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DT2H2X---1.9.5.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : SYN358^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n020.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 : Wed Feb 25 09:50:50 AM UTC 2026

% Result   : Theorem 1.51s 1.25s
% Output   : Refutation 1.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   30 (   2 unt;   0 typ;   3 def)
%            Number of atoms       :  241 (  66 equ;   0 cnn)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives :  154 (  41   ~;  35   |;  24   &;  44   @)
%                                         (   7 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   8 con; 0-2 aty)
%            Number of variables   :   34 (   0   ^;  16   !;  18   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_0,type,
    cQ: $i > $o ).

thf(f38,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f24,f33,f35,f37]) ).

thf(f37,plain,
    ( ~ spl2_1
    | ~ spl2_2 ),
    inference(avatar_contradiction_clause,[status(thm)],[f36]) ).

thf(f36,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_2 ),
    inference(subsumption_resolution,[status(thm)],[f28,f23]) ).

thf(f23,plain,
    ( ! [X0: $i] :
        ( ( cQ @ X0 )
       != $true )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[status(thm)],[f22]) ).

thf(f22,definition,
    ( spl2_1
  <=> ! [X0: $i] :
        ( ( cQ @ X0 )
       != $true ) ),
    introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).

thf(f28,plain,
    ( ( ( cQ @ sK0 )
      = $true )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[status(thm)],[f26]) ).

thf(f26,definition,
    ( spl2_2
  <=> ( ( cQ @ sK0 )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).

thf(f35,plain,
    ( ~ spl2_1
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[status(thm)],[f34]) ).

thf(f34,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(subsumption_resolution,[status(thm)],[f32,f23]) ).

thf(f32,plain,
    ( ( ( cQ @ sK1 )
      = $true )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[status(thm)],[f30]) ).

thf(f30,definition,
    ( spl2_3
  <=> ( ( cQ @ sK1 )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).

thf(f33,plain,
    ( spl2_2
    | spl2_3 ),
    inference(avatar_split_clause,[status(thm)],[f13,f30,f26]) ).

thf(f13,plain,
    ( ( ( cQ @ sK1 )
      = $true )
    | ( ( cQ @ sK0 )
      = $true ) ),
    inference(cnf_transformation,[status(thm)],[f12]) ).

thf(f12,plain,
    ( ( ! [X0: $i] :
          ( ( p != $true )
          | ( ( cQ @ X0 )
           != $true ) )
      | ( p != $true )
      | ! [X1: $i] :
          ( ( cQ @ X1 )
         != $true ) )
    & ( ( ( p = $true )
        & ( ( cQ @ sK0 )
          = $true ) )
      | ( ( p = $true )
        & ( ( cQ @ sK1 )
          = $true ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).

thf(f10,plain,
    ( ? [X2: $i] :
        ( ( p = $true )
        & ( ( cQ @ X2 )
          = $true ) )
   => ( ( p = $true )
      & ( ( cQ @ sK0 )
        = $true ) ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f11,plain,
    ( ? [X3: $i] :
        ( ( cQ @ X3 )
        = $true )
   => ( ( cQ @ sK1 )
      = $true ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f9,plain,
    ( ( ! [X0: $i] :
          ( ( p != $true )
          | ( ( cQ @ X0 )
           != $true ) )
      | ( p != $true )
      | ! [X1: $i] :
          ( ( cQ @ X1 )
         != $true ) )
    & ( ? [X2: $i] :
          ( ( p = $true )
          & ( ( cQ @ X2 )
            = $true ) )
      | ( ( p = $true )
        & ? [X3: $i] :
            ( ( cQ @ X3 )
            = $true ) ) ) ),
    inference(rectify,[status(thm)],[f8]) ).

thf(f8,plain,
    ( ( ! [X1: $i] :
          ( ( p != $true )
          | ( ( cQ @ X1 )
           != $true ) )
      | ( p != $true )
      | ! [X0: $i] :
          ( ( cQ @ X0 )
         != $true ) )
    & ( ? [X1: $i] :
          ( ( p = $true )
          & ( ( cQ @ X1 )
            = $true ) )
      | ( ( p = $true )
        & ? [X0: $i] :
            ( ( cQ @ X0 )
            = $true ) ) ) ),
    inference(flattening,[status(thm)],[f7]) ).

thf(f7,plain,
    ( ( ! [X1: $i] :
          ( ( p != $true )
          | ( ( cQ @ X1 )
           != $true ) )
      | ( p != $true )
      | ! [X0: $i] :
          ( ( cQ @ X0 )
         != $true ) )
    & ( ? [X1: $i] :
          ( ( p = $true )
          & ( ( cQ @ X1 )
            = $true ) )
      | ( ( p = $true )
        & ? [X0: $i] :
            ( ( cQ @ X0 )
            = $true ) ) ) ),
    inference(nnf_transformation,[status(thm)],[f6]) ).

thf(f6,plain,
    ( ( ( p = $true )
      & ? [X0: $i] :
          ( ( cQ @ X0 )
          = $true ) )
  <~> ? [X1: $i] :
        ( ( p = $true )
        & ( ( cQ @ X1 )
          = $true ) ) ),
    inference(ennf_transformation,[status(thm)],[f5]) ).

thf(f5,plain,
    ~ ( ( ( p = $true )
        & ? [X0: $i] :
            ( ( cQ @ X0 )
            = $true ) )
    <=> ? [X1: $i] :
          ( ( p = $true )
          & ( ( cQ @ X1 )
            = $true ) ) ),
    inference(fool_elimination,[status(thm)],[f4]) ).

thf(f4,plain,
    ~ ( ( ? [X0: $i] : ( cQ @ X0 )
        & p )
    <=> ? [X1: $i] :
          ( ( cQ @ X1 )
          & p ) ),
    inference(rectify,[status(thm)],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ? [X0: $i] : ( cQ @ X0 )
        & p )
    <=> ? [X0: $i] :
          ( ( cQ @ X0 )
          & p ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

thf(f1,conjecture,
    ( ( ? [X0: $i] : ( cQ @ X0 )
      & p )
  <=> ? [X0: $i] :
        ( ( cQ @ X0 )
        & p ) ),
    file('/export/starexec/sandbox/tmp/tmp.Tx9x0vjM9a/DTF2THF_28879.p',cX2109) ).

thf(f24,plain,
    ( spl2_1
    | spl2_1 ),
    inference(avatar_split_clause,[status(thm)],[f20,f22,f22]) ).

thf(f20,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cQ @ X0 )
       != $true )
      | ( ( cQ @ X1 )
       != $true ) ),
    inference(subsumption_resolution,[status(thm)],[f18,f19]) ).

thf(f19,plain,
    p = $true,
    inference(duplicate_literal_removal,[status(thm)],[f16]) ).

thf(f16,plain,
    ( ( p = $true )
    | ( p = $true ) ),
    inference(cnf_transformation,[status(thm)],[f12]) ).

thf(f18,plain,
    ! [X0: $i,X1: $i] :
      ( ( p != $true )
      | ( ( cQ @ X0 )
       != $true )
      | ( ( cQ @ X1 )
       != $true ) ),
    inference(duplicate_literal_removal,[status(thm)],[f17]) ).

thf(f17,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cQ @ X0 )
       != $true )
      | ( p != $true )
      | ( ( cQ @ X1 )
       != $true )
      | ( p != $true ) ),
    inference(cnf_transformation,[status(thm)],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SYN358^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32  % Computer : n020.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit : 300
% 0.14/0.32  % WCLimit  : 300
% 0.14/0.32  % DateTime : Tue Feb 24 13:56:12 EST 2026
% 0.14/0.32  % CPUTime  : 
% 0.14/0.32  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44  ---- Original DTF file ---
% 0.18/0.44  thf(spec,logic,$$dhol).
% 0.18/0.44  %------------------------------------------------------------------------------
% 0.18/0.44  % File     : SYN358^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.44  % Domain   : Syntactic
% 0.18/0.44  % Problem  : TPS problem X2109
% 0.18/0.44  % Version  : Especial.
% 0.18/0.44  % English  : 
% 0.18/0.44  
% 0.18/0.44  % Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44  % Source   : [Bro09]
% 0.18/0.44  % Names    : tps_0070 [Bro09]
% 0.18/0.44  %          : X2109 [TPS]
% 0.18/0.44  
% 0.18/0.44  % Status   : Theorem
% 0.18/0.44  % Rating   : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.18/0.44  % Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
% 0.18/0.44  %            Number of atoms       :    4 (   0 equ;   0 cnn)
% 0.18/0.44  %            Maximal formula atoms :    4 (   4 avg)
% 0.18/0.44  %            Number of connectives :    5 (   0   ~;   0   |;   2   &;   2   @)
% 0.18/0.44  %                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
% 0.18/0.44  %            Maximal formula depth :    5 (   5 avg)
% 0.18/0.44  %            Number of types       :    2 (   0 usr)
% 0.18/0.44  %            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
% 0.18/0.44  %            Number of symbols     :    2 (   2 usr;   1 con; 0-1 aty)
% 0.18/0.44  %            Number of variables   :    2 (   0   ^;   0   !;   2   ?;   2   :)
% 0.18/0.44  % SPC      : TH0_THM_NEQ_NAR
% 0.18/0.44  
% 0.18/0.44  % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.44  %            project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.44  %            Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.44  %            license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.44  %          : 
% 0.18/0.44  %------------------------------------------------------------------------------
% 0.18/0.44  thf(cQ,type,
% 0.18/0.44      cQ: $i > $o ).
% 0.18/0.44  
% 0.18/0.44  thf(p,type,
% 0.18/0.44      p: $o ).
% 0.18/0.44  
% 0.18/0.44  thf(cX2109,conjecture,
% 0.18/0.44      ( ? [Xx: $i] :
% 0.18/0.44          ( p
% 0.18/0.44          & ( cQ @ Xx ) )
% 0.18/0.44    <=> ( p
% 0.18/0.44        & ? [Xx: $i] : ( cQ @ Xx ) ) ) ).
% 0.18/0.44  
% 0.18/0.44  %------------------------------------------------------------------------------
% 0.18/0.44  ------------------------
% 1.51/1.22  ---- Embedded in THF ---
% 1.51/1.22  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.22  %%% Generated on Tue Feb 24 13:56:13 EST 2026
% 1.51/1.22  %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.22  %%% Logic specification used:
% 1.51/1.22  %%% thf(spec, logic, $$dhol).
% 1.51/1.22  
% 1.51/1.22  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Tx9x0vjM9a/DTF2DTF28879.p
% See solution above
% 1.51/1.22  ------------------------
% 1.51/1.23  ---- Cleaned THF ---
% 1.51/1.23  thf(cQ,type,
% 1.51/1.23      cQ: $i > $o ).
% 1.51/1.23  
% 1.51/1.23  thf(p,type,
% 1.51/1.23      p: $o ).
% 1.51/1.23  
% 1.51/1.23  thf(cX2109,conjecture,
% 1.51/1.23      ( ? [Xx: $i] :
% 1.51/1.23          ( p
% 1.51/1.23          & ( cQ @ Xx ) )
% 1.51/1.23    <=> ( p
% 1.51/1.23        & ? [Xx: $i] : ( cQ @ Xx ) ) ) ).
% 1.51/1.23  ------------------------
% 1.51/1.25  % (28988)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_28879 for (2999ds/27Mi)
% 1.51/1.25  % (28986)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28879 for (2999ds/183Mi)
% 1.51/1.25  % (28986)First to succeed.
% 1.51/1.25  % (28988)Also succeeded, but the first one will report.
% 1.51/1.25  % (28986)Refutation found. Thanks to Tanya!
% 1.51/1.25  % SZS status Theorem for DTF2THF_28879
% 1.51/1.25  % SZS output start Proof for DTF2THF_28879
% 1.51/1.25  thf(func_def_0, type, cQ: $i > $o).
% 1.51/1.25  thf(f38,plain,(
% 1.51/1.25    $false),
% 1.51/1.25    inference(avatar_sat_refutation,[status(thm)],[f24,f33,f35,f37])).
% 1.51/1.25  thf(f37,plain,(
% 1.51/1.25    ~spl2_1 | ~spl2_2),
% 1.51/1.25    inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.51/1.25  thf(f36,plain,(
% 1.51/1.25    $false | (~spl2_1 | ~spl2_2)),
% 1.51/1.25    inference(subsumption_resolution,[status(thm)],[f28,f23])).
% 1.51/1.25  thf(f23,plain,(
% 1.51/1.25    ( ! [X0 : $i] : (((cQ @ X0) != $true)) ) | ~spl2_1),
% 1.51/1.25    inference(avatar_component_clause,[status(thm)],[f22])).
% 1.51/1.25  thf(f22,definition,(
% 1.51/1.25    spl2_1 <=> ! [X0 : $i] : ((cQ @ X0) != $true)),
% 1.51/1.25    introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.51/1.25  thf(f28,plain,(
% 1.51/1.25    ((cQ @ sK0) = $true) | ~spl2_2),
% 1.51/1.25    inference(avatar_component_clause,[status(thm)],[f26])).
% 1.51/1.25  thf(f26,definition,(
% 1.51/1.25    spl2_2 <=> ((cQ @ sK0) = $true)),
% 1.51/1.25    introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.51/1.25  thf(f35,plain,(
% 1.51/1.25    ~spl2_1 | ~spl2_3),
% 1.51/1.25    inference(avatar_contradiction_clause,[status(thm)],[f34])).
% 1.51/1.25  thf(f34,plain,(
% 1.51/1.25    $false | (~spl2_1 | ~spl2_3)),
% 1.51/1.25    inference(subsumption_resolution,[status(thm)],[f32,f23])).
% 1.51/1.25  thf(f32,plain,(
% 1.51/1.25    ((cQ @ sK1) = $true) | ~spl2_3),
% 1.51/1.25    inference(avatar_component_clause,[status(thm)],[f30])).
% 1.51/1.25  thf(f30,definition,(
% 1.51/1.25    spl2_3 <=> ((cQ @ sK1) = $true)),
% 1.51/1.25    introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.51/1.25  thf(f33,plain,(
% 1.51/1.25    spl2_2 | spl2_3),
% 1.51/1.25    inference(avatar_split_clause,[status(thm)],[f13,f30,f26])).
% 1.51/1.25  thf(f13,plain,(
% 1.51/1.25    ((cQ @ sK1) = $true) | ((cQ @ sK0) = $true)),
% 1.51/1.25    inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.25  thf(f12,plain,(
% 1.51/1.25    (! [X0 : $i] : ((p != $true) | ((cQ @ X0) != $true)) | (p != $true) | ! [X1 : $i] : ((cQ @ X1) != $true)) & (((p = $true) & ((cQ @ sK0) = $true)) | ((p = $true) & ((cQ @ sK1) = $true)))),
% 1.51/1.25    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.51/1.25  thf(f10,plain,(
% 1.51/1.25    ? [X2 : $i] : ((p = $true) & ((cQ @ X2) = $true)) => ((p = $true) & ((cQ @ sK0) = $true))),
% 1.51/1.25    introduced(definition,[],[choice_axiom])).
% 1.51/1.25  thf(f11,plain,(
% 1.51/1.25    ? [X3 : $i] : ((cQ @ X3) = $true) => ((cQ @ sK1) = $true)),
% 1.51/1.25    introduced(definition,[],[choice_axiom])).
% 1.51/1.25  thf(f9,plain,(
% 1.51/1.25    (! [X0 : $i] : ((p != $true) | ((cQ @ X0) != $true)) | (p != $true) | ! [X1 : $i] : ((cQ @ X1) != $true)) & (? [X2 : $i] : ((p = $true) & ((cQ @ X2) = $true)) | ((p = $true) & ? [X3 : $i] : ((cQ @ X3) = $true)))),
% 1.51/1.25    inference(rectify,[status(thm)],[f8])).
% 1.51/1.25  thf(f8,plain,(
% 1.51/1.25    (! [X1 : $i] : ((p != $true) | ((cQ @ X1) != $true)) | (p != $true) | ! [X0 : $i] : ((cQ @ X0) != $true)) & (? [X1 : $i] : ((p = $true) & ((cQ @ X1) = $true)) | ((p = $true) & ? [X0 : $i] : ((cQ @ X0) = $true)))),
% 1.51/1.25    inference(flattening,[status(thm)],[f7])).
% 1.51/1.25  thf(f7,plain,(
% 1.51/1.25    (! [X1 : $i] : ((p != $true) | ((cQ @ X1) != $true)) | ((p != $true) | ! [X0 : $i] : ((cQ @ X0) != $true))) & (? [X1 : $i] : ((p = $true) & ((cQ @ X1) = $true)) | ((p = $true) & ? [X0 : $i] : ((cQ @ X0) = $true)))),
% 1.51/1.25    inference(nnf_transformation,[status(thm)],[f6])).
% 1.51/1.25  thf(f6,plain,(
% 1.51/1.25    ((p = $true) & ? [X0 : $i] : ((cQ @ X0) = $true)) <~> ? [X1 : $i] : ((p = $true) & ((cQ @ X1) = $true))),
% 1.51/1.25    inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.25  thf(f5,plain,(
% 1.51/1.25    ~(((p = $true) & ? [X0 : $i] : ((cQ @ X0) = $true)) <=> ? [X1 : $i] : ((p = $true) & ((cQ @ X1) = $true)))),
% 1.51/1.25    inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.25  thf(f4,plain,(
% 1.51/1.25    ~((? [X0 : $i] : (cQ @ X0) & p) <=> ? [X1 : $i] : ((cQ @ X1) & p))),
% 1.51/1.25    inference(rectify,[status(thm)],[f2])).
% 1.51/1.25  thf(f2,negated_conjecture,(
% 1.51/1.25    ~((? [X0 : $i] : (cQ @ X0) & p) <=> ? [X0 : $i] : ((cQ @ X0) & p))),
% 1.51/1.25    inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.25  thf(f1,conjecture,(
% 1.51/1.25    (? [X0 : $i] : (cQ @ X0) & p) <=> ? [X0 : $i] : ((cQ @ X0) & p)),
% 1.51/1.25    file('/export/starexec/sandbox/tmp/tmp.Tx9x0vjM9a/DTF2THF_28879.p',cX2109)).
% 1.51/1.25  thf(f24,plain,(
% 1.51/1.25    spl2_1 | spl2_1),
% 1.51/1.25    inference(avatar_split_clause,[status(thm)],[f20,f22,f22])).
% 1.51/1.25  thf(f20,plain,(
% 1.51/1.25    ( ! [X0 : $i,X1 : $i] : (((cQ @ X0) != $true) | ((cQ @ X1) != $true)) )),
% 1.51/1.25    inference(subsumption_resolution,[status(thm)],[f18,f19])).
% 1.51/1.25  thf(f19,plain,(
% 1.51/1.25    (p = $true)),
% 1.51/1.25    inference(duplicate_literal_removal,[status(thm)],[f16])).
% 1.51/1.25  thf(f16,plain,(
% 1.51/1.25    (p = $true) | (p = $true)),
% 1.51/1.25    inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.25  thf(f18,plain,(
% 1.51/1.25    ( ! [X0 : $i,X1 : $i] : ((p != $true) | ((cQ @ X0) != $true) | ((cQ @ X1) != $true)) )),
% 1.51/1.25    inference(duplicate_literal_removal,[status(thm)],[f17])).
% 1.51/1.25  thf(f17,plain,(
% 1.51/1.25    ( ! [X0 : $i,X1 : $i] : (((cQ @ X0) != $true) | (p != $true) | ((cQ @ X1) != $true) | (p != $true)) )),
% 1.51/1.25    inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.25  % SZS output end Proof for DTF2THF_28879
% 1.51/1.25  % (28986)------------------------------
% 1.51/1.25  % (28986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25  % (28986)Termination reason: Refutation
% 1.51/1.25  
% 1.51/1.25  % (28986)Memory used [KB]: 5500
% 1.51/1.25  % (28986)Time elapsed: 0.002 s
% 1.51/1.25  % (28986)Instructions burned: 2 (million)
% 1.51/1.25  % (28986)------------------------------
% 1.51/1.25  % (28986)------------------------------
% 1.51/1.25  % (28985)Success in time 0.013 s
%------------------------------------------------------------------------------