TSTP Solution File: SET173+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET173+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 09:12:40 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (  10 unt;   0 def)
%            Number of atoms       :  109 (  12 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  124 (  47   ~;  47   |;  21   &)
%                                         (   7 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   67 (  60   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f759,plain,
    $false,
    inference(unit_resulting_resolution,[],[f58,f158,f74,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ member(sK3(X0,X1),X0)
      | sP0(X0,X1)
      | ~ member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ member(sK3(X0,X1),X0)
            | ~ member(sK3(X0,X1),X1) )
          & ( member(sK3(X0,X1),X0)
            | member(sK3(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f20,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X0)
            | ~ member(X2,X1) )
          & ( member(X2,X0)
            | member(X2,X1) ) )
     => ( ( ~ member(sK3(X0,X1),X0)
          | ~ member(sK3(X0,X1),X1) )
        & ( member(sK3(X0,X1),X0)
          | member(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f74,plain,
    member(sK3(sK1,intersection(sK1,union(sK1,sK2))),sK1),
    inference(subsumption_resolution,[],[f72,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).

fof(f72,plain,
    ( member(sK3(sK1,intersection(sK1,union(sK1,sK2))),sK1)
    | member(sK3(sK1,intersection(sK1,union(sK1,sK2))),intersection(sK1,union(sK1,sK2))) ),
    inference(resolution,[],[f41,f58]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | member(sK3(X0,X1),X0)
      | member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f158,plain,
    ! [X0] : member(sK3(sK1,intersection(sK1,union(sK1,sK2))),intersection(sK1,union(sK1,X0))),
    inference(unit_resulting_resolution,[],[f74,f85,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,intersection(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f85,plain,
    ! [X0] : member(sK3(sK1,intersection(sK1,union(sK1,sK2))),union(sK1,X0)),
    inference(unit_resulting_resolution,[],[f74,f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X0)
      | member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(f58,plain,
    ~ sP0(sK1,intersection(sK1,union(sK1,sK2))),
    inference(unit_resulting_resolution,[],[f32,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ sP0(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ sP0(X1,X0) )
      & ( sP0(X1,X0)
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( X0 = X1
    <=> sP0(X1,X0) ),
    inference(definition_folding,[],[f8,f13]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f32,plain,
    sK1 != intersection(sK1,union(sK1,sK2)),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    sK1 != intersection(sK1,union(sK1,sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f15]) ).

fof(f15,plain,
    ( ? [X0,X1] : intersection(X0,union(X0,X1)) != X0
   => sK1 != intersection(sK1,union(sK1,sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0,X1] : intersection(X0,union(X0,X1)) != X0,
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion_for_intersection) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET173+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n018.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 17:05:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (24080)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (24084)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (24087)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (24089)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)
% 0.15/0.38  % (24090)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)
% 0.15/0.38  % (24085)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (24088)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)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  % (24086)WARNING: value z3 for option sas not known
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [4]
% 0.15/0.38  % (24086)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)
% 0.15/0.39  TRYING [3]
% 0.15/0.39  TRYING [5]
% 0.15/0.40  % (24090)First to succeed.
% 0.15/0.40  % (24090)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24080"
% 0.15/0.40  % (24090)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (24090)------------------------------
% 0.15/0.40  % (24090)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40  % (24090)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (24090)Memory used [KB]: 1087
% 0.15/0.40  % (24090)Time elapsed: 0.028 s
% 0.15/0.40  % (24090)Instructions burned: 50 (million)
% 0.15/0.40  % (24080)Success in time 0.045 s
%------------------------------------------------------------------------------