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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUM619+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:26:15 PM UTC 2026

% Result   : Theorem 157.53s 34.89s
% Output   : CNFRefutation 157.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   88 (  34 unt;   0 def)
%            Number of atoms       :  226 (  29 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  238 ( 100   ~;  91   |;  35   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  12 con; 0-2 aty)
%            Number of variables   :   63 (   0 sgn  62   !;   1   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f25,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ( szszuzczcdt0(X0) != sz00
        & aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X0,szNzAzT0) )
     => ( ( sdtlseqdt0(X1,X0)
          & sdtlseqdt0(X0,X1) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X0,szNzAzT0) )
     => ( sdtlseqdt0(szszuzczcdt0(X1),X0)
        | sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).

fof(f83,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X0,szNzAzT0) )
     => ( sdtlseqdt0(X1,X0)
       => ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
          & ! [X2] :
              ( aElementOf0(X2,sdtlpdtrp0(xN,X0))
             => aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).

fof(f91,axiom,
    ( ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
       => ( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
          & ! [X1] :
              ( aElementOf0(X1,sdtlpdtrp0(xN,X0))
             => sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
          & aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
    & szDzozmdt0(xe) = szNzAzT0
    & aFunction0(xe) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).

fof(f101,axiom,
    ( aSubsetOf0(xQ,szNzAzT0)
    & ! [X0] :
        ( aElementOf0(X0,xQ)
       => aElementOf0(X0,szNzAzT0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).

fof(f103,axiom,
    ( xp = szmzizndt0(xQ)
    & ! [X0] :
        ( aElementOf0(X0,xQ)
       => sdtlseqdt0(xp,X0) )
    & aElementOf0(xp,xQ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).

fof(f105,axiom,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).

fof(f111,axiom,
    ( sdtlpdtrp0(xe,xn) = xp
    & aElementOf0(xn,szNzAzT0)
    & aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
    & aElementOf0(xn,szDzozmdt0(xd)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).

fof(f113,axiom,
    ( aElementOf0(xx,xP)
    & xx != szmzizndt0(xQ)
    & aElementOf0(xx,xQ)
    & aElement0(xx) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5348) ).

fof(f114,axiom,
    ( ? [X0] :
        ( sdtlpdtrp0(xe,X0) = xx
        & aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
    & aElementOf0(xx,szNzAzT0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).

fof(f115,axiom,
    ( xx = sdtlpdtrp0(xe,xm)
    & aElementOf0(xm,szNzAzT0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).

fof(f116,axiom,
    ! [X0] :
      ( aElementOf0(X0,sdtlpdtrp0(xN,xm))
     => sdtlseqdt0(xx,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).

fof(f117,conjecture,
    aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f118,negated_conjecture,
    ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(negated_conjecture,[status(cth)],[f117]) ).

fof(f141,plain,
    ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(flattening,[],[f118]) ).

fof(f171,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | ( szszuzczcdt0(X0) != sz00
        & aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f35]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | X0 = X1 ),
    inference(flattening,[],[f183]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | sdtlseqdt0(szszuzczcdt0(X1),X0)
      | sdtlseqdt0(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | sdtlseqdt0(szszuzczcdt0(X1),X0)
      | sdtlseqdt0(X0,X1) ),
    inference(flattening,[],[f187]) ).

fof(f249,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ sdtlseqdt0(X1,X0)
      | ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
        & ! [X2] :
            ( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
            | aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f250,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ sdtlseqdt0(X1,X0)
      | ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
        & ! [X2] :
            ( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
            | aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
    inference(flattening,[],[f249]) ).

fof(f264,plain,
    ( ! [X0] :
        ( ~ aElementOf0(X0,szNzAzT0)
        | ( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
          & ! [X1] :
              ( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
              | sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
          & aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
    & szDzozmdt0(xe) = szNzAzT0
    & aFunction0(xe) ),
    inference(ennf_transformation,[],[f91]) ).

fof(f273,plain,
    ( aSubsetOf0(xQ,szNzAzT0)
    & ! [X0] :
        ( ~ aElementOf0(X0,xQ)
        | aElementOf0(X0,szNzAzT0) ) ),
    inference(ennf_transformation,[],[f101]) ).

fof(f275,plain,
    ( xp = szmzizndt0(xQ)
    & ! [X0] :
        ( ~ aElementOf0(X0,xQ)
        | sdtlseqdt0(xp,X0) )
    & aElementOf0(xp,xQ) ),
    inference(ennf_transformation,[],[f103]) ).

fof(f279,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
      | sdtlseqdt0(xx,X0) ),
    inference(ennf_transformation,[],[f116]) ).

fof(f464,plain,
    ( xx = sdtlpdtrp0(xe,sK73)
    & aElementOf0(sK73,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aElementOf0(xx,szNzAzT0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(X0,sK73)],[f114]) ).

fof(f514,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
    inference(cnf_transformation,[],[f171]) ).

fof(f525,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f184]) ).

fof(f527,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | sdtlseqdt0(szszuzczcdt0(X1),X0)
      | sdtlseqdt0(X0,X1) ),
    inference(cnf_transformation,[],[f188]) ).

fof(f688,plain,
    ! [X2,X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ sdtlseqdt0(X1,X0)
      | ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
      | aElementOf0(X2,sdtlpdtrp0(xN,X1)) ),
    inference(cnf_transformation,[],[f250]) ).

fof(f816,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f866,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xQ)
      | aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f872,plain,
    xp = szmzizndt0(xQ),
    inference(cnf_transformation,[],[f275]) ).

fof(f873,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xQ)
      | sdtlseqdt0(xp,X0) ),
    inference(cnf_transformation,[],[f275]) ).

fof(f882,plain,
    aElementOf0(xp,xQ),
    inference(cnf_transformation,[],[f105]) ).

fof(f891,plain,
    xp = sdtlpdtrp0(xe,xn),
    inference(cnf_transformation,[],[f111]) ).

fof(f892,plain,
    aElementOf0(xn,szNzAzT0),
    inference(cnf_transformation,[],[f111]) ).

fof(f898,plain,
    szmzizndt0(xQ) != xx,
    inference(cnf_transformation,[],[f113]) ).

fof(f899,plain,
    aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f113]) ).

fof(f903,plain,
    aElementOf0(xx,szNzAzT0),
    inference(cnf_transformation,[],[f464]) ).

fof(f904,plain,
    xx = sdtlpdtrp0(xe,xm),
    inference(cnf_transformation,[],[f115]) ).

fof(f905,plain,
    aElementOf0(xm,szNzAzT0),
    inference(cnf_transformation,[],[f115]) ).

fof(f906,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
      | sdtlseqdt0(xx,X0) ),
    inference(cnf_transformation,[],[f279]) ).

fof(f907,plain,
    ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(cnf_transformation,[],[f141]) ).

tcf(c_97,plain,
    ! [X0: $i] :
      ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f514]) ).

tcf(c_109,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1) ),
    inference(cnf_transformation,[],[f525]) ).

tcf(c_111,plain,
    ! [X0: $i,X1: $i] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(szszuzczcdt0(X0),X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f527]) ).

tcf(c_271,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aElementOf0(X0,sdtlpdtrp0(xN,X2))
      | ~ aElementOf0(X2,szNzAzT0)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ sdtlseqdt0(X2,X1)
      | ~ aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
    inference(cnf_transformation,[],[f688]) ).

tcf(c_400,plain,
    ! [X0: $i] :
      ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f816]) ).

tcf(c_449,plain,
    ! [X0: $i] :
      ( aElementOf0(X0,szNzAzT0)
      | ~ aElementOf0(X0,xQ) ),
    inference(cnf_transformation,[],[f866]) ).

tcf(c_457,plain,
    ! [X0: $i] :
      ( sdtlseqdt0(xp,X0)
      | ~ aElementOf0(X0,xQ) ),
    inference(cnf_transformation,[],[f873]) ).

tcf(c_458,plain,
    szmzizndt0(xQ) = xp,
    inference(cnf_transformation,[],[f872]) ).

tcf(c_466,plain,
    aElementOf0(xp,xQ),
    inference(cnf_transformation,[],[f882]) ).

tcf(c_478,plain,
    aElementOf0(xn,szNzAzT0),
    inference(cnf_transformation,[],[f892]) ).

tcf(c_479,plain,
    sdtlpdtrp0(xe,xn) = xp,
    inference(cnf_transformation,[],[f891]) ).

tcf(c_482,plain,
    aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f899]) ).

tcf(c_483,plain,
    szmzizndt0(xQ) != xx,
    inference(cnf_transformation,[],[f898]) ).

tcf(c_485,plain,
    aElementOf0(xx,szNzAzT0),
    inference(cnf_transformation,[],[f903]) ).

tcf(c_488,plain,
    aElementOf0(xm,szNzAzT0),
    inference(cnf_transformation,[],[f905]) ).

tcf(c_489,plain,
    sdtlpdtrp0(xe,xm) = xx,
    inference(cnf_transformation,[],[f904]) ).

tcf(c_490,plain,
    ! [X0: $i] :
      ( sdtlseqdt0(xx,X0)
      | ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
    inference(cnf_transformation,[],[f906]) ).

tcf(c_491,negated_conjecture,
    ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(cnf_transformation,[],[f907]) ).

tcf(c_3418,plain,
    xp != xx,
    inference(light_normalisation,[status(thm)],[c_483,c_458]) ).

tcf(c_31597,plain,
    ( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(instantiation,[status(thm)],[c_97]) ).

tcf(c_33037,plain,
    ( aElementOf0(xx,sdtlpdtrp0(xN,xm))
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_489,c_400]) ).

tcf(c_33043,plain,
    aElementOf0(xx,sdtlpdtrp0(xN,xm)),
    inference(forward_subsumption_resolution,[status(thm)],[c_33037,c_488]) ).

tcf(c_80274,plain,
    ! [X0: $i] :
      ( aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ sdtlseqdt0(szszuzczcdt0(xn),X0)
      | ~ aElementOf0(xx,sdtlpdtrp0(xN,X0)) ),
    inference(instantiation,[status(thm)],[c_271]) ).

tcf(c_80787,plain,
    ( aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aElementOf0(xm,szNzAzT0)
    | ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ aElementOf0(xx,sdtlpdtrp0(xN,xm)) ),
    inference(instantiation,[status(thm)],[c_80274]) ).

tcf(c_196398,plain,
    aElementOf0(xp,szNzAzT0),
    inference(superposition,[status(thm)],[c_466,c_449]) ).

tcf(c_196423,plain,
    sdtlseqdt0(xp,xx),
    inference(superposition,[status(thm)],[c_482,c_457]) ).

tcf(c_196869,plain,
    ( aElementOf0(xp,sdtlpdtrp0(xN,xn))
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_479,c_400]) ).

tcf(c_196871,plain,
    ( aElementOf0(xx,sdtlpdtrp0(xN,xm))
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_489,c_400]) ).

tcf(c_196877,plain,
    aElementOf0(xx,sdtlpdtrp0(xN,xm)),
    inference(forward_subsumption_resolution,[status(thm)],[c_196871,c_488]) ).

tcf(c_196879,plain,
    aElementOf0(xp,sdtlpdtrp0(xN,xn)),
    inference(forward_subsumption_resolution,[status(thm)],[c_196869,c_478]) ).

tcf(c_201026,plain,
    ( ( xp = xx )
    | ~ sdtlseqdt0(xx,xp)
    | ~ aElementOf0(xx,szNzAzT0)
    | ~ aElementOf0(xp,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_196423,c_109]) ).

tcf(c_201076,plain,
    ~ sdtlseqdt0(xx,xp),
    inference(forward_subsumption_resolution,[status(thm)],[c_201026,c_3418,c_485,c_196398]) ).

tcf(c_203371,plain,
    ! [X0: $i] :
      ( aElementOf0(xp,sdtlpdtrp0(xN,X0))
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ sdtlseqdt0(X0,xn)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_196879,c_271]) ).

tcf(c_203373,plain,
    ! [X0: $i] :
      ( aElementOf0(xx,sdtlpdtrp0(xN,X0))
      | ~ aElementOf0(xm,szNzAzT0)
      | ~ sdtlseqdt0(X0,xm)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_196877,c_271]) ).

tcf(c_203377,plain,
    ! [X0: $i] :
      ( aElementOf0(xx,sdtlpdtrp0(xN,X0))
      | ~ sdtlseqdt0(X0,xm)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_203373,c_488]) ).

tcf(c_203379,plain,
    ! [X0: $i] :
      ( aElementOf0(xp,sdtlpdtrp0(xN,X0))
      | ~ sdtlseqdt0(X0,xn)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_203371,c_478]) ).

tcf(c_203400,plain,
    ( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
    inference(superposition,[status(thm)],[c_203377,c_491]) ).

tcf(c_203437,plain,
    ( sdtlseqdt0(xx,xp)
    | ~ sdtlseqdt0(xm,xn)
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_203379,c_490]) ).

tcf(c_203438,plain,
    ~ sdtlseqdt0(xm,xn),
    inference(forward_subsumption_resolution,[status(thm)],[c_203437,c_201076,c_488]) ).

tcf(c_203463,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xn),xm),
    inference(global_subsumption_just,[status(thm)],[c_203400,c_488,c_478,c_491,c_31597,c_33043,c_80787]) ).

tcf(c_203465,plain,
    ( sdtlseqdt0(xm,xn)
    | ~ aElementOf0(xm,szNzAzT0)
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_111,c_203463]) ).

tcf(c_203466,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_203465,c_203438,c_488,c_478]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM619+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.60  % Computer : n006.cluster.edu
% 0.11/10.60  % Model    : x86_64 x86_64
% 0.11/10.60  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.60  % Memory   : 8046.5625MB
% 0.11/10.60  % OS       : Linux 6.8.0-71-generic
% 0.11/10.60  % CPULimit : 300
% 0.11/10.60  % WCLimit  : 300
% 0.11/10.60  % DateTime : Thu Sep 24 04:56:43 UTC 2026
% 0.11/10.61  % CPUTime  : 
% 0.11/10.61  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.65  Running first-order theorem proving
% 0.11/10.65  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
% 0.11/10.66  
% 0.11/10.66  % ======== iProver multi-core TPTP/SMT =========
% 0.11/10.66  
% 0.11/10.66  % Detected problem language: tptp
% 0.11/10.67  % Proving...
% 157.53/34.89  % SZS status Started for theBenchmark.p
% 157.53/34.89  % SZS status Theorem for theBenchmark.p
% 157.53/34.89  
% 157.53/34.89  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 157.53/34.89  
% 157.53/34.89  % ------  iProver source info
% 157.53/34.89  
% 157.53/34.89  % git: date: 2026-07-19 20:42:38 +0200
% 157.53/34.89  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 157.53/34.89  % git: non_committed_changes: false
% 157.53/34.89  
% 157.53/34.89  % ------ Parsing...
% 157.53/34.89  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 157.53/34.89  
% 157.53/34.89  % ------ Preprocessing... sup_sim: 16  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e % 
% 157.53/34.89  
% 157.53/34.89  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 157.53/34.89  
% 157.53/34.89  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 157.53/34.89  % ------ Proving...
% 157.53/34.89  % ------ Problem Properties 
% 157.53/34.89  
% 157.53/34.89  % 
% 157.53/34.89  % clauses                               396
% 157.53/34.89  % conjectures                           1
% 157.53/34.89  % EPR                                   81
% 157.53/34.89  % Horn                                  321
% 157.53/34.89  % unary                                 73
% 157.53/34.89  % binary                                104
% 157.53/34.89  % lits                                  1199
% 157.53/34.89  % lits eq                               176
% 157.53/34.89  % fd_pure                               0
% 157.53/34.89  % fd_pseudo                             0
% 157.53/34.89  % fd_cond                               11
% 157.53/34.89  % fd_pseudo_cond                        39
% 157.53/34.89  % AC symbols                            0
% 157.53/34.89  
% 157.53/34.89  % ------ Input Options Time Limit: Unbounded
% 157.53/34.89  
% 157.53/34.89  
% 157.53/34.89  % ------ 
% 157.53/34.89  % Current options:
% 157.53/34.89  % ------ 
% 157.53/34.89  
% 157.53/34.89  
% 157.53/34.89  % 
% 157.53/34.89  
% 157.53/34.89  % ------ Proving...
% 157.53/34.89  % 
% 157.53/34.89  
% 157.53/34.89  % SZS status Theorem for theBenchmark.p
% 157.53/34.89  
% 157.53/34.89  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 157.53/34.89  
% 157.53/34.89  
%------------------------------------------------------------------------------