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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU215+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n020.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 02:55:56 PM UTC 2026

% Result   : Theorem 2.76s 1.19s
% Output   : CNFRefutation 2.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   81 (  28 unt;   5 def)
%            Number of atoms       :  359 (  57 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  372 ( 148   ~; 155   |;  44   &)
%                                         (   9 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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  :   10 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   96 (   0 sgn  90   !;   6   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( ( ~ in(X1,relation_dom(X0))
           => ( X2 = apply(X0,X1)
            <=> X2 = empty_set ) )
          & ( in(X1,relation_dom(X0))
           => ( X2 = apply(X0,X1)
            <=> in(ordered_pair(X1,X2),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & relation(X0) )
     => relation(relation_composition(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1)
        & function(X0)
        & relation(X0) )
     => ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(relation_composition(X2,X1)))
           => apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).

fof(f33,conjecture,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(X1))
           => apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).

fof(f34,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => ! [X2] :
            ( ( function(X2)
              & relation(X2) )
           => ( in(X0,relation_dom(X1))
             => apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f33]) ).

fof(f49,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( ( in(X1,relation_dom(X0))
            | ( X2 = apply(X0,X1)
            <=> X2 = empty_set ) )
          & ( ~ in(X1,relation_dom(X0))
            | ( X2 = apply(X0,X1)
            <=> in(ordered_pair(X1,X2),X0) ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( ( in(X1,relation_dom(X0))
            | ( X2 = apply(X0,X1)
            <=> X2 = empty_set ) )
          & ( ~ in(X1,relation_dom(X0))
            | ( X2 = apply(X0,X1)
            <=> in(ordered_pair(X1,X2),X0) ) ) ) ),
    inference(flattening,[],[f49]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ relation(X1)
      | ~ relation(X0)
      | relation(relation_composition(X0,X1)) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ relation(X1)
      | ~ relation(X0)
      | relation(relation_composition(X0,X1)) ),
    inference(flattening,[],[f51]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0)
      | ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) ) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0)
      | ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) ) ),
    inference(flattening,[],[f55]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) ) ) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) ) ) ),
    inference(flattening,[],[f64]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ~ in(X0,relation_dom(relation_composition(X2,X1)))
          | apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ~ in(X0,relation_dom(relation_composition(X2,X1)))
          | apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
    inference(flattening,[],[f66]) ).

fof(f68,plain,
    ? [X0,X1] :
      ( function(X1)
      & relation(X1)
      & ? [X2] :
          ( function(X2)
          & relation(X2)
          & in(X0,relation_dom(X1))
          & apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0)) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f69,plain,
    ? [X0,X1] :
      ( function(X1)
      & relation(X1)
      & ? [X2] :
          ( function(X2)
          & relation(X2)
          & in(X0,relation_dom(X1))
          & apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0)) ) ),
    inference(flattening,[],[f68]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( ( in(X1,relation_dom(X0))
            | ( ( apply(X0,X1) != X2
                | X2 = empty_set )
              & ( empty_set != X2
                | X2 = apply(X0,X1) ) ) )
          & ( ~ in(X1,relation_dom(X0))
            | ( ( apply(X0,X1) != X2
                | in(ordered_pair(X1,X2),X0) )
              & ( ~ in(ordered_pair(X1,X2),X0)
                | X2 = apply(X0,X1) ) ) ) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
              | ( in(apply(X2,X0),relation_dom(X1))
                & in(X0,relation_dom(X2)) ) )
            & ( ~ in(apply(X2,X0),relation_dom(X1))
              | ~ in(X0,relation_dom(X2))
              | in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
              | ( in(apply(X2,X0),relation_dom(X1))
                & in(X0,relation_dom(X2)) ) )
            & ( ~ in(apply(X2,X0),relation_dom(X1))
              | ~ in(X0,relation_dom(X2))
              | in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
    inference(flattening,[],[f89]) ).

fof(f91,plain,
    ( function(sK10)
    & relation(sK10)
    & function(sK11)
    & relation(sK11)
    & in(sK9,relation_dom(sK10))
    & apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f69]) ).

fof(f96,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(X1,relation_dom(X0))
      | apply(X0,X1) != X2
      | empty_set = X2 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ relation(X1)
      | ~ relation(X0)
      | relation(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0)
      | function(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ~ function(X2)
      | ~ relation(X2)
      | ~ in(apply(X2,X0),relation_dom(X1))
      | ~ in(X0,relation_dom(X2))
      | in(X0,relation_dom(relation_composition(X2,X1))) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( ~ function(X1)
      | ~ relation(X1)
      | ~ function(X2)
      | ~ relation(X2)
      | ~ in(X0,relation_dom(relation_composition(X2,X1)))
      | apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f140,plain,
    function(sK10),
    inference(cnf_transformation,[],[f91]) ).

fof(f141,plain,
    relation(sK10),
    inference(cnf_transformation,[],[f91]) ).

fof(f142,plain,
    function(sK11),
    inference(cnf_transformation,[],[f91]) ).

fof(f143,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f91]) ).

fof(f144,plain,
    in(sK9,relation_dom(sK10)),
    inference(cnf_transformation,[],[f91]) ).

fof(f145,plain,
    apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9)),
    inference(cnf_transformation,[],[f91]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(X1,relation_dom(X0))
      | apply(X0,X1) = empty_set ),
    inference(equality_resolution,[],[f96]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i] :
      ( in(X1,relation_dom(X0))
      | ( apply(X0,X1) = empty_set )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f158]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i] :
      ( relation(relation_composition(X1,X0))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f101]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i] :
      ( function(relation_composition(X1,X0))
      | ~ relation(X1)
      | ~ relation(X0)
      | ~ function(X1)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f107]) ).

tcf(c_92,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X1,relation_dom(relation_composition(X0,X2)))
      | ~ relation(X2)
      | ~ relation(X0)
      | ~ function(X2)
      | ~ function(X0)
      | ~ in(X1,relation_dom(X0))
      | ~ in(apply(X0,X1),relation_dom(X2)) ),
    inference(cnf_transformation,[],[f138]) ).

tcf(c_95,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ function(X2)
      | ~ function(X1)
      | ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
    inference(cnf_transformation,[],[f139]) ).

tcf(c_96,negated_conjecture,
    apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9)),
    inference(cnf_transformation,[],[f145]) ).

tcf(c_97,negated_conjecture,
    in(sK9,relation_dom(sK10)),
    inference(cnf_transformation,[],[f144]) ).

tcf(c_98,negated_conjecture,
    relation(sK11),
    inference(cnf_transformation,[],[f143]) ).

tcf(c_99,negated_conjecture,
    function(sK11),
    inference(cnf_transformation,[],[f142]) ).

tcf(c_100,negated_conjecture,
    relation(sK10),
    inference(cnf_transformation,[],[f141]) ).

tcf(c_101,negated_conjecture,
    function(sK10),
    inference(cnf_transformation,[],[f140]) ).

tcf(c_1032,definition,
    iPr_def_10 = relation_dom(sK10),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_1033,definition,
    iPr_def_11 = relation_composition(sK10,sK11),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_1034,definition,
    iPr_def_12 = apply(iPr_def_11,sK9),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_1035,definition,
    iPr_def_13 = apply(sK10,sK9),
    introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).

tcf(c_1036,definition,
    iPr_def_14 = apply(sK11,iPr_def_13),
    introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).

tcf(c_1037,negated_conjecture,
    function(sK10),
    inference(demodulation,[status(thm)],[c_101]) ).

tcf(c_1038,negated_conjecture,
    relation(sK10),
    inference(demodulation,[status(thm)],[c_100]) ).

tcf(c_1039,negated_conjecture,
    function(sK11),
    inference(demodulation,[status(thm)],[c_99]) ).

tcf(c_1040,negated_conjecture,
    relation(sK11),
    inference(demodulation,[status(thm)],[c_98]) ).

tcf(c_1041,negated_conjecture,
    in(sK9,iPr_def_10),
    inference(demodulation,[status(thm)],[c_97,c_1032]) ).

tcf(c_1042,negated_conjecture,
    iPr_def_12 != iPr_def_14,
    inference(demodulation,[status(thm)],[c_96,c_1035,c_1036,c_1033,c_1034]) ).

tcf(c_1966,plain,
    ( relation(iPr_def_11)
    | ~ relation(sK11)
    | ~ relation(sK10) ),
    inference(superposition,[status(thm)],[c_1033,c_57]) ).

tcf(c_1967,plain,
    relation(iPr_def_11),
    inference(forward_subsumption_resolution,[status(thm)],[c_1966,c_1040,c_1038]) ).

tcf(c_2257,plain,
    ( function(iPr_def_11)
    | ~ relation(sK11)
    | ~ relation(sK10)
    | ~ function(sK11)
    | ~ function(sK10) ),
    inference(superposition,[status(thm)],[c_1033,c_64]) ).

tcf(c_2258,plain,
    function(iPr_def_11),
    inference(forward_subsumption_resolution,[status(thm)],[c_2257,c_1040,c_1038,c_1039,c_1037]) ).

tcf(c_2497,plain,
    ! [X0: $i] :
      ( in(sK9,relation_dom(relation_composition(sK10,X0)))
      | ~ relation(sK10)
      | ~ function(sK10)
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(sK9,relation_dom(sK10))
      | ~ in(iPr_def_13,relation_dom(X0)) ),
    inference(superposition,[status(thm)],[c_1035,c_92]) ).

tcf(c_2523,plain,
    ! [X0: $i] :
      ( in(sK9,relation_dom(relation_composition(sK10,X0)))
      | ~ relation(sK10)
      | ~ function(sK10)
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(sK9,iPr_def_10)
      | ~ in(iPr_def_13,relation_dom(X0)) ),
    inference(light_normalisation,[status(thm)],[c_2497,c_1032]) ).

tcf(c_2524,plain,
    ! [X0: $i] :
      ( in(sK9,relation_dom(relation_composition(sK10,X0)))
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(iPr_def_13,relation_dom(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2523,c_1038,c_1037,c_1041]) ).

tcf(c_2577,plain,
    ! [X0: $i] :
      ( ( apply(relation_composition(sK10,sK11),X0) = apply(sK11,apply(sK10,X0)) )
      | ~ relation(sK11)
      | ~ relation(sK10)
      | ~ function(sK11)
      | ~ function(sK10)
      | ~ in(X0,relation_dom(iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_1033,c_95]) ).

tcf(c_2578,plain,
    ! [X0: $i] :
      ( ( apply(sK11,apply(sK10,X0)) = apply(iPr_def_11,X0) )
      | ~ relation(sK11)
      | ~ relation(sK10)
      | ~ function(sK11)
      | ~ function(sK10)
      | ~ in(X0,relation_dom(iPr_def_11)) ),
    inference(light_normalisation,[status(thm)],[c_2577,c_1033]) ).

tcf(c_2579,plain,
    ! [X0: $i] :
      ( ( apply(sK11,apply(sK10,X0)) = apply(iPr_def_11,X0) )
      | ~ in(X0,relation_dom(iPr_def_11)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2578,c_1040,c_1038,c_1039,c_1037]) ).

tcf(c_2719,plain,
    ! [X0: $i] :
      ( ( apply(iPr_def_11,X0) = empty_set )
      | ( apply(sK11,apply(sK10,X0)) = apply(iPr_def_11,X0) )
      | ~ relation(iPr_def_11)
      | ~ function(iPr_def_11) ),
    inference(superposition,[status(thm)],[c_56,c_2579]) ).

tcf(c_2724,plain,
    ! [X0: $i] :
      ( ( apply(iPr_def_11,X0) = empty_set )
      | ( apply(sK11,apply(sK10,X0)) = apply(iPr_def_11,X0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2719,c_1967,c_2258]) ).

tcf(c_2741,plain,
    ( in(sK9,relation_dom(iPr_def_11))
    | ~ relation(sK11)
    | ~ function(sK11)
    | ~ in(iPr_def_13,relation_dom(sK11)) ),
    inference(superposition,[status(thm)],[c_1033,c_2524]) ).

tcf(c_2748,plain,
    ( in(sK9,relation_dom(iPr_def_11))
    | ~ in(iPr_def_13,relation_dom(sK11)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2741,c_1040,c_1039]) ).

tcf(c_2779,plain,
    ( in(sK9,relation_dom(iPr_def_11))
    | ( apply(sK11,iPr_def_13) = empty_set )
    | ~ relation(sK11)
    | ~ function(sK11) ),
    inference(superposition,[status(thm)],[c_56,c_2748]) ).

tcf(c_2780,plain,
    ( in(sK9,relation_dom(iPr_def_11))
    | ( empty_set = iPr_def_14 )
    | ~ relation(sK11)
    | ~ function(sK11) ),
    inference(light_normalisation,[status(thm)],[c_2779,c_1036]) ).

tcf(c_2781,plain,
    ( in(sK9,relation_dom(iPr_def_11))
    | ( empty_set = iPr_def_14 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2780,c_1040,c_1039]) ).

tcf(c_2799,plain,
    ( ( empty_set = iPr_def_14 )
    | ( apply(sK11,apply(sK10,sK9)) = apply(iPr_def_11,sK9) ) ),
    inference(superposition,[status(thm)],[c_2781,c_2579]) ).

tcf(c_2809,plain,
    ( ( iPr_def_12 = iPr_def_14 )
    | ( empty_set = iPr_def_14 ) ),
    inference(light_normalisation,[status(thm)],[c_2799,c_1034,c_1035,c_1036]) ).

tcf(c_2810,plain,
    empty_set = iPr_def_14,
    inference(forward_subsumption_resolution,[status(thm)],[c_2809,c_1042]) ).

tcf(c_2873,plain,
    ! [X0: $i] :
      ( ( apply(iPr_def_11,X0) = iPr_def_14 )
      | ( apply(sK11,apply(sK10,X0)) = apply(iPr_def_11,X0) ) ),
    inference(light_normalisation,[status(thm)],[c_2724,c_2810]) ).

tcf(c_2880,plain,
    ( ( apply(iPr_def_11,sK9) = iPr_def_14 )
    | ( apply(sK11,iPr_def_13) = apply(iPr_def_11,sK9) ) ),
    inference(superposition,[status(thm)],[c_1035,c_2873]) ).

tcf(c_2884,plain,
    iPr_def_12 = iPr_def_14,
    inference(light_normalisation,[status(thm)],[c_2880,c_1034,c_1036]) ).

tcf(c_2885,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2884,c_1042]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU215+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36  % Computer : n020.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
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Thu Sep 24 13:14:18 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41  Running first-order theorem proving
% 0.10/0.41  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
% 0.10/0.42  
% 0.10/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42  
% 0.10/0.42  % Detected problem language: tptp
% 0.10/0.43  % Proving...
% 2.76/1.19  % SZS status Started for theBenchmark.p
% 2.76/1.19  % SZS status Theorem for theBenchmark.p
% 2.76/1.19  
% 2.76/1.19  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.76/1.19  
% 2.76/1.19  % ------  iProver source info
% 2.76/1.19  
% 2.76/1.19  % git: date: 2026-07-19 20:42:38 +0200
% 2.76/1.19  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.76/1.19  % git: non_committed_changes: false
% 2.76/1.19  
% 2.76/1.19  % ------ Parsing...
% 2.76/1.19  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 2.76/1.19  
% 2.76/1.19  % ------ Preprocessing... sup_sim: 2  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 2.76/1.19  
% 2.76/1.19  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 2.76/1.19  
% 2.76/1.19  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.76/1.19  % ------ Proving...
% 2.76/1.19  % ------ Problem Properties 
% 2.76/1.19  
% 2.76/1.19  % 
% 2.76/1.19  % clauses                               58
% 2.76/1.19  % conjectures                           6
% 2.76/1.19  % EPR                                   25
% 2.76/1.19  % Horn                                  55
% 2.76/1.19  % unary                                 30
% 2.76/1.19  % binary                                10
% 2.76/1.19  % lits                                  123
% 2.76/1.19  % lits eq                               12
% 2.76/1.19  % fd_pure                               0
% 2.76/1.19  % fd_pseudo                             0
% 2.76/1.19  % fd_cond                               1
% 2.76/1.19  % fd_pseudo_cond                        2
% 2.76/1.19  % AC symbols                            0
% 2.76/1.19  
% 2.76/1.19  % ------ Schedule dynamic 5 is on 
% 2.76/1.19  
% 2.76/1.19  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.76/1.19  
% 2.76/1.19  
% 2.76/1.19  % ------ 
% 2.76/1.19  % Current options:
% 2.76/1.19  % ------ 
% 2.76/1.19  
% 2.76/1.19  
% 2.76/1.19  % 
% 2.76/1.19  
% 2.76/1.19  % ------ Proving...
% 2.76/1.19  % 
% 2.76/1.19  
% 2.76/1.19  % SZS status Theorem for theBenchmark.p
% 2.76/1.19  
% 2.76/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.76/1.19  
% 2.76/1.19  
%------------------------------------------------------------------------------