TSTP Solution File: SET012+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET012+4 : 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 : n006.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 18:18:20 EDT 2022

% Result   : Theorem 0.16s 0.48s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   54 (   5 unt;   0 def)
%            Number of atoms       :  140 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  140 (  54   ~;  49   |;  22   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   74 (  65   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f134,plain,
    $false,
    inference(avatar_sat_refutation,[],[f56,f97,f133]) ).

fof(f133,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f132]) ).

fof(f132,plain,
    ( $false
    | spl3_2 ),
    inference(subsumption_resolution,[],[f126,f117]) ).

fof(f117,plain,
    ( ~ member(sK0(difference(sK1,difference(sK1,sK2)),sK2),difference(sK1,sK2))
    | spl3_2 ),
    inference(unit_resulting_resolution,[],[f105,f37]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X1,X0))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X1,X0))
        | ~ member(X2,X1)
        | member(X2,X0) )
      & ( ( member(X2,X1)
          & ~ member(X2,X0) )
        | ~ member(X2,difference(X1,X0)) ) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X1,X0))
        | ~ member(X2,X1)
        | member(X2,X0) )
      & ( ( member(X2,X1)
          & ~ member(X2,X0) )
        | ~ member(X2,difference(X1,X0)) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( member(X2,difference(X1,X0))
    <=> ( member(X2,X1)
        & ~ member(X2,X0) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X3,X1] :
      ( ( ~ member(X1,X0)
        & member(X1,X3) )
    <=> member(X1,difference(X3,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).

fof(f105,plain,
    ( member(sK0(difference(sK1,difference(sK1,sK2)),sK2),difference(sK1,difference(sK1,sK2)))
    | spl3_2 ),
    inference(resolution,[],[f55,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f55,plain,
    ( ~ subset(difference(sK1,difference(sK1,sK2)),sK2)
    | spl3_2 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f53,plain,
    ( spl3_2
  <=> subset(difference(sK1,difference(sK1,sK2)),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f126,plain,
    ( member(sK0(difference(sK1,difference(sK1,sK2)),sK2),difference(sK1,sK2))
    | spl3_2 ),
    inference(unit_resulting_resolution,[],[f102,f116,f39]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,X1)
      | member(X2,difference(X1,X0)) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f116,plain,
    ( member(sK0(difference(sK1,difference(sK1,sK2)),sK2),sK1)
    | spl3_2 ),
    inference(unit_resulting_resolution,[],[f105,f38]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,difference(X1,X0)) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f102,plain,
    ( ~ member(sK0(difference(sK1,difference(sK1,sK2)),sK2),sK2)
    | spl3_2 ),
    inference(unit_resulting_resolution,[],[f55,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f97,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f96]) ).

fof(f96,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f95,f67]) ).

fof(f67,plain,
    ( member(sK0(sK2,difference(sK1,difference(sK1,sK2))),sK1)
    | spl3_1 ),
    inference(unit_resulting_resolution,[],[f60,f40]) ).

fof(f40,plain,
    ! [X0] :
      ( member(X0,sK1)
      | ~ member(X0,sK2) ),
    inference(resolution,[],[f34,f31]) ).

fof(f31,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X0)
      | ~ subset(X0,X1)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f34,plain,
    subset(sK2,sK1),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( ~ equal_set(difference(sK1,difference(sK1,sK2)),sK2)
    & subset(sK2,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f26,f27]) ).

fof(f27,plain,
    ( ? [X0,X1] :
        ( ~ equal_set(difference(X0,difference(X0,X1)),X1)
        & subset(X1,X0) )
   => ( ~ equal_set(difference(sK1,difference(sK1,sK2)),sK2)
      & subset(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1] :
      ( ~ equal_set(difference(X0,difference(X0,X1)),X1)
      & subset(X1,X0) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ? [X1,X0] :
      ( ~ equal_set(difference(X1,difference(X1,X0)),X0)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => equal_set(difference(X1,difference(X1,X0)),X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X3] :
        ( subset(X0,X3)
       => equal_set(difference(X3,difference(X3,X0)),X0) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0,X3] :
      ( subset(X0,X3)
     => equal_set(difference(X3,difference(X3,X0)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI23) ).

fof(f60,plain,
    ( member(sK0(sK2,difference(sK1,difference(sK1,sK2))),sK2)
    | spl3_1 ),
    inference(resolution,[],[f51,f32]) ).

fof(f51,plain,
    ( ~ subset(sK2,difference(sK1,difference(sK1,sK2)))
    | spl3_1 ),
    inference(avatar_component_clause,[],[f49]) ).

fof(f49,plain,
    ( spl3_1
  <=> subset(sK2,difference(sK1,difference(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f95,plain,
    ( ~ member(sK0(sK2,difference(sK1,difference(sK1,sK2))),sK1)
    | spl3_1 ),
    inference(subsumption_resolution,[],[f89,f68]) ).

fof(f68,plain,
    ( ! [X0] : ~ member(sK0(sK2,difference(sK1,difference(sK1,sK2))),difference(X0,sK2))
    | spl3_1 ),
    inference(unit_resulting_resolution,[],[f60,f37]) ).

fof(f89,plain,
    ( member(sK0(sK2,difference(sK1,difference(sK1,sK2))),difference(sK1,sK2))
    | ~ member(sK0(sK2,difference(sK1,difference(sK1,sK2))),sK1)
    | spl3_1 ),
    inference(resolution,[],[f57,f39]) ).

fof(f57,plain,
    ( ~ member(sK0(sK2,difference(sK1,difference(sK1,sK2))),difference(sK1,difference(sK1,sK2)))
    | spl3_1 ),
    inference(unit_resulting_resolution,[],[f51,f33]) ).

fof(f56,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f47,f53,f49]) ).

fof(f47,plain,
    ( ~ subset(difference(sK1,difference(sK1,sK2)),sK2)
    | ~ subset(sK2,difference(sK1,difference(sK1,sK2))) ),
    inference(resolution,[],[f35,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( equal_set(X1,X0)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | equal_set(X1,X0)
      | ~ subset(X1,X0) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0] :
      ( equal_set(X1,X0)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( equal_set(X1,X0)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( equal_set(X0,X1)
    <=> ( subset(X0,X1)
        & subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).

fof(f35,plain,
    ~ equal_set(difference(sK1,difference(sK1,sK2)),sK2),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.30  % Computer : n006.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Aug 30 12:50:55 EDT 2022
% 0.10/0.31  % CPUTime    : 
% 0.16/0.44  % (10314)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.46  % (10305)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.16/0.46  % (10314)Instruction limit reached!
% 0.16/0.46  % (10314)------------------------------
% 0.16/0.46  % (10314)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.46  % (10314)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.46  % (10314)Termination reason: Unknown
% 0.16/0.46  % (10314)Termination phase: Saturation
% 0.16/0.46  
% 0.16/0.46  % (10314)Memory used [KB]: 5884
% 0.16/0.46  % (10314)Time elapsed: 0.096 s
% 0.16/0.46  % (10314)Instructions burned: 3 (million)
% 0.16/0.46  % (10314)------------------------------
% 0.16/0.46  % (10314)------------------------------
% 0.16/0.46  % (10323)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.16/0.46  % (10315)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.47  % (10306)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.16/0.47  % (10323)Refutation not found, incomplete strategy% (10323)------------------------------
% 0.16/0.47  % (10323)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48  % (10315)Instruction limit reached!
% 0.16/0.48  % (10315)------------------------------
% 0.16/0.48  % (10315)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48  % (10323)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.48  % (10323)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.48  
% 0.16/0.48  % (10323)Memory used [KB]: 1407
% 0.16/0.48  % (10323)Time elapsed: 0.059 s
% 0.16/0.48  % (10323)Instructions burned: 1 (million)
% 0.16/0.48  % (10323)------------------------------
% 0.16/0.48  % (10323)------------------------------
% 0.16/0.48  % (10315)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.48  % (10315)Termination reason: Unknown
% 0.16/0.48  % (10315)Termination phase: Saturation
% 0.16/0.48  
% 0.16/0.48  % (10315)Memory used [KB]: 6012
% 0.16/0.48  % (10315)Time elapsed: 0.073 s
% 0.16/0.48  % (10315)Instructions burned: 7 (million)
% 0.16/0.48  % (10315)------------------------------
% 0.16/0.48  % (10315)------------------------------
% 0.16/0.48  % (10306)First to succeed.
% 0.16/0.48  % (10306)Refutation found. Thanks to Tanya!
% 0.16/0.48  % SZS status Theorem for theBenchmark
% 0.16/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48  % (10306)------------------------------
% 0.16/0.48  % (10306)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48  % (10306)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.48  % (10306)Termination reason: Refutation
% 0.16/0.48  
% 0.16/0.48  % (10306)Memory used [KB]: 5884
% 0.16/0.48  % (10306)Time elapsed: 0.074 s
% 0.16/0.49  % (10306)Instructions burned: 3 (million)
% 0.16/0.49  % (10306)------------------------------
% 0.16/0.49  % (10306)------------------------------
% 0.16/0.49  % (10298)Success in time 0.17 s
%------------------------------------------------------------------------------