TSTP Solution File: SEU131+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU131+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 May 21 03:53:08 EDT 2024

% Result   : Theorem 0.12s 0.35s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   72 (  15 unt;   0 def)
%            Number of atoms       :  225 (  39 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  244 (  91   ~;  95   |;  37   &)
%                                         (  11 <=>;   8  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :  145 ( 128   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f515,plain,
    $false,
    inference(subsumption_resolution,[],[f506,f473]) ).

fof(f473,plain,
    ~ in(sK5(sK2,sK3),sK3),
    inference(unit_resulting_resolution,[],[f447,f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ in(sK5(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK5(X0,X1),X1)
          & in(sK5(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f36,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK5(X0,X1),X1)
        & in(sK5(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f447,plain,
    ~ subset(sK2,sK3),
    inference(unit_resulting_resolution,[],[f445,f52]) ).

fof(f52,plain,
    ( ~ subset(sK2,sK3)
    | empty_set != set_difference(sK2,sK3) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( ( ~ subset(sK2,sK3)
      | empty_set != set_difference(sK2,sK3) )
    & ( subset(sK2,sK3)
      | empty_set = set_difference(sK2,sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f29,f30]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( ( ~ subset(X0,X1)
          | set_difference(X0,X1) != empty_set )
        & ( subset(X0,X1)
          | set_difference(X0,X1) = empty_set ) )
   => ( ( ~ subset(sK2,sK3)
        | empty_set != set_difference(sK2,sK3) )
      & ( subset(sK2,sK3)
        | empty_set = set_difference(sK2,sK3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ? [X0,X1] :
      ( ( ~ subset(X0,X1)
        | set_difference(X0,X1) != empty_set )
      & ( subset(X0,X1)
        | set_difference(X0,X1) = empty_set ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ? [X0,X1] :
      ( set_difference(X0,X1) = empty_set
    <~> subset(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( set_difference(X0,X1) = empty_set
      <=> subset(X0,X1) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( set_difference(X0,X1) = empty_set
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).

fof(f445,plain,
    empty_set = set_difference(sK2,sK3),
    inference(duplicate_literal_removal,[],[f437]) ).

fof(f437,plain,
    ( empty_set = set_difference(sK2,sK3)
    | empty_set = set_difference(sK2,sK3)
    | empty_set = set_difference(sK2,sK3) ),
    inference(resolution,[],[f246,f227]) ).

fof(f227,plain,
    ! [X0,X1] :
      ( ~ in(sK4(set_difference(X0,X1),empty_set),X1)
      | set_difference(X0,X1) = empty_set ),
    inference(resolution,[],[f154,f71]) ).

fof(f71,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1,X2)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | in(X1,X0)
        | ~ in(X1,X2) )
      & ( ( ~ in(X1,X0)
          & in(X1,X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f44]) ).

fof(f44,plain,
    ! [X1,X3,X0] :
      ( ( sP0(X1,X3,X0)
        | in(X3,X1)
        | ~ in(X3,X0) )
      & ( ( ~ in(X3,X1)
          & in(X3,X0) )
        | ~ sP0(X1,X3,X0) ) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X1,X3,X0] :
      ( ( sP0(X1,X3,X0)
        | in(X3,X1)
        | ~ in(X3,X0) )
      & ( ( ~ in(X3,X1)
          & in(X3,X0) )
        | ~ sP0(X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X1,X3,X0] :
      ( sP0(X1,X3,X0)
    <=> ( ~ in(X3,X1)
        & in(X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( sP0(X1,sK4(set_difference(X0,X1),empty_set),X0)
      | set_difference(X0,X1) = empty_set ),
    inference(resolution,[],[f137,f115]) ).

fof(f115,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,set_difference(X1,X2))
      | sP0(X2,X0,X1) ),
    inference(resolution,[],[f66,f77]) ).

fof(f77,plain,
    ! [X0,X1] : sP1(X0,X1,set_difference(X0,X1)),
    inference(equality_resolution,[],[f73]) ).

fof(f73,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X1,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ~ sP1(X0,X1,X2) )
      & ( sP1(X0,X1,X2)
        | set_difference(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( set_difference(X0,X1) = X2
    <=> sP1(X0,X1,X2) ),
    inference(definition_folding,[],[f3,f27,f26]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( sP1(X0,X1,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> sP0(X1,X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f66,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP1(X0,X1,X2)
      | ~ in(X4,X2)
      | sP0(X1,X4,X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ( ~ sP0(X1,sK6(X0,X1,X2),X0)
            | ~ in(sK6(X0,X1,X2),X2) )
          & ( sP0(X1,sK6(X0,X1,X2),X0)
            | in(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP0(X1,X4,X0) )
            & ( sP0(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f40,f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP0(X1,X3,X0)
            | ~ in(X3,X2) )
          & ( sP0(X1,X3,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP0(X1,sK6(X0,X1,X2),X0)
          | ~ in(sK6(X0,X1,X2),X2) )
        & ( sP0(X1,sK6(X0,X1,X2),X0)
          | in(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP0(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP0(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP0(X1,X4,X0) )
            & ( sP0(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP0(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP0(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ sP0(X1,X3,X0) )
            & ( sP0(X1,X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f137,plain,
    ! [X0] :
      ( in(sK4(X0,empty_set),X0)
      | empty_set = X0 ),
    inference(resolution,[],[f59,f85]) ).

fof(f85,plain,
    ! [X0] : ~ in(X0,empty_set),
    inference(forward_demodulation,[],[f84,f79]) ).

fof(f79,plain,
    empty_set = sK8,
    inference(unit_resulting_resolution,[],[f76,f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f76,plain,
    empty(sK8),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    empty(sK8),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f9,f49]) ).

fof(f49,plain,
    ( ? [X0] : empty(X0)
   => empty(sK8) ),
    introduced(choice_axiom,[]) ).

fof(f9,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f84,plain,
    ! [X0] : ~ in(X0,sK8),
    inference(unit_resulting_resolution,[],[f76,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f59,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),X1)
      | in(sK4(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK4(X0,X1),X1)
          | ~ in(sK4(X0,X1),X0) )
        & ( in(sK4(X0,X1),X1)
          | in(sK4(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f32,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK4(X0,X1),X1)
          | ~ in(sK4(X0,X1),X0) )
        & ( in(sK4(X0,X1),X1)
          | in(sK4(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(f246,plain,
    ! [X0] :
      ( in(sK4(set_difference(sK2,X0),empty_set),sK3)
      | empty_set = set_difference(sK2,X0)
      | empty_set = set_difference(sK2,sK3) ),
    inference(resolution,[],[f228,f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ~ in(X0,sK2)
      | in(X0,sK3)
      | empty_set = set_difference(sK2,sK3) ),
    inference(resolution,[],[f61,f51]) ).

fof(f51,plain,
    ( subset(sK2,sK3)
    | empty_set = set_difference(sK2,sK3) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f61,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f228,plain,
    ! [X0,X1] :
      ( in(sK4(set_difference(X0,X1),empty_set),X0)
      | set_difference(X0,X1) = empty_set ),
    inference(resolution,[],[f154,f70]) ).

fof(f70,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1,X2)
      | in(X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f506,plain,
    in(sK5(sK2,sK3),sK3),
    inference(unit_resulting_resolution,[],[f477,f446,f72]) ).

fof(f72,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X2)
      | in(X1,X0)
      | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f446,plain,
    in(sK5(sK2,sK3),sK2),
    inference(unit_resulting_resolution,[],[f445,f98]) ).

fof(f98,plain,
    ( empty_set != set_difference(sK2,sK3)
    | in(sK5(sK2,sK3),sK2) ),
    inference(resolution,[],[f62,f52]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK5(X0,X1),X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f477,plain,
    ! [X0] : ~ sP0(sK3,X0,sK2),
    inference(unit_resulting_resolution,[],[f85,f450,f67]) ).

fof(f67,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP1(X0,X1,X2)
      | ~ sP0(X1,X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f450,plain,
    sP1(sK2,sK3,empty_set),
    inference(superposition,[],[f77,f445]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : SEU131+1 : TPTP v8.2.0. Released v3.3.0.
% 0.02/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32  % Computer : n009.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Sun May 19 16:10:37 EDT 2024
% 0.12/0.32  % CPUTime    : 
% 0.12/0.32  % (1920)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34  % (1923)WARNING: value z3 for option sas not known
% 0.12/0.34  % (1921)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.34  % (1922)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.34  % (1924)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.34  % (1926)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)
% 0.12/0.34  % (1925)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)
% 0.12/0.34  % (1923)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)
% 0.12/0.34  % (1927)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)
% 0.12/0.34  TRYING [1]
% 0.12/0.34  TRYING [2]
% 0.12/0.34  TRYING [3]
% 0.12/0.34  TRYING [1]
% 0.12/0.34  TRYING [4]
% 0.12/0.35  TRYING [2]
% 0.12/0.35  % (1927)First to succeed.
% 0.12/0.35  % (1927)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1920"
% 0.12/0.35  % (1927)Refutation found. Thanks to Tanya!
% 0.12/0.35  % SZS status Theorem for theBenchmark
% 0.12/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.35  % (1927)------------------------------
% 0.12/0.35  % (1927)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35  % (1927)Termination reason: Refutation
% 0.12/0.35  
% 0.12/0.35  % (1927)Memory used [KB]: 908
% 0.12/0.35  % (1927)Time elapsed: 0.013 s
% 0.12/0.35  % (1927)Instructions burned: 22 (million)
% 0.12/0.35  % (1920)Success in time 0.029 s
%------------------------------------------------------------------------------