TSTP Solution File: SET664+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET664+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_uns --cores 0 -t %d %s

% Computer : n003.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 18:21:48 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   50 (  11 unt;   0 def)
%            Number of atoms       :  184 (  32 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  205 (  71   ~;  58   |;  44   &)
%                                         (   2 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   74 (  59   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f280,plain,
    $false,
    inference(subsumption_resolution,[],[f279,f229]) ).

fof(f229,plain,
    empty_set = range_of(sK10),
    inference(subsumption_resolution,[],[f224,f140]) ).

fof(f140,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(f224,plain,
    ( empty_set = range_of(sK10)
    | ~ ilf_type(range_of(sK10),set_type) ),
    inference(resolution,[],[f193,f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | ~ ilf_type(X0,set_type)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ ilf_type(X0,set_type)
      | ~ subset(X0,empty_set) ),
    inference(flattening,[],[f78]) ).

fof(f78,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(f193,plain,
    subset(range_of(sK10),empty_set),
    inference(unit_resulting_resolution,[],[f140,f140,f167,f136]) ).

fof(f136,plain,
    ! [X2,X0,X1] :
      ( subset(range_of(X2),X1)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,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(f167,plain,
    ilf_type(sK10,relation_type(sK9,empty_set)),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ( ilf_type(sK8,set_type)
    & ilf_type(sK9,set_type)
    & ilf_type(sK10,relation_type(sK9,sK8))
    & ilf_type(sK10,relation_type(sK9,empty_set))
    & empty_set != sK10 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f43,f106,f105,f104]) ).

fof(f104,plain,
    ( ? [X0] :
        ( ilf_type(X0,set_type)
        & ? [X1] :
            ( ilf_type(X1,set_type)
            & ? [X2] :
                ( ilf_type(X2,relation_type(X1,X0))
                & ilf_type(X2,relation_type(X1,empty_set))
                & empty_set != X2 ) ) )
   => ( ilf_type(sK8,set_type)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ? [X2] :
              ( ilf_type(X2,relation_type(X1,sK8))
              & ilf_type(X2,relation_type(X1,empty_set))
              & empty_set != X2 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ( ? [X1] :
        ( ilf_type(X1,set_type)
        & ? [X2] :
            ( ilf_type(X2,relation_type(X1,sK8))
            & ilf_type(X2,relation_type(X1,empty_set))
            & empty_set != X2 ) )
   => ( ilf_type(sK9,set_type)
      & ? [X2] :
          ( ilf_type(X2,relation_type(sK9,sK8))
          & ilf_type(X2,relation_type(sK9,empty_set))
          & empty_set != X2 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ( ? [X2] :
        ( ilf_type(X2,relation_type(sK9,sK8))
        & ilf_type(X2,relation_type(sK9,empty_set))
        & empty_set != X2 )
   => ( ilf_type(sK10,relation_type(sK9,sK8))
      & ilf_type(sK10,relation_type(sK9,empty_set))
      & empty_set != sK10 ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ? [X2] :
              ( ilf_type(X2,relation_type(X1,X0))
              & ilf_type(X2,relation_type(X1,empty_set))
              & empty_set != X2 ) ) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( empty_set != X2
              & ilf_type(X2,relation_type(X1,empty_set))
              & ilf_type(X2,relation_type(X1,X0)) )
          & 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(X1,X0))
               => ( ilf_type(X2,relation_type(X1,empty_set))
                 => 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(X1,X0))
             => ( ilf_type(X2,relation_type(X1,empty_set))
               => empty_set = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).

fof(f279,plain,
    empty_set != range_of(sK10),
    inference(subsumption_resolution,[],[f276,f166]) ).

fof(f166,plain,
    empty_set != sK10,
    inference(cnf_transformation,[],[f107]) ).

fof(f276,plain,
    ( empty_set = sK10
    | empty_set != range_of(sK10) ),
    inference(resolution,[],[f268,f162]) ).

fof(f162,plain,
    ! [X0] :
      ( ~ ilf_type(X0,binary_relation_type)
      | empty_set = X0
      | empty_set != range_of(X0) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ ilf_type(X0,binary_relation_type)
      | ( empty_set != domain_of(X0)
        & empty_set != range_of(X0) ) ),
    inference(flattening,[],[f70]) ).

fof(f70,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(f268,plain,
    ilf_type(sK10,binary_relation_type),
    inference(unit_resulting_resolution,[],[f140,f260,f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ilf_type(X0,binary_relation_type)
      | ~ relation_like(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(duplicate_literal_removal,[],[f155]) ).

fof(f155,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ~ relation_like(X0)
      | ilf_type(X0,binary_relation_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ( ilf_type(X0,binary_relation_type)
          | ~ ilf_type(X0,set_type)
          | ~ relation_like(X0) )
        & ( ( ilf_type(X0,set_type)
            & relation_like(X0) )
          | ~ ilf_type(X0,binary_relation_type) ) ) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ( ilf_type(X0,binary_relation_type)
          | ~ ilf_type(X0,set_type)
          | ~ relation_like(X0) )
        & ( ( ilf_type(X0,set_type)
            & relation_like(X0) )
          | ~ ilf_type(X0,binary_relation_type) ) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ilf_type(X0,binary_relation_type)
      <=> ( ilf_type(X0,set_type)
          & relation_like(X0) ) ) ),
    inference(ennf_transformation,[],[f14]) ).

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

fof(f260,plain,
    relation_like(sK10),
    inference(subsumption_resolution,[],[f259,f140]) ).

fof(f259,plain,
    ( relation_like(sK10)
    | ~ ilf_type(sK9,set_type) ),
    inference(subsumption_resolution,[],[f256,f140]) ).

fof(f256,plain,
    ( ~ ilf_type(empty_set,set_type)
    | relation_like(sK10)
    | ~ ilf_type(sK9,set_type) ),
    inference(resolution,[],[f202,f152]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | relation_like(X2) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [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) ) ) ),
    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(f202,plain,
    ilf_type(sK10,subset_type(cross_product(sK9,empty_set))),
    inference(subsumption_resolution,[],[f201,f140]) ).

fof(f201,plain,
    ( ilf_type(sK10,subset_type(cross_product(sK9,empty_set)))
    | ~ ilf_type(empty_set,set_type) ),
    inference(subsumption_resolution,[],[f198,f140]) ).

fof(f198,plain,
    ( ilf_type(sK10,subset_type(cross_product(sK9,empty_set)))
    | ~ ilf_type(sK9,set_type)
    | ~ ilf_type(empty_set,set_type) ),
    inference(resolution,[],[f167,f121]) ).

fof(f121,plain,
    ! [X3,X0,X1] :
      ( ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
                | ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
            & ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X0,X1)))
                | ~ ilf_type(X3,relation_type(X0,X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [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) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X0,X1)))
               => ilf_type(X3,relation_type(X0,X1)) )
            & ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ilf_type(X2,subset_type(cross_product(X0,X1))) ) ) ) ),
    inference(rectify,[],[f7]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem    : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% 0.02/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:11:07 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (1566)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50  % (1575)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.50  % (1575)Instruction limit reached!
% 0.19/0.50  % (1575)------------------------------
% 0.19/0.50  % (1575)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (1574)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (1574)Instruction limit reached!
% 0.19/0.51  % (1574)------------------------------
% 0.19/0.51  % (1574)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (1561)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.51  % (1574)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (1574)Termination reason: Unknown
% 0.19/0.51  % (1574)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (1574)Memory used [KB]: 6012
% 0.19/0.51  % (1574)Time elapsed: 0.113 s
% 0.19/0.51  % (1574)Instructions burned: 7 (million)
% 0.19/0.51  % (1574)------------------------------
% 0.19/0.51  % (1574)------------------------------
% 0.19/0.51  % (1585)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.51  % (1565)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (1566)Refutation not found, incomplete strategy% (1566)------------------------------
% 0.19/0.51  % (1566)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (1566)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (1566)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (1566)Memory used [KB]: 5884
% 0.19/0.51  % (1566)Time elapsed: 0.112 s
% 0.19/0.51  % (1566)Instructions burned: 2 (million)
% 0.19/0.51  % (1566)------------------------------
% 0.19/0.51  % (1566)------------------------------
% 0.19/0.51  % (1576)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (1575)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (1575)Termination reason: Unknown
% 0.19/0.51  % (1575)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (1575)Memory used [KB]: 1663
% 0.19/0.51  % (1575)Time elapsed: 0.104 s
% 0.19/0.51  % (1575)Instructions burned: 16 (million)
% 0.19/0.51  % (1575)------------------------------
% 0.19/0.51  % (1575)------------------------------
% 0.19/0.51  % (1565)Refutation not found, incomplete strategy% (1565)------------------------------
% 0.19/0.51  % (1565)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (1584)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52  % (1565)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (1565)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (1565)Memory used [KB]: 6012
% 0.19/0.52  % (1565)Time elapsed: 0.113 s
% 0.19/0.52  % (1565)Instructions burned: 5 (million)
% 0.19/0.52  % (1565)------------------------------
% 0.19/0.52  % (1565)------------------------------
% 0.19/0.52  % (1584)First to succeed.
% 0.19/0.52  % (1584)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (1584)------------------------------
% 0.19/0.52  % (1584)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (1584)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (1584)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (1584)Memory used [KB]: 6140
% 0.19/0.52  % (1584)Time elapsed: 0.131 s
% 0.19/0.52  % (1584)Instructions burned: 9 (million)
% 0.19/0.52  % (1584)------------------------------
% 0.19/0.52  % (1584)------------------------------
% 0.19/0.52  % (1557)Success in time 0.174 s
%------------------------------------------------------------------------------