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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 09:54:00 AM UTC 2026

% Result   : Theorem 0.17s 0.47s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  107 (  20 unt;   8 def)
%            Number of atoms       :  282 (   0 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  280 ( 105   ~; 145   |;  11   &)
%                                         (  10 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  13 usr;   9 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  110 (   0 sgn 104   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( distinct_points(X0,X2)
        | distinct_points(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( distinct_points(X0,X1)
     => ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( distinct_points(X0,X1)
     => ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).

fof(f11,axiom,
    ! [X0,X1,X2,X3] :
      ( ( distinct_points(X0,X1)
        & distinct_lines(X2,X3) )
     => ( apart_point_and_line(X0,X2)
        | apart_point_and_line(X0,X3)
        | apart_point_and_line(X1,X2)
        | apart_point_and_line(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).

fof(f12,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( distinct_points(X0,X2)
        | apart_point_and_line(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( equal_points(X0,X1)
    <=> ~ distinct_points(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax1) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( equal_lines(X0,X1)
    <=> ~ distinct_lines(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).

fof(f36,conjecture,
    ! [X0,X1,X2] :
      ( ( distinct_points(X0,X1)
        & equal_points(X1,X2) )
     => ( distinct_points(X0,X2)
        & equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f37,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( distinct_points(X0,X1)
          & equal_points(X1,X2) )
       => ( distinct_points(X0,X2)
          & equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
    inference(negated_conjecture,[status(cth)],[f36]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(X0,X1)
     => equal_lines(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f32]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( equal_points(X0,X1)
     => ~ distinct_points(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f31]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X2)
      | distinct_points(X1,X2)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X2)
      | distinct_points(X1,X2)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f40]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X1,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f50,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X3)
      | ~ distinct_points(X0,X1)
      | ~ distinct_lines(X2,X3) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X3)
      | ~ distinct_points(X0,X1)
      | ~ distinct_lines(X2,X3) ),
    inference(flattening,[],[f50]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X2)
      | apart_point_and_line(X2,X1)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X2)
      | apart_point_and_line(X2,X1)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f52]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | ~ equal_points(X0,X1) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( equal_lines(X0,X1)
      | distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f80,plain,
    ? [X0,X1,X2] :
      ( ( ~ distinct_points(X0,X2)
        | ~ equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
      & distinct_points(X0,X1)
      & equal_points(X1,X2) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f81,plain,
    ? [X0,X1,X2] :
      ( ( ~ distinct_points(X0,X2)
        | ~ equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
      & distinct_points(X0,X1)
      & equal_points(X1,X2) ),
    inference(flattening,[],[f80]) ).

fof(f82,plain,
    ( ( ~ distinct_points(sK0,sK2)
      | ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) )
    & distinct_points(sK0,sK1)
    & equal_points(sK1,sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f81]) ).

fof(f83,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f86,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_points(X0,X1)
      | distinct_points(X1,X2)
      | distinct_points(X0,X2) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X1,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f93,plain,
    ! [X2,X3,X0,X1] :
      ( ~ distinct_lines(X2,X3)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X3)
      | ~ distinct_points(X0,X1)
      | apart_point_and_line(X0,X2) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f94,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | apart_point_and_line(X2,X1)
      | distinct_points(X0,X2) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ~ equal_points(X0,X1)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( equal_lines(X0,X1)
      | distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f121,plain,
    equal_points(sK1,sK2),
    inference(cnf_transformation,[],[f82]) ).

fof(f122,plain,
    distinct_points(sK0,sK1),
    inference(cnf_transformation,[],[f82]) ).

fof(f123,plain,
    ( ~ distinct_points(sK0,sK2)
    | ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f125,definition,
    ( spl3_1
  <=> equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
    introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).

fof(f127,plain,
    ( ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
    | spl3_1 ),
    inference(avatar_component_clause,[],[f125]) ).

fof(f129,definition,
    ( spl3_2
  <=> distinct_points(sK0,sK2) ),
    introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).

fof(f130,plain,
    ( distinct_points(sK0,sK2)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f129]) ).

fof(f132,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f123,f129,f125]) ).

fof(f134,plain,
    ~ distinct_points(sK1,sK2),
    inference(resolution,[],[f119,f121]) ).

fof(f135,plain,
    ( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
    | spl3_1 ),
    inference(resolution,[],[f120,f127]) ).

fof(f137,plain,
    ! [X0] :
      ( distinct_points(sK1,X0)
      | distinct_points(sK0,X0) ),
    inference(resolution,[],[f86,f122]) ).

fof(f138,plain,
    distinct_points(sK0,sK2),
    inference(resolution,[],[f137,f134]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( distinct_points(sK0,X0)
      | distinct_points(X0,X1)
      | distinct_points(sK1,X1) ),
    inference(resolution,[],[f137,f86]) ).

fof(f141,plain,
    spl3_2,
    inference(avatar_split_clause,[],[f138,f129]) ).

fof(f142,plain,
    ( ! [X0] :
        ( distinct_points(sK2,X0)
        | distinct_points(sK0,X0) )
    | ~ spl3_2 ),
    inference(resolution,[],[f130,f86]) ).

fof(f144,plain,
    ( ! [X0,X1] :
        ( distinct_points(sK0,X0)
        | distinct_points(X0,X1)
        | distinct_points(sK2,X1) )
    | ~ spl3_2 ),
    inference(resolution,[],[f142,f86]) ).

fof(f149,plain,
    ! [X0] :
      ( distinct_points(sK0,X0)
      | distinct_points(X0,sK2) ),
    inference(resolution,[],[f140,f134]) ).

fof(f166,plain,
    ( ! [X2,X0,X1] :
        ( distinct_points(sK0,X1)
        | distinct_points(X1,X0)
        | distinct_points(X0,X2)
        | distinct_points(sK2,X2) )
    | ~ spl3_2 ),
    inference(resolution,[],[f144,f86]) ).

fof(f259,plain,
    ( ! [X0,X1] :
        ( ~ distinct_points(X0,X1)
        | apart_point_and_line(X1,line_connecting(sK0,sK1))
        | apart_point_and_line(X1,line_connecting(sK0,sK2))
        | apart_point_and_line(X0,line_connecting(sK0,sK2))
        | apart_point_and_line(X0,line_connecting(sK0,sK1)) )
    | spl3_1 ),
    inference(resolution,[],[f93,f135]) ).

fof(f331,definition,
    ( spl3_5
  <=> apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
    introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).

fof(f333,plain,
    ( apart_point_and_line(sK2,line_connecting(sK0,sK1))
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f331]) ).

fof(f343,definition,
    ( spl3_8
  <=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).

fof(f344,plain,
    ( ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | spl3_8 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f345,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f348,definition,
    ( spl3_9
  <=> ! [X0] :
        ( apart_point_and_line(X0,line_connecting(sK0,sK1))
        | distinct_points(sK0,X0)
        | apart_point_and_line(X0,line_connecting(sK0,sK2)) ) ),
    introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).

fof(f349,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,line_connecting(sK0,sK2))
        | distinct_points(sK0,X0)
        | apart_point_and_line(X0,line_connecting(sK0,sK1)) )
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f348]) ).

fof(f368,definition,
    ( spl3_14
  <=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
    introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).

fof(f369,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | spl3_14 ),
    inference(avatar_component_clause,[],[f368]) ).

fof(f370,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ spl3_14 ),
    inference(avatar_component_clause,[],[f368]) ).

fof(f406,definition,
    ( spl3_22
  <=> ! [X0,X1] :
        ( apart_point_and_line(X0,line_connecting(sK0,sK1))
        | distinct_points(sK2,X1)
        | distinct_points(X0,X1)
        | apart_point_and_line(X0,line_connecting(sK0,sK2)) ) ),
    introduced(definition,[new_symbols(definition,[spl3_22])],[avatar_definition]) ).

fof(f407,plain,
    ( ! [X0,X1] :
        ( apart_point_and_line(X0,line_connecting(sK0,sK2))
        | distinct_points(sK2,X1)
        | distinct_points(X0,X1)
        | apart_point_and_line(X0,line_connecting(sK0,sK1)) )
    | ~ spl3_22 ),
    inference(avatar_component_clause,[],[f406]) ).

fof(f455,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_8 ),
    inference(resolution,[],[f345,f89]) ).

fof(f458,plain,
    ( $false
    | ~ spl3_8 ),
    inference(forward_subsumption_resolution,[],[f455,f122]) ).

fof(f459,plain,
    ~ spl3_8,
    inference(avatar_contradiction_clause,[],[f458]) ).

fof(f465,plain,
    ( ! [X0] :
        ( apart_point_and_line(X0,line_connecting(sK0,sK1))
        | distinct_points(sK2,X0) )
    | ~ spl3_5 ),
    inference(resolution,[],[f333,f94]) ).

fof(f477,plain,
    ( ~ distinct_points(sK0,sK1)
    | ~ spl3_14 ),
    inference(resolution,[],[f370,f90]) ).

fof(f480,plain,
    ( $false
    | ~ spl3_14 ),
    inference(forward_subsumption_resolution,[],[f477,f122]) ).

fof(f481,plain,
    ~ spl3_14,
    inference(avatar_contradiction_clause,[],[f480]) ).

fof(f610,plain,
    ( ! [X2,X0,X1] :
        ( distinct_points(sK0,X0)
        | distinct_points(X1,X2)
        | distinct_points(sK2,X2)
        | apart_point_and_line(X1,line_connecting(sK0,sK1))
        | apart_point_and_line(X1,line_connecting(sK0,sK2))
        | apart_point_and_line(X0,line_connecting(sK0,sK2))
        | apart_point_and_line(X0,line_connecting(sK0,sK1)) )
    | spl3_1
    | ~ spl3_2 ),
    inference(resolution,[],[f166,f259]) ).

fof(f622,plain,
    ( spl3_22
    | spl3_9
    | spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f610,f129,f125,f348,f406]) ).

fof(f632,plain,
    ( distinct_points(sK2,sK1)
    | ~ spl3_5
    | spl3_14 ),
    inference(resolution,[],[f465,f369]) ).

fof(f651,plain,
    ( ! [X0] :
        ( distinct_points(sK2,X0)
        | distinct_points(sK1,X0) )
    | ~ spl3_5
    | spl3_14 ),
    inference(resolution,[],[f632,f86]) ).

fof(f652,plain,
    ( distinct_points(sK0,sK0)
    | apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ distinct_points(sK0,sK2)
    | ~ spl3_9 ),
    inference(resolution,[],[f349,f89]) ).

fof(f660,plain,
    ( distinct_points(sK0,sK0)
    | apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_9 ),
    inference(forward_subsumption_resolution,[],[f652,f149]) ).

fof(f663,plain,
    ( apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ spl3_9 ),
    inference(forward_subsumption_resolution,[],[f660,f83]) ).

fof(f664,plain,
    ( $false
    | spl3_8
    | ~ spl3_9 ),
    inference(forward_subsumption_resolution,[],[f663,f344]) ).

fof(f665,plain,
    ( spl3_8
    | ~ spl3_9 ),
    inference(avatar_contradiction_clause,[],[f664]) ).

fof(f690,plain,
    ( distinct_points(sK1,sK2)
    | ~ spl3_5
    | spl3_14 ),
    inference(resolution,[],[f651,f83]) ).

fof(f693,plain,
    ( $false
    | ~ spl3_5
    | spl3_14 ),
    inference(forward_subsumption_resolution,[],[f690,f134]) ).

fof(f694,plain,
    ( ~ spl3_5
    | spl3_14 ),
    inference(avatar_contradiction_clause,[],[f693]) ).

fof(f702,plain,
    ( ! [X0] :
        ( distinct_points(sK2,X0)
        | distinct_points(sK2,X0)
        | apart_point_and_line(sK2,line_connecting(sK0,sK1))
        | ~ distinct_points(sK0,sK2) )
    | ~ spl3_22 ),
    inference(resolution,[],[f407,f90]) ).

fof(f715,plain,
    ( ! [X0] :
        ( distinct_points(sK2,X0)
        | apart_point_and_line(sK2,line_connecting(sK0,sK1))
        | ~ distinct_points(sK0,sK2) )
    | ~ spl3_22 ),
    inference(duplicate_literal_removal,[],[f702]) ).

fof(f717,definition,
    ( spl3_29
  <=> ! [X0] : distinct_points(sK2,X0) ),
    introduced(definition,[new_symbols(definition,[spl3_29])],[avatar_definition]) ).

fof(f718,plain,
    ( ! [X0] : distinct_points(sK2,X0)
    | ~ spl3_29 ),
    inference(avatar_component_clause,[],[f717]) ).

fof(f723,plain,
    ( ! [X0] :
        ( distinct_points(sK2,X0)
        | apart_point_and_line(sK2,line_connecting(sK0,sK1)) )
    | ~ spl3_2
    | ~ spl3_22 ),
    inference(forward_subsumption_resolution,[],[f715,f130]) ).

fof(f725,plain,
    ( spl3_5
    | spl3_29
    | ~ spl3_2
    | ~ spl3_22 ),
    inference(avatar_split_clause,[],[f723,f406,f129,f717,f331]) ).

fof(f730,plain,
    ( $false
    | ~ spl3_29 ),
    inference(resolution,[],[f718,f83]) ).

fof(f733,plain,
    ~ spl3_29,
    inference(avatar_contradiction_clause,[],[f730]) ).

cnf(s1,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(sat_conversion,[],[f132]) ).

cnf(s2,plain,
    spl3_2,
    inference(sat_conversion,[],[f141]) ).

cnf(s46,plain,
    ~ spl3_8,
    inference(sat_conversion,[],[f459]) ).

cnf(s47,plain,
    ~ spl3_14,
    inference(sat_conversion,[],[f481]) ).

cnf(s61,plain,
    ( spl3_1
    | ~ spl3_2
    | spl3_9
    | spl3_22 ),
    inference(sat_conversion,[],[f622]) ).

cnf(s63,plain,
    ( spl3_8
    | ~ spl3_9 ),
    inference(sat_conversion,[],[f665]) ).

cnf(s68,plain,
    ( ~ spl3_5
    | spl3_14 ),
    inference(sat_conversion,[],[f694]) ).

cnf(s75,plain,
    ( ~ spl3_2
    | spl3_5
    | ~ spl3_22
    | spl3_29 ),
    inference(sat_conversion,[],[f725]) ).

cnf(s77,plain,
    ~ spl3_29,
    inference(sat_conversion,[],[f733]) ).

cnf(s79,plain,
    ( ~ spl3_2
    | spl3_5
    | ~ spl3_22 ),
    inference(rat,[],[s75,s77]) ).

cnf(s81,plain,
    ~ spl3_5,
    inference(rat,[],[s68,s47]) ).

cnf(s82,plain,
    ~ spl3_9,
    inference(rat,[],[s63,s46]) ).

cnf(s122,plain,
    ~ spl3_22,
    inference(rat,[],[s79,s81,s2]) ).

cnf(s123,plain,
    spl3_1,
    inference(rat,[],[s61,s122,s82,s2]) ).

cnf(s126,plain,
    $false,
    inference(rat,[],[s1,s2,s123]) ).

fof(f735,plain,
    $false,
    inference(avatar_sat_refutation,[],[s126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37  % Computer : n006.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Sun Sep 27 07:35:26 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.37  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41  Running first-order model finding
% 0.11/0.41  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47  % (2657597)Will run a generic schedule for satisfiability detection.
% 0.17/0.47  % (2657606)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1630434565:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47  % (2657603)% WARNING: option uhcvi not known.
% 0.17/0.47  % (2657603)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1862088420:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47  % (2657602)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3197150846_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47  % (2657604)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=61280520:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47  % (2657605)dis+10_1_sil=32000:sp=arity:random_seed=3203178148:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47  % (2657607)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=684413599:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47  % (2657608)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=455415187:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47  % TRYING [1]
% 0.17/0.47  % TRYING [2]
% 0.17/0.47  % TRYING [3]
% 0.17/0.47  % TRYING [4]
% 0.17/0.47  % TRYING [5]
% 0.17/0.47  % (2657605) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2657597-2657605"...
% 0.17/0.47  % (2657605)...printing done.
% 0.17/0.47  % (2657605)Refutation found. Thanks to Tanya!
% 0.17/0.47  % SZS status Theorem for theBenchmark
% 0.17/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48  % (2657605)------------------------------
% 0.17/0.48  % (2657605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48  % (2657605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48  % (2657605)CaDiCaL version: 2.1.3
% 0.17/0.48  % (2657605)Termination reason: Refutation
% 0.17/0.48  % (2657605)Time elapsed: 0.014 s
% 0.17/0.48  % (2657605)Peak memory usage: 12 MB
% 0.17/0.48  % (2657605)Instructions burned: 21 (million)
% 0.17/0.48  % (2657597)Success in time 0.06 s
% 0.17/0.48  % Vampire exiting
%------------------------------------------------------------------------------