TSTP Solution File: SYO353^5 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYO353^5 : 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 : n003.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 09:10:59 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   31 (   6 unt;  13 typ;   0 def)
%            Number of atoms       :  144 (  33 equ;   0 cnn)
%            Maximal formula atoms :    4 (   8 avg)
%            Number of connectives :   43 (  15   ~;   7   |;   8   &;   0   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   42 (  41   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   4 con; 0-6 aty)
%            Number of variables   :   32 (   0   ^  23   !;   3   ?;  32   :)
%                                         (   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,
    v: a ).

thf(func_def_2,type,
    u: a ).

thf(func_def_6,type,
    sK0: a > a > $o ).

thf(func_def_7,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_8,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_9,type,
    vAND: $o > $o > $o ).

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

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

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

thf(func_def_13,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f59,plain,
    $false,
    inference(trivial_inequality_removal,[],[f58]) ).

thf(f58,plain,
    $true = $false,
    inference(forward_demodulation,[],[f55,f43]) ).

thf(f43,plain,
    $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,u),v),
    inference(trivial_inequality_removal,[],[f42]) ).

thf(f42,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,u),v) ) ),
    inference(superposition,[],[f13,f4]) ).

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

thf(f13,plain,
    $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,u),v),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,u),v) )
    & ! [X1: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X1),X1) )
    & ! [X2: a > $o] :
        ( ( $true = vAPP(a,$o,X2,v) )
        | ( $true != vAPP(a,$o,X2,u) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).

thf(f9,plain,
    ( ? [X0: a > a > $o] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,u),v) )
        & ! [X1: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) ) )
   => ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,u),v) )
      & ! [X1: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ? [X0: a > a > $o] :
        ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,u),v) )
        & ! [X1: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) ) )
    & ! [X2: a > $o] :
        ( ( $true = vAPP(a,$o,X2,v) )
        | ( $true != vAPP(a,$o,X2,u) ) ) ),
    inference(rectify,[],[f7]) ).

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

thf(f6,plain,
    ~ ( ! [X0: a > $o] :
          ( ( vAPP(a,$o,X0,u) = $true )
         => ( vAPP(a,$o,X0,v) = $true ) )
     => ! [X1: a > a > $o] :
          ( ! [X2: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,X2),X2) = $true )
         => ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,u),v) = $true ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ( ! [X0: a > $o] :
          ( vAPP(a,$o,X0,u)
         => vAPP(a,$o,X0,v) )
     => ! [X1: a > a > $o] :
          ( ! [X2: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,X2),X2)
         => vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,u),v) ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ( ! [X0: a > $o] :
        ( vAPP(a,$o,X0,u)
       => vAPP(a,$o,X0,v) )
   => ! [X1: a > a > $o] :
        ( ! [X2: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,X2),X2)
       => vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,u),v) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE1LEIBEQ1_pme) ).

thf(f55,plain,
    $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,u),v),
    inference(trivial_inequality_removal,[],[f52]) ).

thf(f52,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,u),v) ) ),
    inference(superposition,[],[f11,f12]) ).

thf(f12,plain,
    ! [X1: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK0,X1),X1) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f11,plain,
    ! [X2: a > $o] :
      ( ( $true != vAPP(a,$o,X2,u) )
      | ( $true = vAPP(a,$o,X2,v) ) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO353^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n003.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   : Mon May 20 09:18:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (6478)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (6485)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  % 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  % (6480)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (6481)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  % (6483)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37  % (6482)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  % (6479)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  % (6484)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37  % (6481)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37  % (6482)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  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  % 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  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % (6481)Also succeeded, but the first one will report.
% 0.13/0.37  % (6484)Also succeeded, but the first one will report.
% 0.13/0.37  % (6483)First to succeed.
% 0.13/0.37  % (6483)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6478"
% 0.13/0.37  % (6483)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  % (6483)------------------------------
% 0.13/0.37  % (6483)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (6483)Termination reason: Refutation
% 0.13/0.37  
% 0.13/0.37  % (6483)Memory used [KB]: 766
% 0.13/0.37  % (6483)Time elapsed: 0.005 s
% 0.13/0.37  % (6483)Instructions burned: 5 (million)
% 0.13/0.37  % (6478)Success in time 0.018 s
%------------------------------------------------------------------------------