TSTP Solution File: SEU371+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU371+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 : n003.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 09:37:05 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   52 (  22 unt;   0 def)
%            Number of atoms       :  177 (  42 equ)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  179 (  54   ~;  49   |;  72   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   23 (  21 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :   57 (  55   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3302,plain,
    $false,
    inference(trivial_inequality_removal,[],[f3295]) ).

fof(f3295,plain,
    empty_set != empty_set,
    inference(superposition,[],[f337,f3285]) ).

fof(f3285,plain,
    ! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
    inference(superposition,[],[f3276,f784]) ).

fof(f784,plain,
    ! [X0] : bottom_of_relstr(boole_POSet(X0)) = join_on_relstr(boole_POSet(X0),empty_set),
    inference(resolution,[],[f418,f404]) ).

fof(f404,plain,
    ! [X0] : rel_str(boole_POSet(X0)),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0] :
      ( rel_str(boole_POSet(X0))
      & strict_rel_str(boole_POSet(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).

fof(f418,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( bottom_of_relstr(X0) = join_on_relstr(X0,empty_set)
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( rel_str(X0)
     => bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).

fof(f3276,plain,
    ! [X0] : empty_set = join_on_relstr(boole_POSet(X0),empty_set),
    inference(superposition,[],[f3275,f2024]) ).

fof(f2024,plain,
    ! [X0,X1] : join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1),
    inference(forward_demodulation,[],[f2023,f340]) ).

fof(f340,plain,
    ! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow_1) ).

fof(f2023,plain,
    ! [X0,X1] : join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1),
    inference(subsumption_resolution,[],[f2022,f357]) ).

fof(f357,plain,
    ! [X0] : ~ empty_carrier(boole_lattice(X0)),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    ! [X0] :
      ( strict_latt_str(boole_lattice(X0))
      & ~ empty_carrier(boole_lattice(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).

fof(f2022,plain,
    ! [X0,X1] :
      ( join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1)
      | empty_carrier(boole_lattice(X0)) ),
    inference(subsumption_resolution,[],[f2021,f367]) ).

fof(f367,plain,
    ! [X0] : lattice(boole_lattice(X0)),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    ! [X0] :
      ( lattice(boole_lattice(X0))
      & join_absorbing(boole_lattice(X0))
      & meet_absorbing(boole_lattice(X0))
      & meet_associative(boole_lattice(X0))
      & meet_commutative(boole_lattice(X0))
      & join_associative(boole_lattice(X0))
      & join_commutative(boole_lattice(X0))
      & strict_latt_str(boole_lattice(X0))
      & ~ empty_carrier(boole_lattice(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice3) ).

fof(f2021,plain,
    ! [X0,X1] :
      ( join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1)
      | ~ lattice(boole_lattice(X0))
      | empty_carrier(boole_lattice(X0)) ),
    inference(subsumption_resolution,[],[f2020,f402]) ).

fof(f402,plain,
    ! [X0] : latt_str(boole_lattice(X0)),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0] :
      ( latt_str(boole_lattice(X0))
      & strict_latt_str(boole_lattice(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).

fof(f2020,plain,
    ! [X0,X1] :
      ( ~ latt_str(boole_lattice(X0))
      | join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1)
      | ~ lattice(boole_lattice(X0))
      | empty_carrier(boole_lattice(X0)) ),
    inference(resolution,[],[f502,f398]) ).

fof(f398,plain,
    ! [X0] : complete_latt_str(boole_lattice(X0)),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( complete_latt_str(boole_lattice(X0))
      & boolean_lattstr(boole_lattice(X0))
      & complemented_lattstr(boole_lattice(X0))
      & bounded_lattstr(boole_lattice(X0))
      & upper_bounded_semilattstr(boole_lattice(X0))
      & lower_bounded_semilattstr(boole_lattice(X0))
      & distributive_lattstr(boole_lattice(X0))
      & lattice(boole_lattice(X0))
      & join_absorbing(boole_lattice(X0))
      & meet_absorbing(boole_lattice(X0))
      & meet_associative(boole_lattice(X0))
      & meet_commutative(boole_lattice(X0))
      & join_associative(boole_lattice(X0))
      & join_commutative(boole_lattice(X0))
      & strict_latt_str(boole_lattice(X0))
      & ~ empty_carrier(boole_lattice(X0)) ),
    inference(pure_predicate_removal,[],[f59]) ).

fof(f59,axiom,
    ! [X0] :
      ( complete_latt_str(boole_lattice(X0))
      & boolean_lattstr(boole_lattice(X0))
      & complemented_lattstr(boole_lattice(X0))
      & bounded_lattstr(boole_lattice(X0))
      & upper_bounded_semilattstr(boole_lattice(X0))
      & lower_bounded_semilattstr(boole_lattice(X0))
      & modular_lattstr(boole_lattice(X0))
      & distributive_lattstr(boole_lattice(X0))
      & lattice(boole_lattice(X0))
      & join_absorbing(boole_lattice(X0))
      & meet_absorbing(boole_lattice(X0))
      & meet_associative(boole_lattice(X0))
      & meet_commutative(boole_lattice(X0))
      & join_associative(boole_lattice(X0))
      & join_commutative(boole_lattice(X0))
      & strict_latt_str(boole_lattice(X0))
      & ~ empty_carrier(boole_lattice(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_knaster) ).

fof(f502,plain,
    ! [X0,X1] :
      ( ~ complete_latt_str(X0)
      | ~ latt_str(X0)
      | join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0] :
      ( ! [X1] :
          ( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
          & join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) )
      | ~ latt_str(X0)
      | ~ complete_latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f183]) ).

fof(f183,plain,
    ! [X0] :
      ( ! [X1] :
          ( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
          & join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) )
      | ~ latt_str(X0)
      | ~ complete_latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f106]) ).

fof(f106,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & complete_latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
          & join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_yellow_0) ).

fof(f3275,plain,
    ! [X0] : empty_set = join_of_latt_set(boole_lattice(X0),empty_set),
    inference(forward_demodulation,[],[f3274,f400]) ).

fof(f400,plain,
    ! [X0] : empty_set = bottom_of_semilattstr(boole_lattice(X0)),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,axiom,
    ! [X0] :
      ( empty_set = bottom_of_semilattstr(boole_lattice(X0))
      & lower_bounded_semilattstr(boole_lattice(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice3) ).

fof(f3274,plain,
    ! [X0] : bottom_of_semilattstr(boole_lattice(X0)) = join_of_latt_set(boole_lattice(X0),empty_set),
    inference(subsumption_resolution,[],[f3273,f357]) ).

fof(f3273,plain,
    ! [X0] :
      ( empty_carrier(boole_lattice(X0))
      | bottom_of_semilattstr(boole_lattice(X0)) = join_of_latt_set(boole_lattice(X0),empty_set) ),
    inference(subsumption_resolution,[],[f3272,f367]) ).

fof(f3272,plain,
    ! [X0] :
      ( ~ lattice(boole_lattice(X0))
      | empty_carrier(boole_lattice(X0))
      | bottom_of_semilattstr(boole_lattice(X0)) = join_of_latt_set(boole_lattice(X0),empty_set) ),
    inference(subsumption_resolution,[],[f3271,f402]) ).

fof(f3271,plain,
    ! [X0] :
      ( ~ latt_str(boole_lattice(X0))
      | ~ lattice(boole_lattice(X0))
      | empty_carrier(boole_lattice(X0))
      | bottom_of_semilattstr(boole_lattice(X0)) = join_of_latt_set(boole_lattice(X0),empty_set) ),
    inference(resolution,[],[f942,f398]) ).

fof(f942,plain,
    ! [X0] :
      ( ~ complete_latt_str(X0)
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0)
      | bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set) ),
    inference(resolution,[],[f489,f488]) ).

fof(f488,plain,
    ! [X0] :
      ( ~ sP4(X0)
      | bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f271,plain,
    ! [X0] :
      ( ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
        & latt_str(X0)
        & lower_bounded_semilattstr(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
      | ~ sP4(X0) ),
    inference(nnf_transformation,[],[f245]) ).

fof(f245,plain,
    ! [X0] :
      ( ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
        & latt_str(X0)
        & lower_bounded_semilattstr(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
      | ~ sP4(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f489,plain,
    ! [X0] :
      ( sP4(X0)
      | ~ latt_str(X0)
      | ~ complete_latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f246]) ).

fof(f246,plain,
    ! [X0] :
      ( sP4(X0)
      | ~ latt_str(X0)
      | ~ complete_latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(definition_folding,[],[f180,f245]) ).

fof(f180,plain,
    ! [X0] :
      ( ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
        & latt_str(X0)
        & lower_bounded_semilattstr(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
      | ~ latt_str(X0)
      | ~ complete_latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
        & latt_str(X0)
        & lower_bounded_semilattstr(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
      | ~ latt_str(X0)
      | ~ complete_latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f112]) ).

fof(f112,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & complete_latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
        & latt_str(X0)
        & lower_bounded_semilattstr(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).

fof(f337,plain,
    empty_set != bottom_of_relstr(boole_POSet(sK12)),
    inference(cnf_transformation,[],[f262]) ).

fof(f262,plain,
    empty_set != bottom_of_relstr(boole_POSet(sK12)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f127,f261]) ).

fof(f261,plain,
    ( ? [X0] : empty_set != bottom_of_relstr(boole_POSet(X0))
   => empty_set != bottom_of_relstr(boole_POSet(sK12)) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ? [X0] : empty_set != bottom_of_relstr(boole_POSet(X0)),
    inference(ennf_transformation,[],[f104]) ).

fof(f104,negated_conjecture,
    ~ ! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
    inference(negated_conjecture,[],[f103]) ).

fof(f103,conjecture,
    ! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SEU371+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.28  % Computer : n003.cluster.edu
% 0.10/0.28  % Model    : x86_64 x86_64
% 0.10/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28  % Memory   : 8042.1875MB
% 0.10/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28  % CPULimit   : 300
% 0.10/0.28  % WCLimit    : 300
% 0.10/0.28  % DateTime   : Fri May  3 11:12:35 EDT 2024
% 0.14/0.28  % CPUTime    : 
% 0.14/0.28  % (26933)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.29  % (26937)WARNING: value z3 for option sas not known
% 0.14/0.29  % (26940)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)
% 0.14/0.30  % (26939)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)
% 0.14/0.30  % (26937)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)
% 0.14/0.30  % (26938)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.30  % (26935)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.30  % (26941)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)
% 0.14/0.30  % (26936)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.30  TRYING [1]
% 0.14/0.30  TRYING [2]
% 0.14/0.31  TRYING [3]
% 0.14/0.33  TRYING [4]
% 0.14/0.33  TRYING [1]
% 0.14/0.33  TRYING [2]
% 0.14/0.35  TRYING [1]
% 0.14/0.35  TRYING [2]
% 0.14/0.35  TRYING [3]
% 0.14/0.36  TRYING [3]
% 0.14/0.37  % (26937)First to succeed.
% 0.14/0.37  % (26937)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26933"
% 0.14/0.37  % (26937)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37  % (26937)------------------------------
% 0.14/0.37  % (26937)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37  % (26937)Termination reason: Refutation
% 0.14/0.37  
% 0.14/0.37  % (26937)Memory used [KB]: 2637
% 0.14/0.37  % (26937)Time elapsed: 0.075 s
% 0.14/0.37  % (26937)Instructions burned: 234 (million)
% 0.14/0.37  % (26933)Success in time 0.078 s
%------------------------------------------------------------------------------