TSTP Solution File: SEV421_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEV421_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 : Tue May 21 04:15:45 EDT 2024

% Result   : Theorem 0.13s 0.35s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   43
% Syntax   : Number of formulae    :  127 (  15 unt;  15 typ;   0 def)
%            Number of atoms       :  299 ( 140 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  308 ( 121   ~; 107   |;  48   &)
%                                         (  25 <=>;   5  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  121 (  12 atm;  32 fun;  46 num;  31 var)
%            Number of types       :    4 (   2 usr;   1 ari)
%            Number of type conns  :   14 (   9   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   15 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  193 ( 175   !;  18   ?; 193   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    set: $tType ).

tff(type_def_6,type,
    element: $tType ).

tff(func_def_0,type,
    empty_set: set ).

tff(func_def_1,type,
    singleton: element > set ).

tff(func_def_2,type,
    intersection: ( set * set ) > set ).

tff(func_def_3,type,
    union: ( set * set ) > set ).

tff(func_def_4,type,
    difference: ( set * set ) > set ).

tff(func_def_5,type,
    complement: set > set ).

tff(func_def_6,type,
    cardinality: set > $int ).

tff(func_def_11,type,
    sK0: element ).

tff(func_def_12,type,
    sK1: set ).

tff(func_def_13,type,
    sK2: $int ).

tff(func_def_14,type,
    sK3: set > element ).

tff(pred_def_1,type,
    member: ( element * set ) > $o ).

tff(pred_def_2,type,
    subset: ( set * set ) > $o ).

tff(f130,plain,
    $false,
    inference(avatar_sat_refutation,[],[f103,f108,f110,f112,f129]) ).

tff(f129,plain,
    ( ~ spl4_1
    | spl4_2 ),
    inference(avatar_contradiction_clause,[],[f128]) ).

tff(f128,plain,
    ( $false
    | ~ spl4_1
    | spl4_2 ),
    inference(subsumption_resolution,[],[f127,f101]) ).

tff(f101,plain,
    ( ( empty_set != sK1 )
    | spl4_2 ),
    inference(avatar_component_clause,[],[f100]) ).

tff(f100,plain,
    ( spl4_2
  <=> ( empty_set = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

tff(f127,plain,
    ( ( empty_set = sK1 )
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f125,f98]) ).

tff(f98,plain,
    ( ( 0 = sK2 )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f96]) ).

tff(f96,plain,
    ( spl4_1
  <=> ( 0 = sK2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

tff(f125,plain,
    ( ( 0 != sK2 )
    | ( empty_set = sK1 ) ),
    inference(superposition,[],[f65,f62]) ).

tff(f62,plain,
    sK2 = cardinality(sK1),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ( ( ( empty_set != sK1 )
      | ( 0 != sK2 ) )
    & ( ( empty_set = sK1 )
      | ( 0 = sK2 ) )
    & ( sK2 = cardinality(sK1) )
    & ~ member(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f41,f42]) ).

tff(f42,plain,
    ( ? [X0: element,X1: set,X2: $int] :
        ( ( ( empty_set != X1 )
          | ( 0 != X2 ) )
        & ( ( empty_set = X1 )
          | ( 0 = X2 ) )
        & ( cardinality(X1) = X2 )
        & ~ member(X0,X1) )
   => ( ( ( empty_set != sK1 )
        | ( 0 != sK2 ) )
      & ( ( empty_set = sK1 )
        | ( 0 = sK2 ) )
      & ( sK2 = cardinality(sK1) )
      & ~ member(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f41,plain,
    ? [X0: element,X1: set,X2: $int] :
      ( ( ( empty_set != X1 )
        | ( 0 != X2 ) )
      & ( ( empty_set = X1 )
        | ( 0 = X2 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(flattening,[],[f40]) ).

tff(f40,plain,
    ? [X0: element,X1: set,X2: $int] :
      ( ( ( empty_set != X1 )
        | ( 0 != X2 ) )
      & ( ( empty_set = X1 )
        | ( 0 = X2 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(nnf_transformation,[],[f39]) ).

tff(f39,plain,
    ? [X0: element,X1: set,X2: $int] :
      ( ( ( 0 = X2 )
      <~> ( empty_set = X1 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(flattening,[],[f38]) ).

tff(f38,plain,
    ? [X0: element,X1: set,X2: $int] :
      ( ( ( 0 = X2 )
      <~> ( empty_set = X1 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(ennf_transformation,[],[f27]) ).

tff(f27,plain,
    ~ ! [X0: element,X1: set,X2: $int] :
        ( ( ( cardinality(X1) = X2 )
          & ~ member(X0,X1) )
       => ( ( 0 = X2 )
        <=> ( empty_set = X1 ) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X1: element,X6: set,X7: $int] :
        ( ( ( cardinality(X6) = X7 )
          & ~ member(X1,X6) )
       => ( ( 0 = X7 )
        <=> ( empty_set = X6 ) ) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X1: element,X6: set,X7: $int] :
      ( ( ( cardinality(X6) = X7 )
        & ~ member(X1,X6) )
     => ( ( 0 = X7 )
      <=> ( empty_set = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',vc1) ).

tff(f65,plain,
    ! [X0: set] :
      ( ( cardinality(X0) != 0 )
      | ( empty_set = X0 ) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,plain,
    ! [X0: set] :
      ( ( ( cardinality(X0) = 0 )
        | ( empty_set != X0 ) )
      & ( ( empty_set = X0 )
        | ( cardinality(X0) != 0 ) ) ),
    inference(nnf_transformation,[],[f8]) ).

tff(f8,axiom,
    ! [X0: set] :
      ( ( cardinality(X0) = 0 )
    <=> ( empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_empty_set) ).

tff(f112,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f111]) ).

tff(f111,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f98,f26,f25,f24,f23,f22,f21,f19,f18,f17,f16,f15,f64,f65,f67,f70,f69,f71,f74,f73,f76,f93,f94,f75,f78,f77,f80,f79,f83,f82,f81,f86,f85,f84,f89,f88,f87,f61,f20,f91,f62,f90,f92,f63,f102,f106]) ).

tff(f106,plain,
    ( ( 0 = sK2 )
    | ~ spl4_2 ),
    inference(forward_demodulation,[],[f104,f90]) ).

tff(f104,plain,
    ( ( sK2 = cardinality(empty_set) )
    | ~ spl4_2 ),
    inference(superposition,[],[f62,f102]) ).

tff(f102,plain,
    ( ( empty_set = sK1 )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f100]) ).

tff(f63,plain,
    ( ( empty_set = sK1 )
    | ( 0 = sK2 ) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f92,plain,
    ! [X1: element] : member(X1,singleton(X1)),
    inference(equality_resolution,[],[f72]) ).

tff(f72,plain,
    ! [X0: element,X1: element] :
      ( member(X0,singleton(X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f50,plain,
    ! [X0: element,X1: element] :
      ( ( member(X0,singleton(X1))
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ~ member(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f30]) ).

tff(f30,plain,
    ! [X0: element,X1: element] :
      ( member(X0,singleton(X1))
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X1: element,X2: element] :
      ( member(X1,singleton(X2))
    <=> ( X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).

tff(f90,plain,
    0 = cardinality(empty_set),
    inference(equality_resolution,[],[f66]) ).

tff(f66,plain,
    ! [X0: set] :
      ( ( cardinality(X0) = 0 )
      | ( empty_set != X0 ) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f91,plain,
    ! [X1: element] : ~ member(X1,empty_set),
    inference(equality_resolution,[],[f68]) ).

tff(f68,plain,
    ! [X0: set,X1: element] :
      ( ~ member(X1,X0)
      | ( empty_set != X0 ) ),
    inference(cnf_transformation,[],[f48]) ).

tff(f48,plain,
    ! [X0: set] :
      ( ( ! [X1: element] : ~ member(X1,X0)
        | ( empty_set != X0 ) )
      & ( ( empty_set = X0 )
        | member(sK3(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f46,f47]) ).

tff(f47,plain,
    ! [X0: set] :
      ( ? [X2: element] : member(X2,X0)
     => member(sK3(X0),X0) ),
    introduced(choice_axiom,[]) ).

tff(f46,plain,
    ! [X0: set] :
      ( ( ! [X1: element] : ~ member(X1,X0)
        | ( empty_set != X0 ) )
      & ( ( empty_set = X0 )
        | ? [X2: element] : member(X2,X0) ) ),
    inference(rectify,[],[f45]) ).

tff(f45,plain,
    ! [X0: set] :
      ( ( ! [X1: element] : ~ member(X1,X0)
        | ( empty_set != X0 ) )
      & ( ( empty_set = X0 )
        | ? [X1: element] : member(X1,X0) ) ),
    inference(nnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: set] :
      ( ! [X1: element] : ~ member(X1,X0)
    <=> ( empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).

tff(f20,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f61,plain,
    ~ member(sK0,sK1),
    inference(cnf_transformation,[],[f43]) ).

tff(f87,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f60,plain,
    ! [X0: element,X1: set,X2: set] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(flattening,[],[f59]) ).

tff(f59,plain,
    ! [X0: element,X1: set,X2: set] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(nnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: element,X1: set,X2: set] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X1: element,X2: set,X3: set] :
      ( member(X1,intersection(X2,X3))
    <=> ( member(X1,X3)
        & member(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).

tff(f88,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f89,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f84,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f58]) ).

tff(f58,plain,
    ! [X0: element,X1: set,X2: set] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f57]) ).

tff(f57,plain,
    ! [X0: element,X1: set,X2: set] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: element,X1: set,X2: set] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X1: element,X2: set,X3: set] :
      ( member(X1,union(X2,X3))
    <=> ( member(X1,X3)
        | member(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

tff(f85,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

tff(f86,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f58]) ).

tff(f81,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,X2)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f56]) ).

tff(f56,plain,
    ! [X0: element,X1: set,X2: set] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f55]) ).

tff(f55,plain,
    ! [X0: element,X1: set,X2: set] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f35]) ).

tff(f35,plain,
    ! [X0: element,X1: set,X2: set] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X3: element,X2: set,X4: set] :
      ( member(X3,difference(X4,X2))
    <=> ( ~ member(X3,X2)
        & member(X3,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).

tff(f82,plain,
    ! [X2: set,X0: element,X1: set] :
      ( ~ member(X0,X1)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f56]) ).

tff(f83,plain,
    ! [X2: set,X0: element,X1: set] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f56]) ).

tff(f79,plain,
    ! [X0: element,X1: set] :
      ( ( cardinality(X1) = cardinality(union(singleton(X0),X1)) )
      | ( singleton(X0) != intersection(singleton(X0),X1) ) ),
    inference(cnf_transformation,[],[f54]) ).

tff(f54,plain,
    ! [X0: element,X1: set] :
      ( ( ( singleton(X0) = intersection(singleton(X0),X1) )
        | ( cardinality(X1) != cardinality(union(singleton(X0),X1)) ) )
      & ( ( cardinality(X1) = cardinality(union(singleton(X0),X1)) )
        | ( singleton(X0) != intersection(singleton(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: element,X1: set] :
      ( ( singleton(X0) = intersection(singleton(X0),X1) )
    <=> ( cardinality(X1) = cardinality(union(singleton(X0),X1)) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X1: element,X0: set] :
      ( ( singleton(X1) = intersection(singleton(X1),X0) )
    <=> ( cardinality(X0) = cardinality(union(singleton(X1),X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_intersection_1) ).

tff(f80,plain,
    ! [X0: element,X1: set] :
      ( ( singleton(X0) = intersection(singleton(X0),X1) )
      | ( cardinality(X1) != cardinality(union(singleton(X0),X1)) ) ),
    inference(cnf_transformation,[],[f54]) ).

tff(f77,plain,
    ! [X0: element,X1: set] :
      ( ( cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) )
      | ( empty_set != intersection(singleton(X0),X1) ) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ! [X0: element,X1: set] :
      ( ( ( empty_set = intersection(singleton(X0),X1) )
        | ( cardinality(union(singleton(X0),X1)) != $sum(cardinality(X1),1) ) )
      & ( ( cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) )
        | ( empty_set != intersection(singleton(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: element,X1: set] :
      ( ( empty_set = intersection(singleton(X0),X1) )
    <=> ( cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X1: element,X0: set] :
      ( ( empty_set = intersection(singleton(X1),X0) )
    <=> ( cardinality(union(singleton(X1),X0)) = $sum(cardinality(X0),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_intersection_2) ).

tff(f78,plain,
    ! [X0: element,X1: set] :
      ( ( empty_set = intersection(singleton(X0),X1) )
      | ( cardinality(union(singleton(X0),X1)) != $sum(cardinality(X1),1) ) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f75,plain,
    ! [X0: set,X1: set] :
      ( ( empty_set = intersection(X0,X1) )
      | ( 0 != cardinality(intersection(X0,X1)) ) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X0: set,X1: set] :
      ( ( ( 0 = cardinality(intersection(X0,X1)) )
        | ( empty_set != intersection(X0,X1) ) )
      & ( ( empty_set = intersection(X0,X1) )
        | ( 0 != cardinality(intersection(X0,X1)) ) ) ),
    inference(nnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: set,X1: set] :
      ( ( 0 = cardinality(intersection(X0,X1)) )
    <=> ( empty_set = intersection(X0,X1) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X0: set,X5: set] :
      ( ( 0 = cardinality(intersection(X0,X5)) )
    <=> ( empty_set = intersection(X0,X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_intersection_3) ).

tff(f94,plain,
    0 = cardinality(empty_set),
    inference(global_subsumption,[],[f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f64,f63,f62,f61,f90,f65,f91,f67,f70,f69,f92,f71,f74,f73,f76,f93]) ).

tff(f93,plain,
    ! [X0: set,X1: set] :
      ( ( 0 = cardinality(empty_set) )
      | ( empty_set != intersection(X0,X1) ) ),
    inference(inner_rewriting,[],[f76]) ).

tff(f76,plain,
    ! [X0: set,X1: set] :
      ( ( 0 = cardinality(intersection(X0,X1)) )
      | ( empty_set != intersection(X0,X1) ) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f73,plain,
    ! [X0: set,X1: set] :
      ( ( cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) )
      | ( empty_set != intersection(X0,X1) ) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f51,plain,
    ! [X0: set,X1: set] :
      ( ( ( empty_set = intersection(X0,X1) )
        | ( cardinality(union(X0,X1)) != $sum(cardinality(X0),cardinality(X1)) ) )
      & ( ( cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) )
        | ( empty_set != intersection(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: set,X1: set] :
      ( ( empty_set = intersection(X0,X1) )
    <=> ( cardinality(union(X0,X1)) = $sum(cardinality(X0),cardinality(X1)) ) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X2: set,X3: set] :
      ( ( empty_set = intersection(X2,X3) )
    <=> ( cardinality(union(X2,X3)) = $sum(cardinality(X2),cardinality(X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cardinality_union) ).

tff(f74,plain,
    ! [X0: set,X1: set] :
      ( ( empty_set = intersection(X0,X1) )
      | ( cardinality(union(X0,X1)) != $sum(cardinality(X0),cardinality(X1)) ) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f71,plain,
    ! [X0: element,X1: element] :
      ( ( X0 = X1 )
      | ~ member(X0,singleton(X1)) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f69,plain,
    ! [X0: element,X1: set] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

tff(f49,plain,
    ! [X0: element,X1: set] :
      ( ( member(X0,X1)
        | member(X0,complement(X1)) )
      & ( ~ member(X0,complement(X1))
        | ~ member(X0,X1) ) ),
    inference(nnf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: element,X1: set] :
      ( member(X0,X1)
    <=> ~ member(X0,complement(X1)) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X1: element,X0: set] :
      ( member(X1,X0)
    <=> ~ member(X1,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).

tff(f70,plain,
    ! [X0: element,X1: set] :
      ( member(X0,X1)
      | member(X0,complement(X1)) ),
    inference(cnf_transformation,[],[f49]) ).

tff(f67,plain,
    ! [X0: set] :
      ( ( empty_set = X0 )
      | member(sK3(X0),X0) ),
    inference(cnf_transformation,[],[f48]) ).

tff(f64,plain,
    ( ( empty_set != sK1 )
    | ( 0 != sK2 ) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f15,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f16,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f17,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f19,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f21,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f22,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f23,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f24,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f25,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f26,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f110,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f109]) ).

tff(f109,plain,
    ( $false
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f26,f25,f24,f23,f22,f21,f19,f18,f17,f16,f15,f64,f65,f67,f70,f69,f71,f74,f73,f76,f93,f94,f75,f78,f77,f80,f79,f83,f82,f81,f86,f85,f84,f89,f88,f87,f61,f20,f91,f62,f90,f92,f63,f102,f106]) ).

tff(f108,plain,
    ( spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f107]) ).

tff(f107,plain,
    ( $false
    | spl4_1
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f106,f97]) ).

tff(f97,plain,
    ( ( 0 != sK2 )
    | spl4_1 ),
    inference(avatar_component_clause,[],[f96]) ).

tff(f103,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f63,f100,f96]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEV421_1 : TPTP v8.2.0. Released v5.0.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32  % Computer : n032.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Sun May 19 19:08:22 EDT 2024
% 0.13/0.33  % CPUTime    : 
% 0.13/0.33  % (31025)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.34  % (31029)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.34  % (31029)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.34  % (31029)Terminated due to inappropriate strategy.
% 0.13/0.34  % (31029)------------------------------
% 0.13/0.34  % (31029)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.34  % (31029)Termination reason: Inappropriate
% 0.13/0.34  
% 0.13/0.34  % (31029)Memory used [KB]: 801
% 0.13/0.34  % (31029)Time elapsed: 0.002 s
% 0.13/0.34  % (31029)Instructions burned: 3 (million)
% 0.13/0.34  % (31029)------------------------------
% 0.13/0.34  % (31029)------------------------------
% 0.13/0.34  % (31027)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.34  % (31028)WARNING: value z3 for option sas not known
% 0.13/0.34  % (31030)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)
% 0.13/0.34  % (31027)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.34  % (31027)Terminated due to inappropriate strategy.
% 0.13/0.34  % (31027)------------------------------
% 0.13/0.34  % (31027)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.34  % (31027)Termination reason: Inappropriate
% 0.13/0.34  
% 0.13/0.34  % (31027)Memory used [KB]: 802
% 0.13/0.34  % (31027)Time elapsed: 0.002 s
% 0.13/0.34  % (31027)Instructions burned: 3 (million)
% 0.13/0.34  % (31027)------------------------------
% 0.13/0.34  % (31027)------------------------------
% 0.13/0.34  % (31028)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)
% 0.13/0.34  % (31026)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.35  % (31032)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)
% 0.13/0.35  % (31031)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)
% 0.13/0.35  % (31026)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.35  % (31026)Terminated due to inappropriate strategy.
% 0.13/0.35  % (31026)------------------------------
% 0.13/0.35  % (31026)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.35  % (31026)Termination reason: Inappropriate
% 0.13/0.35  
% 0.13/0.35  % (31026)Memory used [KB]: 801
% 0.13/0.35  % (31026)Time elapsed: 0.002 s
% 0.13/0.35  % (31026)Instructions burned: 3 (million)
% 0.13/0.35  % (31026)------------------------------
% 0.13/0.35  % (31026)------------------------------
% 0.13/0.35  % (31028)First to succeed.
% 0.13/0.35  % (31030)Also succeeded, but the first one will report.
% 0.13/0.35  % (31032)Also succeeded, but the first one will report.
% 0.13/0.35  % (31031)Also succeeded, but the first one will report.
% 0.13/0.35  % (31028)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31025"
% 0.13/0.35  % (31028)Refutation found. Thanks to Tanya!
% 0.13/0.35  % SZS status Theorem for theBenchmark
% 0.13/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.35  % (31028)------------------------------
% 0.13/0.35  % (31028)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.35  % (31028)Termination reason: Refutation
% 0.13/0.35  
% 0.13/0.35  % (31028)Memory used [KB]: 859
% 0.13/0.35  % (31028)Time elapsed: 0.007 s
% 0.13/0.35  % (31028)Instructions burned: 9 (million)
% 0.13/0.35  % (31025)Success in time 0.007 s
%------------------------------------------------------------------------------