TSTP Solution File: SEV053^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEV053^5 : 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 : n019.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 04:14:22 EDT 2024

% Result   : Theorem 0.20s 0.37s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   37 (   6 unt;  16 typ;   0 def)
%            Number of atoms       :  355 (  46 equ;   0 cnn)
%            Maximal formula atoms :    5 (  16 avg)
%            Number of connectives :   66 (  25   ~;  16   |;  16   &;   0   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   22 (  21   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   3 con; 0-6 aty)
%            Number of variables   :   57 (   0   ^  47   !;   4   ?;  57   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

thf(func_def_2,type,
    cF: b > b ).

thf(func_def_3,type,
    cA: b > a ).

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

thf(func_def_8,type,
    sK0: b ).

thf(func_def_10,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_11,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

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

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

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

thf(func_def_16,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f70,plain,
    $false,
    inference(trivial_inequality_removal,[],[f63]) ).

thf(f63,plain,
    $true = $false,
    inference(superposition,[],[f44,f56]) ).

thf(f56,plain,
    ! [X0: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X0)))) ),
    inference(trivial_inequality_removal,[],[f53]) ).

thf(f53,plain,
    ! [X0: b] :
      ( ( $true != $true )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X0)))) ) ),
    inference(superposition,[],[f52,f13]) ).

thf(f13,plain,
    ! [X1: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X1)),vAPP(b,a,cA,vAPP(b,b,cF,X1))) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))) )
    & ! [X1: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X1)),vAPP(b,a,cA,vAPP(b,b,cF,X1))) )
    & ! [X2: a,X3: a,X4: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X4) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X3),X4) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).

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

thf(f9,plain,
    ( ? [X0: b] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X0)))) )
    & ! [X1: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X1)),vAPP(b,a,cA,vAPP(b,b,cF,X1))) )
    & ! [X2: a,X3: a,X4: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X4) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X3),X4) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,plain,
    ( ? [X4: b] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) != $true )
    & ! [X0: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,X0))) )
    & ! [X1: a,X2: a,X3: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X3) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) )
        | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2) != $true ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ( ? [X4: b] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) != $true )
    & ! [X0: b] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),vAPP(b,a,cA,vAPP(b,b,cF,X0))) )
    & ! [X1: a,X2: a,X3: a] :
        ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X3) )
        | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) )
        | ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2) != $true ) ) ),
    inference(ennf_transformation,[],[f6]) ).

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

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

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

thf(f1,conjecture,
    ( ( ! [X3: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X3)),vAPP(b,a,cA,vAPP(b,b,cF,X3)))
      & ! [X0: a,X1: a,X2: a] :
          ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X1),X2)
            & vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X0),X1) )
         => vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X0),X2) ) )
   => ! [X4: b] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X4)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,X4)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM89B_pme) ).

thf(f52,plain,
    ! [X0: b,X1: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,vAPP(b,b,cF,X0))),X1) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),X1) ) ),
    inference(trivial_inequality_removal,[],[f48]) ).

thf(f48,plain,
    ! [X0: b,X1: a] :
      ( ( $true != $true )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,vAPP(b,b,cF,X0))),X1) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,X0)),X1) ) ),
    inference(superposition,[],[f12,f13]) ).

thf(f12,plain,
    ! [X2: a,X3: a,X4: a] :
      ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X3) )
      | ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X3),X4) )
      | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,X2),X4) ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f44,plain,
    $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))),
    inference(trivial_inequality_removal,[],[f43]) ).

thf(f43,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))) ) ),
    inference(superposition,[],[f14,f4]) ).

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

thf(f14,plain,
    $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cL,vAPP(b,a,cA,sK0)),vAPP(b,a,cA,vAPP(b,b,cF,vAPP(b,b,cF,sK0)))),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEV053^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n019.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun May 19 19:13:38 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (8849)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (8855)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.36  % (8856)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)
% 0.14/0.36  % Exception at run slice level
% 0.14/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37  % (8855)First to succeed.
% 0.14/0.37  % (8855)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8849"
% 0.14/0.37  % (8850)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (8851)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.37  % (8855)Refutation found. Thanks to Tanya!
% 0.20/0.37  % SZS status Theorem for theBenchmark
% 0.20/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.37  % (8855)------------------------------
% 0.20/0.37  % (8855)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.37  % (8855)Termination reason: Refutation
% 0.20/0.37  
% 0.20/0.37  % (8855)Memory used [KB]: 776
% 0.20/0.37  % (8855)Time elapsed: 0.006 s
% 0.20/0.37  % (8855)Instructions burned: 8 (million)
% 0.20/0.37  % (8849)Success in time 0.018 s
%------------------------------------------------------------------------------