TSTP Solution File: ANA002-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ANA002-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:32:44 EDT 2023

% Result   : Unsatisfiable 166.52s 150.99s
% Output   : CNFRefutation 166.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  117 (  39 unt;  11 typ;   0 def)
%            Number of atoms       :  245 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  245 ( 106   ~; 139   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   88 (;  88   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in_interval > less_than_or_equal > q > #nlpp > k > h > g > f > upper_bound > n0 > lower_bound > l

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(in_interval,type,
    in_interval: ( $i * $i * $i ) > $o ).

tff(lower_bound,type,
    lower_bound: $i ).

tff(l,type,
    l: $i ).

tff(less_than_or_equal,type,
    less_than_or_equal: ( $i * $i ) > $o ).

tff(f,type,
    f: $i > $i ).

tff(g,type,
    g: $i > $i ).

tff(q,type,
    q: ( $i * $i ) > $i ).

tff(n0,type,
    n0: $i ).

tff(h,type,
    h: $i > $i ).

tff(k,type,
    k: $i > $i ).

tff(upper_bound,type,
    upper_bound: $i ).

tff(f_130,axiom,
    less_than_or_equal(n0,f(upper_bound)),
    file(unknown,unknown) ).

tff(f_128,axiom,
    less_than_or_equal(lower_bound,upper_bound),
    file(unknown,unknown) ).

tff(f_129,axiom,
    less_than_or_equal(f(lower_bound),n0),
    file(unknown,unknown) ).

tff(f_113,axiom,
    ! [X] :
      ( less_than_or_equal(X,l)
      | ~ less_than_or_equal(X,upper_bound)
      | ~ less_than_or_equal(f(X),n0) ),
    file(unknown,unknown) ).

tff(f_117,axiom,
    ! [X] :
      ( less_than_or_equal(g(X),upper_bound)
      | less_than_or_equal(l,X) ),
    file(unknown,unknown) ).

tff(f_126,axiom,
    ! [X] :
      ( ~ less_than_or_equal(g(X),X)
      | less_than_or_equal(l,X) ),
    file(unknown,unknown) ).

tff(f_35,axiom,
    ! [Lower,X,Upper] :
      ( in_interval(Lower,X,Upper)
      | ~ less_than_or_equal(Lower,X)
      | ~ less_than_or_equal(X,Upper) ),
    file(unknown,unknown) ).

tff(f_121,axiom,
    ! [X] :
      ( less_than_or_equal(f(g(X)),n0)
      | less_than_or_equal(l,X) ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ! [X,Y] :
      ( less_than_or_equal(f(X),n0)
      | ~ less_than_or_equal(Y,X)
      | ~ less_than_or_equal(f(Y),n0)
      | less_than_or_equal(Y,h(X))
      | ~ in_interval(lower_bound,X,upper_bound) ),
    file(unknown,unknown) ).

tff(f_133,axiom,
    ! [X] : ~ in_interval(f(X),n0,f(X)),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ! [X] : less_than_or_equal(X,X),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [X,Z,Y] :
      ( less_than_or_equal(X,Z)
      | ~ less_than_or_equal(X,Y)
      | ~ less_than_or_equal(Y,Z) ),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X] :
      ( less_than_or_equal(f(X),n0)
      | ~ less_than_or_equal(X,h(X))
      | ~ in_interval(lower_bound,X,upper_bound) ),
    file(unknown,unknown) ).

tff(f_42,axiom,
    ! [X,Y] :
      ( less_than_or_equal(X,Y)
      | less_than_or_equal(Y,X) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ! [X,Y] :
      ( less_than_or_equal(n0,f(X))
      | ~ less_than_or_equal(X,Y)
      | ~ less_than_or_equal(n0,f(Y))
      | less_than_or_equal(k(X),Y)
      | ~ in_interval(lower_bound,X,upper_bound) ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [X,Y] :
      ( ~ less_than_or_equal(X,q(Y,X))
      | less_than_or_equal(X,Y) ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [X,Y] :
      ( ~ less_than_or_equal(q(X,Y),X)
      | less_than_or_equal(Y,X) ),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [X] :
      ( less_than_or_equal(n0,f(X))
      | ~ less_than_or_equal(k(X),X)
      | ~ in_interval(lower_bound,X,upper_bound) ),
    file(unknown,unknown) ).

tff(c_34,plain,
    less_than_or_equal(n0,f(upper_bound)),
    inference(cnfTransformation,[status(thm)],[f_130]) ).

tff(c_30,plain,
    less_than_or_equal(lower_bound,upper_bound),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_32,plain,
    less_than_or_equal(f(lower_bound),n0),
    inference(cnfTransformation,[status(thm)],[f_129]) ).

tff(c_176,plain,
    ! [X_45] :
      ( ~ less_than_or_equal(f(X_45),n0)
      | ~ less_than_or_equal(X_45,upper_bound)
      | less_than_or_equal(X_45,l) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_188,plain,
    ( ~ less_than_or_equal(lower_bound,upper_bound)
    | less_than_or_equal(lower_bound,l) ),
    inference(resolution,[status(thm)],[c_32,c_176]) ).

tff(c_194,plain,
    less_than_or_equal(lower_bound,l),
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_188]) ).

tff(c_24,plain,
    ! [X_21] :
      ( less_than_or_equal(l,X_21)
      | less_than_or_equal(g(X_21),upper_bound) ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_57,plain,
    ! [X_30] :
      ( less_than_or_equal(l,X_30)
      | ~ less_than_or_equal(g(X_30),X_30) ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_70,plain,
    less_than_or_equal(l,upper_bound),
    inference(resolution,[status(thm)],[c_24,c_57]) ).

tff(c_2,plain,
    ! [X_2,Upper_3,Lower_1] :
      ( ~ less_than_or_equal(X_2,Upper_3)
      | ~ less_than_or_equal(Lower_1,X_2)
      | in_interval(Lower_1,X_2,Upper_3) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_26,plain,
    ! [X_22] :
      ( less_than_or_equal(l,X_22)
      | less_than_or_equal(f(g(X_22)),n0) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_3199,plain,
    ! [X_118] :
      ( ~ less_than_or_equal(g(X_118),upper_bound)
      | less_than_or_equal(g(X_118),l)
      | less_than_or_equal(l,X_118) ),
    inference(resolution,[status(thm)],[c_26,c_176]) ).

tff(c_3259,plain,
    ! [X_21] :
      ( less_than_or_equal(g(X_21),l)
      | less_than_or_equal(l,X_21) ),
    inference(resolution,[status(thm)],[c_24,c_3199]) ).

tff(c_476,plain,
    ! [X_63,Y_64] :
      ( ~ in_interval(lower_bound,X_63,upper_bound)
      | less_than_or_equal(Y_64,h(X_63))
      | ~ less_than_or_equal(f(Y_64),n0)
      | ~ less_than_or_equal(Y_64,X_63)
      | less_than_or_equal(f(X_63),n0) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_6582,plain,
    ! [X_154,X_155] :
      ( ~ in_interval(lower_bound,X_154,upper_bound)
      | less_than_or_equal(g(X_155),h(X_154))
      | ~ less_than_or_equal(g(X_155),X_154)
      | less_than_or_equal(f(X_154),n0)
      | less_than_or_equal(l,X_155) ),
    inference(resolution,[status(thm)],[c_26,c_476]) ).

tff(c_28,plain,
    ! [X_23] :
      ( less_than_or_equal(l,X_23)
      | ~ less_than_or_equal(g(X_23),X_23) ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_20812,plain,
    ! [X_284] :
      ( ~ in_interval(lower_bound,X_284,upper_bound)
      | ~ less_than_or_equal(g(h(X_284)),X_284)
      | less_than_or_equal(f(X_284),n0)
      | less_than_or_equal(l,h(X_284)) ),
    inference(resolution,[status(thm)],[c_6582,c_28]) ).

tff(c_21196,plain,
    ( ~ in_interval(lower_bound,l,upper_bound)
    | less_than_or_equal(f(l),n0)
    | less_than_or_equal(l,h(l)) ),
    inference(resolution,[status(thm)],[c_3259,c_20812]) ).

tff(c_91133,plain,
    ~ in_interval(lower_bound,l,upper_bound),
    inference(splitLeft,[status(thm)],[c_21196]) ).

tff(c_91136,plain,
    ( ~ less_than_or_equal(l,upper_bound)
    | ~ less_than_or_equal(lower_bound,l) ),
    inference(resolution,[status(thm)],[c_2,c_91133]) ).

tff(c_91140,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_194,c_70,c_91136]) ).

tff(c_91141,plain,
    ( less_than_or_equal(l,h(l))
    | less_than_or_equal(f(l),n0) ),
    inference(splitRight,[status(thm)],[c_21196]) ).

tff(c_91143,plain,
    less_than_or_equal(f(l),n0),
    inference(splitLeft,[status(thm)],[c_91141]) ).

tff(c_260,plain,
    ! [X_49,Upper_50,Lower_51] :
      ( ~ less_than_or_equal(X_49,Upper_50)
      | ~ less_than_or_equal(Lower_51,X_49)
      | in_interval(Lower_51,X_49,Upper_50) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_36,plain,
    ! [X_24] : ~ in_interval(f(X_24),n0,f(X_24)),
    inference(cnfTransformation,[status(thm)],[f_133]) ).

tff(c_264,plain,
    ! [X_24] :
      ( ~ less_than_or_equal(n0,f(X_24))
      | ~ less_than_or_equal(f(X_24),n0) ),
    inference(resolution,[status(thm)],[c_260,c_36]) ).

tff(c_91657,plain,
    ~ less_than_or_equal(n0,f(l)),
    inference(resolution,[status(thm)],[c_91143,c_264]) ).

tff(c_91142,plain,
    in_interval(lower_bound,l,upper_bound),
    inference(splitRight,[status(thm)],[c_21196]) ).

tff(c_4,plain,
    ! [X_4] : less_than_or_equal(X_4,X_4),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_98,plain,
    ! [Y_39,Z_40,X_41] :
      ( ~ less_than_or_equal(Y_39,Z_40)
      | ~ less_than_or_equal(X_41,Y_39)
      | less_than_or_equal(X_41,Z_40) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_129,plain,
    ! [X_41] :
      ( ~ less_than_or_equal(X_41,n0)
      | less_than_or_equal(X_41,f(upper_bound)) ),
    inference(resolution,[status(thm)],[c_34,c_98]) ).

tff(c_4505,plain,
    ! [X_133] :
      ( ~ in_interval(lower_bound,X_133,upper_bound)
      | less_than_or_equal(lower_bound,h(X_133))
      | ~ less_than_or_equal(lower_bound,X_133)
      | less_than_or_equal(f(X_133),n0) ),
    inference(resolution,[status(thm)],[c_32,c_476]) ).

tff(c_18969,plain,
    ! [X_274] :
      ( ~ less_than_or_equal(n0,f(X_274))
      | ~ in_interval(lower_bound,X_274,upper_bound)
      | less_than_or_equal(lower_bound,h(X_274))
      | ~ less_than_or_equal(lower_bound,X_274) ),
    inference(resolution,[status(thm)],[c_4505,c_264]) ).

tff(c_19052,plain,
    ( ~ in_interval(lower_bound,upper_bound,upper_bound)
    | less_than_or_equal(lower_bound,h(upper_bound))
    | ~ less_than_or_equal(lower_bound,upper_bound)
    | ~ less_than_or_equal(n0,n0) ),
    inference(resolution,[status(thm)],[c_129,c_18969]) ).

tff(c_19099,plain,
    ( ~ in_interval(lower_bound,upper_bound,upper_bound)
    | less_than_or_equal(lower_bound,h(upper_bound)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_30,c_19052]) ).

tff(c_19103,plain,
    ~ in_interval(lower_bound,upper_bound,upper_bound),
    inference(splitLeft,[status(thm)],[c_19099]) ).

tff(c_19106,plain,
    ( ~ less_than_or_equal(upper_bound,upper_bound)
    | ~ less_than_or_equal(lower_bound,upper_bound) ),
    inference(resolution,[status(thm)],[c_2,c_19103]) ).

tff(c_19110,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_4,c_19106]) ).

tff(c_19112,plain,
    in_interval(lower_bound,upper_bound,upper_bound),
    inference(splitRight,[status(thm)],[c_19099]) ).

tff(c_21136,plain,
    ( ~ in_interval(lower_bound,upper_bound,upper_bound)
    | less_than_or_equal(f(upper_bound),n0)
    | less_than_or_equal(l,h(upper_bound)) ),
    inference(resolution,[status(thm)],[c_24,c_20812]) ).

tff(c_21239,plain,
    ( less_than_or_equal(f(upper_bound),n0)
    | less_than_or_equal(l,h(upper_bound)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_19112,c_21136]) ).

tff(c_21328,plain,
    less_than_or_equal(l,h(upper_bound)),
    inference(splitLeft,[status(thm)],[c_21239]) ).

tff(c_8,plain,
    ! [Y_9,Z_8,X_7] :
      ( ~ less_than_or_equal(Y_9,Z_8)
      | ~ less_than_or_equal(X_7,Y_9)
      | less_than_or_equal(X_7,Z_8) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_21398,plain,
    ! [X_285] :
      ( ~ less_than_or_equal(X_285,l)
      | less_than_or_equal(X_285,h(upper_bound)) ),
    inference(resolution,[status(thm)],[c_21328,c_8]) ).

tff(c_14,plain,
    ! [X_14] :
      ( ~ in_interval(lower_bound,X_14,upper_bound)
      | ~ less_than_or_equal(X_14,h(X_14))
      | less_than_or_equal(f(X_14),n0) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_21439,plain,
    ( ~ in_interval(lower_bound,upper_bound,upper_bound)
    | less_than_or_equal(f(upper_bound),n0)
    | ~ less_than_or_equal(upper_bound,l) ),
    inference(resolution,[status(thm)],[c_21398,c_14]) ).

tff(c_21482,plain,
    ( less_than_or_equal(f(upper_bound),n0)
    | ~ less_than_or_equal(upper_bound,l) ),
    inference(demodulation,[status(thm),theory(equality)],[c_19112,c_21439]) ).

tff(c_21578,plain,
    ~ less_than_or_equal(upper_bound,l),
    inference(splitLeft,[status(thm)],[c_21482]) ).

tff(c_6,plain,
    ! [Y_6,X_5] :
      ( less_than_or_equal(Y_6,X_5)
      | less_than_or_equal(X_5,Y_6) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_191,plain,
    ! [X_45] :
      ( ~ less_than_or_equal(X_45,upper_bound)
      | less_than_or_equal(X_45,l)
      | less_than_or_equal(n0,f(X_45)) ),
    inference(resolution,[status(thm)],[c_6,c_176]) ).

tff(c_392,plain,
    ! [X_57,Y_58] :
      ( ~ in_interval(lower_bound,X_57,upper_bound)
      | less_than_or_equal(k(X_57),Y_58)
      | ~ less_than_or_equal(n0,f(Y_58))
      | ~ less_than_or_equal(X_57,Y_58)
      | less_than_or_equal(n0,f(X_57)) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_7382,plain,
    ! [X_162,X_163,Y_164] :
      ( ~ less_than_or_equal(X_162,k(X_163))
      | less_than_or_equal(X_162,Y_164)
      | ~ in_interval(lower_bound,X_163,upper_bound)
      | ~ less_than_or_equal(n0,f(Y_164))
      | ~ less_than_or_equal(X_163,Y_164)
      | less_than_or_equal(n0,f(X_163)) ),
    inference(resolution,[status(thm)],[c_392,c_8]) ).

tff(c_28589,plain,
    ! [Y_327,Y_328,X_329] :
      ( less_than_or_equal(Y_327,Y_328)
      | ~ in_interval(lower_bound,X_329,upper_bound)
      | ~ less_than_or_equal(n0,f(Y_328))
      | ~ less_than_or_equal(X_329,Y_328)
      | less_than_or_equal(n0,f(X_329))
      | less_than_or_equal(k(X_329),Y_327) ),
    inference(resolution,[status(thm)],[c_6,c_7382]) ).

tff(c_694583,plain,
    ! [Y_1700,X_1701,X_1702] :
      ( less_than_or_equal(Y_1700,X_1701)
      | ~ in_interval(lower_bound,X_1702,upper_bound)
      | ~ less_than_or_equal(X_1702,X_1701)
      | less_than_or_equal(n0,f(X_1702))
      | less_than_or_equal(k(X_1702),Y_1700)
      | ~ less_than_or_equal(X_1701,upper_bound)
      | less_than_or_equal(X_1701,l) ),
    inference(resolution,[status(thm)],[c_191,c_28589]) ).

tff(c_696179,plain,
    ! [Y_1700] :
      ( less_than_or_equal(Y_1700,upper_bound)
      | ~ in_interval(lower_bound,l,upper_bound)
      | less_than_or_equal(n0,f(l))
      | less_than_or_equal(k(l),Y_1700)
      | ~ less_than_or_equal(upper_bound,upper_bound)
      | less_than_or_equal(upper_bound,l) ),
    inference(resolution,[status(thm)],[c_70,c_694583]) ).

tff(c_697875,plain,
    ! [Y_1700] :
      ( less_than_or_equal(Y_1700,upper_bound)
      | less_than_or_equal(n0,f(l))
      | less_than_or_equal(k(l),Y_1700)
      | less_than_or_equal(upper_bound,l) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_91142,c_696179]) ).

tff(c_697893,plain,
    ! [Y_1703] :
      ( less_than_or_equal(Y_1703,upper_bound)
      | less_than_or_equal(k(l),Y_1703) ),
    inference(negUnitSimplification,[status(thm)],[c_21578,c_91657,c_697875]) ).

tff(c_10,plain,
    ! [X_10,Y_11] :
      ( less_than_or_equal(X_10,Y_11)
      | ~ less_than_or_equal(X_10,q(Y_11,X_10)) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_702774,plain,
    ! [Y_1709] :
      ( less_than_or_equal(k(l),Y_1709)
      | less_than_or_equal(q(Y_1709,k(l)),upper_bound) ),
    inference(resolution,[status(thm)],[c_697893,c_10]) ).

tff(c_73,plain,
    ! [Y_31,X_32] :
      ( less_than_or_equal(Y_31,X_32)
      | ~ less_than_or_equal(q(X_32,Y_31),X_32) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_82,plain,
    ! [Y_31,X_5] :
      ( less_than_or_equal(Y_31,X_5)
      | less_than_or_equal(X_5,q(X_5,Y_31)) ),
    inference(resolution,[status(thm)],[c_6,c_73]) ).

tff(c_8064,plain,
    ! [X_172,Y_173] :
      ( less_than_or_equal(k(X_172),Y_173)
      | ~ in_interval(lower_bound,X_172,upper_bound)
      | ~ less_than_or_equal(n0,f(q(Y_173,k(X_172))))
      | ~ less_than_or_equal(X_172,q(Y_173,k(X_172)))
      | less_than_or_equal(n0,f(X_172)) ),
    inference(resolution,[status(thm)],[c_392,c_10]) ).

tff(c_54579,plain,
    ! [X_447,Y_448] :
      ( less_than_or_equal(k(X_447),Y_448)
      | ~ in_interval(lower_bound,X_447,upper_bound)
      | ~ less_than_or_equal(X_447,q(Y_448,k(X_447)))
      | less_than_or_equal(n0,f(X_447))
      | ~ less_than_or_equal(q(Y_448,k(X_447)),upper_bound)
      | less_than_or_equal(q(Y_448,k(X_447)),l) ),
    inference(resolution,[status(thm)],[c_191,c_8064]) ).

tff(c_54825,plain,
    ! [X_5] :
      ( ~ in_interval(lower_bound,X_5,upper_bound)
      | less_than_or_equal(n0,f(X_5))
      | ~ less_than_or_equal(q(X_5,k(X_5)),upper_bound)
      | less_than_or_equal(q(X_5,k(X_5)),l)
      | less_than_or_equal(k(X_5),X_5) ),
    inference(resolution,[status(thm)],[c_82,c_54579]) ).

tff(c_702780,plain,
    ( ~ in_interval(lower_bound,l,upper_bound)
    | less_than_or_equal(n0,f(l))
    | less_than_or_equal(q(l,k(l)),l)
    | less_than_or_equal(k(l),l) ),
    inference(resolution,[status(thm)],[c_702774,c_54825]) ).

tff(c_703083,plain,
    ( less_than_or_equal(n0,f(l))
    | less_than_or_equal(q(l,k(l)),l)
    | less_than_or_equal(k(l),l) ),
    inference(demodulation,[status(thm),theory(equality)],[c_91142,c_702780]) ).

tff(c_703084,plain,
    ( less_than_or_equal(q(l,k(l)),l)
    | less_than_or_equal(k(l),l) ),
    inference(negUnitSimplification,[status(thm)],[c_91657,c_703083]) ).

tff(c_719444,plain,
    less_than_or_equal(k(l),l),
    inference(splitLeft,[status(thm)],[c_703084]) ).

tff(c_18,plain,
    ! [X_17] :
      ( ~ in_interval(lower_bound,X_17,upper_bound)
      | ~ less_than_or_equal(k(X_17),X_17)
      | less_than_or_equal(n0,f(X_17)) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_719719,plain,
    ( ~ in_interval(lower_bound,l,upper_bound)
    | less_than_or_equal(n0,f(l)) ),
    inference(resolution,[status(thm)],[c_719444,c_18]) ).

tff(c_720004,plain,
    less_than_or_equal(n0,f(l)),
    inference(demodulation,[status(thm),theory(equality)],[c_91142,c_719719]) ).

tff(c_720006,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_91657,c_720004]) ).

tff(c_720008,plain,
    ~ less_than_or_equal(k(l),l),
    inference(splitRight,[status(thm)],[c_703084]) ).

tff(c_720007,plain,
    less_than_or_equal(q(l,k(l)),l),
    inference(splitRight,[status(thm)],[c_703084]) ).

tff(c_12,plain,
    ! [Y_13,X_12] :
      ( less_than_or_equal(Y_13,X_12)
      | ~ less_than_or_equal(q(X_12,Y_13),X_12) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_720649,plain,
    less_than_or_equal(k(l),l),
    inference(resolution,[status(thm)],[c_720007,c_12]) ).

tff(c_720930,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_720008,c_720649]) ).

tff(c_720932,plain,
    ~ less_than_or_equal(f(l),n0),
    inference(splitRight,[status(thm)],[c_91141]) ).

tff(c_720931,plain,
    less_than_or_equal(l,h(l)),
    inference(splitRight,[status(thm)],[c_91141]) ).

tff(c_721020,plain,
    ( ~ in_interval(lower_bound,l,upper_bound)
    | less_than_or_equal(f(l),n0) ),
    inference(resolution,[status(thm)],[c_720931,c_14]) ).

tff(c_721104,plain,
    less_than_or_equal(f(l),n0),
    inference(demodulation,[status(thm),theory(equality)],[c_91142,c_721020]) ).

tff(c_721328,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_720932,c_721104]) ).

tff(c_721329,plain,
    less_than_or_equal(f(upper_bound),n0),
    inference(splitRight,[status(thm)],[c_21482]) ).

tff(c_721724,plain,
    ~ less_than_or_equal(n0,f(upper_bound)),
    inference(resolution,[status(thm)],[c_721329,c_264]) ).

tff(c_721764,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_721724]) ).

tff(c_721765,plain,
    less_than_or_equal(f(upper_bound),n0),
    inference(splitRight,[status(thm)],[c_21239]) ).

tff(c_721807,plain,
    ~ less_than_or_equal(n0,f(upper_bound)),
    inference(resolution,[status(thm)],[c_721765,c_264]) ).

tff(c_721850,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_721807]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ANA002-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n027.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 15:50:24 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 166.52/150.99  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 166.52/151.00  
% 166.52/151.00  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 166.52/151.05  
% 166.52/151.05  Inference rules
% 166.52/151.05  ----------------------
% 166.52/151.05  #Ref     : 0
% 166.52/151.05  #Sup     : 173655
% 166.52/151.05  #Fact    : 326
% 166.52/151.05  #Define  : 0
% 166.52/151.05  #Split   : 53
% 166.52/151.05  #Chain   : 0
% 166.52/151.05  #Close   : 0
% 166.52/151.05  
% 166.52/151.05  Ordering : KBO
% 166.52/151.05  
% 166.52/151.05  Simplification rules
% 166.52/151.05  ----------------------
% 166.52/151.05  #Subsume      : 92620
% 166.52/151.05  #Demod        : 80671
% 166.52/151.05  #Tautology    : 38289
% 166.52/151.05  #SimpNegUnit  : 6017
% 166.52/151.05  #BackRed      : 0
% 166.52/151.05  
% 166.52/151.05  #Partial instantiations: 0
% 166.52/151.05  #Strategies tried      : 1
% 166.52/151.05  
% 166.52/151.05  Timing (in seconds)
% 166.52/151.05  ----------------------
% 166.52/151.05  Preprocessing        : 0.44
% 166.52/151.05  Parsing              : 0.24
% 166.52/151.05  CNF conversion       : 0.03
% 166.52/151.05  Main loop            : 149.55
% 166.52/151.06  Inferencing          : 7.14
% 166.52/151.06  Reduction            : 35.40
% 166.52/151.06  Demodulation         : 25.36
% 166.52/151.06  BG Simplification    : 0.44
% 166.52/151.06  Subsumption          : 93.35
% 166.52/151.06  Abstraction          : 1.01
% 166.52/151.06  MUC search           : 0.00
% 166.52/151.06  Cooper               : 0.00
% 166.52/151.06  Total                : 150.07
% 166.52/151.06  Index Insertion      : 0.00
% 166.52/151.06  Index Deletion       : 0.00
% 166.52/151.06  Index Matching       : 0.00
% 166.52/151.06  BG Taut test         : 0.00
%------------------------------------------------------------------------------