_51') )
| ~ ssList(W_1891) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_5996,c_12941]) ).
tff(c_17584,plain,
( ( '#skF_47'('#skF_50') = nil )
| ( tl(app('#skF_50','#skF_47'('#skF_51'))) != '#skF_47'('#skF_51') )
| ~ ssList('#skF_47'('#skF_50'))
| ~ ssList('#skF_47'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_17570,c_13181]) ).
tff(c_17659,plain,
'#skF_47'('#skF_50') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_5996,c_5966,c_5945,c_5995,c_17584]) ).
tff(c_17661,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7258,c_17659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC015+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.10 % 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 : n013.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 : Thu Aug 3 21:11:32 EDT 2023
% 0.09/0.30 % CPUTime :
% 16.54/5.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.61/5.24
% 16.61/5.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.61/5.27
% 16.61/5.27 Inference rules
% 16.61/5.27 ----------------------
% 16.61/5.27 #Ref : 2
% 16.61/5.27 #Sup : 3769
% 16.61/5.27 #Fact : 0
% 16.61/5.27 #Define : 0
% 16.61/5.27 #Split : 56
% 16.61/5.27 #Chain : 0
% 16.61/5.27 #Close : 0
% 16.61/5.27
% 16.61/5.27 Ordering : KBO
% 16.61/5.27
% 16.61/5.27 Simplification rules
% 16.61/5.27 ----------------------
% 16.61/5.27 #Subsume : 477
% 16.61/5.27 #Demod : 2696
% 16.61/5.27 #Tautology : 1003
% 16.61/5.28 #SimpNegUnit : 208
% 16.61/5.28 #BackRed : 359
% 16.61/5.28
% 16.61/5.28 #Partial instantiations: 0
% 16.61/5.28 #Strategies tried : 1
% 16.61/5.28
% 16.61/5.28 Timing (in seconds)
% 16.61/5.28 ----------------------
% 16.61/5.28 Preprocessing : 1.12
% 16.61/5.28 Parsing : 0.50
% 16.61/5.28 CNF conversion : 0.15
% 16.61/5.28 Main loop : 3.09
% 16.61/5.28 Inferencing : 0.91
% 16.61/5.28 Reduction : 1.10
% 16.61/5.28 Demodulation : 0.77
% 16.61/5.28 BG Simplification : 0.13
% 16.61/5.28 Subsumption : 0.75
% 16.61/5.28 Abstraction : 0.09
% 16.61/5.28 MUC search : 0.00
% 16.61/5.28 Cooper : 0.00
% 16.61/5.28 Total : 4.28
% 16.61/5.28 Index Insertion : 0.00
% 16.61/5.28 Index Deletion : 0.00
% 16.61/5.28 Index Matching : 0.00
% 16.61/5.28 BG Taut test : 0.00
%------------------------------------------------------------------------------