TSTP Solution File: SEV450^1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n020.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 : Mon Jun 24 16:03:55 EDT 2024

% Result   : Theorem 0.12s 0.40s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   53 (  12 unt;   0 typ;   0 def)
%            Number of atoms       :  276 (  69 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  318 (  34   ~;  55   |;   0   &; 224   @)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   7 con; 0-4 aty)
%            Number of variables   :   70 (   0   ^  66   !;   4   ?;  70   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_6,type,
    sK0: $tType ).

thf(func_def_0,type,
    'const/sets/UNION': 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).

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

thf(func_def_3,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_11,type,
    sK1: sK0 > $o ).

thf(func_def_13,type,
    sK3: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_14,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(func_def_15,type,
    sK5: sK0 ).

thf(f185,plain,
    $false,
    inference(avatar_sat_refutation,[],[f52,f61,f122,f128,f184]) ).

thf(f184,plain,
    ( ~ spl2_1
    | ~ spl2_4 ),
    inference(avatar_contradiction_clause,[],[f183]) ).

thf(f183,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f182]) ).

thf(f182,plain,
    ( ( $true = $false )
    | ~ spl2_1
    | ~ spl2_4 ),
    inference(forward_demodulation,[],[f176,f60]) ).

thf(f60,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f58]) ).

thf(f58,plain,
    ( spl2_4
  <=> ( ( sK1 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f176,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f172]) ).

thf(f172,plain,
    ( ( $true = $false )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ~ spl2_1 ),
    inference(superposition,[],[f164,f40]) ).

thf(f40,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
        = $false )
      | ( ( X1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( X1 @ X2 ) ),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType,X1: X0 > $o,X2: X0] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( X1 @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).

thf(f164,plain,
    ( ( $true
      = ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f163]) ).

thf(f163,plain,
    ( ( $true
      = ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
    | ( $true = $false )
    | ~ spl2_1 ),
    inference(duplicate_literal_removal,[],[f159]) ).

thf(f159,plain,
    ( ( $true
      = ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
    | ( $true = $false )
    | ( $true
      = ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
    | ~ spl2_1 ),
    inference(superposition,[],[f47,f64]) ).

thf(f64,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
      ( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
        = $false )
      | ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
        = $true )
      | ( $true
        = ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
    inference(trivial_inequality_removal,[],[f62]) ).

thf(f62,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
      ( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
        = $false )
      | ( $true = $false )
      | ( $true
        = ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
      | ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
        = $true ) ),
    inference(superposition,[],[f39,f36]) ).

thf(f36,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
        = $false )
      | ( $true
        = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
      | ( $true
        = ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f35]) ).

thf(f35,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
        = $false )
      | ( $true
        = ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
          | ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
      = ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
        | ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
      ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
      = ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
        | ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,plain,
    ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
      ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
        = ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
      | ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0] :
      ( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) )
        = ( 'const/sets/IN' @ X0 @ X4 @ X2 ) )
      | ( 'const/sets/IN' @ X0 @ X4 @ X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).

thf(f39,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
        = $true )
      | ( ( X1 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f47,plain,
    ( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
      = $true )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f45]) ).

thf(f45,plain,
    ( spl2_1
  <=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f128,plain,
    ( ~ spl2_2
    | ~ spl2_4 ),
    inference(avatar_contradiction_clause,[],[f127]) ).

thf(f127,plain,
    ( $false
    | ~ spl2_2
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f123]) ).

thf(f123,plain,
    ( ( $true = $false )
    | ~ spl2_2
    | ~ spl2_4 ),
    inference(backward_demodulation,[],[f51,f60]) ).

thf(f51,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f49]) ).

thf(f49,plain,
    ( spl2_2
  <=> ( $true
      = ( sK1 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f122,plain,
    ( spl2_4
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f117,f54,f58]) ).

thf(f54,plain,
    ( spl2_3
  <=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f117,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f114]) ).

thf(f114,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( $true = $false )
    | ~ spl2_3 ),
    inference(superposition,[],[f39,f108]) ).

thf(f108,plain,
    ( ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
      = $false )
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f107]) ).

thf(f107,plain,
    ( ( $true = $false )
    | ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
      = $false )
    | ~ spl2_3 ),
    inference(superposition,[],[f56,f94]) ).

thf(f94,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
      ( ( $true
        = ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
      | ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
        = $false ) ),
    inference(trivial_inequality_removal,[],[f91]) ).

thf(f91,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
      ( ( $true
        = ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
      | ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
        = $false )
      | ( $true = $false ) ),
    inference(superposition,[],[f37,f40]) ).

thf(f37,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( $true
        = ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) )
      | ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f34]) ).

thf(f34,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( $false
        = ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
          | ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) )
      | ( $true
        = ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f56,plain,
    ( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
      = $false )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f54]) ).

thf(f61,plain,
    ( spl2_3
    | spl2_4 ),
    inference(avatar_split_clause,[],[f43,f58,f54]) ).

thf(f43,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f41]) ).

thf(f41,plain,
    ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
   != ( sK1 @ sK5 ) ),
    inference(negative_extensionality,[],[f16]) ).

thf(f16,plain,
    ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
   != sK1 ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
   != sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).

thf(f13,plain,
    ( ? [X0: $tType,X1: X0 > $o] :
        ( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
       != X1 )
   => ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
     != sK1 ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ? [X0: $tType,X1: X0 > $o] :
      ( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
     != X1 ),
    inference(ennf_transformation,[],[f11]) ).

thf(f11,plain,
    ~ ! [X0: $tType,X1: X0 > $o] :
        ( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
        = X1 ),
    inference(rectify,[],[f5]) ).

thf(f5,negated_conjecture,
    ~ ! [X0: $tType,X2: X0 > $o] :
        ( ( 'const/sets/UNION' @ X0 @ X2 @ X2 )
        = X2 ),
    inference(negated_conjecture,[],[f4]) ).

thf(f4,conjecture,
    ! [X0: $tType,X2: X0 > $o] :
      ( ( 'const/sets/UNION' @ X0 @ X2 @ X2 )
      = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNION_IDEMPOT_') ).

thf(f52,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f42,f49,f45]) ).

thf(f42,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 21 19:32:39 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.35  This is a TH1_THM_EQU_NAR problem
% 0.12/0.36  Running higher-order theorem proving
% 0.12/0.36  Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.38  % (29628)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.38  % (29631)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.38  % (29629)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 (2999ds/4Mi)
% 0.12/0.38  % (29630)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 (2999ds/27Mi)
% 0.12/0.38  % (29632)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 (2999ds/2Mi)
% 0.12/0.38  % (29633)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 (2999ds/275Mi)
% 0.12/0.38  % (29634)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.38  % Exception at run slice level
% 0.12/0.38  User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.12/0.38  % (29631)Instruction limit reached!
% 0.12/0.38  % (29631)------------------------------
% 0.12/0.38  % (29631)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (29631)Termination reason: Unknown
% 0.12/0.38  % (29631)Termination phase: Saturation
% 0.12/0.38  
% 0.12/0.38  % (29631)Memory used [KB]: 5373
% 0.12/0.38  % (29631)Time elapsed: 0.004 s
% 0.12/0.38  % (29631)Instructions burned: 2 (million)
% 0.12/0.38  % (29631)------------------------------
% 0.12/0.38  % (29631)------------------------------
% 0.12/0.38  % (29633)Refutation not found, incomplete strategy
% 0.12/0.38  % (29633)------------------------------
% 0.12/0.38  % (29633)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (29633)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38  
% 0.12/0.38  
% 0.12/0.38  % (29633)Memory used [KB]: 5500
% 0.12/0.38  % (29633)Time elapsed: 0.005 s
% 0.12/0.38  % (29633)Instructions burned: 3 (million)
% 0.12/0.38  % (29633)------------------------------
% 0.12/0.38  % (29633)------------------------------
% 0.12/0.38  % (29629)Instruction limit reached!
% 0.12/0.38  % (29629)------------------------------
% 0.12/0.38  % (29629)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (29629)Termination reason: Unknown
% 0.12/0.38  % (29629)Termination phase: Saturation
% 0.12/0.38  
% 0.12/0.38  % (29629)Memory used [KB]: 5500
% 0.12/0.38  % (29629)Time elapsed: 0.005 s
% 0.12/0.38  % (29629)Instructions burned: 5 (million)
% 0.12/0.38  % (29629)------------------------------
% 0.12/0.38  % (29629)------------------------------
% 0.12/0.39  % (29634)Instruction limit reached!
% 0.12/0.39  % (29634)------------------------------
% 0.12/0.39  % (29634)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (29634)Termination reason: Unknown
% 0.12/0.39  % (29634)Termination phase: Saturation
% 0.12/0.39  
% 0.12/0.39  % (29634)Memory used [KB]: 5628
% 0.12/0.39  % (29634)Time elapsed: 0.016 s
% 0.12/0.39  % (29634)Instructions burned: 18 (million)
% 0.12/0.39  % (29634)------------------------------
% 0.12/0.39  % (29634)------------------------------
% 0.12/0.39  % (29630)First to succeed.
% 0.12/0.40  % (29630)Refutation found. Thanks to Tanya!
% 0.12/0.40  % SZS status Theorem for theBenchmark
% 0.12/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.40  % (29630)------------------------------
% 0.12/0.40  % (29630)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40  % (29630)Termination reason: Refutation
% 0.12/0.40  
% 0.12/0.40  % (29630)Memory used [KB]: 5628
% 0.12/0.40  % (29630)Time elapsed: 0.017 s
% 0.12/0.40  % (29630)Instructions burned: 20 (million)
% 0.12/0.40  % (29630)------------------------------
% 0.12/0.40  % (29630)------------------------------
% 0.12/0.40  % (29627)Success in time 0.031 s
%------------------------------------------------------------------------------