TSTP Solution File: SEU957^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU957^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 04:07:06 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   59 (  11 unt;  17 typ;   0 def)
%            Number of atoms       :  242 (  70 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  105 (  39   ~;  25   |;  14   &;   0   @)
%                                         (   7 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   77 (  76   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;   9 con; 0-6 aty)
%            Number of variables   :  103 (   0   ^  55   !;  42   ?; 103   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    a: $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_7,type,
    b: $tType ).

thf(func_def_0,type,
    a: $tType ).

thf(func_def_1,type,
    b: $tType ).

thf(func_def_5,type,
    sK0: ( b > a ) > b ).

thf(func_def_6,type,
    sK1: ( b > a ) > b ).

thf(func_def_7,type,
    sK2: a > b ).

thf(func_def_8,type,
    sK3: b > a ).

thf(func_def_9,type,
    sK4: ( a > $o ) > a ).

thf(func_def_11,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_12,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_13,type,
    vAND: $o > $o > $o ).

thf(func_def_14,type,
    vOR: $o > $o > $o ).

thf(func_def_15,type,
    vIMP: $o > $o > $o ).

thf(func_def_16,type,
    vNOT: $o > $o ).

thf(func_def_17,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f90,plain,
    $false,
    inference(avatar_sat_refutation,[],[f22,f27,f31,f35,f45,f51,f86,f89]) ).

thf(f89,plain,
    ( ~ spl5_3
    | ~ spl5_7 ),
    inference(avatar_contradiction_clause,[],[f88]) ).

thf(f88,plain,
    ( $false
    | ~ spl5_3
    | ~ spl5_7 ),
    inference(trivial_inequality_removal,[],[f87]) ).

thf(f87,plain,
    ( ( vAPP(sTfun(b,a),b,sK0,sK3) != vAPP(sTfun(b,a),b,sK0,sK3) )
    | ~ spl5_3
    | ~ spl5_7 ),
    inference(superposition,[],[f30,f85]) ).

thf(f85,plain,
    ( ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(sTfun(b,a),b,sK0,sK3) )
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f83]) ).

thf(f83,plain,
    ( spl5_7
  <=> ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(sTfun(b,a),b,sK0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

thf(f30,plain,
    ( ! [X0: b > a] : ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) )
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f29]) ).

thf(f29,plain,
    ( spl5_3
  <=> ! [X0: b > a] : ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

thf(f86,plain,
    ( spl5_7
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(avatar_split_clause,[],[f47,f43,f20,f83]) ).

thf(f20,plain,
    ( spl5_1
  <=> ! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

thf(f43,plain,
    ( spl5_5
  <=> ! [X0: b > a] : ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

thf(f47,plain,
    ( ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(sTfun(b,a),b,sK0,sK3) )
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(forward_demodulation,[],[f46,f21]) ).

thf(f21,plain,
    ( ! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f20]) ).

thf(f46,plain,
    ( ( vAPP(sTfun(b,a),b,sK1,sK3) = vAPP(a,b,sK2,vAPP(b,a,sK3,vAPP(sTfun(b,a),b,sK0,sK3))) )
    | ~ spl5_1
    | ~ spl5_5 ),
    inference(superposition,[],[f21,f44]) ).

thf(f44,plain,
    ( ! [X0: b > a] : ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) )
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f43]) ).

thf(f51,plain,
    spl5_6,
    inference(avatar_split_clause,[],[f4,f49]) ).

thf(f49,plain,
    ( spl5_6
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

thf(f4,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f45,plain,
    spl5_5,
    inference(avatar_split_clause,[],[f17,f43]) ).

thf(f17,plain,
    ! [X0: b > a] : ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ! [X0: b > a] :
        ( ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) )
        & ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ) )
    & ! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 )
    & ! [X7: a > $o] :
        ( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
        | ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10]) ).

thf(f10,plain,
    ! [X0: b > a] :
      ( ? [X1: b,X2: b] :
          ( ( X1 != X2 )
          & ( vAPP(b,a,X0,X1) = vAPP(b,a,X0,X2) ) )
     => ( ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) )
        & ( vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK0,X0)) = vAPP(b,a,X0,vAPP(sTfun(b,a),b,sK1,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X3: a > b] :
      ! [X4: b] :
      ? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
   => ! [X4: b] :
      ? [X5: a] : ( vAPP(a,b,sK2,X5) = X4 ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X4: b] :
      ( ? [X5: a] : ( vAPP(a,b,sK2,X5) = X4 )
     => ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ( ? [X6: ( a > $o ) > a] :
      ! [X7: a > $o] :
        ( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,X6,X7)) )
        | ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) )
   => ! [X7: a > $o] :
        ( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
        | ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ( ! [X0: b > a] :
      ? [X1: b,X2: b] :
        ( ( X1 != X2 )
        & ( vAPP(b,a,X0,X1) = vAPP(b,a,X0,X2) ) )
    & ? [X3: a > b] :
      ! [X4: b] :
      ? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
    & ? [X6: ( a > $o ) > a] :
      ! [X7: a > $o] :
        ( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,X6,X7)) )
        | ! [X8: a] : ( $true != vAPP(a,$o,X7,X8) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,plain,
    ( ! [X6: b > a] :
      ? [X7: b,X8: b] :
        ( ( X7 != X8 )
        & ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) ) )
    & ? [X3: a > b] :
      ! [X4: b] :
      ? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
    & ? [X0: ( a > $o ) > a] :
      ! [X1: a > $o] :
        ( ( vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) = $true )
        | ! [X2: a] : ( vAPP(a,$o,X1,X2) != $true ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ( ! [X6: b > a] :
      ? [X7: b,X8: b] :
        ( ( X7 != X8 )
        & ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) ) )
    & ? [X3: a > b] :
      ! [X4: b] :
      ? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
    & ? [X0: ( a > $o ) > a] :
      ! [X1: a > $o] :
        ( ( vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) = $true )
        | ! [X2: a] : ( vAPP(a,$o,X1,X2) != $true ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ( ? [X0: ( a > $o ) > a] :
        ! [X1: a > $o] :
          ( ? [X2: a] : ( vAPP(a,$o,X1,X2) = $true )
         => ( vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) = $true ) )
     => ( ? [X3: a > b] :
          ! [X4: b] :
          ? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
       => ? [X6: b > a] :
          ! [X7: b,X8: b] :
            ( ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) )
           => ( X7 = X8 ) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ( ? [X0: ( a > $o ) > a] :
        ! [X1: a > $o] :
          ( ? [X2: a] : vAPP(a,$o,X1,X2)
         => vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) )
     => ( ? [X3: a > b] :
          ! [X4: b] :
          ? [X5: a] : ( vAPP(a,b,X3,X5) = X4 )
       => ? [X6: b > a] :
          ! [X7: b,X8: b] :
            ( ( vAPP(b,a,X6,X7) = vAPP(b,a,X6,X8) )
           => ( X7 = X8 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ? [X0: ( a > $o ) > a] :
        ! [X1: a > $o] :
          ( ? [X2: a] : vAPP(a,$o,X1,X2)
         => vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) )
     => ( ? [X3: a > b] :
          ! [X4: b] :
          ? [X1: a] : ( vAPP(a,b,X3,X1) = X4 )
       => ? [X5: b > a] :
          ! [X6: b,X7: b] :
            ( ( vAPP(b,a,X5,X6) = vAPP(b,a,X5,X7) )
           => ( X6 = X7 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ? [X0: ( a > $o ) > a] :
      ! [X1: a > $o] :
        ( ? [X2: a] : vAPP(a,$o,X1,X2)
       => vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,X0,X1)) )
   => ( ? [X3: a > b] :
        ! [X4: b] :
        ? [X1: a] : ( vAPP(a,b,X3,X1) = X4 )
     => ? [X5: b > a] :
        ! [X6: b,X7: b] :
          ( ( vAPP(b,a,X5,X6) = vAPP(b,a,X5,X7) )
         => ( X6 = X7 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM607_pme) ).

thf(f35,plain,
    spl5_4,
    inference(avatar_split_clause,[],[f15,f33]) ).

thf(f33,plain,
    ( spl5_4
  <=> ! [X7: a > $o,X8: a] :
        ( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
        | ( $true != vAPP(a,$o,X7,X8) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

thf(f15,plain,
    ! [X8: a,X7: a > $o] :
      ( ( $true = vAPP(a,$o,X7,vAPP(sTfun(a,$o),a,sK4,X7)) )
      | ( $true != vAPP(a,$o,X7,X8) ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f31,plain,
    spl5_3,
    inference(avatar_split_clause,[],[f18,f29]) ).

thf(f18,plain,
    ! [X0: b > a] : ( vAPP(sTfun(b,a),b,sK0,X0) != vAPP(sTfun(b,a),b,sK1,X0) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f27,plain,
    ~ spl5_2,
    inference(avatar_split_clause,[],[f3,f24]) ).

thf(f24,plain,
    ( spl5_2
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

thf(f3,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

thf(f22,plain,
    spl5_1,
    inference(avatar_split_clause,[],[f16,f20]) ).

thf(f16,plain,
    ! [X4: b] : ( vAPP(a,b,sK2,vAPP(b,a,sK3,X4)) = X4 ),
    inference(cnf_transformation,[],[f14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem    : SEU957^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n005.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sun May 19 18:14:53 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (27278)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (27281)WARNING: value z3 for option sas not known
% 0.15/0.39  % (27279)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (27280)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (27282)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (27281)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39  % (27283)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39  % (27284)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39  % (27285)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39  % Exception at run slice level% Exception at run slice level
% 0.15/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39  
% 0.15/0.39  % Exception at run slice levelUser error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39  
% 0.15/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39  % (27285)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39  % (27284)Also succeeded, but the first one will report.
% 0.15/0.39  % (27283)First to succeed.
% 0.15/0.39  % (27285)Also succeeded, but the first one will report.
% 0.15/0.39  % (27281)Also succeeded, but the first one will report.
% 0.15/0.39  % (27283)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27278"
% 0.15/0.39  % (27283)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (27283)------------------------------
% 0.15/0.39  % (27283)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (27283)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (27283)Memory used [KB]: 790
% 0.15/0.39  % (27283)Time elapsed: 0.006 s
% 0.15/0.39  % (27283)Instructions burned: 7 (million)
% 0.15/0.39  % (27278)Success in time 0.007 s
%------------------------------------------------------------------------------