TSTP Solution File: NUM660^1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM660^1 : 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 : n012.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 02:12:40 EDT 2024

% Result   : Theorem 0.13s 0.35s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   59 (   9 unt;  14 typ;   0 def)
%            Number of atoms       :  237 (  51 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  100 (  46   ~;  35   |;   1   &;   0   @)
%                                         (   6 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   22 (  21   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;  10 con; 0-6 aty)
%            Number of variables   :   23 (   0   ^  17   !;   0   ?;  23   :)
%                                         (   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,
    more: nat > nat > $o ).

thf(func_def_5,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(f87,plain,
    $false,
    inference(avatar_sat_refutation,[],[f26,f31,f36,f40,f75,f79,f86]) ).

thf(f86,plain,
    ( spl0_3
    | ~ spl0_4
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(avatar_contradiction_clause,[],[f85]) ).

thf(f85,plain,
    ( $false
    | spl0_3
    | ~ spl0_4
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f84]) ).

thf(f84,plain,
    ( ( $true = $false )
    | spl0_3
    | ~ spl0_4
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(forward_demodulation,[],[f83,f52]) ).

thf(f52,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $false )
    | spl0_3
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f50]) ).

thf(f50,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $false )
    | spl0_3
    | ~ spl0_4 ),
    inference(superposition,[],[f35,f39]) ).

thf(f39,plain,
    ( ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f38]) ).

thf(f38,plain,
    ( spl0_4
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f35,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true )
    | spl0_3 ),
    inference(avatar_component_clause,[],[f33]) ).

thf(f33,plain,
    ( spl0_3
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f83,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $true )
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f80]) ).

thf(f80,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) = $true )
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(superposition,[],[f78,f74]) ).

thf(f74,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f72]) ).

thf(f72,plain,
    ( spl0_5
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f78,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true ) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f77]) ).

thf(f77,plain,
    ( spl0_6
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f79,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f21,f77]) ).

thf(f21,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f17]) ).

thf(f17,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f12]) ).

thf(f12,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) = $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) = $true ) ),
    inference(fool_elimination,[],[f11]) ).

thf(f11,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz11) ).

thf(f75,plain,
    ( spl0_5
    | spl0_1 ),
    inference(avatar_split_clause,[],[f20,f23,f72]) ).

thf(f23,plain,
    ( spl0_1
  <=> ( x = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f20,plain,
    ( ( x = y )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
    inference(cnf_transformation,[],[f16]) ).

thf(f16,plain,
    ( ( x = y )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
    inference(ennf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
   => ( x = y ) ),
    inference(flattening,[],[f10]) ).

thf(f10,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
   => ( x = y ) ),
    inference(fool_elimination,[],[f9]) ).

thf(f9,plain,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y)
   => ( x = y ) ),
    inference(rectify,[],[f1]) ).

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

thf(f40,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f6,f38]) ).

thf(f6,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f36,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f18,f33]) ).

thf(f18,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true,
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ( ( x != y )
    & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true ) ),
    inference(ennf_transformation,[],[f13]) ).

thf(f13,plain,
    ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true )
     => ( x = y ) ),
    inference(flattening,[],[f8]) ).

thf(f8,plain,
    ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x) != $true )
     => ( x = y ) ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,plain,
    ~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x)
     => ( x = y ) ),
    inference(rectify,[],[f4]) ).

thf(f4,negated_conjecture,
    ~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x)
     => ( x = y ) ),
    inference(negated_conjecture,[],[f3]) ).

thf(f3,conjecture,
    ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,y),x)
   => ( x = y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).

thf(f31,plain,
    ~ spl0_2,
    inference(avatar_split_clause,[],[f5,f28]) ).

thf(f28,plain,
    ( spl0_2
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f5,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

thf(f26,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f19,f23]) ).

thf(f19,plain,
    x != y,
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 05:54:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (16305)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35  % (16309)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.35  % Exception at run slice level
% 0.13/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.35  % (16310)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)
% 0.13/0.35  % (16306)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.35  % (16310)First to succeed.
% 0.13/0.35  % Exception at run slice level
% 0.13/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.35  % (16310)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16305"
% 0.13/0.35  % (16310)Refutation found. Thanks to Tanya!
% 0.13/0.35  % SZS status Theorem for theBenchmark
% 0.13/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.35  % (16310)------------------------------
% 0.13/0.35  % (16310)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.35  % (16310)Termination reason: Refutation
% 0.13/0.35  
% 0.13/0.35  % (16310)Memory used [KB]: 780
% 0.13/0.35  % (16310)Time elapsed: 0.004 s
% 0.13/0.35  % (16310)Instructions burned: 5 (million)
% 0.13/0.35  % (16305)Success in time 0.01 s
%------------------------------------------------------------------------------