TSTP Solution File: SEU355+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU355+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 : Sun May  5 09:36:13 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   59 (  15 unt;   0 def)
%            Number of atoms       :  213 (   4 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  253 (  99   ~;  83   |;  43   &)
%                                         (  10 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  139 ( 125   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f188,plain,
    $false,
    inference(unit_resulting_resolution,[],[f172,f156,f157,f83]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0,X1,X2)
      | ~ sP2(X2,X1,X0)
      | relstr_element_smaller(X1,X0,X2) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ( ( relstr_element_smaller(X1,X0,X2)
          | ~ sP2(X2,X1,X0) )
        & ( sP2(X2,X1,X0)
          | ~ relstr_element_smaller(X1,X0,X2) ) )
      | ~ sP3(X0,X1,X2) ),
    inference(rectify,[],[f55]) ).

fof(f55,plain,
    ! [X1,X0,X2] :
      ( ( ( relstr_element_smaller(X0,X1,X2)
          | ~ sP2(X2,X0,X1) )
        & ( sP2(X2,X0,X1)
          | ~ relstr_element_smaller(X0,X1,X2) ) )
      | ~ sP3(X1,X0,X2) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X1,X0,X2] :
      ( ( relstr_element_smaller(X0,X1,X2)
      <=> sP2(X2,X0,X1) )
      | ~ sP3(X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f157,plain,
    ! [X0] : sP3(X0,sK4,sK5),
    inference(unit_resulting_resolution,[],[f71,f72,f88]) ).

fof(f88,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,the_carrier(X0))
      | sP3(X1,X0,X2)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( sP3(X1,X0,X2)
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(definition_folding,[],[f32,f44,f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( sP2(X2,X0,X1)
    <=> ! [X3] :
          ( related(X0,X2,X3)
          | ~ in(X3,X1)
          | ~ element(X3,the_carrier(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f32,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X2,X3)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X2,X3)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1,X2] :
          ( element(X2,the_carrier(X0))
         => ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( element(X3,the_carrier(X0))
               => ( in(X3,X1)
                 => related(X0,X2,X3) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).

fof(f72,plain,
    element(sK5,the_carrier(sK4)),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ( ( ~ relstr_element_smaller(sK4,empty_set,sK5)
      | ~ relstr_set_smaller(sK4,empty_set,sK5) )
    & element(sK5,the_carrier(sK4))
    & rel_str(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f28,f47,f46]) ).

fof(f46,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ relstr_element_smaller(X0,empty_set,X1)
              | ~ relstr_set_smaller(X0,empty_set,X1) )
            & element(X1,the_carrier(X0)) )
        & rel_str(X0) )
   => ( ? [X1] :
          ( ( ~ relstr_element_smaller(sK4,empty_set,X1)
            | ~ relstr_set_smaller(sK4,empty_set,X1) )
          & element(X1,the_carrier(sK4)) )
      & rel_str(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ( ? [X1] :
        ( ( ~ relstr_element_smaller(sK4,empty_set,X1)
          | ~ relstr_set_smaller(sK4,empty_set,X1) )
        & element(X1,the_carrier(sK4)) )
   => ( ( ~ relstr_element_smaller(sK4,empty_set,sK5)
        | ~ relstr_set_smaller(sK4,empty_set,sK5) )
      & element(sK5,the_carrier(sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ relstr_element_smaller(X0,empty_set,X1)
            | ~ relstr_set_smaller(X0,empty_set,X1) )
          & element(X1,the_carrier(X0)) )
      & rel_str(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( rel_str(X0)
       => ! [X1] :
            ( element(X1,the_carrier(X0))
           => ( relstr_element_smaller(X0,empty_set,X1)
              & relstr_set_smaller(X0,empty_set,X1) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ( relstr_element_smaller(X0,empty_set,X1)
            & relstr_set_smaller(X0,empty_set,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).

fof(f71,plain,
    rel_str(sK4),
    inference(cnf_transformation,[],[f48]) ).

fof(f156,plain,
    ! [X0,X1] : sP2(X0,X1,empty_set),
    inference(unit_resulting_resolution,[],[f107,f86]) ).

fof(f86,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | in(sK7(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ~ related(X1,X0,sK7(X0,X1,X2))
          & in(sK7(X0,X1,X2),X2)
          & element(sK7(X0,X1,X2),the_carrier(X1)) ) )
      & ( ! [X4] :
            ( related(X1,X0,X4)
            | ~ in(X4,X2)
            | ~ element(X4,the_carrier(X1)) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f58,f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ related(X1,X0,X3)
          & in(X3,X2)
          & element(X3,the_carrier(X1)) )
     => ( ~ related(X1,X0,sK7(X0,X1,X2))
        & in(sK7(X0,X1,X2),X2)
        & element(sK7(X0,X1,X2),the_carrier(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ~ related(X1,X0,X3)
            & in(X3,X2)
            & element(X3,the_carrier(X1)) ) )
      & ( ! [X4] :
            ( related(X1,X0,X4)
            | ~ in(X4,X2)
            | ~ element(X4,the_carrier(X1)) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f57]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( ( sP2(X2,X0,X1)
        | ? [X3] :
            ( ~ related(X0,X2,X3)
            & in(X3,X1)
            & element(X3,the_carrier(X0)) ) )
      & ( ! [X3] :
            ( related(X0,X2,X3)
            | ~ in(X3,X1)
            | ~ element(X3,the_carrier(X0)) )
        | ~ sP2(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f107,plain,
    ! [X0] : ~ in(X0,empty_set),
    inference(forward_demodulation,[],[f106,f101]) ).

fof(f101,plain,
    empty_set = sK11,
    inference(unit_resulting_resolution,[],[f98,f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f98,plain,
    empty(sK11),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    empty(sK11),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f15,f67]) ).

fof(f67,plain,
    ( ? [X0] : empty(X0)
   => empty(sK11) ),
    introduced(choice_axiom,[]) ).

fof(f15,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f106,plain,
    ! [X0] : ~ in(X0,sK11),
    inference(unit_resulting_resolution,[],[f98,f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f172,plain,
    ~ relstr_element_smaller(sK4,empty_set,sK5),
    inference(unit_resulting_resolution,[],[f166,f73]) ).

fof(f73,plain,
    ( ~ relstr_set_smaller(sK4,empty_set,sK5)
    | ~ relstr_element_smaller(sK4,empty_set,sK5) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f166,plain,
    relstr_set_smaller(sK4,empty_set,sK5),
    inference(unit_resulting_resolution,[],[f146,f147,f76]) ).

fof(f76,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,X2)
      | ~ sP0(X2,X1,X0)
      | relstr_set_smaller(X1,X0,X2) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( ( relstr_set_smaller(X1,X0,X2)
          | ~ sP0(X2,X1,X0) )
        & ( sP0(X2,X1,X0)
          | ~ relstr_set_smaller(X1,X0,X2) ) )
      | ~ sP1(X0,X1,X2) ),
    inference(rectify,[],[f49]) ).

fof(f49,plain,
    ! [X1,X0,X2] :
      ( ( ( relstr_set_smaller(X0,X1,X2)
          | ~ sP0(X2,X0,X1) )
        & ( sP0(X2,X0,X1)
          | ~ relstr_set_smaller(X0,X1,X2) ) )
      | ~ sP1(X1,X0,X2) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X1,X0,X2] :
      ( ( relstr_set_smaller(X0,X1,X2)
      <=> sP0(X2,X0,X1) )
      | ~ sP1(X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f147,plain,
    ! [X0] : sP1(X0,sK4,sK5),
    inference(unit_resulting_resolution,[],[f71,f72,f81]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,the_carrier(X0))
      | sP1(X1,X0,X2)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( sP1(X1,X0,X2)
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(definition_folding,[],[f30,f41,f40]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( sP0(X2,X0,X1)
    <=> ! [X3] :
          ( related(X0,X3,X2)
          | ~ in(X3,X1)
          | ~ element(X3,the_carrier(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f30,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_set_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X3,X2)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_set_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X3,X2)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1,X2] :
          ( element(X2,the_carrier(X0))
         => ( relstr_set_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( element(X3,the_carrier(X0))
               => ( in(X3,X1)
                 => related(X0,X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).

fof(f146,plain,
    ! [X0,X1] : sP0(X0,X1,empty_set),
    inference(unit_resulting_resolution,[],[f107,f79]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | in(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ~ related(X1,sK6(X0,X1,X2),X0)
          & in(sK6(X0,X1,X2),X2)
          & element(sK6(X0,X1,X2),the_carrier(X1)) ) )
      & ( ! [X4] :
            ( related(X1,X4,X0)
            | ~ in(X4,X2)
            | ~ element(X4,the_carrier(X1)) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f52,f53]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ related(X1,X3,X0)
          & in(X3,X2)
          & element(X3,the_carrier(X1)) )
     => ( ~ related(X1,sK6(X0,X1,X2),X0)
        & in(sK6(X0,X1,X2),X2)
        & element(sK6(X0,X1,X2),the_carrier(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ~ related(X1,X3,X0)
            & in(X3,X2)
            & element(X3,the_carrier(X1)) ) )
      & ( ! [X4] :
            ( related(X1,X4,X0)
            | ~ in(X4,X2)
            | ~ element(X4,the_carrier(X1)) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ( sP0(X2,X0,X1)
        | ? [X3] :
            ( ~ related(X0,X3,X2)
            & in(X3,X1)
            & element(X3,the_carrier(X0)) ) )
      & ( ! [X3] :
            ( related(X0,X3,X2)
            | ~ in(X3,X1)
            | ~ element(X3,the_carrier(X0)) )
        | ~ sP0(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU355+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n002.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 11:32:42 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (14656)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (14659)WARNING: value z3 for option sas not known
% 0.15/0.38  % (14660)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (14658)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (14657)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (14659)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)
% 0.15/0.38  % (14661)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)
% 0.15/0.38  % (14662)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)
% 0.15/0.38  % (14663)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)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  % (14663)First to succeed.
% 0.15/0.38  TRYING [3]
% 0.15/0.38  % (14659)Also succeeded, but the first one will report.
% 0.15/0.38  % (14662)Also succeeded, but the first one will report.
% 0.15/0.38  % (14663)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14656"
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  % (14663)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (14663)------------------------------
% 0.15/0.38  % (14663)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (14663)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (14663)Memory used [KB]: 843
% 0.15/0.38  % (14663)Time elapsed: 0.007 s
% 0.15/0.38  % (14663)Instructions burned: 8 (million)
% 0.15/0.38  % (14656)Success in time 0.022 s
%------------------------------------------------------------------------------