TSTP Solution File: ANA003-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ANA003-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Mon May 20 18:38:51 EDT 2024

% Result   : Unsatisfiable 125.01s 22.18s
% Output   : Refutation 125.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  204 (  80 unt;  16 typ;   0 def)
%            Number of atoms       :  423 ( 170 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives : 1566 ( 227   ~; 135   |;   0   &;1204   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   6 con; 0-2 aty)
%            Number of variables   :  169 (   0   ^ 169   !;   0   ?; 169   :)

% Comments : 
%------------------------------------------------------------------------------
thf(less_than_type,type,
    less_than: $i > $i > $o ).

thf(n0_type,type,
    n0: $i ).

thf(fp31_type,type,
    fp31: $i > $i ).

thf(absolute_type,type,
    absolute: $i > $i ).

thf(add_type,type,
    add: $i > $i > $i ).

thf(minus_type,type,
    minus: $i > $i ).

thf(a_type,type,
    a: $i ).

thf(f_type,type,
    f: $i > $i ).

thf(l1_type,type,
    l1: $i ).

thf(fp32_type,type,
    fp32: $i > $i ).

thf(g_type,type,
    g: $i > $i ).

thf(l2_type,type,
    l2: $i ).

thf(b_type,type,
    b: $i ).

thf(fp33_type,type,
    fp33: $i > $i ).

thf(minimum_type,type,
    minimum: $i > $i > $i ).

thf(half_type,type,
    half: $i > $i ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ ( half @ B ) )
      | ~ ( less_than @ C @ ( half @ B ) )
      | ( less_than @ ( add @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(49,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ ( half @ B ) )
      | ~ ( less_than @ C @ ( half @ B ) )
      | ( less_than @ ( add @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(5,negated_conjecture,
    less_than @ n0 @ b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).

thf(22,plain,
    less_than @ n0 @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp32 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).

thf(27,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp32 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(32,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp32 @ A ) ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(120,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ b )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22,32]) ).

thf(121,plain,
    less_than @ n0 @ ( fp32 @ b ),
    inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( b ))]]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp31 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp31 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(34,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp31 @ A ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(627,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ b ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[121,34]) ).

thf(628,plain,
    less_than @ n0 @ ( fp31 @ ( fp32 @ b ) ),
    inference(pattern_uni,[status(thm)],[627:[bind(A,$thf( fp32 @ b ))]]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( add @ n0 @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

thf(37,plain,
    ! [A: $i] :
      ( ( add @ n0 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(38,plain,
    ! [A: $i] :
      ( ( add @ n0 @ A )
      = A ),
    inference(lifteq,[status(thm)],[37]) ).

thf(6,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).

thf(24,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(30,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(262,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A )
      | ( ( less_than @ n0 @ ( fp32 @ b ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[121,30]) ).

thf(263,plain,
    less_than @ ( absolute @ ( add @ ( fp33 @ ( fp32 @ b ) ) @ ( minus @ a ) ) ) @ ( fp32 @ b ),
    inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( fp32 @ b ))]]) ).

thf(10,axiom,
    ! [A: $i] :
      ~ ( less_than @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_less_than) ).

thf(39,plain,
    ! [A: $i] :
      ~ ( less_than @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(40,plain,
    ! [A: $i] :
      ~ ( less_than @ A @ A ),
    inference(polarity_switch,[status(thm)],[39]) ).

thf(521,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ ( add @ ( fp33 @ ( fp32 @ b ) ) @ ( minus @ a ) ) ) @ ( fp32 @ b ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[263,40]) ).

thf(537,plain,
    ! [A: $i] :
      ( ( ( absolute @ ( add @ ( fp33 @ ( fp32 @ b ) ) @ ( minus @ a ) ) )
       != A )
      | ( ( fp32 @ b )
       != A ) ),
    inference(simp,[status(thm)],[521]) ).

thf(548,plain,
    ( ( absolute @ ( add @ ( fp33 @ ( fp32 @ b ) ) @ ( minus @ a ) ) )
   != ( fp32 @ b ) ),
    inference(simp,[status(thm)],[537]) ).

thf(551,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != ( fp32 @ b ) )
      | ( ( add @ n0 @ A )
       != ( add @ ( fp33 @ ( fp32 @ b ) ) @ ( minus @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[38,548]) ).

thf(553,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != ( fp32 @ b ) )
      | ( ( fp33 @ ( fp32 @ b ) )
       != n0 )
      | ( A
       != ( minus @ a ) ) ),
    inference(simp,[status(thm)],[551]) ).

thf(555,plain,
    ( ( ( fp32 @ b )
     != ( absolute @ ( minus @ a ) ) )
    | ( ( fp33 @ ( fp32 @ b ) )
     != n0 ) ),
    inference(simp,[status(thm)],[553]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_than) ).

thf(41,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(42,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    inference(cnf,[status(esa)],[41]) ).

thf(2,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp31 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( f @ B ) @ ( minus @ l1 ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp31 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( f @ B ) @ ( minus @ l1 ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(621,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ A ) )
      | ( ( less_than @ n0 @ b )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22,34]) ).

thf(622,plain,
    less_than @ n0 @ ( fp31 @ b ),
    inference(pattern_uni,[status(thm)],[621:[bind(A,$thf( b ))]]) ).

thf(832,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp31 @ b ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[622,32]) ).

thf(833,plain,
    less_than @ n0 @ ( fp32 @ ( fp31 @ b ) ),
    inference(pattern_uni,[status(thm)],[832:[bind(A,$thf( fp31 @ b ))]]) ).

thf(896,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp31 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[833,32]) ).

thf(897,plain,
    less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp31 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( fp32 @ ( fp31 @ b ) ))]]) ).

thf(123,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( ( less_than @ n0 @ ( fp32 @ A ) )
       != ( less_than @ B @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[32,40]) ).

thf(127,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( n0 != B )
      | ( ( fp32 @ A )
       != B ) ),
    inference(simp,[status(thm)],[123]) ).

thf(132,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( ( fp32 @ A )
       != n0 ) ),
    inference(simp,[status(thm)],[127]) ).

thf(1429,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp31 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[897,132]) ).

thf(1430,plain,
    ( ( fp32 @ ( fp32 @ ( fp32 @ ( fp31 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[1429:[bind(A,$thf( fp32 @ ( fp32 @ ( fp31 @ b ) ) ))]]) ).

thf(133,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ b ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[121,32]) ).

thf(134,plain,
    less_than @ n0 @ ( fp32 @ ( fp32 @ b ) ),
    inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( fp32 @ b ))]]) ).

thf(195,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[134,32]) ).

thf(196,plain,
    less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( fp32 @ ( fp32 @ b ) ))]]) ).

thf(834,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ A ) )
      | ( ( less_than @ n0 @ ( fp31 @ b ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[622,34]) ).

thf(835,plain,
    less_than @ n0 @ ( fp31 @ ( fp31 @ b ) ),
    inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( fp31 @ b ))]]) ).

thf(928,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[835,32]) ).

thf(929,plain,
    less_than @ n0 @ ( fp32 @ ( fp31 @ ( fp31 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[928:[bind(A,$thf( fp31 @ ( fp31 @ b ) ))]]) ).

thf(1513,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp31 @ ( fp31 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[929,132]) ).

thf(1514,plain,
    ( ( fp32 @ ( fp32 @ ( fp31 @ ( fp31 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[1513:[bind(A,$thf( fp32 @ ( fp31 @ ( fp31 @ b ) ) ))]]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_2) ).

thf(45,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(46,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ A ) ),
    inference(cnf,[status(esa)],[45]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( half @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6_2) ).

thf(57,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( half @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(4,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp32 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( g @ B ) @ ( minus @ l2 ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp32 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( g @ B ) @ ( minus @ l2 ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp32 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( g @ B ) @ ( minus @ l2 ) ) ) @ A ) ),
    inference(cnf,[status(esa)],[28]) ).

thf(930,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ A ) )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[835,34]) ).

thf(931,plain,
    less_than @ n0 @ ( fp31 @ ( fp31 @ ( fp31 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[930:[bind(A,$thf( fp31 @ ( fp31 @ b ) ))]]) ).

thf(1547,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ ( fp31 @ b ) ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[931,40]) ).

thf(1576,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp31 @ ( fp31 @ ( fp31 @ b ) ) )
       != A ) ),
    inference(simp,[status(thm)],[1547]) ).

thf(1581,plain,
    ( ( fp31 @ ( fp31 @ ( fp31 @ b ) ) )
   != n0 ),
    inference(simp,[status(thm)],[1576]) ).

thf(270,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A )
      | ( ( less_than @ n0 @ b )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22,30]) ).

thf(271,plain,
    less_than @ ( absolute @ ( add @ ( fp33 @ b ) @ ( minus @ a ) ) ) @ b,
    inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( b ))]]) ).

thf(330,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ ( add @ ( fp33 @ b ) @ ( minus @ a ) ) ) @ b )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[271,40]) ).

thf(342,plain,
    ! [A: $i] :
      ( ( ( absolute @ ( add @ ( fp33 @ b ) @ ( minus @ a ) ) )
       != A )
      | ( b != A ) ),
    inference(simp,[status(thm)],[330]) ).

thf(353,plain,
    ( ( absolute @ ( add @ ( fp33 @ b ) @ ( minus @ a ) ) )
   != b ),
    inference(simp,[status(thm)],[342]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ( minus @ ( add @ A @ B ) )
      = ( add @ ( minus @ A ) @ ( minus @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

thf(61,plain,
    ! [B: $i,A: $i] :
      ( ( minus @ ( add @ A @ B ) )
      = ( add @ ( minus @ A ) @ ( minus @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(635,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[134,34]) ).

thf(636,plain,
    less_than @ n0 @ ( fp31 @ ( fp32 @ ( fp32 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[635:[bind(A,$thf( fp32 @ ( fp32 @ b ) ))]]) ).

thf(1118,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ ( fp32 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[636,132]) ).

thf(1119,plain,
    ( ( fp32 @ ( fp31 @ ( fp32 @ ( fp32 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[1118:[bind(A,$thf( fp31 @ ( fp32 @ ( fp32 @ b ) ) ))]]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( add @ A @ n0 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

thf(35,plain,
    ! [A: $i] :
      ( ( add @ A @ n0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(36,plain,
    ! [A: $i] :
      ( ( add @ A @ n0 )
      = A ),
    inference(lifteq,[status(thm)],[35]) ).

thf(334,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ A ) @ b )
      | ( ( add @ A @ n0 )
       != ( add @ ( fp33 @ b ) @ ( minus @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[36,271]) ).

thf(338,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ A ) @ b )
      | ( A
       != ( fp33 @ b ) )
      | ( ( minus @ a )
       != n0 ) ),
    inference(simp,[status(thm)],[334]) ).

thf(349,plain,
    ( ( less_than @ ( absolute @ ( fp33 @ b ) ) @ b )
    | ( ( minus @ a )
     != n0 ) ),
    inference(simp,[status(thm)],[338]) ).

thf(7,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).

thf(26,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(33,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
    inference(cnf,[status(esa)],[26]) ).

thf(357,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != b )
      | ( ( add @ n0 @ A )
       != ( add @ ( fp33 @ b ) @ ( minus @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[38,353]) ).

thf(359,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != b )
      | ( ( fp33 @ b )
       != n0 )
      | ( A
       != ( minus @ a ) ) ),
    inference(simp,[status(thm)],[357]) ).

thf(361,plain,
    ( ( ( absolute @ ( minus @ a ) )
     != b )
    | ( ( fp33 @ b )
     != n0 ) ),
    inference(simp,[status(thm)],[359]) ).

thf(63,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ b )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[22,40]) ).

thf(64,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( b != A ) ),
    inference(simp,[status(thm)],[63]) ).

thf(65,plain,
    b != n0,
    inference(simp,[status(thm)],[64]) ).

thf(898,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp31 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[833,34]) ).

thf(899,plain,
    less_than @ n0 @ ( fp31 @ ( fp32 @ ( fp31 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[898:[bind(A,$thf( fp32 @ ( fp31 @ b ) ))]]) ).

thf(1463,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ ( fp31 @ b ) ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[899,40]) ).

thf(1494,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp31 @ ( fp32 @ ( fp31 @ b ) ) )
       != A ) ),
    inference(simp,[status(thm)],[1463]) ).

thf(1498,plain,
    ( ( fp31 @ ( fp32 @ ( fp31 @ b ) ) )
   != n0 ),
    inference(simp,[status(thm)],[1494]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( add @ ( add @ A @ B ) @ C )
      = ( add @ A @ ( add @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

thf(53,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( add @ ( add @ A @ B ) @ C )
      = ( add @ A @ ( add @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(224,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[196,132]) ).

thf(225,plain,
    ( ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ b ) ) ))]]) ).

thf(211,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[196,32]) ).

thf(212,plain,
    less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ),
    inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ b ) ) ))]]) ).

thf(243,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[212,32]) ).

thf(244,plain,
    less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ))]]) ).

thf(310,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[244,32]) ).

thf(311,plain,
    less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ))]]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ n0 @ ( minimum @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_1) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ n0 @ ( minimum @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ n0 @ ( minimum @ A @ B ) ) ),
    inference(cnf,[status(esa)],[43]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( half @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(59,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( half @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(866,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ A ) )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[628,34]) ).

thf(867,plain,
    less_than @ n0 @ ( fp31 @ ( fp31 @ ( fp32 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( fp31 @ ( fp32 @ b ) ))]]) ).

thf(1193,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ ( fp32 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[867,132]) ).

thf(1194,plain,
    ( ( fp32 @ ( fp31 @ ( fp31 @ ( fp32 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[1193:[bind(A,$thf( fp31 @ ( fp31 @ ( fp32 @ b ) ) ))]]) ).

thf(358,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != b )
      | ( ( add @ A @ n0 )
       != ( add @ ( fp33 @ b ) @ ( minus @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[36,353]) ).

thf(360,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != b )
      | ( A
       != ( fp33 @ b ) )
      | ( ( minus @ a )
       != n0 ) ),
    inference(simp,[status(thm)],[358]) ).

thf(362,plain,
    ( ( ( absolute @ ( fp33 @ b ) )
     != b )
    | ( ( minus @ a )
     != n0 ) ),
    inference(simp,[status(thm)],[360]) ).

thf(860,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ b ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[628,40]) ).

thf(877,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp31 @ ( fp32 @ b ) )
       != A ) ),
    inference(simp,[status(thm)],[860]) ).

thf(880,plain,
    ( ( fp31 @ ( fp32 @ b ) )
   != n0 ),
    inference(simp,[status(thm)],[877]) ).

thf(366,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[311,132]) ).

thf(367,plain,
    ( ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) ))]]) ).

thf(828,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ b ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[622,40]) ).

thf(844,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp31 @ b )
       != A ) ),
    inference(simp,[status(thm)],[828]) ).

thf(848,plain,
    ( ( fp31 @ b )
   != n0 ),
    inference(simp,[status(thm)],[844]) ).

thf(1555,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ ( fp31 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[931,132]) ).

thf(1556,plain,
    ( ( fp32 @ ( fp31 @ ( fp31 @ ( fp31 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[1555:[bind(A,$thf( fp31 @ ( fp31 @ ( fp31 @ b ) ) ))]]) ).

thf(826,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp31 @ b ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[622,132]) ).

thf(827,plain,
    ( ( fp32 @ ( fp31 @ b ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( fp31 @ b ))]]) ).

thf(214,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[196,40]) ).

thf(220,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp32 @ ( fp32 @ ( fp32 @ b ) ) )
       != A ) ),
    inference(simp,[status(thm)],[214]) ).

thf(223,plain,
    ( ( fp32 @ ( fp32 @ ( fp32 @ b ) ) )
   != n0 ),
    inference(simp,[status(thm)],[220]) ).

thf(924,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ b ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[835,40]) ).

thf(940,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp31 @ ( fp31 @ b ) )
       != A ) ),
    inference(simp,[status(thm)],[924]) ).

thf(944,plain,
    ( ( fp31 @ ( fp31 @ b ) )
   != n0 ),
    inference(simp,[status(thm)],[940]) ).

thf(1471,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ ( fp31 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[899,132]) ).

thf(1472,plain,
    ( ( fp32 @ ( fp31 @ ( fp32 @ ( fp31 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[1471:[bind(A,$thf( fp31 @ ( fp32 @ ( fp31 @ b ) ) ))]]) ).

thf(1120,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ ( fp32 @ b ) ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[636,40]) ).

thf(1142,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp31 @ ( fp32 @ ( fp32 @ b ) ) )
       != A ) ),
    inference(simp,[status(thm)],[1120]) ).

thf(1145,plain,
    ( ( fp31 @ ( fp32 @ ( fp32 @ b ) ) )
   != n0 ),
    inference(simp,[status(thm)],[1142]) ).

thf(331,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ A ) @ b )
      | ( ( add @ n0 @ A )
       != ( add @ ( fp33 @ b ) @ ( minus @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[38,271]) ).

thf(344,plain,
    ! [A: $i] :
      ( ( less_than @ ( absolute @ A ) @ b )
      | ( ( fp33 @ b )
       != n0 )
      | ( A
       != ( minus @ a ) ) ),
    inference(simp,[status(thm)],[331]) ).

thf(355,plain,
    ( ( less_than @ ( absolute @ ( minus @ a ) ) @ b )
    | ( ( fp33 @ b )
     != n0 ) ),
    inference(simp,[status(thm)],[344]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_3) ).

thf(47,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(48,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ B ) ),
    inference(cnf,[status(esa)],[47]) ).

thf(66,plain,
    ! [A: $i] :
      ( ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b )
      | ( ( less_than @ n0 @ b )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22,33]) ).

thf(67,plain,
    ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ b ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ b ) ) @ ( minus @ l2 ) ) ) ) @ b ),
    inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( b ))]]) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp31 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( f @ B ) @ ( minus @ l1 ) ) ) @ A ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(1192,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ ( fp32 @ b ) ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[867,40]) ).

thf(1213,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp31 @ ( fp31 @ ( fp32 @ b ) ) )
       != A ) ),
    inference(simp,[status(thm)],[1192]) ).

thf(1221,plain,
    ( ( fp31 @ ( fp31 @ ( fp32 @ b ) ) )
   != n0 ),
    inference(simp,[status(thm)],[1213]) ).

thf(858,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[628,132]) ).

thf(859,plain,
    ( ( fp32 @ ( fp31 @ ( fp32 @ b ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( fp31 @ ( fp32 @ b ) ))]]) ).

thf(136,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ b ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[121,40]) ).

thf(142,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp32 @ b )
       != A ) ),
    inference(simp,[status(thm)],[136]) ).

thf(143,plain,
    ( ( fp32 @ b )
   != n0 ),
    inference(simp,[status(thm)],[142]) ).

thf(552,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != ( fp32 @ b ) )
      | ( ( add @ A @ n0 )
       != ( add @ ( fp33 @ ( fp32 @ b ) ) @ ( minus @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[36,548]) ).

thf(554,plain,
    ! [A: $i] :
      ( ( ( absolute @ A )
       != ( fp32 @ b ) )
      | ( A
       != ( fp33 @ ( fp32 @ b ) ) )
      | ( ( minus @ a )
       != n0 ) ),
    inference(simp,[status(thm)],[552]) ).

thf(556,plain,
    ( ( ( absolute @ ( fp33 @ ( fp32 @ b ) ) )
     != ( fp32 @ b ) )
    | ( ( minus @ a )
     != n0 ) ),
    inference(simp,[status(thm)],[554]) ).

thf(864,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp32 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[628,32]) ).

thf(865,plain,
    less_than @ n0 @ ( fp32 @ ( fp31 @ ( fp32 @ b ) ) ),
    inference(pattern_uni,[status(thm)],[864:[bind(A,$thf( fp31 @ ( fp32 @ b ) ))]]) ).

thf(1156,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp31 @ ( fp32 @ b ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[865,132]) ).

thf(1157,plain,
    ( ( fp32 @ ( fp32 @ ( fp31 @ ( fp32 @ b ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[1156:[bind(A,$thf( fp32 @ ( fp31 @ ( fp32 @ b ) ) ))]]) ).

thf(890,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp31 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[833,132]) ).

thf(891,plain,
    ( ( fp32 @ ( fp32 @ ( fp31 @ b ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( fp32 @ ( fp31 @ b ) ))]]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( add @ A @ B )
      = ( add @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6_1) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ( add @ A @ B )
      = ( add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(198,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ b ) ) )
     != ( less_than @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[134,40]) ).

thf(204,plain,
    ! [A: $i] :
      ( ( n0 != A )
      | ( ( fp32 @ ( fp32 @ b ) )
       != A ) ),
    inference(simp,[status(thm)],[198]) ).

thf(207,plain,
    ( ( fp32 @ ( fp32 @ b ) )
   != n0 ),
    inference(simp,[status(thm)],[204]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ ( add @ ( absolute @ A ) @ ( absolute @ B ) ) @ C )
      | ( less_than @ ( absolute @ ( add @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).

thf(51,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ ( add @ ( absolute @ A ) @ ( absolute @ B ) ) @ C )
      | ( less_than @ ( absolute @ ( add @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(241,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[212,132]) ).

thf(242,plain,
    ( ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ))]]) ).

thf(368,plain,
    ! [A: $i] :
      ( ( less_than @ n0 @ ( fp32 @ A ) )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[311,32]) ).

thf(369,plain,
    less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) ))]]) ).

thf(922,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp31 @ ( fp31 @ b ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[835,132]) ).

thf(923,plain,
    ( ( fp32 @ ( fp31 @ ( fp31 @ b ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[922:[bind(A,$thf( fp31 @ ( fp31 @ b ) ))]]) ).

thf(308,plain,
    ! [A: $i] :
      ( ( ( fp32 @ A )
       != n0 )
      | ( ( less_than @ n0 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) )
       != ( less_than @ n0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[244,132]) ).

thf(309,plain,
    ( ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ) )
   != n0 ),
    inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ ( fp32 @ b ) ) ) ) ))]]) ).

thf(41646,plain,
    $false,
    inference(e,[status(thm)],[49,628,555,42,24,37,25,1430,196,1514,46,57,29,121,1581,353,61,1119,132,349,33,28,38,361,65,1498,53,225,212,622,41,134,244,311,45,32,34,22,44,59,27,1194,362,271,880,39,367,848,1556,827,636,223,35,944,548,1472,1145,355,48,263,67,31,1221,859,143,43,556,931,1157,891,40,26,55,23,207,929,899,835,30,51,867,865,833,36,242,897,47,369,923,309]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA003-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 07:47:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.02/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.26/1.04  % [INFO] 	 Parsing done (128ms). 
% 1.26/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.77/1.28  % [INFO] 	 eprover registered as external prover. 
% 1.77/1.28  % [INFO] 	 cvc4 registered as external prover. 
% 1.77/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 2.13/1.39  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 2.13/1.40  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.13/1.40  % [INFO] 	 Type checking passed. 
% 2.13/1.41  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 125.01/22.18  % External prover 'e' found a proof!
% 125.01/22.18  % [INFO] 	 Killing All external provers ... 
% 125.01/22.18  % Time passed: 21665ms (effective reasoning time: 21122ms)
% 125.01/22.18  % Axioms used in derivation (14): axiom_7, axiom_2_2, left_identity, axiom_3, right_identity, axiom_6_2, axiom_5, axiom_2_1, c_17, axiom_6_1, axiom_8, transitivity_of_less_than, reflexivity_of_less_than, axiom_2_3
% 125.01/22.18  % No. of inferences in proof: 188
% 125.01/22.18  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21665 ms resp. 21122 ms w/o parsing
% 125.01/22.25  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 125.01/22.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------