TSTP Solution File: SWW624_2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW624_2 : TPTP v8.1.2. 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 : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:07:50 EDT 2023

% Result   : Theorem 50.46s 25.17s
% Output   : CNFRefutation 50.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   84
% Syntax   : Number of formulae    :  140 (  51 unt;  70 typ;   0 def)
%            Number of atoms       :   90 (  33 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   55 (  35   ~;  11   |;   4   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number arithmetic     :  129 (  22 atm;  50 fun;  55 num;   2 var)
%            Number of types       :    8 (   6 usr;   1 ari)
%            Number of type conns  :   80 (  39   >;  41   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   68 (  59 usr;  30 con; 0-5 aty)
%            Number of variables   :  122 (; 122   !;   0   ?; 122   :)

% Comments : 
%------------------------------------------------------------------------------
%$ permut > mem > sort > le > sorted > match_list > match_bool > rev_append > prefix > num_occ > infix_plpl > cons > reverse > mod > length > div > cons_proj_2 > cons_proj_1 > #nlpp > witness > tb2t1 > tb2t > t2tb1 > t2tb > nil > list > abs > tuple02 > tuple01 > true > real > qtmark > int > false > elt1 > bool1 > #skF_3 > #skF_13 > #skF_5 > #skF_6 > #skF_4 > #skF_12 > #skF_8 > #skF_10 > #skF_14 > #skF_15 > #skF_11 > #skF_1 > #skF_9 > #skF_7 > #skF_2

%Foreground sorts:
tff(elt,type,
    elt: $tType ).

tff(bool,type,
    bool: $tType ).

tff(tuple0,type,
    tuple0: $tType ).

tff(list_elt,type,
    list_elt: $tType ).

tff(ty,type,
    ty: $tType ).

tff(uni,type,
    uni: $tType ).

%Background operators:
tff('#skE_7',type,
    '#skE_7': $int ).

tff('#skE_11',type,
    '#skE_11': $int ).

tff('#skE_12',type,
    '#skE_12': $int ).

tff('#skE_2',type,
    '#skE_2': $int ).

tff('#skE_1',type,
    '#skE_1': $int ).

tff('#skE_6',type,
    '#skE_6': $int ).

tff('#skE_13',type,
    '#skE_13': $int ).

tff('#skE_10',type,
    '#skE_10': $int ).

tff('#skE_5',type,
    '#skE_5': $int ).

tff('#skE_8',type,
    '#skE_8': $int ).

tff('#skE_4',type,
    '#skE_4': $int ).

tff('#skE_3',type,
    '#skE_3': $int ).

tff('#skE_9',type,
    '#skE_9': $int ).

tff('#skE_14',type,
    '#skE_14': $int ).

%Foreground operators:
tff(list,type,
    list: ty > ty ).

tff('#skF_3',type,
    '#skF_3': ( ty * uni * uni ) > uni ).

tff(prefix,type,
    prefix: ( ty * $int * uni ) > uni ).

tff(elt1,type,
    elt1: ty ).

tff(cons_proj_1,type,
    cons_proj_1: ( ty * uni ) > uni ).

tff(cons,type,
    cons: ( ty * uni * uni ) > uni ).

tff(t2tb,type,
    t2tb: list_elt > uni ).

tff(nil,type,
    nil: ty > uni ).

tff('#skF_13',type,
    '#skF_13': ( list_elt * list_elt ) > elt ).

tff(permut,type,
    permut: ( ty * uni * uni ) > $o ).

tff('#skF_5',type,
    '#skF_5': list_elt > elt ).

tff(tuple02,type,
    tuple02: tuple0 ).

tff(div,type,
    div: ( $int * $int ) > $int ).

tff(tuple01,type,
    tuple01: ty ).

tff(int,type,
    int: ty ).

tff('#skF_6',type,
    '#skF_6': list_elt > elt ).

tff(abs,type,
    abs: $int > $int ).

tff(rev_append,type,
    rev_append: ( ty * uni * uni ) > uni ).

tff(real,type,
    real: ty ).

tff(sorted,type,
    sorted: list_elt > $o ).

tff(match_bool,type,
    match_bool: ( ty * bool * uni * uni ) > uni ).

tff(false,type,
    false: bool ).

tff('#skF_4',type,
    '#skF_4': list_elt > elt ).

tff('#skF_12',type,
    '#skF_12': ( list_elt * list_elt ) > elt ).

tff('#skF_8',type,
    '#skF_8': ( elt * list_elt ) > elt ).

tff(mod,type,
    mod: ( $int * $int ) > $int ).

tff(tb2t,type,
    tb2t: uni > list_elt ).

tff(reverse,type,
    reverse: ( ty * uni ) > uni ).

tff('#skF_10',type,
    '#skF_10': ( list_elt * list_elt ) > elt ).

tff(length,type,
    length: ( ty * uni ) > $int ).

tff(le,type,
    le: ( elt * elt ) > $o ).

tff(qtmark,type,
    qtmark: ty ).

tff(t2tb1,type,
    t2tb1: elt > uni ).

tff(num_occ,type,
    num_occ: ( ty * uni * uni ) > $int ).

tff(bool1,type,
    bool1: ty ).

tff('#skF_14',type,
    '#skF_14': elt ).

tff('#skF_15',type,
    '#skF_15': list_elt ).

tff('#skF_11',type,
    '#skF_11': ( list_elt * elt ) > elt ).

tff('#skF_1',type,
    '#skF_1': ( ty * uni * uni ) > uni ).

tff('#skF_9',type,
    '#skF_9': ( list_elt * list_elt ) > elt ).

tff('#skF_7',type,
    '#skF_7': list_elt > list_elt ).

tff(match_list,type,
    match_list: ( ty * ty * uni * uni * uni ) > uni ).

tff(sort,type,
    sort: ( ty * uni ) > $o ).

tff(true,type,
    true: bool ).

tff(cons_proj_2,type,
    cons_proj_2: ( ty * uni ) > uni ).

tff(mem,type,
    mem: ( ty * uni * uni ) > $o ).

tff(tb2t1,type,
    tb2t1: uni > elt ).

tff(witness,type,
    witness: ty > uni ).

tff(infix_plpl,type,
    infix_plpl: ( ty * uni * uni ) > uni ).

tff('#skF_2',type,
    '#skF_2': ( ty * uni * uni ) > uni ).

tff(f_195,axiom,
    ! [A: ty,L: uni] : permut(A,L,L),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_refl) ).

tff(f_356,axiom,
    ! [A: ty,L: uni] : ( prefix(A,0,L) = nil(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prefix_def1) ).

tff(f_96,axiom,
    ! [A: ty,L: uni] :
      ( ( length(A,L) = 0 )
    <=> ( L = nil(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nil) ).

tff(f_479,negated_conjecture,
    ~ ( permut(elt1,prefix(elt1,length(elt1,nil(elt1)),nil(elt1)),nil(elt1))
      & ! [X: elt,X1: list_elt] :
          ( permut(elt1,prefix(elt1,length(elt1,t2tb(X1)),t2tb(X1)),t2tb(X1))
         => permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1(X),t2tb(X1))),cons(elt1,t2tb1(X),t2tb(X1))),cons(elt1,t2tb1(X),t2tb(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_prefix) ).

tff(f_199,axiom,
    ! [A: ty,L1: uni,L2: uni] :
      ( permut(A,L1,L2)
     => permut(A,L2,L1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_sym) ).

tff(f_209,axiom,
    ! [A: ty,X: uni,L1: uni,L2: uni] :
      ( permut(A,L1,L2)
     => permut(A,cons(A,X,L1),cons(A,X,L2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_cons) ).

tff(f_360,axiom,
    ! [A: ty,Na: $int,X: uni,L: uni] :
      ( $less(0,Na)
     => ( prefix(A,Na,cons(A,X,L)) = cons(A,X,prefix(A,$difference(Na,1),L)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prefix_def2) ).

tff(f_90,axiom,
    ! [A: ty] :
      ( ( length(A,nil(A)) = 0 )
      & ! [X: uni,X1: uni] : ( length(A,cons(A,X,X1)) = $sum(1,length(A,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_def) ).

tff(f_103,axiom,
    ! [A: ty,L2: uni] :
      ( ( infix_plpl(A,nil(A),L2) = L2 )
      & ! [X: uni,X1: uni] : ( infix_plpl(A,cons(A,X,X1),L2) = cons(A,X,infix_plpl(A,X1,L2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infix_plpl_def) ).

tff(f_167,axiom,
    ! [A: ty] :
      ( ( reverse(A,nil(A)) = nil(A) )
      & ! [X: uni,X1: uni] : ( reverse(A,cons(A,X,X1)) = infix_plpl(A,reverse(A,X1),cons(A,X,nil(A))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reverse_def) ).

tff(f_171,axiom,
    ! [A: ty,L: uni,X: uni] : ( reverse(A,cons(A,X,L)) = infix_plpl(A,reverse(A,L),cons(A,X,nil(A))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reverse_cons) ).

tff(f_179,axiom,
    ! [A: ty,L: uni] : ( length(A,reverse(A,L)) = length(A,L) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reverse_length) ).

tff(f_109,axiom,
    ! [A: ty,L1: uni,L2: uni] : ( length(A,infix_plpl(A,L1,L2)) = $sum(length(A,L1),length(A,L2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',append_length) ).

tff(f_92,axiom,
    ! [A: ty,L: uni] : $lesseq(0,length(A,L)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_nonnegative) ).

tff(c_122,plain,
    ! [A_136: ty,L_137: uni] : permut(A_136,L_137,L_137),
    inference(cnfTransformation,[status(thm)],[f_195]) ).

tff(c_333,plain,
    ! [A_249: ty,L_250: uni] : ( prefix(A_249,0,L_250) = nil(A_249) ),
    inference(cnfTransformation,[status(thm)],[f_356]) ).

tff(c_348,plain,
    ! [A_58: ty] : ( length(A_58,nil(A_58)) = 0 ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_302,plain,
    ( permut(elt1,prefix(elt1,length(elt1,t2tb('#skF_15')),t2tb('#skF_15')),t2tb('#skF_15'))
    | ~ permut(elt1,prefix(elt1,length(elt1,nil(elt1)),nil(elt1)),nil(elt1)) ),
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_387,plain,
    ( permut(elt1,prefix(elt1,length(elt1,t2tb('#skF_15')),t2tb('#skF_15')),t2tb('#skF_15'))
    | ~ permut(elt1,prefix(elt1,0,nil(elt1)),nil(elt1)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_348,c_302]) ).

tff(c_393,plain,
    permut(elt1,prefix(elt1,length(elt1,t2tb('#skF_15')),t2tb('#skF_15')),t2tb('#skF_15')),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_333,c_387]) ).

tff(c_449,plain,
    length(elt1,t2tb('#skF_15')) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_393]) ).

tff(c_456,plain,
    permut(elt1,prefix(elt1,'#skE_1',t2tb('#skF_15')),t2tb('#skF_15')),
    inference(demodulation,[status(thm),theory(equality)],[c_449,c_393]) ).

tff(c_762,plain,
    ! [A_554: ty,L2_555: uni,L1_556: uni] :
      ( permut(A_554,L2_555,L1_556)
      | ~ permut(A_554,L1_556,L2_555) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_769,plain,
    permut(elt1,t2tb('#skF_15'),prefix(elt1,'#skE_1',t2tb('#skF_15'))),
    inference(resolution,[status(thm)],[c_456,c_762]) ).

tff(c_4486,plain,
    ! [A_1114: ty,X_1115: uni,L1_1116: uni,L2_1117: uni] :
      ( permut(A_1114,cons(A_1114,X_1115,L1_1116),cons(A_1114,X_1115,L2_1117))
      | ~ permut(A_1114,L1_1116,L2_1117) ),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_124,plain,
    ! [A_138: ty,L2_140: uni,L1_139: uni] :
      ( permut(A_138,L2_140,L1_139)
      | ~ permut(A_138,L1_139,L2_140) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_87123,plain,
    ! [A_4980: ty,X_4981: uni,L2_4982: uni,L1_4983: uni] :
      ( permut(A_4980,cons(A_4980,X_4981,L2_4982),cons(A_4980,X_4981,L1_4983))
      | ~ permut(A_4980,L1_4983,L2_4982) ),
    inference(resolution,[status(thm)],[c_4486,c_124]) ).

tff(c_93328,plain,
    ! [X_4981: uni] : permut(elt1,cons(elt1,X_4981,prefix(elt1,'#skE_1',t2tb('#skF_15'))),cons(elt1,X_4981,t2tb('#skF_15'))),
    inference(resolution,[status(thm)],[c_769,c_87123]) ).

tff(c_21007,plain,
    ! [A_2248: ty,N_2249a: $int,X_2251: uni,L_2250: uni] :
      ( ( prefix(A_2248,N_2249a,cons(A_2248,X_2251,L_2250)) = cons(A_2248,X_2251,prefix(A_2248,$sum($uminus(1),N_2249a),L_2250)) )
      | ~ $less(0,N_2249a) ),
    inference(cnfTransformation,[status(thm)],[f_360]) ).

tff(c_453,plain,
    length(elt1,t2tb('#skF_15')) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_393]) ).

tff(c_351,plain,
    ! [A_51: ty,X_54: uni,X1_55: uni] : ( length(A_51,cons(A_51,X_54,X1_55)) = $sum(1,length(A_51,X1_55)) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_303,plain,
    ( ~ permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
    | ~ permut(elt1,prefix(elt1,length(elt1,nil(elt1)),nil(elt1)),nil(elt1)) ),
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_385,plain,
    ( ~ permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
    | ~ permut(elt1,prefix(elt1,0,nil(elt1)),nil(elt1)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_348,c_303]) ).

tff(c_390,plain,
    ~ permut(elt1,prefix(elt1,length(elt1,cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_333,c_385]) ).

tff(c_395,plain,
    ~ permut(elt1,prefix(elt1,$sum(1,length(elt1,t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),
    inference(demodulation,[status(thm),theory(equality)],[c_351,c_390]) ).

tff(c_569,plain,
    ~ permut(elt1,prefix(elt1,$sum(1,'#skE_1'),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15'))),
    inference(demodulation,[status(thm),theory(equality)],[c_453,c_395]) ).

tff(c_21236,plain,
    ( ~ permut(elt1,cons(elt1,t2tb1('#skF_14'),prefix(elt1,$sum($uminus(1),$sum(1,'#skE_1')),t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
    | ~ $less(0,$sum(1,'#skE_1')) ),
    inference(superposition,[status(thm),theory(equality)],[c_21007,c_569]) ).

tff(c_21239,plain,
    ( ~ permut(elt1,cons(elt1,t2tb1('#skF_14'),prefix(elt1,'#skE_1',t2tb('#skF_15'))),cons(elt1,t2tb1('#skF_14'),t2tb('#skF_15')))
    | ~ $less($uminus(1),'#skE_1') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_21236]) ).

tff(c_194365,plain,
    ~ $less($uminus(1),'#skE_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_93328,c_21239]) ).

tff(c_53,plain,
    ! [A_63: ty,L2_64: uni] : ( infix_plpl(A_63,nil(A_63),L2_64) = L2_64 ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_98,plain,
    ! [A_108: ty] : ( reverse(A_108,nil(A_108)) = nil(A_108) ),
    inference(cnfTransformation,[status(thm)],[f_167]) ).

tff(c_8283,plain,
    ! [A_1447: ty,L_1448: uni,X_1449: uni] : ( infix_plpl(A_1447,reverse(A_1447,L_1448),cons(A_1447,X_1449,nil(A_1447))) = reverse(A_1447,cons(A_1447,X_1449,L_1448)) ),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_8330,plain,
    ! [A_108: ty,X_1449: uni] : ( infix_plpl(A_108,nil(A_108),cons(A_108,X_1449,nil(A_108))) = reverse(A_108,cons(A_108,X_1449,nil(A_108))) ),
    inference(superposition,[status(thm),theory(equality)],[c_98,c_8283]) ).

tff(c_8354,plain,
    ! [A_108: ty,X_1449: uni] : ( reverse(A_108,cons(A_108,X_1449,nil(A_108))) = cons(A_108,X_1449,nil(A_108)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_53,c_8330]) ).

tff(c_340,plain,
    ! [A_125: ty,L_126: uni] : ( length(A_125,reverse(A_125,L_126)) = length(A_125,L_126) ),
    inference(cnfTransformation,[status(thm)],[f_179]) ).

tff(c_347,plain,
    ! [A_75: ty,L1_76: uni,L2_77: uni] : ( length(A_75,infix_plpl(A_75,L1_76,L2_77)) = $sum(length(A_75,L1_76),length(A_75,L2_77)) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_8301,plain,
    ! [A_1447: ty,X_1449: uni,L_1448: uni] : ( length(A_1447,reverse(A_1447,cons(A_1447,X_1449,L_1448))) = $sum(length(A_1447,reverse(A_1447,L_1448)),length(A_1447,cons(A_1447,X_1449,nil(A_1447)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_8283,c_347]) ).

tff(c_8346,plain,
    ! [A_1447: ty,X_1449: uni,L_1448: uni] : ( length(A_1447,reverse(A_1447,cons(A_1447,X_1449,L_1448))) = $sum(length(A_1447,L_1448),$sum(1,0)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_348,c_351,c_340,c_8301]) ).

tff(c_63319,plain,
    ! [A_4147: ty,X_4148: uni,L_4149: uni] : ( length(A_4147,reverse(A_4147,cons(A_4147,X_4148,L_4149))) = $sum(1,length(A_4147,L_4149)) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8346]) ).

tff(c_63563,plain,
    ! [A_108: ty,X_1449: uni] : ( length(A_108,cons(A_108,X_1449,nil(A_108))) = $sum(1,length(A_108,nil(A_108))) ),
    inference(superposition,[status(thm),theory(equality)],[c_8354,c_63319]) ).

tff(c_63811,plain,
    ! [A_108: ty,X_1449: uni] : ( length(A_108,cons(A_108,X_1449,nil(A_108))) = $sum(1,0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_348,c_63563]) ).

tff(c_63827,plain,
    ! [A_4204: ty,X_4205: uni] : ( length(A_4204,cons(A_4204,X_4205,nil(A_4204))) = 1 ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_63811]) ).

tff(c_3651,plain,
    ! [A_1036: ty,L1_1037: uni,L2_1038: uni] : ( length(A_1036,infix_plpl(A_1036,L1_1037,L2_1038)) = $sum(length(A_1036,L1_1037),length(A_1036,L2_1038)) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_44,plain,
    ! [A_56: ty,L_57: uni] : $lesseq(0,length(A_56,L_57)),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_350,plain,
    ! [A_56: ty,L_57: uni] : ~ $less(length(A_56,L_57),0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_44]) ).

tff(c_3659,plain,
    ! [A_1036: ty,L1_1037: uni,L2_1038: uni] : ~ $less($sum(length(A_1036,L1_1037),length(A_1036,L2_1038)),0),
    inference(superposition,[status(thm),theory(equality)],[c_3651,c_350]) ).

tff(c_3683,plain,
    ! [A_1039: ty,L2_1040: uni,L1_1041: uni] : ~ $less($sum(length(A_1039,L2_1040),length(A_1039,L1_1041)),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3659]) ).

tff(c_3752,plain,
    ! [L1_1051: uni] : ~ $less($sum('#skE_1',length(elt1,L1_1051)),0),
    inference(superposition,[status(thm),theory(equality)],[c_453,c_3683]) ).

tff(c_3863,plain,
    ! [L1_1058: uni,L2_1059: uni] : ~ $less($sum('#skE_1',$sum(length(elt1,L1_1058),length(elt1,L2_1059))),0),
    inference(superposition,[status(thm),theory(equality)],[c_347,c_3752]) ).

tff(c_3944,plain,
    ! [L1_1058: uni] : ~ $less($sum('#skE_1',$sum(length(elt1,L1_1058),'#skE_1')),0),
    inference(superposition,[status(thm),theory(equality)],[c_453,c_3863]) ).

tff(c_4304,plain,
    ! [L1_1101: uni] : ~ $less($sum($product(2,'#skE_1'),length(elt1,L1_1101)),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3944]) ).

tff(c_6861,plain,
    ! [L1_1354: uni,L2_1355: uni] : ~ $less($sum($product(2,'#skE_1'),$sum(length(elt1,L1_1354),length(elt1,L2_1355))),0),
    inference(superposition,[status(thm),theory(equality)],[c_347,c_4304]) ).

tff(c_6974,plain,
    ! [L1_1354: uni] : ~ $less($sum($product(2,'#skE_1'),$sum(length(elt1,L1_1354),'#skE_1')),0),
    inference(superposition,[status(thm),theory(equality)],[c_453,c_6861]) ).

tff(c_7431,plain,
    ! [L1_1400: uni] : ~ $less($sum($product(3,'#skE_1'),length(elt1,L1_1400)),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6974]) ).

tff(c_8604,plain,
    ! [L1_1466: uni,L2_1467: uni] : ~ $less($sum($product(3,'#skE_1'),$sum(length(elt1,L1_1466),length(elt1,L2_1467))),0),
    inference(superposition,[status(thm),theory(equality)],[c_347,c_7431]) ).

tff(c_8717,plain,
    ! [L1_1466: uni] : ~ $less($sum($product(3,'#skE_1'),$sum(length(elt1,L1_1466),'#skE_1')),0),
    inference(superposition,[status(thm),theory(equality)],[c_453,c_8604]) ).

tff(c_8720,plain,
    ! [L1_1466: uni] : ~ $less($sum($product(4,'#skE_1'),length(elt1,L1_1466)),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8717]) ).

tff(c_64181,plain,
    ~ $less($sum($product(4,'#skE_1'),1),0),
    inference(superposition,[status(thm),theory(equality)],[c_63827,c_8720]) ).

tff(c_64183,plain,
    ~ $less($product(2,'#skE_1'),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_64181]) ).

tff(c_194366,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_194365,c_64183]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWW624_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14  % 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
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 18:51:51 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 50.46/25.17  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.46/25.18  
% 50.46/25.18  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.46/25.21  
% 50.46/25.21  Inference rules
% 50.46/25.21  ----------------------
% 50.46/25.21  #Ref     : 4
% 50.46/25.21  #Sup     : 29778
% 50.46/25.21  #Fact    : 25
% 50.46/25.21  #Define  : 22
% 50.46/25.21  #Split   : 107
% 50.46/25.21  #Chain   : 0
% 50.46/25.21  #Close   : 3
% 50.46/25.21  
% 50.46/25.21  Ordering : LPO
% 50.46/25.21  
% 50.46/25.21  Simplification rules
% 50.46/25.21  ----------------------
% 50.46/25.21  #Subsume      : 1454
% 50.46/25.21  #Demod        : 10062
% 50.46/25.21  #Tautology    : 15734
% 50.46/25.21  #SimpNegUnit  : 209
% 50.46/25.21  #BackRed      : 19
% 50.46/25.21  
% 50.46/25.21  #Partial instantiations: 896
% 50.46/25.21  #Strategies tried      : 1
% 50.46/25.21  
% 50.46/25.21  Timing (in seconds)
% 50.46/25.21  ----------------------
% 50.46/25.21  Preprocessing        : 0.96
% 50.46/25.21  Parsing              : 0.51
% 50.46/25.21  CNF conversion       : 0.07
% 50.46/25.21  Main loop            : 23.16
% 50.46/25.21  Inferencing          : 2.96
% 50.46/25.21  Reduction            : 9.47
% 50.46/25.21  Demodulation         : 7.46
% 50.46/25.21  BG Simplification    : 1.12
% 50.46/25.21  Subsumption          : 7.66
% 50.46/25.21  Abstraction          : 0.57
% 50.46/25.21  MUC search           : 0.04
% 50.46/25.22  Cooper               : 0.12
% 50.46/25.22  Total                : 24.18
% 50.46/25.22  Index Insertion      : 0.00
% 50.46/25.22  Index Deletion       : 0.00
% 50.46/25.22  Index Matching       : 0.00
% 50.46/25.22  BG Taut test         : 0.00
%------------------------------------------------------------------------------