TSTP Solution File: SEU344+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 : Wed Aug 31 18:33:19 EDT 2022

% Result   : Theorem 1.91s 0.62s
% Output   : Refutation 1.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   54 (  13 unt;   0 def)
%            Number of atoms       :  186 (  30 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  205 (  73   ~;  81   |;  30   &)
%                                         (   5 <=>;  15  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   71 (  57   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f512,plain,
    $false,
    inference(subsumption_resolution,[],[f511,f299]) ).

fof(f299,plain,
    ! [X0] : ~ empty_carrier(boole_lattice(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0] :
      ( ~ empty_carrier(boole_lattice(X0))
      & strict_latt_str(boole_lattice(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).

fof(f511,plain,
    empty_carrier(boole_lattice(sK10)),
    inference(subsumption_resolution,[],[f510,f286]) ).

fof(f286,plain,
    element(sK11,the_carrier(boole_lattice(sK10))),
    inference(cnf_transformation,[],[f201]) ).

fof(f201,plain,
    ( element(sK12,the_carrier(boole_lattice(sK10)))
    & ( ~ below(boole_lattice(sK10),sK11,sK12)
      | ~ subset(sK11,sK12) )
    & ( below(boole_lattice(sK10),sK11,sK12)
      | subset(sK11,sK12) )
    & element(sK11,the_carrier(boole_lattice(sK10))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f198,f200,f199]) ).

fof(f199,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( element(X2,the_carrier(boole_lattice(X0)))
            & ( ~ below(boole_lattice(X0),X1,X2)
              | ~ subset(X1,X2) )
            & ( below(boole_lattice(X0),X1,X2)
              | subset(X1,X2) ) )
        & element(X1,the_carrier(boole_lattice(X0))) )
   => ( ? [X2] :
          ( element(X2,the_carrier(boole_lattice(sK10)))
          & ( ~ below(boole_lattice(sK10),sK11,X2)
            | ~ subset(sK11,X2) )
          & ( below(boole_lattice(sK10),sK11,X2)
            | subset(sK11,X2) ) )
      & element(sK11,the_carrier(boole_lattice(sK10))) ) ),
    introduced(choice_axiom,[]) ).

fof(f200,plain,
    ( ? [X2] :
        ( element(X2,the_carrier(boole_lattice(sK10)))
        & ( ~ below(boole_lattice(sK10),sK11,X2)
          | ~ subset(sK11,X2) )
        & ( below(boole_lattice(sK10),sK11,X2)
          | subset(sK11,X2) ) )
   => ( element(sK12,the_carrier(boole_lattice(sK10)))
      & ( ~ below(boole_lattice(sK10),sK11,sK12)
        | ~ subset(sK11,sK12) )
      & ( below(boole_lattice(sK10),sK11,sK12)
        | subset(sK11,sK12) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f198,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( element(X2,the_carrier(boole_lattice(X0)))
          & ( ~ below(boole_lattice(X0),X1,X2)
            | ~ subset(X1,X2) )
          & ( below(boole_lattice(X0),X1,X2)
            | subset(X1,X2) ) )
      & element(X1,the_carrier(boole_lattice(X0))) ),
    inference(flattening,[],[f197]) ).

fof(f197,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( element(X2,the_carrier(boole_lattice(X0)))
          & ( ~ below(boole_lattice(X0),X1,X2)
            | ~ subset(X1,X2) )
          & ( below(boole_lattice(X0),X1,X2)
            | subset(X1,X2) ) )
      & element(X1,the_carrier(boole_lattice(X0))) ),
    inference(nnf_transformation,[],[f157]) ).

fof(f157,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( element(X2,the_carrier(boole_lattice(X0)))
          & ( subset(X1,X2)
          <~> below(boole_lattice(X0),X1,X2) ) )
      & element(X1,the_carrier(boole_lattice(X0))) ),
    inference(ennf_transformation,[],[f74]) ).

fof(f74,negated_conjecture,
    ~ ! [X1,X0] :
        ( element(X1,the_carrier(boole_lattice(X0)))
       => ! [X2] :
            ( element(X2,the_carrier(boole_lattice(X0)))
           => ( subset(X1,X2)
            <=> below(boole_lattice(X0),X1,X2) ) ) ),
    inference(negated_conjecture,[],[f73]) ).

fof(f73,conjecture,
    ! [X1,X0] :
      ( element(X1,the_carrier(boole_lattice(X0)))
     => ! [X2] :
          ( element(X2,the_carrier(boole_lattice(X0)))
         => ( subset(X1,X2)
          <=> below(boole_lattice(X0),X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice3) ).

fof(f510,plain,
    ( ~ element(sK11,the_carrier(boole_lattice(sK10)))
    | empty_carrier(boole_lattice(sK10)) ),
    inference(subsumption_resolution,[],[f509,f289]) ).

fof(f289,plain,
    element(sK12,the_carrier(boole_lattice(sK10))),
    inference(cnf_transformation,[],[f201]) ).

fof(f509,plain,
    ( ~ element(sK12,the_carrier(boole_lattice(sK10)))
    | empty_carrier(boole_lattice(sK10))
    | ~ element(sK11,the_carrier(boole_lattice(sK10))) ),
    inference(subsumption_resolution,[],[f508,f490]) ).

fof(f490,plain,
    subset(sK11,sK12),
    inference(superposition,[],[f262,f486]) ).

fof(f486,plain,
    sK12 = set_union2(sK11,sK12),
    inference(subsumption_resolution,[],[f485,f242]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | set_union2(X1,X0) = X0 ),
    inference(cnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | set_union2(X1,X0) = X0 ),
    inference(rectify,[],[f109]) ).

fof(f109,plain,
    ! [X1,X0] :
      ( ~ subset(X0,X1)
      | set_union2(X0,X1) = X1 ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f485,plain,
    ( sK12 = set_union2(sK11,sK12)
    | subset(sK11,sK12) ),
    inference(forward_demodulation,[],[f484,f466]) ).

fof(f466,plain,
    join(boole_lattice(sK10),sK11,sK12) = set_union2(sK11,sK12),
    inference(resolution,[],[f458,f286]) ).

fof(f458,plain,
    ! [X1] :
      ( ~ element(X1,the_carrier(boole_lattice(sK10)))
      | join(boole_lattice(sK10),X1,sK12) = set_union2(X1,sK12) ),
    inference(resolution,[],[f225,f289]) ).

fof(f225,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,the_carrier(boole_lattice(X1)))
      | set_union2(X0,X2) = join(boole_lattice(X1),X0,X2)
      | ~ element(X0,the_carrier(boole_lattice(X1))) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( set_union2(X0,X2) = join(boole_lattice(X1),X0,X2)
            & set_intersection2(X0,X2) = meet(boole_lattice(X1),X0,X2) )
          | ~ element(X2,the_carrier(boole_lattice(X1))) )
      | ~ element(X0,the_carrier(boole_lattice(X1))) ),
    inference(ennf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X1,X0] :
      ( element(X0,the_carrier(boole_lattice(X1)))
     => ! [X2] :
          ( element(X2,the_carrier(boole_lattice(X1)))
         => ( set_union2(X0,X2) = join(boole_lattice(X1),X0,X2)
            & set_intersection2(X0,X2) = meet(boole_lattice(X1),X0,X2) ) ) ),
    inference(rectify,[],[f70]) ).

fof(f70,axiom,
    ! [X1,X0] :
      ( element(X1,the_carrier(boole_lattice(X0)))
     => ! [X2] :
          ( element(X2,the_carrier(boole_lattice(X0)))
         => ( join(boole_lattice(X0),X1,X2) = set_union2(X1,X2)
            & meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).

fof(f484,plain,
    ( subset(sK11,sK12)
    | sK12 = join(boole_lattice(sK10),sK11,sK12) ),
    inference(subsumption_resolution,[],[f483,f314]) ).

fof(f314,plain,
    ! [X0] : join_semilatt_str(boole_lattice(X0)),
    inference(resolution,[],[f246,f284]) ).

fof(f284,plain,
    ! [X0] : latt_str(boole_lattice(X0)),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( latt_str(boole_lattice(X0))
      & strict_latt_str(boole_lattice(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).

fof(f246,plain,
    ! [X0] :
      ( ~ latt_str(X0)
      | join_semilatt_str(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ latt_str(X0)
      | ( meet_semilatt_str(X0)
        & join_semilatt_str(X0) ) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( latt_str(X0)
     => ( meet_semilatt_str(X0)
        & join_semilatt_str(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).

fof(f483,plain,
    ( ~ join_semilatt_str(boole_lattice(sK10))
    | sK12 = join(boole_lattice(sK10),sK11,sK12)
    | subset(sK11,sK12) ),
    inference(subsumption_resolution,[],[f482,f289]) ).

fof(f482,plain,
    ( ~ element(sK12,the_carrier(boole_lattice(sK10)))
    | sK12 = join(boole_lattice(sK10),sK11,sK12)
    | ~ join_semilatt_str(boole_lattice(sK10))
    | subset(sK11,sK12) ),
    inference(subsumption_resolution,[],[f481,f286]) ).

fof(f481,plain,
    ( ~ element(sK11,the_carrier(boole_lattice(sK10)))
    | sK12 = join(boole_lattice(sK10),sK11,sK12)
    | ~ join_semilatt_str(boole_lattice(sK10))
    | ~ element(sK12,the_carrier(boole_lattice(sK10)))
    | subset(sK11,sK12) ),
    inference(subsumption_resolution,[],[f480,f299]) ).

fof(f480,plain,
    ( empty_carrier(boole_lattice(sK10))
    | subset(sK11,sK12)
    | ~ element(sK12,the_carrier(boole_lattice(sK10)))
    | sK12 = join(boole_lattice(sK10),sK11,sK12)
    | ~ join_semilatt_str(boole_lattice(sK10))
    | ~ element(sK11,the_carrier(boole_lattice(sK10))) ),
    inference(resolution,[],[f267,f287]) ).

fof(f287,plain,
    ( below(boole_lattice(sK10),sK11,sK12)
    | subset(sK11,sK12) ),
    inference(cnf_transformation,[],[f201]) ).

fof(f267,plain,
    ! [X2,X0,X1] :
      ( ~ below(X0,X1,X2)
      | join(X0,X1,X2) = X2
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f190]) ).

fof(f190,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ( ( below(X0,X1,X2)
                  | join(X0,X1,X2) != X2 )
                & ( join(X0,X1,X2) = X2
                  | ~ below(X0,X1,X2) ) )
              | ~ element(X2,the_carrier(X0)) ) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 )
              | ~ element(X2,the_carrier(X0)) ) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 )
              | ~ element(X2,the_carrier(X0)) ) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( ( join_semilatt_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).

fof(f262,plain,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(f508,plain,
    ( ~ subset(sK11,sK12)
    | ~ element(sK11,the_carrier(boole_lattice(sK10)))
    | ~ element(sK12,the_carrier(boole_lattice(sK10)))
    | empty_carrier(boole_lattice(sK10)) ),
    inference(subsumption_resolution,[],[f507,f487]) ).

fof(f487,plain,
    sK12 = join(boole_lattice(sK10),sK11,sK12),
    inference(backward_demodulation,[],[f466,f486]) ).

fof(f507,plain,
    ( sK12 != join(boole_lattice(sK10),sK11,sK12)
    | ~ element(sK11,the_carrier(boole_lattice(sK10)))
    | ~ subset(sK11,sK12)
    | ~ element(sK12,the_carrier(boole_lattice(sK10)))
    | empty_carrier(boole_lattice(sK10)) ),
    inference(subsumption_resolution,[],[f504,f314]) ).

fof(f504,plain,
    ( ~ join_semilatt_str(boole_lattice(sK10))
    | ~ element(sK11,the_carrier(boole_lattice(sK10)))
    | ~ element(sK12,the_carrier(boole_lattice(sK10)))
    | sK12 != join(boole_lattice(sK10),sK11,sK12)
    | ~ subset(sK11,sK12)
    | empty_carrier(boole_lattice(sK10)) ),
    inference(resolution,[],[f268,f288]) ).

fof(f288,plain,
    ( ~ below(boole_lattice(sK10),sK11,sK12)
    | ~ subset(sK11,sK12) ),
    inference(cnf_transformation,[],[f201]) ).

fof(f268,plain,
    ! [X2,X0,X1] :
      ( below(X0,X1,X2)
      | join(X0,X1,X2) != X2
      | empty_carrier(X0)
      | ~ element(X2,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | ~ element(X1,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f190]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 15:12:50 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.56  % (1441)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.56  % (1448)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.57  % (1440)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.57  % (1441)Instruction limit reached!
% 0.19/0.57  % (1441)------------------------------
% 0.19/0.57  % (1441)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57  % (1449)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.57  % (1457)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.58  % (1456)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.59  % (1441)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59  % (1441)Termination reason: Unknown
% 0.19/0.59  % (1441)Termination phase: Saturation
% 0.19/0.59  
% 0.19/0.59  % (1441)Memory used [KB]: 5628
% 0.19/0.59  % (1441)Time elapsed: 0.150 s
% 0.19/0.59  % (1441)Instructions burned: 7 (million)
% 0.19/0.59  % (1441)------------------------------
% 0.19/0.59  % (1441)------------------------------
% 0.19/0.59  TRYING [1]
% 0.19/0.60  TRYING [2]
% 0.19/0.62  % (1456)First to succeed.
% 0.19/0.62  % (1455)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.91/0.62  % (1456)Refutation found. Thanks to Tanya!
% 1.91/0.62  % SZS status Theorem for theBenchmark
% 1.91/0.62  % SZS output start Proof for theBenchmark
% See solution above
% 1.91/0.62  % (1456)------------------------------
% 1.91/0.62  % (1456)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.91/0.62  % (1456)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.91/0.62  % (1456)Termination reason: Refutation
% 1.91/0.62  
% 1.91/0.62  % (1456)Memory used [KB]: 1279
% 1.91/0.62  % (1456)Time elapsed: 0.200 s
% 1.91/0.62  % (1456)Instructions burned: 15 (million)
% 1.91/0.62  % (1456)------------------------------
% 1.91/0.62  % (1456)------------------------------
% 1.91/0.62  % (1433)Success in time 0.271 s
%------------------------------------------------------------------------------