↑ Up

iProver---3.9.4.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:56:11 PM UTC 2026

% Result   : Theorem 3.84s 1.19s
% Output   : CNFRefutation 3.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   74 (  17 unt;   3 def)
%            Number of atoms       :  324 (  58 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  364 ( 140   ~; 144   |;  64   &)
%                                         (   7 <=>;   7  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  135 (   0 sgn 117   !;  18   ?;  23   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0,X1,X2] :
      ( X2 = set_intersection2(X0,X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(f23,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <=> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l82_funct_1) ).

fof(f24,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
        <=> ( in(X1,X0)
            & in(X1,relation_dom(X2)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f23]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( X1 = relation_dom_restriction(X2,X0)
          <=> ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | relation(relation_dom_restriction(X0,X1)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    inference(flattening,[],[f53]) ).

fof(f58,plain,
    ? [X0,X1,X2] :
      ( function(X2)
      & relation(X2)
      & ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <~> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f59,plain,
    ? [X0,X1,X2] :
      ( function(X2)
      & relation(X2)
      & ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <~> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) ) ),
    inference(flattening,[],[f58]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( X1 = relation_dom_restriction(X2,X0)
          <=> ( ! [X3] :
                  ( ~ in(X3,relation_dom(X1))
                  | apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( X1 = relation_dom_restriction(X2,X0)
          <=> ( ! [X3] :
                  ( ~ in(X3,relation_dom(X1))
                  | apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
    inference(flattening,[],[f63]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) != X2
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | ( in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | ( in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) ) )
        | X2 = set_intersection2(X0,X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) != X2
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | ( in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | ( in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) ) )
        | X2 = set_intersection2(X0,X1) ) ),
    inference(flattening,[],[f68]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) != X2
        | ! [X4] :
            ( ( ~ in(X4,X2)
              | ( in(X4,X1)
                & in(X4,X0) ) )
            & ( ~ in(X4,X1)
              | ~ in(X4,X0)
              | in(X4,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | ( in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) ) )
        | X2 = set_intersection2(X0,X1) ) ),
    inference(rectify,[],[f69]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) != X2
        | ! [X4] :
            ( ( ~ in(X4,X2)
              | ( in(X4,X1)
                & in(X4,X0) ) )
            & ( ~ in(X4,X1)
              | ~ in(X4,X0)
              | in(X4,X2) ) ) )
      & ( ( ( in(sK0(X0,X1,X2),X2)
            | ( in(sK0(X0,X1,X2),X1)
              & in(sK0(X0,X1,X2),X0) ) )
          & ( ~ in(sK0(X0,X1,X2),X2)
            | ~ in(sK0(X0,X1,X2),X1)
            | ~ in(sK0(X0,X1,X2),X0) ) )
        | X2 = set_intersection2(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f70]) ).

fof(f73,plain,
    ? [X0,X1,X2] :
      ( function(X2)
      & relation(X2)
      & ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
        | ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) )
      & ( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
        | ~ in(X1,X0)
        | ~ in(X1,relation_dom(X2)) ) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f74,plain,
    ? [X0,X1,X2] :
      ( function(X2)
      & relation(X2)
      & ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
        | ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) )
      & ( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
        | ~ in(X1,X0)
        | ~ in(X1,relation_dom(X2)) ) ),
    inference(flattening,[],[f73]) ).

fof(f75,plain,
    ( function(sK4)
    & relation(sK4)
    & ( in(sK3,relation_dom(relation_dom_restriction(sK4,sK2)))
      | ( in(sK3,sK2)
        & in(sK3,relation_dom(sK4)) ) )
    & ( ~ in(sK3,relation_dom(relation_dom_restriction(sK4,sK2)))
      | ~ in(sK3,sK2)
      | ~ in(sK3,relation_dom(sK4)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f74]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( relation_dom_restriction(X2,X0) != X1
              | ( ! [X3] :
                    ( ~ in(X3,relation_dom(X1))
                    | apply(X1,X3) = apply(X2,X3) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
            & ( ? [X3] :
                  ( in(X3,relation_dom(X1))
                  & apply(X1,X3) != apply(X2,X3) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
              | X1 = relation_dom_restriction(X2,X0) ) ) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( relation_dom_restriction(X2,X0) != X1
              | ( ! [X3] :
                    ( ~ in(X3,relation_dom(X1))
                    | apply(X1,X3) = apply(X2,X3) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
            & ( ? [X3] :
                  ( in(X3,relation_dom(X1))
                  & apply(X1,X3) != apply(X2,X3) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
              | X1 = relation_dom_restriction(X2,X0) ) ) ) ),
    inference(flattening,[],[f84]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( relation_dom_restriction(X2,X0) != X1
              | ( ! [X4] :
                    ( ~ in(X4,relation_dom(X1))
                    | apply(X1,X4) = apply(X2,X4) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
            & ( ? [X3] :
                  ( in(X3,relation_dom(X1))
                  & apply(X1,X3) != apply(X2,X3) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
              | X1 = relation_dom_restriction(X2,X0) ) ) ) ),
    inference(rectify,[],[f85]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( relation_dom_restriction(X2,X0) != X1
              | ( ! [X4] :
                    ( ~ in(X4,relation_dom(X1))
                    | apply(X1,X4) = apply(X2,X4) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
            & ( ( in(sK13(X1,X2),relation_dom(X1))
                & apply(X1,sK13(X1,X2)) != apply(X2,sK13(X1,X2)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
              | X1 = relation_dom_restriction(X2,X0) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X1,X2))],[f86]) ).

fof(f94,plain,
    ! [X2,X0,X1,X4] :
      ( set_intersection2(X0,X1) != X2
      | ~ in(X4,X2)
      | in(X4,X1) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f95,plain,
    ! [X2,X0,X1,X4] :
      ( set_intersection2(X0,X1) != X2
      | ~ in(X4,X2)
      | in(X4,X0) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f96,plain,
    ! [X2,X0,X1,X4] :
      ( set_intersection2(X0,X1) != X2
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | relation(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | function(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f117,plain,
    function(sK4),
    inference(cnf_transformation,[],[f75]) ).

fof(f118,plain,
    relation(sK4),
    inference(cnf_transformation,[],[f75]) ).

fof(f119,plain,
    ( in(sK3,relation_dom(relation_dom_restriction(sK4,sK2)))
    | in(sK3,sK2) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f120,plain,
    ( in(sK3,relation_dom(relation_dom_restriction(sK4,sK2)))
    | in(sK3,relation_dom(sK4)) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f121,plain,
    ( ~ in(sK3,relation_dom(relation_dom_restriction(sK4,sK2)))
    | ~ in(sK3,sK2)
    | ~ in(sK3,relation_dom(sK4)) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f141,plain,
    ! [X2,X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ~ function(X2)
      | ~ relation(X2)
      | relation_dom_restriction(X2,X0) != X1
      | relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f147,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f96]) ).

fof(f148,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_intersection2(X0,X1))
      | in(X4,X0) ),
    inference(equality_resolution,[],[f95]) ).

fof(f149,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_intersection2(X0,X1))
      | in(X4,X1) ),
    inference(equality_resolution,[],[f94]) ).

fof(f150,plain,
    ! [X2,X0] :
      ( ~ function(relation_dom_restriction(X2,X0))
      | ~ relation(relation_dom_restriction(X2,X0))
      | ~ function(X2)
      | ~ relation(X2)
      | relation_dom(relation_dom_restriction(X2,X0)) = set_intersection2(relation_dom(X2),X0) ),
    inference(equality_resolution,[],[f141]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,set_intersection2(X2,X1))
      | ~ in(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f147]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X1)
      | ~ in(X0,set_intersection2(X1,X2)) ),
    inference(cnf_transformation,[],[f148]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X2)
      | ~ in(X0,set_intersection2(X1,X2)) ),
    inference(cnf_transformation,[],[f149]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f100]) ).

tcf(c_69,plain,
    ! [X0: $i,X1: $i] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f109]) ).

tcf(c_76,negated_conjecture,
    ( ~ in(sK3,sK2)
    | ~ in(sK3,relation_dom(sK4))
    | ~ in(sK3,relation_dom(relation_dom_restriction(sK4,sK2))) ),
    inference(cnf_transformation,[],[f121]) ).

tcf(c_77,negated_conjecture,
    ( in(sK3,relation_dom(sK4))
    | in(sK3,relation_dom(relation_dom_restriction(sK4,sK2))) ),
    inference(cnf_transformation,[],[f120]) ).

tcf(c_78,negated_conjecture,
    ( in(sK3,sK2)
    | in(sK3,relation_dom(relation_dom_restriction(sK4,sK2))) ),
    inference(cnf_transformation,[],[f119]) ).

tcf(c_79,negated_conjecture,
    relation(sK4),
    inference(cnf_transformation,[],[f118]) ).

tcf(c_80,negated_conjecture,
    function(sK4),
    inference(cnf_transformation,[],[f117]) ).

tcf(c_101,plain,
    ! [X0: $i,X1: $i] :
      ( ( set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ relation(relation_dom_restriction(X0,X1))
      | ~ function(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[],[f150]) ).

tcf(c_131,plain,
    ! [X0: $i,X1: $i] :
      ( ( set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_101,c_59,c_69,c_101]) ).

tcf(c_884,definition,
    iPr_def_10 = relation_dom_restriction(sK4,sK2),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_885,definition,
    iPr_def_11 = relation_dom(iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_886,definition,
    iPr_def_12 = relation_dom(sK4),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_887,negated_conjecture,
    function(sK4),
    inference(demodulation,[status(thm)],[c_80]) ).

tcf(c_888,negated_conjecture,
    relation(sK4),
    inference(demodulation,[status(thm)],[c_79]) ).

tcf(c_889,negated_conjecture,
    ( in(sK3,iPr_def_11)
    | in(sK3,sK2) ),
    inference(demodulation,[status(thm)],[c_78,c_884,c_885]) ).

tcf(c_890,negated_conjecture,
    ( in(sK3,iPr_def_12)
    | in(sK3,iPr_def_11) ),
    inference(demodulation,[status(thm)],[c_77,c_886]) ).

tcf(c_891,negated_conjecture,
    ( ~ in(sK3,iPr_def_12)
    | ~ in(sK3,iPr_def_11)
    | ~ in(sK3,sK2) ),
    inference(demodulation,[status(thm)],[c_76]) ).

tcf(c_1833,plain,
    ! [X0: $i] :
      ( ( set_intersection2(relation_dom(sK4),X0) = relation_dom(relation_dom_restriction(sK4,X0)) )
      | ~ relation(sK4) ),
    inference(superposition,[status(thm)],[c_887,c_131]) ).

tcf(c_1845,plain,
    ! [X0: $i] :
      ( ( relation_dom(relation_dom_restriction(sK4,X0)) = set_intersection2(iPr_def_12,X0) )
      | ~ relation(sK4) ),
    inference(light_normalisation,[status(thm)],[c_1833,c_886]) ).

tcf(c_1846,plain,
    ! [X0: $i] : relation_dom(relation_dom_restriction(sK4,X0)) = set_intersection2(iPr_def_12,X0),
    inference(forward_subsumption_resolution,[status(thm)],[c_1845,c_888]) ).

tcf(c_2062,plain,
    set_intersection2(iPr_def_12,sK2) = relation_dom(iPr_def_10),
    inference(superposition,[status(thm)],[c_884,c_1846]) ).

tcf(c_2067,plain,
    set_intersection2(iPr_def_12,sK2) = iPr_def_11,
    inference(light_normalisation,[status(thm)],[c_2062,c_885]) ).

tcf(c_2168,plain,
    ! [X0: $i] :
      ( in(X0,iPr_def_11)
      | ~ in(X0,iPr_def_12)
      | ~ in(X0,sK2) ),
    inference(superposition,[status(thm)],[c_2067,c_56]) ).

tcf(c_2169,plain,
    ! [X0: $i] :
      ( in(X0,sK2)
      | ~ in(X0,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_2067,c_58]) ).

tcf(c_2170,plain,
    ! [X0: $i] :
      ( in(X0,iPr_def_12)
      | ~ in(X0,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_2067,c_57]) ).

tcf(c_2815,plain,
    ( ~ in(sK3,iPr_def_12)
    | ~ in(sK3,sK2) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_891,c_2168]) ).

tcf(c_2822,plain,
    ( in(sK3,iPr_def_11)
    | ~ in(sK3,iPr_def_12) ),
    inference(superposition,[status(thm)],[c_889,c_2168]) ).

tcf(c_2916,plain,
    in(sK3,sK2),
    inference(backward_subsumption_resolution,[status(thm)],[c_889,c_2169]) ).

tcf(c_2957,plain,
    in(sK3,iPr_def_11),
    inference(global_subsumption_just,[status(thm)],[c_2822,c_890,c_2815,c_2916]) ).

tcf(c_2965,plain,
    ~ in(sK3,iPr_def_12),
    inference(global_subsumption_just,[status(thm)],[c_2815,c_2815,c_2916]) ).

tcf(c_3073,plain,
    in(sK3,iPr_def_12),
    inference(superposition,[status(thm)],[c_2957,c_2170]) ).

tcf(c_3075,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_3073,c_2965]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36  % Computer : n013.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Thu Sep 24 13:16:07 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41  Running first-order theorem proving
% 0.13/0.41  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.42  
% 0.13/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42  
% 0.13/0.42  % Detected problem language: tptp
% 0.13/0.43  % Proving...
% 3.84/1.19  % SZS status Started for theBenchmark.p
% 3.84/1.19  % SZS status Theorem for theBenchmark.p
% 3.84/1.19  
% 3.84/1.19  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.84/1.19  
% 3.84/1.19  % ------  iProver source info
% 3.84/1.19  
% 3.84/1.19  % git: date: 2026-07-19 20:42:38 +0200
% 3.84/1.19  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.84/1.19  % git: non_committed_changes: false
% 3.84/1.19  
% 3.84/1.19  % ------ Parsing...
% 3.84/1.19  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.84/1.19  
% 3.84/1.19  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e % 
% 3.84/1.19  
% 3.84/1.19  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 3.84/1.19  
% 3.84/1.19  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.84/1.19  % ------ Proving...
% 3.84/1.19  % ------ Problem Properties 
% 3.84/1.19  
% 3.84/1.19  % 
% 3.84/1.19  % clauses                               50
% 3.84/1.19  % conjectures                           5
% 3.84/1.19  % EPR                                   27
% 3.84/1.19  % Horn                                  44
% 3.84/1.19  % unary                                 24
% 3.84/1.19  % binary                                13
% 3.84/1.19  % lits                                  99
% 3.84/1.19  % lits eq                               18
% 3.84/1.19  % fd_pure                               0
% 3.84/1.19  % fd_pseudo                             0
% 3.84/1.19  % fd_cond                               1
% 3.84/1.19  % fd_pseudo_cond                        6
% 3.84/1.19  % AC symbols                            0
% 3.84/1.19  
% 3.84/1.19  % ------ Schedule dynamic 5 is on 
% 3.84/1.19  
% 3.84/1.19  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.84/1.19  
% 3.84/1.19  
% 3.84/1.19  % ------ 
% 3.84/1.19  % Current options:
% 3.84/1.19  % ------ 
% 3.84/1.19  
% 3.84/1.19  
% 3.84/1.19  % 
% 3.84/1.19  
% 3.84/1.19  % ------ Proving...
% 3.84/1.19  % 
% 3.84/1.19  
% 3.84/1.19  % SZS status Theorem for theBenchmark.p
% 3.84/1.19  
% 3.84/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/1.20  
% 3.84/1.20  
%------------------------------------------------------------------------------