%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWW671_2 : TPTP v9.0.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 09:53:10 PM UTC 2025
% Result : Theorem 209.66s 153.76s
% Output : CNFRefutation 210.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 22
% Syntax : Number of formulae : 1792 (1038 unt; 0 typ; 0 def)
% Number of atoms : 4140 (2133 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 4012 (1664 ~;2311 |; 22 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 6171 ( 974 atm;2626 fun;2490 num; 81 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 115 ( 109 usr; 89 con; 0-5 aty)
% Number of variables : 356 ( 356 !; 0 ?; 356 :)
% Comments :
%------------------------------------------------------------------------------
%$ zero_at1 > sort1 > no_zero1 > match_option1 > match_list1 > match_bool1 > nth1 > cons > some_proj_11 > some > length1 > cons_proj_21 > cons_proj_11 > #nlpp > witness1 > tb2t2 > tb2t1 > tb2t > t2tb2 > t2tb1 > t2tb > option > none > nil > list > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > bool > #skF_5 > #skF_2 > #skF_7 > #skF_11 > #skF_1
%Foreground sorts:
tff(option_int,type,
option_int: $tType ).
tff(tuple02,type,
tuple02: $tType ).
tff(list_int,type,
list_int: $tType ).
tff(bool1,type,
bool1: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skE_46',type,
'#skE_46': $int ).
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_21',type,
'#skE_21': $int ).
tff('#skE_62',type,
'#skE_62': $int ).
tff('#skE_30',type,
'#skE_30': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_25',type,
'#skE_25': $int ).
tff('#skE_52',type,
'#skE_52': $int ).
tff('#skE_28',type,
'#skE_28': $int ).
tff('#skE_48',type,
'#skE_48': $int ).
tff('#skE_23',type,
'#skE_23': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skE_41',type,
'#skE_41': $int ).
tff('#skE_43',type,
'#skE_43': $int ).
tff('#skE_37',type,
'#skE_37': $int ).
tff('#skE_42',type,
'#skE_42': $int ).
tff('#skE_57',type,
'#skE_57': $int ).
tff('#skF_6',type,
'#skF_6': $int ).
tff('#skE_63',type,
'#skE_63': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_33',type,
'#skE_33': $int ).
tff('#skE_20',type,
'#skE_20': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skE_26',type,
'#skE_26': $int ).
tff('#skE_32',type,
'#skE_32': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_24',type,
'#skE_24': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_38',type,
'#skE_38': $int ).
tff('#skE_31',type,
'#skE_31': $int ).
tff('#skE_51',type,
'#skE_51': $int ).
tff('#skE_15',type,
'#skE_15': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skF_8',type,
'#skF_8': $int ).
tff('#skE_36',type,
'#skE_36': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_54',type,
'#skE_54': $int ).
tff('#skE_64',type,
'#skE_64': $int ).
tff('#skE_60',type,
'#skE_60': $int ).
tff('#skE_50',type,
'#skE_50': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_10',type,
'#skF_10': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skF_12',type,
'#skF_12': $int ).
tff('#skE_22',type,
'#skE_22': $int ).
tff('#skE_16',type,
'#skE_16': $int ).
tff('#skE_17',type,
'#skE_17': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_55',type,
'#skE_55': $int ).
tff('#skE_67',type,
'#skE_67': $int ).
tff('#skE_58',type,
'#skE_58': $int ).
tff('#skE_47',type,
'#skE_47': $int ).
tff('#skE_68',type,
'#skE_68': $int ).
tff('#skE_40',type,
'#skE_40': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skE_29',type,
'#skE_29': $int ).
tff('#skE_44',type,
'#skE_44': $int ).
tff('#skE_49',type,
'#skE_49': $int ).
tff('#skE_34',type,
'#skE_34': $int ).
tff('#skE_45',type,
'#skE_45': $int ).
tff('#skE_27',type,
'#skE_27': $int ).
tff('#skE_59',type,
'#skE_59': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
tff('#skE_18',type,
'#skE_18': $int ).
tff('#skE_35',type,
'#skE_35': $int ).
tff('#skE_61',type,
'#skE_61': $int ).
tff('#skE_39',type,
'#skE_39': $int ).
tff('#skE_66',type,
'#skE_66': $int ).
tff('#skE_19',type,
'#skE_19': $int ).
tff('#skE_53',type,
'#skE_53': $int ).
tff('#skE_65',type,
'#skE_65': $int ).
tff('#skE_14',type,
'#skE_14': $int ).
tff('#skE_56',type,
'#skE_56': $int ).
%Foreground operators:
tff(list,type,
list: ty > ty ).
tff(tb2t1,type,
tb2t1: uni > list_int ).
tff(length1,type,
length1: ( ty * uni ) > $int ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff(some_proj_11,type,
some_proj_11: ( ty * uni ) > uni ).
tff(t2tb2,type,
t2tb2: $int > uni ).
tff(no_zero1,type,
no_zero1: list_int > $o ).
tff(nil,type,
nil: ty > uni ).
tff(true1,type,
true1: bool1 ).
tff(match_list1,type,
match_list1: ( ty * ty * uni * uni * uni ) > uni ).
tff(int,type,
int: ty ).
tff(false1,type,
false1: bool1 ).
tff('#skF_5',type,
'#skF_5': list_int ).
tff(zero_at1,type,
zero_at1: ( list_int * $int ) > $o ).
tff(sort1,type,
sort1: ( ty * uni ) > $o ).
tff(witness1,type,
witness1: ty > uni ).
tff(real,type,
real: ty ).
tff('#skF_2',type,
'#skF_2': list_int > $int ).
tff('#skF_7',type,
'#skF_7': list_int ).
tff(match_bool1,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(t2tb,type,
t2tb: option_int > uni ).
tff(option,type,
option: ty > ty ).
tff(none,type,
none: ty > uni ).
tff(tuple0,type,
tuple0: ty ).
tff(qtmark,type,
qtmark: ty ).
tff('#skF_11',type,
'#skF_11': list_int ).
tff('#skF_1',type,
'#skF_1': ( list_int * $int ) > $int ).
tff(bool,type,
bool: ty ).
tff(some,type,
some: ( ty * uni ) > uni ).
tff(t2tb1,type,
t2tb1: list_int > uni ).
tff(nth1,type,
nth1: ( ty * $int * uni ) > uni ).
tff(tb2t,type,
tb2t: uni > option_int ).
tff(tuple03,type,
tuple03: tuple02 ).
tff(cons_proj_11,type,
cons_proj_11: ( ty * uni ) > uni ).
tff(tb2t2,type,
tb2t2: uni > $int ).
tff(cons_proj_21,type,
cons_proj_21: ( ty * uni ) > uni ).
tff(match_option1,type,
match_option1: ( ty * ty * uni * uni * uni ) > uni ).
tff(f_139,axiom,
! [A: ty,Na: $int] :
( ( nth1(A,Na,nil(A)) = none(A) )
& ! [X: uni,X1: uni] :
( ( ( Na = 0 )
=> ( nth1(A,Na,cons(A,X,X1)) = some(A,X) ) )
& ( ( Na != 0 )
=> ( nth1(A,Na,cons(A,X,X1)) = nth1(A,$difference(Na,1),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nth_def) ).
tff(f_151,axiom,
! [J: uni] : ( t2tb1(tb2t1(J)) = J ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR1) ).
tff(f_169,axiom,
! [L: list_int,Ia: $int] :
( zero_at1(L,Ia)
<=> ( ( tb2t(nth1(int,Ia,t2tb1(L))) = tb2t(some(int,t2tb2(0))) )
& ! [Ja: $int] :
( ( $lesseq(0,Ja)
& $less(Ja,Ia) )
=> ( tb2t(nth1(int,Ja,t2tb1(L))) != tb2t(some(int,t2tb2(0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_at_def) ).
tff(f_96,axiom,
! [A: ty,L: uni] :
( ( length1(A,L) = 0 )
<=> ( L = nil(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nil) ).
tff(f_235,negated_conjecture,
~ ! [Ia: $int] :
( ( ( $lesseq(Ia,Ia)
& $less(Ia,$sum(Ia,length1(int,nil(int))))
& zero_at1(tb2t1(nil(int)),$difference(Ia,Ia)) )
| ( ( Ia = $sum(Ia,length1(int,nil(int))) )
& no_zero1(tb2t1(nil(int))) ) )
& ! [Xa: $int,X1: list_int] :
( ( ( Xa = 0 )
=> ( ( $lesseq(Ia,Ia)
& $less(Ia,$sum(Ia,length1(int,cons(int,t2tb2(Xa),t2tb1(X1)))))
& zero_at1(tb2t1(cons(int,t2tb2(Xa),t2tb1(X1))),$difference(Ia,Ia)) )
| ( ( Ia = $sum(Ia,length1(int,cons(int,t2tb2(Xa),t2tb1(X1)))) )
& no_zero1(tb2t1(cons(int,t2tb2(Xa),t2tb1(X1)))) ) ) )
& ( ( Xa != 0 )
=> ( ( tb2t1(cons(int,t2tb2(Xa),t2tb1(X1))) != tb2t1(nil(int)) )
& ! [X2a: $int,X3: list_int] :
( ( tb2t1(cons(int,t2tb2(Xa),t2tb1(X1))) = tb2t1(cons(int,t2tb2(X2a),t2tb1(X3))) )
=> ( X3 = X1 ) )
& ! [Resulta: $int] :
( ( ( $lesseq($sum(Ia,1),Resulta)
& $less(Resulta,$sum($sum(Ia,1),length1(int,t2tb1(X1))))
& zero_at1(X1,$difference(Resulta,$sum(Ia,1))) )
| ( ( Resulta = $sum($sum(Ia,1),length1(int,t2tb1(X1))) )
& no_zero1(X1) ) )
=> ( ( $lesseq(Ia,Resulta)
& $less(Resulta,$sum(Ia,length1(int,cons(int,t2tb2(Xa),t2tb1(X1)))))
& zero_at1(tb2t1(cons(int,t2tb2(Xa),t2tb1(X1))),$difference(Resulta,Ia)) )
| ( ( Resulta = $sum(Ia,length1(int,cons(int,t2tb2(Xa),t2tb1(X1)))) )
& no_zero1(tb2t1(cons(int,t2tb2(Xa),t2tb1(X1)))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_search) ).
tff(f_92,axiom,
! [A: ty,L: uni] : $lesseq(0,length1(A,L)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nonnegative) ).
tff(f_71,axiom,
! [A: ty,V: uni,V1: uni] : ( nil(A) != cons(A,V,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nil_Cons1) ).
tff(f_113,axiom,
! [A: ty,V: uni] : ( none(A) != some(A,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',none_Some1) ).
tff(f_145,axiom,
! [J: uni] : ( t2tb(tb2t(J)) = J ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR) ).
tff(f_155,axiom,
! [Ia: $int] : ( tb2t2(t2tb2(Ia)) = Ia ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL2) ).
tff(f_153,axiom,
! [Xa: $int] : sort1(int,t2tb2(Xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2tb_sort2) ).
tff(f_119,axiom,
! [A: ty,U: uni] :
( sort1(A,U)
=> ( some_proj_11(A,some(A,U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',some_proj_1_def1) ).
tff(f_100,axiom,
! [A: ty,X: uni] : sort1(option(A),some(A,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',some_sort1) ).
tff(f_125,axiom,
! [A: ty,U: uni] :
( sort1(option(A),U)
=> ( ( U = none(A) )
| ( U = some(A,some_proj_11(A,U)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',option_inversion1) ).
tff(f_179,axiom,
! [L: list_int] :
( no_zero1(L)
<=> ! [Ja: $int] :
( ( $lesseq(0,Ja)
& $less(Ja,length1(int,t2tb1(L))) )
=> ( tb2t(nth1(int,Ja,t2tb1(L))) != tb2t(some(int,t2tb2(0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_zero_def) ).
tff(f_110,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni] :
( sort1(A1,Z1)
=> ( match_option1(A1,A,some(A,U),Z,Z1) = Z1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_option_Some1) ).
tff(f_149,axiom,
! [I: list_int] : ( tb2t1(t2tb1(I)) = I ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL1) ).
tff(f_90,axiom,
! [A: ty] :
( ( length1(A,nil(A)) = 0 )
& ! [X: uni,X1: uni] : ( length1(A,cons(A,X,X1)) = $sum(1,length1(A,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_def) ).
tff(f_36,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z)
=> ( match_bool1(A,true1,Z,Z1) = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_bool_True) ).
tff(f_81,axiom,
! [A: ty,U: uni,U1: uni] : ( cons_proj_21(A,cons(A,U,U1)) = U1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cons_proj_2_def1) ).
tff(f_127,axiom,
! [A: ty,Xa: $int,X1: uni] : sort1(option(A),nth1(A,Xa,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nth_sort1) ).
tff(f_85,axiom,
! [A: ty,U: uni] :
( ( U = nil(A) )
| ( U = cons(A,cons_proj_11(A,U),cons_proj_21(A,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',list_inversion1) ).
tff(c_816,plain,
! [A_88: ty,X_92: uni,X1_93: uni] : ( nth1(A_88,0,cons(A_88,X_92,X1_93)) = some(A_88,X_92) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_86,plain,
! [J_99: uni] : ( t2tb1(tb2t1(J_99)) = J_99 ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_1072333,plain,
! [L_57478: list_int,I_57479a: $int] :
( $less('#skF_1'(L_57478,I_57479a),I_57479a)
| zero_at1(L_57478,I_57479a)
| ( tb2t(nth1(int,I_57479a,t2tb1(L_57478))) != tb2t(some(int,t2tb2(0))) ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_819,plain,
! [A_58: ty] : ( length1(A_58,nil(A_58)) = 0 ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_205,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_896,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_205]) ).
tff(c_578544,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_896]) ).
tff(c_970205,plain,
length1(int,t2tb1('#skF_5')) = '#skE_29',
inference(define,[status(thm),theory(equality)],[c_578544]) ).
tff(c_44,plain,
! [A_56: ty,L_57: uni] : $lesseq(0,length1(A_56,L_57)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_821,plain,
! [A_56: ty,L_57: uni] : ~ $less(length1(A_56,L_57),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_44]) ).
tff(c_970220,plain,
~ $less('#skE_29',0),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_821]) ).
tff(c_28,plain,
! [A_36: ty,V_37: uni,V1_38: uni] : ( cons(A_36,V_37,V1_38) != nil(A_36) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_61,plain,
! [A_77: ty,V_78: uni] : ( some(A_77,V_78) != none(A_77) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_80,plain,
! [J_96: uni] : ( t2tb(tb2t(J_96)) = J_96 ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_817,plain,
! [A_88: ty,N_89a: $int] : ( nth1(A_88,N_89a,nil(A_88)) = none(A_88) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_191,plain,
( ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 )
| ( '#skF_4' != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_647,plain,
( ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| ( '#skF_4' != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_191]) ).
tff(c_578255,plain,
( ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| ( '#skF_4' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_647]) ).
tff(c_578748,plain,
'#skF_4' != 0,
inference(splitLeft,[status(thm)],[c_578255]) ).
tff(c_810,plain,
! [I_101a: $int] : ( tb2t2(t2tb2(I_101a)) = I_101a ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_811,plain,
! [X_100a: $int] : sort1(int,t2tb2(X_100a)),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_578879,plain,
! [A_38313: ty,U_38314: uni] :
( ( some_proj_11(A_38313,some(A_38313,U_38314)) = U_38314 )
| ~ sort1(A_38313,U_38314) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_578929,plain,
! [X_100a: $int] : ( some_proj_11(int,some(int,t2tb2(X_100a))) = t2tb2(X_100a) ),
inference(resolution,[status(thm)],[c_811,c_578879]) ).
tff(c_209,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 )
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_894,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_209]) ).
tff(c_578520,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_894]) ).
tff(c_578800,plain,
~ $less('#skF_8',$sum(1,'#skF_3')),
inference(splitLeft,[status(thm)],[c_578520]) ).
tff(c_53,plain,
! [A_61: ty,X_62: uni] : sort1(option(A_61),some(A_61,X_62)),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_749688,plain,
! [A_46187: ty,U_46188: uni] :
( ( some(A_46187,some_proj_11(A_46187,U_46188)) = U_46188 )
| ( none(A_46187) = U_46188 )
| ~ sort1(option(A_46187),U_46188) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_749711,plain,
! [A_61: ty,X_62: uni] :
( ( some(A_61,some_proj_11(A_61,some(A_61,X_62))) = some(A_61,X_62) )
| ( some(A_61,X_62) = none(A_61) ) ),
inference(resolution,[status(thm)],[c_53,c_749688]) ).
tff(c_749736,plain,
! [A_61: ty,X_62: uni] : ( some(A_61,some_proj_11(A_61,some(A_61,X_62))) = some(A_61,X_62) ),
inference(negUnitSimplification,[status(thm)],[c_61,c_749711]) ).
tff(c_111,plain,
! [L_108: list_int] :
( $lesseq(0,'#skF_2'(L_108))
| no_zero1(L_108) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_800,plain,
! [L_108: list_int] :
( ~ $less('#skF_2'(L_108),0)
| no_zero1(L_108) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_111]) ).
tff(c_678130,plain,
! [A1_43078: ty,A_43079: ty,Z_43080: uni,Z1_43076: uni,U_43077: uni] :
( ( match_option1(A1_43078,A_43079,some(A_43079,U_43077),Z_43080,Z1_43076) = Z1_43076 )
| ~ sort1(A1_43078,Z1_43076) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_678148,plain,
! [A_43079: ty,A_61: ty,X_62: uni,Z_43080: uni,U_43077: uni] : ( match_option1(option(A_61),A_43079,some(A_43079,U_43077),Z_43080,some(A_61,X_62)) = some(A_61,X_62) ),
inference(resolution,[status(thm)],[c_53,c_678130]) ).
tff(c_801,plain,
! [L_108: list_int] :
( $less('#skF_2'(L_108),length1(int,t2tb1(L_108)))
| no_zero1(L_108) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_578819,plain,
length1(int,t2tb1('#skF_5')) = '#skE_29',
inference(define,[status(thm),theory(equality)],[c_578544]) ).
tff(c_207,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_895,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_207]) ).
tff(c_578535,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_895]) ).
tff(c_578956,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578819,c_578535]) ).
tff(c_578958,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578956]) ).
tff(c_578959,plain,
~ no_zero1(tb2t1(nil(int))),
inference(splitLeft,[status(thm)],[c_578958]) ).
tff(c_578963,plain,
$less('#skF_2'(tb2t1(nil(int))),length1(int,t2tb1(tb2t1(nil(int))))),
inference(resolution,[status(thm)],[c_801,c_578959]) ).
tff(c_578969,plain,
$less('#skF_2'(tb2t1(nil(int))),0),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_86,c_578963]) ).
tff(c_578971,plain,
'#skF_2'(tb2t1(nil(int))) = '#skE_30',
inference(define,[status(thm),theory(equality)],[c_578969]) ).
tff(c_578975,plain,
$less('#skE_30',0),
inference(demodulation,[status(thm),theory(equality)],[c_578971,c_578969]) ).
tff(c_578970,plain,
~ $less('#skF_2'(tb2t1(nil(int))),0),
inference(resolution,[status(thm)],[c_800,c_578959]) ).
tff(c_578976,plain,
'#skF_2'(tb2t1(nil(int))) = '#skE_30',
inference(define,[status(thm),theory(equality)],[c_578970]) ).
tff(c_578980,plain,
~ $less('#skE_30',0),
inference(demodulation,[status(thm),theory(equality)],[c_578976,c_578970]) ).
tff(c_578982,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_578975,c_578980]) ).
tff(c_578984,plain,
no_zero1(tb2t1(nil(int))),
inference(splitRight,[status(thm)],[c_578958]) ).
tff(c_201,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_627,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_201]) ).
tff(c_898,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_627]) ).
tff(c_578362,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_898]) ).
tff(c_579074,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_578362]) ).
tff(c_579075,plain,
'#skF_5' != '#skF_7',
inference(splitLeft,[status(thm)],[c_579074]) ).
tff(c_84,plain,
! [I_98: list_int] : ( tb2t1(t2tb1(I_98)) = I_98 ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_1038,plain,
! [A_88: ty,N_89a: $int,X_92: uni,X1_93: uni] :
( ( nth1(A_88,N_89a,cons(A_88,X_92,X1_93)) = nth1(A_88,$sum($uminus(1),N_89a),X1_93) )
| ( N_89a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_102,plain,
! [L_103: list_int,I_104a: $int] :
( $lesseq(0,'#skF_1'(L_103,I_104a))
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_804,plain,
! [L_103: list_int,I_104a: $int] :
( ~ $less('#skF_1'(L_103,I_104a),0)
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_102]) ).
tff(c_203,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_622,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_203]) ).
tff(c_897,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_622]) ).
tff(c_578547,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_897]) ).
tff(c_580023,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_578547]) ).
tff(c_580025,plain,
'#skF_10' = 0,
inference(splitLeft,[status(thm)],[c_580023]) ).
tff(c_822,plain,
! [A_51: ty,X_54: uni,X1_55: uni] : ( length1(A_51,cons(A_51,X_54,X1_55)) = $sum(1,length1(A_51,X1_55)) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_135,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))) != '#skF_9' )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_928,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_135]) ).
tff(c_578461,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_928]) ).
tff(c_578646,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum(1,length1(int,t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578461]) ).
tff(c_578648,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) )
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578646]) ).
tff(c_585041,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_580025,c_578819,c_578648]) ).
tff(c_585043,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_585041]) ).
tff(c_585047,plain,
length1(int,t2tb1('#skF_11')) = '#skE_31',
inference(define,[status(thm),theory(equality)],[c_585043]) ).
tff(c_173,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_911,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_173]) ).
tff(c_578403,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_911]) ).
tff(c_578616,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578403]) ).
tff(c_578618,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578616]) ).
tff(c_585241,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_585047,c_580025,c_578819,c_578618]) ).
tff(c_585243,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_585241]) ).
tff(c_585245,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_585243]) ).
tff(c_585060,plain,
~ $less('#skE_31',0),
inference(superposition,[status(thm),theory(equality)],[c_585047,c_821]) ).
tff(c_585246,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_585245,c_585060]) ).
tff(c_585247,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_585243]) ).
tff(c_585250,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_585247]) ).
tff(c_586120,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_585250]) ).
tff(c_586128,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_586120]) ).
tff(c_586138,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_586128]) ).
tff(c_586142,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_586138]) ).
tff(c_586146,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_586142,c_586138]) ).
tff(c_805,plain,
! [L_103: list_int,I_104a: $int] :
( $less('#skF_1'(L_103,I_104a),I_104a)
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_586132,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_586120]) ).
tff(c_586141,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_586132]) ).
tff(c_586149,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_586141]) ).
tff(c_586151,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_586149,c_586141]) ).
tff(c_586154,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_586146,c_586151]) ).
tff(c_586155,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(splitRight,[status(thm)],[c_585250]) ).
tff(c_586158,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_586155]) ).
tff(c_586301,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_586158]) ).
tff(c_586305,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_586301,c_86]) ).
tff(c_586308,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_586305]) ).
tff(c_586310,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_586308]) ).
tff(c_586315,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_586158]) ).
tff(c_579148,plain,
! [A_38384: ty,Z_38385: uni,Z1_38386: uni] :
( ( match_bool1(A_38384,true1,Z_38385,Z1_38386) = Z_38385 )
| ~ sort1(A_38384,Z_38385) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_579166,plain,
! [A_61: ty,X_62: uni,Z1_38386: uni] : ( match_bool1(option(A_61),true1,some(A_61,X_62),Z1_38386) = some(A_61,X_62) ),
inference(resolution,[status(thm)],[c_53,c_579148]) ).
tff(c_586311,plain,
( no_zero1('#skF_5')
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_586158]) ).
tff(c_586314,plain,
( no_zero1('#skF_5')
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_586311]) ).
tff(c_586578,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitLeft,[status(thm)],[c_586314]) ).
tff(c_586929,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_586578,c_86]) ).
tff(c_586933,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_586929]) ).
tff(c_36,plain,
! [A_46: ty,U_47: uni,U1_48: uni] : ( cons_proj_21(A_46,cons(A_46,U_47,U1_48)) = U1_48 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_587538,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_586933,c_36]) ).
tff(c_587607,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_587538,c_36]) ).
tff(c_587632,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_587607,c_84]) ).
tff(c_587635,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_587632]) ).
tff(c_587637,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_579075,c_587635]) ).
tff(c_587642,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) != tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_586314]) ).
tff(c_586159,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_585250]) ).
tff(c_161,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_917,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_161]) ).
tff(c_578422,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_917]) ).
tff(c_578424,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578422]) ).
tff(c_578628,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum(1,length1(int,t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_822,c_578424]) ).
tff(c_578630,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,t2tb1('#skF_5')) != $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578628]) ).
tff(c_591082,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_585047,c_586159,c_580025,c_578819,c_578630]) ).
tff(c_591083,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_586315,c_587642,c_591082]) ).
tff(c_591085,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( '#skF_8' != $sum(1,$sum('#skF_3','#skE_29')) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_591083]) ).
tff(c_591087,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_591085]) ).
tff(c_591088,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_591087,c_585060]) ).
tff(c_591091,plain,
( ( '#skF_8' != $sum(1,$sum('#skF_3','#skE_29')) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) ),
inference(splitRight,[status(thm)],[c_591085]) ).
tff(c_591449,plain,
~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(splitLeft,[status(thm)],[c_591091]) ).
tff(c_591466,plain,
~ $less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),0),
inference(resolution,[status(thm)],[c_800,c_591449]) ).
tff(c_591470,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = '#skE_33',
inference(define,[status(thm),theory(equality)],[c_591466]) ).
tff(c_591457,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),length1(int,t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))),
inference(resolution,[status(thm)],[c_801,c_591449]) ).
tff(c_591465,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_578819,c_822,c_86,c_591457]) ).
tff(c_600852,plain,
$less('#skE_33',$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_591470,c_591465]) ).
tff(c_802,plain,
! [L_108: list_int] :
( ( tb2t(nth1(int,'#skF_2'(L_108),t2tb1(L_108))) = tb2t(some(int,t2tb2(0))) )
| no_zero1(L_108) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_591453,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_802,c_591449]) ).
tff(c_591463,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_591453]) ).
tff(c_601254,plain,
tb2t(nth1(int,'#skE_33',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_591470,c_591463]) ).
tff(c_601258,plain,
nth1(int,'#skE_33',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_601254,c_80]) ).
tff(c_601262,plain,
nth1(int,'#skE_33',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_601258]) ).
tff(c_587638,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5') ),
inference(splitRight,[status(thm)],[c_586314]) ).
tff(c_587641,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_587638]) ).
tff(c_587643,plain,
no_zero1('#skF_5'),
inference(splitLeft,[status(thm)],[c_587641]) ).
tff(c_104,plain,
! [J_111a: $int,L_108: list_int] :
( ( tb2t(nth1(int,J_111a,t2tb1(L_108))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,length1(int,t2tb1(L_108)))
| ~ no_zero1(L_108)
| ~ $lesseq(0,J_111a) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_803,plain,
! [J_111a: $int,L_108: list_int] :
( ( tb2t(nth1(int,J_111a,t2tb1(L_108))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,length1(int,t2tb1(L_108)))
| ~ no_zero1(L_108)
| $less(J_111a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_104]) ).
tff(c_587647,plain,
! [J_111a: $int] :
( ( tb2t(nth1(int,J_111a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,length1(int,t2tb1('#skF_5')))
| $less(J_111a,0) ),
inference(resolution,[status(thm)],[c_587643,c_803]) ).
tff(c_602193,plain,
! [J_39653a: $int] :
( ( tb2t(nth1(int,J_39653a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_39653a,'#skE_29')
| $less(J_39653a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_578819,c_587647]) ).
tff(c_602197,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less($sum($uminus(1),N_89a),'#skE_29')
| $less($sum($uminus(1),N_89a),0)
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_602193]) ).
tff(c_602944,plain,
! [N_39693a: $int,X_39694: uni] :
( ( tb2t(nth1(int,N_39693a,cons(int,X_39694,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(N_39693a,$sum(1,'#skE_29'))
| $less(N_39693a,1)
| ( N_39693a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_602197]) ).
tff(c_602948,plain,
( ~ $less('#skE_33',$sum(1,'#skE_29'))
| $less('#skE_33',1)
| ( '#skE_33' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_601262,c_602944]) ).
tff(c_602971,plain,
( $less('#skE_33',1)
| ( '#skE_33' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_600852,c_602948]) ).
tff(c_602982,plain,
'#skE_33' = 0,
inference(splitLeft,[status(thm)],[c_602971]) ).
tff(c_602993,plain,
nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_602982,c_601262]) ).
tff(c_818,plain,
! [A_85: ty,X_86a: $int,X1_87: uni] : sort1(option(A_85),nth1(A_85,X_86a,X1_87)),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_579186,plain,
! [A_85: ty,X_86a: $int,X1_87: uni,Z1_38386: uni] : ( match_bool1(option(A_85),true1,nth1(A_85,X_86a,X1_87),Z1_38386) = nth1(A_85,X_86a,X1_87) ),
inference(resolution,[status(thm)],[c_818,c_579148]) ).
tff(c_603235,plain,
! [Z1_38386: uni] : ( match_bool1(option(int),true1,some(int,t2tb2(0)),Z1_38386) = nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ),
inference(superposition,[status(thm),theory(equality)],[c_602993,c_579186]) ).
tff(c_603259,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_579166,c_603235]) ).
tff(c_603320,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_603259,c_578929]) ).
tff(c_603346,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_603320]) ).
tff(c_603398,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_603346,c_810]) ).
tff(c_603413,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_603398]) ).
tff(c_603415,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_603413]) ).
tff(c_603418,plain,
$less('#skE_33',1),
inference(splitRight,[status(thm)],[c_602971]) ).
tff(c_603419,plain,
'#skE_33' != 0,
inference(splitRight,[status(thm)],[c_602971]) ).
tff(c_591467,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = '#skE_33',
inference(define,[status(thm),theory(equality)],[c_591466]) ).
tff(c_591471,plain,
~ $less('#skE_33',0),
inference(demodulation,[status(thm),theory(equality)],[c_591467,c_591466]) ).
tff(c_603420,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_603418,c_603419,c_591471]) ).
tff(c_603423,plain,
'#skF_8' != $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_591091]) ).
tff(c_185,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_659,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_185]) ).
tff(c_905,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_659]) ).
tff(c_578385,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_905]) ).
tff(c_578607,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578385]) ).
tff(c_578609,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578607]) ).
tff(c_603755,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_585047,c_586159,c_580025,c_578819,c_578819,c_578609]) ).
tff(c_603756,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_586315,c_587642,c_603755]) ).
tff(c_603758,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_603756]) ).
tff(c_603760,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_603758]) ).
tff(c_603761,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_603760,c_585060]) ).
tff(c_603762,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))) ),
inference(splitRight,[status(thm)],[c_603758]) ).
tff(c_603764,plain,
$less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(negUnitSimplification,[status(thm)],[c_603423,c_603762]) ).
tff(c_603766,plain,
$less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_603764]) ).
tff(c_181,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_669,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_181]) ).
tff(c_907,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_669]) ).
tff(c_578391,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_907]) ).
tff(c_578610,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578391]) ).
tff(c_578612,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578610]) ).
tff(c_603582,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_585047,c_586159,c_580025,c_578819,c_578612]) ).
tff(c_603583,plain,
( zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_586315,c_587642,c_603582]) ).
tff(c_603585,plain,
( zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_603583]) ).
tff(c_603587,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_603585]) ).
tff(c_603588,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_603587,c_585060]) ).
tff(c_603589,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_603585]) ).
tff(c_603592,plain,
zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_603423,c_603589]) ).
tff(c_807,plain,
! [I_104a: $int,L_103: list_int] :
( ( tb2t(nth1(int,I_104a,t2tb1(L_103))) = tb2t(some(int,t2tb2(0))) )
| ~ zero_at1(L_103,I_104a) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_603603,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_5'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_603592,c_807]) ).
tff(c_604616,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_603603]) ).
tff(c_604622,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_604616]) ).
tff(c_606435,plain,
'#skF_8' = '#skF_3',
inference(splitLeft,[status(thm)],[c_604622]) ).
tff(c_606454,plain,
~ $less('#skF_3',$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_606435,c_578800]) ).
tff(c_606461,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_606454]) ).
tff(c_606462,plain,
! [X_92: uni] : ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) ),
inference(splitRight,[status(thm)],[c_604622]) ).
tff(c_609312,plain,
! [X_39964: uni] : ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_39964,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_606462]) ).
tff(c_603424,plain,
no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(splitRight,[status(thm)],[c_591091]) ).
tff(c_603428,plain,
! [J_111a: $int] :
( ( tb2t(nth1(int,J_111a,t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,length1(int,t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))))
| $less(J_111a,0) ),
inference(resolution,[status(thm)],[c_603424,c_803]) ).
tff(c_603430,plain,
! [J_111a: $int] :
( ( tb2t(nth1(int,J_111a,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,$sum(1,'#skE_29'))
| $less(J_111a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_578819,c_822,c_86,c_86,c_603428]) ).
tff(c_609323,plain,
( ~ $less($sum($uminus('#skF_3'),'#skF_8'),$sum(1,'#skE_29'))
| $less($sum($uminus('#skF_3'),'#skF_8'),0) ),
inference(superposition,[status(thm),theory(equality)],[c_609312,c_603430]) ).
tff(c_609341,plain,
( ~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_609323]) ).
tff(c_609598,plain,
~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitLeft,[status(thm)],[c_609341]) ).
tff(c_609600,plain,
~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_609598]) ).
tff(c_609602,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_603766,c_609600]) ).
tff(c_609605,plain,
$less('#skF_8','#skF_3'),
inference(splitRight,[status(thm)],[c_609341]) ).
tff(c_609608,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_609605,c_578800]) ).
tff(c_609610,plain,
~ no_zero1('#skF_5'),
inference(splitRight,[status(thm)],[c_587641]) ).
tff(c_169,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_695,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_169]) ).
tff(c_913,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_695]) ).
tff(c_578409,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_913]) ).
tff(c_578619,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578409]) ).
tff(c_578621,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578619]) ).
tff(c_611837,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_585047,c_586159,c_580025,c_578621]) ).
tff(c_611839,plain,
( zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_586315,c_609610,c_587642,c_611837]) ).
tff(c_611841,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_611839]) ).
tff(c_611842,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_611841,c_585060]) ).
tff(c_611845,plain,
zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(splitRight,[status(thm)],[c_611839]) ).
tff(c_611856,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_5'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_611845,c_807]) ).
tff(c_614408,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_611856]) ).
tff(c_614414,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_614408]) ).
tff(c_615695,plain,
'#skF_8' = '#skF_3',
inference(splitLeft,[status(thm)],[c_614414]) ).
tff(c_615714,plain,
~ $less('#skF_3',$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_615695,c_578800]) ).
tff(c_615721,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_615714]) ).
tff(c_615726,plain,
'#skF_8' != '#skF_3',
inference(splitRight,[status(thm)],[c_614414]) ).
tff(c_614404,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_5')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_611856,c_80]) ).
tff(c_614411,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_5')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_614404]) ).
tff(c_615229,plain,
! [X_92: uni] :
( ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_614411]) ).
tff(c_615238,plain,
! [X_92: uni] :
( ( nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_615229]) ).
tff(c_624842,plain,
! [X_92: uni] : ( nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) ),
inference(negUnitSimplification,[status(thm)],[c_615726,c_615238]) ).
tff(c_624844,plain,
! [X_92: uni] : ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_624842]) ).
tff(c_609609,plain,
$less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitRight,[status(thm)],[c_587641]) ).
tff(c_609612,plain,
$less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_609609]) ).
tff(c_165,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$difference('#skF_8','#skF_3'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9')
| ~ $lesseq('#skF_3','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_915,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_165]) ).
tff(c_578414,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_915]) ).
tff(c_578416,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578414]) ).
tff(c_578622,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',$sum(1,length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_822,c_578416]) ).
tff(c_578624,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578622]) ).
tff(c_614290,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31')
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_585047,c_586159,c_580025,c_609612,c_578819,c_578624]) ).
tff(c_614291,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less($uminus(1),'#skE_31')
| $less('#skF_8','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_586315,c_587642,c_614290]) ).
tff(c_614293,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less($uminus(1),'#skE_31')
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_614291]) ).
tff(c_614295,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_614293]) ).
tff(c_614296,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_614295,c_585060]) ).
tff(c_614297,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| $less('#skF_8','#skF_3') ),
inference(splitRight,[status(thm)],[c_614293]) ).
tff(c_614300,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_614297]) ).
tff(c_614665,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))),
inference(splitLeft,[status(thm)],[c_614300]) ).
tff(c_614667,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_614665]) ).
tff(c_615054,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_614667]) ).
tff(c_615061,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_615054]) ).
tff(c_615063,plain,
( $less($sum('#skF_3','#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_615061]) ).
tff(c_626812,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_34',
inference(define,[status(thm),theory(equality)],[c_615063]) ).
tff(c_626814,plain,
( $less($sum('#skF_3','#skE_34'),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_626812,c_615063]) ).
tff(c_626818,plain,
( $less($sum('#skE_34','#skF_3'),'#skF_8')
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_626814]) ).
tff(c_628550,plain,
$less($sum('#skE_34','#skF_3'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_624844,c_626818]) ).
tff(c_628552,plain,
$less($sum('#skF_3','#skE_34'),'#skF_8'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_628550]) ).
tff(c_806,plain,
! [L_103: list_int,I_104a: $int] :
( ( tb2t(nth1(int,'#skF_1'(L_103,I_104a),t2tb1(L_103))) = tb2t(some(int,t2tb2(0))) )
| zero_at1(L_103,I_104a)
| ( tb2t(nth1(int,I_104a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) ) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_615046,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_806,c_614667]) ).
tff(c_615055,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_86,c_615046]) ).
tff(c_615057,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_615055]) ).
tff(c_626931,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_34',
inference(define,[status(thm),theory(equality)],[c_615057]) ).
tff(c_626933,plain,
( ( tb2t(nth1(int,'#skE_34',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_626931,c_615057]) ).
tff(c_626937,plain,
( ( tb2t(nth1(int,'#skE_34',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_626933]) ).
tff(c_628875,plain,
tb2t(nth1(int,'#skE_34',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_624844,c_626937]) ).
tff(c_93,plain,
! [J_107a: $int,L_103: list_int,I_104a: $int] :
( ( tb2t(nth1(int,J_107a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) )
| ~ zero_at1(L_103,I_104a)
| ~ $lesseq(0,J_107a)
| ~ $less(J_107a,I_104a) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_808,plain,
! [J_107a: $int,L_103: list_int,I_104a: $int] :
( ( tb2t(nth1(int,J_107a,t2tb1(L_103))) != tb2t(some(int,t2tb2(0))) )
| ~ zero_at1(L_103,I_104a)
| $less(J_107a,0)
| ~ $less(J_107a,I_104a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_93]) ).
tff(c_611849,plain,
! [J_107a: $int] :
( ( tb2t(nth1(int,J_107a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_107a,0)
| ~ $less(J_107a,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(resolution,[status(thm)],[c_611845,c_808]) ).
tff(c_614818,plain,
! [J_40238a: $int] :
( ( tb2t(nth1(int,J_40238a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_40238a,0)
| ~ $less($sum(1,$sum('#skF_3',J_40238a)),'#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_611849]) ).
tff(c_614830,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| $less($sum($uminus(1),N_89a),0)
| ~ $less($sum(1,$sum('#skF_3',$sum($uminus(1),N_89a))),'#skF_8')
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_614818]) ).
tff(c_614840,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| $less(N_89a,1)
| ~ $less($sum('#skF_3',N_89a),'#skF_8')
| ( N_89a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_614830]) ).
tff(c_628880,plain,
( $less('#skE_34',1)
| ~ $less($sum('#skF_3','#skE_34'),'#skF_8')
| ( '#skE_34' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_628875,c_614840]) ).
tff(c_628888,plain,
( $less('#skE_34',1)
| ( '#skE_34' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_628552,c_628880]) ).
tff(c_629171,plain,
'#skE_34' = 0,
inference(splitLeft,[status(thm)],[c_628888]) ).
tff(c_629173,plain,
tb2t(nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_629171,c_628875]) ).
tff(c_629184,plain,
tb2t(some(int,t2tb2('#skF_4'))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_629173]) ).
tff(c_629191,plain,
some(int,t2tb2('#skF_4')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_629184,c_80]) ).
tff(c_629195,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_629191]) ).
tff(c_629255,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_629195,c_578929]) ).
tff(c_629284,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_629255]) ).
tff(c_629341,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_629284,c_810]) ).
tff(c_629356,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_629341]) ).
tff(c_629358,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_629356]) ).
tff(c_629361,plain,
$less('#skE_34',1),
inference(splitRight,[status(thm)],[c_628888]) ).
tff(c_629362,plain,
'#skE_34' != 0,
inference(splitRight,[status(thm)],[c_628888]) ).
tff(c_615050,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_614667]) ).
tff(c_615058,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_615050]) ).
tff(c_615060,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))),0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_615058]) ).
tff(c_626688,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_34',
inference(define,[status(thm),theory(equality)],[c_615060]) ).
tff(c_626690,plain,
( ~ $less('#skE_34',0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_626688,c_615060]) ).
tff(c_626694,plain,
( ~ $less('#skE_34',0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_626690]) ).
tff(c_628218,plain,
~ $less('#skE_34',0),
inference(demodulation,[status(thm),theory(equality)],[c_624844,c_626694]) ).
tff(c_629462,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_629361,c_629362,c_628218]) ).
tff(c_629465,plain,
$less('#skF_8','#skF_3'),
inference(splitRight,[status(thm)],[c_614300]) ).
tff(c_629468,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_629465,c_578800]) ).
tff(c_629472,plain,
'#skF_10' != 0,
inference(splitRight,[status(thm)],[c_580023]) ).
tff(c_215,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_596,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_215]) ).
tff(c_891,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_596]) ).
tff(c_578517,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_891]) ).
tff(c_629706,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_578819,c_578517]) ).
tff(c_629707,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(negUnitSimplification,[status(thm)],[c_629472,c_629706]) ).
tff(c_629709,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_629707]) ).
tff(c_629711,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_629709]) ).
tff(c_629715,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_629711,c_86]) ).
tff(c_629718,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_629715]) ).
tff(c_629720,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_629718]) ).
tff(c_629724,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_629709]) ).
tff(c_219,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_586,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_219]) ).
tff(c_889,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_586]) ).
tff(c_578508,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_889]) ).
tff(c_630015,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_578819,c_578819,c_578508]) ).
tff(c_630016,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' ) ),
inference(negUnitSimplification,[status(thm)],[c_629472,c_629724,c_630015]) ).
tff(c_630018,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_630016]) ).
tff(c_630020,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_630018]) ).
tff(c_629471,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_580023]) ).
tff(c_634528,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),$sum(1,$sum('#skF_3','#skE_29')))))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_630020,c_629471]) ).
tff(c_634529,plain,
( no_zero1('#skF_5')
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),$sum(1,$sum('#skF_3','#skE_29')))))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(negUnitSimplification,[status(thm)],[c_629724,c_634528]) ).
tff(c_634531,plain,
( no_zero1('#skF_5')
| zero_at1('#skF_5','#skE_29')
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_634529]) ).
tff(c_634533,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitLeft,[status(thm)],[c_634531]) ).
tff(c_634752,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_634533,c_86]) ).
tff(c_634756,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_634752]) ).
tff(c_636978,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_634756,c_36]) ).
tff(c_637047,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_636978,c_36]) ).
tff(c_637072,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_637047,c_84]) ).
tff(c_637075,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_637072]) ).
tff(c_637077,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_579075,c_637075]) ).
tff(c_637081,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) != tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_634531]) ).
tff(c_195,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_901,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_195]) ).
tff(c_578371,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_901]) ).
tff(c_578373,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578371]) ).
tff(c_578601,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum(1,length1(int,t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578373]) ).
tff(c_578603,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,t2tb1('#skF_5')) != $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578601]) ).
tff(c_639057,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum($uminus(1),$sum($sum(1,$sum('#skF_3','#skE_29')),$uminus('#skF_3'))) != '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_578819,c_630020,c_578603]) ).
tff(c_639058,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum($uminus(1),$sum($sum(1,$sum('#skF_3','#skE_29')),$uminus('#skF_3'))) != '#skE_29' ) ),
inference(negUnitSimplification,[status(thm)],[c_629472,c_629724,c_637081,c_639057]) ).
tff(c_639060,plain,
~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_639058]) ).
tff(c_639077,plain,
~ $less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),0),
inference(resolution,[status(thm)],[c_800,c_639060]) ).
tff(c_639081,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = '#skE_33',
inference(define,[status(thm),theory(equality)],[c_639077]) ).
tff(c_639068,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),length1(int,t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))),
inference(resolution,[status(thm)],[c_801,c_639060]) ).
tff(c_639076,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_578819,c_822,c_86,c_639068]) ).
tff(c_643349,plain,
$less('#skE_33',$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_639081,c_639076]) ).
tff(c_639064,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_802,c_639060]) ).
tff(c_639074,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_639064]) ).
tff(c_643847,plain,
tb2t(nth1(int,'#skE_33',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_639081,c_639074]) ).
tff(c_643851,plain,
nth1(int,'#skE_33',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_643847,c_80]) ).
tff(c_643855,plain,
nth1(int,'#skE_33',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_643851]) ).
tff(c_637080,plain,
( zero_at1('#skF_5','#skE_29')
| no_zero1('#skF_5') ),
inference(splitRight,[status(thm)],[c_634531]) ).
tff(c_637082,plain,
no_zero1('#skF_5'),
inference(splitLeft,[status(thm)],[c_637080]) ).
tff(c_637086,plain,
! [J_111a: $int] :
( ( tb2t(nth1(int,J_111a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,length1(int,t2tb1('#skF_5')))
| $less(J_111a,0) ),
inference(resolution,[status(thm)],[c_637082,c_803]) ).
tff(c_646098,plain,
! [J_41651a: $int] :
( ( tb2t(nth1(int,J_41651a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_41651a,'#skE_29')
| $less(J_41651a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_578819,c_637086]) ).
tff(c_646102,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less($sum($uminus(1),N_89a),'#skE_29')
| $less($sum($uminus(1),N_89a),0)
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_646098]) ).
tff(c_646696,plain,
! [N_41690a: $int,X_41691: uni] :
( ( tb2t(nth1(int,N_41690a,cons(int,X_41691,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(N_41690a,$sum(1,'#skE_29'))
| $less(N_41690a,1)
| ( N_41690a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_646102]) ).
tff(c_646700,plain,
( ~ $less('#skE_33',$sum(1,'#skE_29'))
| $less('#skE_33',1)
| ( '#skE_33' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_643855,c_646696]) ).
tff(c_646723,plain,
( $less('#skE_33',1)
| ( '#skE_33' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_643349,c_646700]) ).
tff(c_646734,plain,
'#skE_33' = 0,
inference(splitLeft,[status(thm)],[c_646723]) ).
tff(c_646745,plain,
nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_646734,c_643855]) ).
tff(c_647050,plain,
! [Z1_38386: uni] : ( match_bool1(option(int),true1,some(int,t2tb2(0)),Z1_38386) = nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ),
inference(superposition,[status(thm),theory(equality)],[c_646745,c_579186]) ).
tff(c_647074,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_579166,c_647050]) ).
tff(c_647135,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_647074,c_578929]) ).
tff(c_647161,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_647135]) ).
tff(c_647213,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_647161,c_810]) ).
tff(c_647228,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_647213]) ).
tff(c_647230,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_647228]) ).
tff(c_647233,plain,
$less('#skE_33',1),
inference(splitRight,[status(thm)],[c_646723]) ).
tff(c_647234,plain,
'#skE_33' != 0,
inference(splitRight,[status(thm)],[c_646723]) ).
tff(c_639078,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = '#skE_33',
inference(define,[status(thm),theory(equality)],[c_639077]) ).
tff(c_639082,plain,
~ $less('#skE_33',0),
inference(demodulation,[status(thm),theory(equality)],[c_639078,c_639077]) ).
tff(c_647235,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_647233,c_647234,c_639082]) ).
tff(c_647237,plain,
~ no_zero1('#skF_5'),
inference(splitRight,[status(thm)],[c_637080]) ).
tff(c_578983,plain,
( ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_578958]) ).
tff(c_578986,plain,
( ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578983]) ).
tff(c_648240,plain,
( ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| $less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_630020,c_578986]) ).
tff(c_648241,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,$sum('#skF_3','#skE_29'))),
inference(negUnitSimplification,[status(thm)],[c_637081,c_647237,c_629724,c_629472,c_648240]) ).
tff(c_648243,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_648241]) ).
tff(c_648244,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_630018]) ).
tff(c_648247,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_648244]) ).
tff(c_652428,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitLeft,[status(thm)],[c_648247]) ).
tff(c_652780,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_652428,c_86]) ).
tff(c_652784,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_652780]) ).
tff(c_655186,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_652784,c_36]) ).
tff(c_655260,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_655186,c_36]) ).
tff(c_655282,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_655260,c_84]) ).
tff(c_655285,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_655282]) ).
tff(c_655287,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_579075,c_655285]) ).
tff(c_655292,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) != tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_648247]) ).
tff(c_655509,plain,
( no_zero1('#skF_5')
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(negUnitSimplification,[status(thm)],[c_655292,c_629724,c_629471]) ).
tff(c_655511,plain,
zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(splitLeft,[status(thm)],[c_655509]) ).
tff(c_655522,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_5'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_655511,c_807]) ).
tff(c_662153,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_655522]) ).
tff(c_662159,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_662153]) ).
tff(c_663605,plain,
'#skF_8' = '#skF_3',
inference(splitLeft,[status(thm)],[c_662159]) ).
tff(c_663624,plain,
~ $less('#skF_3',$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_663605,c_578800]) ).
tff(c_663631,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_663624]) ).
tff(c_663636,plain,
'#skF_8' != '#skF_3',
inference(splitRight,[status(thm)],[c_662159]) ).
tff(c_662149,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_5')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_655522,c_80]) ).
tff(c_662156,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_5')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_662149]) ).
tff(c_663096,plain,
! [X_92: uni] :
( ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_662156]) ).
tff(c_663107,plain,
! [X_92: uni] :
( ( nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_663096]) ).
tff(c_672535,plain,
! [X_92: uni] : ( nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) ),
inference(negUnitSimplification,[status(thm)],[c_663636,c_663107]) ).
tff(c_672537,plain,
! [X_92: uni] : ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_5'))) = some(int,t2tb2(0)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_672535]) ).
tff(c_655288,plain,
$less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(splitRight,[status(thm)],[c_648247]) ).
tff(c_655291,plain,
$less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_655288]) ).
tff(c_199,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$difference('#skF_8','#skF_3'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 )
| ~ $lesseq('#skF_3','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_899,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_199]) ).
tff(c_578555,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_899]) ).
tff(c_578557,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578555]) ).
tff(c_578673,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',$sum(1,length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578557]) ).
tff(c_578675,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578673]) ).
tff(c_659260,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_578819,c_578675]) ).
tff(c_659261,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| $less('#skF_8','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_629472,c_629724,c_655292,c_659260]) ).
tff(c_659263,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_659261]) ).
tff(c_659264,plain,
~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitLeft,[status(thm)],[c_659263]) ).
tff(c_659267,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_655291,c_659264]) ).
tff(c_659268,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| $less('#skF_8','#skF_3') ),
inference(splitRight,[status(thm)],[c_659263]) ).
tff(c_659271,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_659268]) ).
tff(c_659523,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))),
inference(splitLeft,[status(thm)],[c_659271]) ).
tff(c_659525,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_659523]) ).
tff(c_659940,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_659525]) ).
tff(c_659947,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_659940]) ).
tff(c_659949,plain,
( $less($sum('#skF_3','#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_659947]) ).
tff(c_673775,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_34',
inference(define,[status(thm),theory(equality)],[c_659949]) ).
tff(c_673777,plain,
( $less($sum('#skF_3','#skE_34'),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_673775,c_659949]) ).
tff(c_673781,plain,
( $less($sum('#skE_34','#skF_3'),'#skF_8')
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_673777]) ).
tff(c_675562,plain,
$less($sum('#skE_34','#skF_3'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_672537,c_673781]) ).
tff(c_675564,plain,
$less($sum('#skF_3','#skE_34'),'#skF_8'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_675562]) ).
tff(c_659932,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_806,c_659525]) ).
tff(c_659941,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_86,c_659932]) ).
tff(c_659943,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_659941]) ).
tff(c_673931,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_34',
inference(define,[status(thm),theory(equality)],[c_659943]) ).
tff(c_673933,plain,
( ( tb2t(nth1(int,'#skE_34',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_673931,c_659943]) ).
tff(c_673937,plain,
( ( tb2t(nth1(int,'#skE_34',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_673933]) ).
tff(c_675896,plain,
tb2t(nth1(int,'#skE_34',cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_672537,c_673937]) ).
tff(c_655515,plain,
! [J_107a: $int] :
( ( tb2t(nth1(int,J_107a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_107a,0)
| ~ $less(J_107a,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(resolution,[status(thm)],[c_655511,c_808]) ).
tff(c_662560,plain,
! [J_42398a: $int] :
( ( tb2t(nth1(int,J_42398a,t2tb1('#skF_5'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_42398a,0)
| ~ $less($sum(1,$sum('#skF_3',J_42398a)),'#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_655515]) ).
tff(c_662568,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| $less($sum($uminus(1),N_89a),0)
| ~ $less($sum(1,$sum('#skF_3',$sum($uminus(1),N_89a))),'#skF_8')
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_662560]) ).
tff(c_662576,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) )
| $less(N_89a,1)
| ~ $less($sum('#skF_3',N_89a),'#skF_8')
| ( N_89a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_662568]) ).
tff(c_675901,plain,
( $less('#skE_34',1)
| ~ $less($sum('#skF_3','#skE_34'),'#skF_8')
| ( '#skE_34' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_675896,c_662576]) ).
tff(c_675909,plain,
( $less('#skE_34',1)
| ( '#skE_34' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_675564,c_675901]) ).
tff(c_676116,plain,
'#skE_34' = 0,
inference(splitLeft,[status(thm)],[c_675909]) ).
tff(c_676118,plain,
tb2t(nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_676116,c_675896]) ).
tff(c_676129,plain,
tb2t(some(int,t2tb2('#skF_4'))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_676118]) ).
tff(c_676136,plain,
some(int,t2tb2('#skF_4')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_676129,c_80]) ).
tff(c_676140,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_676136]) ).
tff(c_676203,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_676140,c_578929]) ).
tff(c_676233,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_676203]) ).
tff(c_676281,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_676233,c_810]) ).
tff(c_676296,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_676281]) ).
tff(c_676298,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_676296]) ).
tff(c_676301,plain,
$less('#skE_34',1),
inference(splitRight,[status(thm)],[c_675909]) ).
tff(c_676302,plain,
'#skE_34' != 0,
inference(splitRight,[status(thm)],[c_675909]) ).
tff(c_659936,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_659525]) ).
tff(c_659944,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_659936]) ).
tff(c_659946,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))),0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_659944]) ).
tff(c_673688,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_34',
inference(define,[status(thm),theory(equality)],[c_659946]) ).
tff(c_673690,plain,
( ~ $less('#skE_34',0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_673688,c_659946]) ).
tff(c_673694,plain,
( ~ $less('#skE_34',0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_673690]) ).
tff(c_675319,plain,
~ $less('#skE_34',0),
inference(demodulation,[status(thm),theory(equality)],[c_672537,c_673694]) ).
tff(c_676480,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_676301,c_676302,c_675319]) ).
tff(c_676483,plain,
$less('#skF_8','#skF_3'),
inference(splitRight,[status(thm)],[c_659271]) ).
tff(c_676486,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_676483,c_578800]) ).
tff(c_676489,plain,
~ zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(splitRight,[status(thm)],[c_655509]) ).
tff(c_648248,plain,
'#skF_8' != $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_630018]) ).
tff(c_629723,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_629709]) ).
tff(c_677002,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_655292,c_676489,c_648248,c_629723]) ).
tff(c_677004,plain,
'#skF_5' = '#skF_7',
inference(splitRight,[status(thm)],[c_579074]) ).
tff(c_677008,plain,
length1(int,t2tb1('#skF_7')) = '#skE_29',
inference(demodulation,[status(thm),theory(equality)],[c_677004,c_578819]) ).
tff(c_213,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_601,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_213]) ).
tff(c_892,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_601]) ).
tff(c_578526,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_892]) ).
tff(c_677243,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677008,c_677004,c_677004,c_677004,c_578526]) ).
tff(c_677245,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_677243]) ).
tff(c_677247,plain,
'#skF_10' = 0,
inference(splitLeft,[status(thm)],[c_677245]) ).
tff(c_132,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))) != '#skF_9' )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_929,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_132]) ).
tff(c_578339,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_929]) ).
tff(c_578589,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum(1,length1(int,t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578339]) ).
tff(c_578591,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) )
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578589]) ).
tff(c_681291,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677247,c_677004,c_677004,c_677008,c_677004,c_677004,c_578591]) ).
tff(c_681293,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_681291]) ).
tff(c_681297,plain,
length1(int,t2tb1('#skF_11')) = '#skE_31',
inference(define,[status(thm),theory(equality)],[c_681293]) ).
tff(c_820,plain,
! [A_58: ty,L_59: uni] :
( ( nil(A_58) = L_59 )
| ( length1(A_58,L_59) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_681309,plain,
( ( t2tb1('#skF_11') = nil(int) )
| ( '#skE_31' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_681297,c_820]) ).
tff(c_681314,plain,
'#skE_31' != 0,
inference(splitLeft,[status(thm)],[c_681309]) ).
tff(c_171,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_912,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_171]) ).
tff(c_578315,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_912]) ).
tff(c_578679,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578315]) ).
tff(c_578681,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578679]) ).
tff(c_681494,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_681297,c_677247,c_677004,c_677004,c_677008,c_677004,c_677004,c_578681]) ).
tff(c_681496,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_681494]) ).
tff(c_681498,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_681496]) ).
tff(c_681310,plain,
~ $less('#skE_31',0),
inference(superposition,[status(thm),theory(equality)],[c_681297,c_821]) ).
tff(c_681499,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_681498,c_681310]) ).
tff(c_681500,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))) ),
inference(splitRight,[status(thm)],[c_681496]) ).
tff(c_681503,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_681500]) ).
tff(c_683430,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_681503]) ).
tff(c_683438,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_683430]) ).
tff(c_683448,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_683438]) ).
tff(c_683452,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_683448]) ).
tff(c_683456,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_683452,c_683448]) ).
tff(c_683442,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_683430]) ).
tff(c_683451,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_683442]) ).
tff(c_683461,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_683451]) ).
tff(c_683463,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_683461,c_683451]) ).
tff(c_683466,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_683456,c_683463]) ).
tff(c_683467,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) ) ),
inference(splitRight,[status(thm)],[c_681503]) ).
tff(c_683470,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_683467]) ).
tff(c_683613,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_683470]) ).
tff(c_683617,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_683613,c_86]) ).
tff(c_683620,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_683617]) ).
tff(c_683622,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_683620]) ).
tff(c_683627,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_683470]) ).
tff(c_683471,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_681503]) ).
tff(c_167,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_700,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_167]) ).
tff(c_914,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_700]) ).
tff(c_578279,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_914]) ).
tff(c_578661,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578279]) ).
tff(c_578663,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578661]) ).
tff(c_684294,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_681297,c_683471,c_677247,c_677004,c_677004,c_677004,c_677004,c_578663]) ).
tff(c_684296,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_7')
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_683627,c_684294]) ).
tff(c_684298,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_684296]) ).
tff(c_684299,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_684298,c_681310]) ).
tff(c_684302,plain,
( no_zero1('#skF_7')
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_684296]) ).
tff(c_684304,plain,
zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(splitLeft,[status(thm)],[c_684302]) ).
tff(c_684315,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_684304,c_807]) ).
tff(c_689692,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_684315]) ).
tff(c_689698,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_689692]) ).
tff(c_691724,plain,
'#skF_8' = '#skF_3',
inference(splitLeft,[status(thm)],[c_689698]) ).
tff(c_691740,plain,
~ $less('#skF_3',$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_691724,c_578800]) ).
tff(c_691747,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_691740]) ).
tff(c_691748,plain,
! [X_92: uni] : ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) ),
inference(splitRight,[status(thm)],[c_689698]) ).
tff(c_701838,plain,
! [X_44148: uni] : ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_44148,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_691748]) ).
tff(c_701847,plain,
! [X_44148: uni] : ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_44148,t2tb1('#skF_7'))) = t2tb(tb2t(some(int,t2tb2(0)))) ),
inference(superposition,[status(thm),theory(equality)],[c_701838,c_80]) ).
tff(c_701861,plain,
! [X_44148: uni] : ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_44148,t2tb1('#skF_7'))) = some(int,t2tb2(0)) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_701847]) ).
tff(c_701863,plain,
! [X_44148: uni] : ( nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_44148,t2tb1('#skF_7'))) = some(int,t2tb2(0)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_701861]) ).
tff(c_683623,plain,
( no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))) ),
inference(splitRight,[status(thm)],[c_683470]) ).
tff(c_683626,plain,
( no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_683623]) ).
tff(c_683628,plain,
$less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(splitLeft,[status(thm)],[c_683626]) ).
tff(c_683630,plain,
$less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_683628]) ).
tff(c_163,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$difference('#skF_8','#skF_3'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9')
| ~ $lesseq('#skF_3','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_916,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_163]) ).
tff(c_578418,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_916]) ).
tff(c_578420,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578418]) ).
tff(c_578625,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',$sum(1,length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_822,c_578420]) ).
tff(c_578627,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int)))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578625]) ).
tff(c_686787,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31')
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_681297,c_683471,c_677247,c_677004,c_677008,c_677004,c_677004,c_677004,c_578627]) ).
tff(c_686788,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ~ $less($uminus(1),'#skE_31')
| $less('#skF_8','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_683627,c_686787]) ).
tff(c_686790,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ~ $less($uminus(1),'#skE_31')
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_686788]) ).
tff(c_686792,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_686790]) ).
tff(c_686793,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_686792,c_681310]) ).
tff(c_686794,plain,
( ~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8'))
| $less('#skF_8','#skF_3') ),
inference(splitRight,[status(thm)],[c_686790]) ).
tff(c_686797,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8'))
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_683630,c_686794]) ).
tff(c_686799,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_686797]) ).
tff(c_687000,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),
inference(splitLeft,[status(thm)],[c_686799]) ).
tff(c_687002,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_687000]) ).
tff(c_687413,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_687002]) ).
tff(c_687421,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_687413]) ).
tff(c_687423,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_687421]) ).
tff(c_706122,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),0),
inference(demodulation,[status(thm),theory(equality)],[c_701863,c_687423]) ).
tff(c_706124,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_706122]) ).
tff(c_706125,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_39',
inference(define,[status(thm),theory(equality)],[c_706124]) ).
tff(c_706129,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_39',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_706125]) ).
tff(c_687417,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_687002]) ).
tff(c_687424,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_687417]) ).
tff(c_687426,plain,
( $less($sum('#skF_3','#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_687424]) ).
tff(c_706350,plain,
$less($sum('#skF_3','#skE_39'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_701863,c_706129,c_687426]) ).
tff(c_706352,plain,
$less($sum('#skE_39','#skF_3'),'#skF_8'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_706350]) ).
tff(c_687409,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_806,c_687002]) ).
tff(c_687418,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_86,c_687409]) ).
tff(c_687420,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_687418]) ).
tff(c_706726,plain,
tb2t(nth1(int,'#skE_39',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_701863,c_706129,c_687420]) ).
tff(c_684308,plain,
! [J_107a: $int] :
( ( tb2t(nth1(int,J_107a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_107a,0)
| ~ $less(J_107a,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(resolution,[status(thm)],[c_684304,c_808]) ).
tff(c_690099,plain,
! [J_43691a: $int] :
( ( tb2t(nth1(int,J_43691a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_43691a,0)
| ~ $less($sum(1,$sum('#skF_3',J_43691a)),'#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_684308]) ).
tff(c_690107,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| $less($sum($uminus(1),N_89a),0)
| ~ $less($sum(1,$sum('#skF_3',$sum($uminus(1),N_89a))),'#skF_8')
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_690099]) ).
tff(c_690115,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| $less(N_89a,1)
| ~ $less($sum('#skF_3',N_89a),'#skF_8')
| ( N_89a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_690107]) ).
tff(c_706731,plain,
( $less('#skE_39',1)
| ~ $less($sum('#skF_3','#skE_39'),'#skF_8')
| ( '#skE_39' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_706726,c_690115]) ).
tff(c_706738,plain,
( $less('#skE_39',1)
| ~ $less($sum('#skE_39','#skF_3'),'#skF_8')
| ( '#skE_39' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_706731]) ).
tff(c_707169,plain,
( $less('#skE_39',1)
| ( '#skE_39' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_706352,c_706738]) ).
tff(c_707171,plain,
'#skE_39' = 0,
inference(splitLeft,[status(thm)],[c_707169]) ).
tff(c_707173,plain,
tb2t(nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_707171,c_706726]) ).
tff(c_707184,plain,
tb2t(some(int,t2tb2('#skF_4'))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_707173]) ).
tff(c_707191,plain,
some(int,t2tb2('#skF_4')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_707184,c_80]) ).
tff(c_707195,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_707191]) ).
tff(c_707264,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_707195,c_578929]) ).
tff(c_707296,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_707264]) ).
tff(c_707350,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_707296,c_810]) ).
tff(c_707365,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_707350]) ).
tff(c_707367,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_707365]) ).
tff(c_707370,plain,
$less('#skE_39',1),
inference(splitRight,[status(thm)],[c_707169]) ).
tff(c_707371,plain,
'#skE_39' != 0,
inference(splitRight,[status(thm)],[c_707169]) ).
tff(c_706130,plain,
~ $less('#skE_39',0),
inference(demodulation,[status(thm),theory(equality)],[c_706125,c_706124]) ).
tff(c_707571,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_707370,c_707371,c_706130]) ).
tff(c_707574,plain,
$less('#skF_8','#skF_3'),
inference(splitRight,[status(thm)],[c_686799]) ).
tff(c_707937,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_707574,c_578800]) ).
tff(c_707940,plain,
~ zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(splitRight,[status(thm)],[c_684302]) ).
tff(c_179,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$difference('#skF_8',$sum(1,'#skF_3')))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_674,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_179]) ).
tff(c_908,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_674]) ).
tff(c_578397,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_908]) ).
tff(c_578613,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578397]) ).
tff(c_578615,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578613]) ).
tff(c_709395,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_681297,c_683471,c_677247,c_677004,c_677008,c_677004,c_677004,c_677004,c_578615]) ).
tff(c_709396,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_683627,c_707940,c_709395]) ).
tff(c_709398,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_709396]) ).
tff(c_709400,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_709398]) ).
tff(c_709401,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_709400,c_681310]) ).
tff(c_709404,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_709398]) ).
tff(c_709408,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,$sum('#skE_29','#skF_3'))),
inference(demodulation,[status(thm),theory(equality)],[c_709404,c_683630]) ).
tff(c_709415,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_709408]) ).
tff(c_709417,plain,
~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(splitRight,[status(thm)],[c_683626]) ).
tff(c_709419,plain,
~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_709417]) ).
tff(c_159,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_918,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_159]) ).
tff(c_578429,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_918]) ).
tff(c_578431,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578429]) ).
tff(c_578631,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum(1,length1(int,t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_822,c_578431]) ).
tff(c_578633,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,t2tb1('#skF_5')) != $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578631]) ).
tff(c_711446,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_681297,c_683471,c_677247,c_677004,c_677008,c_677004,c_677004,c_677004,c_578633]) ).
tff(c_711447,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_683627,c_711446]) ).
tff(c_711449,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( '#skF_8' != $sum(1,$sum('#skF_3','#skE_29')) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_711447]) ).
tff(c_711451,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_711449]) ).
tff(c_711452,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_711451,c_681310]) ).
tff(c_711455,plain,
( ( '#skF_8' != $sum(1,$sum('#skF_3','#skE_29')) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) ),
inference(splitRight,[status(thm)],[c_711449]) ).
tff(c_711511,plain,
~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),
inference(splitLeft,[status(thm)],[c_711455]) ).
tff(c_711528,plain,
~ $less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),0),
inference(resolution,[status(thm)],[c_800,c_711511]) ).
tff(c_711532,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = '#skE_37',
inference(define,[status(thm),theory(equality)],[c_711528]) ).
tff(c_711519,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),length1(int,t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))),
inference(resolution,[status(thm)],[c_801,c_711511]) ).
tff(c_711527,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_677008,c_822,c_86,c_711519]) ).
tff(c_711758,plain,
$less('#skE_37',$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_711532,c_711527]) ).
tff(c_711515,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_802,c_711511]) ).
tff(c_711525,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_711515]) ).
tff(c_721775,plain,
tb2t(nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_711532,c_711525]) ).
tff(c_721779,plain,
nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_721775,c_80]) ).
tff(c_721783,plain,
nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_721779]) ).
tff(c_709416,plain,
no_zero1('#skF_7'),
inference(splitRight,[status(thm)],[c_683626]) ).
tff(c_709612,plain,
! [J_111a: $int] :
( ( tb2t(nth1(int,J_111a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,length1(int,t2tb1('#skF_7')))
| $less(J_111a,0) ),
inference(resolution,[status(thm)],[c_709416,c_803]) ).
tff(c_723855,plain,
! [J_45064a: $int] :
( ( tb2t(nth1(int,J_45064a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_45064a,'#skE_29')
| $less(J_45064a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_677008,c_709612]) ).
tff(c_723859,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less($sum($uminus(1),N_89a),'#skE_29')
| $less($sum($uminus(1),N_89a),0)
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_723855]) ).
tff(c_724528,plain,
! [N_45089a: $int,X_45090: uni] :
( ( tb2t(nth1(int,N_45089a,cons(int,X_45090,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(N_45089a,$sum(1,'#skE_29'))
| $less(N_45089a,1)
| ( N_45089a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_723859]) ).
tff(c_724532,plain,
( ~ $less('#skE_37',$sum(1,'#skE_29'))
| $less('#skE_37',1)
| ( '#skE_37' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_721783,c_724528]) ).
tff(c_724555,plain,
( $less('#skE_37',1)
| ( '#skE_37' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_711758,c_724532]) ).
tff(c_724566,plain,
'#skE_37' = 0,
inference(splitLeft,[status(thm)],[c_724555]) ).
tff(c_724577,plain,
nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_724566,c_721783]) ).
tff(c_678167,plain,
! [A_85: ty,A_43079: ty,X1_87: uni,X_86a: $int,Z_43080: uni,U_43077: uni] : ( match_option1(option(A_85),A_43079,some(A_43079,U_43077),Z_43080,nth1(A_85,X_86a,X1_87)) = nth1(A_85,X_86a,X1_87) ),
inference(resolution,[status(thm)],[c_818,c_678130]) ).
tff(c_724592,plain,
! [A_43079: ty,U_43077: uni,Z_43080: uni] : ( match_option1(option(int),A_43079,some(A_43079,U_43077),Z_43080,some(int,t2tb2(0))) = nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) ),
inference(superposition,[status(thm),theory(equality)],[c_724577,c_678167]) ).
tff(c_724631,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_678148,c_724592]) ).
tff(c_724720,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_724631,c_578929]) ).
tff(c_724752,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_724720]) ).
tff(c_724984,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_724752,c_810]) ).
tff(c_724999,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_724984]) ).
tff(c_725001,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_724999]) ).
tff(c_725004,plain,
$less('#skE_37',1),
inference(splitRight,[status(thm)],[c_724555]) ).
tff(c_725005,plain,
'#skE_37' != 0,
inference(splitRight,[status(thm)],[c_724555]) ).
tff(c_711529,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = '#skE_37',
inference(define,[status(thm),theory(equality)],[c_711528]) ).
tff(c_711533,plain,
~ $less('#skE_37',0),
inference(demodulation,[status(thm),theory(equality)],[c_711529,c_711528]) ).
tff(c_725006,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_725004,c_725005,c_711533]) ).
tff(c_725009,plain,
'#skF_8' != $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_711455]) ).
tff(c_183,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_664,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_183]) ).
tff(c_906,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_664]) ).
tff(c_578306,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_906]) ).
tff(c_578670,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578306]) ).
tff(c_578672,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578670]) ).
tff(c_725198,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_681297,c_683471,c_677247,c_677004,c_677008,c_677004,c_677008,c_677004,c_677004,c_578672]) ).
tff(c_725199,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_683627,c_725198]) ).
tff(c_725201,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_725199]) ).
tff(c_725203,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_725201]) ).
tff(c_678424,plain,
! [A_43107: ty,U_43108: uni] :
( ( cons(A_43107,cons_proj_11(A_43107,U_43108),cons_proj_21(A_43107,U_43108)) = U_43108 )
| ( nil(A_43107) = U_43108 ) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_678433,plain,
! [A_43107: ty,U_43108: uni] :
( ( $sum(1,length1(A_43107,cons_proj_21(A_43107,U_43108))) = length1(A_43107,U_43108) )
| ( nil(A_43107) = U_43108 ) ),
inference(superposition,[status(thm),theory(equality)],[c_678424,c_822]) ).
tff(c_711456,plain,
! [A_44557: ty,U_44558: uni] :
( ( length1(A_44557,cons_proj_21(A_44557,U_44558)) = $sum($uminus(1),length1(A_44557,U_44558)) )
| ( nil(A_44557) = U_44558 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_678433]) ).
tff(c_711464,plain,
! [A_44557: ty,U_44558: uni] :
( ~ $less($sum($uminus(1),length1(A_44557,U_44558)),0)
| ( nil(A_44557) = U_44558 ) ),
inference(superposition,[status(thm),theory(equality)],[c_711456,c_821]) ).
tff(c_711483,plain,
! [A_44559: ty,U_44560: uni] :
( ~ $less(length1(A_44559,U_44560),1)
| ( nil(A_44559) = U_44560 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_711464]) ).
tff(c_711501,plain,
( ~ $less('#skE_31',1)
| ( t2tb1('#skF_11') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_681297,c_711483]) ).
tff(c_725042,plain,
~ $less('#skE_31',1),
inference(splitLeft,[status(thm)],[c_711501]) ).
tff(c_725204,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_725203,c_725042]) ).
tff(c_725205,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))) ),
inference(splitRight,[status(thm)],[c_725201]) ).
tff(c_725207,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_709419,c_725009,c_725205]) ).
tff(c_725208,plain,
t2tb1('#skF_11') = nil(int),
inference(splitRight,[status(thm)],[c_711501]) ).
tff(c_725214,plain,
length1(int,nil(int)) = '#skE_31',
inference(demodulation,[status(thm),theory(equality)],[c_725208,c_681297]) ).
tff(c_725216,plain,
'#skE_31' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_819,c_725214]) ).
tff(c_725218,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_681314,c_725216]) ).
tff(c_725219,plain,
t2tb1('#skF_11') = nil(int),
inference(splitRight,[status(thm)],[c_681309]) ).
tff(c_725344,plain,
tb2t1(nil(int)) = '#skF_11',
inference(superposition,[status(thm),theory(equality)],[c_725219,c_84]) ).
tff(c_725348,plain,
no_zero1('#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_725344,c_578984]) ).
tff(c_726188,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0)
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_725348,c_725344,c_819,c_725219,c_725219,c_677247,c_725344,c_677004,c_677004,c_677008,c_677004,c_677004,c_578618]) ).
tff(c_726189,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_726188]) ).
tff(c_726191,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_726189]) ).
tff(c_726193,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0),
inference(splitLeft,[status(thm)],[c_726191]) ).
tff(c_726197,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),nil(int)))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_726193]) ).
tff(c_726204,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_726197]) ).
tff(c_726208,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0) = '#skE_41',
inference(define,[status(thm),theory(equality)],[c_726204]) ).
tff(c_726212,plain,
~ $less('#skE_41',0),
inference(demodulation,[status(thm),theory(equality)],[c_726208,c_726204]) ).
tff(c_726201,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),nil(int)))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_726193]) ).
tff(c_726207,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_726201]) ).
tff(c_726213,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0) = '#skE_41',
inference(define,[status(thm),theory(equality)],[c_726207]) ).
tff(c_726215,plain,
$less('#skE_41',0),
inference(demodulation,[status(thm),theory(equality)],[c_726213,c_726207]) ).
tff(c_726218,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_726212,c_726215]) ).
tff(c_726223,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0),
inference(splitRight,[status(thm)],[c_726191]) ).
tff(c_726784,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_725348,c_725344,c_819,c_725219,c_726223,c_677247,c_725219,c_677004,c_725344,c_677004,c_677004,c_677004,c_578663]) ).
tff(c_726786,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_726784]) ).
tff(c_726788,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11',
inference(splitLeft,[status(thm)],[c_726786]) ).
tff(c_726792,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1('#skF_11'),
inference(superposition,[status(thm),theory(equality)],[c_726788,c_86]) ).
tff(c_726795,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_725219,c_726792]) ).
tff(c_726797,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_726795]) ).
tff(c_726801,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) != '#skF_11',
inference(splitRight,[status(thm)],[c_726786]) ).
tff(c_726800,plain,
( no_zero1('#skF_7')
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_726786]) ).
tff(c_726803,plain,
zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(splitLeft,[status(thm)],[c_726800]) ).
tff(c_726817,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_726803,c_807]) ).
tff(c_731634,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_726817]) ).
tff(c_731640,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_731634]) ).
tff(c_732428,plain,
'#skF_8' = '#skF_3',
inference(splitLeft,[status(thm)],[c_731640]) ).
tff(c_732447,plain,
~ $less('#skF_3',$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_732428,c_578800]) ).
tff(c_732454,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_732447]) ).
tff(c_732455,plain,
! [X_92: uni] : ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) ),
inference(splitRight,[status(thm)],[c_731640]) ).
tff(c_736391,plain,
! [X_45601: uni] : ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_45601,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_732455]) ).
tff(c_736400,plain,
! [X_45601: uni] : ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_45601,t2tb1('#skF_7'))) = t2tb(tb2t(some(int,t2tb2(0)))) ),
inference(superposition,[status(thm),theory(equality)],[c_736391,c_80]) ).
tff(c_736414,plain,
! [X_45601: uni] : ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_45601,t2tb1('#skF_7'))) = some(int,t2tb2(0)) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_736400]) ).
tff(c_736416,plain,
! [X_45601: uni] : ( nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_45601,t2tb1('#skF_7'))) = some(int,t2tb2(0)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_736414]) ).
tff(c_725221,plain,
'#skE_31' = 0,
inference(splitRight,[status(thm)],[c_681309]) ).
tff(c_725223,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_681297,c_677247,c_677004,c_677004,c_677008,c_677004,c_677004,c_578681]) ).
tff(c_725225,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_725223]) ).
tff(c_725227,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_725225]) ).
tff(c_725291,plain,
~ $less($uminus(1),0),
inference(demodulation,[status(thm),theory(equality)],[c_725221,c_725227]) ).
tff(c_725293,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_725291]) ).
tff(c_725294,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))) ),
inference(splitRight,[status(thm)],[c_725225]) ).
tff(c_725297,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_725294]) ).
tff(c_726672,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_725344,c_726223,c_725219,c_725297]) ).
tff(c_726674,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| no_zero1('#skF_7')
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_726672]) ).
tff(c_726675,plain,
$less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitLeft,[status(thm)],[c_726674]) ).
tff(c_726677,plain,
$less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_726675]) ).
tff(c_729869,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0)
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_725348,c_725344,c_819,c_725219,c_726223,c_677247,c_725219,c_677004,c_725344,c_726677,c_677008,c_677004,c_677004,c_677004,c_578627]) ).
tff(c_729870,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less($uminus(1),0)
| $less('#skF_8','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_726801,c_729869]) ).
tff(c_729871,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8'))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_729870]) ).
tff(c_729873,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_729871]) ).
tff(c_729874,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),
inference(splitLeft,[status(thm)],[c_729873]) ).
tff(c_729876,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_729874]) ).
tff(c_729884,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_729876]) ).
tff(c_729892,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_729884]) ).
tff(c_729894,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_729892]) ).
tff(c_737559,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),0),
inference(demodulation,[status(thm),theory(equality)],[c_736416,c_729894]) ).
tff(c_737561,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_737559]) ).
tff(c_737562,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_39',
inference(define,[status(thm),theory(equality)],[c_737561]) ).
tff(c_737566,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_39',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_737562]) ).
tff(c_729888,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_729876]) ).
tff(c_729895,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_729888]) ).
tff(c_729897,plain,
( $less($sum('#skF_3','#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_729895]) ).
tff(c_737846,plain,
$less($sum('#skF_3','#skE_39'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_736416,c_737566,c_729897]) ).
tff(c_737848,plain,
$less($sum('#skE_39','#skF_3'),'#skF_8'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_737846]) ).
tff(c_729880,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_806,c_729876]) ).
tff(c_729889,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_86,c_729880]) ).
tff(c_729891,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_729889]) ).
tff(c_738167,plain,
tb2t(nth1(int,'#skE_39',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_736416,c_737566,c_729891]) ).
tff(c_726810,plain,
! [J_107a: $int] :
( ( tb2t(nth1(int,J_107a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_107a,0)
| ~ $less(J_107a,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(resolution,[status(thm)],[c_726803,c_808]) ).
tff(c_731947,plain,
! [J_45440a: $int] :
( ( tb2t(nth1(int,J_45440a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_45440a,0)
| ~ $less($sum(1,$sum('#skF_3',J_45440a)),'#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_726810]) ).
tff(c_731955,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| $less($sum($uminus(1),N_89a),0)
| ~ $less($sum(1,$sum('#skF_3',$sum($uminus(1),N_89a))),'#skF_8')
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_731947]) ).
tff(c_731963,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| $less(N_89a,1)
| ~ $less($sum('#skF_3',N_89a),'#skF_8')
| ( N_89a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_731955]) ).
tff(c_738172,plain,
( $less('#skE_39',1)
| ~ $less($sum('#skF_3','#skE_39'),'#skF_8')
| ( '#skE_39' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_738167,c_731963]) ).
tff(c_738179,plain,
( $less('#skE_39',1)
| ~ $less($sum('#skE_39','#skF_3'),'#skF_8')
| ( '#skE_39' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_738172]) ).
tff(c_738376,plain,
( $less('#skE_39',1)
| ( '#skE_39' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_737848,c_738179]) ).
tff(c_738378,plain,
'#skE_39' = 0,
inference(splitLeft,[status(thm)],[c_738376]) ).
tff(c_738380,plain,
tb2t(nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_738378,c_738167]) ).
tff(c_738391,plain,
tb2t(some(int,t2tb2('#skF_4'))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_738380]) ).
tff(c_738398,plain,
some(int,t2tb2('#skF_4')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_738391,c_80]) ).
tff(c_738402,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_738398]) ).
tff(c_738471,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_738402,c_578929]) ).
tff(c_738503,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_738471]) ).
tff(c_738548,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_738503,c_810]) ).
tff(c_738563,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_738548]) ).
tff(c_738565,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_738563]) ).
tff(c_738568,plain,
$less('#skE_39',1),
inference(splitRight,[status(thm)],[c_738376]) ).
tff(c_738569,plain,
'#skE_39' != 0,
inference(splitRight,[status(thm)],[c_738376]) ).
tff(c_737567,plain,
~ $less('#skE_39',0),
inference(demodulation,[status(thm),theory(equality)],[c_737562,c_737561]) ).
tff(c_738761,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_738568,c_738569,c_737567]) ).
tff(c_738764,plain,
$less('#skF_8','#skF_3'),
inference(splitRight,[status(thm)],[c_729873]) ).
tff(c_738767,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_738764,c_578800]) ).
tff(c_738770,plain,
~ zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(splitRight,[status(thm)],[c_726800]) ).
tff(c_740630,plain,
( zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_725348,c_725344,c_819,c_725219,c_726223,c_677247,c_725219,c_677004,c_725344,c_677008,c_677004,c_677004,c_677004,c_578615]) ).
tff(c_740631,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_726801,c_738770,c_740630]) ).
tff(c_740633,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_740631]) ).
tff(c_740512,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_725348,c_725344,c_819,c_725219,c_726223,c_677247,c_725219,c_677004,c_725344,c_677008,c_677004,c_677004,c_677004,c_578633]) ).
tff(c_740513,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_726801,c_740512]) ).
tff(c_740515,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( '#skF_8' != $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_740513]) ).
tff(c_740517,plain,
'#skF_8' != $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_740515]) ).
tff(c_740645,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_740633,c_740517]) ).
tff(c_740649,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_740515]) ).
tff(c_740670,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,$sum('#skF_3','#skE_29'))),
inference(demodulation,[status(thm),theory(equality)],[c_740649,c_726677]) ).
tff(c_740677,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_740670]) ).
tff(c_740680,plain,
( no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' ) ),
inference(splitRight,[status(thm)],[c_726674]) ).
tff(c_740687,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11',
inference(splitLeft,[status(thm)],[c_740680]) ).
tff(c_740691,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1('#skF_11'),
inference(superposition,[status(thm),theory(equality)],[c_740687,c_86]) ).
tff(c_740694,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_725219,c_740691]) ).
tff(c_740696,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_740694]) ).
tff(c_740699,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) != '#skF_11',
inference(splitRight,[status(thm)],[c_740680]) ).
tff(c_740679,plain,
~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitRight,[status(thm)],[c_726674]) ).
tff(c_740682,plain,
~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_740679]) ).
tff(c_743209,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_725348,c_725344,c_819,c_725219,c_726223,c_677247,c_725219,c_677004,c_725344,c_677008,c_677004,c_677008,c_677004,c_677004,c_578672]) ).
tff(c_743210,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_740699,c_740682,c_743209]) ).
tff(c_743212,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_743210]) ).
tff(c_742572,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_725348,c_725344,c_819,c_725219,c_726223,c_677247,c_725219,c_677004,c_725344,c_677008,c_677004,c_677004,c_677004,c_578633]) ).
tff(c_742573,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != '#skE_29' )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_740699,c_742572]) ).
tff(c_742575,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( '#skF_8' != $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_742573]) ).
tff(c_742577,plain,
'#skF_8' != $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_742575]) ).
tff(c_743225,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_743212,c_742577]) ).
tff(c_743228,plain,
~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),
inference(splitRight,[status(thm)],[c_742575]) ).
tff(c_743246,plain,
~ $less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),0),
inference(resolution,[status(thm)],[c_800,c_743228]) ).
tff(c_743256,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = '#skE_37',
inference(define,[status(thm),theory(equality)],[c_743246]) ).
tff(c_743237,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),length1(int,t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))),
inference(resolution,[status(thm)],[c_801,c_743228]) ).
tff(c_743245,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_677008,c_822,c_86,c_743237]) ).
tff(c_743270,plain,
$less('#skE_37',$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_743256,c_743245]) ).
tff(c_743233,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_802,c_743228]) ).
tff(c_743243,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_743233]) ).
tff(c_745930,plain,
tb2t(nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_743256,c_743243]) ).
tff(c_745934,plain,
nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_745930,c_80]) ).
tff(c_745938,plain,
nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_745934]) ).
tff(c_740697,plain,
no_zero1('#skF_7'),
inference(splitRight,[status(thm)],[c_740680]) ).
tff(c_740703,plain,
! [J_111a: $int] :
( ( tb2t(nth1(int,J_111a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_111a,length1(int,t2tb1('#skF_7')))
| $less(J_111a,0) ),
inference(resolution,[status(thm)],[c_740697,c_803]) ).
tff(c_746591,plain,
! [J_45983a: $int] :
( ( tb2t(nth1(int,J_45983a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_45983a,'#skE_29')
| $less(J_45983a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_677008,c_740703]) ).
tff(c_746595,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less($sum($uminus(1),N_89a),'#skE_29')
| $less($sum($uminus(1),N_89a),0)
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_746591]) ).
tff(c_747520,plain,
! [N_46020a: $int,X_46021: uni] :
( ( tb2t(nth1(int,N_46020a,cons(int,X_46021,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(N_46020a,$sum(1,'#skE_29'))
| $less(N_46020a,1)
| ( N_46020a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_746595]) ).
tff(c_747524,plain,
( ~ $less('#skE_37',$sum(1,'#skE_29'))
| $less('#skE_37',1)
| ( '#skE_37' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_745938,c_747520]) ).
tff(c_747547,plain,
( $less('#skE_37',1)
| ( '#skE_37' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_743270,c_747524]) ).
tff(c_747558,plain,
'#skE_37' = 0,
inference(splitLeft,[status(thm)],[c_747547]) ).
tff(c_747569,plain,
nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_747558,c_745938]) ).
tff(c_747584,plain,
! [A_43079: ty,U_43077: uni,Z_43080: uni] : ( match_option1(option(int),A_43079,some(A_43079,U_43077),Z_43080,some(int,t2tb2(0))) = nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) ),
inference(superposition,[status(thm),theory(equality)],[c_747569,c_678167]) ).
tff(c_747623,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_678148,c_747584]) ).
tff(c_747712,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_747623,c_578929]) ).
tff(c_747744,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_747712]) ).
tff(c_747996,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_747744,c_810]) ).
tff(c_748011,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_747996]) ).
tff(c_748013,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_748011]) ).
tff(c_748016,plain,
$less('#skE_37',1),
inference(splitRight,[status(thm)],[c_747547]) ).
tff(c_748017,plain,
'#skE_37' != 0,
inference(splitRight,[status(thm)],[c_747547]) ).
tff(c_743253,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = '#skE_37',
inference(define,[status(thm),theory(equality)],[c_743246]) ).
tff(c_743257,plain,
~ $less('#skE_37',0),
inference(demodulation,[status(thm),theory(equality)],[c_743253,c_743246]) ).
tff(c_748018,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_748016,c_748017,c_743257]) ).
tff(c_748022,plain,
'#skF_10' != 0,
inference(splitRight,[status(thm)],[c_677245]) ).
tff(c_748164,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677004,c_677004,c_677004,c_578547]) ).
tff(c_748166,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) ) ),
inference(negUnitSimplification,[status(thm)],[c_748022,c_748164]) ).
tff(c_748168,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_748166]) ).
tff(c_748218,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_748168,c_86]) ).
tff(c_748221,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_748218]) ).
tff(c_748223,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_748221]) ).
tff(c_748227,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_748166]) ).
tff(c_748716,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677008,c_677004,c_677004,c_677004,c_578517]) ).
tff(c_748717,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' ) ),
inference(negUnitSimplification,[status(thm)],[c_748022,c_748227,c_748716]) ).
tff(c_748719,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_748717]) ).
tff(c_748721,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_748719]) ).
tff(c_193,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))) != '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_902,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_193]) ).
tff(c_578364,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum('#skF_8',$uminus('#skF_3')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_902]) ).
tff(c_578366,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578364]) ).
tff(c_578598,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( $sum(1,length1(int,t2tb1('#skF_5'))) != $sum($uminus('#skF_3'),'#skF_8') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578366]) ).
tff(c_578600,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))))
| ( length1(int,t2tb1('#skF_5')) != $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578598]) ).
tff(c_754740,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum($sum(1,$sum('#skF_3','#skE_29')),$uminus('#skF_3'))) != '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_748721,c_677008,c_677004,c_677004,c_677004,c_578600]) ).
tff(c_754741,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))))
| ( $sum($uminus(1),$sum($sum(1,$sum('#skF_3','#skE_29')),$uminus('#skF_3'))) != '#skE_29' ) ),
inference(negUnitSimplification,[status(thm)],[c_748022,c_748227,c_754740]) ).
tff(c_754743,plain,
~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_754741]) ).
tff(c_754760,plain,
~ $less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),0),
inference(resolution,[status(thm)],[c_800,c_754743]) ).
tff(c_754764,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = '#skE_37',
inference(define,[status(thm),theory(equality)],[c_754760]) ).
tff(c_754751,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),length1(int,t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))),
inference(resolution,[status(thm)],[c_801,c_754743]) ).
tff(c_754759,plain,
$less('#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_677008,c_822,c_86,c_754751]) ).
tff(c_754773,plain,
$less('#skE_37',$sum(1,'#skE_29')),
inference(demodulation,[status(thm),theory(equality)],[c_754764,c_754759]) ).
tff(c_754747,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_802,c_754743]) ).
tff(c_754757,plain,
tb2t(nth1(int,'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_754747]) ).
tff(c_762364,plain,
tb2t(nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_754764,c_754757]) ).
tff(c_762368,plain,
nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_762364,c_80]) ).
tff(c_762378,plain,
nth1(int,'#skE_37',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_762368]) ).
tff(c_578816,plain,
length1(int,t2tb1('#skF_5')) = '#skE_29',
inference(define,[status(thm),theory(equality)],[c_578544]) ).
tff(c_578818,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578816,c_578544]) ).
tff(c_578821,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578818]) ).
tff(c_749992,plain,
( $less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677004,c_748721,c_677004,c_578821]) ).
tff(c_749993,plain,
( $less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7') ),
inference(negUnitSimplification,[status(thm)],[c_748022,c_748227,c_749992]) ).
tff(c_749995,plain,
no_zero1('#skF_7'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_749993]) ).
tff(c_753536,plain,
! [J_46364a: $int,L_46365: list_int] :
( ( tb2t(nth1(int,J_46364a,t2tb1(L_46365))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_46364a,length1(int,t2tb1(L_46365)))
| ~ no_zero1(L_46365)
| $less(J_46364a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_104]) ).
tff(c_753544,plain,
! [J_46364a: $int] :
( ( tb2t(nth1(int,J_46364a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_46364a,length1(int,t2tb1('#skF_7')))
| $less(J_46364a,0) ),
inference(resolution,[status(thm)],[c_749995,c_753536]) ).
tff(c_760477,plain,
! [J_46619a: $int] :
( ( tb2t(nth1(int,J_46619a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_46619a,'#skE_29')
| $less(J_46619a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_677008,c_753544]) ).
tff(c_760481,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less($sum($uminus(1),N_89a),'#skE_29')
| $less($sum($uminus(1),N_89a),0)
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_760477]) ).
tff(c_763905,plain,
! [N_46706a: $int,X_46707: uni] :
( ( tb2t(nth1(int,N_46706a,cons(int,X_46707,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(N_46706a,$sum(1,'#skE_29'))
| $less(N_46706a,1)
| ( N_46706a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_760481]) ).
tff(c_763909,plain,
( ~ $less('#skE_37',$sum(1,'#skE_29'))
| $less('#skE_37',1)
| ( '#skE_37' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_762378,c_763905]) ).
tff(c_763940,plain,
( $less('#skE_37',1)
| ( '#skE_37' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_754773,c_763909]) ).
tff(c_763951,plain,
'#skE_37' = 0,
inference(splitLeft,[status(thm)],[c_763940]) ).
tff(c_763962,plain,
nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_763951,c_762378]) ).
tff(c_749735,plain,
! [A_85: ty,X_86a: $int,X1_87: uni] :
( ( some(A_85,some_proj_11(A_85,nth1(A_85,X_86a,X1_87))) = nth1(A_85,X_86a,X1_87) )
| ( nth1(A_85,X_86a,X1_87) = none(A_85) ) ),
inference(resolution,[status(thm)],[c_818,c_749688]) ).
tff(c_763983,plain,
( ( nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = some(int,some_proj_11(int,some(int,t2tb2(0)))) )
| ( nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = none(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_763962,c_749735]) ).
tff(c_764055,plain,
( ( some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)) )
| ( some(int,t2tb2('#skF_4')) = none(int) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_816,c_749736,c_763983]) ).
tff(c_764057,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(negUnitSimplification,[status(thm)],[c_61,c_764055]) ).
tff(c_764179,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_764057,c_578929]) ).
tff(c_764214,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_764179]) ).
tff(c_764560,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_764214,c_810]) ).
tff(c_764578,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_764560]) ).
tff(c_764580,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_764578]) ).
tff(c_764583,plain,
$less('#skE_37',1),
inference(splitRight,[status(thm)],[c_763940]) ).
tff(c_764584,plain,
'#skE_37' != 0,
inference(splitRight,[status(thm)],[c_763940]) ).
tff(c_754761,plain,
'#skF_2'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = '#skE_37',
inference(define,[status(thm),theory(equality)],[c_754760]) ).
tff(c_754765,plain,
~ $less('#skE_37',0),
inference(demodulation,[status(thm),theory(equality)],[c_754761,c_754760]) ).
tff(c_764585,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_764583,c_764584,c_754765]) ).
tff(c_764589,plain,
'#skF_8' != $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_748719]) ).
tff(c_748021,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_677245]) ).
tff(c_773483,plain,
zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_764589,c_748227,c_748021]) ).
tff(c_773494,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_773483,c_807]) ).
tff(c_774544,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_773494,c_80]) ).
tff(c_774551,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_774544]) ).
tff(c_765295,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677004,c_677004,c_578821]) ).
tff(c_765296,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_7') ),
inference(negUnitSimplification,[status(thm)],[c_748022,c_748227,c_765295]) ).
tff(c_765298,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_765296]) ).
tff(c_765299,plain,
no_zero1('#skF_7'),
inference(splitLeft,[status(thm)],[c_765298]) ).
tff(c_769419,plain,
! [J_47005a: $int,L_47006: list_int] :
( ( tb2t(nth1(int,J_47005a,t2tb1(L_47006))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_47005a,length1(int,t2tb1(L_47006)))
| ~ no_zero1(L_47006)
| $less(J_47005a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_104]) ).
tff(c_769427,plain,
! [J_47005a: $int] :
( ( tb2t(nth1(int,J_47005a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_47005a,length1(int,t2tb1('#skF_7')))
| $less(J_47005a,0) ),
inference(resolution,[status(thm)],[c_765299,c_769419]) ).
tff(c_778177,plain,
! [J_47300a: $int] :
( ( tb2t(nth1(int,J_47300a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| ~ $less(J_47300a,'#skE_29')
| $less(J_47300a,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_677008,c_769427]) ).
tff(c_778181,plain,
( ~ $less($sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),'#skE_29')
| $less($sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),0) ),
inference(superposition,[status(thm),theory(equality)],[c_774551,c_778177]) ).
tff(c_778191,plain,
( ~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_778181]) ).
tff(c_778196,plain,
~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(negUnitSimplification,[status(thm)],[c_578800,c_778191]) ).
tff(c_778198,plain,
~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_778196]) ).
tff(c_197,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$difference('#skF_8','#skF_3'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 )
| ~ $lesseq('#skF_3','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_900,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_197]) ).
tff(c_578565,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_900]) ).
tff(c_578567,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',length1(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578565]) ).
tff(c_578577,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum('#skF_3',$sum(1,length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578567]) ).
tff(c_578579,plain,
( ( '#skF_5' != '#skF_7' )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578577]) ).
tff(c_771866,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677008,c_677004,c_677004,c_677004,c_578579]) ).
tff(c_771867,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| $less('#skF_8','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_748022,c_748227,c_771866]) ).
tff(c_771869,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_771867]) ).
tff(c_771870,plain,
~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitLeft,[status(thm)],[c_771869]) ).
tff(c_771872,plain,
~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_771870]) ).
tff(c_217,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))))
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_591,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_217]) ).
tff(c_890,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_591]) ).
tff(c_578505,plain,
( ( '#skF_5' != '#skF_7' )
| $less('#skF_8',$sum(1,$sum('#skF_3',length1(int,t2tb1('#skF_5')))))
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_890]) ).
tff(c_748024,plain,
( $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677008,c_677004,c_677008,c_677004,c_677004,c_578505]) ).
tff(c_748026,plain,
( $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_748024]) ).
tff(c_748028,plain,
'#skF_10' = 0,
inference(splitLeft,[status(thm)],[c_748026]) ).
tff(c_748036,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_748028,c_748022]) ).
tff(c_748037,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))) ),
inference(splitRight,[status(thm)],[c_748026]) ).
tff(c_748040,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_748037]) ).
tff(c_772615,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_771872,c_764589,c_748227,c_748040]) ).
tff(c_772617,plain,
$less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitRight,[status(thm)],[c_771869]) ).
tff(c_772621,plain,
$less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_772617]) ).
tff(c_778200,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_778198,c_772621]) ).
tff(c_778202,plain,
~ no_zero1('#skF_7'),
inference(splitRight,[status(thm)],[c_765298]) ).
tff(c_677005,plain,
( ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_579074]) ).
tff(c_781867,plain,
( ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| no_zero1('#skF_7')
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_677004,c_677004,c_677004,c_677005]) ).
tff(c_781869,plain,
zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_778202,c_748227,c_748022,c_781867]) ).
tff(c_781874,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_781869,c_807]) ).
tff(c_786792,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_781874,c_80]) ).
tff(c_786799,plain,
nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_786792]) ).
tff(c_786825,plain,
! [X_92: uni] :
( ( nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_7'))) = some(int,t2tb2(0)) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_786799,c_1038]) ).
tff(c_786847,plain,
! [X_92: uni] :
( ( nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_7'))) = some(int,t2tb2(0)) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_786825]) ).
tff(c_787977,plain,
'#skF_8' = '#skF_3',
inference(splitLeft,[status(thm)],[c_786847]) ).
tff(c_787993,plain,
~ $less('#skF_3',$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_787977,c_578800]) ).
tff(c_787999,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_787993]) ).
tff(c_788004,plain,
'#skF_8' != '#skF_3',
inference(splitRight,[status(thm)],[c_786847]) ).
tff(c_786796,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( $sum($uminus('#skF_3'),'#skF_8') = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_781874]) ).
tff(c_786802,plain,
! [X_92: uni] :
( ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( '#skF_8' = '#skF_3' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_786796]) ).
tff(c_789610,plain,
! [X_92: uni] : ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) ),
inference(negUnitSimplification,[status(thm)],[c_788004,c_786802]) ).
tff(c_789612,plain,
! [X_92: uni] : ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,X_92,t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_789610]) ).
tff(c_778201,plain,
$less('#skF_8',$sum(1,$sum('#skF_3','#skE_29'))),
inference(splitRight,[status(thm)],[c_765298]) ).
tff(c_778204,plain,
$less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_778201]) ).
tff(c_784207,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 )
| $less('#skF_8','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_578984,c_677004,c_677008,c_677004,c_677004,c_677004,c_578579]) ).
tff(c_784208,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| ~ $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| $less('#skF_8','#skF_3') ),
inference(negUnitSimplification,[status(thm)],[c_748022,c_748227,c_784207]) ).
tff(c_784210,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8'))
| ~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_784208]) ).
tff(c_784211,plain,
~ $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3'))),
inference(splitLeft,[status(thm)],[c_784210]) ).
tff(c_784214,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_778204,c_784211]) ).
tff(c_784215,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8'))
| $less('#skF_8','#skF_3') ),
inference(splitRight,[status(thm)],[c_784210]) ).
tff(c_784218,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))
| $less('#skF_8','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_784215]) ).
tff(c_784220,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),
inference(splitLeft,[status(thm)],[c_784218]) ).
tff(c_784222,plain,
~ zero_at1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_784220]) ).
tff(c_784234,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_784222]) ).
tff(c_784241,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),$sum($uminus('#skF_3'),'#skF_8'))
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_784234]) ).
tff(c_784243,plain,
( $less($sum('#skF_3','#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3')))),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_784241]) ).
tff(c_887643,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_38',
inference(define,[status(thm),theory(equality)],[c_784243]) ).
tff(c_887645,plain,
( $less($sum('#skF_3','#skE_38'),'#skF_8')
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_887643,c_784243]) ).
tff(c_887649,plain,
( $less($sum('#skE_38','#skF_3'),'#skF_8')
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_887645]) ).
tff(c_938713,plain,
$less($sum('#skE_38','#skF_3'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_789612,c_887649]) ).
tff(c_938715,plain,
$less($sum('#skF_3','#skE_38'),'#skF_8'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_938713]) ).
tff(c_784226,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_806,c_784222]) ).
tff(c_784235,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_86,c_784226]) ).
tff(c_784237,plain,
( ( tb2t(nth1(int,'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_784235]) ).
tff(c_889027,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_38',
inference(define,[status(thm),theory(equality)],[c_784237]) ).
tff(c_889029,plain,
( ( tb2t(nth1(int,'#skE_38',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_889027,c_784237]) ).
tff(c_889033,plain,
( ( tb2t(nth1(int,'#skE_38',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))) )
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_889029]) ).
tff(c_969811,plain,
tb2t(nth1(int,'#skE_38',cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_789612,c_889033]) ).
tff(c_781969,plain,
! [J_47555a: $int,L_47556: list_int,I_47557a: $int] :
( ( tb2t(nth1(int,J_47555a,t2tb1(L_47556))) != tb2t(some(int,t2tb2(0))) )
| ~ zero_at1(L_47556,I_47557a)
| $less(J_47555a,0)
| ~ $less(J_47555a,I_47557a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_93]) ).
tff(c_781973,plain,
! [J_47555a: $int] :
( ( tb2t(nth1(int,J_47555a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_47555a,0)
| ~ $less(J_47555a,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(resolution,[status(thm)],[c_781869,c_781969]) ).
tff(c_788510,plain,
! [J_47785a: $int] :
( ( tb2t(nth1(int,J_47785a,t2tb1('#skF_7'))) != tb2t(some(int,t2tb2(0))) )
| $less(J_47785a,0)
| ~ $less($sum(1,$sum('#skF_3',J_47785a)),'#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_781973]) ).
tff(c_788522,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| $less($sum($uminus(1),N_89a),0)
| ~ $less($sum(1,$sum('#skF_3',$sum($uminus(1),N_89a))),'#skF_8')
| ( N_89a = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1038,c_788510]) ).
tff(c_788532,plain,
! [N_89a: $int,X_92: uni] :
( ( tb2t(nth1(int,N_89a,cons(int,X_92,t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) )
| $less(N_89a,1)
| ~ $less($sum('#skF_3',N_89a),'#skF_8')
| ( N_89a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_788522]) ).
tff(c_969842,plain,
( $less('#skE_38',1)
| ~ $less($sum('#skF_3','#skE_38'),'#skF_8')
| ( '#skE_38' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_969811,c_788532]) ).
tff(c_969872,plain,
( $less('#skE_38',1)
| ( '#skE_38' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_938715,c_969842]) ).
tff(c_969880,plain,
'#skE_38' = 0,
inference(splitLeft,[status(thm)],[c_969872]) ).
tff(c_969882,plain,
tb2t(nth1(int,0,cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_969880,c_969811]) ).
tff(c_969893,plain,
tb2t(some(int,t2tb2('#skF_4'))) = tb2t(some(int,t2tb2(0))),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_969882]) ).
tff(c_969903,plain,
some(int,t2tb2('#skF_4')) = t2tb(tb2t(some(int,t2tb2(0)))),
inference(superposition,[status(thm),theory(equality)],[c_969893,c_80]) ).
tff(c_969907,plain,
some(int,t2tb2('#skF_4')) = some(int,t2tb2(0)),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_969903]) ).
tff(c_970006,plain,
some_proj_11(int,some(int,t2tb2(0))) = t2tb2('#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_969907,c_578929]) ).
tff(c_970048,plain,
t2tb2('#skF_4') = t2tb2(0),
inference(demodulation,[status(thm),theory(equality)],[c_578929,c_970006]) ).
tff(c_970138,plain,
tb2t2(t2tb2(0)) = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_970048,c_810]) ).
tff(c_970168,plain,
'#skF_4' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_810,c_970138]) ).
tff(c_970170,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_578748,c_970168]) ).
tff(c_970173,plain,
$less('#skE_38',1),
inference(splitRight,[status(thm)],[c_969872]) ).
tff(c_970174,plain,
'#skE_38' != 0,
inference(splitRight,[status(thm)],[c_969872]) ).
tff(c_784230,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_784222]) ).
tff(c_784238,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum($uminus('#skF_3'),'#skF_8')),0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_784230]) ).
tff(c_784240,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))),0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_784238]) ).
tff(c_882873,plain,
'#skF_1'(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))),$sum('#skF_8',$uminus('#skF_3'))) = '#skE_38',
inference(define,[status(thm),theory(equality)],[c_784240]) ).
tff(c_882875,plain,
( ~ $less('#skE_38',0)
| ( tb2t(nth1(int,$sum('#skF_8',$uminus('#skF_3')),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_882873,c_784240]) ).
tff(c_882879,plain,
( ~ $less('#skE_38',0)
| ( tb2t(nth1(int,$sum($uminus('#skF_3'),'#skF_8'),cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_882875]) ).
tff(c_910564,plain,
~ $less('#skE_38',0),
inference(demodulation,[status(thm),theory(equality)],[c_789612,c_882879]) ).
tff(c_970175,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_970173,c_970174,c_910564]) ).
tff(c_970178,plain,
$less('#skF_8','#skF_3'),
inference(splitRight,[status(thm)],[c_784218]) ).
tff(c_970181,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_970178,c_578800]) ).
tff(c_970185,plain,
$less('#skF_8',$sum(1,'#skF_3')),
inference(splitRight,[status(thm)],[c_578520]) ).
tff(c_970530,plain,
! [A_53284: ty,L_53285: uni] :
( ( nil(A_53284) = L_53285 )
| ( length1(A_53284,L_53285) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_970538,plain,
( ( t2tb1('#skF_5') = nil(int) )
| ( '#skE_29' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_970530]) ).
tff(c_970550,plain,
'#skE_29' != 0,
inference(splitLeft,[status(thm)],[c_970538]) ).
tff(c_211,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 )
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_893,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_211]) ).
tff(c_578359,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_893]) ).
tff(c_970225,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_578359]) ).
tff(c_970226,plain,
~ no_zero1(tb2t1(nil(int))),
inference(splitLeft,[status(thm)],[c_970225]) ).
tff(c_970231,plain,
~ $less('#skF_2'(tb2t1(nil(int))),0),
inference(resolution,[status(thm)],[c_800,c_970226]) ).
tff(c_970232,plain,
'#skF_2'(tb2t1(nil(int))) = '#skE_30',
inference(define,[status(thm),theory(equality)],[c_970231]) ).
tff(c_970236,plain,
~ $less('#skE_30',0),
inference(demodulation,[status(thm),theory(equality)],[c_970232,c_970231]) ).
tff(c_970235,plain,
'#skF_2'(tb2t1(nil(int))) = '#skE_30',
inference(define,[status(thm),theory(equality)],[c_970231]) ).
tff(c_970488,plain,
! [L_53276: list_int] :
( $less('#skF_2'(L_53276),length1(int,t2tb1(L_53276)))
| no_zero1(L_53276) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_970492,plain,
$less('#skF_2'(tb2t1(nil(int))),length1(int,t2tb1(tb2t1(nil(int))))),
inference(resolution,[status(thm)],[c_970488,c_970226]) ).
tff(c_970493,plain,
$less('#skE_30',0),
inference(demodulation,[status(thm),theory(equality)],[c_970235,c_819,c_86,c_970492]) ).
tff(c_970495,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_970236,c_970493]) ).
tff(c_970497,plain,
no_zero1(tb2t1(nil(int))),
inference(splitRight,[status(thm)],[c_970225]) ).
tff(c_970521,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_970497,c_970205,c_578535]) ).
tff(c_970523,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_970521]) ).
tff(c_970525,plain,
'#skF_10' = 0,
inference(splitLeft,[status(thm)],[c_970523]) ).
tff(c_137,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))) != '#skF_9' )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_927,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_137]) ).
tff(c_578264,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_927]) ).
tff(c_578658,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum(1,length1(int,t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578264]) ).
tff(c_578660,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) )
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578658]) ).
tff(c_974998,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_970525,c_578660]) ).
tff(c_975002,plain,
length1(int,t2tb1('#skF_11')) = '#skE_31',
inference(define,[status(thm),theory(equality)],[c_974998]) ).
tff(c_975013,plain,
( ( t2tb1('#skF_11') = nil(int) )
| ( '#skE_31' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_975002,c_820]) ).
tff(c_975018,plain,
'#skE_31' != 0,
inference(splitLeft,[status(thm)],[c_975013]) ).
tff(c_177,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9')
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_909,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_177]) ).
tff(c_578309,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_909]) ).
tff(c_578676,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578309]) ).
tff(c_578678,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578676]) ).
tff(c_991066,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_975002,c_970525,c_578678]) ).
tff(c_991068,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_991066]) ).
tff(c_971912,plain,
! [A_53420: ty,U_53421: uni] :
( ( cons(A_53420,cons_proj_11(A_53420,U_53421),cons_proj_21(A_53420,U_53421)) = U_53421 )
| ( nil(A_53420) = U_53421 ) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_971921,plain,
! [A_53420: ty,U_53421: uni] :
( ( $sum(1,length1(A_53420,cons_proj_21(A_53420,U_53421))) = length1(A_53420,U_53421) )
| ( nil(A_53420) = U_53421 ) ),
inference(superposition,[status(thm),theory(equality)],[c_971912,c_822]) ).
tff(c_975482,plain,
! [A_53634: ty,U_53635: uni] :
( ( length1(A_53634,cons_proj_21(A_53634,U_53635)) = $sum($uminus(1),length1(A_53634,U_53635)) )
| ( nil(A_53634) = U_53635 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_971921]) ).
tff(c_975490,plain,
! [A_53634: ty,U_53635: uni] :
( ~ $less($sum($uminus(1),length1(A_53634,U_53635)),0)
| ( nil(A_53634) = U_53635 ) ),
inference(superposition,[status(thm),theory(equality)],[c_975482,c_821]) ).
tff(c_975509,plain,
! [A_53636: ty,U_53637: uni] :
( ~ $less(length1(A_53636,U_53637),1)
| ( nil(A_53636) = U_53637 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_975490]) ).
tff(c_975527,plain,
( ~ $less('#skE_31',1)
| ( t2tb1('#skF_11') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_975002,c_975509]) ).
tff(c_975553,plain,
~ $less('#skE_31',1),
inference(splitLeft,[status(thm)],[c_975527]) ).
tff(c_991069,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_991068,c_975553]) ).
tff(c_991072,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_991066]) ).
tff(c_991490,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_991072]) ).
tff(c_991498,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_991490]) ).
tff(c_991508,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_991498]) ).
tff(c_991512,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_991508]) ).
tff(c_991516,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_991512,c_991508]) ).
tff(c_991502,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_991490]) ).
tff(c_991511,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_991502]) ).
tff(c_991522,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_991511]) ).
tff(c_991524,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_991522,c_991511]) ).
tff(c_991527,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_991516,c_991524]) ).
tff(c_991530,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(splitRight,[status(thm)],[c_991072]) ).
tff(c_991733,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_991530]) ).
tff(c_991737,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_991733,c_86]) ).
tff(c_991740,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_991737]) ).
tff(c_991742,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_991740]) ).
tff(c_991746,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_991530]) ).
tff(c_175,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9')
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_910,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_175]) ).
tff(c_578258,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_910]) ).
tff(c_578571,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578258]) ).
tff(c_578573,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578571]) ).
tff(c_975288,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_975002,c_970525,c_578573]) ).
tff(c_975290,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_975288]) ).
tff(c_975014,plain,
~ $less('#skE_31',0),
inference(superposition,[status(thm),theory(equality)],[c_975002,c_821]) ).
tff(c_975291,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_975290,c_975014]) ).
tff(c_975294,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( '#skF_5' != '#skF_7' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5') ),
inference(splitRight,[status(thm)],[c_975288]) ).
tff(c_990018,plain,
'#skF_5' != '#skF_7',
inference(splitLeft,[status(thm)],[c_975294]) ).
tff(c_991745,plain,
( no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_991530]) ).
tff(c_992355,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitLeft,[status(thm)],[c_991745]) ).
tff(c_992359,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_992355,c_86]) ).
tff(c_992363,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_992359]) ).
tff(c_992422,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_992363,c_36]) ).
tff(c_992511,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_992422,c_36]) ).
tff(c_992559,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_992511,c_84]) ).
tff(c_992562,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_992559]) ).
tff(c_992564,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_990018,c_992562]) ).
tff(c_992567,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) != tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_991745]) ).
tff(c_991531,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_991072]) ).
tff(c_976216,plain,
'#skF_5' != '#skF_7',
inference(splitLeft,[status(thm)],[c_975294]) ).
tff(c_977856,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_975002,c_970525,c_578678]) ).
tff(c_977858,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_977856]) ).
tff(c_977859,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_977858,c_975553]) ).
tff(c_977862,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_977856]) ).
tff(c_977864,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_977862]) ).
tff(c_977872,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_977864]) ).
tff(c_977882,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_977872]) ).
tff(c_977886,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_977882]) ).
tff(c_977890,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_977886,c_977882]) ).
tff(c_977876,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_977864]) ).
tff(c_977885,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_977876]) ).
tff(c_977896,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_977885]) ).
tff(c_977898,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_977896,c_977885]) ).
tff(c_977901,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_977890,c_977898]) ).
tff(c_977904,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(splitRight,[status(thm)],[c_977862]) ).
tff(c_978375,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_977904]) ).
tff(c_978379,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_978375,c_86]) ).
tff(c_978382,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_978379]) ).
tff(c_978384,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_978382]) ).
tff(c_978388,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_977904]) ).
tff(c_978387,plain,
( no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_977904]) ).
tff(c_978390,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitLeft,[status(thm)],[c_978387]) ).
tff(c_978400,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_978390,c_86]) ).
tff(c_978404,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_978400]) ).
tff(c_978467,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_978404,c_36]) ).
tff(c_978539,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_978467,c_36]) ).
tff(c_978565,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_978539,c_84]) ).
tff(c_978568,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_978565]) ).
tff(c_978570,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_976216,c_978568]) ).
tff(c_978573,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) != tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_978387]) ).
tff(c_977905,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_977862]) ).
tff(c_189,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9')
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_649,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_189]) ).
tff(c_903,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_649]) ).
tff(c_578379,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_903]) ).
tff(c_578604,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578379]) ).
tff(c_578606,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578604]) ).
tff(c_982013,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_975002,c_977905,c_970525,c_970205,c_578606]) ).
tff(c_982014,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_978388,c_978573,c_982013]) ).
tff(c_982016,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_982014]) ).
tff(c_982018,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_982016]) ).
tff(c_971967,plain,
! [A_53420: ty,U_53421: uni] :
( ( length1(A_53420,cons_proj_21(A_53420,U_53421)) = $sum($uminus(1),length1(A_53420,U_53421)) )
| ( nil(A_53420) = U_53421 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_971921]) ).
tff(c_975512,plain,
! [A_53420: ty,U_53421: uni] :
( ~ $less($sum($uminus(1),length1(A_53420,U_53421)),1)
| ( cons_proj_21(A_53420,U_53421) = nil(A_53420) )
| ( nil(A_53420) = U_53421 ) ),
inference(superposition,[status(thm),theory(equality)],[c_971967,c_975509]) ).
tff(c_975580,plain,
! [A_53643: ty,U_53644: uni] :
( ~ $less(length1(A_53643,U_53644),2)
| ( cons_proj_21(A_53643,U_53644) = nil(A_53643) )
| ( nil(A_53643) = U_53644 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_975512]) ).
tff(c_975598,plain,
( ~ $less('#skE_31',2)
| ( cons_proj_21(int,t2tb1('#skF_11')) = nil(int) )
| ( t2tb1('#skF_11') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_975002,c_975580]) ).
tff(c_979806,plain,
~ $less('#skE_31',2),
inference(splitLeft,[status(thm)],[c_975598]) ).
tff(c_982019,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_982018,c_979806]) ).
tff(c_982022,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_982016]) ).
tff(c_982023,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_982022,c_970185]) ).
tff(c_982026,plain,
$less('#skE_29',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_982023]) ).
tff(c_975603,plain,
( ~ $less('#skE_29',2)
| ( cons_proj_21(int,t2tb1('#skF_5')) = nil(int) )
| ( t2tb1('#skF_5') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_975580]) ).
tff(c_976220,plain,
~ $less('#skE_29',2),
inference(splitLeft,[status(thm)],[c_975603]) ).
tff(c_982027,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_982026,c_976220]) ).
tff(c_982030,plain,
$less('#skE_31',2),
inference(splitRight,[status(thm)],[c_975598]) ).
tff(c_975488,plain,
! [A_53634: ty,U_53635: uni] :
( ( cons_proj_21(A_53634,U_53635) = nil(A_53634) )
| ( $sum($uminus(1),length1(A_53634,U_53635)) != 0 )
| ( nil(A_53634) = U_53635 ) ),
inference(superposition,[status(thm),theory(equality)],[c_975482,c_820]) ).
tff(c_975554,plain,
! [A_53641: ty,U_53642: uni] :
( ( cons_proj_21(A_53641,U_53642) = nil(A_53641) )
| ( length1(A_53641,U_53642) != 1 )
| ( nil(A_53641) = U_53642 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_975488]) ).
tff(c_975572,plain,
( ( cons_proj_21(int,t2tb1('#skF_11')) = nil(int) )
| ( '#skE_31' != 1 )
| ( t2tb1('#skF_11') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_975002,c_975554]) ).
tff(c_977853,plain,
'#skE_31' != 1,
inference(splitLeft,[status(thm)],[c_975572]) ).
tff(c_982031,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_982030,c_977853,c_975553]) ).
tff(c_982034,plain,
'#skE_31' = 1,
inference(splitRight,[status(thm)],[c_975572]) ).
tff(c_982040,plain,
length1(int,t2tb1('#skF_11')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_982034,c_975002]) ).
tff(c_982087,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_982040,c_970525,c_578678]) ).
tff(c_982089,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_982087]) ).
tff(c_982091,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_982089]) ).
tff(c_982099,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_982091]) ).
tff(c_982109,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_982099]) ).
tff(c_982115,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_982109]) ).
tff(c_982119,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_982115,c_982109]) ).
tff(c_982118,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_982109]) ).
tff(c_982103,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_982091]) ).
tff(c_982112,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_982103]) ).
tff(c_982126,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_982118,c_982112]) ).
tff(c_982127,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_982119,c_982126]) ).
tff(c_982131,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_982089]) ).
tff(c_982433,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_970497,c_982040,c_982131,c_970525,c_970205,c_578618]) ).
tff(c_982434,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skE_29','#skF_3')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_982433]) ).
tff(c_982436,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| $less('#skF_8',$sum(1,$sum('#skF_3','#skE_29')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_982434]) ).
tff(c_982438,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_982436]) ).
tff(c_982442,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_982438,c_86]) ).
tff(c_982445,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_982442]) ).
tff(c_982447,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_982445]) ).
tff(c_982452,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_982436]) ).
tff(c_986338,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_982040,c_982131,c_970525,c_970205,c_578606]) ).
tff(c_986339,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),1) ),
inference(negUnitSimplification,[status(thm)],[c_982452,c_986338]) ).
tff(c_986341,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_986339]) ).
tff(c_986343,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_986341]) ).
tff(c_986344,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_986343,c_970185]) ).
tff(c_986347,plain,
$less('#skE_29',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_986344]) ).
tff(c_986348,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_986347,c_976220]) ).
tff(c_986351,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_986341]) ).
tff(c_986361,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_986351,c_86]) ).
tff(c_986365,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_986361]) ).
tff(c_986432,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_986365,c_36]) ).
tff(c_986514,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_986432,c_36]) ).
tff(c_986540,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_986514,c_84]) ).
tff(c_986543,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_986540]) ).
tff(c_986545,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_976216,c_986543]) ).
tff(c_986548,plain,
$less('#skE_29',2),
inference(splitRight,[status(thm)],[c_975603]) ).
tff(c_975577,plain,
( ( cons_proj_21(int,t2tb1('#skF_5')) = nil(int) )
| ( '#skE_29' != 1 )
| ( t2tb1('#skF_5') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_975554]) ).
tff(c_975901,plain,
'#skE_29' != 1,
inference(splitLeft,[status(thm)],[c_975577]) ).
tff(c_975531,plain,
( ~ $less('#skE_29',1)
| ( t2tb1('#skF_5') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_975509]) ).
tff(c_975546,plain,
~ $less('#skE_29',1),
inference(splitLeft,[status(thm)],[c_975531]) ).
tff(c_986551,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_986548,c_975901,c_975546]) ).
tff(c_986553,plain,
'#skF_5' = '#skF_7',
inference(splitRight,[status(thm)],[c_975294]) ).
tff(c_986554,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(splitRight,[status(thm)],[c_975294]) ).
tff(c_986587,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_986553,c_986553,c_986554]) ).
tff(c_986589,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_986587]) ).
tff(c_986593,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_986589]) ).
tff(c_986600,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_986593]) ).
tff(c_986604,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_986600]) ).
tff(c_986608,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_986604,c_986600]) ).
tff(c_986597,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_986589]) ).
tff(c_986603,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_986597]) ).
tff(c_986613,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_986603]) ).
tff(c_986615,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_986613,c_986603]) ).
tff(c_986618,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_986608,c_986615]) ).
tff(c_986622,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_986587]) ).
tff(c_986557,plain,
length1(int,t2tb1('#skF_7')) = '#skE_29',
inference(demodulation,[status(thm),theory(equality)],[c_986553,c_970205]) ).
tff(c_187,plain,
( ( '#skF_5' != '#skF_7' )
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9')
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_654,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_187]) ).
tff(c_904,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_654]) ).
tff(c_578303,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_904]) ).
tff(c_578667,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578303]) ).
tff(c_578669,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578667]) ).
tff(c_989966,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_975002,c_986622,c_970525,c_986553,c_986557,c_986553,c_986553,c_578669]) ).
tff(c_989968,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_989966]) ).
tff(c_989970,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_989968]) ).
tff(c_989971,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_989970,c_975553]) ).
tff(c_989974,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(splitRight,[status(thm)],[c_989968]) ).
tff(c_989981,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_989974]) ).
tff(c_989982,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_989981,c_970185]) ).
tff(c_989985,plain,
$less('#skE_29',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_989982]) ).
tff(c_986846,plain,
( ~ $less('#skE_29',2)
| ( cons_proj_21(int,t2tb1('#skF_7')) = nil(int) )
| ( t2tb1('#skF_7') = nil(int) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_986553,c_986553,c_975603]) ).
tff(c_986848,plain,
~ $less('#skE_29',2),
inference(splitLeft,[status(thm)],[c_986846]) ).
tff(c_989986,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_989985,c_986848]) ).
tff(c_989989,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_989974]) ).
tff(c_989999,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_989989,c_86]) ).
tff(c_990002,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_989999]) ).
tff(c_990004,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_990002]) ).
tff(c_990007,plain,
$less('#skE_29',2),
inference(splitRight,[status(thm)],[c_986846]) ).
tff(c_990008,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_990007,c_975901,c_975546]) ).
tff(c_990011,plain,
'#skE_29' = 1,
inference(splitRight,[status(thm)],[c_975577]) ).
tff(c_990017,plain,
length1(int,t2tb1('#skF_5')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_990011,c_970205]) ).
tff(c_996786,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_975002,c_991531,c_970525,c_990017,c_578606]) ).
tff(c_996787,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ~ $less($uminus(1),'#skE_31') ),
inference(negUnitSimplification,[status(thm)],[c_991746,c_992567,c_996786]) ).
tff(c_996789,plain,
( ( '#skF_8' = $sum(2,'#skF_3') )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_996787]) ).
tff(c_996791,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_996789]) ).
tff(c_995086,plain,
~ $less('#skE_31',2),
inference(splitLeft,[status(thm)],[c_975598]) ).
tff(c_996792,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_996791,c_995086]) ).
tff(c_996795,plain,
'#skF_8' = $sum(2,'#skF_3'),
inference(splitRight,[status(thm)],[c_996789]) ).
tff(c_996796,plain,
$less($sum(2,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_996795,c_970185]) ).
tff(c_996799,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_996796]) ).
tff(c_996802,plain,
$less('#skE_31',2),
inference(splitRight,[status(thm)],[c_975598]) ).
tff(c_993056,plain,
'#skE_31' != 1,
inference(splitLeft,[status(thm)],[c_975572]) ).
tff(c_996803,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_996802,c_993056,c_975553]) ).
tff(c_996806,plain,
'#skE_31' = 1,
inference(splitRight,[status(thm)],[c_975572]) ).
tff(c_996815,plain,
length1(int,t2tb1('#skF_11')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_996806,c_975002]) ).
tff(c_999987,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_996815,c_991531,c_970525,c_990017,c_578606]) ).
tff(c_999988,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ~ $less($uminus(1),1) ),
inference(negUnitSimplification,[status(thm)],[c_991746,c_992567,c_999987]) ).
tff(c_999990,plain,
'#skF_8' = $sum(2,'#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_999988]) ).
tff(c_999991,plain,
$less($sum(2,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_999990,c_970185]) ).
tff(c_999994,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_999991]) ).
tff(c_999996,plain,
'#skF_5' = '#skF_7',
inference(splitRight,[status(thm)],[c_975294]) ).
tff(c_999997,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(splitRight,[status(thm)],[c_975294]) ).
tff(c_1000066,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_999996,c_999996,c_999997]) ).
tff(c_1000068,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_1000066]) ).
tff(c_1000072,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_1000068]) ).
tff(c_1000079,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1000072]) ).
tff(c_1000390,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1000079]) ).
tff(c_1000394,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1000390,c_1000079]) ).
tff(c_1000076,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_1000068]) ).
tff(c_1000082,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1000076]) ).
tff(c_1000395,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1000082]) ).
tff(c_1000397,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1000395,c_1000082]) ).
tff(c_1000400,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1000394,c_1000397]) ).
tff(c_1000404,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_1000066]) ).
tff(c_1000003,plain,
length1(int,t2tb1('#skF_7')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_999996,c_990017]) ).
tff(c_1003323,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_975002,c_1000404,c_970525,c_999996,c_1000003,c_999996,c_999996,c_578669]) ).
tff(c_1003325,plain,
( ( '#skF_8' = $sum(2,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1003323]) ).
tff(c_1003327,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_1003325]) ).
tff(c_1003328,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1003327,c_975553]) ).
tff(c_1003331,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_8' = $sum(2,'#skF_3') ) ),
inference(splitRight,[status(thm)],[c_1003325]) ).
tff(c_1003333,plain,
'#skF_8' = $sum(2,'#skF_3'),
inference(splitLeft,[status(thm)],[c_1003331]) ).
tff(c_1003334,plain,
$less($sum(2,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1003333,c_970185]) ).
tff(c_1003337,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1003334]) ).
tff(c_1003340,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_1003331]) ).
tff(c_1003349,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_1003340,c_86]) ).
tff(c_1003352,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1003349]) ).
tff(c_1003354,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1003352]) ).
tff(c_1003355,plain,
t2tb1('#skF_11') = nil(int),
inference(splitRight,[status(thm)],[c_975527]) ).
tff(c_1003359,plain,
length1(int,nil(int)) = '#skE_31',
inference(demodulation,[status(thm),theory(equality)],[c_1003355,c_975002]) ).
tff(c_1003360,plain,
'#skE_31' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_819,c_1003359]) ).
tff(c_1003362,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_975018,c_1003360]) ).
tff(c_1003363,plain,
t2tb1('#skF_5') = nil(int),
inference(splitRight,[status(thm)],[c_975531]) ).
tff(c_1003367,plain,
length1(int,nil(int)) = '#skE_29',
inference(demodulation,[status(thm),theory(equality)],[c_1003363,c_970205]) ).
tff(c_1003368,plain,
'#skE_29' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_819,c_1003367]) ).
tff(c_1003370,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_970550,c_1003368]) ).
tff(c_1003371,plain,
t2tb1('#skF_11') = nil(int),
inference(splitRight,[status(thm)],[c_975013]) ).
tff(c_1003381,plain,
tb2t1(nil(int)) = '#skF_11',
inference(superposition,[status(thm),theory(equality)],[c_1003371,c_84]) ).
tff(c_1003391,plain,
no_zero1('#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_1003381,c_970497]) ).
tff(c_1003404,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0)
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1003391,c_1003381,c_819,c_1003371,c_1003371,c_970525,c_1003381,c_578573]) ).
tff(c_1003406,plain,
( ( '#skF_5' != '#skF_7' )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1003404]) ).
tff(c_1003408,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0),
inference(splitLeft,[status(thm)],[c_1003406]) ).
tff(c_1003413,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),nil(int)))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_1003408]) ).
tff(c_1003420,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1003413]) ).
tff(c_1003424,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0) = '#skE_41',
inference(define,[status(thm),theory(equality)],[c_1003420]) ).
tff(c_1003428,plain,
~ $less('#skE_41',0),
inference(demodulation,[status(thm),theory(equality)],[c_1003424,c_1003420]) ).
tff(c_1003417,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),nil(int)))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_1003408]) ).
tff(c_1003423,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1003417]) ).
tff(c_1003429,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0) = '#skE_41',
inference(define,[status(thm),theory(equality)],[c_1003423]) ).
tff(c_1003431,plain,
$less('#skE_41',0),
inference(demodulation,[status(thm),theory(equality)],[c_1003429,c_1003423]) ).
tff(c_1003434,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1003428,c_1003431]) ).
tff(c_1003437,plain,
( ( '#skF_5' != '#skF_7' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' )
| no_zero1('#skF_5') ),
inference(splitRight,[status(thm)],[c_1003406]) ).
tff(c_1003462,plain,
'#skF_5' != '#skF_7',
inference(splitLeft,[status(thm)],[c_1003437]) ).
tff(c_1003438,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0),
inference(splitRight,[status(thm)],[c_1003406]) ).
tff(c_1010790,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1003391,c_1003381,c_819,c_1003371,c_1003438,c_970525,c_1003371,c_1003381,c_578678]) ).
tff(c_1010792,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1010790]) ).
tff(c_1010794,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11',
inference(splitLeft,[status(thm)],[c_1010792]) ).
tff(c_1010798,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1('#skF_11'),
inference(superposition,[status(thm),theory(equality)],[c_1010794,c_86]) ).
tff(c_1010801,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1003371,c_1010798]) ).
tff(c_1010803,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1010801]) ).
tff(c_1010807,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != '#skF_11',
inference(splitRight,[status(thm)],[c_1010792]) ).
tff(c_1005864,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1003391,c_1003381,c_819,c_1003371,c_1003438,c_970525,c_1003371,c_1003381,c_578678]) ).
tff(c_1005866,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1005864]) ).
tff(c_1005868,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11',
inference(splitLeft,[status(thm)],[c_1005866]) ).
tff(c_1005872,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1('#skF_11'),
inference(superposition,[status(thm),theory(equality)],[c_1005868,c_86]) ).
tff(c_1005875,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1003371,c_1005872]) ).
tff(c_1005877,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1005875]) ).
tff(c_1005881,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != '#skF_11',
inference(splitRight,[status(thm)],[c_1005866]) ).
tff(c_1009964,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1003391,c_1003381,c_819,c_1003371,c_1003438,c_970525,c_1003371,c_1003381,c_970205,c_578606]) ).
tff(c_1009965,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_1005881,c_1009964]) ).
tff(c_1009967,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1009965]) ).
tff(c_1009969,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_1009967]) ).
tff(c_1009970,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1009969,c_970185]) ).
tff(c_1009973,plain,
$less('#skE_29',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1009970]) ).
tff(c_1004177,plain,
! [A_54576: ty,U_54577: uni] :
( ( length1(A_54576,cons_proj_21(A_54576,U_54577)) = $sum($uminus(1),length1(A_54576,U_54577)) )
| ( nil(A_54576) = U_54577 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_971921]) ).
tff(c_1004185,plain,
! [A_54576: ty,U_54577: uni] :
( ~ $less($sum($uminus(1),length1(A_54576,U_54577)),0)
| ( nil(A_54576) = U_54577 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1004177,c_821]) ).
tff(c_1004204,plain,
! [A_54578: ty,U_54579: uni] :
( ~ $less(length1(A_54578,U_54579),1)
| ( nil(A_54578) = U_54579 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1004185]) ).
tff(c_1004207,plain,
! [A_53420: ty,U_53421: uni] :
( ~ $less($sum($uminus(1),length1(A_53420,U_53421)),1)
| ( cons_proj_21(A_53420,U_53421) = nil(A_53420) )
| ( nil(A_53420) = U_53421 ) ),
inference(superposition,[status(thm),theory(equality)],[c_971967,c_1004204]) ).
tff(c_1004262,plain,
! [A_54584: ty,U_54585: uni] :
( ~ $less(length1(A_54584,U_54585),2)
| ( cons_proj_21(A_54584,U_54585) = nil(A_54584) )
| ( nil(A_54584) = U_54585 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1004207]) ).
tff(c_1004281,plain,
( ~ $less('#skE_29',2)
| ( cons_proj_21(int,t2tb1('#skF_5')) = nil(int) )
| ( t2tb1('#skF_5') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_1004262]) ).
tff(c_1004825,plain,
~ $less('#skE_29',2),
inference(splitLeft,[status(thm)],[c_1004281]) ).
tff(c_1009974,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1009973,c_1004825]) ).
tff(c_1009977,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_1009967]) ).
tff(c_1009982,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_1009977,c_86]) ).
tff(c_1009986,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1009982]) ).
tff(c_1010053,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1009986,c_36]) ).
tff(c_1010136,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1010053,c_36]) ).
tff(c_1010162,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_1010136,c_84]) ).
tff(c_1010165,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_1010162]) ).
tff(c_1010167,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1003462,c_1010165]) ).
tff(c_1010170,plain,
$less('#skE_29',2),
inference(splitRight,[status(thm)],[c_1004281]) ).
tff(c_1004183,plain,
! [A_54576: ty,U_54577: uni] :
( ( cons_proj_21(A_54576,U_54577) = nil(A_54576) )
| ( $sum($uminus(1),length1(A_54576,U_54577)) != 0 )
| ( nil(A_54576) = U_54577 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1004177,c_820]) ).
tff(c_1004238,plain,
! [A_54582: ty,U_54583: uni] :
( ( cons_proj_21(A_54582,U_54583) = nil(A_54582) )
| ( length1(A_54582,U_54583) != 1 )
| ( nil(A_54582) = U_54583 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1004183]) ).
tff(c_1004257,plain,
( ( cons_proj_21(int,t2tb1('#skF_5')) = nil(int) )
| ( '#skE_29' != 1 )
| ( t2tb1('#skF_5') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_1004238]) ).
tff(c_1004261,plain,
'#skE_29' != 1,
inference(splitLeft,[status(thm)],[c_1004257]) ).
tff(c_1004222,plain,
( ~ $less('#skE_29',1)
| ( t2tb1('#skF_5') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_970205,c_1004204]) ).
tff(c_1004226,plain,
~ $less('#skE_29',1),
inference(splitLeft,[status(thm)],[c_1004222]) ).
tff(c_1010171,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1010170,c_1004261,c_1004226]) ).
tff(c_1010174,plain,
'#skE_29' = 1,
inference(splitRight,[status(thm)],[c_1004257]) ).
tff(c_1010180,plain,
length1(int,t2tb1('#skF_5')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_1010174,c_970205]) ).
tff(c_1015506,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1003391,c_1003381,c_819,c_1003371,c_1003438,c_970525,c_1003371,c_1003381,c_1010180,c_578606]) ).
tff(c_1015507,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_1010807,c_1015506]) ).
tff(c_1015509,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( '#skF_8' = $sum(2,'#skF_3') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1015507]) ).
tff(c_1015511,plain,
'#skF_8' = $sum(2,'#skF_3'),
inference(splitLeft,[status(thm)],[c_1015509]) ).
tff(c_1015512,plain,
$less($sum(2,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1015511,c_970185]) ).
tff(c_1015515,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1015512]) ).
tff(c_1015518,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_1015509]) ).
tff(c_1015586,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_1015518,c_86]) ).
tff(c_1015590,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1015586]) ).
tff(c_1015658,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1015590,c_36]) ).
tff(c_1015740,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1015658,c_36]) ).
tff(c_1015795,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_1015740,c_84]) ).
tff(c_1015798,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_1015795]) ).
tff(c_1015800,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1003462,c_1015798]) ).
tff(c_1015801,plain,
t2tb1('#skF_5') = nil(int),
inference(splitRight,[status(thm)],[c_1004222]) ).
tff(c_1015805,plain,
length1(int,nil(int)) = '#skE_29',
inference(demodulation,[status(thm),theory(equality)],[c_1015801,c_970205]) ).
tff(c_1015806,plain,
'#skE_29' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_819,c_1015805]) ).
tff(c_1015808,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_970550,c_1015806]) ).
tff(c_1015810,plain,
'#skF_5' = '#skF_7',
inference(splitRight,[status(thm)],[c_1003437]) ).
tff(c_1015811,plain,
( no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = '#skF_11' ) ),
inference(splitRight,[status(thm)],[c_1003437]) ).
tff(c_1015835,plain,
( no_zero1('#skF_7')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1015810,c_1015810,c_1015811]) ).
tff(c_1015837,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11',
inference(splitLeft,[status(thm)],[c_1015835]) ).
tff(c_1015841,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1('#skF_11'),
inference(superposition,[status(thm),theory(equality)],[c_1015837,c_86]) ).
tff(c_1015844,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1003371,c_1015841]) ).
tff(c_1015846,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1015844]) ).
tff(c_1015849,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) != '#skF_11',
inference(splitRight,[status(thm)],[c_1015835]) ).
tff(c_1015818,plain,
length1(int,t2tb1('#skF_7')) = '#skE_29',
inference(demodulation,[status(thm),theory(equality)],[c_1015810,c_970205]) ).
tff(c_1019300,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1003391,c_1003381,c_819,c_1003371,c_1003438,c_970525,c_1003371,c_1003381,c_1015810,c_1015818,c_1015810,c_1015810,c_578669]) ).
tff(c_1019301,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_1015849,c_1019300]) ).
tff(c_1019303,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1019301]) ).
tff(c_1019304,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1019303,c_970185]) ).
tff(c_1019307,plain,
$less('#skE_29',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1019304]) ).
tff(c_1016241,plain,
! [A_54982: ty,U_54983: uni] :
( ( length1(A_54982,cons_proj_21(A_54982,U_54983)) = $sum($uminus(1),length1(A_54982,U_54983)) )
| ( nil(A_54982) = U_54983 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_971921]) ).
tff(c_1016249,plain,
! [A_54982: ty,U_54983: uni] :
( ~ $less($sum($uminus(1),length1(A_54982,U_54983)),0)
| ( nil(A_54982) = U_54983 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1016241,c_821]) ).
tff(c_1016268,plain,
! [A_54984: ty,U_54985: uni] :
( ~ $less(length1(A_54984,U_54985),1)
| ( nil(A_54984) = U_54985 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1016249]) ).
tff(c_1016271,plain,
! [A_53420: ty,U_53421: uni] :
( ~ $less($sum($uminus(1),length1(A_53420,U_53421)),1)
| ( cons_proj_21(A_53420,U_53421) = nil(A_53420) )
| ( nil(A_53420) = U_53421 ) ),
inference(superposition,[status(thm),theory(equality)],[c_971967,c_1016268]) ).
tff(c_1016328,plain,
! [A_54990: ty,U_54991: uni] :
( ~ $less(length1(A_54990,U_54991),2)
| ( cons_proj_21(A_54990,U_54991) = nil(A_54990) )
| ( nil(A_54990) = U_54991 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1016271]) ).
tff(c_1016343,plain,
( ~ $less('#skE_29',2)
| ( cons_proj_21(int,t2tb1('#skF_7')) = nil(int) )
| ( t2tb1('#skF_7') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1015818,c_1016328]) ).
tff(c_1018419,plain,
~ $less('#skE_29',2),
inference(splitLeft,[status(thm)],[c_1016343]) ).
tff(c_1019308,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1019307,c_1018419]) ).
tff(c_1019311,plain,
$less('#skE_29',2),
inference(splitRight,[status(thm)],[c_1016343]) ).
tff(c_1016247,plain,
! [A_54982: ty,U_54983: uni] :
( ( cons_proj_21(A_54982,U_54983) = nil(A_54982) )
| ( $sum($uminus(1),length1(A_54982,U_54983)) != 0 )
| ( nil(A_54982) = U_54983 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1016241,c_820]) ).
tff(c_1016306,plain,
! [A_54988: ty,U_54989: uni] :
( ( cons_proj_21(A_54988,U_54989) = nil(A_54988) )
| ( length1(A_54988,U_54989) != 1 )
| ( nil(A_54988) = U_54989 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1016247]) ).
tff(c_1016321,plain,
( ( cons_proj_21(int,t2tb1('#skF_7')) = nil(int) )
| ( '#skE_29' != 1 )
| ( t2tb1('#skF_7') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1015818,c_1016306]) ).
tff(c_1017625,plain,
'#skE_29' != 1,
inference(splitLeft,[status(thm)],[c_1016321]) ).
tff(c_1016283,plain,
( ~ $less('#skE_29',1)
| ( t2tb1('#skF_7') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1015818,c_1016268]) ).
tff(c_1016301,plain,
~ $less('#skE_29',1),
inference(splitLeft,[status(thm)],[c_1016283]) ).
tff(c_1019312,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1019311,c_1017625,c_1016301]) ).
tff(c_1019315,plain,
'#skE_29' = 1,
inference(splitRight,[status(thm)],[c_1016321]) ).
tff(c_1019321,plain,
length1(int,t2tb1('#skF_7')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_1019315,c_1015818]) ).
tff(c_1020169,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1003391,c_1003381,c_819,c_1003371,c_1003438,c_970525,c_1003371,c_1003381,c_1015810,c_1019321,c_1015810,c_1015810,c_578669]) ).
tff(c_1020170,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 1 )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_1015849,c_1020169]) ).
tff(c_1020172,plain,
'#skF_8' = $sum(2,'#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1020170]) ).
tff(c_1020173,plain,
$less($sum(2,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1020172,c_970185]) ).
tff(c_1020176,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1020173]) ).
tff(c_1020177,plain,
t2tb1('#skF_7') = nil(int),
inference(splitRight,[status(thm)],[c_1016283]) ).
tff(c_1020183,plain,
length1(int,nil(int)) = '#skE_29',
inference(demodulation,[status(thm),theory(equality)],[c_1020177,c_1015818]) ).
tff(c_1020185,plain,
'#skE_29' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_819,c_1020183]) ).
tff(c_1020187,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_970550,c_1020185]) ).
tff(c_1020188,plain,
t2tb1('#skF_5') = nil(int),
inference(splitRight,[status(thm)],[c_970538]) ).
tff(c_1020198,plain,
tb2t1(nil(int)) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_1020188,c_84]) ).
tff(c_1020206,plain,
no_zero1('#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1020198,c_970497]) ).
tff(c_153,plain,
( ( '#skF_5' != '#skF_7' )
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))) != '#skF_9' )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_730,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_153]) ).
tff(c_921,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_730]) ).
tff(c_578327,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_921]) ).
tff(c_578580,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum(1,length1(int,t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578327]) ).
tff(c_578582,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) )
| ~ no_zero1(tb2t1(nil(int)))
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578580]) ).
tff(c_1029135,plain,
( ( '#skF_5' != '#skF_7' )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1020206,c_1020198,c_970525,c_1020198,c_1020188,c_819,c_1020188,c_578582]) ).
tff(c_1029137,plain,
( ( '#skF_5' != '#skF_7' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1029135]) ).
tff(c_1029141,plain,
length1(int,t2tb1('#skF_11')) = '#skE_31',
inference(define,[status(thm),theory(equality)],[c_1029137]) ).
tff(c_1029164,plain,
( ( t2tb1('#skF_11') = nil(int) )
| ( '#skE_31' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1029141,c_820]) ).
tff(c_1029169,plain,
'#skE_31' != 0,
inference(splitLeft,[status(thm)],[c_1029164]) ).
tff(c_1029173,plain,
( ( '#skF_5' != '#skF_7' )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1020206,c_1020198,c_1029141,c_970525,c_1020198,c_1020188,c_819,c_1020188,c_578669]) ).
tff(c_1029175,plain,
( ( '#skF_5' != '#skF_7' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1029173]) ).
tff(c_1029177,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_1029175]) ).
tff(c_1021568,plain,
! [A_55251: ty,U_55252: uni] :
( ( cons(A_55251,cons_proj_11(A_55251,U_55252),cons_proj_21(A_55251,U_55252)) = U_55252 )
| ( nil(A_55251) = U_55252 ) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_1021574,plain,
! [A_55251: ty,U_55252: uni] :
( ( $sum(1,length1(A_55251,cons_proj_21(A_55251,U_55252))) = length1(A_55251,U_55252) )
| ( nil(A_55251) = U_55252 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1021568,c_822]) ).
tff(c_1025204,plain,
! [A_55446: ty,U_55447: uni] :
( ( length1(A_55446,cons_proj_21(A_55446,U_55447)) = $sum($uminus(1),length1(A_55446,U_55447)) )
| ( nil(A_55446) = U_55447 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1021574]) ).
tff(c_1025212,plain,
! [A_55446: ty,U_55447: uni] :
( ~ $less($sum($uminus(1),length1(A_55446,U_55447)),0)
| ( nil(A_55446) = U_55447 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1025204,c_821]) ).
tff(c_1025224,plain,
! [A_55446: ty,U_55447: uni] :
( ~ $less(length1(A_55446,U_55447),1)
| ( nil(A_55446) = U_55447 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1025212]) ).
tff(c_1029163,plain,
( ~ $less('#skE_31',1)
| ( t2tb1('#skF_11') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1029141,c_1025224]) ).
tff(c_1029171,plain,
~ $less('#skE_31',1),
inference(splitLeft,[status(thm)],[c_1029163]) ).
tff(c_1029178,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1029177,c_1029171]) ).
tff(c_1029181,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( '#skF_5' != '#skF_7' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ( '#skF_8' = $sum(1,'#skF_3') ) ),
inference(splitRight,[status(thm)],[c_1029175]) ).
tff(c_1031819,plain,
'#skF_5' != '#skF_7',
inference(splitLeft,[status(thm)],[c_1029181]) ).
tff(c_1031096,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1020206,c_1020198,c_1029141,c_970525,c_1020188,c_1020198,c_819,c_1020188,c_1020188,c_578606]) ).
tff(c_1031098,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1031096]) ).
tff(c_1031100,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_1031098]) ).
tff(c_1021613,plain,
! [A_55251: ty,U_55252: uni] :
( ( length1(A_55251,cons_proj_21(A_55251,U_55252)) = $sum($uminus(1),length1(A_55251,U_55252)) )
| ( nil(A_55251) = U_55252 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1021574]) ).
tff(c_1025231,plain,
! [A_55448: ty,U_55449: uni] :
( ~ $less(length1(A_55448,U_55449),1)
| ( nil(A_55448) = U_55449 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1025212]) ).
tff(c_1025234,plain,
! [A_55251: ty,U_55252: uni] :
( ~ $less($sum($uminus(1),length1(A_55251,U_55252)),1)
| ( cons_proj_21(A_55251,U_55252) = nil(A_55251) )
| ( nil(A_55251) = U_55252 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1021613,c_1025231]) ).
tff(c_1025242,plain,
! [A_55251: ty,U_55252: uni] :
( ~ $less(length1(A_55251,U_55252),2)
| ( cons_proj_21(A_55251,U_55252) = nil(A_55251) )
| ( nil(A_55251) = U_55252 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1025234]) ).
tff(c_1029161,plain,
( ~ $less('#skE_31',2)
| ( cons_proj_21(int,t2tb1('#skF_11')) = nil(int) )
| ( t2tb1('#skF_11') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1029141,c_1025242]) ).
tff(c_1029197,plain,
~ $less('#skE_31',2),
inference(splitLeft,[status(thm)],[c_1029161]) ).
tff(c_1031101,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1031100,c_1029197]) ).
tff(c_1031104,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) ) ),
inference(splitRight,[status(thm)],[c_1031098]) ).
tff(c_1035960,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_1031104]) ).
tff(c_1035968,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_1035960]) ).
tff(c_1035978,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1035968]) ).
tff(c_1035982,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1035978]) ).
tff(c_1035986,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1035982,c_1035978]) ).
tff(c_1035972,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_1035960]) ).
tff(c_1035981,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1035972]) ).
tff(c_1035987,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1035981]) ).
tff(c_1035989,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1035987,c_1035981]) ).
tff(c_1035992,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1035986,c_1035989]) ).
tff(c_1035996,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_1031104]) ).
tff(c_1031523,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_1020206,c_1020198,c_1029141,c_970525,c_1020188,c_1020198,c_819,c_1020188,c_1020188,c_578612]) ).
tff(c_1031525,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1031523]) ).
tff(c_1031527,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_1031525]) ).
tff(c_1031528,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1031527,c_1029197]) ).
tff(c_1031531,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) ) ),
inference(splitRight,[status(thm)],[c_1031525]) ).
tff(c_1037477,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1035996,c_1031531]) ).
tff(c_1037479,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))),
inference(splitLeft,[status(thm)],[c_1037477]) ).
tff(c_1037483,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int)))),
inference(superposition,[status(thm),theory(equality)],[c_1037479,c_86]) ).
tff(c_1037487,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),nil(int)),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1037483]) ).
tff(c_1037544,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),nil(int))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1037487,c_36]) ).
tff(c_1037572,plain,
t2tb1('#skF_7') = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_1037544]) ).
tff(c_1037950,plain,
tb2t1(nil(int)) = '#skF_7',
inference(superposition,[status(thm),theory(equality)],[c_1037572,c_84]) ).
tff(c_1037954,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_1037950,c_1020198]) ).
tff(c_1037956,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1031819,c_1037954]) ).
tff(c_1037960,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) != tb2t1(cons(int,t2tb2('#skF_4'),nil(int))),
inference(splitRight,[status(thm)],[c_1037477]) ).
tff(c_1035995,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' ) ),
inference(splitRight,[status(thm)],[c_1031104]) ).
tff(c_1037962,plain,
( ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' ) ),
inference(negUnitSimplification,[status(thm)],[c_1037960,c_1035995]) ).
tff(c_1037964,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5',
inference(splitLeft,[status(thm)],[c_1037962]) ).
tff(c_1037973,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = t2tb1('#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_1037964,c_86]) ).
tff(c_1037976,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1020188,c_1037973]) ).
tff(c_1037978,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1037976]) ).
tff(c_1037981,plain,
'#skF_8' = $sum(1,'#skF_3'),
inference(splitRight,[status(thm)],[c_1037962]) ).
tff(c_1037983,plain,
$less($sum(1,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1037981,c_970185]) ).
tff(c_1037986,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1037983]) ).
tff(c_1037988,plain,
'#skF_5' = '#skF_7',
inference(splitRight,[status(thm)],[c_1029181]) ).
tff(c_1037992,plain,
t2tb1('#skF_7') = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1037988,c_1020188]) ).
tff(c_1030003,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_1020206,c_1020198,c_1029141,c_970525,c_1020188,c_1020198,c_819,c_1020188,c_578615]) ).
tff(c_1030005,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1030003]) ).
tff(c_1030007,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_1030005]) ).
tff(c_1030008,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1030007,c_1029197]) ).
tff(c_1030011,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( '#skF_5' != '#skF_7' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_1030005]) ).
tff(c_1044282,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_1037988,c_1037988,c_1037988,c_1030011]) ).
tff(c_1044284,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_1044282]) ).
tff(c_1044292,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_1044284]) ).
tff(c_1044302,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1044292]) ).
tff(c_1044306,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1044302]) ).
tff(c_1044310,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1044306,c_1044302]) ).
tff(c_1044296,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_1044284]) ).
tff(c_1044305,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1044296]) ).
tff(c_1044311,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1044305]) ).
tff(c_1044313,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1044311,c_1044305]) ).
tff(c_1044316,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1044310,c_1044313]) ).
tff(c_1044320,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_1044282]) ).
tff(c_1037989,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' ) ),
inference(splitRight,[status(thm)],[c_1029181]) ).
tff(c_1046808,plain,
( ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1037988,c_1044320,c_1037989]) ).
tff(c_1046810,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7',
inference(splitLeft,[status(thm)],[c_1046808]) ).
tff(c_1046816,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1046810,c_86]) ).
tff(c_1046819,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1037992,c_1046816]) ).
tff(c_1046821,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1046819]) ).
tff(c_1046824,plain,
'#skF_8' = $sum(1,'#skF_3'),
inference(splitRight,[status(thm)],[c_1046808]) ).
tff(c_1046826,plain,
$less($sum(1,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1046824,c_970185]) ).
tff(c_1046829,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1046826]) ).
tff(c_1046832,plain,
$less('#skE_31',2),
inference(splitRight,[status(thm)],[c_1029161]) ).
tff(c_1025210,plain,
! [A_55446: ty,U_55447: uni] :
( ( cons_proj_21(A_55446,U_55447) = nil(A_55446) )
| ( $sum($uminus(1),length1(A_55446,U_55447)) != 0 )
| ( nil(A_55446) = U_55447 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1025204,c_820]) ).
tff(c_1025222,plain,
! [A_55446: ty,U_55447: uni] :
( ( cons_proj_21(A_55446,U_55447) = nil(A_55446) )
| ( length1(A_55446,U_55447) != 1 )
| ( nil(A_55446) = U_55447 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1025210]) ).
tff(c_1029162,plain,
( ( cons_proj_21(int,t2tb1('#skF_11')) = nil(int) )
| ( '#skE_31' != 1 )
| ( t2tb1('#skF_11') = nil(int) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1029141,c_1025222]) ).
tff(c_1029187,plain,
'#skE_31' != 1,
inference(splitLeft,[status(thm)],[c_1029162]) ).
tff(c_1046833,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1046832,c_1029187,c_1029171]) ).
tff(c_1046836,plain,
'#skE_31' = 1,
inference(splitRight,[status(thm)],[c_1029162]) ).
tff(c_1046842,plain,
length1(int,t2tb1('#skF_11')) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_1046836,c_1029141]) ).
tff(c_1047207,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_1020206,c_1020198,c_1046842,c_970525,c_1020188,c_1020198,c_819,c_1020188,c_1020188,c_578633]) ).
tff(c_1047209,plain,
( ( '#skF_5' != '#skF_7' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( '#skF_8' != $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1047207]) ).
tff(c_1047211,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitLeft,[status(thm)],[c_1047209]) ).
tff(c_1047219,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_1047211]) ).
tff(c_1047229,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1047219]) ).
tff(c_1047349,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1047229]) ).
tff(c_1047353,plain,
~ $less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1047349,c_1047229]) ).
tff(c_1047352,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1047229]) ).
tff(c_1047223,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_1047211]) ).
tff(c_1047232,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1047223]) ).
tff(c_1047360,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1047352,c_1047232]) ).
tff(c_1047361,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1047353,c_1047360]) ).
tff(c_1047365,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_1047209]) ).
tff(c_1047458,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_1020206,c_1020198,c_1046842,c_1047365,c_970525,c_1020188,c_1020198,c_819,c_1020188,c_578615]) ).
tff(c_1047460,plain,
( ( '#skF_5' != '#skF_7' )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1047458]) ).
tff(c_1047461,plain,
'#skF_5' != '#skF_7',
inference(splitLeft,[status(thm)],[c_1047460]) ).
tff(c_1049135,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1020206,c_1020198,c_1046842,c_1047365,c_970525,c_1020188,c_1020198,c_819,c_1020188,c_1020188,c_578606]) ).
tff(c_1049137,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1049135]) ).
tff(c_1049139,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5',
inference(splitLeft,[status(thm)],[c_1049137]) ).
tff(c_1049143,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = t2tb1('#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_1049139,c_86]) ).
tff(c_1049146,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1020188,c_1049143]) ).
tff(c_1049148,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1049146]) ).
tff(c_1049152,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) != '#skF_5',
inference(splitRight,[status(thm)],[c_1049137]) ).
tff(c_1049632,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_1020206,c_1020198,c_1046842,c_1047365,c_970525,c_1020188,c_1020198,c_819,c_1020188,c_1020188,c_1020188,c_578630]) ).
tff(c_1049633,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ~ $less($uminus(1),1) ),
inference(negUnitSimplification,[status(thm)],[c_1049152,c_1049632]) ).
tff(c_1049635,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( '#skF_8' != $sum(1,'#skF_3') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1049633]) ).
tff(c_1049637,plain,
'#skF_8' != $sum(1,'#skF_3'),
inference(splitLeft,[status(thm)],[c_1049635]) ).
tff(c_1049151,plain,
( ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) ) ),
inference(splitRight,[status(thm)],[c_1049137]) ).
tff(c_1050858,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))),
inference(negUnitSimplification,[status(thm)],[c_1049637,c_1049151]) ).
tff(c_1050862,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int)))),
inference(superposition,[status(thm),theory(equality)],[c_1050858,c_86]) ).
tff(c_1050866,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),nil(int)),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1050862]) ).
tff(c_1050911,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),nil(int))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1050866,c_36]) ).
tff(c_1050935,plain,
t2tb1('#skF_7') = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_1050911]) ).
tff(c_1051005,plain,
tb2t1(nil(int)) = '#skF_7',
inference(superposition,[status(thm),theory(equality)],[c_1050935,c_84]) ).
tff(c_1051290,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_1051005,c_1020198]) ).
tff(c_1051292,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1047461,c_1051290]) ).
tff(c_1051296,plain,
'#skF_8' = $sum(1,'#skF_3'),
inference(splitRight,[status(thm)],[c_1049635]) ).
tff(c_1051297,plain,
$less($sum(1,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1051296,c_970185]) ).
tff(c_1051300,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1051297]) ).
tff(c_1051302,plain,
'#skF_5' = '#skF_7',
inference(splitRight,[status(thm)],[c_1047460]) ).
tff(c_1051306,plain,
t2tb1('#skF_7') = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1051302,c_1020188]) ).
tff(c_1051304,plain,
no_zero1('#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_1051302,c_1020206]) ).
tff(c_1051305,plain,
tb2t1(nil(int)) = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_1051302,c_1020198]) ).
tff(c_1052578,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7' )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1051304,c_1051305,c_1046842,c_1047365,c_970525,c_1051306,c_1051302,c_1051305,c_819,c_1051306,c_1051302,c_1051306,c_1051302,c_1051306,c_578606]) ).
tff(c_1052580,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1052578]) ).
tff(c_1052582,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7',
inference(splitLeft,[status(thm)],[c_1052580]) ).
tff(c_1052586,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1052582,c_86]) ).
tff(c_1052589,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1051306,c_1052586]) ).
tff(c_1052591,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1052589]) ).
tff(c_1052595,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) != '#skF_7',
inference(splitRight,[status(thm)],[c_1052580]) ).
tff(c_1053530,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7' )
| ~ $less($uminus(1),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_1051304,c_1051305,c_1046842,c_1047365,c_970525,c_1051306,c_1051302,c_1051305,c_819,c_1051306,c_1051302,c_1051306,c_1051302,c_1051306,c_1051302,c_1051306,c_578630]) ).
tff(c_1053531,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ~ $less($uminus(1),1) ),
inference(negUnitSimplification,[status(thm)],[c_1052595,c_1053530]) ).
tff(c_1053533,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( '#skF_8' != $sum(1,'#skF_3') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1053531]) ).
tff(c_1053535,plain,
'#skF_8' != $sum(1,'#skF_3'),
inference(splitLeft,[status(thm)],[c_1053533]) ).
tff(c_1051303,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_5' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_1047460]) ).
tff(c_1055784,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_7' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_1051302,c_1051302,c_1051303]) ).
tff(c_1055786,plain,
zero_at1('#skF_7',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_1053535,c_1052595,c_1055784]) ).
tff(c_1055794,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_7'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_1055786,c_807]) ).
tff(c_1055799,plain,
tb2t(some(int,t2tb2(0))) = tb2t(none(int)),
inference(demodulation,[status(thm),theory(equality)],[c_817,c_1051306,c_1055794]) ).
tff(c_1055824,plain,
some(int,t2tb2(0)) = t2tb(tb2t(none(int))),
inference(superposition,[status(thm),theory(equality)],[c_1055799,c_80]) ).
tff(c_1055827,plain,
some(int,t2tb2(0)) = none(int),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_1055824]) ).
tff(c_1055829,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_61,c_1055827]) ).
tff(c_1055833,plain,
'#skF_8' = $sum(1,'#skF_3'),
inference(splitRight,[status(thm)],[c_1053533]) ).
tff(c_1055834,plain,
$less($sum(1,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1055833,c_970185]) ).
tff(c_1055837,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1055834]) ).
tff(c_1055838,plain,
t2tb1('#skF_11') = nil(int),
inference(splitRight,[status(thm)],[c_1029163]) ).
tff(c_1055842,plain,
length1(int,nil(int)) = '#skE_31',
inference(demodulation,[status(thm),theory(equality)],[c_1055838,c_1029141]) ).
tff(c_1055843,plain,
'#skE_31' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_819,c_1055842]) ).
tff(c_1055845,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1029169,c_1055843]) ).
tff(c_1055846,plain,
t2tb1('#skF_11') = nil(int),
inference(splitRight,[status(thm)],[c_1029164]) ).
tff(c_1055856,plain,
tb2t1(nil(int)) = '#skF_11',
inference(superposition,[status(thm),theory(equality)],[c_1055846,c_84]) ).
tff(c_1055870,plain,
( ( '#skF_5' != '#skF_7' )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0)
| ~ $less($uminus(1),0)
| ~ no_zero1('#skF_11') ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1055856,c_819,c_1055846,c_1055846,c_970525,c_1055856,c_1020188,c_819,c_1020188,c_578669]) ).
tff(c_1055872,plain,
( ( '#skF_5' != '#skF_7' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0)
| ~ no_zero1('#skF_11') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1055870]) ).
tff(c_1055873,plain,
~ no_zero1('#skF_11'),
inference(splitLeft,[status(thm)],[c_1055872]) ).
tff(c_1055860,plain,
'#skF_5' = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_1055856,c_1020198]) ).
tff(c_1055891,plain,
no_zero1('#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_1055860,c_1020206]) ).
tff(c_1055894,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1055873,c_1055891]) ).
tff(c_1055896,plain,
no_zero1('#skF_11'),
inference(splitRight,[status(thm)],[c_1055872]) ).
tff(c_1056407,plain,
( ( '#skF_7' != '#skF_11' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0)
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_1055896,c_1055856,c_819,c_1055846,c_970525,c_1055846,c_1055846,c_1055860,c_1055856,c_819,c_1055846,c_1055860,c_1055846,c_1055860,c_1055860,c_578633]) ).
tff(c_1056409,plain,
( ( '#skF_7' != '#skF_11' )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( '#skF_8' != $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1056407]) ).
tff(c_1056411,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0),
inference(splitLeft,[status(thm)],[c_1056409]) ).
tff(c_1056419,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),nil(int)))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_804,c_1056411]) ).
tff(c_1056429,plain,
~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1056419]) ).
tff(c_1056433,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0) = '#skE_41',
inference(define,[status(thm),theory(equality)],[c_1056429]) ).
tff(c_1056437,plain,
~ $less('#skE_41',0),
inference(demodulation,[status(thm),theory(equality)],[c_1056433,c_1056429]) ).
tff(c_1056423,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),nil(int)))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_805,c_1056411]) ).
tff(c_1056432,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1056423]) ).
tff(c_1056442,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),nil(int))),0) = '#skE_41',
inference(define,[status(thm),theory(equality)],[c_1056432]) ).
tff(c_1056444,plain,
$less('#skE_41',0),
inference(demodulation,[status(thm),theory(equality)],[c_1056442,c_1056432]) ).
tff(c_1056447,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1056437,c_1056444]) ).
tff(c_1056451,plain,
zero_at1(tb2t1(cons(int,t2tb2(0),nil(int))),0),
inference(splitRight,[status(thm)],[c_1056409]) ).
tff(c_1056710,plain,
( ( '#skF_7' != '#skF_11' )
| zero_at1('#skF_11',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_1055896,c_1055856,c_819,c_1055846,c_1056451,c_970525,c_1055846,c_1055846,c_1055856,c_1055860,c_819,c_1055846,c_1055860,c_1055860,c_1055860,c_578615]) ).
tff(c_1056712,plain,
( ( '#skF_7' != '#skF_11' )
| zero_at1('#skF_11',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1056710]) ).
tff(c_1056713,plain,
'#skF_7' != '#skF_11',
inference(splitLeft,[status(thm)],[c_1056712]) ).
tff(c_1057717,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1055896,c_1055856,c_819,c_1055846,c_1056451,c_970525,c_1055846,c_1055846,c_1055856,c_1055860,c_819,c_1055846,c_1055860,c_1055846,c_1055860,c_578606]) ).
tff(c_1057719,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1057717]) ).
tff(c_1057721,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11',
inference(splitLeft,[status(thm)],[c_1057719]) ).
tff(c_1057725,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = t2tb1('#skF_11'),
inference(superposition,[status(thm),theory(equality)],[c_1057721,c_86]) ).
tff(c_1057728,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1055846,c_1057725]) ).
tff(c_1057730,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1057728]) ).
tff(c_1057734,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) != '#skF_11',
inference(splitRight,[status(thm)],[c_1057719]) ).
tff(c_1058214,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_1055896,c_1055856,c_819,c_1055846,c_1056451,c_970525,c_1055846,c_1055846,c_1055856,c_1055860,c_819,c_1055846,c_1055860,c_1055846,c_1055860,c_1055846,c_1055860,c_578630]) ).
tff(c_1058215,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_1057734,c_1058214]) ).
tff(c_1058217,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( '#skF_8' != $sum(1,'#skF_3') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1058215]) ).
tff(c_1058219,plain,
'#skF_8' != $sum(1,'#skF_3'),
inference(splitLeft,[status(thm)],[c_1058217]) ).
tff(c_1057733,plain,
( ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) ) ),
inference(splitRight,[status(thm)],[c_1057719]) ).
tff(c_1058846,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))),
inference(negUnitSimplification,[status(thm)],[c_1058219,c_1057733]) ).
tff(c_1058850,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int)))),
inference(superposition,[status(thm),theory(equality)],[c_1058846,c_86]) ).
tff(c_1058854,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),nil(int)),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1058850]) ).
tff(c_1058899,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),nil(int))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1058854,c_36]) ).
tff(c_1058923,plain,
t2tb1('#skF_7') = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_1058899]) ).
tff(c_1058988,plain,
tb2t1(nil(int)) = '#skF_7',
inference(superposition,[status(thm),theory(equality)],[c_1058923,c_84]) ).
tff(c_1058991,plain,
'#skF_7' = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_1055856,c_1058988]) ).
tff(c_1058993,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1056713,c_1058991]) ).
tff(c_1058997,plain,
'#skF_8' = $sum(1,'#skF_3'),
inference(splitRight,[status(thm)],[c_1058217]) ).
tff(c_1058998,plain,
$less($sum(1,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1058997,c_970185]) ).
tff(c_1059001,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1058998]) ).
tff(c_1059003,plain,
'#skF_7' = '#skF_11',
inference(splitRight,[status(thm)],[c_1056712]) ).
tff(c_1060028,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_1055896,c_1055856,c_819,c_1055846,c_1056451,c_970525,c_1055846,c_1055846,c_1055856,c_1055860,c_819,c_1055846,c_1055860,c_1055846,c_1055846,c_1055860,c_1059003,c_578606]) ).
tff(c_1060030,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ( '#skF_8' = $sum(1,'#skF_3') )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1060028]) ).
tff(c_1060032,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11',
inference(splitLeft,[status(thm)],[c_1060030]) ).
tff(c_1060036,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = t2tb1('#skF_11'),
inference(superposition,[status(thm),theory(equality)],[c_1060032,c_86]) ).
tff(c_1060039,plain,
cons(int,t2tb2('#skF_4'),nil(int)) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_1055846,c_1060036]) ).
tff(c_1060041,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1060039]) ).
tff(c_1060045,plain,
tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) != '#skF_11',
inference(splitRight,[status(thm)],[c_1060030]) ).
tff(c_1060255,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ~ $less($uminus(1),0) ),
inference(demodulation,[status(thm),theory(equality)],[c_1055896,c_1055856,c_819,c_1055846,c_1056451,c_970525,c_1055846,c_1055846,c_1055856,c_1055860,c_819,c_1055846,c_1055860,c_1055846,c_1055860,c_1055846,c_1055846,c_1055860,c_1059003,c_578630]) ).
tff(c_1060256,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) != 0 )
| ~ $less($uminus(1),0) ),
inference(negUnitSimplification,[status(thm)],[c_1060045,c_1060255]) ).
tff(c_1060258,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),nil(int))) = tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) )
| ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_4'),nil(int))))
| ( '#skF_8' != $sum(1,'#skF_3') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1060256]) ).
tff(c_1060260,plain,
'#skF_8' != $sum(1,'#skF_3'),
inference(splitLeft,[status(thm)],[c_1060258]) ).
tff(c_1059004,plain,
( ( tb2t1(cons(int,t2tb2('#skF_4'),nil(int))) = '#skF_11' )
| ( '#skF_8' = $sum(1,'#skF_3') )
| zero_at1('#skF_11',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))) ),
inference(splitRight,[status(thm)],[c_1056712]) ).
tff(c_1062004,plain,
zero_at1('#skF_11',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_1060260,c_1060045,c_1059004]) ).
tff(c_1062012,plain,
tb2t(nth1(int,$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')),t2tb1('#skF_11'))) = tb2t(some(int,t2tb2(0))),
inference(resolution,[status(thm)],[c_1062004,c_807]) ).
tff(c_1062017,plain,
tb2t(some(int,t2tb2(0))) = tb2t(none(int)),
inference(demodulation,[status(thm),theory(equality)],[c_817,c_1055846,c_1062012]) ).
tff(c_1062042,plain,
some(int,t2tb2(0)) = t2tb(tb2t(none(int))),
inference(superposition,[status(thm),theory(equality)],[c_1062017,c_80]) ).
tff(c_1062045,plain,
some(int,t2tb2(0)) = none(int),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_1062042]) ).
tff(c_1062047,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_61,c_1062045]) ).
tff(c_1062051,plain,
'#skF_8' = $sum(1,'#skF_3'),
inference(splitRight,[status(thm)],[c_1060258]) ).
tff(c_1062052,plain,
$less($sum(1,'#skF_3'),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1062051,c_970185]) ).
tff(c_1062055,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1062052]) ).
tff(c_1062060,plain,
'#skF_10' != 0,
inference(splitRight,[status(thm)],[c_970523]) ).
tff(c_970184,plain,
( ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_5' != '#skF_7' )
| ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5') ),
inference(splitRight,[status(thm)],[c_578520]) ).
tff(c_1062084,plain,
( ( '#skF_5' != '#skF_7' )
| ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_970497,c_970184]) ).
tff(c_1062086,plain,
( ( '#skF_5' != '#skF_7' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5') ),
inference(negUnitSimplification,[status(thm)],[c_1062060,c_1062084]) ).
tff(c_1062087,plain,
'#skF_5' != '#skF_7',
inference(splitLeft,[status(thm)],[c_1062086]) ).
tff(c_1063171,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_970497,c_578547]) ).
tff(c_1063173,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| zero_at1('#skF_5',$sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')))
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) ) ),
inference(negUnitSimplification,[status(thm)],[c_1062060,c_1063171]) ).
tff(c_1063175,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_1063173]) ).
tff(c_1063179,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_1063175,c_86]) ).
tff(c_1063182,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1063179]) ).
tff(c_1063184,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1063182]) ).
tff(c_1063188,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) != tb2t1(nil(int)),
inference(splitRight,[status(thm)],[c_1063173]) ).
tff(c_970498,plain,
( ( '#skF_10' = 0 )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(splitRight,[status(thm)],[c_970225]) ).
tff(c_1065686,plain,
( no_zero1('#skF_5')
| ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) ) ),
inference(negUnitSimplification,[status(thm)],[c_1063188,c_1062060,c_970498]) ).
tff(c_1065688,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitLeft,[status(thm)],[c_1065686]) ).
tff(c_1066339,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = t2tb1(tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')))),
inference(superposition,[status(thm),theory(equality)],[c_1065688,c_86]) ).
tff(c_1066343,plain,
cons(int,t2tb2('#skF_6'),t2tb1('#skF_7')) = cons(int,t2tb2('#skF_4'),t2tb1('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1066339]) ).
tff(c_1066394,plain,
cons_proj_21(int,cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1066343,c_36]) ).
tff(c_1066463,plain,
t2tb1('#skF_5') = t2tb1('#skF_7'),
inference(superposition,[status(thm),theory(equality)],[c_1066394,c_36]) ).
tff(c_1066485,plain,
tb2t1(t2tb1('#skF_7')) = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_1066463,c_84]) ).
tff(c_1066488,plain,
'#skF_5' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_84,c_1066485]) ).
tff(c_1066490,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1062087,c_1066488]) ).
tff(c_1066493,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) != tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_1065686]) ).
tff(c_223,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 )
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_576,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_223]) ).
tff(c_887,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_576]) ).
tff(c_578493,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_887]) ).
tff(c_1063400,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_970205,c_578493]) ).
tff(c_1063401,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' ) ),
inference(negUnitSimplification,[status(thm)],[c_1062060,c_1063188,c_1063400]) ).
tff(c_1063403,plain,
( ( tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) )
| ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1063401]) ).
tff(c_1063405,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitLeft,[status(thm)],[c_1063403]) ).
tff(c_1063406,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1063405,c_970185]) ).
tff(c_1063408,plain,
$less('#skE_29',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1063406]) ).
tff(c_1063410,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_970220,c_1063408]) ).
tff(c_1063413,plain,
tb2t1(cons(int,t2tb2('#skF_6'),t2tb1('#skF_7'))) = tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))),
inference(splitRight,[status(thm)],[c_1063403]) ).
tff(c_1067085,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1066493,c_1063413]) ).
tff(c_1067087,plain,
'#skF_5' = '#skF_7',
inference(splitRight,[status(thm)],[c_1062086]) ).
tff(c_1067091,plain,
length1(int,t2tb1('#skF_7')) = '#skE_29',
inference(demodulation,[status(thm),theory(equality)],[c_1067087,c_970205]) ).
tff(c_221,plain,
( ( '#skF_5' != '#skF_7' )
| ( $sum($sum(1,'#skF_3'),length1(int,t2tb1('#skF_5'))) = '#skF_8' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_10' = 0 )
| $lesseq($sum('#skF_3',1),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_581,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum('#skF_8',$uminus('#skF_3'))) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_221]) ).
tff(c_888,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_581]) ).
tff(c_578356,plain,
( ( '#skF_5' != '#skF_7' )
| ( length1(int,t2tb1('#skF_5')) = $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_5'))) = tb2t1(nil(int)) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 )
| ~ $less('#skF_8',$sum(1,'#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_888]) ).
tff(c_1067261,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) )
| ( '#skF_10' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_970185,c_970497,c_1067087,c_1067091,c_1067087,c_1067087,c_578356]) ).
tff(c_1067262,plain,
( ( $sum($uminus(1),$sum($uminus('#skF_3'),'#skF_8')) = '#skE_29' )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) ) ),
inference(negUnitSimplification,[status(thm)],[c_1062060,c_1067261]) ).
tff(c_1067264,plain,
( ( '#skF_8' = $sum(1,$sum('#skF_3','#skE_29')) )
| ( tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1067262]) ).
tff(c_1067266,plain,
tb2t1(cons(int,t2tb2('#skF_4'),t2tb1('#skF_7'))) = tb2t1(nil(int)),
inference(splitLeft,[status(thm)],[c_1067264]) ).
tff(c_1067604,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = t2tb1(tb2t1(nil(int))),
inference(superposition,[status(thm),theory(equality)],[c_1067266,c_86]) ).
tff(c_1067607,plain,
cons(int,t2tb2('#skF_4'),t2tb1('#skF_7')) = nil(int),
inference(demodulation,[status(thm),theory(equality)],[c_86,c_1067604]) ).
tff(c_1067609,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1067607]) ).
tff(c_1067612,plain,
'#skF_8' = $sum(1,$sum('#skF_3','#skE_29')),
inference(splitRight,[status(thm)],[c_1067264]) ).
tff(c_1067614,plain,
$less($sum(1,$sum('#skF_3','#skE_29')),$sum(1,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1067612,c_970185]) ).
tff(c_1067616,plain,
$less('#skE_29',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1067614]) ).
tff(c_1067618,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_970220,c_1067616]) ).
tff(c_1067622,plain,
'#skF_4' = 0,
inference(splitRight,[status(thm)],[c_578255]) ).
tff(c_1067621,plain,
( ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_10' = 0 ) ),
inference(splitRight,[status(thm)],[c_578255]) ).
tff(c_1067705,plain,
~ no_zero1(tb2t1(nil(int))),
inference(splitLeft,[status(thm)],[c_1067621]) ).
tff(c_1067710,plain,
~ $less('#skF_2'(tb2t1(nil(int))),0),
inference(resolution,[status(thm)],[c_800,c_1067705]) ).
tff(c_1067714,plain,
'#skF_2'(tb2t1(nil(int))) = '#skE_30',
inference(define,[status(thm),theory(equality)],[c_1067710]) ).
tff(c_1067718,plain,
~ $less('#skE_30',0),
inference(demodulation,[status(thm),theory(equality)],[c_1067714,c_1067710]) ).
tff(c_1067717,plain,
'#skF_2'(tb2t1(nil(int))) = '#skE_30',
inference(define,[status(thm),theory(equality)],[c_1067710]) ).
tff(c_1067782,plain,
! [L_57142: list_int] :
( $less('#skF_2'(L_57142),length1(int,t2tb1(L_57142)))
| no_zero1(L_57142) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_1067786,plain,
$less('#skF_2'(tb2t1(nil(int))),length1(int,t2tb1(tb2t1(nil(int))))),
inference(resolution,[status(thm)],[c_1067782,c_1067705]) ).
tff(c_1067787,plain,
$less('#skE_30',0),
inference(demodulation,[status(thm),theory(equality)],[c_1067717,c_819,c_86,c_1067786]) ).
tff(c_1067789,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1067718,c_1067787]) ).
tff(c_1067791,plain,
no_zero1(tb2t1(nil(int))),
inference(splitRight,[status(thm)],[c_1067621]) ).
tff(c_1067792,plain,
'#skF_10' = 0,
inference(splitRight,[status(thm)],[c_1067621]) ).
tff(c_113,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))) != '#skF_9' )
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ( '#skF_4' != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_936,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_4' != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_113]) ).
tff(c_578499,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_4' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_936]) ).
tff(c_578574,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( $sum(1,length1(int,t2tb1('#skF_11'))) != 0 )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_4' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578499]) ).
tff(c_578576,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) )
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_4' != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578574]) ).
tff(c_1070230,plain,
( ~ no_zero1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))))
| ( length1(int,t2tb1('#skF_11')) != $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1067622,c_1067791,c_1067792,c_578576]) ).
tff(c_1070234,plain,
length1(int,t2tb1('#skF_11')) = '#skE_31',
inference(define,[status(thm),theory(equality)],[c_1070230]) ).
tff(c_157,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),$difference('#skF_9','#skF_9'))
| ~ $less('#skF_9',$sum('#skF_9',length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11')))))
| ~ no_zero1(tb2t1(nil(int)))
| ( $sum('#skF_12',length1(int,nil(int))) != '#skF_12' )
| ~ $lesseq('#skF_9','#skF_9')
| ( '#skF_4' != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_919,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( length1(int,nil(int)) != 0 )
| ( '#skF_4' != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_157]) ).
tff(c_578252,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,length1(int,cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_4' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_819,c_919]) ).
tff(c_578568,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less(0,$sum(1,length1(int,t2tb1('#skF_11'))))
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_4' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_578252]) ).
tff(c_578570,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2('#skF_10'),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),length1(int,t2tb1('#skF_11')))
| ~ no_zero1(tb2t1(nil(int)))
| ( '#skF_4' != 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_578568]) ).
tff(c_1070504,plain,
( ~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0)
| ~ $less($uminus(1),'#skE_31') ),
inference(demodulation,[status(thm),theory(equality)],[c_1067622,c_1067791,c_1070234,c_1067792,c_578570]) ).
tff(c_1070506,plain,
~ $less($uminus(1),'#skE_31'),
inference(splitLeft,[status(thm)],[c_1070504]) ).
tff(c_1070246,plain,
~ $less('#skE_31',0),
inference(superposition,[status(thm),theory(equality)],[c_1070234,c_821]) ).
tff(c_1070507,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1070506,c_1070246]) ).
tff(c_1070510,plain,
~ zero_at1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),
inference(splitRight,[status(thm)],[c_1070504]) ).
tff(c_1072341,plain,
( $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_1072333,c_1070510]) ).
tff(c_1072345,plain,
$less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0),
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1072341]) ).
tff(c_1072346,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1072345]) ).
tff(c_1072350,plain,
$less('#skE_32',0),
inference(demodulation,[status(thm),theory(equality)],[c_1072346,c_1072345]) ).
tff(c_1072349,plain,
'#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0) = '#skE_32',
inference(define,[status(thm),theory(equality)],[c_1072345]) ).
tff(c_1072571,plain,
! [L_57489: list_int,I_57490a: $int] :
( ~ $less('#skF_1'(L_57489,I_57490a),0)
| zero_at1(L_57489,I_57490a)
| ( tb2t(nth1(int,I_57490a,t2tb1(L_57489))) != tb2t(some(int,t2tb2(0))) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_102]) ).
tff(c_1072579,plain,
( ~ $less('#skF_1'(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11'))),0),0)
| ( tb2t(nth1(int,0,t2tb1(tb2t1(cons(int,t2tb2(0),t2tb1('#skF_11')))))) != tb2t(some(int,t2tb2(0))) ) ),
inference(resolution,[status(thm)],[c_1072571,c_1070510]) ).
tff(c_1072583,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_816,c_86,c_1072350,c_1072349,c_1072579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW671_2 : TPTP v9.0.0. Released v6.1.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 06:22:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 146.53/101.93 ***********************************************************************
% 146.53/101.94 After 99.8 sec it's time to try something different, got 99.5 sec left
% 146.53/101.94 ***********************************************************************
% 209.66/153.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 210.18/154.06
% 210.18/154.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------