TSTP Solution File: SEU236+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU236+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 : Fri May  3 03:05:09 EDT 2024

% Result   : Theorem 150.23s 20.69s
% Output   : CNFRefutation 150.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   97 (  23 unt;   0 def)
%            Number of atoms       :  293 (  14 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  315 ( 119   ~; 124   |;  49   &)
%                                         (   9 <=>;  13  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  136 (   4 sgn  94   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f10,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f22,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(f28,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(f39,axiom,
    ! [X0] :
      ( ordinal(X0)
    <=> ( epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).

fof(f105,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ( ordinal(succ(X0))
        & epsilon_connected(succ(X0))
        & epsilon_transitive(succ(X0))
        & ~ empty(succ(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).

fof(f153,axiom,
    ! [X0,X1] :
      ( ( ordinal(X1)
        & ordinal(X0) )
     => ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

fof(f186,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X1,X2)
        & subset(X0,X1) )
     => subset(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(f206,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ( in(X0,X1)
          <=> ordinal_subset(succ(X0),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).

fof(f207,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => ! [X1] :
            ( ordinal(X1)
           => ( in(X0,X1)
            <=> ordinal_subset(succ(X0),X1) ) ) ),
    inference(negated_conjecture,[],[f206]) ).

fof(f216,axiom,
    ! [X0,X1,X2] :
      ( subset(unordered_pair(X0,X1),X2)
    <=> ( in(X1,X2)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

fof(f231,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => set_union2(singleton(X0),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).

fof(f254,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f263,axiom,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(f269,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X2,X1)
        & subset(X0,X1) )
     => subset(set_union2(X0,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).

fof(f313,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f363,plain,
    ! [X0] :
      ( ( ordinal(succ(X0))
        & epsilon_connected(succ(X0))
        & epsilon_transitive(succ(X0))
        & ~ empty(succ(X0)) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f105]) ).

fof(f397,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f153]) ).

fof(f398,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f397]) ).

fof(f435,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f186]) ).

fof(f436,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f435]) ).

fof(f464,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( in(X0,X1)
          <~> ordinal_subset(succ(X0),X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f207]) ).

fof(f482,plain,
    ! [X0,X1] :
      ( set_union2(singleton(X0),X1) = X1
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f231]) ).

fof(f529,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f269]) ).

fof(f530,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f529]) ).

fof(f609,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X1] :
            ( subset(X1,X0)
            | ~ in(X1,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(nnf_transformation,[],[f313]) ).

fof(f610,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f609]) ).

fof(f611,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK27(X0),X0)
        & in(sK27(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f612,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK27(X0),X0)
          & in(sK27(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f610,f611]) ).

fof(f652,plain,
    ! [X0] :
      ( ( ordinal(X0)
        | ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0) )
      & ( ( epsilon_connected(X0)
          & epsilon_transitive(X0) )
        | ~ ordinal(X0) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f653,plain,
    ! [X0] :
      ( ( ordinal(X0)
        | ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0) )
      & ( ( epsilon_connected(X0)
          & epsilon_transitive(X0) )
        | ~ ordinal(X0) ) ),
    inference(flattening,[],[f652]) ).

fof(f743,plain,
    ! [X0,X1] :
      ( ( ( ordinal_subset(X0,X1)
          | ~ subset(X0,X1) )
        & ( subset(X0,X1)
          | ~ ordinal_subset(X0,X1) ) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f398]) ).

fof(f768,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(succ(X0),X1)
            | ~ in(X0,X1) )
          & ( ordinal_subset(succ(X0),X1)
            | in(X0,X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(nnf_transformation,[],[f464]) ).

fof(f769,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(succ(X0),X1)
            | ~ in(X0,X1) )
          & ( ordinal_subset(succ(X0),X1)
            | in(X0,X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(flattening,[],[f768]) ).

fof(f770,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ ordinal_subset(succ(X0),X1)
              | ~ in(X0,X1) )
            & ( ordinal_subset(succ(X0),X1)
              | in(X0,X1) )
            & ordinal(X1) )
        & ordinal(X0) )
   => ( ? [X1] :
          ( ( ~ ordinal_subset(succ(sK87),X1)
            | ~ in(sK87,X1) )
          & ( ordinal_subset(succ(sK87),X1)
            | in(sK87,X1) )
          & ordinal(X1) )
      & ordinal(sK87) ) ),
    introduced(choice_axiom,[]) ).

fof(f771,plain,
    ( ? [X1] :
        ( ( ~ ordinal_subset(succ(sK87),X1)
          | ~ in(sK87,X1) )
        & ( ordinal_subset(succ(sK87),X1)
          | in(sK87,X1) )
        & ordinal(X1) )
   => ( ( ~ ordinal_subset(succ(sK87),sK88)
        | ~ in(sK87,sK88) )
      & ( ordinal_subset(succ(sK87),sK88)
        | in(sK87,sK88) )
      & ordinal(sK88) ) ),
    introduced(choice_axiom,[]) ).

fof(f772,plain,
    ( ( ~ ordinal_subset(succ(sK87),sK88)
      | ~ in(sK87,sK88) )
    & ( ordinal_subset(succ(sK87),sK88)
      | in(sK87,sK88) )
    & ordinal(sK88)
    & ordinal(sK87) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88])],[f769,f771,f770]) ).

fof(f780,plain,
    ! [X0,X1,X2] :
      ( ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f216]) ).

fof(f781,plain,
    ! [X0,X1,X2] :
      ( ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f780]) ).

fof(f834,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f892,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f22]) ).

fof(f914,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ in(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f612]) ).

fof(f967,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f653]) ).

fof(f1072,plain,
    ! [X0] :
      ( ordinal(succ(X0))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f363]) ).

fof(f1157,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ ordinal_subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f743]) ).

fof(f1158,plain,
    ! [X0,X1] :
      ( ordinal_subset(X0,X1)
      | ~ subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f743]) ).

fof(f1204,plain,
    ! [X2,X0,X1] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f436]) ).

fof(f1233,plain,
    ordinal(sK87),
    inference(cnf_transformation,[],[f772]) ).

fof(f1234,plain,
    ordinal(sK88),
    inference(cnf_transformation,[],[f772]) ).

fof(f1235,plain,
    ( ordinal_subset(succ(sK87),sK88)
    | in(sK87,sK88) ),
    inference(cnf_transformation,[],[f772]) ).

fof(f1236,plain,
    ( ~ ordinal_subset(succ(sK87),sK88)
    | ~ in(sK87,sK88) ),
    inference(cnf_transformation,[],[f772]) ).

fof(f1252,plain,
    ! [X2,X0,X1] :
      ( in(X0,X2)
      | ~ subset(unordered_pair(X0,X1),X2) ),
    inference(cnf_transformation,[],[f781]) ).

fof(f1275,plain,
    ! [X0,X1] :
      ( set_union2(singleton(X0),X1) = X1
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f482]) ).

fof(f1319,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f254]) ).

fof(f1332,plain,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    inference(cnf_transformation,[],[f263]) ).

fof(f1343,plain,
    ! [X2,X0,X1] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f530]) ).

fof(f1356,plain,
    ! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
    inference(definition_unfolding,[],[f892,f1319]) ).

fof(f1433,plain,
    ! [X0] :
      ( ordinal(set_union2(X0,unordered_pair(X0,X0)))
      | ~ ordinal(X0) ),
    inference(definition_unfolding,[],[f1072,f1356]) ).

fof(f1471,plain,
    ( ~ ordinal_subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | ~ in(sK87,sK88) ),
    inference(definition_unfolding,[],[f1236,f1356]) ).

fof(f1472,plain,
    ( ordinal_subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | in(sK87,sK88) ),
    inference(definition_unfolding,[],[f1235,f1356]) ).

fof(f1480,plain,
    ! [X0,X1] :
      ( set_union2(unordered_pair(X0,X0),X1) = X1
      | ~ in(X0,X1) ),
    inference(definition_unfolding,[],[f1275,f1319]) ).

cnf(c_61,plain,
    set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f834]) ).

cnf(c_142,plain,
    ( ~ in(X0,X1)
    | ~ epsilon_transitive(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f914]) ).

cnf(c_195,plain,
    ( ~ ordinal(X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f967]) ).

cnf(c_294,plain,
    ( ~ ordinal(X0)
    | ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
    inference(cnf_transformation,[],[f1433]) ).

cnf(c_382,plain,
    ( ~ subset(X0,X1)
    | ~ ordinal(X0)
    | ~ ordinal(X1)
    | ordinal_subset(X0,X1) ),
    inference(cnf_transformation,[],[f1158]) ).

cnf(c_383,plain,
    ( ~ ordinal_subset(X0,X1)
    | ~ ordinal(X0)
    | ~ ordinal(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f1157]) ).

cnf(c_429,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X0)
    | subset(X2,X1) ),
    inference(cnf_transformation,[],[f1204]) ).

cnf(c_458,negated_conjecture,
    ( ~ ordinal_subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | ~ in(sK87,sK88) ),
    inference(cnf_transformation,[],[f1471]) ).

cnf(c_459,negated_conjecture,
    ( ordinal_subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | in(sK87,sK88) ),
    inference(cnf_transformation,[],[f1472]) ).

cnf(c_460,negated_conjecture,
    ordinal(sK88),
    inference(cnf_transformation,[],[f1234]) ).

cnf(c_461,negated_conjecture,
    ordinal(sK87),
    inference(cnf_transformation,[],[f1233]) ).

cnf(c_479,plain,
    ( ~ subset(unordered_pair(X0,X1),X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f1252]) ).

cnf(c_500,plain,
    ( ~ in(X0,X1)
    | set_union2(unordered_pair(X0,X0),X1) = X1 ),
    inference(cnf_transformation,[],[f1480]) ).

cnf(c_555,plain,
    subset(X0,set_union2(X0,X1)),
    inference(cnf_transformation,[],[f1332]) ).

cnf(c_566,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X1)
    | subset(set_union2(X0,X2),X1) ),
    inference(cnf_transformation,[],[f1343]) ).

cnf(c_16496,plain,
    epsilon_transitive(sK88),
    inference(superposition,[status(thm)],[c_460,c_195]) ).

cnf(c_31739,plain,
    subset(X0,set_union2(X1,X0)),
    inference(superposition,[status(thm)],[c_61,c_555]) ).

cnf(c_41275,plain,
    ( ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | ~ ordinal(sK88)
    | subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | in(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_459,c_383]) ).

cnf(c_41446,plain,
    ( ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | in(sK87,sK88) ),
    inference(global_subsumption_just,[status(thm)],[c_41275,c_460,c_41275]) ).

cnf(c_41454,plain,
    ( ~ subset(X0,set_union2(sK87,unordered_pair(sK87,sK87)))
    | ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | subset(X0,sK88)
    | in(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_41446,c_429]) ).

cnf(c_41493,plain,
    ( ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | subset(unordered_pair(sK87,sK87),sK88)
    | in(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_31739,c_41454]) ).

cnf(c_42408,plain,
    ( ~ ordinal(sK87)
    | subset(unordered_pair(sK87,sK87),sK88)
    | in(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_294,c_41493]) ).

cnf(c_46396,plain,
    subset(X0,set_union2(X1,X0)),
    inference(superposition,[status(thm)],[c_61,c_555]) ).

cnf(c_53979,plain,
    ( ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | ~ ordinal(sK88)
    | subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | in(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_459,c_383]) ).

cnf(c_54314,plain,
    ( ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | in(sK87,sK88) ),
    inference(global_subsumption_just,[status(thm)],[c_53979,c_41446]) ).

cnf(c_54322,plain,
    ( ~ subset(X0,set_union2(sK87,unordered_pair(sK87,sK87)))
    | ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | subset(X0,sK88)
    | in(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_54314,c_429]) ).

cnf(c_54437,plain,
    ( ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | subset(unordered_pair(sK87,sK87),sK88)
    | in(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_46396,c_54322]) ).

cnf(c_55896,plain,
    ( subset(unordered_pair(sK87,sK87),sK88)
    | in(sK87,sK88) ),
    inference(global_subsumption_just,[status(thm)],[c_54437,c_461,c_42408]) ).

cnf(c_55909,plain,
    in(sK87,sK88),
    inference(superposition,[status(thm)],[c_55896,c_479]) ).

cnf(c_66565,plain,
    ( ~ epsilon_transitive(sK88)
    | subset(sK87,sK88) ),
    inference(superposition,[status(thm)],[c_55909,c_142]) ).

cnf(c_76875,negated_conjecture,
    in(sK87,sK88),
    inference(global_subsumption_just,[status(thm)],[c_459,c_55909]) ).

cnf(c_85269,plain,
    set_union2(unordered_pair(sK87,sK87),sK88) = sK88,
    inference(superposition,[status(thm)],[c_76875,c_500]) ).

cnf(c_85730,plain,
    subset(unordered_pair(sK87,sK87),sK88),
    inference(superposition,[status(thm)],[c_85269,c_555]) ).

cnf(c_110684,plain,
    ( ~ subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
    | ~ ordinal(set_union2(sK87,unordered_pair(sK87,sK87)))
    | ~ ordinal(sK88)
    | ordinal_subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88) ),
    inference(instantiation,[status(thm)],[c_382]) ).

cnf(c_112549,plain,
    ( ~ ordinal(sK87)
    | ordinal(set_union2(sK87,unordered_pair(sK87,sK87))) ),
    inference(instantiation,[status(thm)],[c_294]) ).

cnf(c_116226,plain,
    ( ~ subset(unordered_pair(sK87,sK87),sK88)
    | ~ subset(sK87,sK88)
    | subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88) ),
    inference(instantiation,[status(thm)],[c_566]) ).

cnf(c_116227,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_116226,c_112549,c_110684,c_85730,c_66565,c_55909,c_16496,c_458,c_460,c_461]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEU236+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.30  % Computer : n022.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Thu May  2 17:45:12 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.15/0.41  Running first-order theorem proving
% 0.15/0.41  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 150.23/20.69  % SZS status Started for theBenchmark.p
% 150.23/20.69  % SZS status Theorem for theBenchmark.p
% 150.23/20.69  
% 150.23/20.69  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 150.23/20.69  
% 150.23/20.69  ------  iProver source info
% 150.23/20.69  
% 150.23/20.69  git: date: 2024-05-02 19:28:25 +0000
% 150.23/20.69  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 150.23/20.69  git: non_committed_changes: false
% 150.23/20.69  
% 150.23/20.69  ------ Parsing...
% 150.23/20.69  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 150.23/20.69  
% 150.23/20.69  ------ Preprocessing... sup_sim: 40  sf_s  rm: 6 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 150.23/20.69  
% 150.23/20.69  ------ Preprocessing... gs_s  sp: 2 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 150.23/20.69  
% 150.23/20.69  ------ Preprocessing... sf_s  rm: 3 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 150.23/20.69  ------ Proving...
% 150.23/20.69  ------ Problem Properties 
% 150.23/20.69  
% 150.23/20.69  
% 150.23/20.69  clauses                                 460
% 150.23/20.69  conjectures                             4
% 150.23/20.69  EPR                                     83
% 150.23/20.69  Horn                                    366
% 150.23/20.69  unary                                   82
% 150.23/20.69  binary                                  132
% 150.23/20.69  lits                                    1299
% 150.23/20.69  lits eq                                 238
% 150.23/20.69  fd_pure                                 0
% 150.23/20.69  fd_pseudo                               0
% 150.23/20.69  fd_cond                                 17
% 150.23/20.69  fd_pseudo_cond                          92
% 150.23/20.69  AC symbols                              0
% 150.23/20.69  
% 150.23/20.69  ------ Input Options Time Limit: Unbounded
% 150.23/20.69  
% 150.23/20.69  
% 150.23/20.69  ------ 
% 150.23/20.69  Current options:
% 150.23/20.69  ------ 
% 150.23/20.69  
% 150.23/20.69  
% 150.23/20.69  
% 150.23/20.69  
% 150.23/20.69  ------ Proving...
% 150.23/20.69  
% 150.23/20.69  
% 150.23/20.69  % SZS status Theorem for theBenchmark.p
% 150.23/20.69  
% 150.23/20.69  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 150.23/20.69  
% 150.23/20.70  
%------------------------------------------------------------------------------