TSTP Solution File: SET632+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET632+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 : n025.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 18:21:41 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   60 (  11 unt;   0 def)
%            Number of atoms       :  176 (  18 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  183 (  67   ~;  53   |;  47   &)
%                                         (   9 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   93 (  73   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f111,plain,
    $false,
    inference(avatar_sat_refutation,[],[f71,f77,f110]) ).

fof(f110,plain,
    spl6_2,
    inference(avatar_contradiction_clause,[],[f109]) ).

fof(f109,plain,
    ( $false
    | spl6_2 ),
    inference(subsumption_resolution,[],[f106,f90]) ).

fof(f90,plain,
    ( member(sK4(empty_set,sK2),sK0)
    | spl6_2 ),
    inference(resolution,[],[f58,f81]) ).

fof(f81,plain,
    ( member(sK4(empty_set,sK2),sK2)
    | spl6_2 ),
    inference(resolution,[],[f70,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | member(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( member(sK4(X0,X1),X1)
          & ~ member(sK4(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f26,f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & ~ member(X3,X0) )
     => ( member(sK4(X0,X1),X1)
        & ~ member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f70,plain,
    ( ~ subset(sK2,empty_set)
    | spl6_2 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f68,plain,
    ( spl6_2
  <=> subset(sK2,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ member(X0,sK2)
      | member(X0,sK0) ),
    inference(resolution,[],[f34,f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,X0)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f34,plain,
    subset(sK2,sK0),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( subset(sK2,sK1)
    & empty_set != sK2
    & subset(sK2,sK0)
    & disjoint(sK1,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0,X1,X2] :
        ( subset(X2,X1)
        & empty_set != X2
        & subset(X2,X0)
        & disjoint(X1,X0) )
   => ( subset(sK2,sK1)
      & empty_set != sK2
      & subset(sK2,sK0)
      & disjoint(sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1,X2] :
      ( subset(X2,X1)
      & empty_set != X2
      & subset(X2,X0)
      & disjoint(X1,X0) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X2,X1,X0] :
      ( subset(X0,X1)
      & empty_set != X0
      & subset(X0,X2)
      & disjoint(X1,X2) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X0,X2,X1] :
      ( empty_set != X0
      & subset(X0,X2)
      & disjoint(X1,X2)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( ( subset(X0,X2)
          & disjoint(X1,X2)
          & subset(X0,X1) )
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X2,X1] :
      ( ( subset(X0,X2)
        & disjoint(X1,X2)
        & subset(X0,X1) )
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th114) ).

fof(f106,plain,
    ( ~ member(sK4(empty_set,sK2),sK0)
    | spl6_2 ),
    inference(resolution,[],[f73,f98]) ).

fof(f98,plain,
    ( member(sK4(empty_set,sK2),sK1)
    | spl6_2 ),
    inference(resolution,[],[f61,f81]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ member(X0,sK2)
      | member(X0,sK1) ),
    inference(resolution,[],[f36,f43]) ).

fof(f36,plain,
    subset(sK2,sK1),
    inference(cnf_transformation,[],[f20]) ).

fof(f73,plain,
    ! [X0] :
      ( ~ member(X0,sK1)
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f55,f40]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | intersect(X0,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X0)
            | ~ member(X2,X1) ) )
      & ( ( member(sK3(X0,X1),X0)
          & member(sK3(X0,X1),X1) )
        | ~ intersect(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X0)
          & member(X3,X1) )
     => ( member(sK3(X0,X1),X0)
        & member(sK3(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X0)
            | ~ member(X2,X1) ) )
      & ( ? [X3] :
            ( member(X3,X0)
            & member(X3,X1) )
        | ~ intersect(X0,X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( ( intersect(X1,X0)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
        | ~ intersect(X1,X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] :
      ( intersect(X1,X0)
    <=> ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) )
    <=> intersect(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).

fof(f55,plain,
    ~ intersect(sK1,sK0),
    inference(resolution,[],[f33,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | ~ disjoint(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
     => ~ intersect(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> ~ intersect(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).

fof(f33,plain,
    disjoint(sK1,sK0),
    inference(cnf_transformation,[],[f20]) ).

fof(f77,plain,
    spl6_1,
    inference(avatar_contradiction_clause,[],[f76]) ).

fof(f76,plain,
    ( $false
    | spl6_1 ),
    inference(subsumption_resolution,[],[f74,f44]) ).

fof(f44,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f74,plain,
    ( member(sK4(sK2,empty_set),empty_set)
    | spl6_1 ),
    inference(resolution,[],[f66,f42]) ).

fof(f66,plain,
    ( ~ subset(empty_set,sK2)
    | spl6_1 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f64,plain,
    ( spl6_1
  <=> subset(empty_set,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f71,plain,
    ( ~ spl6_1
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f62,f68,f64]) ).

fof(f62,plain,
    ( ~ subset(sK2,empty_set)
    | ~ subset(empty_set,sK2) ),
    inference(resolution,[],[f52,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | sQ5_eqProxy(X0,X1)
      | ~ subset(X1,X0) ),
    inference(equality_proxy_replacement,[],[f47,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ5_eqProxy])]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) )
      & ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f52,plain,
    ~ sQ5_eqProxy(empty_set,sK2),
    inference(equality_proxy_replacement,[],[f35,f51]) ).

fof(f35,plain,
    empty_set != sK2,
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET632+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % 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 : n025.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 14:16:30 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.48  % (2520)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)
% 0.20/0.49  % (2520)Refutation not found, incomplete strategy% (2520)------------------------------
% 0.20/0.49  % (2520)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (2536)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)
% 0.20/0.50  % (2528)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)
% 0.20/0.50  % (2515)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50  % (2528)Instruction limit reached!
% 0.20/0.50  % (2528)------------------------------
% 0.20/0.50  % (2528)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (2523)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.50  % (2536)Refutation not found, incomplete strategy% (2536)------------------------------
% 0.20/0.50  % (2536)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (2520)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (2520)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50  % (2523)First to succeed.
% 0.20/0.50  
% 0.20/0.50  % (2520)Memory used [KB]: 6012
% 0.20/0.50  % (2520)Time elapsed: 0.103 s
% 0.20/0.50  % (2520)Instructions burned: 9 (million)
% 0.20/0.50  % (2520)------------------------------
% 0.20/0.50  % (2520)------------------------------
% 0.20/0.50  % (2523)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (2523)------------------------------
% 0.20/0.50  % (2523)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (2523)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (2523)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (2523)Memory used [KB]: 5884
% 0.20/0.50  % (2523)Time elapsed: 0.105 s
% 0.20/0.50  % (2523)Instructions burned: 2 (million)
% 0.20/0.50  % (2523)------------------------------
% 0.20/0.50  % (2523)------------------------------
% 0.20/0.50  % (2512)Success in time 0.157 s
%------------------------------------------------------------------------------