TSTP Solution File: NUM783_8 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM783_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.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 May 21 02:13:24 EDT 2024

% Result   : Theorem 0.15s 0.33s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  205 (   9 unt;  17 typ;   0 def)
%            Number of atoms       :  894 (  90 equ)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  569 ( 254   ~; 278   |;   6   &)
%                                         (  28 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  393 ( 391 fml;   2 var)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   24 (  11   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   33 (  30 usr;  21 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   61 (  61   !;   0   ?;  61   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    rat: $tType ).

tff(func_def_0,type,
    x0: rat ).

tff(func_def_1,type,
    y0: rat ).

tff(func_def_4,type,
    bG0: $o ).

tff(func_def_5,type,
    bG1: $o ).

tff(func_def_6,type,
    bG2: $o ).

tff(func_def_7,type,
    bG3: ( rat * rat ) > $o ).

tff(func_def_8,type,
    bG4: ( rat * rat ) > $o ).

tff(func_def_9,type,
    bG5: ( rat * rat ) > $o ).

tff(func_def_10,type,
    bG6: ( rat * rat ) > $o ).

tff(func_def_11,type,
    bG7: ( rat * rat ) > $o ).

tff(func_def_12,type,
    bG8: ( rat * rat ) > $o ).

tff(pred_def_1,type,
    or3: ( $o * $o * $o ) > $o ).

tff(pred_def_2,type,
    is: ( rat * rat ) > $o ).

tff(pred_def_3,type,
    more: ( rat * rat ) > $o ).

tff(pred_def_4,type,
    less: ( rat * rat ) > $o ).

tff(pred_def_5,type,
    ec3: ( $o * $o * $o ) > $o ).

tff(f457,plain,
    $false,
    inference(avatar_sat_refutation,[],[f71,f72,f81,f82,f91,f92,f113,f123,f194,f200,f215,f233,f244,f251,f256,f264,f315,f332,f347,f388,f403,f410,f417,f418,f422,f425,f438,f456]) ).

tff(f456,plain,
    ( ~ spl9_2
    | ~ spl9_6
    | ~ spl9_13
    | spl9_15 ),
    inference(avatar_contradiction_clause,[],[f455]) ).

tff(f455,plain,
    ( $false
    | ~ spl9_2
    | ~ spl9_6
    | ~ spl9_13
    | spl9_15 ),
    inference(subsumption_resolution,[],[f454,f208]) ).

tff(f208,plain,
    ( ~ or3($true,$false,$true)
    | spl9_15 ),
    inference(avatar_component_clause,[],[f206]) ).

tff(f206,plain,
    ( spl9_15
  <=> or3($true,$false,$true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).

tff(f454,plain,
    ( or3($true,$false,$true)
    | ~ spl9_2
    | ~ spl9_6
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f453,f426]) ).

tff(f426,plain,
    ( ( $true = bG3(y0,x0) )
    | ~ spl9_6 ),
    inference(resolution,[],[f90,f51]) ).

tff(f51,plain,
    ! [X0: rat,X1: rat] :
      ( ~ is(X1,X0)
      | ( $true = bG3(X0,X1) ) ),
    inference(cnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: rat,X1: rat] :
      ( ( is(X1,X0)
        | ( $true != bG3(X0,X1) ) )
      & ( ( $true = bG3(X0,X1) )
        | ~ is(X1,X0) ) ),
    inference(nnf_transformation,[],[f26]) ).

tff(f26,plain,
    ! [X0: rat,X1: rat] :
      ( is(X1,X0)
    <=> ( $true = bG3(X0,X1) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,plain,
    ! [X1: rat,X0: rat] :
      ( is(X0,X1)
    <=> ( $true = bG3(X1,X0) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG3])]) ).

tff(f90,plain,
    ( is(x0,y0)
    | ~ spl9_6 ),
    inference(avatar_component_clause,[],[f88]) ).

tff(f88,plain,
    ( spl9_6
  <=> is(x0,y0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).

tff(f453,plain,
    ( or3(bG3(y0,x0),$false,$true)
    | ~ spl9_2
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f450,f356]) ).

tff(f356,plain,
    ( ( $true = bG5(y0,x0) )
    | ~ spl9_2 ),
    inference(resolution,[],[f70,f47]) ).

tff(f47,plain,
    ! [X0: rat,X1: rat] :
      ( ~ less(X1,X0)
      | ( $true = bG5(X0,X1) ) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f35,plain,
    ! [X0: rat,X1: rat] :
      ( ( less(X1,X0)
        | ( $true != bG5(X0,X1) ) )
      & ( ( $true = bG5(X0,X1) )
        | ~ less(X1,X0) ) ),
    inference(nnf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0: rat,X1: rat] :
      ( less(X1,X0)
    <=> ( $true = bG5(X0,X1) ) ),
    inference(rectify,[],[f16]) ).

tff(f16,plain,
    ! [X1: rat,X0: rat] :
      ( less(X0,X1)
    <=> ( $true = bG5(X1,X0) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG5])]) ).

tff(f70,plain,
    ( less(x0,y0)
    | ~ spl9_2 ),
    inference(avatar_component_clause,[],[f68]) ).

tff(f68,plain,
    ( spl9_2
  <=> less(x0,y0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

tff(f450,plain,
    ( or3(bG3(y0,x0),$false,bG5(y0,x0))
    | ~ spl9_13 ),
    inference(superposition,[],[f61,f189]) ).

tff(f189,plain,
    ( ( $false = bG4(y0,x0) )
    | ~ spl9_13 ),
    inference(avatar_component_clause,[],[f187]) ).

tff(f187,plain,
    ( spl9_13
  <=> ( $false = bG4(y0,x0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).

tff(f61,plain,
    ! [X0: rat,X1: rat] : or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0)),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: rat,X1: rat] : or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0)),
    inference(ennf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: rat,X1: rat] :
      ~ ~ or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0)),
    inference(pure_predicate_removal,[],[f20]) ).

tff(f20,plain,
    ! [X0: rat,X1: rat] :
      ~ ( or3(bG3(X1,X0),bG4(X1,X0),bG5(X1,X0))
       => ~ ec3(bG6(X1,X0),bG7(X1,X0),bG8(X1,X0)) ),
    inference(fool_elimination,[],[f13,f19,f18,f17,f16,f15,f14]) ).

tff(f15,plain,
    ! [X1: rat,X0: rat] :
      ( more(X0,X1)
    <=> ( $true = bG4(X1,X0) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG4])]) ).

tff(f17,plain,
    ! [X1: rat,X0: rat] :
      ( is(X0,X1)
    <=> ( $true = bG6(X1,X0) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG6])]) ).

tff(f18,plain,
    ! [X1: rat,X0: rat] :
      ( more(X0,X1)
    <=> ( $true = bG7(X1,X0) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG7])]) ).

tff(f19,plain,
    ! [X1: rat,X0: rat] :
      ( less(X0,X1)
    <=> ( $true = bG8(X1,X0) ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG8])]) ).

tff(f13,plain,
    ! [X0: rat,X1: rat] :
      ~ ( or3(is(X0,X1),more(X0,X1),less(X0,X1))
       => ~ ec3(is(X0,X1),more(X0,X1),less(X0,X1)) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X1: rat,X2: rat] :
      ~ ( or3(is(X1,X2),more(X1,X2),less(X1,X2))
       => ~ ec3(is(X1,X2),more(X1,X2),less(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81) ).

tff(f438,plain,
    ( ~ spl9_14
    | ~ spl9_1
    | ~ spl9_5
    | spl9_10 ),
    inference(avatar_split_clause,[],[f437,f120,f84,f64,f191]) ).

tff(f191,plain,
    ( spl9_14
  <=> or3($true,$true,$true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).

tff(f64,plain,
    ( spl9_1
  <=> ( $true = bG2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

tff(f84,plain,
    ( spl9_5
  <=> ( $true = bG0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).

tff(f120,plain,
    ( spl9_10
  <=> or3(bG0,$true,bG2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).

tff(f437,plain,
    ( ~ or3($true,$true,$true)
    | ~ spl9_1
    | ~ spl9_5
    | spl9_10 ),
    inference(forward_demodulation,[],[f392,f85]) ).

tff(f85,plain,
    ( ( $true = bG0 )
    | ~ spl9_5 ),
    inference(avatar_component_clause,[],[f84]) ).

tff(f392,plain,
    ( ~ or3(bG0,$true,$true)
    | ~ spl9_1
    | spl9_10 ),
    inference(forward_demodulation,[],[f122,f65]) ).

tff(f65,plain,
    ( ( $true = bG2 )
    | ~ spl9_1 ),
    inference(avatar_component_clause,[],[f64]) ).

tff(f122,plain,
    ( ~ or3(bG0,$true,bG2)
    | spl9_10 ),
    inference(avatar_component_clause,[],[f120]) ).

tff(f425,plain,
    ( spl9_13
    | spl9_4 ),
    inference(avatar_split_clause,[],[f423,f78,f187]) ).

tff(f78,plain,
    ( spl9_4
  <=> more(x0,y0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).

tff(f423,plain,
    ( ( $false = bG4(y0,x0) )
    | spl9_4 ),
    inference(resolution,[],[f79,f160]) ).

tff(f160,plain,
    ! [X0: rat,X1: rat] :
      ( more(X1,X0)
      | ( $false = bG4(X0,X1) ) ),
    inference(trivial_inequality_removal,[],[f159]) ).

tff(f159,plain,
    ! [X0: rat,X1: rat] :
      ( ( $true != $true )
      | more(X1,X0)
      | ( $false = bG4(X0,X1) ) ),
    inference(superposition,[],[f50,f6]) ).

tff(f6,plain,
    ! [X0: $o] :
      ( ( $true = (X0) )
      | ( $false = (X0) ) ),
    introduced(fool_axiom,[]) ).

tff(f50,plain,
    ! [X0: rat,X1: rat] :
      ( ( $true != bG4(X0,X1) )
      | more(X1,X0) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: rat,X1: rat] :
      ( ( more(X1,X0)
        | ( $true != bG4(X0,X1) ) )
      & ( ( $true = bG4(X0,X1) )
        | ~ more(X1,X0) ) ),
    inference(nnf_transformation,[],[f25]) ).

tff(f25,plain,
    ! [X0: rat,X1: rat] :
      ( more(X1,X0)
    <=> ( $true = bG4(X0,X1) ) ),
    inference(rectify,[],[f15]) ).

tff(f79,plain,
    ( ~ more(x0,y0)
    | spl9_4 ),
    inference(avatar_component_clause,[],[f78]) ).

tff(f422,plain,
    ( spl9_9
    | spl9_3 ),
    inference(avatar_split_clause,[],[f421,f74,f116]) ).

tff(f116,plain,
    ( spl9_9
  <=> ( $false = bG1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).

tff(f74,plain,
    ( spl9_3
  <=> ( $true = bG1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).

tff(f421,plain,
    ( ( $false = bG1 )
    | spl9_3 ),
    inference(trivial_inequality_removal,[],[f420]) ).

tff(f420,plain,
    ( ( $true != $true )
    | ( $false = bG1 )
    | spl9_3 ),
    inference(superposition,[],[f76,f6]) ).

tff(f76,plain,
    ( ( $true != bG1 )
    | spl9_3 ),
    inference(avatar_component_clause,[],[f74]) ).

tff(f418,plain,
    ( ~ spl9_12
    | ~ spl9_1 ),
    inference(avatar_split_clause,[],[f389,f64,f130]) ).

tff(f130,plain,
    ( spl9_12
  <=> or3(bG0,bG1,$true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).

tff(f389,plain,
    ( ~ or3(bG0,bG1,$true)
    | ~ spl9_1 ),
    inference(forward_demodulation,[],[f59,f65]) ).

tff(f59,plain,
    ~ or3(bG0,bG1,bG2),
    inference(cnf_transformation,[],[f27]) ).

tff(f27,plain,
    ~ or3(bG0,bG1,bG2),
    inference(flattening,[],[f10]) ).

tff(f10,plain,
    ~ or3(bG0,bG1,bG2),
    inference(fool_elimination,[],[f4,f9,f8,f7]) ).

tff(f7,plain,
    ( is(x0,y0)
  <=> ( $true = bG0 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG0])]) ).

tff(f8,plain,
    ( more(x0,y0)
  <=> ( $true = bG1 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG1])]) ).

tff(f9,plain,
    ( less(x0,y0)
  <=> ( $true = bG2 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG2])]) ).

tff(f4,negated_conjecture,
    ~ or3(is(x0,y0),more(x0,y0),less(x0,y0)),
    inference(negated_conjecture,[],[f3]) ).

tff(f3,conjecture,
    or3(is(x0,y0),more(x0,y0),less(x0,y0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81a) ).

tff(f417,plain,
    ( ~ spl9_5
    | ~ spl9_7 ),
    inference(avatar_contradiction_clause,[],[f416]) ).

tff(f416,plain,
    ( $false
    | ~ spl9_5
    | ~ spl9_7 ),
    inference(trivial_inequality_removal,[],[f415]) ).

tff(f415,plain,
    ( ( $true = $false )
    | ~ spl9_5
    | ~ spl9_7 ),
    inference(forward_demodulation,[],[f85,f108]) ).

tff(f108,plain,
    ( ( $false = bG0 )
    | ~ spl9_7 ),
    inference(avatar_component_clause,[],[f106]) ).

tff(f106,plain,
    ( spl9_7
  <=> ( $false = bG0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).

tff(f410,plain,
    ( ~ spl9_1
    | ~ spl9_2
    | ~ spl9_3
    | ~ spl9_4
    | spl9_6
    | ~ spl9_7 ),
    inference(avatar_contradiction_clause,[],[f409]) ).

tff(f409,plain,
    ( $false
    | ~ spl9_1
    | ~ spl9_2
    | ~ spl9_3
    | ~ spl9_4
    | spl9_6
    | ~ spl9_7 ),
    inference(subsumption_resolution,[],[f408,f396]) ).

tff(f396,plain,
    ( ~ or3($false,$true,$true)
    | ~ spl9_1
    | ~ spl9_3
    | ~ spl9_7 ),
    inference(forward_demodulation,[],[f390,f75]) ).

tff(f75,plain,
    ( ( $true = bG1 )
    | ~ spl9_3 ),
    inference(avatar_component_clause,[],[f74]) ).

tff(f390,plain,
    ( ~ or3($false,bG1,$true)
    | ~ spl9_1
    | ~ spl9_7 ),
    inference(forward_demodulation,[],[f389,f108]) ).

tff(f408,plain,
    ( or3($false,$true,$true)
    | ~ spl9_2
    | ~ spl9_4
    | spl9_6 ),
    inference(forward_demodulation,[],[f407,f307]) ).

tff(f307,plain,
    ( ( $false = bG3(y0,x0) )
    | spl9_6 ),
    inference(resolution,[],[f165,f89]) ).

tff(f89,plain,
    ( ~ is(x0,y0)
    | spl9_6 ),
    inference(avatar_component_clause,[],[f88]) ).

tff(f165,plain,
    ! [X0: rat,X1: rat] :
      ( is(X1,X0)
      | ( $false = bG3(X0,X1) ) ),
    inference(trivial_inequality_removal,[],[f164]) ).

tff(f164,plain,
    ! [X0: rat,X1: rat] :
      ( ( $true != $true )
      | is(X1,X0)
      | ( $false = bG3(X0,X1) ) ),
    inference(superposition,[],[f52,f6]) ).

tff(f52,plain,
    ! [X0: rat,X1: rat] :
      ( ( $true != bG3(X0,X1) )
      | is(X1,X0) ),
    inference(cnf_transformation,[],[f37]) ).

tff(f407,plain,
    ( or3(bG3(y0,x0),$true,$true)
    | ~ spl9_2
    | ~ spl9_4 ),
    inference(forward_demodulation,[],[f404,f356]) ).

tff(f404,plain,
    ( or3(bG3(y0,x0),$true,bG5(y0,x0))
    | ~ spl9_4 ),
    inference(superposition,[],[f61,f394]) ).

tff(f394,plain,
    ( ( $true = bG4(y0,x0) )
    | ~ spl9_4 ),
    inference(resolution,[],[f80,f49]) ).

tff(f49,plain,
    ! [X0: rat,X1: rat] :
      ( ~ more(X1,X0)
      | ( $true = bG4(X0,X1) ) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f80,plain,
    ( more(x0,y0)
    | ~ spl9_4 ),
    inference(avatar_component_clause,[],[f78]) ).

tff(f403,plain,
    ( ~ spl9_14
    | ~ spl9_1
    | ~ spl9_3
    | spl9_8 ),
    inference(avatar_split_clause,[],[f402,f110,f74,f64,f191]) ).

tff(f110,plain,
    ( spl9_8
  <=> or3($true,bG1,bG2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).

tff(f402,plain,
    ( ~ or3($true,$true,$true)
    | ~ spl9_1
    | ~ spl9_3
    | spl9_8 ),
    inference(forward_demodulation,[],[f391,f75]) ).

tff(f391,plain,
    ( ~ or3($true,bG1,$true)
    | ~ spl9_1
    | spl9_8 ),
    inference(forward_demodulation,[],[f112,f65]) ).

tff(f112,plain,
    ( ~ or3($true,bG1,bG2)
    | spl9_8 ),
    inference(avatar_component_clause,[],[f110]) ).

tff(f388,plain,
    ( ~ spl9_1
    | ~ spl9_2
    | spl9_6
    | ~ spl9_7
    | ~ spl9_9
    | ~ spl9_13 ),
    inference(avatar_contradiction_clause,[],[f387]) ).

tff(f387,plain,
    ( $false
    | ~ spl9_1
    | ~ spl9_2
    | spl9_6
    | ~ spl9_7
    | ~ spl9_9
    | ~ spl9_13 ),
    inference(subsumption_resolution,[],[f386,f363]) ).

tff(f363,plain,
    ( ~ or3($false,$false,$true)
    | ~ spl9_1
    | ~ spl9_7
    | ~ spl9_9 ),
    inference(forward_demodulation,[],[f355,f65]) ).

tff(f355,plain,
    ( ~ or3($false,$false,bG2)
    | ~ spl9_7
    | ~ spl9_9 ),
    inference(forward_demodulation,[],[f354,f108]) ).

tff(f354,plain,
    ( ~ or3(bG0,$false,bG2)
    | ~ spl9_9 ),
    inference(forward_demodulation,[],[f59,f118]) ).

tff(f118,plain,
    ( ( $false = bG1 )
    | ~ spl9_9 ),
    inference(avatar_component_clause,[],[f116]) ).

tff(f386,plain,
    ( or3($false,$false,$true)
    | ~ spl9_2
    | spl9_6
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f385,f307]) ).

tff(f385,plain,
    ( or3(bG3(y0,x0),$false,$true)
    | ~ spl9_2
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f382,f356]) ).

tff(f382,plain,
    ( or3(bG3(y0,x0),$false,bG5(y0,x0))
    | ~ spl9_13 ),
    inference(superposition,[],[f61,f189]) ).

tff(f347,plain,
    ( ~ spl9_3
    | ~ spl9_9 ),
    inference(avatar_contradiction_clause,[],[f346]) ).

tff(f346,plain,
    ( $false
    | ~ spl9_3
    | ~ spl9_9 ),
    inference(trivial_inequality_removal,[],[f343]) ).

tff(f343,plain,
    ( ( $true = $false )
    | ~ spl9_3
    | ~ spl9_9 ),
    inference(backward_demodulation,[],[f75,f118]) ).

tff(f332,plain,
    ( spl9_2
    | ~ spl9_4
    | spl9_6
    | ~ spl9_7
    | spl9_10
    | ~ spl9_11 ),
    inference(avatar_contradiction_clause,[],[f331]) ).

tff(f331,plain,
    ( $false
    | spl9_2
    | ~ spl9_4
    | spl9_6
    | ~ spl9_7
    | spl9_10
    | ~ spl9_11 ),
    inference(subsumption_resolution,[],[f330,f289]) ).

tff(f289,plain,
    ( ~ or3($false,$true,$false)
    | ~ spl9_7
    | spl9_10
    | ~ spl9_11 ),
    inference(forward_demodulation,[],[f249,f108]) ).

tff(f249,plain,
    ( ~ or3(bG0,$true,$false)
    | spl9_10
    | ~ spl9_11 ),
    inference(forward_demodulation,[],[f122,f128]) ).

tff(f128,plain,
    ( ( $false = bG2 )
    | ~ spl9_11 ),
    inference(avatar_component_clause,[],[f126]) ).

tff(f126,plain,
    ( spl9_11
  <=> ( $false = bG2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).

tff(f330,plain,
    ( or3($false,$true,$false)
    | spl9_2
    | ~ spl9_4
    | spl9_6 ),
    inference(forward_demodulation,[],[f329,f307]) ).

tff(f329,plain,
    ( or3(bG3(y0,x0),$true,$false)
    | spl9_2
    | ~ spl9_4 ),
    inference(forward_demodulation,[],[f326,f201]) ).

tff(f201,plain,
    ( ( $false = bG5(y0,x0) )
    | spl9_2 ),
    inference(resolution,[],[f69,f156]) ).

tff(f156,plain,
    ! [X0: rat,X1: rat] :
      ( less(X1,X0)
      | ( $false = bG5(X0,X1) ) ),
    inference(trivial_inequality_removal,[],[f155]) ).

tff(f155,plain,
    ! [X0: rat,X1: rat] :
      ( ( $true != $true )
      | less(X1,X0)
      | ( $false = bG5(X0,X1) ) ),
    inference(superposition,[],[f48,f6]) ).

tff(f48,plain,
    ! [X0: rat,X1: rat] :
      ( ( $true != bG5(X0,X1) )
      | less(X1,X0) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f69,plain,
    ( ~ less(x0,y0)
    | spl9_2 ),
    inference(avatar_component_clause,[],[f68]) ).

tff(f326,plain,
    ( or3(bG3(y0,x0),$true,bG5(y0,x0))
    | ~ spl9_4 ),
    inference(superposition,[],[f61,f320]) ).

tff(f320,plain,
    ( ( $true = bG4(y0,x0) )
    | ~ spl9_4 ),
    inference(resolution,[],[f80,f49]) ).

tff(f315,plain,
    ( spl9_2
    | spl9_6
    | ~ spl9_7
    | ~ spl9_9
    | ~ spl9_11
    | ~ spl9_13 ),
    inference(avatar_contradiction_clause,[],[f314]) ).

tff(f314,plain,
    ( $false
    | spl9_2
    | spl9_6
    | ~ spl9_7
    | ~ spl9_9
    | ~ spl9_11
    | ~ spl9_13 ),
    inference(subsumption_resolution,[],[f313,f285]) ).

tff(f285,plain,
    ( ~ or3($false,$false,$false)
    | ~ spl9_7
    | ~ spl9_9
    | ~ spl9_11 ),
    inference(forward_demodulation,[],[f278,f118]) ).

tff(f278,plain,
    ( ~ or3($false,bG1,$false)
    | ~ spl9_7
    | ~ spl9_11 ),
    inference(backward_demodulation,[],[f245,f108]) ).

tff(f245,plain,
    ( ~ or3(bG0,bG1,$false)
    | ~ spl9_11 ),
    inference(forward_demodulation,[],[f59,f128]) ).

tff(f313,plain,
    ( or3($false,$false,$false)
    | spl9_2
    | spl9_6
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f312,f189]) ).

tff(f312,plain,
    ( or3($false,bG4(y0,x0),$false)
    | spl9_2
    | spl9_6 ),
    inference(forward_demodulation,[],[f309,f201]) ).

tff(f309,plain,
    ( or3($false,bG4(y0,x0),bG5(y0,x0))
    | spl9_6 ),
    inference(superposition,[],[f61,f307]) ).

tff(f264,plain,
    ( spl9_7
    | spl9_5 ),
    inference(avatar_split_clause,[],[f263,f84,f106]) ).

tff(f263,plain,
    ( ( $false = bG0 )
    | spl9_5 ),
    inference(trivial_inequality_removal,[],[f262]) ).

tff(f262,plain,
    ( ( $true != $true )
    | ( $false = bG0 )
    | spl9_5 ),
    inference(superposition,[],[f86,f6]) ).

tff(f86,plain,
    ( ( $true != bG0 )
    | spl9_5 ),
    inference(avatar_component_clause,[],[f84]) ).

tff(f256,plain,
    ( ~ spl9_4
    | ~ spl9_13 ),
    inference(avatar_contradiction_clause,[],[f255]) ).

tff(f255,plain,
    ( $false
    | ~ spl9_4
    | ~ spl9_13 ),
    inference(trivial_inequality_removal,[],[f254]) ).

tff(f254,plain,
    ( ( $true = $false )
    | ~ spl9_4
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f252,f189]) ).

tff(f252,plain,
    ( ( $true = bG4(y0,x0) )
    | ~ spl9_4 ),
    inference(resolution,[],[f80,f49]) ).

tff(f251,plain,
    ( ~ spl9_16
    | ~ spl9_5
    | spl9_10
    | ~ spl9_11 ),
    inference(avatar_split_clause,[],[f250,f126,f120,f84,f230]) ).

tff(f230,plain,
    ( spl9_16
  <=> or3($true,$true,$false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).

tff(f250,plain,
    ( ~ or3($true,$true,$false)
    | ~ spl9_5
    | spl9_10
    | ~ spl9_11 ),
    inference(forward_demodulation,[],[f249,f85]) ).

tff(f244,plain,
    ( spl9_2
    | ~ spl9_5
    | ~ spl9_6
    | ~ spl9_9
    | ~ spl9_11
    | ~ spl9_13 ),
    inference(avatar_contradiction_clause,[],[f243]) ).

tff(f243,plain,
    ( $false
    | spl9_2
    | ~ spl9_5
    | ~ spl9_6
    | ~ spl9_9
    | ~ spl9_11
    | ~ spl9_13 ),
    inference(subsumption_resolution,[],[f242,f210]) ).

tff(f210,plain,
    ( ~ or3($true,$false,$false)
    | ~ spl9_5
    | ~ spl9_9
    | ~ spl9_11 ),
    inference(backward_demodulation,[],[f197,f128]) ).

tff(f197,plain,
    ( ~ or3($true,$false,bG2)
    | ~ spl9_5
    | ~ spl9_9 ),
    inference(forward_demodulation,[],[f196,f85]) ).

tff(f196,plain,
    ( ~ or3(bG0,$false,bG2)
    | ~ spl9_9 ),
    inference(forward_demodulation,[],[f59,f118]) ).

tff(f242,plain,
    ( or3($true,$false,$false)
    | spl9_2
    | ~ spl9_6
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f241,f161]) ).

tff(f161,plain,
    ( ( $true = bG3(y0,x0) )
    | ~ spl9_6 ),
    inference(resolution,[],[f51,f90]) ).

tff(f241,plain,
    ( or3(bG3(y0,x0),$false,$false)
    | spl9_2
    | ~ spl9_13 ),
    inference(forward_demodulation,[],[f236,f201]) ).

tff(f236,plain,
    ( or3(bG3(y0,x0),$false,bG5(y0,x0))
    | ~ spl9_13 ),
    inference(superposition,[],[f61,f189]) ).

tff(f233,plain,
    ( spl9_13
    | spl9_16
    | spl9_2
    | ~ spl9_6 ),
    inference(avatar_split_clause,[],[f228,f88,f68,f230,f187]) ).

tff(f228,plain,
    ( or3($true,$true,$false)
    | ( $false = bG4(y0,x0) )
    | spl9_2
    | ~ spl9_6 ),
    inference(superposition,[],[f222,f6]) ).

tff(f222,plain,
    ( or3($true,bG4(y0,x0),$false)
    | spl9_2
    | ~ spl9_6 ),
    inference(forward_demodulation,[],[f219,f161]) ).

tff(f219,plain,
    ( or3(bG3(y0,x0),bG4(y0,x0),$false)
    | spl9_2 ),
    inference(superposition,[],[f61,f201]) ).

tff(f215,plain,
    ( ~ spl9_15
    | ~ spl9_5
    | ~ spl9_9
    | spl9_12 ),
    inference(avatar_split_clause,[],[f146,f130,f116,f84,f206]) ).

tff(f146,plain,
    ( ~ or3($true,$false,$true)
    | ~ spl9_5
    | ~ spl9_9
    | spl9_12 ),
    inference(forward_demodulation,[],[f145,f85]) ).

tff(f145,plain,
    ( ~ or3(bG0,$false,$true)
    | ~ spl9_9
    | spl9_12 ),
    inference(forward_demodulation,[],[f132,f118]) ).

tff(f132,plain,
    ( ~ or3(bG0,bG1,$true)
    | spl9_12 ),
    inference(avatar_component_clause,[],[f130]) ).

tff(f200,plain,
    ( spl9_11
    | spl9_1 ),
    inference(avatar_split_clause,[],[f199,f64,f126]) ).

tff(f199,plain,
    ( ( $false = bG2 )
    | spl9_1 ),
    inference(trivial_inequality_removal,[],[f198]) ).

tff(f198,plain,
    ( ( $true != $true )
    | ( $false = bG2 )
    | spl9_1 ),
    inference(superposition,[],[f66,f6]) ).

tff(f66,plain,
    ( ( $true != bG2 )
    | spl9_1 ),
    inference(avatar_component_clause,[],[f64]) ).

tff(f194,plain,
    ( spl9_13
    | spl9_14
    | ~ spl9_2
    | ~ spl9_6 ),
    inference(avatar_split_clause,[],[f184,f88,f68,f191,f187]) ).

tff(f184,plain,
    ( or3($true,$true,$true)
    | ( $false = bG4(y0,x0) )
    | ~ spl9_2
    | ~ spl9_6 ),
    inference(superposition,[],[f177,f6]) ).

tff(f177,plain,
    ( or3($true,bG4(y0,x0),$true)
    | ~ spl9_2
    | ~ spl9_6 ),
    inference(forward_demodulation,[],[f172,f154]) ).

tff(f154,plain,
    ( ( $true = bG5(y0,x0) )
    | ~ spl9_2 ),
    inference(resolution,[],[f47,f70]) ).

tff(f172,plain,
    ( or3($true,bG4(y0,x0),bG5(y0,x0))
    | ~ spl9_6 ),
    inference(superposition,[],[f61,f161]) ).

tff(f123,plain,
    ( spl9_9
    | ~ spl9_10 ),
    inference(avatar_split_clause,[],[f97,f120,f116]) ).

tff(f97,plain,
    ( ~ or3(bG0,$true,bG2)
    | ( $false = bG1 ) ),
    inference(superposition,[],[f59,f6]) ).

tff(f113,plain,
    ( spl9_7
    | ~ spl9_8 ),
    inference(avatar_split_clause,[],[f95,f110,f106]) ).

tff(f95,plain,
    ( ~ or3($true,bG1,bG2)
    | ( $false = bG0 ) ),
    inference(superposition,[],[f59,f6]) ).

tff(f92,plain,
    ( ~ spl9_6
    | spl9_5 ),
    inference(avatar_split_clause,[],[f57,f84,f88]) ).

tff(f57,plain,
    ( ( $true = bG0 )
    | ~ is(x0,y0) ),
    inference(cnf_transformation,[],[f40]) ).

tff(f40,plain,
    ( ( is(x0,y0)
      | ( $true != bG0 ) )
    & ( ( $true = bG0 )
      | ~ is(x0,y0) ) ),
    inference(nnf_transformation,[],[f7]) ).

tff(f91,plain,
    ( ~ spl9_5
    | spl9_6 ),
    inference(avatar_split_clause,[],[f58,f88,f84]) ).

tff(f58,plain,
    ( is(x0,y0)
    | ( $true != bG0 ) ),
    inference(cnf_transformation,[],[f40]) ).

tff(f82,plain,
    ( ~ spl9_4
    | spl9_3 ),
    inference(avatar_split_clause,[],[f55,f74,f78]) ).

tff(f55,plain,
    ( ( $true = bG1 )
    | ~ more(x0,y0) ),
    inference(cnf_transformation,[],[f39]) ).

tff(f39,plain,
    ( ( more(x0,y0)
      | ( $true != bG1 ) )
    & ( ( $true = bG1 )
      | ~ more(x0,y0) ) ),
    inference(nnf_transformation,[],[f8]) ).

tff(f81,plain,
    ( ~ spl9_3
    | spl9_4 ),
    inference(avatar_split_clause,[],[f56,f78,f74]) ).

tff(f56,plain,
    ( more(x0,y0)
    | ( $true != bG1 ) ),
    inference(cnf_transformation,[],[f39]) ).

tff(f72,plain,
    ( ~ spl9_2
    | spl9_1 ),
    inference(avatar_split_clause,[],[f53,f64,f68]) ).

tff(f53,plain,
    ( ( $true = bG2 )
    | ~ less(x0,y0) ),
    inference(cnf_transformation,[],[f38]) ).

tff(f38,plain,
    ( ( less(x0,y0)
      | ( $true != bG2 ) )
    & ( ( $true = bG2 )
      | ~ less(x0,y0) ) ),
    inference(nnf_transformation,[],[f9]) ).

tff(f71,plain,
    ( ~ spl9_1
    | spl9_2 ),
    inference(avatar_split_clause,[],[f54,f68,f64]) ).

tff(f54,plain,
    ( less(x0,y0)
    | ( $true != bG2 ) ),
    inference(cnf_transformation,[],[f38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : NUM783_8 : TPTP v8.2.0. Released v8.0.0.
% 0.00/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30  % Computer : n012.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Mon May 20 03:42:23 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.09/0.30  % (5734)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32  % (5737)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.15/0.32  % (5739)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.32  % (5738)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.32  % (5740)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.32  % (5735)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.32  % (5741)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.32  % (5736)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.32  Detected minimum model sizes of [1,1,1]
% 0.15/0.32  Detected maximum model sizes of [1,1,2]
% 0.15/0.32  TRYING [1,1,1]
% 0.15/0.32  TRYING [1,1,2]
% 0.15/0.32  Detected minimum model sizes of [1,1]
% 0.15/0.32  Detected maximum model sizes of [2,2]
% 0.15/0.32  Detected minimum model sizes of [1,1]
% 0.15/0.32  Detected maximum model sizes of [2,2]
% 0.15/0.32  TRYING [1,1]
% 0.15/0.32  TRYING [1,1]
% 0.15/0.32  Detected minimum model sizes of [1,1,1]
% 0.15/0.32  Detected maximum model sizes of [1,1,2]
% 0.15/0.32  TRYING [1,1,1]
% 0.15/0.32  TRYING [1,2]
% 0.15/0.32  Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32  TRYING [1,2]
% 0.15/0.32  % (5738)Refutation not found, incomplete strategy% (5738)------------------------------
% 0.15/0.32  % (5738)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32  % (5738)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32  
% 0.15/0.32  % (5738)Memory used [KB]: 740
% 0.15/0.32  % (5738)Time elapsed: 0.004 s
% 0.15/0.32  % (5738)Instructions burned: 5 (million)
% 0.15/0.32  TRYING [1,1,2]
% 0.15/0.32  Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32  % (5738)------------------------------
% 0.15/0.32  % (5738)------------------------------
% 0.15/0.32  % (5735)Refutation not found, incomplete strategy% (5735)------------------------------
% 0.15/0.32  % (5735)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32  % (5735)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32  
% 0.15/0.32  % (5735)Memory used [KB]: 739
% 0.15/0.32  % (5735)Time elapsed: 0.004 s
% 0.15/0.32  % (5735)Instructions burned: 5 (million)
% 0.15/0.32  Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32  % (5741)Refutation not found, incomplete strategy% (5741)------------------------------
% 0.15/0.32  % (5741)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32  % (5741)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32  
% 0.15/0.32  % (5741)Memory used [KB]: 740
% 0.15/0.32  % (5741)Time elapsed: 0.004 s
% 0.15/0.32  % (5741)Instructions burned: 5 (million)
% 0.15/0.32  Cannot enumerate next child to try in an incomplete setup
% 0.15/0.32  % (5736)Refutation not found, incomplete strategy% (5736)------------------------------
% 0.15/0.32  % (5736)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.32  % (5736)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32  
% 0.15/0.32  % (5736)Memory used [KB]: 740
% 0.15/0.32  % (5736)Time elapsed: 0.004 s
% 0.15/0.32  % (5736)Instructions burned: 5 (million)
% 0.15/0.32  % (5735)------------------------------
% 0.15/0.32  % (5735)------------------------------
% 0.15/0.32  % (5741)------------------------------
% 0.15/0.32  % (5741)------------------------------
% 0.15/0.32  % (5736)------------------------------
% 0.15/0.32  % (5736)------------------------------
% 0.15/0.33  % (5740)First to succeed.
% 0.15/0.33  % (5740)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5734"
% 0.15/0.33  % (5740)Refutation found. Thanks to Tanya!
% 0.15/0.33  % SZS status Theorem for theBenchmark
% 0.15/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.33  % (5740)------------------------------
% 0.15/0.33  % (5740)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.33  % (5740)Termination reason: Refutation
% 0.15/0.33  
% 0.15/0.33  % (5740)Memory used [KB]: 908
% 0.15/0.33  % (5740)Time elapsed: 0.012 s
% 0.15/0.33  % (5740)Instructions burned: 20 (million)
% 0.15/0.33  % (5734)Success in time 0.026 s
%------------------------------------------------------------------------------