TSTP Solution File: SEV486^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% 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 : 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 04:13:57 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   33 (  11 unt;  11 typ;   0 def)
%            Number of atoms       :  126 (  25 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  242 (   9   ~;   3   |;   5   &; 214   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (   9 usr;   4 con; 0-4 aty)
%                                         (   0  !!;  10  ??;   0 @@+;   0 @@-)
%            Number of variables   :   67 (  25   ^  28   !;   7   ?;  67   :)
%                                         (   7  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_6,type,
    'type/nums/num': $tType ).

thf(func_def_0,type,
    'type/nums/num': $tType ).

thf(func_def_1,type,
    'const/sets/SETSPEC': 
      !>[X0: $tType] : ( X0 > $o > X0 > $o ) ).

thf(func_def_2,type,
    'const/sets/HAS_SIZE': 
      !>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' > $o ) ).

thf(func_def_3,type,
    'const/sets/GSPEC': 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).

thf(func_def_4,type,
    'const/sets/FINITE': 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_5,type,
    'const/sets/CARD': 
      !>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).

thf(func_def_6,type,
    'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).

thf(func_def_8,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_17,type,
    sK0: 'type/nums/num' ).

thf(func_def_19,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(f46,plain,
    $false,
    inference(trivial_inequality_removal,[],[f45]) ).

thf(f45,plain,
    $true != $true,
    inference(superposition,[],[f17,f30]) ).

thf(f30,plain,
    ! [X0: 'type/nums/num'] :
      ( $true
      = ( 'const/sets/FINITE' @ 'type/nums/num'
        @ ( 'const/sets/GSPEC' @ 'type/nums/num'
          @ ^ [Y0: 'type/nums/num'] :
              ( ?? @ 'type/nums/num'
              @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) ),
    inference(trivial_inequality_removal,[],[f26]) ).

thf(f26,plain,
    ! [X0: 'type/nums/num'] :
      ( ( $true = $false )
      | ( $true
        = ( 'const/sets/FINITE' @ 'type/nums/num'
          @ ( 'const/sets/GSPEC' @ 'type/nums/num'
            @ ^ [Y0: 'type/nums/num'] :
                ( ?? @ 'type/nums/num'
                @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) ) ),
    inference(superposition,[],[f16,f21]) ).

thf(f21,plain,
    ! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
      ( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
        = $false )
      | ( ( 'const/sets/FINITE' @ X0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
      ( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
        = $false )
      | ( $true
        = ( ( 'const/sets/FINITE' @ X0 @ X1 )
          & ( ( 'const/sets/CARD' @ X0 @ X1 )
            = X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
      ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
      = ( ( 'const/sets/FINITE' @ X0 @ X1 )
        & ( ( 'const/sets/CARD' @ X0 @ X1 )
          = X2 ) ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
      ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
      = ( ( 'const/sets/FINITE' @ X0 @ X1 )
        & ( ( 'const/sets/CARD' @ X0 @ X1 )
          = X2 ) ) ),
    inference(fool_elimination,[],[f10]) ).

thf(f10,plain,
    ! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
      ( ( ( 'const/sets/CARD' @ X0 @ X1 )
        = X2 )
      & ( ( 'const/sets/FINITE' @ X0 @ X1 )
        = ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
      ( ( ( 'const/sets/CARD' @ X0 @ X1 )
        = X2 )
      & ( ( 'const/sets/FINITE' @ X0 @ X1 )
        = ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).

thf(f16,plain,
    ! [X0: 'type/nums/num'] :
      ( ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
        @ ( 'const/sets/GSPEC' @ 'type/nums/num'
          @ ^ [Y0: 'type/nums/num'] :
              ( ?? @ 'type/nums/num'
              @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) )
        @ X0 )
      = $true ),
    inference(cnf_transformation,[],[f9]) ).

thf(f9,plain,
    ! [X0: 'type/nums/num'] :
      ( ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
        @ ( 'const/sets/GSPEC' @ 'type/nums/num'
          @ ^ [Y0: 'type/nums/num'] :
              ( ?? @ 'type/nums/num'
              @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) )
        @ X0 )
      = $true ),
    inference(fool_elimination,[],[f8]) ).

thf(f8,plain,
    ! [X0: 'type/nums/num'] :
      ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
      @ ( 'const/sets/GSPEC' @ 'type/nums/num'
        @ ^ [X1: 'type/nums/num'] :
          ? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) )
      @ X0 ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X0: 'type/nums/num'] :
      ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
      @ ( 'const/sets/GSPEC' @ 'type/nums/num'
        @ ^ [X1: 'type/nums/num'] :
          ? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) )
      @ X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_NUMSEG_LT_') ).

thf(f17,plain,
    ( $true
   != ( 'const/sets/FINITE' @ 'type/nums/num'
      @ ( 'const/sets/GSPEC' @ 'type/nums/num'
        @ ^ [Y0: 'type/nums/num'] :
            ( ?? @ 'type/nums/num'
            @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( $true
   != ( 'const/sets/FINITE' @ 'type/nums/num'
      @ ( 'const/sets/GSPEC' @ 'type/nums/num'
        @ ^ [Y0: 'type/nums/num'] :
            ( ?? @ 'type/nums/num'
            @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).

thf(f13,plain,
    ( ? [X0: 'type/nums/num'] :
        ( $true
       != ( 'const/sets/FINITE' @ 'type/nums/num'
          @ ( 'const/sets/GSPEC' @ 'type/nums/num'
            @ ^ [Y0: 'type/nums/num'] :
                ( ?? @ 'type/nums/num'
                @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) )
   => ( $true
     != ( 'const/sets/FINITE' @ 'type/nums/num'
        @ ( 'const/sets/GSPEC' @ 'type/nums/num'
          @ ^ [Y0: 'type/nums/num'] :
              ( ?? @ 'type/nums/num'
              @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ? [X0: 'type/nums/num'] :
      ( $true
     != ( 'const/sets/FINITE' @ 'type/nums/num'
        @ ( 'const/sets/GSPEC' @ 'type/nums/num'
          @ ^ [Y0: 'type/nums/num'] :
              ( ?? @ 'type/nums/num'
              @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) ),
    inference(ennf_transformation,[],[f7]) ).

thf(f7,plain,
    ~ ! [X0: 'type/nums/num'] :
        ( $true
        = ( 'const/sets/FINITE' @ 'type/nums/num'
          @ ( 'const/sets/GSPEC' @ 'type/nums/num'
            @ ^ [Y0: 'type/nums/num'] :
                ( ?? @ 'type/nums/num'
                @ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) ),
    inference(fool_elimination,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: 'type/nums/num'] :
        ( 'const/sets/FINITE' @ 'type/nums/num'
        @ ( 'const/sets/GSPEC' @ 'type/nums/num'
          @ ^ [X1: 'type/nums/num'] :
            ? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
    inference(rectify,[],[f4]) ).

thf(f4,negated_conjecture,
    ~ ! [X0: 'type/nums/num'] :
        ( 'const/sets/FINITE' @ 'type/nums/num'
        @ ( 'const/sets/GSPEC' @ 'type/nums/num'
          @ ^ [X1: 'type/nums/num'] :
            ? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
    inference(negated_conjecture,[],[f3]) ).

thf(f3,conjecture,
    ! [X0: 'type/nums/num'] :
      ( 'const/sets/FINITE' @ 'type/nums/num'
      @ ( 'const/sets/GSPEC' @ 'type/nums/num'
        @ ^ [X1: 'type/nums/num'] :
          ? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_NUMSEG_LT_') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% 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
% 0.11/0.33  % Computer : n019.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Sun May 19 18:43:53 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  This is a TH1_THM_EQU_NAR problem
% 0.11/0.33  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
% 0.11/0.35  % (8256)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.11/0.35  % (8258)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)
% 0.11/0.35  % (8257)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.11/0.35  % (8259)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.35  % (8261)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.11/0.35  % (8262)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.11/0.35  % (8260)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.35  % (8263)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.11/0.35  % (8259)Instruction limit reached!
% 0.11/0.35  % (8259)------------------------------
% 0.11/0.35  % (8259)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (8259)Termination reason: Unknown
% 0.11/0.35  % (8259)Termination phase: Saturation
% 0.11/0.35  % (8261)Refutation not found, incomplete strategy
% 0.11/0.35  % (8261)------------------------------
% 0.11/0.35  % (8261)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (8261)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.35  
% 0.11/0.35  
% 0.11/0.35  % (8260)Instruction limit reached!
% 0.11/0.35  % (8260)------------------------------
% 0.11/0.35  % (8260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (8261)Memory used [KB]: 5500
% 0.11/0.35  % (8260)Termination reason: Unknown
% 0.11/0.35  % (8261)Time elapsed: 0.002 s
% 0.11/0.35  % (8260)Termination phase: Saturation
% 0.11/0.35  
% 0.11/0.35  % (8261)Instructions burned: 1 (million)
% 0.11/0.35  % (8261)------------------------------
% 0.11/0.35  % (8261)------------------------------
% 0.11/0.35  % (8260)Memory used [KB]: 5500
% 0.11/0.35  % (8260)Time elapsed: 0.003 s
% 0.11/0.35  % (8260)Instructions burned: 2 (million)
% 0.11/0.35  % (8260)------------------------------
% 0.11/0.35  % (8260)------------------------------
% 0.11/0.35  
% 0.11/0.35  % (8259)Memory used [KB]: 5500
% 0.11/0.35  % (8259)Time elapsed: 0.003 s
% 0.11/0.35  % (8259)Instructions burned: 2 (million)
% 0.11/0.35  % (8259)------------------------------
% 0.11/0.35  % (8259)------------------------------
% 0.11/0.35  % (8257)Instruction limit reached!
% 0.11/0.35  % (8257)------------------------------
% 0.11/0.35  % (8257)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (8257)Termination reason: Unknown
% 0.11/0.35  % (8257)Termination phase: Saturation
% 0.11/0.35  
% 0.11/0.35  % (8257)Memory used [KB]: 5500
% 0.11/0.35  % (8257)Time elapsed: 0.004 s
% 0.11/0.35  % (8257)Instructions burned: 4 (million)
% 0.11/0.35  % (8257)------------------------------
% 0.11/0.35  % (8257)------------------------------
% 0.11/0.35  % (8263)Instruction limit reached!
% 0.11/0.35  % (8263)------------------------------
% 0.11/0.35  % (8263)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (8263)Termination reason: Unknown
% 0.11/0.35  % (8263)Termination phase: Saturation
% 0.11/0.35  
% 0.11/0.35  % (8263)Memory used [KB]: 5500
% 0.11/0.35  % (8263)Time elapsed: 0.004 s
% 0.11/0.35  % (8263)Instructions burned: 4 (million)
% 0.11/0.35  % (8263)------------------------------
% 0.11/0.35  % (8263)------------------------------
% 0.11/0.35  % (8258)First to succeed.
% 0.11/0.35  % (8258)Refutation found. Thanks to Tanya!
% 0.11/0.35  % SZS status Theorem for theBenchmark
% 0.11/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35  % (8258)------------------------------
% 0.11/0.35  % (8258)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (8258)Termination reason: Refutation
% 0.11/0.35  
% 0.11/0.35  % (8258)Memory used [KB]: 5500
% 0.11/0.35  % (8258)Time elapsed: 0.007 s
% 0.11/0.35  % (8258)Instructions burned: 7 (million)
% 0.11/0.35  % (8258)------------------------------
% 0.11/0.35  % (8258)------------------------------
% 0.11/0.35  % (8255)Success in time 0.006 s
% 0.11/0.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------