TSTP Solution File: SEV043^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEV043^5 : 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 : n012.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 04:14:19 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   38 (   7 unt;  13 typ;   0 def)
%            Number of atoms       :  377 (  77 equ;   0 cnn)
%            Maximal formula atoms :   14 (  15 avg)
%            Number of connectives :  113 (  39   ~;  28   |;  28   &;   0   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   36 (  35   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   4 con; 0-6 aty)
%            Number of variables   :   92 (   0   ^  70   !;  16   ?;  92   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

thf(func_def_4,type,
    sK0: a > a > $o ).

thf(func_def_5,type,
    sK1: a ).

thf(func_def_6,type,
    sK2: a ).

thf(func_def_8,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_9,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_10,type,
    vAND: $o > $o > $o ).

thf(func_def_11,type,
    vOR: $o > $o > $o ).

thf(func_def_12,type,
    vIMP: $o > $o > $o ).

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

thf(func_def_14,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f98,plain,
    $false,
    inference(trivial_inequality_removal,[],[f97]) ).

thf(f97,plain,
    $true = $false,
    inference(forward_demodulation,[],[f96,f46]) ).

thf(f46,plain,
    $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK1),
    inference(trivial_inequality_removal,[],[f45]) ).

thf(f45,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK1) ) ),
    inference(superposition,[],[f16,f4]) ).

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

thf(f16,plain,
    $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK1),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK1) )
    & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK2) )
    & ! [X3: a,X4: a,X5: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X3),X5) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X4),X5) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X3),X4) ) )
    & ! [X6: a,X7: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X7),X6) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X6),X7) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10]) ).

thf(f10,plain,
    ( ? [X0: a > a > $o] :
        ( ? [X1: a,X2: a] :
            ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) != $true )
            & ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) = $true ) )
        & ! [X3: a,X4: a,X5: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X3),X5) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X4),X5) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X3),X4) ) )
        & ! [X6: a,X7: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X7),X6) )
            | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X6),X7) ) ) )
   => ( ? [X2: a,X1: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X1),X1) )
          & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X1),X2) ) )
      & ! [X5: a,X4: a,X3: a] :
          ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X3),X5) )
          | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X4),X5) )
          | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X3),X4) ) )
      & ! [X7: a,X6: a] :
          ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X7),X6) )
          | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X6),X7) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X2: a,X1: a] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X1),X1) )
        & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X1),X2) ) )
   => ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK1) )
      & ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK2) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

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

thf(f2,negated_conjecture,
    ~ ! [X0: a > a > $o] :
        ( ( ! [X1: a,X2: a,X3: a] :
              ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X3)
                & vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) )
             => vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) )
          & ! [X1: a,X2: a] :
              ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2)
             => vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X1) ) )
       => ! [X1: a,X2: a] :
            ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2)
           => vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > a > $o] :
      ( ( ! [X1: a,X2: a,X3: a] :
            ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X3)
              & vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) )
           => vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) )
        & ! [X1: a,X2: a] :
            ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2)
           => vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X1) ) )
     => ! [X1: a,X2: a] :
          ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2)
         => vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM510_pme) ).

thf(f96,plain,
    $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK1),
    inference(trivial_inequality_removal,[],[f90]) ).

thf(f90,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK1) ) ),
    inference(superposition,[],[f63,f54]) ).

thf(f54,plain,
    $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK2),sK1),
    inference(trivial_inequality_removal,[],[f50]) ).

thf(f50,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK2),sK1) ) ),
    inference(superposition,[],[f13,f15]) ).

thf(f15,plain,
    $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),sK2),
    inference(cnf_transformation,[],[f12]) ).

thf(f13,plain,
    ! [X6: a,X7: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X6),X7) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X7),X6) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f63,plain,
    ! [X0: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK2),X0) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),X0) ) ),
    inference(trivial_inequality_removal,[],[f57]) ).

thf(f57,plain,
    ! [X0: a] :
      ( ( $true != $true )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK2),X0) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,sK1),X0) ) ),
    inference(superposition,[],[f14,f15]) ).

thf(f14,plain,
    ! [X3: a,X4: a,X5: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X3),X4) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X4),X5) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X3),X5) ) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEV043^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 19:18:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (20875)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (20876)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  % (20879)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.37  % (20880)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37  % (20878)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.37  % (20881)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37  % (20882)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  % (20877)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (20878)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37  % (20879)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  % Exception at run slice levelUser error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % (20878)Also succeeded, but the first one will report.
% 0.13/0.37  % (20880)Also succeeded, but the first one will report.
% 0.13/0.37  % (20881)First to succeed.
% 0.13/0.37  % (20881)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20875"
% 0.13/0.37  % (20881)Refutation found. Thanks to Tanya!
% 0.13/0.37  % SZS status Theorem for theBenchmark
% 0.13/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37  % (20881)------------------------------
% 0.13/0.37  % (20881)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (20881)Termination reason: Refutation
% 0.13/0.37  
% 0.13/0.37  % (20881)Memory used [KB]: 771
% 0.13/0.37  % (20881)Time elapsed: 0.006 s
% 0.13/0.37  % (20881)Instructions burned: 8 (million)
% 0.13/0.37  % (20875)Success in time 0.008 s
%------------------------------------------------------------------------------