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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU361+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n006.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 02:57:13 PM UTC 2026

% Result   : Theorem 3.16s 1.53s
% Output   : CNFRefutation 3.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   71 (  23 unt;   2 def)
%            Number of atoms       :  290 (  24 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  333 ( 130   ~; 119   |;  56   &)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   4 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   93 (   0 sgn  87   !;   6   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( rel_str(X0)
     => bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( rel_str(X0)
     => element(join_on_relstr(X0,X1),the_carrier(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).

fof(f22,axiom,
    ! [X0] :
      ( ( rel_str(X0)
        & antisymmetric_relstr(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( ( ( ! [X3] :
                      ( element(X3,the_carrier(X0))
                     => ( relstr_set_smaller(X0,X2,X3)
                       => related(X0,X1,X3) ) )
                  & relstr_set_smaller(X0,X2,X1) )
               => ( ex_sup_of_relstr_set(X0,X2)
                  & X1 = join_on_relstr(X0,X2) ) )
              & ( ( ex_sup_of_relstr_set(X0,X2)
                  & X1 = join_on_relstr(X0,X2) )
               => ( ! [X3] :
                      ( element(X3,the_carrier(X0))
                     => ( relstr_set_smaller(X0,X2,X3)
                       => related(X0,X1,X3) ) )
                  & relstr_set_smaller(X0,X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_yellow_0) ).

fof(f23,axiom,
    ! [X0] :
      ( ( rel_str(X0)
        & lower_bounded_relstr(X0)
        & antisymmetric_relstr(X0)
        & ~ empty_carrier(X0) )
     => ( ex_inf_of_relstr_set(X0,the_carrier(X0))
        & ex_sup_of_relstr_set(X0,empty_set) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).

fof(f24,conjecture,
    ! [X0] :
      ( ( rel_str(X0)
        & lower_bounded_relstr(X0)
        & antisymmetric_relstr(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => related(X0,bottom_of_relstr(X0),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).

fof(f25,negated_conjecture,
    ~ ! [X0] :
        ( ( rel_str(X0)
          & lower_bounded_relstr(X0)
          & antisymmetric_relstr(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,the_carrier(X0))
           => related(X0,bottom_of_relstr(X0),X1) ) ),
    inference(negated_conjecture,[status(cth)],[f24]) ).

fof(f27,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ( relstr_element_smaller(X0,empty_set,X1)
            & relstr_set_smaller(X0,empty_set,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).

fof(f30,plain,
    ! [X0] :
      ( ( rel_str(X0)
        & antisymmetric_relstr(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( ( ( ! [X4] :
                      ( element(X4,the_carrier(X0))
                     => ( relstr_set_smaller(X0,X2,X4)
                       => related(X0,X1,X4) ) )
                  & relstr_set_smaller(X0,X2,X1) )
               => ( ex_sup_of_relstr_set(X0,X2)
                  & X1 = join_on_relstr(X0,X2) ) )
              & ( ( ex_sup_of_relstr_set(X0,X2)
                  & X1 = join_on_relstr(X0,X2) )
               => ( ! [X3] :
                      ( element(X3,the_carrier(X0))
                     => ( relstr_set_smaller(X0,X2,X3)
                       => related(X0,X1,X3) ) )
                  & relstr_set_smaller(X0,X2,X1) ) ) ) ) ),
    inference(rectify,[],[f22]) ).

fof(f31,plain,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => relstr_set_smaller(X0,empty_set,X1) ) ),
    inference(pure_predicate_removal,[],[f27]) ).

fof(f32,plain,
    ! [X0] :
      ( ( rel_str(X0)
        & lower_bounded_relstr(X0)
        & antisymmetric_relstr(X0)
        & ~ empty_carrier(X0) )
     => ex_sup_of_relstr_set(X0,empty_set) ),
    inference(pure_predicate_removal,[],[f23]) ).

fof(f36,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ rel_str(X0)
      | element(join_on_relstr(X0,X1),the_carrier(X0)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0)
      | ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ( ? [X4] :
                    ( element(X4,the_carrier(X0))
                    & relstr_set_smaller(X0,X2,X4)
                    & ~ related(X0,X1,X4) )
                | ~ relstr_set_smaller(X0,X2,X1)
                | ( ex_sup_of_relstr_set(X0,X2)
                  & X1 = join_on_relstr(X0,X2) ) )
              & ( ~ ex_sup_of_relstr_set(X0,X2)
                | join_on_relstr(X0,X2) != X1
                | ( ! [X3] :
                      ( ~ element(X3,the_carrier(X0))
                      | ~ relstr_set_smaller(X0,X2,X3)
                      | related(X0,X1,X3) )
                  & relstr_set_smaller(X0,X2,X1) ) ) ) ) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0)
      | ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ( ? [X4] :
                    ( element(X4,the_carrier(X0))
                    & relstr_set_smaller(X0,X2,X4)
                    & ~ related(X0,X1,X4) )
                | ~ relstr_set_smaller(X0,X2,X1)
                | ( ex_sup_of_relstr_set(X0,X2)
                  & X1 = join_on_relstr(X0,X2) ) )
              & ( ~ ex_sup_of_relstr_set(X0,X2)
                | join_on_relstr(X0,X2) != X1
                | ( ! [X3] :
                      ( ~ element(X3,the_carrier(X0))
                      | ~ relstr_set_smaller(X0,X2,X3)
                      | related(X0,X1,X3) )
                  & relstr_set_smaller(X0,X2,X1) ) ) ) ) ),
    inference(flattening,[],[f45]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ antisymmetric_relstr(X0)
      | empty_carrier(X0)
      | ex_sup_of_relstr_set(X0,empty_set) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f48,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ antisymmetric_relstr(X0)
      | empty_carrier(X0)
      | ex_sup_of_relstr_set(X0,empty_set) ),
    inference(flattening,[],[f47]) ).

fof(f49,plain,
    ? [X0] :
      ( rel_str(X0)
      & lower_bounded_relstr(X0)
      & antisymmetric_relstr(X0)
      & ~ empty_carrier(X0)
      & ? [X1] :
          ( element(X1,the_carrier(X0))
          & ~ related(X0,bottom_of_relstr(X0),X1) ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f50,plain,
    ? [X0] :
      ( rel_str(X0)
      & lower_bounded_relstr(X0)
      & antisymmetric_relstr(X0)
      & ~ empty_carrier(X0)
      & ? [X1] :
          ( element(X1,the_carrier(X0))
          & ~ related(X0,bottom_of_relstr(X0),X1) ) ),
    inference(flattening,[],[f49]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | relstr_set_smaller(X0,empty_set,X1) ) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f62,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0)
      | ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ( ( element(sK7(X0,X1,X2),the_carrier(X0))
                  & relstr_set_smaller(X0,X2,sK7(X0,X1,X2))
                  & ~ related(X0,X1,sK7(X0,X1,X2)) )
                | ~ relstr_set_smaller(X0,X2,X1)
                | ( ex_sup_of_relstr_set(X0,X2)
                  & X1 = join_on_relstr(X0,X2) ) )
              & ( ~ ex_sup_of_relstr_set(X0,X2)
                | join_on_relstr(X0,X2) != X1
                | ( ! [X3] :
                      ( ~ element(X3,the_carrier(X0))
                      | ~ relstr_set_smaller(X0,X2,X3)
                      | related(X0,X1,X3) )
                  & relstr_set_smaller(X0,X2,X1) ) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f46]) ).

fof(f63,plain,
    ( rel_str(sK8)
    & lower_bounded_relstr(sK8)
    & antisymmetric_relstr(sK8)
    & ~ empty_carrier(sK8)
    & element(sK9,the_carrier(sK8))
    & ~ related(sK8,bottom_of_relstr(sK8),sK9) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f50]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ rel_str(X0)
      | element(join_on_relstr(X0,X1),the_carrier(X0)) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f87,plain,
    ! [X2,X3,X0,X1] :
      ( ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ ex_sup_of_relstr_set(X0,X2)
      | join_on_relstr(X0,X2) != X1
      | ~ element(X3,the_carrier(X0))
      | ~ relstr_set_smaller(X0,X2,X3)
      | related(X0,X1,X3) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ antisymmetric_relstr(X0)
      | empty_carrier(X0)
      | ex_sup_of_relstr_set(X0,empty_set) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f90,plain,
    rel_str(sK8),
    inference(cnf_transformation,[],[f63]) ).

fof(f91,plain,
    lower_bounded_relstr(sK8),
    inference(cnf_transformation,[],[f63]) ).

fof(f92,plain,
    antisymmetric_relstr(sK8),
    inference(cnf_transformation,[],[f63]) ).

fof(f93,plain,
    ~ empty_carrier(sK8),
    inference(cnf_transformation,[],[f63]) ).

fof(f94,plain,
    element(sK9,the_carrier(sK8)),
    inference(cnf_transformation,[],[f63]) ).

fof(f95,plain,
    ~ related(sK8,bottom_of_relstr(sK8),sK9),
    inference(cnf_transformation,[],[f63]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ~ rel_str(X0)
      | ~ element(X1,the_carrier(X0))
      | relstr_set_smaller(X0,empty_set,X1) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f101,plain,
    ! [X2,X3,X0] :
      ( ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0)
      | ~ element(join_on_relstr(X0,X2),the_carrier(X0))
      | ~ ex_sup_of_relstr_set(X0,X2)
      | ~ element(X3,the_carrier(X0))
      | ~ relstr_set_smaller(X0,X2,X3)
      | related(X0,join_on_relstr(X0,X2),X3) ),
    inference(equality_resolution,[],[f87]) ).

tcf(c_50,plain,
    ! [X0: $i] :
      ( ( join_on_relstr(X0,empty_set) = bottom_of_relstr(X0) )
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f65]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i] :
      ( element(join_on_relstr(X0,X1),the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f66]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( related(X0,join_on_relstr(X0,X1),X2)
      | ~ antisymmetric_relstr(X0)
      | ~ rel_str(X0)
      | ~ ex_sup_of_relstr_set(X0,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ relstr_set_smaller(X0,X1,X2)
      | ~ element(join_on_relstr(X0,X1),the_carrier(X0)) ),
    inference(cnf_transformation,[],[f101]) ).

tcf(c_74,plain,
    ! [X0: $i] :
      ( empty_carrier(X0)
      | ex_sup_of_relstr_set(X0,empty_set)
      | ~ lower_bounded_relstr(X0)
      | ~ antisymmetric_relstr(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_75,negated_conjecture,
    ~ related(sK8,bottom_of_relstr(sK8),sK9),
    inference(cnf_transformation,[],[f95]) ).

tcf(c_76,negated_conjecture,
    element(sK9,the_carrier(sK8)),
    inference(cnf_transformation,[],[f94]) ).

tcf(c_77,negated_conjecture,
    ~ empty_carrier(sK8),
    inference(cnf_transformation,[],[f93]) ).

tcf(c_78,negated_conjecture,
    antisymmetric_relstr(sK8),
    inference(cnf_transformation,[],[f92]) ).

tcf(c_79,negated_conjecture,
    lower_bounded_relstr(sK8),
    inference(cnf_transformation,[],[f91]) ).

tcf(c_80,negated_conjecture,
    rel_str(sK8),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_82,plain,
    ! [X0: $i,X1: $i] :
      ( relstr_set_smaller(X1,empty_set,X0)
      | ~ rel_str(X1)
      | ~ element(X0,the_carrier(X1)) ),
    inference(cnf_transformation,[],[f97]) ).

tcf(c_98,plain,
    ( empty_carrier(sK8)
    | ex_sup_of_relstr_set(sK8,empty_set)
    | ~ lower_bounded_relstr(sK8)
    | ~ antisymmetric_relstr(sK8)
    | ~ rel_str(sK8) ),
    inference(instantiation,[status(thm)],[c_74]) ).

tcf(c_110,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( related(X0,join_on_relstr(X0,X1),X2)
      | ~ antisymmetric_relstr(X0)
      | ~ rel_str(X0)
      | ~ ex_sup_of_relstr_set(X0,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ relstr_set_smaller(X0,X1,X2) ),
    inference(global_subsumption_just,[status(thm)],[c_67,c_51,c_67]) ).

tcf(c_473,plain,
    ! [X0: $i] :
      ( empty_carrier(X0)
      | ex_sup_of_relstr_set(X0,empty_set)
      | ~ antisymmetric_relstr(X0)
      | ~ rel_str(X0)
      | ( X0 != sK8 ) ),
    inference(resolution_lifted,[status(thm)],[c_74,c_79]) ).

tcf(c_474,plain,
    ( empty_carrier(sK8)
    | ex_sup_of_relstr_set(sK8,empty_set)
    | ~ antisymmetric_relstr(sK8)
    | ~ rel_str(sK8) ),
    inference(unflattening,[status(thm)],[c_473]) ).

tcf(c_475,plain,
    ex_sup_of_relstr_set(sK8,empty_set),
    inference(global_subsumption_just,[status(thm)],[c_474,c_80,c_79,c_78,c_77,c_98]) ).

tcf(c_581,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( related(X0,join_on_relstr(X0,X1),X2)
      | ~ rel_str(X0)
      | ~ ex_sup_of_relstr_set(X0,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ relstr_set_smaller(X0,X1,X2)
      | ( X0 != sK8 ) ),
    inference(resolution_lifted,[status(thm)],[c_110,c_78]) ).

tcf(c_582,plain,
    ! [X0: $i,X1: $i] :
      ( related(sK8,join_on_relstr(sK8,X0),X1)
      | ~ rel_str(sK8)
      | ~ ex_sup_of_relstr_set(sK8,X0)
      | ~ element(X1,the_carrier(sK8))
      | ~ relstr_set_smaller(sK8,X0,X1) ),
    inference(unflattening,[status(thm)],[c_581]) ).

tcf(c_584,plain,
    ! [X0: $i,X1: $i] :
      ( related(sK8,join_on_relstr(sK8,X0),X1)
      | ~ relstr_set_smaller(sK8,X0,X1)
      | ~ element(X1,the_carrier(sK8))
      | ~ ex_sup_of_relstr_set(sK8,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_582,c_80,c_582]) ).

tcf(c_585,plain,
    ! [X0: $i,X1: $i] :
      ( related(sK8,join_on_relstr(sK8,X0),X1)
      | ~ ex_sup_of_relstr_set(sK8,X0)
      | ~ element(X1,the_carrier(sK8))
      | ~ relstr_set_smaller(sK8,X0,X1) ),
    inference(renaming,[status(thm)],[c_584]) ).

tcf(c_758,plain,
    ! [X0: $i,X1: $i] :
      ( relstr_set_smaller(X0,empty_set,X1)
      | ~ element(X1,the_carrier(X0))
      | ( X0 != sK8 ) ),
    inference(resolution_lifted,[status(thm)],[c_82,c_80]) ).

tcf(c_759,plain,
    ! [X0: $i] :
      ( relstr_set_smaller(sK8,empty_set,X0)
      | ~ element(X0,the_carrier(sK8)) ),
    inference(unflattening,[status(thm)],[c_758]) ).

tcf(c_794,plain,
    ! [X0: $i] :
      ( ( join_on_relstr(X0,empty_set) = bottom_of_relstr(X0) )
      | ( X0 != sK8 ) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_80]) ).

tcf(c_795,plain,
    join_on_relstr(sK8,empty_set) = bottom_of_relstr(sK8),
    inference(unflattening,[status(thm)],[c_794]) ).

tcf(c_1481,definition,
    iPr_def_10 = join_on_relstr(sK8,empty_set),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_1482,definition,
    iPr_def_11 = bottom_of_relstr(sK8),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_1484,plain,
    iPr_def_10 = iPr_def_11,
    inference(demodulation,[status(thm)],[c_795,c_1482,c_1481]) ).

tcf(c_1487,plain,
    ! [X0: $i] :
      ( relstr_set_smaller(sK8,empty_set,X0)
      | ~ element(X0,iPr_def_12) ),
    inference(demodulation,[status(thm)],[c_759]) ).

tcf(c_1495,plain,
    ! [X0: $i,X1: $i] :
      ( related(sK8,join_on_relstr(sK8,X0),X1)
      | ~ ex_sup_of_relstr_set(sK8,X0)
      | ~ element(X1,iPr_def_12)
      | ~ relstr_set_smaller(sK8,X0,X1) ),
    inference(demodulation,[status(thm)],[c_585]) ).

tcf(c_1497,plain,
    ex_sup_of_relstr_set(sK8,empty_set),
    inference(demodulation,[status(thm)],[c_475]) ).

tcf(c_1498,negated_conjecture,
    element(sK9,iPr_def_12),
    inference(demodulation,[status(thm)],[c_76]) ).

tcf(c_1499,negated_conjecture,
    ~ related(sK8,iPr_def_11,sK9),
    inference(demodulation,[status(thm)],[c_75]) ).

tcf(c_1933,plain,
    ~ related(sK8,iPr_def_10,sK9),
    inference(light_normalisation,[status(thm)],[c_1499,c_1484]) ).

tcf(c_2013,plain,
    ! [X0: $i] :
      ( related(sK8,iPr_def_10,X0)
      | ~ ex_sup_of_relstr_set(sK8,empty_set)
      | ~ element(X0,iPr_def_12)
      | ~ relstr_set_smaller(sK8,empty_set,X0) ),
    inference(superposition,[status(thm)],[c_1481,c_1495]) ).

tcf(c_2017,plain,
    ! [X0: $i] :
      ( related(sK8,iPr_def_10,X0)
      | ~ element(X0,iPr_def_12)
      | ~ relstr_set_smaller(sK8,empty_set,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2013,c_1497]) ).

tcf(c_2042,plain,
    ! [X0: $i] :
      ( related(sK8,iPr_def_10,X0)
      | ~ element(X0,iPr_def_12) ),
    inference(global_subsumption_just,[status(thm)],[c_2017,c_1487,c_2017]) ).

tcf(c_2051,plain,
    ~ element(sK9,iPr_def_12),
    inference(superposition,[status(thm)],[c_2042,c_1933]) ).

tcf(c_2052,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2051,c_1498]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : SEU361+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44  % Computer : n006.cluster.edu
% 0.18/0.44  % Model    : x86_64 x86_64
% 0.18/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44  % Memory   : 8046.5625MB
% 0.18/0.44  % OS       : Linux 6.8.0-71-generic
% 0.18/0.44  % CPULimit : 300
% 0.18/0.44  % WCLimit  : 300
% 0.18/0.44  % DateTime : Thu Sep 24 13:49:56 UTC 2026
% 0.18/0.44  % CPUTime  : 
% 0.18/0.44  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.26/0.51  Running first-order theorem proving
% 0.26/0.51  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.26/0.52  
% 0.26/0.52  % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52  
% 0.26/0.53  % Detected problem language: tptp
% 0.26/0.54  % Proving...
% 3.16/1.53  % SZS status Started for theBenchmark.p
% 3.16/1.53  % SZS status Theorem for theBenchmark.p
% 3.16/1.53  
% 3.16/1.53  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.16/1.53  
% 3.16/1.53  % ------  iProver source info
% 3.16/1.53  
% 3.16/1.53  % git: date: 2026-07-19 20:42:38 +0200
% 3.16/1.53  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.16/1.53  % git: non_committed_changes: false
% 3.16/1.53  
% 3.16/1.53  % ------ Parsing...
% 3.16/1.53  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.16/1.53  
% 3.16/1.53  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 6 0s  sf_e  pe_s  pe_e % 
% 3.16/1.53  
% 3.16/1.53  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 3.16/1.53  
% 3.16/1.53  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.16/1.53  % ------ Proving...
% 3.16/1.53  % ------ Problem Properties 
% 3.16/1.53  
% 3.16/1.53  % 
% 3.16/1.53  % clauses                               35
% 3.16/1.53  % conjectures                           2
% 3.16/1.53  % EPR                                   17
% 3.16/1.53  % Horn                                  30
% 3.16/1.53  % unary                                 19
% 3.16/1.53  % binary                                7
% 3.16/1.53  % lits                                  67
% 3.16/1.53  % lits eq                               10
% 3.16/1.53  % fd_pure                               0
% 3.16/1.53  % fd_pseudo                             0
% 3.16/1.53  % fd_cond                               1
% 3.16/1.53  % fd_pseudo_cond                        4
% 3.16/1.53  % AC symbols                            0
% 3.16/1.53  
% 3.16/1.53  % ------ Schedule dynamic 5 is on 
% 3.16/1.53  
% 3.16/1.53  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.16/1.53  
% 3.16/1.53  
% 3.16/1.53  % ------ 
% 3.16/1.53  % Current options:
% 3.16/1.53  % ------ 
% 3.16/1.53  
% 3.16/1.53  
% 3.16/1.53  % 
% 3.16/1.53  
% 3.16/1.53  % ------ Proving...
% 3.16/1.53  % 
% 3.16/1.53  
% 3.16/1.53  % SZS status Theorem for theBenchmark.p
% 3.16/1.53  
% 3.16/1.53  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.16/1.53  
% 3.16/1.53  
%------------------------------------------------------------------------------