↑ Up

DT2H2X---1.9.5.THM-Ref.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : SEV392^5 : 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 : n010.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 09:41:09 AM UTC 2026

% Result   : Theorem 1.49s 1.40s
% Output   : Refutation 1.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   19 (   7 unt;   0 typ;   0 def)
%            Number of atoms       :  137 (  33 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :  126 (   9   ~;  16   |;  17   &;  73   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (  18   ^;  10   !;   2   ?;  30   :)

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

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

thf(func_def_11,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(f29,plain,
    $false,
    inference(subsumption_resolution,[status(thm)],[f28,f11]) ).

thf(f11,plain,
    ( $true
   != ( cS @ sK0 ) ),
    inference(cnf_transformation,[status(thm)],[f9]) ).

thf(f9,plain,
    ( ( ( ^ [Y0: $i] :
            ( ( cS @ Y0 )
            | ( cR @ Y0 ) ) )
      = ( ^ [Y0: $i] :
            ( ( cS @ Y0 )
            & ( cR @ Y0 ) ) ) )
    & ( $true
     != ( cS @ sK0 ) )
    & ( ( cR @ sK0 )
      = $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).

thf(f8,plain,
    ( ? [X0: $i] :
        ( ( ( cS @ X0 )
         != $true )
        & ( ( cR @ X0 )
          = $true ) )
   => ( ( $true
       != ( cS @ sK0 ) )
      & ( ( cR @ sK0 )
        = $true ) ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f7,plain,
    ( ( ( ^ [Y0: $i] :
            ( ( cS @ Y0 )
            | ( cR @ Y0 ) ) )
      = ( ^ [Y0: $i] :
            ( ( cS @ Y0 )
            & ( cR @ Y0 ) ) ) )
    & ? [X0: $i] :
        ( ( ( cS @ X0 )
         != $true )
        & ( ( cR @ X0 )
          = $true ) ) ),
    inference(ennf_transformation,[status(thm)],[f6]) ).

thf(f6,plain,
    ~ ( ( ( ^ [Y0: $i] :
              ( ( cS @ Y0 )
              | ( cR @ Y0 ) ) )
        = ( ^ [Y0: $i] :
              ( ( cS @ Y0 )
              & ( cR @ Y0 ) ) ) )
     => ! [X0: $i] :
          ( ( ( cR @ X0 )
            = $true )
         => ( ( cS @ X0 )
            = $true ) ) ),
    inference(rectify,[status(thm)],[f5]) ).

thf(f5,plain,
    ~ ( ( ( ^ [Y0: $i] :
              ( ( cS @ Y0 )
              | ( cR @ Y0 ) ) )
        = ( ^ [Y0: $i] :
              ( ( cS @ Y0 )
              & ( cR @ Y0 ) ) ) )
     => ! [X2: $i] :
          ( ( $true
            = ( cR @ X2 ) )
         => ( ( cS @ X2 )
            = $true ) ) ),
    inference(fool_elimination,[status(thm)],[f4]) ).

thf(f4,plain,
    ~ ( ( ( ^ [X0: $i] :
              ( ( cR @ X0 )
              & ( cS @ X0 ) ) )
        = ( ^ [X1: $i] :
              ( ( cR @ X1 )
              | ( cS @ X1 ) ) ) )
     => ! [X2: $i] :
          ( ( cR @ X2 )
         => ( cS @ X2 ) ) ),
    inference(rectify,[status(thm)],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ( ^ [X0: $i] :
              ( ( cR @ X0 )
              & ( cS @ X0 ) ) )
        = ( ^ [X1: $i] :
              ( ( cR @ X1 )
              | ( cS @ X1 ) ) ) )
     => ! [X0: $i] :
          ( ( cR @ X0 )
         => ( cS @ X0 ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

thf(f1,conjecture,
    ( ( ( ^ [X0: $i] :
            ( ( cR @ X0 )
            & ( cS @ X0 ) ) )
      = ( ^ [X1: $i] :
            ( ( cR @ X1 )
            | ( cS @ X1 ) ) ) )
   => ! [X0: $i] :
        ( ( cR @ X0 )
       => ( cS @ X0 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SfJ8pWAfEU/DTF2THF_28933.p',cTHM38_pme) ).

thf(f28,plain,
    ( $true
    = ( cS @ sK0 ) ),
    inference(trivial_inequality_removal,[status(thm)],[f26]) ).

thf(f26,plain,
    ( ( $true = $false )
    | ( $true
      = ( cS @ sK0 ) ) ),
    inference(superposition,[status(thm)],[f10,f21]) ).

thf(f21,plain,
    ! [X1: $i] :
      ( ( ( cR @ X1 )
        = $false )
      | ( ( cS @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f20]) ).

thf(f20,plain,
    ! [X1: $i] :
      ( ( ( cS @ X1 )
        = $true )
      | ( $false
        = ( ( cS @ X1 )
          | ( cR @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f15]) ).

thf(f15,plain,
    ! [X1: $i] :
      ( ( $true
        = ( ( cS @ X1 )
          & ( cR @ X1 ) ) )
      | ( $false
        = ( ( cS @ X1 )
          | ( cR @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f14]) ).

thf(f14,plain,
    ! [X1: $i] :
      ( ( ( cS @ X1 )
        & ( cR @ X1 ) )
      = ( ( cS @ X1 )
        | ( cR @ X1 ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f13]) ).

thf(f13,plain,
    ! [X1: $i] :
      ( ( ^ [Y0: $i] :
            ( ( cS @ Y0 )
            & ( cR @ Y0 ) )
        @ X1 )
      = ( ^ [Y0: $i] :
            ( ( cS @ Y0 )
            | ( cR @ Y0 ) )
        @ X1 ) ),
    inference(argument_congruence,[status(thm)],[f12]) ).

thf(f12,plain,
    ( ( ^ [Y0: $i] :
          ( ( cS @ Y0 )
          | ( cR @ Y0 ) ) )
    = ( ^ [Y0: $i] :
          ( ( cS @ Y0 )
          & ( cR @ Y0 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f9]) ).

thf(f10,plain,
    ( ( cR @ sK0 )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV392^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34  % Computer : n010.cluster.edu
% 0.18/0.34  % Model    : x86_64 x86_64
% 0.18/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34  % Memory   : 8042.1875MB
% 0.18/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34  % CPULimit : 300
% 0.18/0.34  % WCLimit  : 300
% 0.18/0.34  % DateTime : Tue Feb 24 12:45:48 EST 2026
% 0.18/0.34  % CPUTime  : 
% 0.18/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.44  ---- Original DTF file ---
% 0.20/0.45  thf(spec,logic,$$dhol).
% 0.20/0.45  %------------------------------------------------------------------------------
% 0.20/0.45  % File     : SEV392^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.45  % Domain   : Set Theory
% 0.20/0.45  % Problem  : TPS problem THM38
% 0.20/0.45  % Version  : Especial.
% 0.20/0.45  % English  :
% 0.20/0.45  
% 0.20/0.45  % Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.45  % Source   : [Bro09]
% 0.20/0.45  % Names    : tps_0284 [Bro09]
% 0.20/0.45  %          : THM38 [TPS]
% 0.20/0.45  
% 0.20/0.45  % Status   : Theorem
% 0.20/0.45  % Rating   : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.20/0.45  % Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
% 0.20/0.45  %            Number of atoms       :    7 (   1 equ;   0 cnn)
% 0.20/0.45  %            Maximal formula atoms :    3 (   7 avg)
% 0.20/0.45  %            Number of connectives :   10 (   0   ~;   1   |;   1   &;   6   @)
% 0.20/0.45  %                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
% 0.20/0.45  %            Maximal formula depth :    5 (   5 avg)
% 0.20/0.45  %            Number of types       :    2 (   0 usr)
% 0.20/0.45  %            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
% 0.20/0.45  %            Number of symbols     :    3 (   2 usr;   0 con; 1-2 aty)
% 0.20/0.45  %            Number of variables   :    3 (   2   ^;   1   !;   0   ?;   3   :)
% 0.20/0.45  % SPC      : TH0_THM_EQU_NAR
% 0.20/0.45  
% 0.20/0.45  % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.45  %            project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.45  %            Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.45  %            license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.45  %          : Polymorphic definitions expanded.
% 0.20/0.45  %------------------------------------------------------------------------------
% 0.20/0.45  thf(cS,type,
% 0.20/0.45      cS: $i > $o ).
% 0.20/0.45  
% 0.20/0.45  thf(cR,type,
% 0.20/0.45      cR: $i > $o ).
% 0.20/0.45  
% 0.20/0.45  thf(cTHM38_pme,conjecture,
% 0.20/0.45      ( ( ( ^ [Xx: $i] :
% 0.20/0.45              ( ( cR @ Xx )
% 0.20/0.45              & ( cS @ Xx ) ) )
% 0.20/0.45        = ( ^ [Xz: $i] :
% 0.20/0.45              ( ( cR @ Xz )
% 0.20/0.45              | ( cS @ Xz ) ) ) )
% 0.20/0.45     => ! [Xx: $i] :
% 0.20/0.45          ( ( cR @ Xx )
% 0.20/0.45         => ( cS @ Xx ) ) ) ).
% 0.20/0.45  
% 0.20/0.45  %------------------------------------------------------------------------------
% 0.20/0.45  ------------------------
% 1.49/1.36  ---- Embedded in THF ---
% 1.49/1.36  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.36  %%% Generated on Tue Feb 24 12:45:49 EST 2026
% 1.49/1.36  %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.36  %%% Logic specification used:
% 1.49/1.36  %%% thf(spec, logic, $$dhol).
% 1.49/1.36  
% 1.49/1.36  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SfJ8pWAfEU/DTF2DTF28933.p
% See solution above
% 1.49/1.36  ------------------------
% 1.49/1.37  ---- Cleaned THF ---
% 1.49/1.37  thf(cS,type,
% 1.49/1.37      cS: $i > $o ).
% 1.49/1.37  
% 1.49/1.37  thf(cR,type,
% 1.49/1.37      cR: $i > $o ).
% 1.49/1.37  
% 1.49/1.37  thf(cTHM38_pme,conjecture,
% 1.49/1.37      ( ( ( ^ [Xx: $i] :
% 1.49/1.37              ( ( cR @ Xx )
% 1.49/1.37              & ( cS @ Xx ) ) )
% 1.49/1.37        = ( ^ [Xz: $i] :
% 1.49/1.37              ( ( cR @ Xz )
% 1.49/1.37              | ( cS @ Xz ) ) ) )
% 1.49/1.37     => ! [Xx: $i] :
% 1.49/1.37          ( ( cR @ Xx )
% 1.49/1.37         => ( cS @ Xx ) ) ) ).
% 1.49/1.37  ------------------------
% 1.49/1.39  % (29031)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28933 for (3000ds/183Mi)
% 1.49/1.39  % (29035)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_28933 for (3000ds/2Mi)
% 1.49/1.39  % (29036)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_28933 for (3000ds/275Mi)
% 1.49/1.39  % (29034)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28933 for (3000ds/2Mi)
% 1.49/1.39  % (29032)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_28933 for (3000ds/4Mi)
% 1.49/1.39  % (29033)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_28933 for (3000ds/27Mi)
% 1.49/1.39  % (29037)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28933 for (3000ds/18Mi)
% 1.49/1.39  % (29034)Instruction limit reached!
% 1.49/1.39  % (29034)------------------------------
% 1.49/1.39  % (29034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.39  % (29034)Termination reason: Unknown
% 1.49/1.39  % (29035)Instruction limit reached!
% 1.49/1.39  % (29035)------------------------------
% 1.49/1.39  % (29035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.39  % (29034)Termination phase: Saturation
% 1.49/1.39  
% 1.49/1.39  % (29034)Memory used [KB]: 5500
% 1.49/1.39  % (29034)Time elapsed: 0.003 s
% 1.49/1.39  % (29034)Instructions burned: 2 (million)
% 1.49/1.39  % (29034)------------------------------
% 1.49/1.39  % (29034)------------------------------
% 1.49/1.39  % (29035)Termination reason: Unknown
% 1.49/1.39  % (29035)Termination phase: Saturation
% 1.49/1.39  
% 1.49/1.39  % (29035)Memory used [KB]: 5500
% 1.49/1.39  % (29035)Time elapsed: 0.003 s
% 1.49/1.39  % (29035)Instructions burned: 2 (million)
% 1.49/1.39  % (29035)------------------------------
% 1.49/1.39  % (29035)------------------------------
% 1.49/1.39  % (29037)First to succeed.
% 1.49/1.40  % (29031)Also succeeded, but the first one will report.
% 1.49/1.40  % (29032)Instruction limit reached!
% 1.49/1.40  % (29032)------------------------------
% 1.49/1.40  % (29032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.40  % (29032)Termination reason: Unknown
% 1.49/1.40  % (29032)Termination phase: Saturation
% 1.49/1.40  
% 1.49/1.40  % (29032)Memory used [KB]: 5500
% 1.49/1.40  % (29032)Time elapsed: 0.005 s
% 1.49/1.40  % (29032)Instructions burned: 5 (million)
% 1.49/1.40  % (29032)------------------------------
% 1.49/1.40  % (29032)------------------------------
% 1.49/1.40  % (29037)Refutation found. Thanks to Tanya!
% 1.49/1.40  % SZS status Theorem for DTF2THF_28933
% 1.49/1.40  % SZS output start Proof for DTF2THF_28933
% 1.49/1.40  thf(func_def_0, type, cS: $i > $o).
% 1.49/1.40  thf(func_def_1, type, cR: $i > $o).
% 1.49/1.40  thf(func_def_11, type, ph2: !>[X0: $tType]:(X0)).
% 1.49/1.40  thf(f29,plain,(
% 1.49/1.40    $false),
% 1.49/1.40    inference(subsumption_resolution,[status(thm)],[f28,f11])).
% 1.49/1.40  thf(f11,plain,(
% 1.49/1.40    ($true != (cS @ sK0))),
% 1.49/1.40    inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.40  thf(f9,plain,(
% 1.49/1.40    ((^[Y0 : $i]: ((cS @ Y0) | (cR @ Y0))) = (^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0)))) & (($true != (cS @ sK0)) & ((cR @ sK0) = $true))),
% 1.49/1.40    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.49/1.40  thf(f8,plain,(
% 1.49/1.40    ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true)) => (($true != (cS @ sK0)) & ((cR @ sK0) = $true))),
% 1.49/1.40    introduced(definition,[],[choice_axiom])).
% 1.49/1.40  thf(f7,plain,(
% 1.49/1.40    ((^[Y0 : $i]: ((cS @ Y0) | (cR @ Y0))) = (^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0)))) & ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true))),
% 1.49/1.40    inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.40  thf(f6,plain,(
% 1.49/1.40    ~(((^[Y0 : $i]: ((cS @ Y0) | (cR @ Y0))) = (^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0)))) => ! [X0 : $i] : (((cR @ X0) = $true) => ((cS @ X0) = $true)))),
% 1.49/1.40    inference(rectify,[status(thm)],[f5])).
% 1.49/1.40  thf(f5,plain,(
% 1.49/1.40    ~(((^[Y0 : $i]: ((cS @ Y0) | (cR @ Y0))) = (^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0)))) => ! [X2 : $i] : (($true = (cR @ X2)) => ((cS @ X2) = $true)))),
% 1.49/1.40    inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.40  thf(f4,plain,(
% 1.49/1.40    ~(((^[X0 : $i] : ((cR @ X0) & (cS @ X0))) = (^[X1 : $i] : ((cR @ X1) | (cS @ X1)))) => ! [X2 : $i] : ((cR @ X2) => (cS @ X2)))),
% 1.49/1.40    inference(rectify,[status(thm)],[f2])).
% 1.49/1.40  thf(f2,negated_conjecture,(
% 1.49/1.40    ~(((^[X0 : $i] : ((cR @ X0) & (cS @ X0))) = (^[X1 : $i] : ((cR @ X1) | (cS @ X1)))) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0)))),
% 1.49/1.40    inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.40  thf(f1,conjecture,(
% 1.49/1.40    ((^[X0 : $i] : ((cR @ X0) & (cS @ X0))) = (^[X1 : $i] : ((cR @ X1) | (cS @ X1)))) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0))),
% 1.49/1.40    file('/export/starexec/sandbox/tmp/tmp.SfJ8pWAfEU/DTF2THF_28933.p',cTHM38_pme)).
% 1.49/1.40  thf(f28,plain,(
% 1.49/1.40    ($true = (cS @ sK0))),
% 1.49/1.40    inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.49/1.40  thf(f26,plain,(
% 1.49/1.40    ($true = $false) | ($true = (cS @ sK0))),
% 1.49/1.40    inference(superposition,[status(thm)],[f10,f21])).
% 1.49/1.40  thf(f21,plain,(
% 1.49/1.40    ( ! [X1 : $i] : (((cR @ X1) = $false) | ((cS @ X1) = $true)) )),
% 1.49/1.40    inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.49/1.40  thf(f20,plain,(
% 1.49/1.40    ( ! [X1 : $i] : (((cS @ X1) = $true) | ($false = ((cS @ X1) | (cR @ X1)))) )),
% 1.49/1.40    inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.49/1.40  thf(f15,plain,(
% 1.49/1.40    ( ! [X1 : $i] : (($true = ((cS @ X1) & (cR @ X1))) | ($false = ((cS @ X1) | (cR @ X1)))) )),
% 1.49/1.40    inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.49/1.40  thf(f14,plain,(
% 1.49/1.40    ( ! [X1 : $i] : ((((cS @ X1) & (cR @ X1)) = ((cS @ X1) | (cR @ X1)))) )),
% 1.49/1.40    inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.49/1.40  thf(f13,plain,(
% 1.49/1.40    ( ! [X1 : $i] : ((((^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))) @ X1) = ((^[Y0 : $i]: ((cS @ Y0) | (cR @ Y0))) @ X1))) )),
% 1.49/1.40    inference(argument_congruence,[status(thm)],[f12])).
% 1.49/1.40  thf(f12,plain,(
% 1.49/1.40    ((^[Y0 : $i]: ((cS @ Y0) | (cR @ Y0))) = (^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))))),
% 1.49/1.40    inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.40  thf(f10,plain,(
% 1.49/1.40    ((cR @ sK0) = $true)),
% 1.49/1.40    inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.40  % SZS output end Proof for DTF2THF_28933
% 1.49/1.40  % (29037)------------------------------
% 1.49/1.40  % (29037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.40  % (29037)Termination reason: Refutation
% 1.49/1.40  
% 1.49/1.40  % (29037)Memory used [KB]: 5500
% 1.49/1.40  % (29037)Time elapsed: 0.004 s
% 1.49/1.40  % (29037)Instructions burned: 2 (million)
% 1.49/1.40  % (29037)------------------------------
% 1.49/1.40  % (29037)------------------------------
% 1.49/1.40  % (29030)Success in time 0.018 s
%------------------------------------------------------------------------------