TSTP Solution File: SWC187+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC187+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 : n027.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 11:01:33 EDT 2023
% Result : Theorem 76.47s 60.38s
% Output : CNFRefutation 77.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 113
% Syntax : Number of formulae : 648 ( 242 unt; 79 typ; 0 def)
% Number of atoms : 1333 ( 495 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 1406 ( 642 ~; 653 |; 19 &)
% ( 9 <=>; 83 =>; 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 : 60 ( 60 usr; 11 con; 0-2 aty)
% Number of variables : 294 (; 285 !; 9 ?; 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_55 > #skF_22 > #skF_37 > #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_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(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_1027,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ( app(app(Z,cons(Y,nil)),X1) != U )
| ( ~ memberP(Z,Y)
& ~ memberP(X1,Y) ) ) ) ) )
| ( ! [X2] :
( ssItem(X2)
=> ( ( cons(X2,nil) != W )
| ~ memberP(X,X2) ) )
& ( ( nil != X )
| ( nil != W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_108,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& ( app(V,W) = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
tff(f_560,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).
tff(f_318,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
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_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_517,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
tff(f_855,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil = app(U,V) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
tff(f_834,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) = app(cons(V,nil),U) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
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_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_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
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_344,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( ( cons(W,U) = cons(X,V) )
=> ( ( W = X )
& ( V = U ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).
tff(f_378,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( hd(cons(V,U)) = V ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
tff(f_392,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( tl(cons(V,U)) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
tff(f_796,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( ( nil != V )
& ( nil != U )
& ( hd(V) = hd(U) )
& ( tl(V) = tl(U) ) )
=> ( V = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax77) ).
tff(f_577,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( ( U = V )
& frontsegP(W,X) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
tff(f_869,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil != U )
=> ( hd(app(U,V)) = hd(U) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
tff(f_135,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& ( app(app(W,V),X) = U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
tff(f_512,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( ( U = V )
| memberP(W,U) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
tff(f_544,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(U,V)
& frontsegP(V,U) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax41) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_120,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( ssList(W)
& ( app(W,V) = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
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(f_87,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& ( app(W,cons(V,X)) = U ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
tff(f_498,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(V,U)
| memberP(W,U) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
tff(f_612,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(U,V)
& rearsegP(V,U) )
=> ( U = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax48) ).
tff(f_844,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(app(U,V),W) = app(U,app(V,W)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
tff(f_96,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& ( cons(V,nil) = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
tff(f_758,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
tff(c_392,plain,
ssItem('#skF_52'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_400,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_6081,plain,
! [U_1608] :
( ( app(U_1608,nil) = U_1608 )
| ~ ssList(U_1608) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_6101,plain,
app('#skF_50',nil) = '#skF_50',
inference(resolution,[status(thm)],[c_400,c_6081]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_109927,plain,
! [V_3403,W_3404] :
( frontsegP(app(V_3403,W_3404),V_3403)
| ~ ssList(W_3404)
| ~ ssList(V_3403)
| ~ ssList(app(V_3403,W_3404)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_110100,plain,
( frontsegP('#skF_50','#skF_50')
| ~ ssList(nil)
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_50',nil)) ),
inference(superposition,[status(thm),theory(equality)],[c_6101,c_109927]) ).
tff(c_110233,plain,
frontsegP('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_6101,c_400,c_168,c_110100]) ).
tff(c_238,plain,
! [U_960,W_966,V_964] :
( frontsegP(app(U_960,W_966),V_964)
| ~ frontsegP(U_960,V_964)
| ~ ssList(W_966)
| ~ ssList(V_964)
| ~ ssList(U_960) ),
inference(cnfTransformation,[status(thm)],[f_560]) ).
tff(c_166,plain,
! [V_861,U_859] :
( ssList(cons(V_861,U_859))
| ~ ssItem(V_861)
| ~ ssList(U_859) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_390,plain,
ssList('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_192,plain,
! [U_896,V_898] :
( ssList(app(U_896,V_898))
| ~ ssList(V_898)
| ~ ssList(U_896) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_388,plain,
ssList('#skF_54'),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_410,plain,
( ssItem('#skF_55')
| ( nil = '#skF_50' ) ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_430,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_410]) ).
tff(c_330,plain,
! [U_1045] :
( ( hd(U_1045) = '#skF_46'(U_1045) )
| ( nil = U_1045 )
| ~ ssList(U_1045) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_3188,plain,
! [U_1462] :
( ( hd(U_1462) = '#skF_46'(U_1462) )
| ( U_1462 = '#skF_50' )
| ~ ssList(U_1462) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_330]) ).
tff(c_3291,plain,
( ( hd('#skF_54') = '#skF_46'('#skF_54') )
| ( '#skF_54' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_388,c_3188]) ).
tff(c_4559,plain,
'#skF_54' = '#skF_50',
inference(splitLeft,[status(thm)],[c_3291]) ).
tff(c_998,plain,
! [U_1329] :
( ( hd(U_1329) = '#skF_46'(U_1329) )
| ( U_1329 = '#skF_50' )
| ~ ssList(U_1329) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_330]) ).
tff(c_1108,plain,
( ( hd('#skF_53') = '#skF_46'('#skF_53') )
| ( '#skF_53' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_998]) ).
tff(c_1112,plain,
'#skF_53' = '#skF_50',
inference(splitLeft,[status(thm)],[c_1108]) ).
tff(c_384,plain,
( memberP('#skF_54','#skF_52')
| memberP('#skF_53','#skF_52') ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_484,plain,
memberP('#skF_53','#skF_52'),
inference(splitLeft,[status(thm)],[c_384]) ).
tff(c_1118,plain,
memberP('#skF_50','#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_1112,c_484]) ).
tff(c_228,plain,
! [U_948] :
( ~ memberP(nil,U_948)
| ~ ssItem(U_948) ),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_465,plain,
! [U_948] :
( ~ memberP('#skF_50',U_948)
| ~ ssItem(U_948) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_228]) ).
tff(c_1140,plain,
~ ssItem('#skF_52'),
inference(resolution,[status(thm)],[c_1118,c_465]) ).
tff(c_1144,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_392,c_1140]) ).
tff(c_1146,plain,
'#skF_53' != '#skF_50',
inference(splitRight,[status(thm)],[c_1108]) ).
tff(c_1109,plain,
( ( hd('#skF_54') = '#skF_46'('#skF_54') )
| ( '#skF_54' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_388,c_998]) ).
tff(c_1304,plain,
'#skF_54' = '#skF_50',
inference(splitLeft,[status(thm)],[c_1109]) ).
tff(c_394,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_386,plain,
app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') = '#skF_48',
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_421,plain,
app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_394,c_386]) ).
tff(c_515,plain,
app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_430,c_421]) ).
tff(c_1307,plain,
app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1304,c_515]) ).
tff(c_352,plain,
! [U_1077,V_1079] :
( ( nil = U_1077 )
| ( app(U_1077,V_1079) != nil )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(cnfTransformation,[status(thm)],[f_855]) ).
tff(c_2175,plain,
! [U_1382,V_1383] :
( ( U_1382 = '#skF_50' )
| ( app(U_1382,V_1383) != '#skF_50' )
| ~ ssList(V_1383)
| ~ ssList(U_1382) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_430,c_352]) ).
tff(c_2177,plain,
( ( app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50' )
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
inference(superposition,[status(thm),theory(equality)],[c_1307,c_2175]) ).
tff(c_2186,plain,
( ( app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50' )
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_2177]) ).
tff(c_2219,plain,
~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
inference(splitLeft,[status(thm)],[c_2186]) ).
tff(c_2222,plain,
( ~ ssList(cons('#skF_52','#skF_50'))
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_192,c_2219]) ).
tff(c_2225,plain,
~ ssList(cons('#skF_52','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_2222]) ).
tff(c_2228,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_2225]) ).
tff(c_2232,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_2228]) ).
tff(c_2233,plain,
app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50',
inference(splitRight,[status(thm)],[c_2186]) ).
tff(c_2174,plain,
! [U_1077,V_1079] :
( ( U_1077 = '#skF_50' )
| ( app(U_1077,V_1079) != '#skF_50' )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_430,c_352]) ).
tff(c_2284,plain,
( ( '#skF_53' = '#skF_50' )
| ~ ssList(cons('#skF_52','#skF_50'))
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_2233,c_2174]) ).
tff(c_2295,plain,
( ( '#skF_53' = '#skF_50' )
| ~ ssList(cons('#skF_52','#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_2284]) ).
tff(c_2296,plain,
~ ssList(cons('#skF_52','#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_1146,c_2295]) ).
tff(c_2302,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_2296]) ).
tff(c_2306,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_2302]) ).
tff(c_2308,plain,
'#skF_54' != '#skF_50',
inference(splitRight,[status(thm)],[c_1109]) ).
tff(c_354,plain,
! [V_1079,U_1077] :
( ( nil = V_1079 )
| ( app(U_1077,V_1079) != nil )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(cnfTransformation,[status(thm)],[f_855]) ).
tff(c_2785,plain,
! [V_1410,U_1411] :
( ( V_1410 = '#skF_50' )
| ( app(U_1411,V_1410) != '#skF_50' )
| ~ ssList(V_1410)
| ~ ssList(U_1411) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_430,c_354]) ).
tff(c_2795,plain,
( ( '#skF_54' = '#skF_50' )
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
inference(superposition,[status(thm),theory(equality)],[c_515,c_2785]) ).
tff(c_2815,plain,
( ( '#skF_54' = '#skF_50' )
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2795]) ).
tff(c_2816,plain,
~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
inference(negUnitSimplification,[status(thm)],[c_2308,c_2815]) ).
tff(c_2827,plain,
( ~ ssList(cons('#skF_52','#skF_50'))
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_192,c_2816]) ).
tff(c_2830,plain,
~ ssList(cons('#skF_52','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_2827]) ).
tff(c_2833,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_2830]) ).
tff(c_2837,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_2833]) ).
tff(c_2838,plain,
memberP('#skF_54','#skF_52'),
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_4563,plain,
memberP('#skF_50','#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_4559,c_2838]) ).
tff(c_4574,plain,
~ ssItem('#skF_52'),
inference(resolution,[status(thm)],[c_4563,c_465]) ).
tff(c_4578,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_392,c_4574]) ).
tff(c_4580,plain,
'#skF_54' != '#skF_50',
inference(splitRight,[status(thm)],[c_3291]) ).
tff(c_2937,plain,
app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_430,c_421]) ).
tff(c_5852,plain,
! [V_1580,U_1581] :
( ( V_1580 = '#skF_50' )
| ( app(U_1581,V_1580) != '#skF_50' )
| ~ ssList(V_1580)
| ~ ssList(U_1581) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_430,c_354]) ).
tff(c_5858,plain,
( ( '#skF_54' = '#skF_50' )
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
inference(superposition,[status(thm),theory(equality)],[c_2937,c_5852]) ).
tff(c_5876,plain,
( ( '#skF_54' = '#skF_50' )
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5858]) ).
tff(c_5877,plain,
~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
inference(negUnitSimplification,[status(thm)],[c_4580,c_5876]) ).
tff(c_5925,plain,
( ~ ssList(cons('#skF_52','#skF_50'))
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_192,c_5877]) ).
tff(c_5928,plain,
~ ssList(cons('#skF_52','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_5925]) ).
tff(c_5932,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_5928]) ).
tff(c_5936,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_5932]) ).
tff(c_5937,plain,
ssItem('#skF_55'),
inference(splitRight,[status(thm)],[c_410]) ).
tff(c_5938,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_410]) ).
tff(c_408,plain,
( ( cons('#skF_55',nil) = '#skF_50' )
| ( nil = '#skF_50' ) ),
inference(cnfTransformation,[status(thm)],[f_1027]) ).
tff(c_5992,plain,
cons('#skF_55',nil) = '#skF_50',
inference(negUnitSimplification,[status(thm)],[c_5938,c_408]) ).
tff(c_108619,plain,
! [V_3392,U_3393] :
( ( app(cons(V_3392,nil),U_3393) = cons(V_3392,U_3393) )
| ~ ssItem(V_3392)
| ~ ssList(U_3393) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_108647,plain,
! [U_3393] :
( ( cons('#skF_55',U_3393) = app('#skF_50',U_3393) )
| ~ ssItem('#skF_55')
| ~ ssList(U_3393) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_108619]) ).
tff(c_108656,plain,
! [U_3394] :
( ( cons('#skF_55',U_3394) = app('#skF_50',U_3394) )
| ~ ssList(U_3394) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_108647]) ).
tff(c_108816,plain,
cons('#skF_55','#skF_50') = app('#skF_50','#skF_50'),
inference(resolution,[status(thm)],[c_400,c_108656]) ).
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_109140,plain,
( ( app('#skF_50','#skF_50') != '#skF_50' )
| ~ ssItem('#skF_55')
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_108816,c_170]) ).
tff(c_109161,plain,
app('#skF_50','#skF_50') != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_400,c_5937,c_109140]) ).
tff(c_109143,plain,
( ssList(app('#skF_50','#skF_50'))
| ~ ssItem('#skF_55')
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_108816,c_166]) ).
tff(c_109163,plain,
ssList(app('#skF_50','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_5937,c_109143]) ).
tff(c_5997,plain,
memberP('#skF_53','#skF_52'),
inference(splitLeft,[status(thm)],[c_384]) ).
tff(c_6746,plain,
! [U_1664] :
( ( tl(U_1664) = '#skF_47'(U_1664) )
| ( nil = U_1664 )
| ~ ssList(U_1664) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_6862,plain,
( ( tl('#skF_53') = '#skF_47'('#skF_53') )
| ( nil = '#skF_53' ) ),
inference(resolution,[status(thm)],[c_390,c_6746]) ).
tff(c_51424,plain,
nil = '#skF_53',
inference(splitLeft,[status(thm)],[c_6862]) ).
tff(c_51589,plain,
! [U_2409] :
( ~ memberP('#skF_53',U_2409)
| ~ ssItem(U_2409) ),
inference(demodulation,[status(thm),theory(equality)],[c_51424,c_228]) ).
tff(c_51592,plain,
~ ssItem('#skF_52'),
inference(resolution,[status(thm)],[c_5997,c_51589]) ).
tff(c_51596,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_392,c_51592]) ).
tff(c_51598,plain,
nil != '#skF_53',
inference(splitRight,[status(thm)],[c_6862]) ).
tff(c_6610,plain,
! [U_1663] :
( ( hd(U_1663) = '#skF_46'(U_1663) )
| ( nil = U_1663 )
| ~ ssList(U_1663) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_6726,plain,
( ( hd('#skF_53') = '#skF_46'('#skF_53') )
| ( nil = '#skF_53' ) ),
inference(resolution,[status(thm)],[c_390,c_6610]) ).
tff(c_51733,plain,
hd('#skF_53') = '#skF_46'('#skF_53'),
inference(negUnitSimplification,[status(thm)],[c_51598,c_6726]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_51737,plain,
( ssItem('#skF_46'('#skF_53'))
| ( nil = '#skF_53' )
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_51733,c_184]) ).
tff(c_51741,plain,
( ssItem('#skF_46'('#skF_53'))
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_51737]) ).
tff(c_51742,plain,
ssItem('#skF_46'('#skF_53')),
inference(negUnitSimplification,[status(thm)],[c_51598,c_51741]) ).
tff(c_51597,plain,
tl('#skF_53') = '#skF_47'('#skF_53'),
inference(splitRight,[status(thm)],[c_6862]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_51615,plain,
( ssList('#skF_47'('#skF_53'))
| ( nil = '#skF_53' )
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_51597,c_188]) ).
tff(c_51619,plain,
( ssList('#skF_47'('#skF_53'))
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_51615]) ).
tff(c_51620,plain,
ssList('#skF_47'('#skF_53')),
inference(negUnitSimplification,[status(thm)],[c_51598,c_51619]) ).
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_51641,plain,
( ( tl('#skF_47'('#skF_53')) = '#skF_47'('#skF_47'('#skF_53')) )
| ( '#skF_47'('#skF_53') = nil ) ),
inference(resolution,[status(thm)],[c_51620,c_334]) ).
tff(c_105365,plain,
'#skF_47'('#skF_53') = nil,
inference(splitLeft,[status(thm)],[c_51641]) ).
tff(c_52117,plain,
! [U_2433] :
( ( cons(hd(U_2433),tl(U_2433)) = U_2433 )
| ( nil = U_2433 )
| ~ ssList(U_2433) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_52151,plain,
( ( cons('#skF_46'('#skF_53'),tl('#skF_53')) = '#skF_53' )
| ( nil = '#skF_53' )
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_51733,c_52117]) ).
tff(c_52181,plain,
( ( cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_51597,c_52151]) ).
tff(c_52182,plain,
cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53',
inference(negUnitSimplification,[status(thm)],[c_51598,c_52181]) ).
tff(c_105369,plain,
cons('#skF_46'('#skF_53'),nil) = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_105365,c_52182]) ).
tff(c_121304,plain,
! [X_3546,W_3547,V_3548,U_3549] :
( ( X_3546 = W_3547 )
| ( cons(X_3546,V_3548) != cons(W_3547,U_3549) )
| ~ ssItem(X_3546)
| ~ ssItem(W_3547)
| ~ ssList(V_3548)
| ~ ssList(U_3549) ),
inference(cnfTransformation,[status(thm)],[f_344]) ).
tff(c_121354,plain,
! [W_3547,U_3549] :
( ( W_3547 = '#skF_55' )
| ( cons(W_3547,U_3549) != '#skF_50' )
| ~ ssItem('#skF_55')
| ~ ssItem(W_3547)
| ~ ssList(nil)
| ~ ssList(U_3549) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_121304]) ).
tff(c_121996,plain,
! [W_3556,U_3557] :
( ( W_3556 = '#skF_55' )
| ( cons(W_3556,U_3557) != '#skF_50' )
| ~ ssItem(W_3556)
| ~ ssList(U_3557) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_5937,c_121354]) ).
tff(c_122014,plain,
( ( '#skF_46'('#skF_53') = '#skF_55' )
| ( '#skF_53' != '#skF_50' )
| ~ ssItem('#skF_46'('#skF_53'))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_105369,c_121996]) ).
tff(c_122040,plain,
( ( '#skF_46'('#skF_53') = '#skF_55' )
| ( '#skF_53' != '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_51742,c_122014]) ).
tff(c_122052,plain,
'#skF_53' != '#skF_50',
inference(splitLeft,[status(thm)],[c_122040]) ).
tff(c_105373,plain,
tl('#skF_53') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_105365,c_51597]) ).
tff(c_6697,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_400,c_6610]) ).
tff(c_6732,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_5938,c_6697]) ).
tff(c_51691,plain,
! [V_2412,U_2413] :
( ( hd(cons(V_2412,U_2413)) = V_2412 )
| ~ ssItem(V_2412)
| ~ ssList(U_2413) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_51703,plain,
( ( hd('#skF_50') = '#skF_55' )
| ~ ssItem('#skF_55')
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_51691]) ).
tff(c_51707,plain,
'#skF_46'('#skF_50') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_5937,c_6732,c_51703]) ).
tff(c_51709,plain,
hd('#skF_50') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_51707,c_6732]) ).
tff(c_6833,plain,
( ( tl('#skF_50') = '#skF_47'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_400,c_6746]) ).
tff(c_6868,plain,
tl('#skF_50') = '#skF_47'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_5938,c_6833]) ).
tff(c_51846,plain,
! [V_2416,U_2417] :
( ( tl(cons(V_2416,U_2417)) = U_2417 )
| ~ ssItem(V_2416)
| ~ ssList(U_2417) ),
inference(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_51858,plain,
( ( tl('#skF_50') = nil )
| ~ ssItem('#skF_55')
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_51846]) ).
tff(c_51862,plain,
'#skF_47'('#skF_50') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_5937,c_6868,c_51858]) ).
tff(c_51866,plain,
tl('#skF_50') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_51862,c_6868]) ).
tff(c_124556,plain,
! [V_3587,U_3588] :
( ( V_3587 = U_3588 )
| ( tl(V_3587) != tl(U_3588) )
| ( hd(V_3587) != hd(U_3588) )
| ( nil = U_3588 )
| ( nil = V_3587 )
| ~ ssList(V_3587)
| ~ ssList(U_3588) ),
inference(cnfTransformation,[status(thm)],[f_796]) ).
tff(c_124602,plain,
! [U_3588] :
( ( U_3588 = '#skF_50' )
| ( tl(U_3588) != nil )
| ( hd(U_3588) != hd('#skF_50') )
| ( nil = U_3588 )
| ( nil = '#skF_50' )
| ~ ssList('#skF_50')
| ~ ssList(U_3588) ),
inference(superposition,[status(thm),theory(equality)],[c_51866,c_124556]) ).
tff(c_124666,plain,
! [U_3588] :
( ( U_3588 = '#skF_50' )
| ( tl(U_3588) != nil )
| ( hd(U_3588) != '#skF_55' )
| ( nil = U_3588 )
| ( nil = '#skF_50' )
| ~ ssList(U_3588) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_51709,c_124602]) ).
tff(c_124725,plain,
! [U_3589] :
( ( U_3589 = '#skF_50' )
| ( tl(U_3589) != nil )
| ( hd(U_3589) != '#skF_55' )
| ( nil = U_3589 )
| ~ ssList(U_3589) ),
inference(negUnitSimplification,[status(thm)],[c_5938,c_124666]) ).
tff(c_124848,plain,
( ( '#skF_53' = '#skF_50' )
| ( tl('#skF_53') != nil )
| ( hd('#skF_53') != '#skF_55' )
| ( nil = '#skF_53' ) ),
inference(resolution,[status(thm)],[c_390,c_124725]) ).
tff(c_124922,plain,
( ( '#skF_53' = '#skF_50' )
| ( '#skF_46'('#skF_53') != '#skF_55' )
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_51733,c_105373,c_124848]) ).
tff(c_124923,plain,
'#skF_46'('#skF_53') != '#skF_55',
inference(negUnitSimplification,[status(thm)],[c_51598,c_122052,c_124922]) ).
tff(c_124281,plain,
! [V_3583,U_3584,W_3585,X_3586] :
( ( V_3583 = U_3584 )
| ~ frontsegP(cons(U_3584,W_3585),cons(V_3583,X_3586))
| ~ ssList(X_3586)
| ~ ssList(W_3585)
| ~ ssItem(V_3583)
| ~ ssItem(U_3584) ),
inference(cnfTransformation,[status(thm)],[f_577]) ).
tff(c_124371,plain,
! [V_3583,X_3586] :
( ( V_3583 = '#skF_55' )
| ~ frontsegP('#skF_50',cons(V_3583,X_3586))
| ~ ssList(X_3586)
| ~ ssList(nil)
| ~ ssItem(V_3583)
| ~ ssItem('#skF_55') ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_124281]) ).
tff(c_133174,plain,
! [V_3680,X_3681] :
( ( V_3680 = '#skF_55' )
| ~ frontsegP('#skF_50',cons(V_3680,X_3681))
| ~ ssList(X_3681)
| ~ ssItem(V_3680) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_168,c_124371]) ).
tff(c_133216,plain,
( ( '#skF_46'('#skF_53') = '#skF_55' )
| ~ frontsegP('#skF_50','#skF_53')
| ~ ssList(nil)
| ~ ssItem('#skF_46'('#skF_53')) ),
inference(superposition,[status(thm),theory(equality)],[c_105369,c_133174]) ).
tff(c_133256,plain,
( ( '#skF_46'('#skF_53') = '#skF_55' )
| ~ frontsegP('#skF_50','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_51742,c_168,c_133216]) ).
tff(c_133257,plain,
~ frontsegP('#skF_50','#skF_53'),
inference(negUnitSimplification,[status(thm)],[c_124923,c_133256]) ).
tff(c_108150,plain,
! [U_3385,V_3386] :
( ( hd(app(U_3385,V_3386)) = hd(U_3385) )
| ( nil = U_3385 )
| ~ ssList(V_3386)
| ~ ssList(U_3385) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_108333,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = hd('#skF_50') )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_108150]) ).
tff(c_108520,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_51709,c_108333]) ).
tff(c_108539,plain,
~ ssList(app('#skF_53',cons('#skF_52',nil))),
inference(splitLeft,[status(thm)],[c_108520]) ).
tff(c_108542,plain,
( ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_192,c_108539]) ).
tff(c_108545,plain,
~ ssList(cons('#skF_52',nil)),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_108542]) ).
tff(c_108548,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_108545]) ).
tff(c_108552,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_108548]) ).
tff(c_108554,plain,
ssList(app('#skF_53',cons('#skF_52',nil))),
inference(splitRight,[status(thm)],[c_108520]) ).
tff(c_126110,plain,
! [W_3601,V_3602,X_3603] :
( segmentP(app(app(W_3601,V_3602),X_3603),V_3602)
| ~ ssList(X_3603)
| ~ ssList(W_3601)
| ~ ssList(V_3602)
| ~ ssList(app(app(W_3601,V_3602),X_3603)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_126364,plain,
( segmentP('#skF_50',cons('#skF_52',nil))
| ~ ssList('#skF_54')
| ~ ssList('#skF_53')
| ~ ssList(cons('#skF_52',nil))
| ~ ssList(app(app('#skF_53',cons('#skF_52',nil)),'#skF_54')) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_126110]) ).
tff(c_126521,plain,
( segmentP('#skF_50',cons('#skF_52',nil))
| ~ ssList(cons('#skF_52',nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_421,c_390,c_388,c_126364]) ).
tff(c_126565,plain,
~ ssList(cons('#skF_52',nil)),
inference(splitLeft,[status(thm)],[c_126521]) ).
tff(c_126568,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_126565]) ).
tff(c_126572,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_126568]) ).
tff(c_126574,plain,
ssList(cons('#skF_52',nil)),
inference(splitRight,[status(thm)],[c_126521]) ).
tff(c_26,plain,
! [V_40,W_43] :
( frontsegP(app(V_40,W_43),V_40)
| ~ ssList(W_43)
| ~ ssList(V_40)
| ~ ssList(app(V_40,W_43)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_110811,plain,
! [U_3411,W_3412,V_3413] :
( frontsegP(app(U_3411,W_3412),V_3413)
| ~ frontsegP(U_3411,V_3413)
| ~ ssList(W_3412)
| ~ ssList(V_3413)
| ~ ssList(U_3411) ),
inference(cnfTransformation,[status(thm)],[f_560]) ).
tff(c_110993,plain,
! [V_3413] :
( frontsegP('#skF_50',V_3413)
| ~ frontsegP(app('#skF_53',cons('#skF_52',nil)),V_3413)
| ~ ssList('#skF_54')
| ~ ssList(V_3413)
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_110811]) ).
tff(c_134755,plain,
! [V_3691] :
( frontsegP('#skF_50',V_3691)
| ~ frontsegP(app('#skF_53',cons('#skF_52',nil)),V_3691)
| ~ ssList(V_3691) ),
inference(demodulation,[status(thm),theory(equality)],[c_108554,c_388,c_110993]) ).
tff(c_134763,plain,
( frontsegP('#skF_50','#skF_53')
| ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53')
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(resolution,[status(thm)],[c_26,c_134755]) ).
tff(c_134777,plain,
frontsegP('#skF_50','#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_108554,c_390,c_126574,c_134763]) ).
tff(c_134779,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_133257,c_134777]) ).
tff(c_134781,plain,
'#skF_53' = '#skF_50',
inference(splitRight,[status(thm)],[c_122040]) ).
tff(c_134864,plain,
memberP('#skF_50','#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_134781,c_5997]) ).
tff(c_121914,plain,
! [W_3553,U_3554,V_3555] :
( memberP(W_3553,U_3554)
| ( V_3555 = U_3554 )
| ~ memberP(cons(V_3555,W_3553),U_3554)
| ~ ssList(W_3553)
| ~ ssItem(V_3555)
| ~ ssItem(U_3554) ),
inference(cnfTransformation,[status(thm)],[f_512]) ).
tff(c_121962,plain,
! [U_3554] :
( memberP(nil,U_3554)
| ( U_3554 = '#skF_55' )
| ~ memberP('#skF_50',U_3554)
| ~ ssList(nil)
| ~ ssItem('#skF_55')
| ~ ssItem(U_3554) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_121914]) ).
tff(c_137246,plain,
! [U_3719] :
( memberP(nil,U_3719)
| ( U_3719 = '#skF_55' )
| ~ memberP('#skF_50',U_3719)
| ~ ssItem(U_3719) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_168,c_121962]) ).
tff(c_137251,plain,
! [U_3720] :
( ( U_3720 = '#skF_55' )
| ~ memberP('#skF_50',U_3720)
| ~ ssItem(U_3720) ),
inference(resolution,[status(thm)],[c_137246,c_228]) ).
tff(c_137254,plain,
( ( '#skF_52' = '#skF_55' )
| ~ ssItem('#skF_52') ),
inference(resolution,[status(thm)],[c_134864,c_137251]) ).
tff(c_137263,plain,
'#skF_52' = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_392,c_137254]) ).
tff(c_110109,plain,
( frontsegP('#skF_50',app('#skF_53',cons('#skF_52',nil)))
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil)))
| ~ ssList(app(app('#skF_53',cons('#skF_52',nil)),'#skF_54')) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_109927]) ).
tff(c_110239,plain,
frontsegP('#skF_50',app('#skF_53',cons('#skF_52',nil))),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_421,c_108554,c_388,c_110109]) ).
tff(c_134830,plain,
frontsegP('#skF_50',app('#skF_50',cons('#skF_52',nil))),
inference(demodulation,[status(thm),theory(equality)],[c_134781,c_110239]) ).
tff(c_137271,plain,
frontsegP('#skF_50',app('#skF_50',cons('#skF_55',nil))),
inference(demodulation,[status(thm),theory(equality)],[c_137263,c_134830]) ).
tff(c_137276,plain,
frontsegP('#skF_50',app('#skF_50','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_5992,c_137271]) ).
tff(c_234,plain,
! [V_958,U_956] :
( ( V_958 = U_956 )
| ~ frontsegP(V_958,U_956)
| ~ frontsegP(U_956,V_958)
| ~ ssList(V_958)
| ~ ssList(U_956) ),
inference(cnfTransformation,[status(thm)],[f_544]) ).
tff(c_138295,plain,
( ( app('#skF_50','#skF_50') = '#skF_50' )
| ~ frontsegP(app('#skF_50','#skF_50'),'#skF_50')
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_50','#skF_50')) ),
inference(resolution,[status(thm)],[c_137276,c_234]) ).
tff(c_138301,plain,
( ( app('#skF_50','#skF_50') = '#skF_50' )
| ~ frontsegP(app('#skF_50','#skF_50'),'#skF_50') ),
inference(demodulation,[status(thm),theory(equality)],[c_109163,c_400,c_138295]) ).
tff(c_138302,plain,
~ frontsegP(app('#skF_50','#skF_50'),'#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_109161,c_138301]) ).
tff(c_138306,plain,
( ~ frontsegP('#skF_50','#skF_50')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_238,c_138302]) ).
tff(c_138313,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_400,c_110233,c_138306]) ).
tff(c_138315,plain,
'#skF_47'('#skF_53') != nil,
inference(splitRight,[status(thm)],[c_51641]) ).
tff(c_6018,plain,
! [U_1604] :
( ( app(nil,U_1604) = U_1604 )
| ~ ssList(U_1604) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_6034,plain,
app(nil,'#skF_53') = '#skF_53',
inference(resolution,[status(thm)],[c_390,c_6018]) ).
tff(c_73275,plain,
! [V_2811,W_2812] :
( frontsegP(app(V_2811,W_2812),V_2811)
| ~ ssList(W_2812)
| ~ ssList(V_2811)
| ~ ssList(app(V_2811,W_2812)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_73484,plain,
( frontsegP('#skF_53',nil)
| ~ ssList('#skF_53')
| ~ ssList(nil)
| ~ ssList(app(nil,'#skF_53')) ),
inference(superposition,[status(thm),theory(equality)],[c_6034,c_73275]) ).
tff(c_73617,plain,
frontsegP('#skF_53',nil),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_6034,c_168,c_390,c_73484]) ).
tff(c_73643,plain,
( ( nil = '#skF_53' )
| ~ frontsegP(nil,'#skF_53')
| ~ ssList('#skF_53')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_73617,c_234]) ).
tff(c_73646,plain,
( ( nil = '#skF_53' )
| ~ frontsegP(nil,'#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_390,c_73643]) ).
tff(c_73647,plain,
~ frontsegP(nil,'#skF_53'),
inference(negUnitSimplification,[status(thm)],[c_51598,c_73646]) ).
tff(c_6037,plain,
app(nil,'#skF_50') = '#skF_50',
inference(resolution,[status(thm)],[c_400,c_6018]) ).
tff(c_72878,plain,
! [W_2809,V_2810] :
( rearsegP(app(W_2809,V_2810),V_2810)
| ~ ssList(W_2809)
| ~ ssList(V_2810)
| ~ ssList(app(W_2809,V_2810)) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_73081,plain,
( rearsegP('#skF_50','#skF_50')
| ~ ssList(nil)
| ~ ssList('#skF_50')
| ~ ssList(app(nil,'#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_6037,c_72878]) ).
tff(c_73216,plain,
rearsegP('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_6037,c_400,c_168,c_73081]) ).
tff(c_6727,plain,
( ( hd('#skF_54') = '#skF_46'('#skF_54') )
| ( nil = '#skF_54' ) ),
inference(resolution,[status(thm)],[c_388,c_6610]) ).
tff(c_6882,plain,
nil = '#skF_54',
inference(splitLeft,[status(thm)],[c_6727]) ).
tff(c_7166,plain,
( ( hd('#skF_53') = '#skF_46'('#skF_53') )
| ( '#skF_54' = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_6726]) ).
tff(c_7167,plain,
'#skF_54' = '#skF_53',
inference(splitLeft,[status(thm)],[c_7166]) ).
tff(c_6916,plain,
! [U_948] :
( ~ memberP('#skF_54',U_948)
| ~ ssItem(U_948) ),
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_228]) ).
tff(c_7289,plain,
! [U_1678] :
( ~ memberP('#skF_53',U_1678)
| ~ ssItem(U_1678) ),
inference(demodulation,[status(thm),theory(equality)],[c_7167,c_6916]) ).
tff(c_7292,plain,
~ ssItem('#skF_52'),
inference(resolution,[status(thm)],[c_5997,c_7289]) ).
tff(c_7296,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_392,c_7292]) ).
tff(c_7298,plain,
'#skF_54' != '#skF_53',
inference(splitRight,[status(thm)],[c_7166]) ).
tff(c_6907,plain,
app('#skF_54','#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_6037]) ).
tff(c_16300,plain,
! [W_1892,U_1893,V_1894] :
( ( W_1892 = U_1893 )
| ( app(W_1892,V_1894) != app(U_1893,V_1894) )
| ~ ssList(W_1892)
| ~ ssList(V_1894)
| ~ ssList(U_1893) ),
inference(cnfTransformation,[status(thm)],[f_815]) ).
tff(c_16548,plain,
! [W_1892] :
( ( W_1892 = '#skF_54' )
| ( app(W_1892,'#skF_50') != '#skF_50' )
| ~ ssList(W_1892)
| ~ ssList('#skF_50')
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_6907,c_16300]) ).
tff(c_23393,plain,
! [W_1999] :
( ( W_1999 = '#skF_54' )
| ( app(W_1999,'#skF_50') != '#skF_50' )
| ~ ssList(W_1999) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_400,c_16548]) ).
tff(c_23528,plain,
( ( '#skF_54' = '#skF_53' )
| ( app('#skF_53','#skF_50') != '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_23393]) ).
tff(c_23604,plain,
app('#skF_53','#skF_50') != '#skF_50',
inference(negUnitSimplification,[status(thm)],[c_7298,c_23528]) ).
tff(c_6914,plain,
cons('#skF_55','#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_5992]) ).
tff(c_6901,plain,
app(app('#skF_53',cons('#skF_52','#skF_54')),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_421]) ).
tff(c_43556,plain,
! [W_2306,V_2307,X_2308] :
( segmentP(app(app(W_2306,V_2307),X_2308),V_2307)
| ~ ssList(X_2308)
| ~ ssList(W_2306)
| ~ ssList(V_2307)
| ~ ssList(app(app(W_2306,V_2307),X_2308)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_43840,plain,
( segmentP('#skF_50',cons('#skF_52','#skF_54'))
| ~ ssList('#skF_54')
| ~ ssList('#skF_53')
| ~ ssList(cons('#skF_52','#skF_54'))
| ~ ssList(app(app('#skF_53',cons('#skF_52','#skF_54')),'#skF_54')) ),
inference(superposition,[status(thm),theory(equality)],[c_6901,c_43556]) ).
tff(c_44007,plain,
( segmentP('#skF_50',cons('#skF_52','#skF_54'))
| ~ ssList(cons('#skF_52','#skF_54')) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_6901,c_390,c_388,c_43840]) ).
tff(c_44056,plain,
~ ssList(cons('#skF_52','#skF_54')),
inference(splitLeft,[status(thm)],[c_44007]) ).
tff(c_44131,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_54') ),
inference(resolution,[status(thm)],[c_166,c_44056]) ).
tff(c_44135,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_44131]) ).
tff(c_44137,plain,
ssList(cons('#skF_52','#skF_54')),
inference(splitRight,[status(thm)],[c_44007]) ).
tff(c_6537,plain,
! [U_1657,V_1658] :
( ssList(app(U_1657,V_1658))
| ~ ssList(V_1658)
| ~ ssList(U_1657) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_356,plain,
! [U_1080] :
( ( app(U_1080,nil) = U_1080 )
| ~ ssList(U_1080) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_6578,plain,
! [U_1657,V_1658] :
( ( app(app(U_1657,V_1658),nil) = app(U_1657,V_1658) )
| ~ ssList(V_1658)
| ~ ssList(U_1657) ),
inference(resolution,[status(thm)],[c_6537,c_356]) ).
tff(c_50329,plain,
! [U_2399,V_2400] :
( ( app(app(U_2399,V_2400),'#skF_54') = app(U_2399,V_2400) )
| ~ ssList(V_2400)
| ~ ssList(U_2399) ),
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_6578]) ).
tff(c_50419,plain,
( ( app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50' )
| ~ ssList(cons('#skF_52','#skF_54'))
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_50329,c_6901]) ).
tff(c_50815,plain,
app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_44137,c_50419]) ).
tff(c_12,plain,
! [W_27,V_19,X_29] :
( memberP(app(W_27,cons(V_19,X_29)),V_19)
| ~ ssList(X_29)
| ~ ssList(W_27)
| ~ ssItem(V_19)
| ~ ssList(app(W_27,cons(V_19,X_29))) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_51066,plain,
( memberP('#skF_50','#skF_52')
| ~ ssList('#skF_54')
| ~ ssList('#skF_53')
| ~ ssItem('#skF_52')
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_54'))) ),
inference(superposition,[status(thm),theory(equality)],[c_50815,c_12]) ).
tff(c_51137,plain,
memberP('#skF_50','#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_50815,c_392,c_390,c_388,c_51066]) ).
tff(c_38486,plain,
! [W_2238,U_2239,V_2240] :
( memberP(W_2238,U_2239)
| ( V_2240 = U_2239 )
| ~ memberP(cons(V_2240,W_2238),U_2239)
| ~ ssList(W_2238)
| ~ ssItem(V_2240)
| ~ ssItem(U_2239) ),
inference(cnfTransformation,[status(thm)],[f_512]) ).
tff(c_38537,plain,
! [U_2239] :
( memberP('#skF_54',U_2239)
| ( U_2239 = '#skF_55' )
| ~ memberP('#skF_50',U_2239)
| ~ ssList('#skF_54')
| ~ ssItem('#skF_55')
| ~ ssItem(U_2239) ),
inference(superposition,[status(thm),theory(equality)],[c_6914,c_38486]) ).
tff(c_41283,plain,
! [U_2277] :
( memberP('#skF_54',U_2277)
| ( U_2277 = '#skF_55' )
| ~ memberP('#skF_50',U_2277)
| ~ ssItem(U_2277) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_388,c_38537]) ).
tff(c_41287,plain,
! [U_2277] :
( ( U_2277 = '#skF_55' )
| ~ memberP('#skF_50',U_2277)
| ~ ssItem(U_2277) ),
inference(resolution,[status(thm)],[c_41283,c_6916]) ).
tff(c_51182,plain,
( ( '#skF_52' = '#skF_55' )
| ~ ssItem('#skF_52') ),
inference(resolution,[status(thm)],[c_51137,c_41287]) ).
tff(c_51185,plain,
'#skF_52' = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_392,c_51182]) ).
tff(c_51187,plain,
app('#skF_53',cons('#skF_55','#skF_54')) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_51185,c_50815]) ).
tff(c_51224,plain,
app('#skF_53','#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_6914,c_51187]) ).
tff(c_51226,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23604,c_51224]) ).
tff(c_51228,plain,
nil != '#skF_54',
inference(splitRight,[status(thm)],[c_6727]) ).
tff(c_71330,plain,
! [U_2793,V_2794] :
( ( hd(app(U_2793,V_2794)) = hd(U_2793) )
| ( nil = U_2793 )
| ~ ssList(V_2794)
| ~ ssList(U_2793) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_71546,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = hd('#skF_50') )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_71330]) ).
tff(c_71763,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_51709,c_71546]) ).
tff(c_71804,plain,
~ ssList(app('#skF_53',cons('#skF_52',nil))),
inference(splitLeft,[status(thm)],[c_71763]) ).
tff(c_71807,plain,
( ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_192,c_71804]) ).
tff(c_71810,plain,
~ ssList(cons('#skF_52',nil)),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_71807]) ).
tff(c_71813,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_71810]) ).
tff(c_71817,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_71813]) ).
tff(c_71819,plain,
ssList(app('#skF_53',cons('#skF_52',nil))),
inference(splitRight,[status(thm)],[c_71763]) ).
tff(c_6035,plain,
app(nil,'#skF_54') = '#skF_54',
inference(resolution,[status(thm)],[c_388,c_6018]) ).
tff(c_75326,plain,
! [W_2830,U_2831,V_2832] :
( ( W_2830 = U_2831 )
| ( app(W_2830,V_2832) != app(U_2831,V_2832) )
| ~ ssList(W_2830)
| ~ ssList(V_2832)
| ~ ssList(U_2831) ),
inference(cnfTransformation,[status(thm)],[f_815]) ).
tff(c_75590,plain,
! [W_2830] :
( ( nil = W_2830 )
| ( app(W_2830,'#skF_54') != '#skF_54' )
| ~ ssList(W_2830)
| ~ ssList('#skF_54')
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_6035,c_75326]) ).
tff(c_82189,plain,
! [W_2923] :
( ( nil = W_2923 )
| ( app(W_2923,'#skF_54') != '#skF_54' )
| ~ ssList(W_2923) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_75590]) ).
tff(c_82195,plain,
( ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ( app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') != '#skF_54' ) ),
inference(resolution,[status(thm)],[c_71819,c_82189]) ).
tff(c_82330,plain,
( ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ( '#skF_54' != '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_82195]) ).
tff(c_86426,plain,
'#skF_54' != '#skF_50',
inference(splitLeft,[status(thm)],[c_82330]) ).
tff(c_51227,plain,
hd('#skF_54') = '#skF_46'('#skF_54'),
inference(splitRight,[status(thm)],[c_6727]) ).
tff(c_6863,plain,
( ( tl('#skF_54') = '#skF_47'('#skF_54') )
| ( nil = '#skF_54' ) ),
inference(resolution,[status(thm)],[c_388,c_6746]) ).
tff(c_51229,plain,
nil = '#skF_54',
inference(splitLeft,[status(thm)],[c_6863]) ).
tff(c_51230,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_51228,c_51229]) ).
tff(c_51231,plain,
tl('#skF_54') = '#skF_47'('#skF_54'),
inference(splitRight,[status(thm)],[c_6863]) ).
tff(c_51660,plain,
( ssList('#skF_47'('#skF_54'))
| ( nil = '#skF_54' )
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_51231,c_188]) ).
tff(c_51664,plain,
( ssList('#skF_47'('#skF_54'))
| ( nil = '#skF_54' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_51660]) ).
tff(c_51665,plain,
ssList('#skF_47'('#skF_54')),
inference(negUnitSimplification,[status(thm)],[c_51228,c_51664]) ).
tff(c_51686,plain,
( ( tl('#skF_47'('#skF_54')) = '#skF_47'('#skF_47'('#skF_54')) )
| ( '#skF_47'('#skF_54') = nil ) ),
inference(resolution,[status(thm)],[c_51665,c_334]) ).
tff(c_68030,plain,
'#skF_47'('#skF_54') = nil,
inference(splitLeft,[status(thm)],[c_51686]) ).
tff(c_68039,plain,
tl('#skF_54') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_68030,c_51231]) ).
tff(c_88669,plain,
! [V_3004,U_3005] :
( ( V_3004 = U_3005 )
| ( tl(V_3004) != tl(U_3005) )
| ( hd(V_3004) != hd(U_3005) )
| ( nil = U_3005 )
| ( nil = V_3004 )
| ~ ssList(V_3004)
| ~ ssList(U_3005) ),
inference(cnfTransformation,[status(thm)],[f_796]) ).
tff(c_88721,plain,
! [V_3004] :
( ( V_3004 = '#skF_50' )
| ( tl(V_3004) != nil )
| ( hd(V_3004) != hd('#skF_50') )
| ( nil = '#skF_50' )
| ( nil = V_3004 )
| ~ ssList(V_3004)
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_51866,c_88669]) ).
tff(c_88786,plain,
! [V_3004] :
( ( V_3004 = '#skF_50' )
| ( tl(V_3004) != nil )
| ( hd(V_3004) != '#skF_55' )
| ( nil = '#skF_50' )
| ( nil = V_3004 )
| ~ ssList(V_3004) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_51709,c_88721]) ).
tff(c_97515,plain,
! [V_3108] :
( ( V_3108 = '#skF_50' )
| ( tl(V_3108) != nil )
| ( hd(V_3108) != '#skF_55' )
| ( nil = V_3108 )
| ~ ssList(V_3108) ),
inference(negUnitSimplification,[status(thm)],[c_5938,c_88786]) ).
tff(c_97656,plain,
( ( '#skF_54' = '#skF_50' )
| ( tl('#skF_54') != nil )
| ( hd('#skF_54') != '#skF_55' )
| ( nil = '#skF_54' ) ),
inference(resolution,[status(thm)],[c_388,c_97515]) ).
tff(c_97742,plain,
( ( '#skF_54' = '#skF_50' )
| ( '#skF_46'('#skF_54') != '#skF_55' )
| ( nil = '#skF_54' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_51227,c_68039,c_97656]) ).
tff(c_97743,plain,
'#skF_46'('#skF_54') != '#skF_55',
inference(negUnitSimplification,[status(thm)],[c_51228,c_86426,c_97742]) ).
tff(c_51650,plain,
( ssItem('#skF_46'('#skF_54'))
| ( nil = '#skF_54' )
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_51227,c_184]) ).
tff(c_51654,plain,
( ssItem('#skF_46'('#skF_54'))
| ( nil = '#skF_54' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_51650]) ).
tff(c_51655,plain,
ssItem('#skF_46'('#skF_54')),
inference(negUnitSimplification,[status(thm)],[c_51228,c_51654]) ).
tff(c_52160,plain,
( ( cons(hd('#skF_54'),'#skF_47'('#skF_54')) = '#skF_54' )
| ( nil = '#skF_54' )
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_51231,c_52117]) ).
tff(c_52187,plain,
( ( cons('#skF_46'('#skF_54'),'#skF_47'('#skF_54')) = '#skF_54' )
| ( nil = '#skF_54' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_51227,c_52160]) ).
tff(c_52188,plain,
cons('#skF_46'('#skF_54'),'#skF_47'('#skF_54')) = '#skF_54',
inference(negUnitSimplification,[status(thm)],[c_51228,c_52187]) ).
tff(c_226,plain,
! [V_945,W_947] :
( memberP(cons(V_945,W_947),V_945)
| ~ ssList(W_947)
| ~ ssItem(V_945) ),
inference(cnfTransformation,[status(thm)],[f_512]) ).
tff(c_67479,plain,
( memberP('#skF_54','#skF_46'('#skF_54'))
| ~ ssList('#skF_47'('#skF_54'))
| ~ ssItem('#skF_46'('#skF_54')) ),
inference(superposition,[status(thm),theory(equality)],[c_52188,c_226]) ).
tff(c_67496,plain,
memberP('#skF_54','#skF_46'('#skF_54')),
inference(demodulation,[status(thm),theory(equality)],[c_51655,c_51665,c_67479]) ).
tff(c_74236,plain,
! [W_2816,U_2817,V_2818] :
( ~ memberP(W_2816,U_2817)
| memberP(app(V_2818,W_2816),U_2817)
| ~ ssList(W_2816)
| ~ ssList(V_2818)
| ~ ssItem(U_2817) ),
inference(cnfTransformation,[status(thm)],[f_498]) ).
tff(c_74428,plain,
! [U_2817] :
( ~ memberP('#skF_54',U_2817)
| memberP('#skF_50',U_2817)
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil)))
| ~ ssItem(U_2817) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_74236]) ).
tff(c_75315,plain,
! [U_2829] :
( ~ memberP('#skF_54',U_2829)
| memberP('#skF_50',U_2829)
| ~ ssItem(U_2829) ),
inference(demodulation,[status(thm),theory(equality)],[c_71819,c_388,c_74428]) ).
tff(c_75318,plain,
( memberP('#skF_50','#skF_46'('#skF_54'))
| ~ ssItem('#skF_46'('#skF_54')) ),
inference(resolution,[status(thm)],[c_67496,c_75315]) ).
tff(c_75321,plain,
memberP('#skF_50','#skF_46'('#skF_54')),
inference(demodulation,[status(thm),theory(equality)],[c_51655,c_75318]) ).
tff(c_85906,plain,
! [W_2965,U_2966,V_2967] :
( memberP(W_2965,U_2966)
| ( V_2967 = U_2966 )
| ~ memberP(cons(V_2967,W_2965),U_2966)
| ~ ssList(W_2965)
| ~ ssItem(V_2967)
| ~ ssItem(U_2966) ),
inference(cnfTransformation,[status(thm)],[f_512]) ).
tff(c_85960,plain,
! [U_2966] :
( memberP(nil,U_2966)
| ( U_2966 = '#skF_55' )
| ~ memberP('#skF_50',U_2966)
| ~ ssList(nil)
| ~ ssItem('#skF_55')
| ~ ssItem(U_2966) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_85906]) ).
tff(c_98189,plain,
! [U_3114] :
( memberP(nil,U_3114)
| ( U_3114 = '#skF_55' )
| ~ memberP('#skF_50',U_3114)
| ~ ssItem(U_3114) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_168,c_85960]) ).
tff(c_98194,plain,
! [U_3115] :
( ( U_3115 = '#skF_55' )
| ~ memberP('#skF_50',U_3115)
| ~ ssItem(U_3115) ),
inference(resolution,[status(thm)],[c_98189,c_228]) ).
tff(c_98197,plain,
( ( '#skF_46'('#skF_54') = '#skF_55' )
| ~ ssItem('#skF_46'('#skF_54')) ),
inference(resolution,[status(thm)],[c_75321,c_98194]) ).
tff(c_98203,plain,
'#skF_46'('#skF_54') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_51655,c_98197]) ).
tff(c_98205,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_97743,c_98203]) ).
tff(c_98207,plain,
'#skF_54' = '#skF_50',
inference(splitRight,[status(thm)],[c_82330]) ).
tff(c_73072,plain,
( rearsegP('#skF_50','#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil)))
| ~ ssList('#skF_54')
| ~ ssList(app(app('#skF_53',cons('#skF_52',nil)),'#skF_54')) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_72878]) ).
tff(c_73210,plain,
rearsegP('#skF_50','#skF_54'),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_421,c_388,c_71819,c_73072]) ).
tff(c_254,plain,
! [V_993,U_991] :
( ( V_993 = U_991 )
| ~ rearsegP(V_993,U_991)
| ~ rearsegP(U_991,V_993)
| ~ ssList(V_993)
| ~ ssList(U_991) ),
inference(cnfTransformation,[status(thm)],[f_612]) ).
tff(c_73222,plain,
( ( '#skF_54' = '#skF_50' )
| ~ rearsegP('#skF_54','#skF_50')
| ~ ssList('#skF_50')
| ~ ssList('#skF_54') ),
inference(resolution,[status(thm)],[c_73210,c_254]) ).
tff(c_73225,plain,
( ( '#skF_54' = '#skF_50' )
| ~ rearsegP('#skF_54','#skF_50') ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_400,c_73222]) ).
tff(c_74593,plain,
~ rearsegP('#skF_54','#skF_50'),
inference(splitLeft,[status(thm)],[c_73225]) ).
tff(c_98264,plain,
~ rearsegP('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_98207,c_74593]) ).
tff(c_98313,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_73216,c_98264]) ).
tff(c_98314,plain,
'#skF_54' = '#skF_50',
inference(splitRight,[status(thm)],[c_73225]) ).
tff(c_98474,plain,
app(app('#skF_53',cons('#skF_52',nil)),'#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_98314,c_421]) ).
tff(c_99472,plain,
! [W_3129,U_3130,V_3131] :
( ( W_3129 = U_3130 )
| ( app(W_3129,V_3131) != app(U_3130,V_3131) )
| ~ ssList(W_3129)
| ~ ssList(V_3131)
| ~ ssList(U_3130) ),
inference(cnfTransformation,[status(thm)],[f_815]) ).
tff(c_99726,plain,
! [U_3130] :
( ( nil = U_3130 )
| ( app(U_3130,'#skF_50') != '#skF_50' )
| ~ ssList(nil)
| ~ ssList('#skF_50')
| ~ ssList(U_3130) ),
inference(superposition,[status(thm),theory(equality)],[c_6037,c_99472]) ).
tff(c_101894,plain,
! [U_3159] :
( ( nil = U_3159 )
| ( app(U_3159,'#skF_50') != '#skF_50' )
| ~ ssList(U_3159) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_168,c_99726]) ).
tff(c_101900,plain,
( ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ( app(app('#skF_53',cons('#skF_52',nil)),'#skF_50') != '#skF_50' ) ),
inference(resolution,[status(thm)],[c_71819,c_101894]) ).
tff(c_102030,plain,
app('#skF_53',cons('#skF_52',nil)) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_98474,c_101900]) ).
tff(c_102318,plain,
( frontsegP(nil,'#skF_53')
| ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53')
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_102030,c_26]) ).
tff(c_102351,plain,
( frontsegP(nil,'#skF_53')
| ~ ssList(cons('#skF_52',nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_102030,c_390,c_102318]) ).
tff(c_102352,plain,
~ ssList(cons('#skF_52',nil)),
inference(negUnitSimplification,[status(thm)],[c_73647,c_102351]) ).
tff(c_102385,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_102352]) ).
tff(c_102389,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_102385]) ).
tff(c_102391,plain,
'#skF_47'('#skF_54') != nil,
inference(splitRight,[status(thm)],[c_51686]) ).
tff(c_6036,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_168,c_6018]) ).
tff(c_57957,plain,
! [V_2583,W_2584] :
( frontsegP(app(V_2583,W_2584),V_2583)
| ~ ssList(W_2584)
| ~ ssList(V_2583)
| ~ ssList(app(V_2583,W_2584)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_58160,plain,
( frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(app(nil,nil)) ),
inference(superposition,[status(thm),theory(equality)],[c_6036,c_57957]) ).
tff(c_58298,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_6036,c_168,c_168,c_58160]) ).
tff(c_55825,plain,
! [U_2556,V_2557] :
( ( hd(app(U_2556,V_2557)) = hd(U_2556) )
| ( nil = U_2556 )
| ~ ssList(V_2557)
| ~ ssList(U_2556) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_56020,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = hd('#skF_50') )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_55825]) ).
tff(c_56219,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_51709,c_56020]) ).
tff(c_56238,plain,
~ ssList(app('#skF_53',cons('#skF_52',nil))),
inference(splitLeft,[status(thm)],[c_56219]) ).
tff(c_56241,plain,
( ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_192,c_56238]) ).
tff(c_56244,plain,
~ ssList(cons('#skF_52',nil)),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_56241]) ).
tff(c_56247,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_56244]) ).
tff(c_56251,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_56247]) ).
tff(c_56252,plain,
( ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' ) ),
inference(splitRight,[status(thm)],[c_56219]) ).
tff(c_56320,plain,
hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55',
inference(splitLeft,[status(thm)],[c_56252]) ).
tff(c_358,plain,
! [U_1081,V_1083] :
( ( hd(app(U_1081,V_1083)) = hd(U_1081) )
| ( nil = U_1081 )
| ~ ssList(V_1083)
| ~ ssList(U_1081) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_56324,plain,
( ( hd('#skF_53') = '#skF_55' )
| ( nil = '#skF_53' )
| ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_56320,c_358]) ).
tff(c_56337,plain,
( ( '#skF_46'('#skF_53') = '#skF_55' )
| ( nil = '#skF_53' )
| ~ ssList(cons('#skF_52',nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_51733,c_56324]) ).
tff(c_56338,plain,
( ( '#skF_46'('#skF_53') = '#skF_55' )
| ~ ssList(cons('#skF_52',nil)) ),
inference(negUnitSimplification,[status(thm)],[c_51598,c_56337]) ).
tff(c_56347,plain,
~ ssList(cons('#skF_52',nil)),
inference(splitLeft,[status(thm)],[c_56338]) ).
tff(c_56350,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_56347]) ).
tff(c_56354,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_56350]) ).
tff(c_56355,plain,
'#skF_46'('#skF_53') = '#skF_55',
inference(splitRight,[status(thm)],[c_56338]) ).
tff(c_52166,plain,
( ( cons(hd('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
| ( nil = '#skF_53' )
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_51597,c_52117]) ).
tff(c_52193,plain,
( ( cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_51733,c_52166]) ).
tff(c_52194,plain,
cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53',
inference(negUnitSimplification,[status(thm)],[c_51598,c_52193]) ).
tff(c_56358,plain,
cons('#skF_55','#skF_47'('#skF_53')) = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_56355,c_52194]) ).
tff(c_56541,plain,
! [V_2570,U_2571] :
( ( app(cons(V_2570,nil),U_2571) = cons(V_2570,U_2571) )
| ~ ssItem(V_2570)
| ~ ssList(U_2571) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_56566,plain,
! [U_2571] :
( ( cons('#skF_55',U_2571) = app('#skF_50',U_2571) )
| ~ ssItem('#skF_55')
| ~ ssList(U_2571) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_56541]) ).
tff(c_56581,plain,
! [U_2572] :
( ( cons('#skF_55',U_2572) = app('#skF_50',U_2572) )
| ~ ssList(U_2572) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_56566]) ).
tff(c_56623,plain,
cons('#skF_55','#skF_47'('#skF_53')) = app('#skF_50','#skF_47'('#skF_53')),
inference(resolution,[status(thm)],[c_51620,c_56581]) ).
tff(c_56728,plain,
app('#skF_50','#skF_47'('#skF_53')) = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_56358,c_56623]) ).
tff(c_57968,plain,
( frontsegP('#skF_53','#skF_50')
| ~ ssList('#skF_47'('#skF_53'))
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_50','#skF_47'('#skF_53'))) ),
inference(superposition,[status(thm),theory(equality)],[c_56728,c_57957]) ).
tff(c_58172,plain,
frontsegP('#skF_53','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_56728,c_400,c_51620,c_57968]) ).
tff(c_58815,plain,
( ( '#skF_53' = '#skF_50' )
| ~ frontsegP('#skF_50','#skF_53')
| ~ ssList('#skF_53')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_58172,c_234]) ).
tff(c_58818,plain,
( ( '#skF_53' = '#skF_50' )
| ~ frontsegP('#skF_50','#skF_53') ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_390,c_58815]) ).
tff(c_59366,plain,
~ frontsegP('#skF_50','#skF_53'),
inference(splitLeft,[status(thm)],[c_58818]) ).
tff(c_346,plain,
! [V_1069,U_1067] :
( ( app(cons(V_1069,nil),U_1067) = cons(V_1069,U_1067) )
| ~ ssItem(V_1069)
| ~ ssList(U_1067) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_56356,plain,
ssList(cons('#skF_52',nil)),
inference(splitRight,[status(thm)],[c_56338]) ).
tff(c_65634,plain,
! [U_2670,V_2671,W_2672] :
( ( app(app(U_2670,V_2671),W_2672) = app(U_2670,app(V_2671,W_2672)) )
| ~ ssList(W_2672)
| ~ ssList(V_2671)
| ~ ssList(U_2670) ),
inference(cnfTransformation,[status(thm)],[f_844]) ).
tff(c_65930,plain,
( ( app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50' )
| ~ ssList('#skF_54')
| ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_65634]) ).
tff(c_66099,plain,
app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_56356,c_388,c_65930]) ).
tff(c_66953,plain,
( ( app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50' )
| ~ ssItem('#skF_52')
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_346,c_66099]) ).
tff(c_66992,plain,
app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_66953]) ).
tff(c_67022,plain,
( frontsegP('#skF_50','#skF_53')
| ~ ssList(cons('#skF_52','#skF_54'))
| ~ ssList('#skF_53')
| ~ ssList(app('#skF_53',cons('#skF_52','#skF_54'))) ),
inference(superposition,[status(thm),theory(equality)],[c_66992,c_26]) ).
tff(c_67059,plain,
( frontsegP('#skF_50','#skF_53')
| ~ ssList(cons('#skF_52','#skF_54')) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_66992,c_390,c_67022]) ).
tff(c_67060,plain,
~ ssList(cons('#skF_52','#skF_54')),
inference(negUnitSimplification,[status(thm)],[c_59366,c_67059]) ).
tff(c_67076,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_54') ),
inference(resolution,[status(thm)],[c_166,c_67060]) ).
tff(c_67080,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_67076]) ).
tff(c_67081,plain,
'#skF_53' = '#skF_50',
inference(splitRight,[status(thm)],[c_58818]) ).
tff(c_24,plain,
! [U_30] :
( ssItem('#skF_5'(U_30))
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_51899,plain,
! [U_2423] :
( ( cons('#skF_5'(U_2423),nil) = U_2423 )
| ~ singletonP(U_2423)
| ~ ssList(U_2423) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_326,plain,
! [U_1044] :
( equalelemsP(cons(U_1044,nil))
| ~ ssItem(U_1044) ),
inference(cnfTransformation,[status(thm)],[f_758]) ).
tff(c_51980,plain,
! [U_2431] :
( equalelemsP(U_2431)
| ~ ssItem('#skF_5'(U_2431))
| ~ singletonP(U_2431)
| ~ ssList(U_2431) ),
inference(superposition,[status(thm),theory(equality)],[c_51899,c_326]) ).
tff(c_51985,plain,
! [U_2432] :
( equalelemsP(U_2432)
| ~ singletonP(U_2432)
| ~ ssList(U_2432) ),
inference(resolution,[status(thm)],[c_24,c_51980]) ).
tff(c_52109,plain,
( equalelemsP('#skF_53')
| ~ singletonP('#skF_53') ),
inference(resolution,[status(thm)],[c_390,c_51985]) ).
tff(c_52198,plain,
~ singletonP('#skF_53'),
inference(splitLeft,[status(thm)],[c_52109]) ).
tff(c_53176,plain,
'#skF_47'('#skF_53') = nil,
inference(splitLeft,[status(thm)],[c_51641]) ).
tff(c_53180,plain,
cons('#skF_46'('#skF_53'),nil) = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_53176,c_52194]) ).
tff(c_52356,plain,
! [V_2435] :
( singletonP(cons(V_2435,nil))
| ~ ssItem(V_2435)
| ~ ssList(cons(V_2435,nil)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_52366,plain,
! [V_861] :
( singletonP(cons(V_861,nil))
| ~ ssItem(V_861)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_52356]) ).
tff(c_52374,plain,
! [V_861] :
( singletonP(cons(V_861,nil))
| ~ ssItem(V_861) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_52366]) ).
tff(c_53217,plain,
( singletonP('#skF_53')
| ~ ssItem('#skF_46'('#skF_53')) ),
inference(superposition,[status(thm),theory(equality)],[c_53180,c_52374]) ).
tff(c_53258,plain,
singletonP('#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_51742,c_53217]) ).
tff(c_53260,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52198,c_53258]) ).
tff(c_53262,plain,
'#skF_47'('#skF_53') != nil,
inference(splitRight,[status(thm)],[c_51641]) ).
tff(c_196,plain,
! [U_906] :
( ( app(nil,U_906) = U_906 )
| ~ ssList(U_906) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_51645,plain,
app(nil,'#skF_47'('#skF_53')) = '#skF_47'('#skF_53'),
inference(resolution,[status(thm)],[c_51620,c_196]) ).
tff(c_58130,plain,
( frontsegP('#skF_47'('#skF_53'),nil)
| ~ ssList('#skF_47'('#skF_53'))
| ~ ssList(nil)
| ~ ssList(app(nil,'#skF_47'('#skF_53'))) ),
inference(superposition,[status(thm),theory(equality)],[c_51645,c_57957]) ).
tff(c_58278,plain,
frontsegP('#skF_47'('#skF_53'),nil),
inference(demodulation,[status(thm),theory(equality)],[c_51620,c_51645,c_168,c_51620,c_58130]) ).
tff(c_58842,plain,
( ( '#skF_47'('#skF_53') = nil )
| ~ frontsegP(nil,'#skF_47'('#skF_53'))
| ~ ssList('#skF_47'('#skF_53'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_58278,c_234]) ).
tff(c_58845,plain,
( ( '#skF_47'('#skF_53') = nil )
| ~ frontsegP(nil,'#skF_47'('#skF_53')) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_51620,c_58842]) ).
tff(c_58846,plain,
~ frontsegP(nil,'#skF_47'('#skF_53')),
inference(negUnitSimplification,[status(thm)],[c_53262,c_58845]) ).
tff(c_67086,plain,
~ frontsegP(nil,'#skF_47'('#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_67081,c_58846]) ).
tff(c_67158,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58298,c_51862,c_67086]) ).
tff(c_67159,plain,
app('#skF_53',cons('#skF_52',nil)) = nil,
inference(splitRight,[status(thm)],[c_56252]) ).
tff(c_67162,plain,
app(nil,'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_67159,c_421]) ).
tff(c_67190,plain,
'#skF_54' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_67162,c_6035]) ).
tff(c_52110,plain,
( equalelemsP('#skF_54')
| ~ singletonP('#skF_54') ),
inference(resolution,[status(thm)],[c_388,c_51985]) ).
tff(c_52288,plain,
~ singletonP('#skF_54'),
inference(splitLeft,[status(thm)],[c_52110]) ).
tff(c_51687,plain,
( ( hd('#skF_47'('#skF_54')) = '#skF_46'('#skF_47'('#skF_54')) )
| ( '#skF_47'('#skF_54') = nil ) ),
inference(resolution,[status(thm)],[c_51665,c_330]) ).
tff(c_52972,plain,
'#skF_47'('#skF_54') = nil,
inference(splitLeft,[status(thm)],[c_51687]) ).
tff(c_52979,plain,
tl('#skF_54') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_52972,c_51231]) ).
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_52996,plain,
( ( cons(hd('#skF_54'),nil) = '#skF_54' )
| ( nil = '#skF_54' )
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_52979,c_340]) ).
tff(c_53003,plain,
( ( cons('#skF_46'('#skF_54'),nil) = '#skF_54' )
| ( nil = '#skF_54' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_51227,c_52996]) ).
tff(c_53004,plain,
cons('#skF_46'('#skF_54'),nil) = '#skF_54',
inference(negUnitSimplification,[status(thm)],[c_51228,c_53003]) ).
tff(c_53012,plain,
( singletonP('#skF_54')
| ~ ssItem('#skF_46'('#skF_54')) ),
inference(superposition,[status(thm),theory(equality)],[c_53004,c_52374]) ).
tff(c_53053,plain,
singletonP('#skF_54'),
inference(demodulation,[status(thm),theory(equality)],[c_51655,c_53012]) ).
tff(c_53055,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52288,c_53053]) ).
tff(c_53057,plain,
'#skF_47'('#skF_54') != nil,
inference(splitRight,[status(thm)],[c_51687]) ).
tff(c_67297,plain,
'#skF_47'('#skF_50') != nil,
inference(demodulation,[status(thm),theory(equality)],[c_67190,c_53057]) ).
tff(c_67338,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_51862,c_67297]) ).
tff(c_67340,plain,
singletonP('#skF_54'),
inference(splitRight,[status(thm)],[c_52110]) ).
tff(c_190,plain,
! [V_895,U_893] :
( ( tl(cons(V_895,U_893)) = U_893 )
| ~ ssItem(V_895)
| ~ ssList(U_893) ),
inference(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_51908,plain,
! [U_2423] :
( ( tl(U_2423) = nil )
| ~ ssItem('#skF_5'(U_2423))
| ~ ssList(nil)
| ~ singletonP(U_2423)
| ~ ssList(U_2423) ),
inference(superposition,[status(thm),theory(equality)],[c_51899,c_190]) ).
tff(c_103172,plain,
! [U_3187] :
( ( tl(U_3187) = nil )
| ~ ssItem('#skF_5'(U_3187))
| ~ singletonP(U_3187)
| ~ ssList(U_3187) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_51908]) ).
tff(c_103221,plain,
! [U_3188] :
( ( tl(U_3188) = nil )
| ~ singletonP(U_3188)
| ~ ssList(U_3188) ),
inference(resolution,[status(thm)],[c_24,c_103172]) ).
tff(c_103314,plain,
( ( tl('#skF_54') = nil )
| ~ singletonP('#skF_54') ),
inference(resolution,[status(thm)],[c_388,c_103221]) ).
tff(c_103360,plain,
'#skF_47'('#skF_54') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_67340,c_51231,c_103314]) ).
tff(c_103362,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_102391,c_103360]) ).
tff(c_103364,plain,
singletonP('#skF_53'),
inference(splitRight,[status(thm)],[c_52109]) ).
tff(c_140697,plain,
! [U_3803] :
( ( tl(U_3803) = nil )
| ~ ssItem('#skF_5'(U_3803))
| ~ singletonP(U_3803)
| ~ ssList(U_3803) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_51908]) ).
tff(c_140702,plain,
! [U_3804] :
( ( tl(U_3804) = nil )
| ~ singletonP(U_3804)
| ~ ssList(U_3804) ),
inference(resolution,[status(thm)],[c_24,c_140697]) ).
tff(c_140816,plain,
( ( tl('#skF_53') = nil )
| ~ singletonP('#skF_53') ),
inference(resolution,[status(thm)],[c_390,c_140702]) ).
tff(c_140874,plain,
'#skF_47'('#skF_53') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_103364,c_51597,c_140816]) ).
tff(c_140876,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_138315,c_140874]) ).
tff(c_140877,plain,
memberP('#skF_54','#skF_52'),
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_255212,plain,
! [U_5493] :
( ( hd(U_5493) = '#skF_46'(U_5493) )
| ( nil = U_5493 )
| ~ ssList(U_5493) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_255299,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_400,c_255212]) ).
tff(c_255334,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_5938,c_255299]) ).
tff(c_256270,plain,
! [V_5509,U_5510] :
( ( hd(cons(V_5509,U_5510)) = V_5509 )
| ~ ssItem(V_5509)
| ~ ssList(U_5510) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_256282,plain,
( ( hd('#skF_50') = '#skF_55' )
| ~ ssItem('#skF_55')
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_256270]) ).
tff(c_256286,plain,
'#skF_46'('#skF_50') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_5937,c_255334,c_256282]) ).
tff(c_256288,plain,
hd('#skF_50') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_256286,c_255334]) ).
tff(c_263751,plain,
! [U_5733,V_5734] :
( ( hd(app(U_5733,V_5734)) = hd(U_5733) )
| ( nil = U_5733 )
| ~ ssList(V_5734)
| ~ ssList(U_5733) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_263964,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = hd('#skF_50') )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_263751]) ).
tff(c_264190,plain,
( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
| ( app('#skF_53',cons('#skF_52',nil)) = nil )
| ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_256288,c_263964]) ).
tff(c_264238,plain,
~ ssList(app('#skF_53',cons('#skF_52',nil))),
inference(splitLeft,[status(thm)],[c_264190]) ).
tff(c_264241,plain,
( ~ ssList(cons('#skF_52',nil))
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_192,c_264238]) ).
tff(c_264244,plain,
~ ssList(cons('#skF_52',nil)),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_264241]) ).
tff(c_264247,plain,
( ~ ssItem('#skF_52')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_264244]) ).
tff(c_264251,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_264247]) ).
tff(c_264253,plain,
ssList(app('#skF_53',cons('#skF_52',nil))),
inference(splitRight,[status(thm)],[c_264190]) ).
tff(c_276666,plain,
! [W_5871,U_5872,V_5873] :
( ~ memberP(W_5871,U_5872)
| memberP(app(V_5873,W_5871),U_5872)
| ~ ssList(W_5871)
| ~ ssList(V_5873)
| ~ ssItem(U_5872) ),
inference(cnfTransformation,[status(thm)],[f_498]) ).
tff(c_276852,plain,
! [U_5872] :
( ~ memberP('#skF_54',U_5872)
| memberP('#skF_50',U_5872)
| ~ ssList('#skF_54')
| ~ ssList(app('#skF_53',cons('#skF_52',nil)))
| ~ ssItem(U_5872) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_276666]) ).
tff(c_277014,plain,
! [U_5874] :
( ~ memberP('#skF_54',U_5874)
| memberP('#skF_50',U_5874)
| ~ ssItem(U_5874) ),
inference(demodulation,[status(thm),theory(equality)],[c_264253,c_388,c_276852]) ).
tff(c_277020,plain,
( memberP('#skF_50','#skF_52')
| ~ ssItem('#skF_52') ),
inference(resolution,[status(thm)],[c_140877,c_277014]) ).
tff(c_277026,plain,
memberP('#skF_50','#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_277020]) ).
tff(c_281020,plain,
! [W_5928,U_5929,V_5930] :
( memberP(W_5928,U_5929)
| ( V_5930 = U_5929 )
| ~ memberP(cons(V_5930,W_5928),U_5929)
| ~ ssList(W_5928)
| ~ ssItem(V_5930)
| ~ ssItem(U_5929) ),
inference(cnfTransformation,[status(thm)],[f_512]) ).
tff(c_281068,plain,
! [U_5929] :
( memberP(nil,U_5929)
| ( U_5929 = '#skF_55' )
| ~ memberP('#skF_50',U_5929)
| ~ ssList(nil)
| ~ ssItem('#skF_55')
| ~ ssItem(U_5929) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_281020]) ).
tff(c_283668,plain,
! [U_5966] :
( memberP(nil,U_5966)
| ( U_5966 = '#skF_55' )
| ~ memberP('#skF_50',U_5966)
| ~ ssItem(U_5966) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_168,c_281068]) ).
tff(c_283673,plain,
! [U_5967] :
( ( U_5967 = '#skF_55' )
| ~ memberP('#skF_50',U_5967)
| ~ ssItem(U_5967) ),
inference(resolution,[status(thm)],[c_283668,c_228]) ).
tff(c_283679,plain,
( ( '#skF_52' = '#skF_55' )
| ~ ssItem('#skF_52') ),
inference(resolution,[status(thm)],[c_277026,c_283673]) ).
tff(c_283688,plain,
'#skF_52' = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_392,c_283679]) ).
tff(c_140878,plain,
~ memberP('#skF_53','#skF_52'),
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_283697,plain,
~ memberP('#skF_53','#skF_55'),
inference(demodulation,[status(thm),theory(equality)],[c_283688,c_140878]) ).
tff(c_141292,plain,
! [U_3862] :
( ( tl(U_3862) = '#skF_47'(U_3862) )
| ( nil = U_3862 )
| ~ ssList(U_3862) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_141400,plain,
( ( tl('#skF_53') = '#skF_47'('#skF_53') )
| ( nil = '#skF_53' ) ),
inference(resolution,[status(thm)],[c_390,c_141292]) ).
tff(c_141454,plain,
nil = '#skF_53',
inference(splitLeft,[status(thm)],[c_141400]) ).
tff(c_141401,plain,
( ( tl('#skF_54') = '#skF_47'('#skF_54') )
| ( nil = '#skF_54' ) ),
inference(resolution,[status(thm)],[c_388,c_141292]) ).
tff(c_141633,plain,
( ( tl('#skF_54') = '#skF_47'('#skF_54') )
| ( '#skF_54' = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141454,c_141401]) ).
tff(c_141634,plain,
'#skF_54' = '#skF_53',
inference(splitLeft,[status(thm)],[c_141633]) ).
tff(c_141742,plain,
memberP('#skF_53','#skF_52'),
inference(demodulation,[status(thm),theory(equality)],[c_141634,c_140877]) ).
tff(c_141745,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_140878,c_141742]) ).
tff(c_141747,plain,
'#skF_54' != '#skF_53',
inference(splitRight,[status(thm)],[c_141633]) ).
tff(c_141373,plain,
( ( tl('#skF_50') = '#skF_47'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_400,c_141292]) ).
tff(c_141406,plain,
tl('#skF_50') = '#skF_47'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_5938,c_141373]) ).
tff(c_141413,plain,
( ssList('#skF_47'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_141406,c_188]) ).
tff(c_141417,plain,
( ssList('#skF_47'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_141413]) ).
tff(c_141418,plain,
ssList('#skF_47'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_5938,c_141417]) ).
tff(c_141455,plain,
! [U_3863] :
( ( hd(U_3863) = '#skF_46'(U_3863) )
| ( nil = U_3863 )
| ~ ssList(U_3863) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_141547,plain,
( ( hd('#skF_47'('#skF_50')) = '#skF_46'('#skF_47'('#skF_50')) )
| ( '#skF_47'('#skF_50') = nil ) ),
inference(resolution,[status(thm)],[c_141418,c_141455]) ).
tff(c_142628,plain,
( ( hd('#skF_47'('#skF_50')) = '#skF_46'('#skF_47'('#skF_50')) )
| ( '#skF_47'('#skF_50') = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141454,c_141547]) ).
tff(c_142629,plain,
'#skF_47'('#skF_50') = '#skF_53',
inference(splitLeft,[status(thm)],[c_142628]) ).
tff(c_142634,plain,
tl('#skF_50') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_142629,c_141406]) ).
tff(c_141592,plain,
app(app('#skF_53',cons('#skF_52','#skF_53')),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_141454,c_421]) ).
tff(c_253212,plain,
! [W_5471,V_5472,X_5473] :
( segmentP(app(app(W_5471,V_5472),X_5473),V_5472)
| ~ ssList(X_5473)
| ~ ssList(W_5471)
| ~ ssList(V_5472)
| ~ ssList(app(app(W_5471,V_5472),X_5473)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_253451,plain,
( segmentP('#skF_50',cons('#skF_52','#skF_53'))
| ~ ssList('#skF_54')
| ~ ssList('#skF_53')
| ~ ssList(cons('#skF_52','#skF_53'))
| ~ ssList(app(app('#skF_53',cons('#skF_52','#skF_53')),'#skF_54')) ),
inference(superposition,[status(thm),theory(equality)],[c_141592,c_253212]) ).
tff(c_253604,plain,
( segmentP('#skF_50',cons('#skF_52','#skF_53'))
| ~ ssList(cons('#skF_52','#skF_53')) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_141592,c_390,c_388,c_253451]) ).
tff(c_254026,plain,
~ ssList(cons('#skF_52','#skF_53')),
inference(splitLeft,[status(thm)],[c_253604]) ).
tff(c_254029,plain,
( ~ ssItem('#skF_52')
| ~ ssList('#skF_53') ),
inference(resolution,[status(thm)],[c_166,c_254026]) ).
tff(c_254033,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_390,c_392,c_254029]) ).
tff(c_254035,plain,
ssList(cons('#skF_52','#skF_53')),
inference(splitRight,[status(thm)],[c_253604]) ).
tff(c_141608,plain,
! [U_906] :
( ( app('#skF_53',U_906) = U_906 )
| ~ ssList(U_906) ),
inference(demodulation,[status(thm),theory(equality)],[c_141454,c_196]) ).
tff(c_254148,plain,
app('#skF_53',cons('#skF_52','#skF_53')) = cons('#skF_52','#skF_53'),
inference(resolution,[status(thm)],[c_254035,c_141608]) ).
tff(c_254382,plain,
app(cons('#skF_52','#skF_53'),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_254148,c_141592]) ).
tff(c_227853,plain,
! [V_1069,U_1067] :
( ( app(cons(V_1069,'#skF_53'),U_1067) = cons(V_1069,U_1067) )
| ~ ssItem(V_1069)
| ~ ssList(U_1067) ),
inference(demodulation,[status(thm),theory(equality)],[c_141454,c_346]) ).
tff(c_254624,plain,
( ( cons('#skF_52','#skF_54') = '#skF_50' )
| ~ ssItem('#skF_52')
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_254382,c_227853]) ).
tff(c_254670,plain,
cons('#skF_52','#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_254624]) ).
tff(c_254725,plain,
( ( tl('#skF_50') = '#skF_54' )
| ~ ssItem('#skF_52')
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_254670,c_190]) ).
tff(c_254774,plain,
'#skF_54' = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_142634,c_254725]) ).
tff(c_254776,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_141747,c_254774]) ).
tff(c_254778,plain,
'#skF_47'('#skF_50') != '#skF_53',
inference(splitRight,[status(thm)],[c_142628]) ).
tff(c_141612,plain,
cons('#skF_55','#skF_53') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_141454,c_5992]) ).
tff(c_255191,plain,
! [V_5491,U_5492] :
( ( tl(cons(V_5491,U_5492)) = U_5492 )
| ~ ssItem(V_5491)
| ~ ssList(U_5492) ),
inference(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_255203,plain,
( ( tl('#skF_50') = '#skF_53' )
| ~ ssItem('#skF_55')
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_141612,c_255191]) ).
tff(c_255207,plain,
'#skF_47'('#skF_50') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_5937,c_141406,c_255203]) ).
tff(c_255209,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_254778,c_255207]) ).
tff(c_255211,plain,
nil != '#skF_53',
inference(splitRight,[status(thm)],[c_141400]) ).
tff(c_262860,plain,
! [V_5724,U_5725] :
( ( app(cons(V_5724,nil),U_5725) = cons(V_5724,U_5725) )
| ~ ssItem(V_5724)
| ~ ssList(U_5725) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_262882,plain,
! [U_5725] :
( ( cons('#skF_55',U_5725) = app('#skF_50',U_5725) )
| ~ ssItem('#skF_55')
| ~ ssList(U_5725) ),
inference(superposition,[status(thm),theory(equality)],[c_5992,c_262860]) ).
tff(c_262889,plain,
! [U_5726] :
( ( cons('#skF_55',U_5726) = app('#skF_50',U_5726) )
| ~ ssList(U_5726) ),
inference(demodulation,[status(thm),theory(equality)],[c_5937,c_262882]) ).
tff(c_263054,plain,
cons('#skF_55','#skF_54') = app('#skF_50','#skF_54'),
inference(resolution,[status(thm)],[c_388,c_262889]) ).
tff(c_263160,plain,
( ssList(app('#skF_50','#skF_54'))
| ~ ssItem('#skF_55')
| ~ ssList('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_263054,c_166]) ).
tff(c_263177,plain,
ssList(app('#skF_50','#skF_54')),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5937,c_263160]) ).
tff(c_255328,plain,
( ( hd('#skF_53') = '#skF_46'('#skF_53') )
| ( nil = '#skF_53' ) ),
inference(resolution,[status(thm)],[c_390,c_255212]) ).
tff(c_256066,plain,
hd('#skF_53') = '#skF_46'('#skF_53'),
inference(negUnitSimplification,[status(thm)],[c_255211,c_255328]) ).
tff(c_348,plain,
! [U_1070,V_1074,W_1076] :
( ( app(app(U_1070,V_1074),W_1076) = app(U_1070,app(V_1074,W_1076)) )
| ~ ssList(W_1076)
| ~ ssList(V_1074)
| ~ ssList(U_1070) ),
inference(cnfTransformation,[status(thm)],[f_844]) ).
tff(c_283696,plain,
app(app('#skF_53',cons('#skF_55',nil)),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_283688,c_421]) ).
tff(c_283703,plain,
app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_5992,c_283696]) ).
tff(c_284788,plain,
( ( app('#skF_53',app('#skF_50','#skF_54')) = '#skF_50' )
| ~ ssList('#skF_54')
| ~ ssList('#skF_50')
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_348,c_283703]) ).
tff(c_284833,plain,
app('#skF_53',app('#skF_50','#skF_54')) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_400,c_388,c_284788]) ).
tff(c_284947,plain,
( ( hd('#skF_53') = hd('#skF_50') )
| ( nil = '#skF_53' )
| ~ ssList(app('#skF_50','#skF_54'))
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_284833,c_358]) ).
tff(c_284986,plain,
( ( '#skF_46'('#skF_53') = '#skF_55' )
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_263177,c_256066,c_256288,c_284947]) ).
tff(c_284987,plain,
'#skF_46'('#skF_53') = '#skF_55',
inference(negUnitSimplification,[status(thm)],[c_255211,c_284986]) ).
tff(c_256070,plain,
( ssItem('#skF_46'('#skF_53'))
| ( nil = '#skF_53' )
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_256066,c_184]) ).
tff(c_256074,plain,
( ssItem('#skF_46'('#skF_53'))
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_256070]) ).
tff(c_256075,plain,
ssItem('#skF_46'('#skF_53')),
inference(negUnitSimplification,[status(thm)],[c_255211,c_256074]) ).
tff(c_255210,plain,
tl('#skF_53') = '#skF_47'('#skF_53'),
inference(splitRight,[status(thm)],[c_141400]) ).
tff(c_255341,plain,
( ssList('#skF_47'('#skF_53'))
| ( nil = '#skF_53' )
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_255210,c_188]) ).
tff(c_255345,plain,
( ssList('#skF_47'('#skF_53'))
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_255341]) ).
tff(c_255346,plain,
ssList('#skF_47'('#skF_53')),
inference(negUnitSimplification,[status(thm)],[c_255211,c_255345]) ).
tff(c_260147,plain,
! [U_5618] :
( ( cons(hd(U_5618),tl(U_5618)) = U_5618 )
| ( nil = U_5618 )
| ~ ssList(U_5618) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_260214,plain,
( ( cons(hd('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
| ( nil = '#skF_53' )
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_255210,c_260147]) ).
tff(c_260256,plain,
( ( cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
| ( nil = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_256066,c_260214]) ).
tff(c_260257,plain,
cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53',
inference(negUnitSimplification,[status(thm)],[c_255211,c_260256]) ).
tff(c_260393,plain,
( memberP('#skF_53','#skF_46'('#skF_53'))
| ~ ssList('#skF_47'('#skF_53'))
| ~ ssItem('#skF_46'('#skF_53')) ),
inference(superposition,[status(thm),theory(equality)],[c_260257,c_226]) ).
tff(c_260410,plain,
memberP('#skF_53','#skF_46'('#skF_53')),
inference(demodulation,[status(thm),theory(equality)],[c_256075,c_255346,c_260393]) ).
tff(c_285008,plain,
memberP('#skF_53','#skF_55'),
inference(demodulation,[status(thm),theory(equality)],[c_284987,c_260410]) ).
tff(c_285013,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_283697,c_285008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC187+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % 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
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Aug 3 21:40:09 EDT 2023
% 0.12/0.35 % CPUTime :
% 76.47/60.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 76.61/60.45
% 76.61/60.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 77.06/60.52
% 77.06/60.52 Inference rules
% 77.06/60.52 ----------------------
% 77.06/60.52 #Ref : 66
% 77.06/60.52 #Sup : 62499
% 77.06/60.52 #Fact : 0
% 77.06/60.52 #Define : 0
% 77.06/60.52 #Split : 476
% 77.06/60.52 #Chain : 0
% 77.06/60.52 #Close : 0
% 77.06/60.52
% 77.06/60.52 Ordering : KBO
% 77.06/60.52
% 77.06/60.52 Simplification rules
% 77.06/60.52 ----------------------
% 77.06/60.52 #Subsume : 7747
% 77.06/60.52 #Demod : 58784
% 77.06/60.52 #Tautology : 15691
% 77.06/60.52 #SimpNegUnit : 6871
% 77.06/60.52 #BackRed : 1521
% 77.06/60.52
% 77.06/60.52 #Partial instantiations: 0
% 77.06/60.52 #Strategies tried : 1
% 77.06/60.52
% 77.06/60.52 Timing (in seconds)
% 77.06/60.52 ----------------------
% 77.06/60.52 Preprocessing : 0.87
% 77.06/60.52 Parsing : 0.42
% 77.06/60.52 CNF conversion : 0.10
% 77.06/60.52 Main loop : 58.41
% 77.06/60.52 Inferencing : 9.70
% 77.06/60.52 Reduction : 29.89
% 77.06/60.52 Demodulation : 22.97
% 77.06/60.52 BG Simplification : 0.40
% 77.06/60.52 Subsumption : 14.76
% 77.06/60.52 Abstraction : 0.63
% 77.06/60.52 MUC search : 0.00
% 77.06/60.52 Cooper : 0.00
% 77.06/60.52 Total : 59.43
% 77.06/60.52 Index Insertion : 0.00
% 77.06/60.52 Index Deletion : 0.00
% 77.06/60.52 Index Matching : 0.00
% 77.06/60.52 BG Taut test : 0.00
%------------------------------------------------------------------------------