TSTP Solution File: SEU126+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU126+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 : n010.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 15:22:17 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   38 (   6 unt;   0 def)
%            Number of atoms       :  140 (  12 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  159 (  57   ~;  58   |;  30   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   91 (  81   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1844,plain,
    $false,
    inference(unit_resulting_resolution,[],[f330,f1063,f1051,f76]) ).

fof(f76,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X1,sK5(X0,X1,X2),X0)
      | sP1(X0,X1,X2)
      | ~ in(sK5(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ( ~ sP0(X1,sK5(X0,X1,X2),X0)
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( sP0(X1,sK5(X0,X1,X2),X0)
            | in(sK5(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,[sK5])],[f43,f44]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP0(X1,X3,X0)
            | ~ in(X3,X2) )
          & ( sP0(X1,X3,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP0(X1,sK5(X0,X1,X2),X0)
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( sP0(X1,sK5(X0,X1,X2),X0)
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,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,[],[f42]) ).

fof(f42,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,[],[f32]) ).

fof(f32,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(f1051,plain,
    sP0(sK3,sK5(sK2,sK3,sK3),sK2),
    inference(subsumption_resolution,[],[f1050,f79]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X0)
      | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,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,[],[f47]) ).

fof(f47,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,[],[f46]) ).

fof(f46,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,[],[f31]) ).

fof(f31,plain,
    ! [X1,X3,X0] :
      ( sP0(X1,X3,X0)
    <=> ( in(X3,X1)
        | in(X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f1050,plain,
    ( sP0(sK3,sK5(sK2,sK3,sK3),sK2)
    | in(sK5(sK2,sK3,sK3),sK3) ),
    inference(resolution,[],[f75,f330]) ).

fof(f75,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X1,X2)
      | sP0(X1,sK5(X0,X1,X2),X0)
      | in(sK5(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f1063,plain,
    in(sK5(sK2,sK3,sK3),sK3),
    inference(subsumption_resolution,[],[f1059,f317]) ).

fof(f317,plain,
    ! [X0] :
      ( ~ in(X0,sK2)
      | in(X0,sK3) ),
    inference(resolution,[],[f68,f54]) ).

fof(f54,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( sK3 != set_union2(sK2,sK3)
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f23,f34]) ).

fof(f34,plain,
    ( ? [X0,X1] :
        ( set_union2(X0,X1) != X1
        & subset(X0,X1) )
   => ( sK3 != set_union2(sK2,sK3)
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0,X1] :
      ( set_union2(X0,X1) != X1
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => set_union2(X0,X1) = X1 ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f68,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK4(X0,X1),X1)
          & in(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f39,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK4(X0,X1),X1)
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,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,[],[f38]) ).

fof(f38,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,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f1059,plain,
    ( in(sK5(sK2,sK3,sK3),sK2)
    | in(sK5(sK2,sK3,sK3),sK3) ),
    inference(resolution,[],[f1051,f77]) ).

fof(f77,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1,X2)
      | in(X1,X2)
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f330,plain,
    ~ sP1(sK2,sK3,sK3),
    inference(unit_resulting_resolution,[],[f55,f81]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,X2)
      | set_union2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ~ sP1(X0,X1,X2) )
      & ( sP1(X0,X1,X2)
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> sP1(X0,X1,X2) ),
    inference(definition_folding,[],[f4,f32,f31]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f55,plain,
    sK3 != set_union2(sK2,sK3),
    inference(cnf_transformation,[],[f35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.33  % Computer : n010.cluster.edu
% 0.09/0.33  % Model    : x86_64 x86_64
% 0.09/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33  % Memory   : 8042.1875MB
% 0.09/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33  % CPULimit   : 300
% 0.09/0.33  % WCLimit    : 300
% 0.09/0.33  % DateTime   : Mon Apr 29 20:33:05 EDT 2024
% 0.09/0.33  % CPUTime    : 
% 0.09/0.34  % (12463)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.35  % (12466)WARNING: value z3 for option sas not known
% 0.15/0.35  % (12467)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.35  % (12470)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)
% 0.15/0.35  % (12469)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)
% 0.15/0.35  % (12468)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)
% 0.15/0.35  % (12466)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)
% 0.15/0.35  TRYING [1]
% 0.15/0.35  TRYING [2]
% 0.15/0.35  TRYING [3]
% 0.15/0.36  TRYING [4]
% 0.15/0.36  % (12465)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  TRYING [5]
% 0.15/0.37  % (12464)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (12470)First to succeed.
% 0.15/0.38  % (12470)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  % (12470)------------------------------
% 0.15/0.38  % (12470)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38  % (12470)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (12470)Memory used [KB]: 1078
% 0.15/0.38  % (12470)Time elapsed: 0.027 s
% 0.15/0.38  % (12470)Instructions burned: 54 (million)
% 0.15/0.38  % (12470)------------------------------
% 0.15/0.38  % (12470)------------------------------
% 0.15/0.38  % (12463)Success in time 0.042 s
%------------------------------------------------------------------------------