TSTP Solution File: NUM667^1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM667^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 02:12:43 EDT 2024

% Result   : Theorem 0.17s 0.34s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   66 (   4 unt;  14 typ;   0 def)
%            Number of atoms       :  316 (  73 equ;   0 cnn)
%            Maximal formula atoms :    4 (   6 avg)
%            Number of connectives :  132 (  62   ~;  38   |;   3   &;   0   @)
%                                         (   4 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   20 (  19   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   9 con; 0-6 aty)
%            Number of variables   :   29 (   0   ^  23   !;   0   ?;  29   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

thf(func_def_1,type,
    x: nat ).

thf(func_def_2,type,
    y: nat ).

thf(func_def_3,type,
    z: nat ).

thf(func_def_4,type,
    less: nat > nat > $o ).

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

thf(func_def_10,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

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

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

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

thf(func_def_15,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f130,plain,
    $false,
    inference(avatar_sat_refutation,[],[f89,f100,f109,f114,f129]) ).

thf(f129,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f128]) ).

thf(f128,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f127,f36]) ).

thf(f36,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true,
    inference(cnf_transformation,[],[f28]) ).

thf(f28,plain,
    ( ( x != z )
    & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true ) ),
    inference(ennf_transformation,[],[f22]) ).

thf(f22,plain,
    ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true )
     => ( x = z ) ),
    inference(flattening,[],[f11]) ).

thf(f11,plain,
    ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) != $true )
     => ( x = z ) ),
    inference(fool_elimination,[],[f10]) ).

thf(f10,plain,
    ~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z)
     => ( x = z ) ),
    inference(rectify,[],[f7]) ).

thf(f7,negated_conjecture,
    ~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z)
     => ( x = z ) ),
    inference(negated_conjecture,[],[f6]) ).

thf(f6,conjecture,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z)
   => ( x = z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz17) ).

thf(f127,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) = $true )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f124]) ).

thf(f124,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) = $true )
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(superposition,[],[f121,f104]) ).

thf(f104,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f102]) ).

thf(f102,plain,
    ( spl0_3
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f121,plain,
    ( ! [X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),X0) ) )
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f116]) ).

thf(f116,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),X0) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f41,f84]) ).

thf(f84,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f82]) ).

thf(f82,plain,
    ( spl0_1
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f41,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) != $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ),
    inference(cnf_transformation,[],[f33]) ).

thf(f33,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) != $true )
      | ( ( X0 != X1 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
    inference(flattening,[],[f32]) ).

thf(f32,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) != $true )
      | ( ( X0 != X1 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f26]) ).

thf(f26,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
       => ( X0 = X1 ) )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) = $true )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ) ),
    inference(flattening,[],[f19]) ).

thf(f19,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
       => ( X0 = X1 ) )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) = $true )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ) ),
    inference(fool_elimination,[],[f18]) ).

thf(f18,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1)
       => ( X0 = X1 ) )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X2) ) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2)
       => ( X1 = X2 ) )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X2),X3)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).

thf(f114,plain,
    ( ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f113]) ).

thf(f113,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f111,f84]) ).

thf(f111,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true )
    | ~ spl0_4 ),
    inference(superposition,[],[f36,f108]) ).

thf(f108,plain,
    ( ( y = z )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f106]) ).

thf(f106,plain,
    ( spl0_4
  <=> ( y = z ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f109,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f39,f106,f102]) ).

thf(f39,plain,
    ( ( y = z )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true ) ),
    inference(cnf_transformation,[],[f30]) ).

thf(f30,plain,
    ( ( y = z )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true ) ),
    inference(ennf_transformation,[],[f24]) ).

thf(f24,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) != $true )
   => ( y = z ) ),
    inference(flattening,[],[f15]) ).

thf(f15,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) != $true )
   => ( y = z ) ),
    inference(fool_elimination,[],[f14]) ).

thf(f14,plain,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z)
   => ( y = z ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z)
   => ( y = z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).

thf(f100,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f99]) ).

thf(f99,plain,
    ( $false
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f98,f36]) ).

thf(f98,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),z) = $true )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f97,f88]) ).

thf(f88,plain,
    ( ( x = y )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f86]) ).

thf(f86,plain,
    ( spl0_2
  <=> ( x = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f97,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true )
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f96,f37]) ).

thf(f37,plain,
    x != z,
    inference(cnf_transformation,[],[f28]) ).

thf(f96,plain,
    ( ( x = z )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),z) = $true )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f39,f88]) ).

thf(f89,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f38,f86,f82]) ).

thf(f38,plain,
    ( ( x = y )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true ) ),
    inference(cnf_transformation,[],[f29]) ).

thf(f29,plain,
    ( ( x = y )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true ) ),
    inference(ennf_transformation,[],[f23]) ).

thf(f23,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true )
   => ( x = y ) ),
    inference(flattening,[],[f13]) ).

thf(f13,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true )
   => ( x = y ) ),
    inference(fool_elimination,[],[f12]) ).

thf(f12,plain,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y)
   => ( x = y ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y)
   => ( x = y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUM667^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n005.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 06:59:38 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  % (19409)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.33  % (19412)WARNING: value z3 for option sas not known
% 0.17/0.34  % (19412)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)
% 0.17/0.34  % (19411)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.34  % (19413)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.34  % (19410)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.34  % Exception at run slice level% (19414)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)
% 0.17/0.34  
% 0.17/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34  % Exception at run slice level
% 0.17/0.34  User error: % (19415)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)
% 0.17/0.34  Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34  % Exception at run slice level
% 0.17/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34  % (19416)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)
% 0.17/0.34  % (19416)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.34  % (19412)First to succeed.
% 0.17/0.34  % (19415)Also succeeded, but the first one will report.
% 0.17/0.34  % (19414)Also succeeded, but the first one will report.
% 0.17/0.34  % (19412)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19409"
% 0.17/0.34  % (19416)Also succeeded, but the first one will report.
% 0.17/0.34  % (19412)Refutation found. Thanks to Tanya!
% 0.17/0.34  % SZS status Theorem for theBenchmark
% 0.17/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.34  % (19412)------------------------------
% 0.17/0.34  % (19412)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.34  % (19412)Termination reason: Refutation
% 0.17/0.34  
% 0.17/0.34  % (19412)Memory used [KB]: 782
% 0.17/0.34  % (19412)Time elapsed: 0.006 s
% 0.17/0.34  % (19412)Instructions burned: 8 (million)
% 0.17/0.34  % (19409)Success in time 0.017 s
%------------------------------------------------------------------------------