TSTP Solution File: SET764+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 : Tue Apr 30 15:13:08 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   35 (   9 unt;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  107 (  42   ~;  28   |;  24   &)
%                                         (   5 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   84 (  70   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f575,plain,
    $false,
    inference(resolution,[],[f570,f200]) ).

fof(f200,plain,
    ~ subset(inverse_image2(sK0,empty_set),empty_set),
    inference(subsumption_resolution,[],[f199,f177]) ).

fof(f177,plain,
    ! [X0] : subset(empty_set,X0),
    inference(resolution,[],[f124,f122]) ).

fof(f122,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

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

fof(f124,plain,
    ! [X0,X1] :
      ( member(sK3(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK3(X0,X1),X1)
          & member(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f74,f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,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,[],[f73]) ).

fof(f73,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,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f199,plain,
    ( ~ subset(empty_set,inverse_image2(sK0,empty_set))
    | ~ subset(inverse_image2(sK0,empty_set),empty_set) ),
    inference(resolution,[],[f126,f121]) ).

fof(f121,plain,
    ~ equal_set(inverse_image2(sK0,empty_set),empty_set),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( ~ equal_set(inverse_image2(sK0,empty_set),empty_set)
    & maps(sK0,sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f60,f71]) ).

fof(f71,plain,
    ( ? [X0,X1,X2] :
        ( ~ equal_set(inverse_image2(X0,empty_set),empty_set)
        & maps(X0,X1,X2) )
   => ( ~ equal_set(inverse_image2(sK0,empty_set),empty_set)
      & maps(sK0,sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ? [X0,X1,X2] :
      ( ~ equal_set(inverse_image2(X0,empty_set),empty_set)
      & maps(X0,X1,X2) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ~ ! [X0,X1,X2] :
        ( maps(X0,X1,X2)
       => equal_set(inverse_image2(X0,empty_set),empty_set) ),
    inference(rectify,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ! [X5,X0,X1] :
        ( maps(X5,X0,X1)
       => equal_set(inverse_image2(X5,empty_set),empty_set) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ! [X5,X0,X1] :
      ( maps(X5,X0,X1)
     => equal_set(inverse_image2(X5,empty_set),empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa14) ).

fof(f126,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

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

fof(f570,plain,
    ! [X0,X1] : subset(inverse_image2(X0,empty_set),X1),
    inference(resolution,[],[f551,f124]) ).

fof(f551,plain,
    ! [X0,X1] : ~ member(X0,inverse_image2(X1,empty_set)),
    inference(resolution,[],[f155,f122]) ).

fof(f155,plain,
    ! [X2,X0,X1] :
      ( member(sK8(X0,X1,X2),X1)
      | ~ member(X2,inverse_image2(X0,X1)) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,inverse_image2(X0,X1))
        | ! [X3] :
            ( ~ apply(X0,X2,X3)
            | ~ member(X3,X1) ) )
      & ( ( apply(X0,X2,sK8(X0,X1,X2))
          & member(sK8(X0,X1,X2),X1) )
        | ~ member(X2,inverse_image2(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f102,f103]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( apply(X0,X2,X4)
          & member(X4,X1) )
     => ( apply(X0,X2,sK8(X0,X1,X2))
        & member(sK8(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,inverse_image2(X0,X1))
        | ! [X3] :
            ( ~ apply(X0,X2,X3)
            | ~ member(X3,X1) ) )
      & ( ? [X4] :
            ( apply(X0,X2,X4)
            & member(X4,X1) )
        | ~ member(X2,inverse_image2(X0,X1)) ) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,inverse_image2(X0,X1))
        | ! [X3] :
            ( ~ apply(X0,X2,X3)
            | ~ member(X3,X1) ) )
      & ( ? [X3] :
            ( apply(X0,X2,X3)
            & member(X3,X1) )
        | ~ member(X2,inverse_image2(X0,X1)) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( member(X2,inverse_image2(X0,X1))
    <=> ? [X3] :
          ( apply(X0,X2,X3)
          & member(X3,X1) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X5,X1,X2] :
      ( member(X2,inverse_image2(X5,X1))
    <=> ? [X4] :
          ( apply(X5,X2,X4)
          & member(X4,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Apr 30 01:08:03 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (2349)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36  % (2353)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.36  TRYING [1]
% 0.21/0.36  TRYING [2]
% 0.21/0.36  % (2352)WARNING: value z3 for option sas not known
% 0.21/0.36  % (2352)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.36  % (2351)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37  % (2350)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37  % (2356)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.37  % (2355)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37  % (2354)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37  TRYING [3]
% 0.21/0.38  TRYING [1]
% 0.21/0.38  % (2352)First to succeed.
% 0.21/0.38  TRYING [2]
% 0.21/0.38  % (2352)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (2352)------------------------------
% 0.21/0.38  % (2352)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38  % (2352)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (2352)Memory used [KB]: 1091
% 0.21/0.38  % (2352)Time elapsed: 0.015 s
% 0.21/0.38  % (2352)Instructions burned: 21 (million)
% 0.21/0.38  % (2352)------------------------------
% 0.21/0.38  % (2352)------------------------------
% 0.21/0.38  % (2349)Success in time 0.032 s
%------------------------------------------------------------------------------