TSTP Solution File: SET691+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET691+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_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 18:25:21 EDT 2022

% Result   : Theorem 0.19s 0.56s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   31 (   8 unt;   0 def)
%            Number of atoms       :   91 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   99 (  39   ~;  32   |;  18   &)
%                                         (   6 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   43 (  37   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f131,plain,
    $false,
    inference(subsumption_resolution,[],[f130,f105]) ).

fof(f105,plain,
    ! [X9] : subset(empty_set,X9),
    inference(resolution,[],[f77,f89]) ).

fof(f89,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f77,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( member(sK2(X0,X1),X0)
          & ~ member(sK2(X0,X1),X1) ) )
      & ( ! [X3] :
            ( ~ member(X3,X0)
            | member(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f45,f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X0)
          & ~ member(X2,X1) )
     => ( member(sK2(X0,X1),X0)
        & ~ member(sK2(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) )
      & ( ! [X3] :
            ( ~ member(X3,X0)
            | member(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) )
      & ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f130,plain,
    ~ subset(empty_set,sK3),
    inference(subsumption_resolution,[],[f129,f94]) ).

fof(f94,plain,
    subset(sK3,empty_set),
    inference(duplicate_literal_removal,[],[f93]) ).

fof(f93,plain,
    ( subset(sK3,empty_set)
    | subset(sK3,empty_set) ),
    inference(resolution,[],[f84,f78]) ).

fof(f78,plain,
    ( equal_set(sK3,empty_set)
    | subset(sK3,empty_set) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ( ( ~ subset(sK3,empty_set)
      | ~ equal_set(sK3,empty_set) )
    & ( subset(sK3,empty_set)
      | equal_set(sK3,empty_set) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f48,f49]) ).

fof(f49,plain,
    ( ? [X0] :
        ( ( ~ subset(X0,empty_set)
          | ~ equal_set(X0,empty_set) )
        & ( subset(X0,empty_set)
          | equal_set(X0,empty_set) ) )
   => ( ( ~ subset(sK3,empty_set)
        | ~ equal_set(sK3,empty_set) )
      & ( subset(sK3,empty_set)
        | equal_set(sK3,empty_set) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ? [X0] :
      ( ( ~ subset(X0,empty_set)
        | ~ equal_set(X0,empty_set) )
      & ( subset(X0,empty_set)
        | equal_set(X0,empty_set) ) ),
    inference(nnf_transformation,[],[f24]) ).

fof(f24,plain,
    ? [X0] :
      ( equal_set(X0,empty_set)
    <~> subset(X0,empty_set) ),
    inference(ennf_transformation,[],[f13]) ).

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

fof(f12,conjecture,
    ! [X0] :
      ( equal_set(X0,empty_set)
    <=> subset(X0,empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI16) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ equal_set(X1,X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | ~ equal_set(X1,X0) )
      & ( equal_set(X1,X0)
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | ~ equal_set(X1,X0) )
      & ( equal_set(X1,X0)
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> equal_set(X1,X0) ),
    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(f129,plain,
    ( ~ subset(sK3,empty_set)
    | ~ subset(empty_set,sK3) ),
    inference(resolution,[],[f83,f96]) ).

fof(f96,plain,
    ~ equal_set(sK3,empty_set),
    inference(resolution,[],[f94,f79]) ).

fof(f79,plain,
    ( ~ subset(sK3,empty_set)
    | ~ equal_set(sK3,empty_set) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( equal_set(X1,X0)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET691+4 : 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_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 14:13:35 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.19/0.55  % (11127)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.55  % (11126)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)
% 0.19/0.55  TRYING [1]
% 0.19/0.55  % (11128)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.55  % (11127)Instruction limit reached!
% 0.19/0.55  % (11127)------------------------------
% 0.19/0.55  % (11127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (11144)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.55  % (11128)Instruction limit reached!
% 0.19/0.55  % (11128)------------------------------
% 0.19/0.55  % (11128)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (11128)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (11128)Termination reason: Unknown
% 0.19/0.55  % (11128)Termination phase: Property scanning
% 0.19/0.55  
% 0.19/0.55  % (11128)Memory used [KB]: 895
% 0.19/0.55  % (11128)Time elapsed: 0.004 s
% 0.19/0.55  % (11128)Instructions burned: 2 (million)
% 0.19/0.55  % (11128)------------------------------
% 0.19/0.55  % (11128)------------------------------
% 0.19/0.55  % (11142)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)
% 0.19/0.56  % (11143)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.56  % (11134)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)
% 0.19/0.56  TRYING [2]
% 0.19/0.56  % (11135)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)
% 0.19/0.56  TRYING [3]
% 0.19/0.56  % (11136)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)
% 0.19/0.56  % (11135)First to succeed.
% 0.19/0.56  % (11127)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56  % (11127)Termination reason: Unknown
% 0.19/0.56  % (11127)Termination phase: Saturation
% 0.19/0.56  
% 0.19/0.56  % (11127)Memory used [KB]: 5500
% 0.19/0.56  % (11127)Time elapsed: 0.130 s
% 0.19/0.56  % (11127)Instructions burned: 7 (million)
% 0.19/0.56  % (11127)------------------------------
% 0.19/0.56  % (11127)------------------------------
% 0.19/0.56  % (11135)Refutation found. Thanks to Tanya!
% 0.19/0.56  % SZS status Theorem for theBenchmark
% 0.19/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.56  % (11135)------------------------------
% 0.19/0.56  % (11135)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56  % (11135)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56  % (11135)Termination reason: Refutation
% 0.19/0.56  
% 0.19/0.56  % (11135)Memory used [KB]: 1023
% 0.19/0.56  % (11135)Time elapsed: 0.143 s
% 0.19/0.56  % (11135)Instructions burned: 3 (million)
% 0.19/0.56  % (11135)------------------------------
% 0.19/0.56  % (11135)------------------------------
% 0.19/0.56  % (11119)Success in time 0.207 s
%------------------------------------------------------------------------------