TSTP Solution File: SET985+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 : Wed Aug 31 18:26:16 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   60 (  14 unt;   0 def)
%            Number of atoms       :  139 (  33 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  124 (  45   ~;  56   |;   6   &)
%                                         (  11 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  11 usr;  10 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :   56 (  52   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f413,plain,
    $false,
    inference(avatar_sat_refutation,[],[f44,f76,f81,f107,f128,f240,f272,f282,f301,f412]) ).

fof(f412,plain,
    ( spl10_29
    | ~ spl10_1
    | ~ spl10_32 ),
    inference(avatar_split_clause,[],[f410,f270,f37,f237]) ).

fof(f237,plain,
    ( spl10_29
  <=> subset(sK3,sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_29])]) ).

fof(f37,plain,
    ( spl10_1
  <=> subset(sF6,sF7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).

fof(f270,plain,
    ( spl10_32
  <=> ! [X6,X7] :
        ( subset(sK3,X7)
        | ~ subset(sF6,cartesian_product2(X6,X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_32])]) ).

fof(f410,plain,
    ( ~ subset(sF6,sF7)
    | subset(sK3,sK5)
    | ~ spl10_32 ),
    inference(superposition,[],[f271,f32]) ).

fof(f32,plain,
    cartesian_product2(sK4,sK5) = sF7,
    introduced(function_definition,[]) ).

fof(f271,plain,
    ( ! [X6,X7] :
        ( ~ subset(sF6,cartesian_product2(X6,X7))
        | subset(sK3,X7) )
    | ~ spl10_32 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f301,plain,
    ~ spl10_8,
    inference(avatar_contradiction_clause,[],[f300]) ).

fof(f300,plain,
    ( $false
    | ~ spl10_8 ),
    inference(resolution,[],[f289,f28]) ).

fof(f28,plain,
    ! [X0] : subset(empty_set,X0),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] : subset(empty_set,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

fof(f289,plain,
    ( ~ subset(empty_set,sK5)
    | ~ spl10_8 ),
    inference(superposition,[],[f25,f75]) ).

fof(f75,plain,
    ( empty_set = sK3
    | ~ spl10_8 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f73,plain,
    ( spl10_8
  <=> empty_set = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).

fof(f25,plain,
    ~ subset(sK3,sK5),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ? [X0] :
      ( ? [X1,X2,X3] :
          ( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
            | subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
          & ~ subset(X1,X3) )
      & ~ empty(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0] :
        ( ~ empty(X0)
       => ! [X1,X3,X2] :
            ( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
              | subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
           => subset(X1,X3) ) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0] :
      ( ~ empty(X0)
     => ! [X1,X3,X2] :
          ( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
            | subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
         => subset(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).

fof(f282,plain,
    ~ spl10_29,
    inference(avatar_contradiction_clause,[],[f281]) ).

fof(f281,plain,
    ( $false
    | ~ spl10_29 ),
    inference(resolution,[],[f239,f25]) ).

fof(f239,plain,
    ( subset(sK3,sK5)
    | ~ spl10_29 ),
    inference(avatar_component_clause,[],[f237]) ).

fof(f272,plain,
    ( spl10_9
    | spl10_32 ),
    inference(avatar_split_clause,[],[f255,f270,f78]) ).

fof(f78,plain,
    ( spl10_9
  <=> empty_set = sF6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).

fof(f255,plain,
    ! [X6,X7] :
      ( subset(sK3,X7)
      | empty_set = sF6
      | ~ subset(sF6,cartesian_product2(X6,X7)) ),
    inference(superposition,[],[f23,f31]) ).

fof(f31,plain,
    sF6 = cartesian_product2(sK2,sK3),
    introduced(function_definition,[]) ).

fof(f23,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subset(cartesian_product2(X2,X1),cartesian_product2(X0,X3))
      | empty_set = cartesian_product2(X2,X1)
      | subset(X1,X3) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X2,X1,X3] :
      ( ( subset(X1,X3)
        & subset(X2,X0) )
      | ~ subset(cartesian_product2(X2,X1),cartesian_product2(X0,X3))
      | empty_set = cartesian_product2(X2,X1) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X3,X2] :
      ( ( subset(X1,X3)
        & subset(X2,X0) )
      | empty_set = cartesian_product2(X2,X1)
      | ~ subset(cartesian_product2(X2,X1),cartesian_product2(X0,X3)) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1,X3,X2] :
      ( subset(cartesian_product2(X2,X1),cartesian_product2(X0,X3))
     => ( ( subset(X1,X3)
          & subset(X2,X0) )
        | empty_set = cartesian_product2(X2,X1) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X1,X0,X3] :
      ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
     => ( empty_set = cartesian_product2(X0,X1)
        | ( subset(X0,X2)
          & subset(X1,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

fof(f240,plain,
    ( ~ spl10_2
    | spl10_29
    | ~ spl10_12 ),
    inference(avatar_split_clause,[],[f147,f105,f237,f41]) ).

fof(f41,plain,
    ( spl10_2
  <=> subset(sF8,sF9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).

fof(f105,plain,
    ( spl10_12
  <=> ! [X9,X8] :
        ( ~ subset(sF8,cartesian_product2(X8,X9))
        | subset(sK3,X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_12])]) ).

fof(f147,plain,
    ( subset(sK3,sK5)
    | ~ subset(sF8,sF9)
    | ~ spl10_12 ),
    inference(superposition,[],[f106,f34]) ).

fof(f34,plain,
    cartesian_product2(sK5,sK4) = sF9,
    introduced(function_definition,[]) ).

fof(f106,plain,
    ( ! [X8,X9] :
        ( ~ subset(sF8,cartesian_product2(X8,X9))
        | subset(sK3,X8) )
    | ~ spl10_12 ),
    inference(avatar_component_clause,[],[f105]) ).

fof(f128,plain,
    ~ spl10_7,
    inference(avatar_contradiction_clause,[],[f127]) ).

fof(f127,plain,
    ( $false
    | ~ spl10_7 ),
    inference(resolution,[],[f124,f17]) ).

fof(f17,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f124,plain,
    ( ~ empty(empty_set)
    | ~ spl10_7 ),
    inference(superposition,[],[f26,f71]) ).

fof(f71,plain,
    ( empty_set = sK2
    | ~ spl10_7 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f69,plain,
    ( spl10_7
  <=> empty_set = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).

fof(f26,plain,
    ~ empty(sK2),
    inference(cnf_transformation,[],[f13]) ).

fof(f107,plain,
    ( spl10_6
    | spl10_12 ),
    inference(avatar_split_clause,[],[f91,f105,f65]) ).

fof(f65,plain,
    ( spl10_6
  <=> empty_set = sF8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).

fof(f91,plain,
    ! [X8,X9] :
      ( ~ subset(sF8,cartesian_product2(X8,X9))
      | empty_set = sF8
      | subset(sK3,X8) ),
    inference(superposition,[],[f22,f33]) ).

fof(f33,plain,
    cartesian_product2(sK3,sK2) = sF8,
    introduced(function_definition,[]) ).

fof(f22,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subset(cartesian_product2(X2,X1),cartesian_product2(X0,X3))
      | empty_set = cartesian_product2(X2,X1)
      | subset(X2,X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f81,plain,
    ( ~ spl10_9
    | spl10_7
    | spl10_8 ),
    inference(avatar_split_clause,[],[f47,f73,f69,f78]) ).

fof(f47,plain,
    ( empty_set = sK3
    | empty_set = sK2
    | empty_set != sF6 ),
    inference(superposition,[],[f19,f31]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( empty_set != cartesian_product2(X1,X0)
      | empty_set = X0
      | empty_set = X1 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X1,X0)
    <=> ( empty_set = X0
        | empty_set = X1 ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( empty_set = cartesian_product2(X0,X1)
    <=> ( empty_set = X0
        | empty_set = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

fof(f76,plain,
    ( ~ spl10_6
    | spl10_7
    | spl10_8 ),
    inference(avatar_split_clause,[],[f48,f73,f69,f65]) ).

fof(f48,plain,
    ( empty_set = sK3
    | empty_set = sK2
    | empty_set != sF8 ),
    inference(superposition,[],[f19,f33]) ).

fof(f44,plain,
    ( spl10_1
    | spl10_2 ),
    inference(avatar_split_clause,[],[f35,f41,f37]) ).

fof(f35,plain,
    ( subset(sF8,sF9)
    | subset(sF6,sF7) ),
    inference(definition_folding,[],[f24,f34,f33,f32,f31]) ).

fof(f24,plain,
    ( subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5))
    | subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4)) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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   : Tue Aug 30 14:32:35 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (15385)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.50  % (15396)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.50  % (15393)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.50  % (15383)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (15388)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (15383)First to succeed.
% 0.19/0.51  % (15383)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (15383)------------------------------
% 0.19/0.51  % (15383)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (15383)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (15383)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (15383)Memory used [KB]: 5628
% 0.19/0.51  % (15383)Time elapsed: 0.115 s
% 0.19/0.51  % (15383)Instructions burned: 6 (million)
% 0.19/0.51  % (15383)------------------------------
% 0.19/0.51  % (15383)------------------------------
% 0.19/0.51  % (15376)Success in time 0.158 s
%------------------------------------------------------------------------------