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DT2H2X---1.9.5.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : SYO099^5 : 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 : n019.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 09:53:22 AM UTC 2026

% Result   : Theorem 1.52s 1.35s
% Output   : Refutation 1.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   19 (   6 unt;   0 typ;   0 def)
%            Number of atoms       :  163 (  45 equ;   0 cnn)
%            Maximal formula atoms :    6 (   8 avg)
%            Number of connectives :  154 (  47   ~;  33   |;   9   &;  62   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   53 (   0   ^;  34   !;  19   ?;  53   :)

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

thf(func_def_1,type,
    cN: $i > $o ).

thf(func_def_2,type,
    cM: $i > $o ).

thf(f20,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[f19]) ).

thf(f19,plain,
    $true != $true,
    inference(superposition,[status(thm)],[f15,f18]) ).

thf(f18,plain,
    ! [X5: $i] :
      ( $true
      = ( cM @ X5 ) ),
    inference(subsumption_resolution,[status(thm)],[f13,f17]) ).

thf(f17,plain,
    ! [X2: $i] :
      ( $true
     != ( cN @ X2 ) ),
    inference(subsumption_resolution,[status(thm)],[f14,f16]) ).

thf(f16,plain,
    ! [X0: $i] :
      ( $true
      = ( cG @ X0 ) ),
    inference(cnf_transformation,[status(thm)],[f12]) ).

thf(f12,plain,
    ( ! [X0: $i] :
        ( $true
        = ( cG @ X0 ) )
    & ( $true
     != ( cM @ sK0 ) )
    & ( ! [X2: $i] :
          ( $true
         != ( cN @ X2 ) )
      | ( $true
       != ( cG @ sK1 ) ) )
    & ( ( ( cN @ sK2 )
        = $true )
      | ! [X5: $i] :
          ( $true
          = ( cM @ X5 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).

thf(f9,plain,
    ( ? [X1: $i] :
        ( $true
       != ( cM @ X1 ) )
   => ( $true
     != ( cM @ sK0 ) ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f10,plain,
    ( ? [X3: $i] :
        ( $true
       != ( cG @ X3 ) )
   => ( $true
     != ( cG @ sK1 ) ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f11,plain,
    ( ? [X4: $i] :
        ( ( cN @ X4 )
        = $true )
   => ( ( cN @ sK2 )
      = $true ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f8,plain,
    ( ! [X0: $i] :
        ( $true
        = ( cG @ X0 ) )
    & ? [X1: $i] :
        ( $true
       != ( cM @ X1 ) )
    & ( ! [X2: $i] :
          ( $true
         != ( cN @ X2 ) )
      | ? [X3: $i] :
          ( $true
         != ( cG @ X3 ) ) )
    & ( ? [X4: $i] :
          ( ( cN @ X4 )
          = $true )
      | ! [X5: $i] :
          ( $true
          = ( cM @ X5 ) ) ) ),
    inference(rectify,[status(thm)],[f7]) ).

thf(f7,plain,
    ( ! [X5: $i] :
        ( ( cG @ X5 )
        = $true )
    & ? [X4: $i] :
        ( ( cM @ X4 )
       != $true )
    & ( ! [X3: $i] :
          ( ( cN @ X3 )
         != $true )
      | ? [X2: $i] :
          ( ( cG @ X2 )
         != $true ) )
    & ( ? [X0: $i] :
          ( $true
          = ( cN @ X0 ) )
      | ! [X1: $i] :
          ( $true
          = ( cM @ X1 ) ) ) ),
    inference(ennf_transformation,[status(thm)],[f6]) ).

thf(f6,plain,
    ~ ( ! [X4: $i] :
          ( ( cM @ X4 )
          = $true )
      | ? [X5: $i] :
          ( ( cG @ X5 )
         != $true )
      | ~ ( ? [X0: $i] :
              ( $true
              = ( cN @ X0 ) )
          | ! [X1: $i] :
              ( $true
              = ( cM @ X1 ) ) )
      | ~ ( ! [X3: $i] :
              ( ( cN @ X3 )
             != $true )
          | ~ ! [X2: $i] :
                ( ( cG @ X2 )
                = $true ) ) ),
    inference(flattening,[status(thm)],[f5]) ).

thf(f5,plain,
    ~ ( ~ ( ? [X0: $i] :
              ( $true
              = ( cN @ X0 ) )
          | ! [X1: $i] :
              ( $true
              = ( cM @ X1 ) ) )
      | ~ ( ~ ! [X2: $i] :
                ( ( cG @ X2 )
                = $true )
          | ! [X3: $i] :
              ( ( cN @ X3 )
             != $true ) )
      | ! [X4: $i] :
          ( ( cM @ X4 )
          = $true )
      | ? [X5: $i] :
          ( ( cG @ X5 )
         != $true ) ),
    inference(fool_elimination,[status(thm)],[f4]) ).

thf(f4,plain,
    ~ ( ~ ( ? [X0: $i] : ( cN @ X0 )
          | ! [X1: $i] : ( cM @ X1 ) )
      | ~ ( ~ ! [X2: $i] : ( cG @ X2 )
          | ! [X3: $i] :
              ~ ( cN @ X3 ) )
      | ! [X4: $i] : ( cM @ X4 )
      | ? [X5: $i] :
          ~ ( cG @ X5 ) ),
    inference(rectify,[status(thm)],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ~ ( ? [X3: $i] : ( cN @ X3 )
          | ! [X2: $i] : ( cM @ X2 ) )
      | ~ ( ~ ! [X5: $i] : ( cG @ X5 )
          | ! [X4: $i] :
              ~ ( cN @ X4 ) )
      | ! [X0: $i] : ( cM @ X0 )
      | ? [X1: $i] :
          ~ ( cG @ X1 ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

thf(f1,conjecture,
    ( ~ ( ? [X3: $i] : ( cN @ X3 )
        | ! [X2: $i] : ( cM @ X2 ) )
    | ~ ( ~ ! [X5: $i] : ( cG @ X5 )
        | ! [X4: $i] :
            ~ ( cN @ X4 ) )
    | ! [X0: $i] : ( cM @ X0 )
    | ? [X1: $i] :
        ~ ( cG @ X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.C7cGrxJIYO/DTF2THF_13856.p',cTHM78) ).

thf(f14,plain,
    ! [X2: $i] :
      ( ( $true
       != ( cN @ X2 ) )
      | ( $true
       != ( cG @ sK1 ) ) ),
    inference(cnf_transformation,[status(thm)],[f12]) ).

thf(f13,plain,
    ! [X5: $i] :
      ( ( ( cN @ sK2 )
        = $true )
      | ( $true
        = ( cM @ X5 ) ) ),
    inference(cnf_transformation,[status(thm)],[f12]) ).

thf(f15,plain,
    ( $true
   != ( cM @ sK0 ) ),
    inference(cnf_transformation,[status(thm)],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SYO099^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30  % Computer : n019.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit : 300
% 0.11/0.30  % WCLimit  : 300
% 0.11/0.30  % DateTime : Tue Feb 24 14:24:24 EST 2026
% 0.11/0.30  % CPUTime  : 
% 0.11/0.30  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39  ---- Original DTF file ---
% 0.16/0.39  thf(spec,logic,$$dhol).
% 0.16/0.39  %------------------------------------------------------------------------------
% 0.16/0.39  % File     : SYO099^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39  % Domain   : Syntactic
% 0.16/0.39  % Problem  : TPS problem THM78
% 0.16/0.39  % Version  : Especial.
% 0.16/0.39  % English  : 
% 0.16/0.39  
% 0.16/0.39  % Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39  % Source   : [Bro09]
% 0.16/0.39  % Names    : tps_0313 [Bro09]
% 0.16/0.39  %          : THM78 [TPS]
% 0.16/0.39  
% 0.16/0.39  % Status   : Theorem
% 0.16/0.39  % Rating   : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.16/0.39  % Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
% 0.16/0.39  %            Number of atoms       :    6 (   0 equ;   0 cnn)
% 0.16/0.39  %            Maximal formula atoms :    6 (   6 avg)
% 0.16/0.39  %            Number of connectives :   16 (   5   ~;   5   |;   0   &;   6   @)
% 0.16/0.39  %                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
% 0.16/0.39  %            Maximal formula depth :    9 (   9 avg)
% 0.16/0.39  %            Number of types       :    2 (   0 usr)
% 0.16/0.39  %            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
% 0.16/0.39  %            Number of symbols     :    3 (   3 usr;   0 con; 1-1 aty)
% 0.16/0.39  %            Number of variables   :    6 (   0   ^;   4   !;   2   ?;   6   :)
% 0.16/0.39  % SPC      : TH0_THM_NEQ_NAR
% 0.16/0.39  
% 0.16/0.39  % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39  %            project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39  %            Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39  %            license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39  %------------------------------------------------------------------------------
% 0.16/0.39  thf(cG,type,
% 0.16/0.39      cG: $i > $o ).
% 0.16/0.39  
% 0.16/0.39  thf(cN,type,
% 0.16/0.39      cN: $i > $o ).
% 0.16/0.39  
% 0.16/0.39  thf(cM,type,
% 0.16/0.39      cM: $i > $o ).
% 0.16/0.39  
% 0.16/0.39  thf(cTHM78,conjecture,
% 0.16/0.39      ( ! [R: $i] : ( cM @ R )
% 0.16/0.39      | ? [X: $i] :
% 0.16/0.39          ~ ( cG @ X )
% 0.16/0.39      | ~ ( ! [Y: $i] : ( cM @ Y )
% 0.16/0.39          | ? [S: $i] : ( cN @ S ) )
% 0.16/0.39      | ~ ( ! [Z: $i] :
% 0.16/0.39              ~ ( cN @ Z )
% 0.16/0.39          | ~ ! [T: $i] : ( cG @ T ) ) ) ).
% 0.16/0.39  
% 0.16/0.39  %------------------------------------------------------------------------------
% 0.16/0.39  ------------------------
% 1.52/1.32  ---- Embedded in THF ---
% 1.52/1.32  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.32  %%% Generated on Tue Feb 24 14:24:25 EST 2026
% 1.52/1.32  %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.32  %%% Logic specification used:
% 1.52/1.32  %%% thf(spec, logic, $$dhol).
% 1.52/1.32  
% 1.52/1.32  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.C7cGrxJIYO/DTF2DTF13856.p
% See solution above
% 1.52/1.32  ------------------------
% 1.52/1.33  ---- Cleaned THF ---
% 1.52/1.33  thf(cG,type,
% 1.52/1.33      cG: $i > $o ).
% 1.52/1.33  
% 1.52/1.33  thf(cN,type,
% 1.52/1.33      cN: $i > $o ).
% 1.52/1.33  
% 1.52/1.33  thf(cM,type,
% 1.52/1.33      cM: $i > $o ).
% 1.52/1.33  
% 1.52/1.33  thf(cTHM78,conjecture,
% 1.52/1.33      ( ! [R: $i] : ( cM @ R )
% 1.52/1.33      | ? [X: $i] :
% 1.52/1.33          ~ ( cG @ X )
% 1.52/1.33      | ~ ( ! [Y: $i] : ( cM @ Y )
% 1.52/1.33          | ? [S: $i] : ( cN @ S ) )
% 1.52/1.33      | ~ ( ! [Z: $i] :
% 1.52/1.33              ~ ( cN @ Z )
% 1.52/1.33          | ~ ! [T: $i] : ( cG @ T ) ) ) ).
% 1.52/1.33  ------------------------
% 1.52/1.35  % (13954)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_13856 for (3000ds/4Mi)
% 1.52/1.35  % (13953)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13856 for (3000ds/183Mi)
% 1.52/1.35  % (13955)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_13856 for (3000ds/27Mi)
% 1.52/1.35  % (13957)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_13856 for (3000ds/2Mi)
% 1.52/1.35  % (13958)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_13856 for (3000ds/275Mi)
% 1.52/1.35  % (13959)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13856 for (3000ds/18Mi)
% 1.52/1.35  % (13957)Instruction limit reached!
% 1.52/1.35  % (13957)------------------------------
% 1.52/1.35  % (13957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.35  % (13957)Termination reason: Unknown
% 1.52/1.35  % (13957)Termination phase: Saturation
% 1.52/1.35  
% 1.52/1.35  % (13957)Memory used [KB]: 5373
% 1.52/1.35  % (13957)Time elapsed: 0.003 s
% 1.52/1.35  % (13957)Instructions burned: 2 (million)
% 1.52/1.35  % (13957)------------------------------
% 1.52/1.35  % (13957)------------------------------
% 1.52/1.35  % (13953)First to succeed.
% 1.52/1.35  % (13956)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13856 for (3000ds/2Mi)
% 1.52/1.35  % (13955)Also succeeded, but the first one will report.
% 1.52/1.35  % (13958)Also succeeded, but the first one will report.
% 1.52/1.35  % (13956)Instruction limit reached!
% 1.52/1.35  % (13956)------------------------------
% 1.52/1.35  % (13956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.35  % (13953)Refutation found. Thanks to Tanya!
% 1.52/1.35  % SZS status Theorem for DTF2THF_13856
% 1.52/1.35  % SZS output start Proof for DTF2THF_13856
% 1.52/1.35  thf(func_def_0, type, cG: $i > $o).
% 1.52/1.35  thf(func_def_1, type, cN: $i > $o).
% 1.52/1.35  thf(func_def_2, type, cM: $i > $o).
% 1.52/1.35  thf(f20,plain,(
% 1.52/1.35    $false),
% 1.52/1.35    inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.52/1.35  thf(f19,plain,(
% 1.52/1.35    ($true != $true)),
% 1.52/1.35    inference(superposition,[status(thm)],[f15,f18])).
% 1.52/1.35  thf(f18,plain,(
% 1.52/1.35    ( ! [X5 : $i] : (($true = (cM @ X5))) )),
% 1.52/1.35    inference(subsumption_resolution,[status(thm)],[f13,f17])).
% 1.52/1.35  thf(f17,plain,(
% 1.52/1.35    ( ! [X2 : $i] : (($true != (cN @ X2))) )),
% 1.52/1.35    inference(subsumption_resolution,[status(thm)],[f14,f16])).
% 1.52/1.35  thf(f16,plain,(
% 1.52/1.35    ( ! [X0 : $i] : (($true = (cG @ X0))) )),
% 1.52/1.35    inference(cnf_transformation,[status(thm)],[f12])).
% 1.52/1.35  thf(f12,plain,(
% 1.52/1.35    ! [X0 : $i] : ($true = (cG @ X0)) & ($true != (cM @ sK0)) & (! [X2 : $i] : ($true != (cN @ X2)) | ($true != (cG @ sK1))) & (((cN @ sK2) = $true) | ! [X5 : $i] : ($true = (cM @ X5)))),
% 1.52/1.35    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.52/1.35  thf(f9,plain,(
% 1.52/1.35    ? [X1 : $i] : ($true != (cM @ X1)) => ($true != (cM @ sK0))),
% 1.52/1.35    introduced(definition,[],[choice_axiom])).
% 1.52/1.35  thf(f10,plain,(
% 1.52/1.35    ? [X3 : $i] : ($true != (cG @ X3)) => ($true != (cG @ sK1))),
% 1.52/1.35    introduced(definition,[],[choice_axiom])).
% 1.52/1.35  thf(f11,plain,(
% 1.52/1.35    ? [X4 : $i] : ((cN @ X4) = $true) => ((cN @ sK2) = $true)),
% 1.52/1.35    introduced(definition,[],[choice_axiom])).
% 1.52/1.35  thf(f8,plain,(
% 1.52/1.35    ! [X0 : $i] : ($true = (cG @ X0)) & ? [X1 : $i] : ($true != (cM @ X1)) & (! [X2 : $i] : ($true != (cN @ X2)) | ? [X3 : $i] : ($true != (cG @ X3))) & (? [X4 : $i] : ((cN @ X4) = $true) | ! [X5 : $i] : ($true = (cM @ X5)))),
% 1.52/1.35    inference(rectify,[status(thm)],[f7])).
% 1.52/1.35  thf(f7,plain,(
% 1.52/1.35    ! [X5 : $i] : ((cG @ X5) = $true) & ? [X4 : $i] : ((cM @ X4) != $true) & (! [X3 : $i] : ((cN @ X3) != $true) | ? [X2 : $i] : ((cG @ X2) != $true)) & (? [X0 : $i] : ($true = (cN @ X0)) | ! [X1 : $i] : ($true = (cM @ X1)))),
% 1.52/1.35    inference(ennf_transformation,[status(thm)],[f6])).
% 1.52/1.35  thf(f6,plain,(
% 1.52/1.35    ~(! [X4 : $i] : ((cM @ X4) = $true) | ? [X5 : $i] : ((cG @ X5) != $true) | ~(? [X0 : $i] : ($true = (cN @ X0)) | ! [X1 : $i] : ($true = (cM @ X1))) | ~(! [X3 : $i] : ((cN @ X3) != $true) | ~! [X2 : $i] : ((cG @ X2) = $true)))),
% 1.52/1.35    inference(flattening,[status(thm)],[f5])).
% 1.52/1.35  thf(f5,plain,(
% 1.52/1.35    ~(~(? [X0 : $i] : ($true = (cN @ X0)) | ! [X1 : $i] : ($true = (cM @ X1))) | ~(~! [X2 : $i] : ((cG @ X2) = $true) | ! [X3 : $i] : ~((cN @ X3) = $true)) | ! [X4 : $i] : ((cM @ X4) = $true) | ? [X5 : $i] : ~((cG @ X5) = $true))),
% 1.52/1.35    inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.35  thf(f4,plain,(
% 1.52/1.35    ~(~(? [X0 : $i] : (cN @ X0) | ! [X1 : $i] : (cM @ X1)) | ~(~! [X2 : $i] : (cG @ X2) | ! [X3 : $i] : ~(cN @ X3)) | ! [X4 : $i] : (cM @ X4) | ? [X5 : $i] : ~(cG @ X5))),
% 1.52/1.35    inference(rectify,[status(thm)],[f2])).
% 1.52/1.35  thf(f2,negated_conjecture,(
% 1.52/1.35    ~(~(? [X3 : $i] : (cN @ X3) | ! [X2 : $i] : (cM @ X2)) | ~(~! [X5 : $i] : (cG @ X5) | ! [X4 : $i] : ~(cN @ X4)) | ! [X0 : $i] : (cM @ X0) | ? [X1 : $i] : ~(cG @ X1))),
% 1.52/1.35    inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.35  thf(f1,conjecture,(
% 1.52/1.35    ~(? [X3 : $i] : (cN @ X3) | ! [X2 : $i] : (cM @ X2)) | ~(~! [X5 : $i] : (cG @ X5) | ! [X4 : $i] : ~(cN @ X4)) | ! [X0 : $i] : (cM @ X0) | ? [X1 : $i] : ~(cG @ X1)),
% 1.52/1.35    file('/export/starexec/sandbox/tmp/tmp.C7cGrxJIYO/DTF2THF_13856.p',cTHM78)).
% 1.52/1.35  thf(f14,plain,(
% 1.52/1.35    ( ! [X2 : $i] : (($true != (cN @ X2)) | ($true != (cG @ sK1))) )),
% 1.52/1.35    inference(cnf_transformation,[status(thm)],[f12])).
% 1.52/1.35  thf(f13,plain,(
% 1.52/1.35    ( ! [X5 : $i] : (((cN @ sK2) = $true) | ($true = (cM @ X5))) )),
% 1.52/1.35    inference(cnf_transformation,[status(thm)],[f12])).
% 1.52/1.35  thf(f15,plain,(
% 1.52/1.35    ($true != (cM @ sK0))),
% 1.52/1.35    inference(cnf_transformation,[status(thm)],[f12])).
% 1.52/1.35  % SZS output end Proof for DTF2THF_13856
% 1.52/1.35  % (13953)------------------------------
% 1.52/1.35  % (13953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.35  % (13953)Termination reason: Refutation
% 1.52/1.35  
% 1.52/1.35  % (13953)Memory used [KB]: 5500
% 1.52/1.35  % (13953)Time elapsed: 0.004 s
% 1.52/1.35  % (13953)Instructions burned: 1 (million)
% 1.52/1.35  % (13953)------------------------------
% 1.52/1.35  % (13953)------------------------------
% 1.52/1.35  % (13952)Success in time 0.018 s
%------------------------------------------------------------------------------