TSTP Solution File: SET663+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n005.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 18:25:16 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   67 (  10 unt;   0 def)
%            Number of atoms       :  200 (  30 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  223 (  90   ~;  86   |;  16   &)
%                                         (   8 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   69 (  63   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f380,plain,
    $false,
    inference(avatar_sat_refutation,[],[f201,f203,f235,f257,f364,f372,f379]) ).

fof(f379,plain,
    ~ spl17_11,
    inference(avatar_contradiction_clause,[],[f378]) ).

fof(f378,plain,
    ( $false
    | ~ spl17_11 ),
    inference(trivial_inequality_removal,[],[f373]) ).

fof(f373,plain,
    ( empty_set != empty_set
    | ~ spl17_11 ),
    inference(superposition,[],[f103,f252]) ).

fof(f252,plain,
    ( empty_set = sK9
    | ~ spl17_11 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f250,plain,
    ( spl17_11
  <=> empty_set = sK9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).

fof(f103,plain,
    empty_set != sK9,
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ? [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
              & ilf_type(X2,relation_type(empty_set,X1))
              & empty_set != X2 ) ) ),
    inference(flattening,[],[f56]) ).

fof(f56,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( empty_set != X2
              & ilf_type(X2,relation_type(empty_set,X1))
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ( ilf_type(X2,relation_type(empty_set,X1))
                 => empty_set = X2 ) ) ) ),
    inference(negated_conjecture,[],[f35]) ).

fof(f35,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ( ilf_type(X2,relation_type(empty_set,X1))
               => empty_set = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_26) ).

fof(f372,plain,
    ( spl17_12
    | ~ spl17_20 ),
    inference(avatar_contradiction_clause,[],[f371]) ).

fof(f371,plain,
    ( $false
    | spl17_12
    | ~ spl17_20 ),
    inference(resolution,[],[f369,f258]) ).

fof(f258,plain,
    ( ~ relation_like(sK9)
    | spl17_12 ),
    inference(resolution,[],[f256,f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ilf_type(X0,binary_relation_type)
      | ~ relation_like(X0) ),
    inference(resolution,[],[f132,f113]) ).

fof(f113,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).

fof(f132,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ~ relation_like(X0)
      | ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ( ilf_type(X0,set_type)
          & relation_like(X0) )
      <=> ilf_type(X0,binary_relation_type) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ( ilf_type(X0,set_type)
          & relation_like(X0) )
      <=> ilf_type(X0,binary_relation_type) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).

fof(f256,plain,
    ( ~ ilf_type(sK9,binary_relation_type)
    | spl17_12 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f254,plain,
    ( spl17_12
  <=> ilf_type(sK9,binary_relation_type) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).

fof(f369,plain,
    ( relation_like(sK9)
    | ~ spl17_20 ),
    inference(resolution,[],[f363,f146]) ).

fof(f146,plain,
    ilf_type(sK9,sF16),
    inference(definition_folding,[],[f104,f145]) ).

fof(f145,plain,
    sF16 = relation_type(empty_set,sK8),
    introduced(function_definition,[]) ).

fof(f104,plain,
    ilf_type(sK9,relation_type(empty_set,sK8)),
    inference(cnf_transformation,[],[f57]) ).

fof(f363,plain,
    ( ! [X1] :
        ( ~ ilf_type(X1,sF16)
        | relation_like(X1) )
    | ~ spl17_20 ),
    inference(avatar_component_clause,[],[f362]) ).

fof(f362,plain,
    ( spl17_20
  <=> ! [X1] :
        ( ~ ilf_type(X1,sF16)
        | relation_like(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).

fof(f364,plain,
    ( ~ spl17_5
    | ~ spl17_4
    | spl17_20 ),
    inference(avatar_split_clause,[],[f359,f362,f183,f187]) ).

fof(f187,plain,
    ( spl17_5
  <=> ilf_type(sK8,set_type) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).

fof(f183,plain,
    ( spl17_4
  <=> ilf_type(empty_set,set_type) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).

fof(f359,plain,
    ! [X1] :
      ( ~ ilf_type(X1,sF16)
      | ~ ilf_type(empty_set,set_type)
      | relation_like(X1)
      | ~ ilf_type(sK8,set_type) ),
    inference(superposition,[],[f356,f145]) ).

fof(f356,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | relation_like(X2)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(duplicate_literal_removal,[],[f355]) ).

fof(f355,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | relation_like(X2) ),
    inference(resolution,[],[f123,f114]) ).

fof(f114,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | relation_like(X2) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( relation_like(X2)
              | ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ) ) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,subset_type(cross_product(X0,X1)))
             => relation_like(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).

fof(f123,plain,
    ! [X3,X0,X1] :
      ( ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X3,relation_type(X0,X1)) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ! [X3] :
                ( ~ ilf_type(X3,relation_type(X0,X1))
                | ilf_type(X3,subset_type(cross_product(X0,X1))) )
            & ! [X2] :
                ( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
                | ilf_type(X2,relation_type(X0,X1)) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
               => ilf_type(X2,relation_type(X0,X1)) )
            & ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
               => ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).

fof(f257,plain,
    ( spl17_11
    | ~ spl17_12
    | ~ spl17_9 ),
    inference(avatar_split_clause,[],[f248,f233,f254,f250]) ).

fof(f233,plain,
    ( spl17_9
  <=> ! [X1] :
        ( subset(domain_of(X1),empty_set)
        | ~ ilf_type(X1,sF16) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).

fof(f248,plain,
    ( ~ ilf_type(sK9,binary_relation_type)
    | empty_set = sK9
    | ~ spl17_9 ),
    inference(trivial_inequality_removal,[],[f247]) ).

fof(f247,plain,
    ( empty_set != empty_set
    | empty_set = sK9
    | ~ ilf_type(sK9,binary_relation_type)
    | ~ spl17_9 ),
    inference(superposition,[],[f136,f242]) ).

fof(f242,plain,
    ( empty_set = domain_of(sK9)
    | ~ spl17_9 ),
    inference(resolution,[],[f241,f146]) ).

fof(f241,plain,
    ( ! [X0] :
        ( ~ ilf_type(X0,sF16)
        | empty_set = domain_of(X0) )
    | ~ spl17_9 ),
    inference(resolution,[],[f240,f113]) ).

fof(f240,plain,
    ( ! [X0] :
        ( ~ ilf_type(domain_of(X0),set_type)
        | ~ ilf_type(X0,sF16)
        | empty_set = domain_of(X0) )
    | ~ spl17_9 ),
    inference(resolution,[],[f234,f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | ~ ilf_type(X0,set_type)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | empty_set = X0
      | ~ subset(X0,empty_set) ),
    inference(flattening,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ subset(X0,empty_set)
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( subset(X0,empty_set)
       => empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f234,plain,
    ( ! [X1] :
        ( subset(domain_of(X1),empty_set)
        | ~ ilf_type(X1,sF16) )
    | ~ spl17_9 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f136,plain,
    ! [X0] :
      ( empty_set != domain_of(X0)
      | ~ ilf_type(X0,binary_relation_type)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( empty_set = X0
      | ( empty_set != domain_of(X0)
        & empty_set != range_of(X0) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( empty_set = X0
      | ( empty_set != domain_of(X0)
        & empty_set != range_of(X0) )
      | ~ ilf_type(X0,binary_relation_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,binary_relation_type)
     => ( ( empty_set = domain_of(X0)
          | empty_set = range_of(X0) )
       => empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(f235,plain,
    ( spl17_9
    | ~ spl17_4
    | ~ spl17_5 ),
    inference(avatar_split_clause,[],[f230,f187,f183,f233]) ).

fof(f230,plain,
    ! [X1] :
      ( ~ ilf_type(sK8,set_type)
      | ~ ilf_type(empty_set,set_type)
      | subset(domain_of(X1),empty_set)
      | ~ ilf_type(X1,sF16) ),
    inference(superposition,[],[f101,f145]) ).

fof(f101,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type)
      | subset(domain_of(X2),X0)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ( subset(range_of(X2),X1)
                & subset(domain_of(X2),X0) )
              | ~ ilf_type(X2,relation_type(X0,X1)) ) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ( subset(range_of(X2),X1)
                & subset(domain_of(X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

fof(f203,plain,
    spl17_4,
    inference(avatar_contradiction_clause,[],[f202]) ).

fof(f202,plain,
    ( $false
    | spl17_4 ),
    inference(resolution,[],[f185,f113]) ).

fof(f185,plain,
    ( ~ ilf_type(empty_set,set_type)
    | spl17_4 ),
    inference(avatar_component_clause,[],[f183]) ).

fof(f201,plain,
    spl17_5,
    inference(avatar_contradiction_clause,[],[f200]) ).

fof(f200,plain,
    ( $false
    | spl17_5 ),
    inference(resolution,[],[f189,f113]) ).

fof(f189,plain,
    ( ~ ilf_type(sK8,set_type)
    | spl17_5 ),
    inference(avatar_component_clause,[],[f187]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % 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 : n005.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 14:10:33 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (29646)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)
% 0.20/0.50  % (29649)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (29648)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)
% 0.20/0.51  % (29669)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.51  % (29656)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51  % (29667)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.51  TRYING [1]
% 0.20/0.51  TRYING [2]
% 0.20/0.51  % (29655)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51  % (29654)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52  % (29663)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.52  % (29673)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.52  % (29654)First to succeed.
% 0.20/0.52  % (29647)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (29665)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.52  % (29657)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.52  % (29659)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (29654)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (29654)------------------------------
% 0.20/0.53  % (29654)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (29654)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (29654)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (29654)Memory used [KB]: 5628
% 0.20/0.53  % (29654)Time elapsed: 0.120 s
% 0.20/0.53  % (29654)Instructions burned: 10 (million)
% 0.20/0.53  % (29654)------------------------------
% 0.20/0.53  % (29654)------------------------------
% 0.20/0.53  % (29642)Success in time 0.173 s
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