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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUM429+1 : 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 : n017.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 02:24:13 PM UTC 2026

% Result   : Theorem 8.96s 7.03s
% Output   : CNFRefutation 8.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   84 (  16 unt;   0 def)
%            Number of atoms       :  285 ( 100 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  350 ( 149   ~; 150   |;  38   &)
%                                         (   5 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  112 (   0 sgn 105   !;   7   ?;  38   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).

fof(f4,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => aInteger0(smndt0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => aInteger0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).

fof(f15,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sdtasdt0(X0,sz00) = sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => ( sdtasdt0(X0,X1) = sz00
       => ( X1 = sz00
          | X0 = sz00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).

fof(f18,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & X1 != sz00
            & aInteger0(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).

fof(f19,axiom,
    ! [X0,X1,X2] :
      ( ( X2 != sz00
        & aInteger0(X2)
        & aInteger0(X1)
        & aInteger0(X0) )
     => ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).

fof(f22,axiom,
    ( aInteger0(xc)
    & xq != sz00
    & aInteger0(xq)
    & aInteger0(xb)
    & aInteger0(xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).

fof(f23,axiom,
    ( sdteqdtlpzmzozddtrp0(xb,xc,xq)
    & sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__853) ).

fof(f24,conjecture,
    ? [X0] :
      ( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
      & aInteger0(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f25,negated_conjecture,
    ~ ? [X0] :
        ( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
        & aInteger0(X0) ),
    inference(negated_conjecture,[status(cth)],[f24]) ).

fof(f27,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | aInteger0(smndt0(X0)) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | aInteger0(sdtpldt0(X0,X1)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | aInteger0(sdtpldt0(X0,X1)) ),
    inference(flattening,[],[f28]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(flattening,[],[f34]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | ( sz00 = sdtasdt0(sz00,X0)
        & sdtasdt0(X0,sz00) = sz00 ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | sz00 != sdtasdt0(X0,X1)
      | X1 = sz00
      | X0 = sz00 ),
    inference(ennf_transformation,[],[f17]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | sz00 != sdtasdt0(X0,X1)
      | X1 = sz00
      | X0 = sz00 ),
    inference(flattening,[],[f47]) ).

fof(f49,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & X1 != sz00
            & aInteger0(X1) ) ) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
    inference(flattening,[],[f50]) ).

fof(f56,plain,
    ! [X0] :
      ( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | ! [X1] :
          ( ( ~ aDivisorOf0(X1,X0)
            | ( ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & X1 != sz00
              & aInteger0(X1) ) )
          & ( ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1)
            | aDivisorOf0(X1,X0) ) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | ! [X1] :
          ( ( ~ aDivisorOf0(X1,X0)
            | ( ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & X1 != sz00
              & aInteger0(X1) ) )
          & ( ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1)
            | aDivisorOf0(X1,X0) ) ) ),
    inference(flattening,[],[f57]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | ! [X1] :
          ( ( ~ aDivisorOf0(X1,X0)
            | ( ? [X3] :
                  ( sdtasdt0(X1,X3) = X0
                  & aInteger0(X3) )
              & X1 != sz00
              & aInteger0(X1) ) )
          & ( ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1)
            | aDivisorOf0(X1,X0) ) ) ),
    inference(rectify,[],[f58]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | ! [X1] :
          ( ( ~ aDivisorOf0(X1,X0)
            | ( sdtasdt0(X1,sK0(X0,X1)) = X0
              & aInteger0(sK0(X0,X1))
              & X1 != sz00
              & aInteger0(X1) ) )
          & ( ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | sz00 = X1
            | ~ aInteger0(X1)
            | aDivisorOf0(X1,X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f59]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | ( ( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
          | aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
        & ( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
          | sdteqdtlpzmzozddtrp0(X0,X1,X2) ) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f62,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f64,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | aInteger0(smndt0(X0)) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | aInteger0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sz00 = sdtasdt0(sz00,X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | sz00 != sdtasdt0(X0,X1)
      | sz00 = X1
      | sz00 = X0 ),
    inference(cnf_transformation,[],[f48]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aDivisorOf0(X1,X0)
      | sdtasdt0(X1,sK0(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f60]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aDivisorOf0(X1,X0)
      | aInteger0(sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f89,plain,
    ! [X2,X0,X1] :
      ( sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f94,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f22]) ).

fof(f95,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f22]) ).

fof(f96,plain,
    aInteger0(xb),
    inference(cnf_transformation,[],[f22]) ).

fof(f97,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f22]) ).

fof(f99,plain,
    sdteqdtlpzmzozddtrp0(xa,xb,xq),
    inference(cnf_transformation,[],[f23]) ).

fof(f100,plain,
    ! [X0] :
      ( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

tcf(c_49,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[],[f62]) ).

tcf(c_51,plain,
    ! [X0: $i] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i] :
      ( aInteger0(sdtpldt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] :
      ( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f68]) ).

tcf(c_67,plain,
    ! [X0: $i] :
      ( ( sdtasdt0(sz00,X0) = sz00 )
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

tcf(c_70,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = sz00 )
      | ( X0 = sz00 )
      | ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | ( sdtasdt0(X0,X1) != sz00 ) ),
    inference(cnf_transformation,[],[f83]) ).

tcf(c_74,plain,
    ! [X0: $i,X1: $i] :
      ( aInteger0(sK0(X1,X0))
      | ~ aInteger0(X1)
      | ~ aDivisorOf0(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

tcf(c_75,plain,
    ! [X0: $i,X1: $i] :
      ( ( sdtasdt0(X0,sK0(X1,X0)) = X1 )
      | ~ aInteger0(X1)
      | ~ aDivisorOf0(X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

tcf(c_77,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
      | ( X2 = sz00 )
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_80,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f97]) ).

tcf(c_81,plain,
    aInteger0(xb),
    inference(cnf_transformation,[],[f96]) ).

tcf(c_82,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f95]) ).

tcf(c_83,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f94]) ).

tcf(c_85,plain,
    sdteqdtlpzmzozddtrp0(xa,xb,xq),
    inference(cnf_transformation,[],[f99]) ).

tcf(c_87,negated_conjecture,
    ! [X0: $i] :
      ( ~ aInteger0(X0)
      | ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,X0) ) ),
    inference(cnf_transformation,[],[f100]) ).

tcf(c_90,plain,
    ( ( sdtasdt0(sz00,sz00) = sz00 )
    | ~ aInteger0(sz00) ),
    inference(instantiation,[status(thm)],[c_67]) ).

tcf(c_105,plain,
    ( ( sz00 = sz00 )
    | ~ aInteger0(sz00)
    | ( sdtasdt0(sz00,sz00) != sz00 ) ),
    inference(instantiation,[status(thm)],[c_70]) ).

tcf(c_511,plain,
    ! [X0: $i] : X0 = X0,
    theory(equality) ).

tcf(c_513,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = X0 )
      | ( X2 != X1 )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( aDivisorOf0(X0,X2)
      | ~ aDivisorOf0(X1,X3)
      | ( X2 != X3 )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_1035,plain,
    ! [X0: $i,X1: $i] :
      ( ( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1) )
      | ( sdtasdt0(xq,X1) != X0 )
      | ( sdtpldt0(xa,smndt0(xb)) != X0 ) ),
    inference(instantiation,[status(thm)],[c_513]) ).

tcf(c_1044,plain,
    ! [X0: $i] :
      ( ( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK0(X0,xq)) )
      | ( sdtpldt0(xa,smndt0(xb)) != X0 )
      | ( sdtasdt0(xq,sK0(X0,xq)) != X0 ) ),
    inference(instantiation,[status(thm)],[c_1035]) ).

tcf(c_1096,plain,
    ( ( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK0(sdtpldt0(smndt0(xb),xa),xq)) )
    | ( sdtpldt0(xa,smndt0(xb)) != sdtpldt0(smndt0(xb),xa) )
    | ( sdtasdt0(xq,sK0(sdtpldt0(smndt0(xb),xa),xq)) != sdtpldt0(smndt0(xb),xa) ) ),
    inference(instantiation,[status(thm)],[c_1044]) ).

tcf(c_1158,plain,
    ( ~ aInteger0(sK0(sdtpldt0(smndt0(xb),xa),xq))
    | ( sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sK0(sdtpldt0(smndt0(xb),xa),xq)) ) ),
    inference(instantiation,[status(thm)],[c_87]) ).

tcf(c_1181,plain,
    ( ( sdtpldt0(xa,smndt0(xb)) = sdtpldt0(smndt0(xb),xa) )
    | ~ aInteger0(xa)
    | ~ aInteger0(smndt0(xb)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_1195,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = xq )
      | ( xq != X1 )
      | ( X0 != X1 ) ),
    inference(instantiation,[status(thm)],[c_513]) ).

tcf(c_1196,plain,
    ( ( sz00 = xq )
    | ( xq != sz00 )
    | ( sz00 != sz00 ) ),
    inference(instantiation,[status(thm)],[c_1195]) ).

tcf(c_1225,plain,
    ! [X0: $i] :
      ( ( sdtasdt0(xq,sK0(X0,xq)) = X0 )
      | ~ aInteger0(X0)
      | ~ aDivisorOf0(xq,X0) ),
    inference(instantiation,[status(thm)],[c_75]) ).

tcf(c_1275,plain,
    xq = xq,
    inference(instantiation,[status(thm)],[c_511]) ).

tcf(c_1281,plain,
    ( aInteger0(sK0(sdtpldt0(smndt0(xb),xa),xq))
    | ~ aInteger0(sdtpldt0(smndt0(xb),xa))
    | ~ aDivisorOf0(xq,sdtpldt0(smndt0(xb),xa)) ),
    inference(instantiation,[status(thm)],[c_74]) ).

tcf(c_1294,plain,
    ( aInteger0(smndt0(xb))
    | ~ aInteger0(xb) ),
    inference(instantiation,[status(thm)],[c_51]) ).

tcf(c_1301,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aDivisorOf0(xq,X0)
      | ~ aDivisorOf0(X2,X1)
      | ( xq != X2 )
      | ( X0 != X1 ) ),
    inference(instantiation,[status(thm)],[c_518]) ).

tcf(c_1335,plain,
    ! [X0: $i,X1: $i] :
      ( aDivisorOf0(xq,sdtpldt0(X0,smndt0(X1)))
      | ( xq = sz00 )
      | ~ aInteger0(xq)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | ~ sdteqdtlpzmzozddtrp0(X0,X1,xq) ),
    inference(instantiation,[status(thm)],[c_77]) ).

tcf(c_1627,plain,
    ( aInteger0(sdtpldt0(smndt0(xb),xa))
    | ~ aInteger0(xa)
    | ~ aInteger0(smndt0(xb)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

tcf(c_1800,plain,
    ( ( sdtpldt0(smndt0(xb),xa) = sdtpldt0(xa,smndt0(xb)) )
    | ~ aInteger0(xa)
    | ~ aInteger0(smndt0(xb)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_2390,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aDivisorOf0(xq,X0)
      | ~ aDivisorOf0(xq,sdtpldt0(X1,smndt0(X2)))
      | ( xq != xq )
      | ( X0 != sdtpldt0(X1,smndt0(X2)) ) ),
    inference(instantiation,[status(thm)],[c_1301]) ).

tcf(c_4401,plain,
    ( aDivisorOf0(xq,sdtpldt0(smndt0(xb),xa))
    | ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    | ( xq != xq )
    | ( sdtpldt0(smndt0(xb),xa) != sdtpldt0(xa,smndt0(xb)) ) ),
    inference(instantiation,[status(thm)],[c_2390]) ).

tcf(c_4928,plain,
    ( ( sdtasdt0(xq,sK0(sdtpldt0(smndt0(xb),xa),xq)) = sdtpldt0(smndt0(xb),xa) )
    | ~ aInteger0(sdtpldt0(smndt0(xb),xa))
    | ~ aDivisorOf0(xq,sdtpldt0(smndt0(xb),xa)) ),
    inference(instantiation,[status(thm)],[c_1225]) ).

tcf(c_6964,plain,
    ( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    | ( xq = sz00 )
    | ~ aInteger0(xq)
    | ~ aInteger0(xb)
    | ~ aInteger0(xa)
    | ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
    inference(instantiation,[status(thm)],[c_1335]) ).

tcf(c_6965,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_6964,c_4928,c_4401,c_1800,c_1627,c_1294,c_1281,c_1275,c_1196,c_1181,c_1158,c_1096,c_105,c_90,c_83,c_85,c_49,c_80,c_81,c_82]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : NUM429+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/5.47  % Computer : n017.cluster.edu
% 0.18/5.47  % Model    : x86_64 x86_64
% 0.18/5.47  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.47  % Memory   : 8046.5625MB
% 0.18/5.47  % OS       : Linux 6.8.0-71-generic
% 0.18/5.47  % CPULimit : 300
% 0.18/5.47  % WCLimit  : 300
% 0.18/5.47  % DateTime : Thu Sep 24 03:50:23 UTC 2026
% 0.18/5.47  % CPUTime  : 
% 0.18/5.47  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/5.52  Running first-order theorem proving
% 0.23/5.52  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
% 0.23/5.54  
% 0.23/5.54  % ======== iProver multi-core TPTP/SMT =========
% 0.23/5.54  
% 0.23/5.54  % Detected problem language: tptp
% 0.23/5.56  % Proving...
% 8.96/7.03  % SZS status Started for theBenchmark.p
% 8.96/7.03  % SZS status Theorem for theBenchmark.p
% 8.96/7.03  
% 8.96/7.03  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.96/7.03  
% 8.96/7.03  % ------  iProver source info
% 8.96/7.03  
% 8.96/7.03  % git: date: 2026-07-19 20:42:38 +0200
% 8.96/7.03  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.96/7.03  % git: non_committed_changes: false
% 8.96/7.03  
% 8.96/7.03  % ------ Parsing...
% 8.96/7.03  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 8.96/7.03  
% 8.96/7.03  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 8.96/7.03  
% 8.96/7.03  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 8.96/7.03  
% 8.96/7.03  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 8.96/7.03  % ------ Proving...
% 8.96/7.03  % ------ Problem Properties 
% 8.96/7.03  
% 8.96/7.03  % 
% 8.96/7.03  % clauses                               39
% 8.96/7.03  % conjectures                           1
% 8.96/7.03  % EPR                                   13
% 8.96/7.03  % Horn                                  33
% 8.96/7.03  % unary                                 9
% 8.96/7.03  % binary                                13
% 8.96/7.03  % lits                                  103
% 8.96/7.03  % lits eq                               27
% 8.96/7.03  % fd_pure                               0
% 8.96/7.03  % fd_pseudo                             0
% 8.96/7.03  % fd_cond                               6
% 8.96/7.03  % fd_pseudo_cond                        0
% 8.96/7.03  % AC symbols                            0
% 8.96/7.03  
% 8.96/7.03  % ------ Input Options Time Limit: Unbounded
% 8.96/7.03  
% 8.96/7.03  
% 8.96/7.03  % ------ 
% 8.96/7.03  % Current options:
% 8.96/7.03  % ------ 
% 8.96/7.03  
% 8.96/7.03  
% 8.96/7.03  % 
% 8.96/7.03  
% 8.96/7.03  % ------ Proving...
% 8.96/7.03  % 
% 8.96/7.03  
% 8.96/7.03  % SZS status Theorem for theBenchmark.p
% 8.96/7.03  
% 8.96/7.03  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.96/7.03  
% 8.96/7.03  
%------------------------------------------------------------------------------