TSTP Solution File: SEV060^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEV060^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n024.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 : Sun May  5 09:43:48 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   52 (  12 unt;  18 typ;   0 def)
%            Number of atoms       :  368 ( 103 equ;   0 cnn)
%            Maximal formula atoms :   14 (  10 avg)
%            Number of connectives :  122 (  37   ~;  32   |;  36   &;   0   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   58 (  57   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   6 con; 0-6 aty)
%            Number of variables   :   91 (   0   ^  57   !;  28   ?;  91   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_6,type,
    a: $tType ).

thf(type_def_7,type,
    sTfun: ( $tType * $tType ) > $tType ).

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

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

thf(func_def_5,type,
    sK0: b ).

thf(func_def_6,type,
    sK1: a ).

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

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

thf(func_def_9,type,
    sK4: b ).

thf(func_def_10,type,
    sK5: 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(f77,plain,
    $false,
    inference(trivial_inequality_removal,[],[f76]) ).

thf(f76,plain,
    $true = $false,
    inference(forward_demodulation,[],[f74,f48]) ).

thf(f48,plain,
    $false = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK0),sK1),
    inference(trivial_inequality_removal,[],[f47]) ).

thf(f47,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK0),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(b,sTfun(a,$o),sK3,sK0),sK1),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK4),sK5) )
    & ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK4),sK5) )
    & ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK0),sK1) )
    & ! [X6: b,X7: a] :
        ( ( ( sK1 = X7 )
          & ( sK0 = X6 ) )
        | ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,X6),X7) )
        | ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,X6),X7) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f10,f12,f11]) ).

thf(f11,plain,
    ( ? [X0: b,X1: a,X2: b > a > $o,X3: b > a > $o] :
        ( ? [X4: b,X5: a] :
            ( ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X2,X4),X5) != $true )
            & ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X4),X5) = $true ) )
        & ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X0),X1) != $true )
        & ! [X6: b,X7: a] :
            ( ( ( X1 = X7 )
              & ( X0 = X6 ) )
            | ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X2,X6),X7) = $true )
            | ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X6),X7) != $true ) ) )
   => ( ? [X5: a,X4: b] :
          ( ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,X4),X5) )
          & ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,X4),X5) ) )
      & ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK0),sK1) )
      & ! [X7: a,X6: b] :
          ( ( ( sK1 = X7 )
            & ( sK0 = X6 ) )
          | ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,X6),X7) )
          | ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,X6),X7) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X5: a,X4: b] :
        ( ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,X4),X5) )
        & ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,X4),X5) ) )
   => ( ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK4),sK5) )
      & ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK4),sK5) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ? [X0: b,X1: a,X2: b > a > $o,X3: b > a > $o] :
      ( ? [X4: b,X5: a] :
          ( ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X2,X4),X5) != $true )
          & ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X4),X5) = $true ) )
      & ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X0),X1) != $true )
      & ! [X6: b,X7: a] :
          ( ( ( X1 = X7 )
            & ( X0 = X6 ) )
          | ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X2,X6),X7) = $true )
          | ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X6),X7) != $true ) ) ),
    inference(rectify,[],[f9]) ).

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

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

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

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

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

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

thf(f1,conjecture,
    ! [X0: b,X1: a,X2: b > a > $o,X3: b > a > $o] :
      ( ( ~ vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X0),X1)
        & ! [X4: b,X5: a] :
            ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X4),X5)
           => ( ( ( X1 = X5 )
                & ( X0 = X4 ) )
              | vAPP(a,$o,vAPP(b,sTfun(a,$o),X2,X4),X5) ) ) )
     => ! [X6: b,X7: a] :
          ( vAPP(a,$o,vAPP(b,sTfun(a,$o),X3,X6),X7)
         => vAPP(a,$o,vAPP(b,sTfun(a,$o),X2,X6),X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM173_pme) ).

thf(f74,plain,
    $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK0),sK1),
    inference(backward_demodulation,[],[f65,f73]) ).

thf(f73,plain,
    sK1 = sK5,
    inference(trivial_inequality_removal,[],[f72]) ).

thf(f72,plain,
    ( ( $true = $false )
    | ( sK1 = sK5 ) ),
    inference(forward_demodulation,[],[f71,f64]) ).

thf(f64,plain,
    $false = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK0),sK5),
    inference(backward_demodulation,[],[f51,f63]) ).

thf(f63,plain,
    sK0 = sK4,
    inference(trivial_inequality_removal,[],[f62]) ).

thf(f62,plain,
    ( ( $true = $false )
    | ( sK0 = sK4 ) ),
    inference(forward_demodulation,[],[f61,f51]) ).

thf(f61,plain,
    ( ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK4),sK5) )
    | ( sK0 = sK4 ) ),
    inference(trivial_inequality_removal,[],[f57]) ).

thf(f57,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK4),sK5) )
    | ( sK0 = sK4 ) ),
    inference(superposition,[],[f14,f17]) ).

thf(f17,plain,
    $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK4),sK5),
    inference(cnf_transformation,[],[f13]) ).

thf(f14,plain,
    ! [X6: b,X7: a] :
      ( ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,X6),X7) )
      | ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,X6),X7) )
      | ( sK0 = X6 ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f51,plain,
    $false = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK4),sK5),
    inference(trivial_inequality_removal,[],[f50]) ).

thf(f50,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK4),sK5) ) ),
    inference(superposition,[],[f18,f4]) ).

thf(f18,plain,
    $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK4),sK5),
    inference(cnf_transformation,[],[f13]) ).

thf(f71,plain,
    ( ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK0),sK5) )
    | ( sK1 = sK5 ) ),
    inference(trivial_inequality_removal,[],[f68]) ).

thf(f68,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,sK0),sK5) )
    | ( sK1 = sK5 ) ),
    inference(superposition,[],[f15,f65]) ).

thf(f15,plain,
    ! [X6: b,X7: a] :
      ( ( $true != vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,X6),X7) )
      | ( $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK2,X6),X7) )
      | ( sK1 = X7 ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f65,plain,
    $true = vAPP(a,$o,vAPP(b,sTfun(a,$o),sK3,sK0),sK5),
    inference(backward_demodulation,[],[f17,f63]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEV060^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 12:04:35 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (13091)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (13095)WARNING: value z3 for option sas not known
% 0.14/0.38  % (13094)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (13095)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)
% 0.14/0.38  % (13093)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (13096)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (13097)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)
% 0.14/0.38  % (13098)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)
% 0.14/0.38  % (13100)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)
% 0.14/0.38  % Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % (13100)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38  % Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % (13098)First to succeed.
% 0.14/0.38  % (13100)Also succeeded, but the first one will report.
% 0.14/0.38  % (13097)Also succeeded, but the first one will report.
% 0.14/0.38  % (13095)Also succeeded, but the first one will report.
% 0.14/0.39  % (13098)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13091"
% 0.14/0.39  % (13098)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (13098)------------------------------
% 0.14/0.39  % (13098)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (13098)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (13098)Memory used [KB]: 777
% 0.14/0.39  % (13098)Time elapsed: 0.006 s
% 0.14/0.39  % (13098)Instructions burned: 7 (million)
% 0.14/0.39  % (13091)Success in time 0.019 s
%------------------------------------------------------------------------------