TSTP Solution File: SEU130+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU130+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 : n031.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 09:27:08 EDT 2024

% Result   : Theorem 0.22s 0.40s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   36 (   5 unt;   0 def)
%            Number of atoms       :  156 (  13 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  187 (  67   ~;  68   |;  39   &)
%                                         (   7 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   87 (  76   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f494,plain,
    $false,
    inference(subsumption_resolution,[],[f493,f49]) ).

fof(f49,plain,
    sK1 != set_intersection2(sK1,sK2),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( sK1 != set_intersection2(sK1,sK2)
    & subset(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f22,f30]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( set_intersection2(X0,X1) != X0
        & subset(X0,X1) )
   => ( sK1 != set_intersection2(sK1,sK2)
      & subset(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ? [X0,X1] :
      ( set_intersection2(X0,X1) != X0
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => set_intersection2(X0,X1) = X0 ),
    inference(negated_conjecture,[],[f14]) ).

fof(f14,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f493,plain,
    sK1 = set_intersection2(sK1,sK2),
    inference(resolution,[],[f485,f73]) ).

fof(f73,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X1,X0,X2)
      | set_intersection2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ~ sP0(X1,X0,X2) )
      & ( sP0(X1,X0,X2)
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> sP0(X1,X0,X2) ),
    inference(definition_folding,[],[f5,f28]) ).

fof(f28,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f485,plain,
    sP0(sK2,sK1,sK1),
    inference(duplicate_literal_removal,[],[f484]) ).

fof(f484,plain,
    ( sP0(sK2,sK1,sK1)
    | sP0(sK2,sK1,sK1) ),
    inference(resolution,[],[f474,f316]) ).

fof(f316,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1,X1),X1)
      | sP0(X0,X1,X1) ),
    inference(factoring,[],[f69]) ).

fof(f69,plain,
    ! [X2,X0,X1] :
      ( in(sK4(X0,X1,X2),X2)
      | in(sK4(X0,X1,X2),X1)
      | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ~ in(sK4(X0,X1,X2),X0)
            | ~ in(sK4(X0,X1,X2),X1)
            | ~ in(sK4(X0,X1,X2),X2) )
          & ( ( in(sK4(X0,X1,X2),X0)
              & in(sK4(X0,X1,X2),X1) )
            | in(sK4(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X0)
              | ~ in(X4,X1) )
            & ( ( in(X4,X0)
                & in(X4,X1) )
              | ~ in(X4,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f40,f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ~ in(X3,X1)
            | ~ in(X3,X2) )
          & ( ( in(X3,X0)
              & in(X3,X1) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK4(X0,X1,X2),X0)
          | ~ in(sK4(X0,X1,X2),X1)
          | ~ in(sK4(X0,X1,X2),X2) )
        & ( ( in(sK4(X0,X1,X2),X0)
            & in(sK4(X0,X1,X2),X1) )
          | in(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f39,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f474,plain,
    ! [X0] :
      ( ~ in(sK4(sK2,X0,X0),sK1)
      | sP0(sK2,X0,X0) ),
    inference(resolution,[],[f449,f138]) ).

fof(f138,plain,
    ! [X0] :
      ( in(X0,sK2)
      | ~ in(X0,sK1) ),
    inference(resolution,[],[f61,f48]) ).

fof(f48,plain,
    subset(sK1,sK2),
    inference(cnf_transformation,[],[f31]) ).

fof(f61,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK3(X0,X1),X1)
          & in(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f35,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK3(X0,X1),X1)
        & in(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,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,[],[f34]) ).

fof(f34,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,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f449,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1,X1),X0)
      | sP0(X0,X1,X1) ),
    inference(subsumption_resolution,[],[f448,f69]) ).

fof(f448,plain,
    ! [X0,X1] :
      ( sP0(X0,X1,X1)
      | ~ in(sK4(X0,X1,X1),X0)
      | ~ in(sK4(X0,X1,X1),X1) ),
    inference(duplicate_literal_removal,[],[f442]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( sP0(X0,X1,X1)
      | ~ in(sK4(X0,X1,X1),X0)
      | ~ in(sK4(X0,X1,X1),X1)
      | sP0(X0,X1,X1) ),
    inference(resolution,[],[f316,f71]) ).

fof(f71,plain,
    ! [X2,X0,X1] :
      ( ~ in(sK4(X0,X1,X2),X2)
      | ~ in(sK4(X0,X1,X2),X0)
      | ~ in(sK4(X0,X1,X2),X1)
      | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU130+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n031.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 12:10:02 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.37  % (7113)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38  % (7116)WARNING: value z3 for option sas not known
% 0.16/0.38  % (7120)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)
% 0.16/0.38  % (7114)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38  % (7115)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38  % (7117)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38  % (7118)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)
% 0.16/0.38  % (7116)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)
% 0.16/0.38  % (7119)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)
% 0.16/0.38  TRYING [1]
% 0.16/0.39  TRYING [2]
% 0.16/0.39  TRYING [3]
% 0.16/0.39  TRYING [1]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [2]
% 0.22/0.40  % (7116)First to succeed.
% 0.22/0.40  % (7116)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7113"
% 0.22/0.40  % (7116)Refutation found. Thanks to Tanya!
% 0.22/0.40  % SZS status Theorem for theBenchmark
% 0.22/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40  % (7116)------------------------------
% 0.22/0.40  % (7116)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40  % (7116)Termination reason: Refutation
% 0.22/0.40  
% 0.22/0.40  % (7116)Memory used [KB]: 885
% 0.22/0.40  % (7116)Time elapsed: 0.017 s
% 0.22/0.40  % (7116)Instructions burned: 21 (million)
% 0.22/0.40  % (7113)Success in time 0.033 s
%------------------------------------------------------------------------------