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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEV566+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n014.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 03:02:39 PM UTC 2026

% Result   : Theorem 62.44s 16.38s
% Output   : CNFRefutation 62.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  210 (  73 unt;  19 def)
%            Number of atoms       :  813 (  83 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  352 ( 136   ~; 190   |;  17   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   23 (  21 usr;  20 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-2 aty)
%            Number of variables   :  201 (   0 sgn 199   !;   2   ?; 110   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subq(X0,X1)
    <=> ! [X2] :
          ( mem(X2,X0)
         => mem(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',subq_def) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subq(X0,X1)
     => ( subq(X1,X0)
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',setext) ).

fof(f4,axiom,
    ! [X0] : ~ mem(X0,e),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',e_ax) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( mem(X0,s(X1))
    <=> X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',s_ax) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( mem(X0,u(X1,X2))
    <=> ( mem(X0,X2)
        | mem(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',u_ax) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( mem(X0,m(X1,X2))
    <=> ( ~ mem(X0,X2)
        & mem(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',m_ax) ).

fof(f8,axiom,
    ! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',a_def) ).

fof(f9,axiom,
    ! [X0] : n(X0) = a(X0,X0),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',n_def) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( mem(X0,p(X1))
    <=> subq(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',p_ax) ).

fof(f26,conjecture,
    ~ subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nsubq_1242_1240) ).

fof(f27,negated_conjecture,
    ~ ~ subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
    inference(negated_conjecture,[status(cth)],[f26]) ).

fof(f28,plain,
    subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
    inference(flattening,[],[f27]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( subq(X0,X1)
    <=> ! [X2] :
          ( ~ mem(X2,X0)
          | mem(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ subq(X0,X1)
      | ~ subq(X1,X0)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f2]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ subq(X0,X1)
      | ~ subq(X1,X0)
      | X0 = X1 ),
    inference(flattening,[],[f30]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( ~ subq(X0,X1)
        | ! [X2] :
            ( ~ mem(X2,X0)
            | mem(X2,X1) ) )
      & ( ? [X2] :
            ( mem(X2,X0)
            & ~ mem(X2,X1) )
        | subq(X0,X1) ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( ~ subq(X0,X1)
        | ! [X3] :
            ( ~ mem(X3,X0)
            | mem(X3,X1) ) )
      & ( ? [X2] :
            ( mem(X2,X0)
            & ~ mem(X2,X1) )
        | subq(X0,X1) ) ),
    inference(rectify,[],[f32]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( ~ subq(X0,X1)
        | ! [X3] :
            ( ~ mem(X3,X0)
            | mem(X3,X1) ) )
      & ( ( mem(sK0(X0,X1),X0)
          & ~ mem(sK0(X0,X1),X1) )
        | subq(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f33]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ~ mem(X0,s(X1))
        | X0 = X1 )
      & ( X0 != X1
        | mem(X0,s(X1)) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( ~ mem(X0,u(X1,X2))
        | mem(X0,X2)
        | mem(X0,X1) )
      & ( ( ~ mem(X0,X2)
          & ~ mem(X0,X1) )
        | mem(X0,u(X1,X2)) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( ~ mem(X0,u(X1,X2))
        | mem(X0,X2)
        | mem(X0,X1) )
      & ( ( ~ mem(X0,X2)
          & ~ mem(X0,X1) )
        | mem(X0,u(X1,X2)) ) ),
    inference(flattening,[],[f36]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( ~ mem(X0,m(X1,X2))
        | ( ~ mem(X0,X2)
          & mem(X0,X1) ) )
      & ( mem(X0,X2)
        | ~ mem(X0,X1)
        | mem(X0,m(X1,X2)) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( ~ mem(X0,m(X1,X2))
        | ( ~ mem(X0,X2)
          & mem(X0,X1) ) )
      & ( mem(X0,X2)
        | ~ mem(X0,X1)
        | mem(X0,m(X1,X2)) ) ),
    inference(flattening,[],[f38]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( ~ mem(X0,p(X1))
        | subq(X0,X1) )
      & ( ~ subq(X0,X1)
        | mem(X0,p(X1)) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f41,plain,
    ! [X3,X0,X1] :
      ( ~ subq(X0,X1)
      | ~ mem(X3,X0)
      | mem(X3,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( mem(sK0(X0,X1),X0)
      | subq(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ mem(sK0(X0,X1),X1)
      | subq(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ subq(X0,X1)
      | ~ subq(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f31]) ).

fof(f45,plain,
    ! [X0] : ~ mem(X0,e),
    inference(cnf_transformation,[],[f4]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ mem(X0,s(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( X0 != X1
      | mem(X0,s(X1)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ mem(X0,u(X1,X2))
      | mem(X0,X2)
      | mem(X0,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ mem(X0,X2)
      | mem(X0,u(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ mem(X0,X1)
      | mem(X0,u(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ mem(X0,m(X1,X2))
      | ~ mem(X0,X2) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( mem(X0,X2)
      | ~ mem(X0,X1)
      | mem(X0,m(X1,X2)) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f54,plain,
    ! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
    inference(cnf_transformation,[],[f8]) ).

fof(f55,plain,
    ! [X0] : n(X0) = a(X0,X0),
    inference(cnf_transformation,[],[f9]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ mem(X0,p(X1))
      | subq(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ subq(X0,X1)
      | mem(X0,p(X1)) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f58,plain,
    subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
    inference(cnf_transformation,[],[f28]) ).

fof(f59,plain,
    ! [X0] : n(X0) = u(X0,s(X0)),
    inference(definition_unfolding,[],[f55,f54]) ).

fof(f60,plain,
    subq(u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(u(e,s(e))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
    inference(definition_unfolding,[],[f58,f59,f59,f59,f59,f59,f54,f59,f59,f59,f59,f59,f59,f59,f59,f59,f54,f59,f59,f59]) ).

fof(f61,plain,
    ! [X1] : mem(X1,s(X1)),
    inference(equality_resolution,[],[f47]) ).

tcf(c_49,plain,
    ! [X0: $i,X1: $i] :
      ( subq(X0,X1)
      | ~ mem(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f43]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i] :
      ( subq(X0,X1)
      | mem(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f42]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( mem(X2,X1)
      | ~ mem(X2,X0)
      | ~ subq(X0,X1) ),
    inference(cnf_transformation,[],[f41]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ subq(X1,X0)
      | ~ subq(X0,X1) ),
    inference(cnf_transformation,[],[f44]) ).

tcf(c_53,plain,
    ! [X0: $i] : ~ mem(X0,e),
    inference(cnf_transformation,[],[f45]) ).

tcf(c_54,plain,
    ! [X0: $i] : mem(X0,s(X0)),
    inference(cnf_transformation,[],[f61]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ mem(X0,s(X1)) ),
    inference(cnf_transformation,[],[f46]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( mem(X0,u(X1,X2))
      | ~ mem(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( mem(X0,u(X2,X1))
      | ~ mem(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( mem(X0,X2)
      | mem(X0,X1)
      | ~ mem(X0,u(X1,X2)) ),
    inference(cnf_transformation,[],[f48]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( mem(X0,X2)
      | mem(X0,m(X1,X2))
      | ~ mem(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ mem(X0,X2)
      | ~ mem(X0,m(X1,X2)) ),
    inference(cnf_transformation,[],[f51]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i] :
      ( mem(X0,p(X1))
      | ~ subq(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

tcf(c_63,plain,
    ! [X0: $i,X1: $i] :
      ( subq(X0,X1)
      | ~ mem(X0,p(X1)) ),
    inference(cnf_transformation,[],[f56]) ).

tcf(c_64,negated_conjecture,
    subq(u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(u(e,s(e))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
    inference(cnf_transformation,[],[f60]) ).

tcf(c_65,plain,
    mem(e,s(e)),
    inference(instantiation,[status(thm)],[c_54]) ).

tcf(c_66,plain,
    ~ mem(e,e),
    inference(instantiation,[status(thm)],[c_53]) ).

tcf(c_71,plain,
    ( ( e = e )
    | ~ mem(e,s(e)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_265,definition,
    iPr_def_10 = s(e),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_266,definition,
    iPr_def_11 = u(e,iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_267,definition,
    iPr_def_12 = s(iPr_def_11),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_268,definition,
    iPr_def_13 = s(iPr_def_12),
    introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).

tcf(c_269,definition,
    iPr_def_14 = u(iPr_def_12,iPr_def_13),
    introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).

tcf(c_270,definition,
    iPr_def_15 = u(iPr_def_11,iPr_def_14),
    introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).

tcf(c_271,definition,
    iPr_def_16 = p(iPr_def_15),
    introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).

tcf(c_272,definition,
    iPr_def_17 = p(iPr_def_12),
    introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).

tcf(c_273,definition,
    iPr_def_18 = s(iPr_def_17),
    introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).

tcf(c_274,definition,
    iPr_def_19 = u(iPr_def_17,iPr_def_18),
    introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).

tcf(c_275,definition,
    iPr_def_20 = m(iPr_def_16,iPr_def_19),
    introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).

tcf(c_276,definition,
    iPr_def_21 = u(iPr_def_11,iPr_def_12),
    introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).

tcf(c_277,definition,
    iPr_def_22 = s(iPr_def_21),
    introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).

tcf(c_278,definition,
    iPr_def_23 = u(iPr_def_12,iPr_def_22),
    introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).

tcf(c_279,definition,
    iPr_def_24 = s(iPr_def_23),
    introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).

tcf(c_280,definition,
    iPr_def_25 = u(iPr_def_20,iPr_def_24),
    introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).

tcf(c_281,definition,
    iPr_def_26 = u(iPr_def_12,iPr_def_19),
    introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).

tcf(c_282,definition,
    iPr_def_27 = m(iPr_def_16,iPr_def_26),
    introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).

tcf(c_283,definition,
    iPr_def_28 = u(iPr_def_27,iPr_def_24),
    introduced(definition,[new_symbols(definition,[iPr_def_28])],[]) ).

tcf(c_284,negated_conjecture,
    subq(iPr_def_25,iPr_def_28),
    inference(demodulation,[status(thm)],[c_64,c_281,c_282,c_283,c_276,c_277,c_278,c_279,c_273,c_272,c_274,c_268,c_267,c_269,c_265,c_266,c_270,c_271,c_275,c_280]) ).

tcf(c_289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( mem(X0,X2)
      | ~ mem(X1,X3)
      | ( X2 != X3 )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_791,plain,
    mem(e,iPr_def_10),
    inference(superposition,[status(thm)],[c_265,c_54]) ).

tcf(c_792,plain,
    mem(iPr_def_11,iPr_def_12),
    inference(superposition,[status(thm)],[c_267,c_54]) ).

tcf(c_805,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_16)
      | ~ subq(X0,iPr_def_15) ),
    inference(superposition,[status(thm)],[c_271,c_62]) ).

tcf(c_830,plain,
    ! [X0: $i] :
      ( subq(X0,iPr_def_12)
      | ~ mem(X0,iPr_def_17) ),
    inference(superposition,[status(thm)],[c_272,c_63]) ).

tcf(c_899,plain,
    ! [X0: $i,X1: $i] :
      ( subq(s(X0),X1)
      | ( sK0(s(X0),X1) = X0 ) ),
    inference(superposition,[status(thm)],[c_50,c_55]) ).

tcf(c_902,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_11 )
      | ~ mem(X0,iPr_def_12) ),
    inference(superposition,[status(thm)],[c_267,c_55]) ).

tcf(c_906,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_23 )
      | ~ mem(X0,iPr_def_24) ),
    inference(superposition,[status(thm)],[c_279,c_55]) ).

tcf(c_933,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_15)
      | ~ mem(X0,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_270,c_56]) ).

tcf(c_937,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_25)
      | ~ mem(X0,iPr_def_20) ),
    inference(superposition,[status(thm)],[c_280,c_56]) ).

tcf(c_938,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_26)
      | ~ mem(X0,iPr_def_12) ),
    inference(superposition,[status(thm)],[c_281,c_56]) ).

tcf(c_972,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_11)
      | ~ mem(X0,iPr_def_10) ),
    inference(superposition,[status(thm)],[c_266,c_57]) ).

tcf(c_1044,plain,
    ! [X0: $i] :
      ( subq(iPr_def_11,X0)
      | mem(sK0(iPr_def_11,X0),iPr_def_15) ),
    inference(superposition,[status(thm)],[c_50,c_933]) ).

tcf(c_1135,plain,
    ! [X0: $i] :
      ( ~ mem(X0,iPr_def_27)
      | ~ mem(X0,iPr_def_26) ),
    inference(superposition,[status(thm)],[c_282,c_61]) ).

tcf(c_1151,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subq(X0,X2)
      | mem(sK0(X0,X2),X1)
      | ~ subq(X0,X1) ),
    inference(superposition,[status(thm)],[c_50,c_51]) ).

tcf(c_1156,plain,
    ! [X0: $i] :
      ( mem(e,X0)
      | ~ subq(iPr_def_10,X0) ),
    inference(superposition,[status(thm)],[c_791,c_51]) ).

tcf(c_1157,plain,
    ! [X0: $i] :
      ( mem(iPr_def_11,X0)
      | ~ subq(iPr_def_12,X0) ),
    inference(superposition,[status(thm)],[c_792,c_51]) ).

tcf(c_1224,plain,
    ( mem(iPr_def_11,e)
    | ~ subq(iPr_def_12,e) ),
    inference(instantiation,[status(thm)],[c_1157]) ).

tcf(c_1310,plain,
    mem(iPr_def_11,iPr_def_26),
    inference(superposition,[status(thm)],[c_792,c_938]) ).

tcf(c_1334,plain,
    ! [X0: $i] :
      ( subq(iPr_def_10,X0)
      | mem(sK0(iPr_def_10,X0),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_50,c_972]) ).

tcf(c_1408,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_10)
      | mem(X0,e)
      | ~ mem(X0,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_266,c_58]) ).

tcf(c_1411,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_18)
      | mem(X0,iPr_def_17)
      | ~ mem(X0,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_274,c_58]) ).

tcf(c_1416,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_27)
      | mem(X0,iPr_def_24)
      | ~ mem(X0,iPr_def_28) ),
    inference(superposition,[status(thm)],[c_283,c_58]) ).

tcf(c_1441,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_10)
      | ~ mem(X0,iPr_def_11) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1408,c_53]) ).

tcf(c_1478,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_20)
      | mem(X0,iPr_def_19)
      | ~ mem(X0,iPr_def_16) ),
    inference(superposition,[status(thm)],[c_275,c_59]) ).

tcf(c_1737,plain,
    ! [X0: $i] :
      ( subq(iPr_def_10,X0)
      | ( sK0(s(e),X0) = e ) ),
    inference(superposition,[status(thm)],[c_265,c_899]) ).

tcf(c_1761,plain,
    ! [X0: $i] :
      ( subq(iPr_def_10,X0)
      | ( sK0(iPr_def_10,X0) = e ) ),
    inference(light_normalisation,[status(thm)],[c_1737,c_265]) ).

tcf(c_1855,plain,
    ! [X0: $i] :
      ( subq(iPr_def_11,X0)
      | mem(sK0(iPr_def_11,X0),iPr_def_10) ),
    inference(superposition,[status(thm)],[c_50,c_1441]) ).

tcf(c_1983,plain,
    subq(iPr_def_11,iPr_def_15),
    inference(superposition,[status(thm)],[c_1044,c_49]) ).

tcf(c_1998,plain,
    mem(iPr_def_11,iPr_def_16),
    inference(superposition,[status(thm)],[c_1983,c_805]) ).

tcf(c_2035,plain,
    ! [X0: $i,X1: $i] :
      ( mem(X1,X0)
      | ~ mem(X1,iPr_def_10)
      | ~ subq(iPr_def_10,X0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

tcf(c_2045,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( mem(X0,X2)
      | ~ mem(X1,iPr_def_10)
      | ( X2 != iPr_def_10 )
      | ( X0 != X1 ) ),
    inference(instantiation,[status(thm)],[c_289]) ).

tcf(c_2046,plain,
    ( mem(e,e)
    | ~ mem(e,iPr_def_10)
    | ( e != iPr_def_10 )
    | ( e != e ) ),
    inference(instantiation,[status(thm)],[c_2045]) ).

tcf(c_2269,plain,
    subq(iPr_def_10,iPr_def_11),
    inference(superposition,[status(thm)],[c_1334,c_49]) ).

tcf(c_2550,plain,
    subq(iPr_def_11,iPr_def_10),
    inference(superposition,[status(thm)],[c_1855,c_49]) ).

tcf(c_2592,plain,
    ( ( iPr_def_10 = iPr_def_11 )
    | ~ subq(iPr_def_10,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_2550,c_52]) ).

tcf(c_2594,plain,
    iPr_def_10 = iPr_def_11,
    inference(forward_subsumption_resolution,[status(thm)],[c_2592,c_2269]) ).

tcf(c_2602,plain,
    mem(iPr_def_10,iPr_def_16),
    inference(demodulation,[status(thm)],[c_1998,c_2594]) ).

tcf(c_2605,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_10 )
      | ~ mem(X0,iPr_def_12) ),
    inference(demodulation,[status(thm)],[c_902,c_2594]) ).

tcf(c_2613,plain,
    ! [X0: $i] :
      ( mem(iPr_def_10,X0)
      | ~ subq(iPr_def_12,X0) ),
    inference(demodulation,[status(thm)],[c_1157,c_2594]) ).

tcf(c_2618,plain,
    mem(iPr_def_10,iPr_def_26),
    inference(demodulation,[status(thm)],[c_1310,c_2594]) ).

tcf(c_2627,plain,
    s(iPr_def_10) = iPr_def_12,
    inference(demodulation,[status(thm)],[c_267,c_2594]) ).

tcf(c_2655,plain,
    ( ( e = iPr_def_10 )
    | ~ mem(e,iPr_def_12) ),
    inference(instantiation,[status(thm)],[c_2605]) ).

tcf(c_2694,plain,
    ! [X0: $i] :
      ( subq(iPr_def_12,X0)
      | ( sK0(s(iPr_def_10),X0) = iPr_def_10 ) ),
    inference(superposition,[status(thm)],[c_2627,c_899]) ).

tcf(c_2696,plain,
    ! [X0: $i] :
      ( subq(iPr_def_12,X0)
      | ( sK0(iPr_def_12,X0) = iPr_def_10 ) ),
    inference(light_normalisation,[status(thm)],[c_2694,c_2627]) ).

tcf(c_2898,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_11)
      | ~ mem(X0,iPr_def_10) ),
    inference(superposition,[status(thm)],[c_266,c_57]) ).

tcf(c_3140,plain,
    ! [X0: $i] :
      ( mem(e,X0)
      | ( sK0(iPr_def_10,X0) = e ) ),
    inference(superposition,[status(thm)],[c_1761,c_1156]) ).

tcf(c_3166,plain,
    ! [X0: $i] :
      ( mem(iPr_def_10,X0)
      | ( sK0(iPr_def_12,X0) = iPr_def_10 ) ),
    inference(superposition,[status(thm)],[c_2696,c_2613]) ).

tcf(c_4407,plain,
    ( mem(iPr_def_10,iPr_def_20)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_2602,c_1478]) ).

tcf(c_4654,plain,
    ( mem(iPr_def_10,iPr_def_25)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_4407,c_937]) ).

tcf(c_4756,plain,
    ! [X0: $i] :
      ( subq(iPr_def_10,X0)
      | mem(sK0(iPr_def_10,X0),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_50,c_2898]) ).

tcf(c_4774,plain,
    ! [X0: $i] :
      ( mem(iPr_def_10,iPr_def_19)
      | mem(iPr_def_10,X0)
      | ~ subq(iPr_def_25,X0) ),
    inference(superposition,[status(thm)],[c_4654,c_51]) ).

tcf(c_5063,plain,
    ( ( e = iPr_def_10 )
    | ( sK0(iPr_def_10,iPr_def_12) = e ) ),
    inference(superposition,[status(thm)],[c_3140,c_2605]) ).

tcf(c_5197,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_10)
      | mem(X0,e)
      | ~ mem(X0,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_266,c_58]) ).

tcf(c_5230,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_10)
      | ~ mem(X0,iPr_def_11) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5197,c_53]) ).

tcf(c_5267,plain,
    sK0(iPr_def_12,e) = iPr_def_10,
    inference(superposition,[status(thm)],[c_3166,c_53]) ).

tcf(c_5277,plain,
    ( subq(iPr_def_10,iPr_def_12)
    | ( sK0(iPr_def_12,iPr_def_17) = iPr_def_10 ) ),
    inference(superposition,[status(thm)],[c_3166,c_830]) ).

tcf(c_6223,plain,
    ( mem(iPr_def_10,iPr_def_28)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_284,c_4774]) ).

tcf(c_6232,plain,
    ( mem(iPr_def_10,iPr_def_27)
    | mem(iPr_def_10,iPr_def_24)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_6223,c_1416]) ).

tcf(c_6355,plain,
    ( mem(iPr_def_10,iPr_def_24)
    | mem(iPr_def_10,iPr_def_19)
    | ~ mem(iPr_def_10,iPr_def_26) ),
    inference(superposition,[status(thm)],[c_6232,c_1135]) ).

tcf(c_6365,plain,
    ( mem(iPr_def_10,iPr_def_24)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6355,c_2618]) ).

tcf(c_6548,plain,
    ( mem(iPr_def_10,iPr_def_19)
    | ( iPr_def_10 = iPr_def_23 ) ),
    inference(superposition,[status(thm)],[c_6365,c_906]) ).

tcf(c_6562,plain,
    ( mem(iPr_def_10,iPr_def_18)
    | mem(iPr_def_10,iPr_def_17)
    | ( iPr_def_10 = iPr_def_23 ) ),
    inference(superposition,[status(thm)],[c_6548,c_1411]) ).

tcf(c_7452,plain,
    ! [X0: $i] :
      ( subq(iPr_def_11,X0)
      | mem(sK0(iPr_def_11,X0),iPr_def_10) ),
    inference(superposition,[status(thm)],[c_50,c_5230]) ).

tcf(c_8710,plain,
    subq(iPr_def_10,iPr_def_11),
    inference(superposition,[status(thm)],[c_4756,c_49]) ).

tcf(c_10378,plain,
    subq(iPr_def_11,iPr_def_10),
    inference(superposition,[status(thm)],[c_7452,c_49]) ).

tcf(c_10466,plain,
    ( ( iPr_def_10 = iPr_def_11 )
    | ~ subq(iPr_def_10,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_10378,c_52]) ).

tcf(c_10468,plain,
    iPr_def_10 = iPr_def_11,
    inference(forward_subsumption_resolution,[status(thm)],[c_10466,c_8710]) ).

tcf(c_12212,plain,
    sK0(iPr_def_10,iPr_def_12) = e,
    inference(global_subsumption_just,[status(thm)],[c_5063,c_65,c_66,c_71,c_791,c_2046,c_5063]) ).

tcf(c_12214,plain,
    ( subq(iPr_def_10,iPr_def_12)
    | ~ mem(e,iPr_def_12) ),
    inference(superposition,[status(thm)],[c_12212,c_49]) ).

tcf(c_12220,plain,
    ~ mem(e,iPr_def_12),
    inference(global_subsumption_just,[status(thm)],[c_12214,c_65,c_66,c_71,c_791,c_2046,c_2655]) ).

tcf(c_16349,plain,
    ! [X0: $i,X1: $i] :
      ( subq(X0,X1)
      | subq(sK0(X0,X1),iPr_def_12)
      | ~ subq(X0,iPr_def_17) ),
    inference(superposition,[status(thm)],[c_1151,c_830]) ).

tcf(c_17624,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_25)
      | ~ mem(X0,iPr_def_20) ),
    inference(superposition,[status(thm)],[c_280,c_56]) ).

tcf(c_17629,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subq(X0,u(X1,X2))
      | ~ mem(sK0(X0,u(X1,X2)),X1) ),
    inference(superposition,[status(thm)],[c_56,c_49]) ).

tcf(c_17661,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subq(X0,u(X1,X2))
      | ~ mem(sK0(X0,u(X1,X2)),X2) ),
    inference(superposition,[status(thm)],[c_57,c_49]) ).

tcf(c_17852,plain,
    ! [X0: $i] :
      ( subq(iPr_def_20,X0)
      | mem(sK0(iPr_def_20,X0),iPr_def_25) ),
    inference(superposition,[status(thm)],[c_50,c_17624]) ).

tcf(c_18073,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_27)
      | mem(X0,iPr_def_24)
      | ~ mem(X0,iPr_def_28) ),
    inference(superposition,[status(thm)],[c_283,c_58]) ).

tcf(c_21826,plain,
    ( subq(iPr_def_12,e)
    | subq(iPr_def_10,iPr_def_12)
    | ~ subq(iPr_def_12,iPr_def_17) ),
    inference(superposition,[status(thm)],[c_5267,c_16349]) ).

tcf(c_26050,plain,
    ! [X0: $i,X1: $i] :
      ( subq(iPr_def_20,X1)
      | mem(sK0(iPr_def_20,X1),X0)
      | ~ subq(iPr_def_25,X0) ),
    inference(superposition,[status(thm)],[c_17852,c_51]) ).

tcf(c_26104,plain,
    ! [X0: $i] :
      ( subq(iPr_def_20,X0)
      | mem(sK0(iPr_def_20,X0),iPr_def_27)
      | mem(sK0(iPr_def_20,X0),iPr_def_24)
      | ~ subq(iPr_def_25,iPr_def_28) ),
    inference(superposition,[status(thm)],[c_26050,c_18073]) ).

tcf(c_26188,plain,
    ! [X0: $i] :
      ( subq(iPr_def_20,X0)
      | mem(sK0(iPr_def_20,X0),iPr_def_27)
      | mem(sK0(iPr_def_20,X0),iPr_def_24) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_26104,c_284]) ).

tcf(c_27533,plain,
    ! [X0: $i] :
      ( subq(iPr_def_20,u(iPr_def_27,X0))
      | mem(sK0(iPr_def_20,u(iPr_def_27,X0)),iPr_def_24) ),
    inference(superposition,[status(thm)],[c_26188,c_17629]) ).

tcf(c_28042,plain,
    subq(iPr_def_20,u(iPr_def_27,iPr_def_24)),
    inference(superposition,[status(thm)],[c_27533,c_17661]) ).

tcf(c_28043,plain,
    subq(iPr_def_20,iPr_def_28),
    inference(light_normalisation,[status(thm)],[c_28042,c_283]) ).

tcf(c_30319,plain,
    ~ mem(iPr_def_11,e),
    inference(instantiation,[status(thm)],[c_53]) ).

tcf(c_31643,plain,
    ( mem(e,iPr_def_12)
    | ( sK0(iPr_def_12,iPr_def_17) = iPr_def_10 ) ),
    inference(superposition,[status(thm)],[c_5277,c_1156]) ).

tcf(c_31644,plain,
    sK0(iPr_def_12,iPr_def_17) = iPr_def_10,
    inference(forward_subsumption_resolution,[status(thm)],[c_31643,c_12220]) ).

tcf(c_31647,plain,
    ( subq(iPr_def_12,iPr_def_17)
    | ~ mem(iPr_def_10,iPr_def_17) ),
    inference(superposition,[status(thm)],[c_31644,c_49]) ).

tcf(c_48692,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_12)
      | ~ subq(iPr_def_10,iPr_def_12)
      | ~ mem(X0,iPr_def_10) ),
    inference(instantiation,[status(thm)],[c_2035]) ).

tcf(c_48693,plain,
    ( mem(e,iPr_def_12)
    | ~ mem(e,iPr_def_10)
    | ~ subq(iPr_def_10,iPr_def_12) ),
    inference(instantiation,[status(thm)],[c_48692]) ).

tcf(c_171943,plain,
    s(iPr_def_10) = iPr_def_12,
    inference(light_normalisation,[status(thm)],[c_267,c_10468]) ).

tcf(c_171944,plain,
    mem(iPr_def_10,iPr_def_12),
    inference(superposition,[status(thm)],[c_171943,c_54]) ).

tcf(c_171948,plain,
    mem(iPr_def_23,iPr_def_24),
    inference(superposition,[status(thm)],[c_279,c_54]) ).

tcf(c_171950,plain,
    u(iPr_def_10,iPr_def_14) = iPr_def_15,
    inference(light_normalisation,[status(thm)],[c_270,c_10468]) ).

tcf(c_171959,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_16)
      | ~ subq(X0,iPr_def_15) ),
    inference(superposition,[status(thm)],[c_271,c_62]) ).

tcf(c_171960,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_17)
      | ~ subq(X0,iPr_def_12) ),
    inference(superposition,[status(thm)],[c_272,c_62]) ).

tcf(c_172019,plain,
    ! [X0: $i] : subq(X0,X0),
    inference(superposition,[status(thm)],[c_50,c_49]) ).

tcf(c_172029,plain,
    ! [X0: $i] :
      ( ( X0 = e )
      | ~ mem(X0,iPr_def_10) ),
    inference(superposition,[status(thm)],[c_265,c_55]) ).

tcf(c_172031,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_17 )
      | ~ mem(X0,iPr_def_18) ),
    inference(superposition,[status(thm)],[c_273,c_55]) ).

tcf(c_172033,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_23 )
      | ~ mem(X0,iPr_def_24) ),
    inference(superposition,[status(thm)],[c_279,c_55]) ).

tcf(c_172056,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_23)
      | ~ mem(X0,iPr_def_12) ),
    inference(superposition,[status(thm)],[c_278,c_56]) ).

tcf(c_172061,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_15)
      | ~ mem(X0,iPr_def_10) ),
    inference(superposition,[status(thm)],[c_171950,c_56]) ).

tcf(c_172114,plain,
    mem(iPr_def_12,iPr_def_17),
    inference(superposition,[status(thm)],[c_172019,c_171960]) ).

tcf(c_172147,plain,
    mem(iPr_def_10,iPr_def_23),
    inference(superposition,[status(thm)],[c_171944,c_172056]) ).

tcf(c_172355,plain,
    ! [X0: $i] :
      ( subq(iPr_def_10,X0)
      | mem(sK0(iPr_def_10,X0),iPr_def_15) ),
    inference(superposition,[status(thm)],[c_50,c_172061]) ).

tcf(c_172419,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_18)
      | mem(X0,iPr_def_17)
      | ~ mem(X0,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_274,c_58]) ).

tcf(c_172423,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_27)
      | mem(X0,iPr_def_24)
      | ~ mem(X0,iPr_def_28) ),
    inference(superposition,[status(thm)],[c_283,c_58]) ).

tcf(c_172469,plain,
    ! [X0: $i] :
      ( mem(X0,iPr_def_20)
      | mem(X0,iPr_def_19)
      | ~ mem(X0,iPr_def_16) ),
    inference(superposition,[status(thm)],[c_275,c_59]) ).

tcf(c_173047,plain,
    subq(iPr_def_10,iPr_def_15),
    inference(superposition,[status(thm)],[c_172355,c_49]) ).

tcf(c_173053,plain,
    mem(iPr_def_10,iPr_def_16),
    inference(superposition,[status(thm)],[c_173047,c_171959]) ).

tcf(c_175026,plain,
    ( mem(iPr_def_10,iPr_def_20)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_173053,c_172469]) ).

tcf(c_175189,plain,
    ! [X0: $i] :
      ( mem(iPr_def_10,iPr_def_19)
      | mem(iPr_def_10,X0)
      | ~ subq(iPr_def_20,X0) ),
    inference(superposition,[status(thm)],[c_175026,c_51]) ).

tcf(c_176025,plain,
    ( mem(iPr_def_10,iPr_def_28)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_28043,c_175189]) ).

tcf(c_176111,plain,
    ( mem(iPr_def_10,iPr_def_27)
    | mem(iPr_def_10,iPr_def_24)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(superposition,[status(thm)],[c_176025,c_172423]) ).

tcf(c_176163,plain,
    ( mem(iPr_def_10,iPr_def_19)
    | mem(iPr_def_10,iPr_def_24) ),
    inference(global_subsumption_just,[status(thm)],[c_176111,c_6365]) ).

tcf(c_176164,plain,
    ( mem(iPr_def_10,iPr_def_24)
    | mem(iPr_def_10,iPr_def_19) ),
    inference(renaming,[status(thm)],[c_176163]) ).

tcf(c_176170,plain,
    ( mem(iPr_def_10,iPr_def_19)
    | ( iPr_def_10 = iPr_def_23 ) ),
    inference(superposition,[status(thm)],[c_176164,c_172033]) ).

tcf(c_176241,plain,
    ( mem(iPr_def_10,iPr_def_18)
    | mem(iPr_def_10,iPr_def_17)
    | ( iPr_def_10 = iPr_def_23 ) ),
    inference(superposition,[status(thm)],[c_176170,c_172419]) ).

tcf(c_176433,plain,
    ( mem(iPr_def_10,iPr_def_18)
    | ( iPr_def_10 = iPr_def_23 ) ),
    inference(global_subsumption_just,[status(thm)],[c_176241,c_65,c_66,c_71,c_791,c_1224,c_2046,c_2655,c_6562,c_21826,c_30319,c_31647,c_48693]) ).

tcf(c_176440,plain,
    ( ( iPr_def_10 = iPr_def_23 )
    | ( iPr_def_10 = iPr_def_17 ) ),
    inference(superposition,[status(thm)],[c_176433,c_172031]) ).

tcf(c_176515,plain,
    ( mem(iPr_def_10,iPr_def_10)
    | ( iPr_def_10 = iPr_def_17 ) ),
    inference(superposition,[status(thm)],[c_176440,c_172147]) ).

tcf(c_176516,plain,
    ( mem(iPr_def_10,iPr_def_24)
    | ( iPr_def_10 = iPr_def_17 ) ),
    inference(superposition,[status(thm)],[c_176440,c_171948]) ).

tcf(c_177097,plain,
    ( ( iPr_def_10 = iPr_def_17 )
    | ( e = iPr_def_10 ) ),
    inference(superposition,[status(thm)],[c_176515,c_172029]) ).

tcf(c_177110,plain,
    iPr_def_10 = iPr_def_17,
    inference(global_subsumption_just,[status(thm)],[c_176516,c_65,c_66,c_71,c_791,c_2046,c_177097]) ).

tcf(c_177145,plain,
    mem(iPr_def_12,iPr_def_10),
    inference(demodulation,[status(thm)],[c_172114,c_177110]) ).

tcf(c_177354,plain,
    e = iPr_def_12,
    inference(superposition,[status(thm)],[c_177145,c_172029]) ).

tcf(c_177396,plain,
    ! [X0: $i] : ~ mem(X0,iPr_def_12),
    inference(demodulation,[status(thm)],[c_53,c_177354]) ).

tcf(c_177397,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_171944,c_177396]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEV566+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.37  % Computer : n014.cluster.edu
% 0.11/5.37  % Model    : x86_64 x86_64
% 0.11/5.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37  % Memory   : 8046.5625MB
% 0.11/5.37  % OS       : Linux 6.8.0-71-generic
% 0.11/5.37  % CPULimit : 300
% 0.11/5.37  % WCLimit  : 300
% 0.11/5.37  % DateTime : Thu Sep 24 15:00:39 UTC 2026
% 0.11/5.37  % CPUTime  : 
% 0.11/5.37  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.41  Running first-order theorem proving
% 0.15/5.41  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.42  
% 0.15/5.42  % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42  
% 0.15/5.42  % Detected problem language: tptp
% 0.15/5.44  % Proving...
% 62.44/16.38  % SZS status Started for theBenchmark.p
% 62.44/16.38  % SZS status Theorem for theBenchmark.p
% 62.44/16.38  
% 62.44/16.38  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 62.44/16.38  
% 62.44/16.38  % ------  iProver source info
% 62.44/16.38  
% 62.44/16.38  % git: date: 2026-07-19 20:42:38 +0200
% 62.44/16.38  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 62.44/16.38  % git: non_committed_changes: false
% 62.44/16.38  
% 62.44/16.38  % ------ Parsing...
% 62.44/16.38  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 62.44/16.38  
% 62.44/16.38  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 62.44/16.38  
% 62.44/16.38  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 62.44/16.38  
% 62.44/16.38  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 62.44/16.38  % ------ Proving...
% 62.44/16.38  % ------ Problem Properties 
% 62.44/16.38  
% 62.44/16.38  % 
% 62.44/16.38  % clauses                               35
% 62.44/16.38  % conjectures                           1
% 62.44/16.38  % EPR                                   4
% 62.44/16.38  % Horn                                  32
% 62.44/16.38  % unary                                 22
% 62.44/16.38  % binary                                9
% 62.44/16.38  % lits                                  52
% 62.44/16.38  % lits eq                               21
% 62.44/16.38  % fd_pure                               0
% 62.44/16.38  % fd_pseudo                             0
% 62.44/16.38  % fd_cond                               0
% 62.44/16.38  % fd_pseudo_cond                        2
% 62.44/16.38  % AC symbols                            0
% 62.44/16.38  
% 62.44/16.38  % ------ Schedule dynamic 5 is on 
% 62.44/16.38  
% 62.44/16.38  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 62.44/16.38  
% 62.44/16.38  
% 62.44/16.38  % ------ 
% 62.44/16.38  % Current options:
% 62.44/16.38  % ------ 
% 62.44/16.38  
% 62.44/16.38  
% 62.44/16.38  % 
% 62.44/16.38  
% 62.44/16.38  % ------ Proving...
% 62.44/16.38  % Proof_search_loop: time out after: 8943 full_loop iterations
% 62.44/16.38  
% 62.44/16.38  % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 62.44/16.38  
% 62.44/16.38  
% 62.44/16.38  % ------ 
% 62.44/16.38  % Current options:
% 62.44/16.38  % ------ 
% 62.44/16.38  
% 62.44/16.38  
% 62.44/16.38  % 
% 62.44/16.38  
% 62.44/16.38  % ------ Proving...
% 62.44/16.38  % 
% 62.44/16.38  
% 62.44/16.38  % SZS status Theorem for theBenchmark.p
% 62.44/16.38  
% 62.44/16.38  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.44/16.38  
% 62.44/16.38  
%------------------------------------------------------------------------------