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

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n008.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 01:44:21 EDT 2024

% Result   : Theorem 0.10s 0.34s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   38 (   5 unt;   7 typ;   0 def)
%            Number of atoms       :  102 (  36 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  114 (  29   ~;  12   |;   1   &;  58   @)
%                                         (   2 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   13 (   0   ^  12   !;   0   ?;  13   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    nat: $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_6,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(f37,plain,
    $false,
    inference(avatar_sat_refutation,[],[f30,f31,f36]) ).

thf(f36,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f35]) ).

thf(f35,plain,
    ( $false
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f34]) ).

thf(f34,plain,
    ( ( $true != $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f19,f33]) ).

thf(f33,plain,
    ( ( ( less @ y @ x )
      = $true )
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f32]) ).

thf(f32,plain,
    ( ( ( less @ y @ x )
      = $true )
    | ( $true != $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f21,f29]) ).

thf(f29,plain,
    ( ( ( more @ x @ y )
      = $true )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f27]) ).

thf(f27,plain,
    ( spl0_2
  <=> ( ( more @ x @ y )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

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

thf(f17,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( less @ X1 @ X0 )
        = $true )
      | ( ( more @ X0 @ X1 )
       != $true ) ),
    inference(rectify,[],[f16]) ).

thf(f16,plain,
    ! [X1: nat,X0: nat] :
      ( ( $true
        = ( less @ X0 @ X1 ) )
      | ( $true
       != ( more @ X1 @ X0 ) ) ),
    inference(ennf_transformation,[],[f11]) ).

thf(f11,plain,
    ! [X1: nat,X0: nat] :
      ( ( $true
        = ( more @ X1 @ X0 ) )
     => ( $true
        = ( less @ X0 @ X1 ) ) ),
    inference(fool_elimination,[],[f10]) ).

thf(f10,plain,
    ! [X0: nat,X1: nat] :
      ( ( more @ X1 @ X0 )
     => ( less @ X0 @ X1 ) ),
    inference(rectify,[],[f2]) ).

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

thf(f19,plain,
    ( ( less @ y @ x )
   != $true ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ( x != y )
    & ( ( less @ y @ x )
     != $true ) ),
    inference(ennf_transformation,[],[f13]) ).

thf(f13,plain,
    ~ ( ( ( less @ y @ x )
       != $true )
     => ( x = y ) ),
    inference(flattening,[],[f9]) ).

thf(f9,plain,
    ~ ( ( ( less @ y @ x )
       != $true )
     => ( x = y ) ),
    inference(fool_elimination,[],[f8]) ).

thf(f8,plain,
    ~ ( ~ ( less @ y @ x )
     => ( x = y ) ),
    inference(rectify,[],[f4]) ).

thf(f4,negated_conjecture,
    ~ ( ~ ( less @ y @ x )
     => ( x = y ) ),
    inference(negated_conjecture,[],[f3]) ).

thf(f3,conjecture,
    ( ~ ( less @ y @ x )
   => ( x = y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).

thf(f31,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f20,f23]) ).

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

thf(f20,plain,
    x != y,
    inference(cnf_transformation,[],[f14]) ).

thf(f30,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f18,f27,f23]) ).

thf(f18,plain,
    ( ( x = y )
    | ( ( more @ x @ y )
      = $true ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ( ( x = y )
    | ( ( more @ x @ y )
      = $true ) ),
    inference(ennf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ( ( more @ x @ y )
     != $true )
   => ( x = y ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ( ( ( more @ x @ y )
     != $true )
   => ( x = y ) ),
    inference(fool_elimination,[],[f6]) ).

thf(f6,plain,
    ( ~ ( more @ x @ y )
   => ( x = y ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( ~ ( more @ x @ y )
   => ( x = y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.32  % Computer : n008.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Mon May 20 05:54:53 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  This is a TH0_THM_EQU_NAR problem
% 0.10/0.32  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.33  % (17228)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.10/0.34  % (17228)First to succeed.
% 0.10/0.34  % (17228)Refutation found. Thanks to Tanya!
% 0.10/0.34  % SZS status Theorem for theBenchmark
% 0.10/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.34  % (17228)------------------------------
% 0.10/0.34  % (17228)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34  % (17228)Termination reason: Refutation
% 0.10/0.34  
% 0.10/0.34  % (17228)Memory used [KB]: 5500
% 0.10/0.34  % (17228)Time elapsed: 0.003 s
% 0.10/0.34  % (17228)Instructions burned: 1 (million)
% 0.10/0.34  % (17228)------------------------------
% 0.10/0.34  % (17228)------------------------------
% 0.10/0.34  % (17225)Success in time 0.01 s
% 0.10/0.34  % Vampire---4.8 exiting
%------------------------------------------------------------------------------