TSTP Solution File: SET638+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET638+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 : n012.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 09:14:36 EDT 2024

% Result   : Theorem 0.20s 0.38s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (  10 unt;   0 def)
%            Number of atoms       :  122 (  12 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  131 (  51   ~;  41   |;  29   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   80 (  68   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f297,plain,
    $false,
    inference(resolution,[],[f295,f39]) ).

fof(f39,plain,
    ~ subset(sK0,sK1),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( ~ subset(sK0,sK1)
    & empty_set = intersection(sK0,sK2)
    & subset(sK0,union(sK1,sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f21]) ).

fof(f21,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(X0,X1)
        & empty_set = intersection(X0,X2)
        & subset(X0,union(X1,X2)) )
   => ( ~ subset(sK0,sK1)
      & empty_set = intersection(sK0,sK2)
      & subset(sK0,union(sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,X1)
      & empty_set = intersection(X0,X2)
      & subset(X0,union(X1,X2)) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,X1)
      & empty_set = intersection(X0,X2)
      & subset(X0,union(X1,X2)) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( empty_set = intersection(X0,X2)
          & subset(X0,union(X1,X2)) )
       => subset(X0,X1) ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X0,X1,X2] :
      ( ( empty_set = intersection(X0,X2)
        & subset(X0,union(X1,X2)) )
     => subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th120) ).

fof(f295,plain,
    subset(sK0,sK1),
    inference(resolution,[],[f292,f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( member(sK4(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK4(X0,X1),X1)
          & member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f30,f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK4(X0,X1),X1)
        & member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f8]) ).

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

fof(f292,plain,
    ~ member(sK4(sK0,sK1),sK0),
    inference(resolution,[],[f291,f97]) ).

fof(f97,plain,
    ~ member(sK4(sK0,sK1),sK1),
    inference(resolution,[],[f56,f39]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f291,plain,
    ! [X0] :
      ( member(X0,sK1)
      | ~ member(X0,sK0) ),
    inference(duplicate_literal_removal,[],[f289]) ).

fof(f289,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | member(X0,sK1)
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f286,f192]) ).

fof(f192,plain,
    ! [X0] :
      ( member(X0,sK2)
      | member(X0,sK1)
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f58,f130]) ).

fof(f130,plain,
    ! [X0] :
      ( member(X0,union(sK1,sK2))
      | ~ member(X0,sK0) ),
    inference(superposition,[],[f62,f87]) ).

fof(f87,plain,
    sK0 = intersection(sK0,union(sK1,sK2)),
    inference(resolution,[],[f46,f37]) ).

fof(f37,plain,
    subset(sK0,union(sK1,sK2)),
    inference(cnf_transformation,[],[f22]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | intersection(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => intersection(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_intersection) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,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,[],[f35]) ).

fof(f35,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,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,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,[],[f33]) ).

fof(f33,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,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

fof(f286,plain,
    ! [X0] :
      ( ~ member(X0,sK2)
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f278,f40]) ).

fof(f40,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f278,plain,
    ! [X0] :
      ( member(X0,empty_set)
      | ~ member(X0,sK2)
      | ~ member(X0,sK0) ),
    inference(superposition,[],[f63,f38]) ).

fof(f38,plain,
    empty_set = intersection(sK0,sK2),
    inference(cnf_transformation,[],[f22]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 16:54:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.36  % (2515)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (2518)WARNING: value z3 for option sas not known
% 0.20/0.37  % (2516)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37  % (2517)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37  % (2519)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (2518)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)
% 0.20/0.37  % (2520)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)
% 0.20/0.37  % (2521)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)
% 0.20/0.37  % (2522)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)
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [3]
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  % (2521)First to succeed.
% 0.20/0.38  % (2521)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2515"
% 0.20/0.38  % (2521)Refutation found. Thanks to Tanya!
% 0.20/0.38  % SZS status Theorem for theBenchmark
% 0.20/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38  % (2521)------------------------------
% 0.20/0.38  % (2521)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.38  % (2521)Termination reason: Refutation
% 0.20/0.38  
% 0.20/0.38  % (2521)Memory used [KB]: 857
% 0.20/0.38  % (2521)Time elapsed: 0.010 s
% 0.20/0.38  % (2521)Instructions burned: 12 (million)
% 0.20/0.38  % (2515)Success in time 0.026 s
%------------------------------------------------------------------------------