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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SET728+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n008.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 02:47:58 PM UTC 2026

% Result   : Theorem 3.46s 11.10s
% Output   : CNFRefutation 3.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    5
% Syntax   : Number of formulae    :  143 (  31 unt;   0 def)
%            Number of atoms       :  522 ( 111 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  647 ( 268   ~; 270   |;  81   &)
%                                         (   7 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-5 aty)
%            Number of variables   :  403 (   0 sgn 377   !;  26   ?; 183   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
    <=> ( ! [X3,X5,X6] :
            ( ( member(X6,X2)
              & member(X5,X2)
              & member(X3,X1) )
           => ( ( apply(X0,X3,X6)
                & apply(X0,X3,X5) )
             => X5 = X6 ) )
        & ! [X3] :
            ( member(X3,X1)
           => ? [X4] :
                ( apply(X0,X3,X4)
                & member(X4,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',maps) ).

fof(f14,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( member(X6,X4)
        & member(X5,X2) )
     => ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',compose_function) ).

fof(f15,axiom,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X0,X1,X2,X3)
    <=> ! [X4,X5,X6] :
          ( ( member(X6,X3)
            & member(X5,X3)
            & member(X4,X2) )
         => ( ( apply(X1,X4,X6)
              & apply(X0,X4,X5) )
           => X5 = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',equal_maps) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( identity(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
         => apply(X0,X2,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',identity) ).

fof(f29,conjecture,
    ! [X0,X1,X2,X3,X4] :
      ( ( identity(compose_function(X0,X2,X4,X3,X4),X4)
        & identity(compose_function(X1,X0,X3,X4,X3),X3)
        & maps(X2,X4,X3)
        & maps(X1,X4,X3)
        & maps(X0,X3,X4) )
     => equal_maps(X1,X2,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII19) ).

fof(f30,negated_conjecture,
    ~ ! [X0,X1,X2,X3,X4] :
        ( ( identity(compose_function(X0,X2,X4,X3,X4),X4)
          & identity(compose_function(X1,X0,X3,X4,X3),X3)
          & maps(X2,X4,X3)
          & maps(X1,X4,X3)
          & maps(X0,X3,X4) )
       => equal_maps(X1,X2,X4,X3) ),
    inference(negated_conjecture,[status(cth)],[f29]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
    <=> ( ! [X5,X6,X7] :
            ( ( member(X7,X2)
              & member(X6,X2)
              & member(X5,X1) )
           => ( ( apply(X0,X5,X7)
                & apply(X0,X5,X6) )
             => X6 = X7 ) )
        & ! [X3] :
            ( member(X3,X1)
           => ? [X4] :
                ( apply(X0,X3,X4)
                & member(X4,X2) ) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( identity(X0,X1)
     => ! [X2] :
          ( member(X2,X1)
         => apply(X0,X2,X2) ) ),
    inference(unused_predicate_definition_removal,[],[f16]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3] :
      ( ! [X4,X5,X6] :
          ( ( member(X6,X3)
            & member(X5,X3)
            & member(X4,X2) )
         => ( ( apply(X1,X4,X6)
              & apply(X0,X4,X5) )
           => X5 = X6 ) )
     => equal_maps(X0,X1,X2,X3) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
     => ( ! [X5,X6,X7] :
            ( ( member(X7,X2)
              & member(X6,X2)
              & member(X5,X1) )
           => ( ( apply(X0,X5,X7)
                & apply(X0,X5,X6) )
             => X6 = X7 ) )
        & ! [X3] :
            ( member(X3,X1)
           => ? [X4] :
                ( apply(X0,X3,X4)
                & member(X4,X2) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f31]) ).

fof(f35,plain,
    ? [X0,X1,X2,X3,X4] :
      ( identity(compose_function(X0,X2,X4,X3,X4),X4)
      & identity(compose_function(X1,X0,X3,X4,X3),X3)
      & maps(X2,X4,X3)
      & maps(X1,X4,X3)
      & maps(X0,X3,X4)
      & ~ equal_maps(X1,X2,X4,X3) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f36,plain,
    ? [X0,X1,X2,X3,X4] :
      ( identity(compose_function(X0,X2,X4,X3,X4),X4)
      & identity(compose_function(X1,X0,X3,X4,X3),X3)
      & maps(X2,X4,X3)
      & maps(X1,X4,X3)
      & maps(X0,X3,X4)
      & ~ equal_maps(X1,X2,X4,X3) ),
    inference(flattening,[],[f35]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ~ maps(X0,X1,X2)
      | ( ! [X5,X6,X7] :
            ( ~ member(X7,X2)
            | ~ member(X6,X2)
            | ~ member(X5,X1)
            | ~ apply(X0,X5,X7)
            | ~ apply(X0,X5,X6)
            | X6 = X7 )
        & ! [X3] :
            ( ~ member(X3,X1)
            | ? [X4] :
                ( apply(X0,X3,X4)
                & member(X4,X2) ) ) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ~ maps(X0,X1,X2)
      | ( ! [X5,X6,X7] :
            ( ~ member(X7,X2)
            | ~ member(X6,X2)
            | ~ member(X5,X1)
            | ~ apply(X0,X5,X7)
            | ~ apply(X0,X5,X6)
            | X6 = X7 )
        & ! [X3] :
            ( ~ member(X3,X1)
            | ? [X4] :
                ( apply(X0,X3,X4)
                & member(X4,X2) ) ) ) ),
    inference(flattening,[],[f37]) ).

fof(f39,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4,X5,X6] :
          ( member(X6,X3)
          & member(X5,X3)
          & member(X4,X2)
          & apply(X1,X4,X6)
          & apply(X0,X4,X5)
          & X5 != X6 )
      | equal_maps(X0,X1,X2,X3) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f40,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4,X5,X6] :
          ( member(X6,X3)
          & member(X5,X3)
          & member(X4,X2)
          & apply(X1,X4,X6)
          & apply(X0,X4,X5)
          & X5 != X6 )
      | equal_maps(X0,X1,X2,X3) ),
    inference(flattening,[],[f39]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ identity(X0,X1)
      | ! [X2] :
          ( ~ member(X2,X1)
          | apply(X0,X2,X2) ) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f42,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f43,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) ) ),
    inference(flattening,[],[f42]) ).

fof(f44,plain,
    ( identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4)
    & identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3)
    & maps(sK2,sK4,sK3)
    & maps(sK1,sK4,sK3)
    & maps(sK0,sK3,sK4)
    & ~ equal_maps(sK1,sK2,sK4,sK3) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f36]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ~ maps(X0,X1,X2)
      | ( ! [X5,X6,X7] :
            ( ~ member(X7,X2)
            | ~ member(X6,X2)
            | ~ member(X5,X1)
            | ~ apply(X0,X5,X7)
            | ~ apply(X0,X5,X6)
            | X6 = X7 )
        & ! [X3] :
            ( ~ member(X3,X1)
            | ( apply(X0,X3,sK5(X0,X2,X3))
              & member(sK5(X0,X2,X3),X2) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f38]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(sK8(X0,X1,X2,X3),X3)
        & member(sK7(X0,X1,X2,X3),X3)
        & member(sK6(X0,X1,X2,X3),X2)
        & apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
        & apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
        & sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) )
      | equal_maps(X0,X1,X2,X3) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X4,sK6(X0,X1,X2,X3)),skolemize(X5,sK7(X0,X1,X2,X3)),skolemize(X6,sK8(X0,X1,X2,X3))],[f40]) ).

fof(f47,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ? [X7] :
              ( apply(X0,X7,X6)
              & apply(X1,X5,X7)
              & member(X7,X3) ) )
        & ( ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) )
          | apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f48,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ? [X8] :
              ( apply(X0,X8,X6)
              & apply(X1,X5,X8)
              & member(X8,X3) ) )
        & ( ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) )
          | apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
    inference(rectify,[],[f47]) ).

fof(f49,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ( apply(X0,sK9(X0,X1,X3,X5,X6),X6)
            & apply(X1,X5,sK9(X0,X1,X3,X5,X6))
            & member(sK9(X0,X1,X3,X5,X6),X3) ) )
        & ( ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) )
          | apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X8,sK9(X0,X1,X3,X5,X6))],[f48]) ).

fof(f50,plain,
    identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4),
    inference(cnf_transformation,[],[f44]) ).

fof(f51,plain,
    identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
    inference(cnf_transformation,[],[f44]) ).

fof(f52,plain,
    maps(sK2,sK4,sK3),
    inference(cnf_transformation,[],[f44]) ).

fof(f53,plain,
    maps(sK1,sK4,sK3),
    inference(cnf_transformation,[],[f44]) ).

fof(f54,plain,
    maps(sK0,sK3,sK4),
    inference(cnf_transformation,[],[f44]) ).

fof(f55,plain,
    ~ equal_maps(sK1,sK2,sK4,sK3),
    inference(cnf_transformation,[],[f44]) ).

fof(f56,plain,
    ! [X2,X0,X1,X6,X7,X5] :
      ( ~ maps(X0,X1,X2)
      | ~ member(X7,X2)
      | ~ member(X6,X2)
      | ~ member(X5,X1)
      | ~ apply(X0,X5,X7)
      | ~ apply(X0,X5,X6)
      | X6 = X7 ),
    inference(cnf_transformation,[],[f45]) ).

fof(f57,plain,
    ! [X2,X3,X0,X1] :
      ( ~ maps(X0,X1,X2)
      | ~ member(X3,X1)
      | apply(X0,X3,sK5(X0,X2,X3)) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f58,plain,
    ! [X2,X3,X0,X1] :
      ( ~ maps(X0,X1,X2)
      | ~ member(X3,X1)
      | member(sK5(X0,X2,X3),X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f59,plain,
    ! [X2,X3,X0,X1] :
      ( member(sK8(X0,X1,X2,X3),X3)
      | equal_maps(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f60,plain,
    ! [X2,X3,X0,X1] :
      ( member(sK7(X0,X1,X2,X3),X3)
      | equal_maps(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f61,plain,
    ! [X2,X3,X0,X1] :
      ( member(sK6(X0,X1,X2,X3),X2)
      | equal_maps(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f62,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
      | equal_maps(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f63,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
      | equal_maps(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f64,plain,
    ! [X2,X3,X0,X1] :
      ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
      | equal_maps(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( ~ identity(X0,X1)
      | ~ member(X2,X1)
      | apply(X0,X2,X2) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f66,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      | apply(X0,sK9(X0,X1,X3,X5,X6),X6) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f67,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      | apply(X1,X5,sK9(X0,X1,X3,X5,X6)) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ member(X6,X4)
      | ~ member(X5,X2)
      | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      | member(sK9(X0,X1,X3,X5,X6),X3) ),
    inference(cnf_transformation,[],[f49]) ).

tcf(c_49,negated_conjecture,
    ~ equal_maps(sK1,sK2,sK4,sK3),
    inference(cnf_transformation,[],[f55]) ).

tcf(c_50,negated_conjecture,
    maps(sK0,sK3,sK4),
    inference(cnf_transformation,[],[f54]) ).

tcf(c_51,negated_conjecture,
    maps(sK1,sK4,sK3),
    inference(cnf_transformation,[],[f53]) ).

tcf(c_52,negated_conjecture,
    maps(sK2,sK4,sK3),
    inference(cnf_transformation,[],[f52]) ).

tcf(c_53,negated_conjecture,
    identity(compose_function(sK1,sK0,sK3,sK4,sK3),sK3),
    inference(cnf_transformation,[],[f51]) ).

tcf(c_54,negated_conjecture,
    identity(compose_function(sK0,sK2,sK4,sK3,sK4),sK4),
    inference(cnf_transformation,[],[f50]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(sK5(X0,X2,X3),X2)
      | ~ member(X3,X1)
      | ~ maps(X0,X1,X2) ),
    inference(cnf_transformation,[],[f58]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( apply(X0,X3,sK5(X0,X2,X3))
      | ~ member(X3,X1)
      | ~ maps(X0,X1,X2) ),
    inference(cnf_transformation,[],[f57]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X4 = X5 )
      | ~ member(X5,X2)
      | ~ member(X4,X2)
      | ~ member(X3,X1)
      | ~ apply(X0,X3,X5)
      | ~ apply(X0,X3,X4)
      | ~ maps(X0,X1,X2) ),
    inference(cnf_transformation,[],[f56]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( equal_maps(X0,X1,X2,X3)
      | ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
    inference(cnf_transformation,[],[f64]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( equal_maps(X0,X1,X2,X3)
      | apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[],[f63]) ).

tcf(c_60,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( equal_maps(X1,X0,X2,X3)
      | apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3)) ),
    inference(cnf_transformation,[],[f62]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( equal_maps(X0,X1,X2,X3)
      | member(sK6(X0,X1,X2,X3),X2) ),
    inference(cnf_transformation,[],[f61]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( equal_maps(X0,X1,X2,X3)
      | member(sK7(X0,X1,X2,X3),X3) ),
    inference(cnf_transformation,[],[f60]) ).

tcf(c_63,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( equal_maps(X0,X1,X2,X3)
      | member(sK8(X0,X1,X2,X3),X3) ),
    inference(cnf_transformation,[],[f59]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( apply(X0,X2,X2)
      | ~ member(X2,X1)
      | ~ identity(X0,X1) ),
    inference(cnf_transformation,[],[f65]) ).

tcf(c_66,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( member(sK9(X0,X1,X3,X5,X6),X3)
      | ~ member(X6,X4)
      | ~ member(X5,X2)
      | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
    inference(cnf_transformation,[],[f68]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( apply(X1,X5,sK9(X0,X1,X3,X5,X6))
      | ~ member(X6,X4)
      | ~ member(X5,X2)
      | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
    inference(cnf_transformation,[],[f67]) ).

tcf(c_68,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( apply(X0,sK9(X0,X1,X3,X5,X6),X6)
      | ~ member(X6,X4)
      | ~ member(X5,X2)
      | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
    inference(cnf_transformation,[],[f66]) ).

tcf(c_285,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( apply(X0,X2,X2)
      | ~ member(X2,X1)
      | ( X1 != sK3 )
      | ( compose_function(sK1,sK0,sK3,sK4,sK3) != X0 ) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_64]) ).

tcf(c_286,plain,
    ! [X0: $i] :
      ( apply(compose_function(sK1,sK0,sK3,sK4,sK3),X0,X0)
      | ~ member(X0,sK3) ),
    inference(unflattening,[status(thm)],[c_285]) ).

tcf(c_294,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( apply(X0,X2,X2)
      | ~ member(X2,X1)
      | ( X1 != sK4 )
      | ( compose_function(sK0,sK2,sK4,sK3,sK4) != X0 ) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_64]) ).

tcf(c_295,plain,
    ! [X0: $i] :
      ( apply(compose_function(sK0,sK2,sK4,sK3,sK4),X0,X0)
      | ~ member(X0,sK4) ),
    inference(unflattening,[status(thm)],[c_294]) ).

tcf(c_307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(sK8(X0,X1,X2,X3),X3)
      | ( X3 != sK3 )
      | ( X2 != sK4 )
      | ( X1 != sK2 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).

tcf(c_308,plain,
    member(sK8(sK1,sK2,sK4,sK3),sK3),
    inference(unflattening,[status(thm)],[c_307]) ).

tcf(c_312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(sK7(X0,X1,X2,X3),X3)
      | ( X3 != sK3 )
      | ( X2 != sK4 )
      | ( X1 != sK2 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).

tcf(c_313,plain,
    member(sK7(sK1,sK2,sK4,sK3),sK3),
    inference(unflattening,[status(thm)],[c_312]) ).

tcf(c_317,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(sK6(X0,X1,X2,X3),X2)
      | ( X3 != sK3 )
      | ( X2 != sK4 )
      | ( X1 != sK2 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).

tcf(c_318,plain,
    member(sK6(sK1,sK2,sK4,sK3),sK4),
    inference(unflattening,[status(thm)],[c_317]) ).

tcf(c_322,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
      | ( X3 != sK3 )
      | ( X2 != sK4 )
      | ( X1 != sK2 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).

tcf(c_323,plain,
    apply(sK1,sK6(sK1,sK2,sK4,sK3),sK7(sK1,sK2,sK4,sK3)),
    inference(unflattening,[status(thm)],[c_322]) ).

tcf(c_327,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X3 != sK3 )
      | ( X2 != sK4 )
      | ( X1 != sK2 )
      | ( X0 != sK1 )
      | ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).

tcf(c_328,plain,
    sK7(sK1,sK2,sK4,sK3) != sK8(sK1,sK2,sK4,sK3),
    inference(unflattening,[status(thm)],[c_327]) ).

tcf(c_332,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
      | ( X3 != sK3 )
      | ( X2 != sK4 )
      | ( X1 != sK2 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).

tcf(c_333,plain,
    apply(sK2,sK6(sK1,sK2,sK4,sK3),sK8(sK1,sK2,sK4,sK3)),
    inference(unflattening,[status(thm)],[c_332]) ).

tcf(c_343,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X4 = X5 )
      | ~ member(X5,X0)
      | ~ member(X4,X0)
      | ~ member(X3,X1)
      | ~ apply(X2,X3,X5)
      | ~ apply(X2,X3,X4)
      | ( X2 != sK0 )
      | ( X1 != sK3 )
      | ( X0 != sK4 ) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).

tcf(c_344,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ member(X2,sK4)
      | ~ member(X1,sK4)
      | ~ member(X0,sK3)
      | ~ apply(sK0,X0,X2)
      | ~ apply(sK0,X0,X1) ),
    inference(unflattening,[status(thm)],[c_343]) ).

tcf(c_364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( apply(X2,X3,sK5(X2,X0,X3))
      | ~ member(X3,X1)
      | ( X2 != sK0 )
      | ( X1 != sK3 )
      | ( X0 != sK4 ) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).

tcf(c_365,plain,
    ! [X0: $i] :
      ( apply(sK0,X0,sK5(sK0,sK4,X0))
      | ~ member(X0,sK3) ),
    inference(unflattening,[status(thm)],[c_364]) ).

tcf(c_373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(sK5(X2,X0,X3),X0)
      | ~ member(X3,X1)
      | ( X2 != sK0 )
      | ( X1 != sK3 )
      | ( X0 != sK4 ) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_55]) ).

tcf(c_374,plain,
    ! [X0: $i] :
      ( member(sK5(sK0,sK4,X0),sK4)
      | ~ member(X0,sK3) ),
    inference(unflattening,[status(thm)],[c_373]) ).

tcf(c_382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X4 = X5 )
      | ~ member(X5,X2)
      | ~ member(X4,X2)
      | ~ member(X3,X1)
      | ~ apply(X0,X3,X5)
      | ~ apply(X0,X3,X4)
      | ( X2 != sK3 )
      | ( X1 != sK4 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).

tcf(c_383,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ member(X2,sK3)
      | ~ member(X1,sK3)
      | ~ member(X0,sK4)
      | ~ apply(sK1,X0,X2)
      | ~ apply(sK1,X0,X1) ),
    inference(unflattening,[status(thm)],[c_382]) ).

tcf(c_403,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( apply(X0,X3,sK5(X0,X2,X3))
      | ~ member(X3,X1)
      | ( X2 != sK3 )
      | ( X1 != sK4 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).

tcf(c_404,plain,
    ! [X0: $i] :
      ( apply(sK1,X0,sK5(sK1,sK3,X0))
      | ~ member(X0,sK4) ),
    inference(unflattening,[status(thm)],[c_403]) ).

tcf(c_412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(sK5(X0,X2,X3),X2)
      | ~ member(X3,X1)
      | ( X2 != sK3 )
      | ( X1 != sK4 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).

tcf(c_413,plain,
    ! [X0: $i] :
      ( member(sK5(sK1,sK3,X0),sK3)
      | ~ member(X0,sK4) ),
    inference(unflattening,[status(thm)],[c_412]) ).

tcf(c_421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X4 = X5 )
      | ~ member(X5,X2)
      | ~ member(X4,X2)
      | ~ member(X3,X1)
      | ~ apply(X0,X3,X5)
      | ~ apply(X0,X3,X4)
      | ( X2 != sK3 )
      | ( X1 != sK4 )
      | ( X0 != sK2 ) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_57]) ).

tcf(c_422,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ member(X2,sK3)
      | ~ member(X1,sK3)
      | ~ member(X0,sK4)
      | ~ apply(sK2,X0,X2)
      | ~ apply(sK2,X0,X1) ),
    inference(unflattening,[status(thm)],[c_421]) ).

tcf(c_442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( apply(X0,X3,sK5(X0,X2,X3))
      | ~ member(X3,X1)
      | ( X2 != sK3 )
      | ( X1 != sK4 )
      | ( X0 != sK2 ) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).

tcf(c_443,plain,
    ! [X0: $i] :
      ( apply(sK2,X0,sK5(sK2,sK3,X0))
      | ~ member(X0,sK4) ),
    inference(unflattening,[status(thm)],[c_442]) ).

tcf(c_451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(sK5(X0,X2,X3),X2)
      | ~ member(X3,X1)
      | ( X2 != sK3 )
      | ( X1 != sK4 )
      | ( X0 != sK2 ) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_55]) ).

tcf(c_452,plain,
    ! [X0: $i] :
      ( member(sK5(sK2,sK3,X0),sK3)
      | ~ member(X0,sK4) ),
    inference(unflattening,[status(thm)],[c_451]) ).

tcf(c_990,plain,
    ! [X0: $i] :
      ( apply(sK1,sK9(sK1,sK0,sK4,X0,X0),X0)
      | ~ member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_286,c_68]) ).

tcf(c_991,plain,
    ! [X0: $i] :
      ( apply(sK0,X0,sK9(sK1,sK0,sK4,X0,X0))
      | ~ member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_286,c_67]) ).

tcf(c_992,plain,
    ! [X0: $i] :
      ( member(sK9(sK1,sK0,sK4,X0,X0),sK4)
      | ~ member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_286,c_66]) ).

tcf(c_1014,plain,
    ! [X0: $i] :
      ( apply(sK0,sK9(sK0,sK2,sK3,X0,X0),X0)
      | ~ member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_295,c_68]) ).

tcf(c_1015,plain,
    ! [X0: $i] :
      ( apply(sK2,X0,sK9(sK0,sK2,sK3,X0,X0))
      | ~ member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_295,c_67]) ).

tcf(c_1016,plain,
    ! [X0: $i] :
      ( member(sK9(sK0,sK2,sK3,X0,X0),sK3)
      | ~ member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_295,c_66]) ).

tcf(c_1045,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK5(sK0,sK4,X0) = X1 )
      | ~ member(X1,sK4)
      | ~ member(X0,sK3)
      | ~ apply(sK0,X0,X1)
      | ~ member(sK5(sK0,sK4,X0),sK4) ),
    inference(superposition,[status(thm)],[c_365,c_344]) ).

tcf(c_1064,plain,
    ! [X0: $i] :
      ( ( sK7(sK1,sK2,sK4,sK3) = X0 )
      | ~ member(X0,sK3)
      | ~ member(sK6(sK1,sK2,sK4,sK3),sK4)
      | ~ member(sK7(sK1,sK2,sK4,sK3),sK3)
      | ~ apply(sK1,sK6(sK1,sK2,sK4,sK3),X0) ),
    inference(superposition,[status(thm)],[c_323,c_383]) ).

tcf(c_1065,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK5(sK1,sK3,X0) = X1 )
      | ~ member(X1,sK3)
      | ~ member(X0,sK4)
      | ~ apply(sK1,X0,X1)
      | ~ member(sK5(sK1,sK3,X0),sK3) ),
    inference(superposition,[status(thm)],[c_404,c_383]) ).

tcf(c_1071,plain,
    ! [X0: $i] :
      ( ( sK7(sK1,sK2,sK4,sK3) = X0 )
      | ~ member(X0,sK3)
      | ~ apply(sK1,sK6(sK1,sK2,sK4,sK3),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1064,c_318,c_313]) ).

tcf(c_1089,plain,
    ! [X0: $i] :
      ( ( sK8(sK1,sK2,sK4,sK3) = X0 )
      | ~ member(X0,sK3)
      | ~ member(sK6(sK1,sK2,sK4,sK3),sK4)
      | ~ member(sK8(sK1,sK2,sK4,sK3),sK3)
      | ~ apply(sK2,sK6(sK1,sK2,sK4,sK3),X0) ),
    inference(superposition,[status(thm)],[c_333,c_422]) ).

tcf(c_1090,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK5(sK2,sK3,X0) = X1 )
      | ~ member(X1,sK3)
      | ~ member(X0,sK4)
      | ~ apply(sK2,X0,X1)
      | ~ member(sK5(sK2,sK3,X0),sK3) ),
    inference(superposition,[status(thm)],[c_443,c_422]) ).

tcf(c_1096,plain,
    ! [X0: $i] :
      ( ( sK8(sK1,sK2,sK4,sK3) = X0 )
      | ~ member(X0,sK3)
      | ~ apply(sK2,sK6(sK1,sK2,sK4,sK3),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1089,c_318,c_308]) ).

tcf(c_1133,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK9(sK1,sK0,sK4,X0,X0) = X1 )
      | ~ member(X1,sK4)
      | ~ member(X0,sK3)
      | ~ apply(sK0,X0,X1)
      | ~ member(sK9(sK1,sK0,sK4,X0,X0),sK4) ),
    inference(superposition,[status(thm)],[c_991,c_344]) ).

tcf(c_1282,plain,
    ( member(sK5(sK1,sK3,sK6(sK1,sK2,sK4,sK3)),sK3)
    | ~ member(sK6(sK1,sK2,sK4,sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_413]) ).

tcf(c_1356,plain,
    ( member(sK5(sK2,sK3,sK6(sK1,sK2,sK4,sK3)),sK3)
    | ~ member(sK6(sK1,sK2,sK4,sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_452]) ).

tcf(c_1369,plain,
    ( ( sK5(sK1,sK3,sK6(sK1,sK2,sK4,sK3)) = sK7(sK1,sK2,sK4,sK3) )
    | ~ member(sK6(sK1,sK2,sK4,sK3),sK4)
    | ~ member(sK5(sK1,sK3,sK6(sK1,sK2,sK4,sK3)),sK3) ),
    inference(superposition,[status(thm)],[c_404,c_1071]) ).

tcf(c_1370,plain,
    ( ( sK5(sK1,sK3,sK6(sK1,sK2,sK4,sK3)) = sK7(sK1,sK2,sK4,sK3) )
    | ~ member(sK5(sK1,sK3,sK6(sK1,sK2,sK4,sK3)),sK3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1369,c_318]) ).

tcf(c_1381,plain,
    ( ( sK5(sK2,sK3,sK6(sK1,sK2,sK4,sK3)) = sK8(sK1,sK2,sK4,sK3) )
    | ~ member(sK6(sK1,sK2,sK4,sK3),sK4)
    | ~ member(sK5(sK2,sK3,sK6(sK1,sK2,sK4,sK3)),sK3) ),
    inference(superposition,[status(thm)],[c_443,c_1096]) ).

tcf(c_1383,plain,
    ( ( sK5(sK2,sK3,sK6(sK1,sK2,sK4,sK3)) = sK8(sK1,sK2,sK4,sK3) )
    | ~ member(sK5(sK2,sK3,sK6(sK1,sK2,sK4,sK3)),sK3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1381,c_318]) ).

tcf(c_1390,plain,
    sK5(sK1,sK3,sK6(sK1,sK2,sK4,sK3)) = sK7(sK1,sK2,sK4,sK3),
    inference(global_subsumption_just,[status(thm)],[c_1370,c_318,c_1282,c_1370]) ).

tcf(c_1396,plain,
    sK5(sK2,sK3,sK6(sK1,sK2,sK4,sK3)) = sK8(sK1,sK2,sK4,sK3),
    inference(global_subsumption_just,[status(thm)],[c_1383,c_318,c_1356,c_1383]) ).

tcf(c_1400,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK5(sK0,sK4,X0) = X1 )
      | ~ member(X1,sK4)
      | ~ member(X0,sK3)
      | ~ apply(sK0,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_1045,c_374,c_1045]) ).

tcf(c_1413,plain,
    ! [X0: $i] :
      ( ( sK5(sK0,sK4,sK9(sK0,sK2,sK3,X0,X0)) = X0 )
      | ~ member(X0,sK4)
      | ~ member(sK9(sK0,sK2,sK3,X0,X0),sK3) ),
    inference(superposition,[status(thm)],[c_1014,c_1400]) ).

tcf(c_1428,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK5(sK1,sK3,X0) = X1 )
      | ~ member(X1,sK3)
      | ~ member(X0,sK4)
      | ~ apply(sK1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_1065,c_413,c_1065]) ).

tcf(c_1446,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK5(sK2,sK3,X0) = X1 )
      | ~ member(X1,sK3)
      | ~ member(X0,sK4)
      | ~ apply(sK2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_1090,c_452,c_1090]) ).

tcf(c_1459,plain,
    ! [X0: $i] :
      ( ( sK9(sK0,sK2,sK3,X0,X0) = sK5(sK2,sK3,X0) )
      | ~ member(X0,sK4)
      | ~ member(sK9(sK0,sK2,sK3,X0,X0),sK3) ),
    inference(superposition,[status(thm)],[c_1015,c_1446]) ).

tcf(c_1482,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK9(sK1,sK0,sK4,X0,X0) = X1 )
      | ~ member(X1,sK4)
      | ~ member(X0,sK3)
      | ~ apply(sK0,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_1133,c_992,c_1133]) ).

tcf(c_1493,plain,
    ! [X0: $i] :
      ( ( sK9(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
      | ~ member(X0,sK3)
      | ~ member(sK5(sK0,sK4,X0),sK4) ),
    inference(superposition,[status(thm)],[c_365,c_1482]) ).

tcf(c_1508,plain,
    ! [X0: $i] :
      ( ( sK9(sK1,sK0,sK4,X0,X0) = sK5(sK0,sK4,X0) )
      | ~ member(X0,sK3) ),
    inference(global_subsumption_just,[status(thm)],[c_1493,c_374,c_1493]) ).

tcf(c_1515,plain,
    sK9(sK1,sK0,sK4,sK8(sK1,sK2,sK4,sK3),sK8(sK1,sK2,sK4,sK3)) = sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3)),
    inference(superposition,[status(thm)],[c_308,c_1508]) ).

tcf(c_1543,plain,
    ( apply(sK1,sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3)),sK8(sK1,sK2,sK4,sK3))
    | ~ member(sK8(sK1,sK2,sK4,sK3),sK3) ),
    inference(superposition,[status(thm)],[c_1515,c_990]) ).

tcf(c_1544,plain,
    ( member(sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3)),sK4)
    | ~ member(sK8(sK1,sK2,sK4,sK3),sK3) ),
    inference(superposition,[status(thm)],[c_1515,c_992]) ).

tcf(c_1545,plain,
    member(sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3)),sK4),
    inference(forward_subsumption_resolution,[status(thm)],[c_1544,c_308]) ).

tcf(c_1546,plain,
    apply(sK1,sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3)),sK8(sK1,sK2,sK4,sK3)),
    inference(forward_subsumption_resolution,[status(thm)],[c_1543,c_308]) ).

tcf(c_1980,plain,
    ( ( sK5(sK1,sK3,sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3))) = sK8(sK1,sK2,sK4,sK3) )
    | ~ member(sK8(sK1,sK2,sK4,sK3),sK3)
    | ~ member(sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3)),sK4) ),
    inference(superposition,[status(thm)],[c_1546,c_1428]) ).

tcf(c_1982,plain,
    sK5(sK1,sK3,sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3))) = sK8(sK1,sK2,sK4,sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_1980,c_308,c_1545]) ).

tcf(c_2423,plain,
    ! [X0: $i] :
      ( ( sK5(sK0,sK4,sK9(sK0,sK2,sK3,X0,X0)) = X0 )
      | ~ member(X0,sK4) ),
    inference(global_subsumption_just,[status(thm)],[c_1413,c_1016,c_1413]) ).

tcf(c_2430,plain,
    sK5(sK0,sK4,sK9(sK0,sK2,sK3,sK6(sK1,sK2,sK4,sK3),sK6(sK1,sK2,sK4,sK3))) = sK6(sK1,sK2,sK4,sK3),
    inference(superposition,[status(thm)],[c_318,c_2423]) ).

tcf(c_3110,plain,
    ! [X0: $i] :
      ( ( sK9(sK0,sK2,sK3,X0,X0) = sK5(sK2,sK3,X0) )
      | ~ member(X0,sK4) ),
    inference(global_subsumption_just,[status(thm)],[c_1459,c_1016,c_1459]) ).

tcf(c_3117,plain,
    sK9(sK0,sK2,sK3,sK6(sK1,sK2,sK4,sK3),sK6(sK1,sK2,sK4,sK3)) = sK5(sK2,sK3,sK6(sK1,sK2,sK4,sK3)),
    inference(superposition,[status(thm)],[c_318,c_3110]) ).

tcf(c_3122,plain,
    sK9(sK0,sK2,sK3,sK6(sK1,sK2,sK4,sK3),sK6(sK1,sK2,sK4,sK3)) = sK8(sK1,sK2,sK4,sK3),
    inference(light_normalisation,[status(thm)],[c_3117,c_1396]) ).

tcf(c_3128,plain,
    sK5(sK0,sK4,sK8(sK1,sK2,sK4,sK3)) = sK6(sK1,sK2,sK4,sK3),
    inference(demodulation,[status(thm)],[c_2430,c_3122]) ).

tcf(c_3131,plain,
    sK5(sK1,sK3,sK6(sK1,sK2,sK4,sK3)) = sK8(sK1,sK2,sK4,sK3),
    inference(demodulation,[status(thm)],[c_1982,c_3128]) ).

tcf(c_3136,plain,
    sK7(sK1,sK2,sK4,sK3) = sK8(sK1,sK2,sK4,sK3),
    inference(light_normalisation,[status(thm)],[c_3131,c_1390]) ).

tcf(c_3137,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_3136,c_328]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET728+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.39  % Computer : n008.cluster.edu
% 0.10/10.39  % Model    : x86_64 x86_64
% 0.10/10.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39  % Memory   : 8046.5625MB
% 0.10/10.39  % OS       : Linux 6.8.0-71-generic
% 0.10/10.39  % CPULimit : 300
% 0.10/10.39  % WCLimit  : 300
% 0.10/10.39  % DateTime : Thu Sep 24 11:47:50 UTC 2026
% 0.10/10.39  % CPUTime  : 
% 0.10/10.39  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.42  Running first-order theorem proving
% 0.15/10.42  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
% 0.15/10.43  
% 0.15/10.43  % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43  
% 0.15/10.44  % Detected problem language: tptp
% 0.15/10.45  % Proving...
% 3.46/11.10  % SZS status Started for theBenchmark.p
% 3.46/11.10  % SZS status Theorem for theBenchmark.p
% 3.46/11.10  
% 3.46/11.10  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.46/11.10  
% 3.46/11.10  % ------  iProver source info
% 3.46/11.10  
% 3.46/11.10  % git: date: 2026-07-19 20:42:38 +0200
% 3.46/11.10  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.46/11.10  % git: non_committed_changes: false
% 3.46/11.10  
% 3.46/11.10  % ------ Parsing...
% 3.46/11.10  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.46/11.10  
% 3.46/11.10  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e % 
% 3.46/11.10  
% 3.46/11.10  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 3.46/11.10  
% 3.46/11.10  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.46/11.10  % ------ Proving...
% 3.46/11.10  % ------ Problem Properties 
% 3.46/11.10  
% 3.46/11.10  % 
% 3.46/11.10  % clauses                               21
% 3.46/11.10  % conjectures                           0
% 3.46/11.10  % EPR                                   3
% 3.46/11.10  % Horn                                  21
% 3.46/11.10  % unary                                 6
% 3.46/11.10  % binary                                8
% 3.46/11.10  % lits                                  58
% 3.46/11.10  % lits eq                               4
% 3.46/11.10  % fd_pure                               0
% 3.46/11.10  % fd_pseudo                             0
% 3.46/11.10  % fd_cond                               0
% 3.46/11.10  % fd_pseudo_cond                        3
% 3.46/11.10  % AC symbols                            0
% 3.46/11.10  
% 3.46/11.10  % ------ Schedule dynamic 5 is on 
% 3.46/11.10  
% 3.46/11.10  % ------ no conjectures: strip conj schedule 
% 3.46/11.10  
% 3.46/11.10  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.46/11.10  
% 3.46/11.10  
% 3.46/11.10  % ------ 
% 3.46/11.10  % Current options:
% 3.46/11.10  % ------ 
% 3.46/11.10  
% 3.46/11.10  
% 3.46/11.10  % 
% 3.46/11.10  
% 3.46/11.10  % ------ Proving...
% 3.46/11.10  % 
% 3.46/11.10  
% 3.46/11.10  % SZS status Theorem for theBenchmark.p
% 3.46/11.10  
% 3.46/11.10  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.46/11.10  
% 3.46/11.10  
%------------------------------------------------------------------------------