TSTP Solution File: SEV273^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEV273^5 : 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 : 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 : Sun May  5 09:44:57 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   40 (   6 unt;  14 typ;   0 def)
%            Number of atoms       :  395 (  96 equ;   0 cnn)
%            Maximal formula atoms :   14 (  15 avg)
%            Number of connectives :  142 (  47   ~;  36   |;  36   &;   0   @)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   37 (  36   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   3 con; 0-6 aty)
%            Number of variables   :   93 (   0   ^  65   !;  22   ?;  93   :)
%                                         (   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_1,type,
    cR: a > a > $o ).

thf(func_def_5,type,
    sK0: a ).

thf(func_def_6,type,
    sK1: ( a > $o ) > a ).

thf(func_def_7,type,
    sK2: a > ( a > $o ) > 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(f122,plain,
    $false,
    inference(trivial_inequality_removal,[],[f121]) ).

thf(f121,plain,
    $true = $false,
    inference(superposition,[],[f48,f114]) ).

thf(f114,plain,
    ! [X0: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0) ),
    inference(equality_resolution,[],[f97]) ).

thf(f97,plain,
    ! [X0: a,X1: a] :
      ( ( X0 != X1 )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0) ) ),
    inference(equality_resolution,[],[f96]) ).

thf(f96,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( X0 != X2 )
      | ( X0 != X1 )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X2) ) ),
    inference(forward_demodulation,[],[f95,f52]) ).

thf(f52,plain,
    ! [X0: a] : ( vAPP(sTfun(a,$o),a,sK1,vAPP(a,sTfun(a,$o),vEQ(a),X0)) = X0 ),
    inference(leibniz_equality_elimination,[],[f14]) ).

thf(f14,plain,
    ! [X1: a > $o,X6: a] :
      ( ( $true != vAPP(a,$o,X1,X6) )
      | ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,sK1,X1)) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK0),sK0) )
    & ! [X1: a > $o] :
        ( ( ! [X3: a] :
              ( ( vAPP(sTfun(a,$o),a,sK1,X1) = X3 )
              | ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),sK2,X3),X1)) )
                & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),sK2,X3),X1)) ) )
              | ( $true != vAPP(a,$o,X1,X3) ) )
          & ! [X5: a] :
              ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,vAPP(sTfun(a,$o),a,sK1,X1)),X5) )
              | ( $true != vAPP(a,$o,X1,X5) ) )
          & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,sK1,X1)) ) )
        | ! [X6: a] : ( $true != vAPP(a,$o,X1,X6) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).

thf(f10,plain,
    ( ? [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0) )
   => ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK0),sK0) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X1: a > $o] :
      ( ? [X2: a] :
          ( ! [X3: a] :
              ( ( X2 = X3 )
              | ? [X4: a] :
                  ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X4) )
                  & ( $true = vAPP(a,$o,X1,X4) ) )
              | ( $true != vAPP(a,$o,X1,X3) ) )
          & ! [X5: a] :
              ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X2),X5) )
              | ( $true != vAPP(a,$o,X1,X5) ) )
          & ( $true = vAPP(a,$o,X1,X2) ) )
     => ( ! [X3: a] :
            ( ( vAPP(sTfun(a,$o),a,sK1,X1) = X3 )
            | ? [X4: a] :
                ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X4) )
                & ( $true = vAPP(a,$o,X1,X4) ) )
            | ( $true != vAPP(a,$o,X1,X3) ) )
        & ! [X5: a] :
            ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,vAPP(sTfun(a,$o),a,sK1,X1)),X5) )
            | ( $true != vAPP(a,$o,X1,X5) ) )
        & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,sK1,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X1: a > $o,X3: a] :
      ( ? [X4: a] :
          ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X4) )
          & ( $true = vAPP(a,$o,X1,X4) ) )
     => ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),sK2,X3),X1)) )
        & ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),sK2,X3),X1)) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

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

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

thf(f1,conjecture,
    ( ! [X0: a > $o] :
        ( ? [X1: a] : vAPP(a,$o,X0,X1)
       => ? [X1: a] :
            ( ! [X3: a] :
                ( ( ! [X2: a] :
                      ( vAPP(a,$o,X0,X2)
                     => vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X2) )
                  & vAPP(a,$o,X0,X3) )
               => ( X1 = X3 ) )
            & ! [X2: a] :
                ( vAPP(a,$o,X0,X2)
               => vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) )
            & vAPP(a,$o,X0,X1) ) )
   => ! [X2: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM542_pme) ).

thf(f95,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( X0 != X1 )
      | ( X0 != X2 )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,vAPP(sTfun(a,$o),a,sK1,vAPP(a,sTfun(a,$o),vEQ(a),X0))),X2) ) ),
    inference(equality_proxy_clausification,[],[f94]) ).

thf(f94,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( X0 != X1 )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,vAPP(sTfun(a,$o),a,sK1,vAPP(a,sTfun(a,$o),vEQ(a),X0))),X2) ) ),
    inference(equality_proxy_clausification,[],[f87]) ).

thf(f87,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,vAPP(sTfun(a,$o),a,sK1,vAPP(a,sTfun(a,$o),vEQ(a),X0))),X2) ) ),
    inference(primitive_instantiation,[],[f15]) ).

thf(f15,plain,
    ! [X1: a > $o,X6: a,X5: a] :
      ( ( $true != vAPP(a,$o,X1,X6) )
      | ( $true != vAPP(a,$o,X1,X5) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,vAPP(sTfun(a,$o),a,sK1,X1)),X5) ) ),
    inference(cnf_transformation,[],[f13]) ).

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

thf(f47,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK0),sK0) ) ),
    inference(superposition,[],[f18,f4]) ).

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

thf(f18,plain,
    $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK0),sK0),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEV273^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n010.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 11:54:03 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (886)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (892)WARNING: value z3 for option sas not known
% 0.15/0.37  % (893)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (894)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)
% 0.15/0.37  % (896)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)
% 0.15/0.37  % (890)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (891)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (892)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)
% 0.15/0.37  % (897)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)
% 0.15/0.37  % Exception at run slice level
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  % Exception at run slice level% (897)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.37  
% 0.15/0.37  User error: % Exception at run slice levelFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38  % (896)First to succeed.
% 0.21/0.38  % (892)Also succeeded, but the first one will report.
% 0.21/0.38  % (896)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-886"
% 0.21/0.38  % (896)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (896)------------------------------
% 0.21/0.38  % (896)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (896)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (896)Memory used [KB]: 856
% 0.21/0.38  % (896)Time elapsed: 0.008 s
% 0.21/0.38  % (896)Instructions burned: 10 (million)
% 0.21/0.38  % (886)Success in time 0.021 s
%------------------------------------------------------------------------------