TSTP Solution File: COM008+2 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : COM008+2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Jun 24 04:55:23 EDT 2024

% Result   : Theorem 31.92s 5.19s
% Output   : CNFRefutation 31.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  112 (  19 unt;   0 def)
%            Number of atoms       :  332 (  49 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  400 ( 180   ~; 187   |;  24   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  164 (   0 sgn  77   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ( transitive_reflexive_rewrite(c,X0)
        & transitive_reflexive_rewrite(b,X0) )
     => goal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',found) ).

fof(f2,axiom,
    ( transitive_reflexive_rewrite(a,c)
    & transitive_reflexive_rewrite(a,b) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( X0 = X1
     => transitive_reflexive_rewrite(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( ( transitive_reflexive_rewrite(X1,X2)
        & transitive_reflexive_rewrite(X0,X1) )
     => transitive_reflexive_rewrite(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( ( rewrite(X0,X2)
        & rewrite(X0,X1) )
     => ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lo_cfl) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( ( transitive_reflexive_rewrite(X0,X2)
        & transitive_reflexive_rewrite(X0,X1)
        & rewrite(a,X0) )
     => ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ih_cfl) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( transitive_reflexive_rewrite(X0,X1)
     => ( ? [X2] :
            ( transitive_reflexive_rewrite(X2,X1)
            & rewrite(X0,X2) )
        | X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_or_rewrite) ).

fof(f9,conjecture,
    goal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).

fof(f10,negated_conjecture,
    ~ goal,
    inference(negated_conjecture,[],[f9]) ).

fof(f11,plain,
    ~ goal,
    inference(flattening,[],[f10]) ).

fof(f12,plain,
    ! [X0] :
      ( goal
      | ~ transitive_reflexive_rewrite(c,X0)
      | ~ transitive_reflexive_rewrite(b,X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f13,plain,
    ! [X0] :
      ( goal
      | ~ transitive_reflexive_rewrite(c,X0)
      | ~ transitive_reflexive_rewrite(b,X0) ),
    inference(flattening,[],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( transitive_reflexive_rewrite(X0,X1)
      | X0 != X1 ),
    inference(ennf_transformation,[],[f3]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X1,X2)
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X1,X2)
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(flattening,[],[f16]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(flattening,[],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) )
      | ~ transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X0,X1)
      | ~ rewrite(a,X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) )
      | ~ transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X0,X1)
      | ~ rewrite(a,X0) ),
    inference(flattening,[],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( transitive_reflexive_rewrite(X2,X1)
          & rewrite(X0,X2) )
      | X0 = X1
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( transitive_reflexive_rewrite(X2,X1)
          & rewrite(X0,X2) )
      | X0 = X1
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(flattening,[],[f22]) ).

fof(f24,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) )
     => ( transitive_reflexive_rewrite(X2,sK0(X1,X2))
        & transitive_reflexive_rewrite(X1,sK0(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( transitive_reflexive_rewrite(X2,sK0(X1,X2))
        & transitive_reflexive_rewrite(X1,sK0(X1,X2)) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f24]) ).

fof(f26,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( transitive_reflexive_rewrite(X2,X3)
          & transitive_reflexive_rewrite(X1,X3) )
     => ( transitive_reflexive_rewrite(X2,sK1(X1,X2))
        & transitive_reflexive_rewrite(X1,sK1(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( transitive_reflexive_rewrite(X2,sK1(X1,X2))
        & transitive_reflexive_rewrite(X1,sK1(X1,X2)) )
      | ~ transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X0,X1)
      | ~ rewrite(a,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f21,f26]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( transitive_reflexive_rewrite(X2,X1)
          & rewrite(X0,X2) )
     => ( transitive_reflexive_rewrite(sK2(X0,X1),X1)
        & rewrite(X0,sK2(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( transitive_reflexive_rewrite(sK2(X0,X1),X1)
        & rewrite(X0,sK2(X0,X1)) )
      | X0 = X1
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f23,f28]) ).

fof(f30,plain,
    ! [X0] :
      ( goal
      | ~ transitive_reflexive_rewrite(c,X0)
      | ~ transitive_reflexive_rewrite(b,X0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f31,plain,
    transitive_reflexive_rewrite(a,b),
    inference(cnf_transformation,[],[f2]) ).

fof(f32,plain,
    transitive_reflexive_rewrite(a,c),
    inference(cnf_transformation,[],[f2]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( transitive_reflexive_rewrite(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f14]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X1,X2)
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( transitive_reflexive_rewrite(X1,sK0(X1,X2))
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( transitive_reflexive_rewrite(X2,sK0(X1,X2))
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( transitive_reflexive_rewrite(X1,sK1(X1,X2))
      | ~ transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X0,X1)
      | ~ rewrite(a,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( transitive_reflexive_rewrite(X2,sK1(X1,X2))
      | ~ transitive_reflexive_rewrite(X0,X2)
      | ~ transitive_reflexive_rewrite(X0,X1)
      | ~ rewrite(a,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( rewrite(X0,sK2(X0,X1))
      | X0 = X1
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( transitive_reflexive_rewrite(sK2(X0,X1),X1)
      | X0 = X1
      | ~ transitive_reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f42,plain,
    ~ goal,
    inference(cnf_transformation,[],[f11]) ).

fof(f43,plain,
    ! [X1] : transitive_reflexive_rewrite(X1,X1),
    inference(equality_resolution,[],[f33]) ).

cnf(c_49,plain,
    ( ~ transitive_reflexive_rewrite(c,X0)
    | ~ transitive_reflexive_rewrite(b,X0)
    | goal ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_50,plain,
    transitive_reflexive_rewrite(a,c),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_51,plain,
    transitive_reflexive_rewrite(a,b),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_52,plain,
    transitive_reflexive_rewrite(X0,X0),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_54,plain,
    ( ~ transitive_reflexive_rewrite(X0,X1)
    | ~ transitive_reflexive_rewrite(X1,X2)
    | transitive_reflexive_rewrite(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_55,plain,
    ( ~ rewrite(X0,X1)
    | ~ rewrite(X0,X2)
    | transitive_reflexive_rewrite(X2,sK0(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_56,plain,
    ( ~ rewrite(X0,X1)
    | ~ rewrite(X0,X2)
    | transitive_reflexive_rewrite(X1,sK0(X1,X2)) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_57,plain,
    ( ~ transitive_reflexive_rewrite(X0,X1)
    | ~ transitive_reflexive_rewrite(X0,X2)
    | ~ rewrite(a,X0)
    | transitive_reflexive_rewrite(X2,sK1(X1,X2)) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_58,plain,
    ( ~ transitive_reflexive_rewrite(X0,X1)
    | ~ transitive_reflexive_rewrite(X0,X2)
    | ~ rewrite(a,X0)
    | transitive_reflexive_rewrite(X1,sK1(X1,X2)) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_59,plain,
    ( ~ transitive_reflexive_rewrite(X0,X1)
    | X0 = X1
    | transitive_reflexive_rewrite(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_60,plain,
    ( ~ transitive_reflexive_rewrite(X0,X1)
    | X0 = X1
    | rewrite(X0,sK2(X0,X1)) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_61,negated_conjecture,
    ~ goal,
    inference(cnf_transformation,[],[f42]) ).

cnf(c_62,plain,
    transitive_reflexive_rewrite(a,a),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_68,plain,
    ( ~ transitive_reflexive_rewrite(b,X0)
    | ~ transitive_reflexive_rewrite(c,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_61,c_49]) ).

cnf(c_69,plain,
    ( ~ transitive_reflexive_rewrite(c,X0)
    | ~ transitive_reflexive_rewrite(b,X0) ),
    inference(renaming,[status(thm)],[c_68]) ).

cnf(c_87,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_89,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_90,plain,
    ( X0 != X1
    | X2 != X3
    | ~ transitive_reflexive_rewrite(X1,X3)
    | transitive_reflexive_rewrite(X0,X2) ),
    theory(equality) ).

cnf(c_98,plain,
    a = a,
    inference(instantiation,[status(thm)],[c_87]) ).

cnf(c_100,plain,
    ( ~ transitive_reflexive_rewrite(c,b)
    | ~ transitive_reflexive_rewrite(b,b) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_101,plain,
    transitive_reflexive_rewrite(b,b),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_102,plain,
    ( ~ transitive_reflexive_rewrite(X0,X1)
    | ~ transitive_reflexive_rewrite(b,X0)
    | transitive_reflexive_rewrite(b,X1) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_103,plain,
    ~ transitive_reflexive_rewrite(b,c),
    inference(superposition,[status(thm)],[c_52,c_69]) ).

cnf(c_107,plain,
    ( X0 != X1
    | b != X2
    | ~ transitive_reflexive_rewrite(X2,X1)
    | transitive_reflexive_rewrite(b,X0) ),
    inference(instantiation,[status(thm)],[c_90]) ).

cnf(c_110,plain,
    ( ~ transitive_reflexive_rewrite(X0,b)
    | ~ transitive_reflexive_rewrite(c,X0)
    | transitive_reflexive_rewrite(c,b) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_111,plain,
    ( ~ transitive_reflexive_rewrite(c,a)
    | ~ transitive_reflexive_rewrite(a,b)
    | transitive_reflexive_rewrite(c,b) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_123,plain,
    ( X0 != X1
    | b != b
    | ~ transitive_reflexive_rewrite(b,X1)
    | transitive_reflexive_rewrite(b,X0) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_124,plain,
    b = b,
    inference(instantiation,[status(thm)],[c_87]) ).

cnf(c_133,plain,
    ( X0 != X1
    | c != X2
    | ~ transitive_reflexive_rewrite(X2,X1)
    | transitive_reflexive_rewrite(c,X0) ),
    inference(instantiation,[status(thm)],[c_90]) ).

cnf(c_134,plain,
    ( ~ transitive_reflexive_rewrite(X0,X1)
    | ~ transitive_reflexive_rewrite(c,X0)
    | transitive_reflexive_rewrite(c,X1) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_135,plain,
    ( c != a
    | a != a
    | ~ transitive_reflexive_rewrite(a,a)
    | transitive_reflexive_rewrite(c,a) ),
    inference(instantiation,[status(thm)],[c_133]) ).

cnf(c_154,plain,
    ( X0 != b
    | b != b
    | ~ transitive_reflexive_rewrite(b,b)
    | transitive_reflexive_rewrite(b,X0) ),
    inference(instantiation,[status(thm)],[c_123]) ).

cnf(c_155,plain,
    ( b != b
    | a != b
    | ~ transitive_reflexive_rewrite(b,b)
    | transitive_reflexive_rewrite(b,a) ),
    inference(instantiation,[status(thm)],[c_154]) ).

cnf(c_171,plain,
    ( X0 != X1
    | c != X1
    | c = X0 ),
    inference(instantiation,[status(thm)],[c_89]) ).

cnf(c_173,plain,
    ( ~ transitive_reflexive_rewrite(X0,b)
    | X0 = b
    | rewrite(X0,sK2(X0,b)) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_174,plain,
    ( ~ transitive_reflexive_rewrite(X0,b)
    | X0 = b
    | transitive_reflexive_rewrite(sK2(X0,b),b) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_175,plain,
    ( ~ transitive_reflexive_rewrite(a,b)
    | a = b
    | transitive_reflexive_rewrite(sK2(a,b),b) ),
    inference(instantiation,[status(thm)],[c_174]) ).

cnf(c_176,plain,
    ( ~ transitive_reflexive_rewrite(a,b)
    | a = b
    | rewrite(a,sK2(a,b)) ),
    inference(instantiation,[status(thm)],[c_173]) ).

cnf(c_207,plain,
    c = c,
    inference(instantiation,[status(thm)],[c_87]) ).

cnf(c_225,plain,
    ( ~ transitive_reflexive_rewrite(X0,c)
    | ~ transitive_reflexive_rewrite(b,X0)
    | transitive_reflexive_rewrite(b,c) ),
    inference(instantiation,[status(thm)],[c_102]) ).

cnf(c_226,plain,
    ( ~ transitive_reflexive_rewrite(b,a)
    | ~ transitive_reflexive_rewrite(a,c)
    | transitive_reflexive_rewrite(b,c) ),
    inference(instantiation,[status(thm)],[c_225]) ).

cnf(c_276,plain,
    ( X0 != c
    | c != c
    | c = X0 ),
    inference(instantiation,[status(thm)],[c_171]) ).

cnf(c_277,plain,
    ( c != c
    | a != c
    | c = a ),
    inference(instantiation,[status(thm)],[c_276]) ).

cnf(c_347,plain,
    ( ~ transitive_reflexive_rewrite(X0,c)
    | X0 = c
    | rewrite(X0,sK2(X0,c)) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_348,plain,
    ( ~ transitive_reflexive_rewrite(X0,c)
    | X0 = c
    | transitive_reflexive_rewrite(sK2(X0,c),c) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_349,plain,
    ( ~ transitive_reflexive_rewrite(a,c)
    | a = c
    | transitive_reflexive_rewrite(sK2(a,c),c) ),
    inference(instantiation,[status(thm)],[c_348]) ).

cnf(c_350,plain,
    ( ~ transitive_reflexive_rewrite(a,c)
    | a = c
    | rewrite(a,sK2(a,c)) ),
    inference(instantiation,[status(thm)],[c_347]) ).

cnf(c_395,plain,
    ( ~ rewrite(X0,sK2(X0,b))
    | ~ rewrite(X0,X1)
    | transitive_reflexive_rewrite(X1,sK0(X1,sK2(X0,b))) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_396,plain,
    ( ~ rewrite(X0,sK2(X0,b))
    | ~ rewrite(X0,X1)
    | transitive_reflexive_rewrite(sK2(X0,b),sK0(X1,sK2(X0,b))) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_400,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),X0)
    | ~ transitive_reflexive_rewrite(sK2(a,b),X1)
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(X0,sK1(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_401,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),X0)
    | ~ transitive_reflexive_rewrite(sK2(a,b),X1)
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(X1,sK1(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_617,plain,
    ( ~ rewrite(X0,sK2(X0,c))
    | ~ rewrite(X0,sK2(X0,b))
    | transitive_reflexive_rewrite(sK2(X0,c),sK0(sK2(X0,c),sK2(X0,b))) ),
    inference(instantiation,[status(thm)],[c_395]) ).

cnf(c_620,plain,
    ( ~ rewrite(a,sK2(a,c))
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,c),sK2(a,b))) ),
    inference(instantiation,[status(thm)],[c_617]) ).

cnf(c_626,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,c),X0)
    | ~ transitive_reflexive_rewrite(sK2(a,c),X1)
    | ~ rewrite(a,sK2(a,c))
    | transitive_reflexive_rewrite(X0,sK1(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_627,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,c),X0)
    | ~ transitive_reflexive_rewrite(sK2(a,c),X1)
    | ~ rewrite(a,sK2(a,c))
    | transitive_reflexive_rewrite(X1,sK1(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_665,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),X0)
    | ~ transitive_reflexive_rewrite(X0,X1)
    | transitive_reflexive_rewrite(sK2(a,b),X1) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_667,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),X0)
    | ~ transitive_reflexive_rewrite(sK2(a,b),b)
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(X0,sK1(X0,b)) ),
    inference(instantiation,[status(thm)],[c_400]) ).

cnf(c_715,plain,
    ( ~ rewrite(X0,sK2(X0,c))
    | ~ rewrite(X0,sK2(X0,b))
    | transitive_reflexive_rewrite(sK2(X0,b),sK0(sK2(X0,c),sK2(X0,b))) ),
    inference(instantiation,[status(thm)],[c_396]) ).

cnf(c_716,plain,
    ( ~ rewrite(a,sK2(a,c))
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,c),sK2(a,b))) ),
    inference(instantiation,[status(thm)],[c_715]) ).

cnf(c_794,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),X0)
    | ~ transitive_reflexive_rewrite(sK2(a,b),b)
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(b,sK1(X0,b)) ),
    inference(instantiation,[status(thm)],[c_401]) ).

cnf(c_1191,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,c),sK2(a,b)))
    | ~ transitive_reflexive_rewrite(sK2(a,c),X0)
    | ~ rewrite(a,sK2(a,c))
    | transitive_reflexive_rewrite(sK0(sK2(a,c),sK2(a,b)),sK1(X0,sK0(sK2(a,c),sK2(a,b)))) ),
    inference(instantiation,[status(thm)],[c_627]) ).

cnf(c_1192,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,c),sK2(a,b)))
    | ~ transitive_reflexive_rewrite(sK2(a,c),X0)
    | ~ rewrite(a,sK2(a,c))
    | transitive_reflexive_rewrite(X0,sK1(X0,sK0(sK2(a,c),sK2(a,b)))) ),
    inference(instantiation,[status(thm)],[c_626]) ).

cnf(c_1224,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,c),sK2(a,b)))
    | ~ transitive_reflexive_rewrite(sK0(sK2(a,c),sK2(a,b)),X0)
    | transitive_reflexive_rewrite(sK2(a,b),X0) ),
    inference(instantiation,[status(thm)],[c_665]) ).

cnf(c_2112,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,c),sK2(a,b)))
    | ~ transitive_reflexive_rewrite(sK2(a,c),c)
    | ~ rewrite(a,sK2(a,c))
    | transitive_reflexive_rewrite(sK0(sK2(a,c),sK2(a,b)),sK1(c,sK0(sK2(a,c),sK2(a,b)))) ),
    inference(instantiation,[status(thm)],[c_1191]) ).

cnf(c_2314,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,c),sK0(sK2(a,c),sK2(a,b)))
    | ~ transitive_reflexive_rewrite(sK2(a,c),c)
    | ~ rewrite(a,sK2(a,c))
    | transitive_reflexive_rewrite(c,sK1(c,sK0(sK2(a,c),sK2(a,b)))) ),
    inference(instantiation,[status(thm)],[c_1192]) ).

cnf(c_4534,plain,
    ( ~ transitive_reflexive_rewrite(sK0(sK2(a,c),sK2(a,b)),sK1(c,sK0(sK2(a,c),sK2(a,b))))
    | ~ transitive_reflexive_rewrite(sK2(a,b),sK0(sK2(a,c),sK2(a,b)))
    | transitive_reflexive_rewrite(sK2(a,b),sK1(c,sK0(sK2(a,c),sK2(a,b)))) ),
    inference(instantiation,[status(thm)],[c_1224]) ).

cnf(c_4860,plain,
    ( ~ transitive_reflexive_rewrite(sK1(c,sK0(sK2(a,c),sK2(a,b))),X0)
    | ~ transitive_reflexive_rewrite(c,sK1(c,sK0(sK2(a,c),sK2(a,b))))
    | transitive_reflexive_rewrite(c,X0) ),
    inference(instantiation,[status(thm)],[c_134]) ).

cnf(c_13831,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),sK1(c,sK0(sK2(a,c),sK2(a,b))))
    | ~ transitive_reflexive_rewrite(sK2(a,b),b)
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(b,sK1(sK1(c,sK0(sK2(a,c),sK2(a,b))),b)) ),
    inference(instantiation,[status(thm)],[c_794]) ).

cnf(c_23287,plain,
    ( ~ transitive_reflexive_rewrite(sK1(c,sK0(sK2(a,c),sK2(a,b))),sK1(sK1(c,sK0(sK2(a,c),sK2(a,b))),b))
    | ~ transitive_reflexive_rewrite(c,sK1(c,sK0(sK2(a,c),sK2(a,b))))
    | transitive_reflexive_rewrite(c,sK1(sK1(c,sK0(sK2(a,c),sK2(a,b))),b)) ),
    inference(instantiation,[status(thm)],[c_4860]) ).

cnf(c_23288,plain,
    ( ~ transitive_reflexive_rewrite(sK2(a,b),sK1(c,sK0(sK2(a,c),sK2(a,b))))
    | ~ transitive_reflexive_rewrite(sK2(a,b),b)
    | ~ rewrite(a,sK2(a,b))
    | transitive_reflexive_rewrite(sK1(c,sK0(sK2(a,c),sK2(a,b))),sK1(sK1(c,sK0(sK2(a,c),sK2(a,b))),b)) ),
    inference(instantiation,[status(thm)],[c_667]) ).

cnf(c_40956,plain,
    ( ~ transitive_reflexive_rewrite(c,sK1(sK1(c,sK0(sK2(a,c),sK2(a,b))),b))
    | ~ transitive_reflexive_rewrite(b,sK1(sK1(c,sK0(sK2(a,c),sK2(a,b))),b)) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_40958,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_40956,c_23288,c_23287,c_13831,c_4534,c_2314,c_2112,c_716,c_620,c_350,c_349,c_277,c_226,c_207,c_176,c_175,c_155,c_135,c_124,c_111,c_103,c_101,c_100,c_98,c_50,c_51,c_62]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : COM008+2 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.35  % Computer : n018.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Thu Jun 20 23:18:39 EDT 2024
% 0.12/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 31.92/5.19  % SZS status Started for theBenchmark.p
% 31.92/5.19  % SZS status Theorem for theBenchmark.p
% 31.92/5.19  
% 31.92/5.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 31.92/5.19  
% 31.92/5.19  ------  iProver source info
% 31.92/5.19  
% 31.92/5.19  git: date: 2024-06-12 09:56:46 +0000
% 31.92/5.19  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 31.92/5.19  git: non_committed_changes: false
% 31.92/5.19  
% 31.92/5.19  ------ Parsing...
% 31.92/5.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 31.92/5.19  
% 31.92/5.19  ------ Preprocessing... sup_sim: 0  sf_s  rm: 2 0s  sf_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e 
% 31.92/5.19  
% 31.92/5.19  ------ Preprocessing...
% 31.92/5.19  
% 31.92/5.19  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 31.92/5.19  ------ Proving...
% 31.92/5.19  ------ Problem Properties 
% 31.92/5.19  
% 31.92/5.19  
% 31.92/5.19  clauses                                 12
% 31.92/5.19  conjectures                             0
% 31.92/5.19  EPR                                     6
% 31.92/5.19  Horn                                    10
% 31.92/5.19  unary                                   3
% 31.92/5.19  binary                                  2
% 31.92/5.19  lits                                    30
% 31.92/5.19  lits eq                                 2
% 31.92/5.19  fd_pure                                 0
% 31.92/5.19  fd_pseudo                               0
% 31.92/5.19  fd_cond                                 0
% 31.92/5.19  fd_pseudo_cond                          2
% 31.92/5.19  AC symbols                              0
% 31.92/5.19  
% 31.92/5.19  ------ Input Options Time Limit: Unbounded
% 31.92/5.19  
% 31.92/5.19  
% 31.92/5.19  ------ 
% 31.92/5.19  Current options:
% 31.92/5.19  ------ 
% 31.92/5.19  
% 31.92/5.19  
% 31.92/5.19  
% 31.92/5.19  
% 31.92/5.19  ------ Proving...
% 31.92/5.19  
% 31.92/5.19  
% 31.92/5.19  % SZS status Theorem for theBenchmark.p
% 31.92/5.19  
% 31.92/5.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.92/5.19  
% 31.92/5.20  
%------------------------------------------------------------------------------