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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : RNG046+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 : n015.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 02:38:18 PM UTC 2026

% Result   : Theorem 3.94s 1.30s
% Output   : CNFRefutation 3.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   71 (  15 unt;   0 def)
%            Number of atoms       :  199 (  90 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  236 ( 108   ~;  92   |;  31   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   85 (   0 sgn  85   !;   0   ?;  48   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => aScalar0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

fof(f12,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => aScalar0(smndt0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

fof(f13,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => ( smndt0(sz0z00) = sz0z00
        & smndt0(smndt0(X0)) = X0
        & sdtpldt0(smndt0(X0),X0) = sz0z00
        & sdtpldt0(X0,smndt0(X0)) = sz0z00
        & sdtasdt0(sz0z00,X0) = sz0z00
        & sdtasdt0(X0,sz0z00) = sz0z00
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( ( aScalar0(X2)
        & aScalar0(X1)
        & aScalar0(X0) )
     => ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        & sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        & sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        & sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1))
        & sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).

fof(f18,axiom,
    ( aScalar0(xy)
    & aScalar0(xx) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).

fof(f19,conjecture,
    sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f20,negated_conjecture,
    sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
    inference(negated_conjecture,[status(cth)],[f19]) ).

fof(f24,plain,
    sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
    inference(flattening,[],[f20]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | aScalar0(sdtasdt0(X0,X1)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | aScalar0(sdtasdt0(X0,X1)) ),
    inference(flattening,[],[f33]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | aScalar0(smndt0(X0)) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f36,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | ( smndt0(sz0z00) = sz0z00
        & smndt0(smndt0(X0)) = X0
        & sdtpldt0(smndt0(X0),X0) = sz0z00
        & sdtpldt0(X0,smndt0(X0)) = sz0z00
        & sdtasdt0(sz0z00,X0) = sz0z00
        & sdtasdt0(X0,sz0z00) = sz0z00
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        & sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        & sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        & sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        & sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        & sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        & sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
    inference(flattening,[],[f37]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1))
        & sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1))
        & sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
    inference(flattening,[],[f43]) ).

fof(f52,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f9]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | aScalar0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | aScalar0(smndt0(X0)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | smndt0(smndt0(X0)) = X0 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ~ aScalar0(X1)
      | ~ aScalar0(X0)
      | smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f73,plain,
    aScalar0(xy),
    inference(cnf_transformation,[],[f18]) ).

fof(f74,plain,
    aScalar0(xx),
    inference(cnf_transformation,[],[f18]) ).

fof(f75,plain,
    sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
    inference(cnf_transformation,[],[f24]) ).

tcf(c_55,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f52]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f54]) ).

tcf(c_58,plain,
    ! [X0: $i] :
      ( aScalar0(smndt0(X0))
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f55]) ).

tcf(c_65,plain,
    ! [X0: $i] :
      ( ( smndt0(smndt0(X0)) = X0 )
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f57]) ).

tcf(c_68,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f66]) ).

tcf(c_70,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

tcf(c_75,plain,
    ! [X0: $i,X1: $i] :
      ( ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1)) )
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f71]) ).

tcf(c_76,plain,
    aScalar0(xx),
    inference(cnf_transformation,[],[f74]) ).

tcf(c_77,plain,
    aScalar0(xy),
    inference(cnf_transformation,[],[f73]) ).

tcf(c_78,negated_conjecture,
    sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
    inference(cnf_transformation,[],[f75]) ).

tcf(c_268,negated_conjecture,
    sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
    inference(subtyping,[status(esa)],[c_78]) ).

tcf(c_271,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(smndt0(X0_iProver_smndt0_0),X1_iProver_smndt0_0) = smndt0(sdtasdt0(X0_iProver_smndt0_0,X1_iProver_smndt0_0)) )
      | ~ aScalar0(X1_iProver_smndt0_0)
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(subtyping,[status(esa)],[c_75]) ).

tcf(c_276,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0,X2_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(X0_iProver_smndt0_0,X1_iProver_smndt0_0) = sdtasdt0(X1_iProver_smndt0_0,X0_iProver_smndt0_0) )
      | ~ aScalar0(X2_iProver_smndt0_0)
      | ~ aScalar0(X1_iProver_smndt0_0)
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(subtyping,[status(esa)],[c_70]) ).

tcf(c_278,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0,X2_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtpldt0(X0_iProver_smndt0_0,X1_iProver_smndt0_0) = sdtpldt0(X1_iProver_smndt0_0,X0_iProver_smndt0_0) )
      | ~ aScalar0(X2_iProver_smndt0_0)
      | ~ aScalar0(X1_iProver_smndt0_0)
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(subtyping,[status(esa)],[c_68]) ).

tcf(c_280,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( smndt0(smndt0(X0_iProver_smndt0_0)) = X0_iProver_smndt0_0 )
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(subtyping,[status(esa)],[c_65]) ).

tcf(c_287,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( aScalar0(smndt0(X0_iProver_smndt0_0))
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(subtyping,[status(esa)],[c_58]) ).

tcf(c_288,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( aScalar0(sdtasdt0(X0_iProver_smndt0_0,X1_iProver_smndt0_0))
      | ~ aScalar0(X1_iProver_smndt0_0)
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(subtyping,[status(esa)],[c_57]) ).

tcf(c_297,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ~ iPr_def_10
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_278]) ).

tcf(c_300,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ~ iPr_def_12
      | ( sdtasdt0(X0_iProver_smndt0_0,X1_iProver_smndt0_0) = sdtasdt0(X1_iProver_smndt0_0,X0_iProver_smndt0_0) )
      | ~ aScalar0(X1_iProver_smndt0_0)
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_276]) ).

tcf(c_301,plain,
    ( iPr_def_12
    | iPr_def_10 ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_276]) ).

tcf(c_305,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0,X2_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( X2_iProver_smndt0_0 = X0_iProver_smndt0_0 )
      | ( X2_iProver_smndt0_0 != X1_iProver_smndt0_0 )
      | ( X0_iProver_smndt0_0 != X1_iProver_smndt0_0 ) ),
    theory(equality) ).

tcf(c_312,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( smndt0(X0_iProver_smndt0_0) = smndt0(X1_iProver_smndt0_0) )
      | ( X0_iProver_smndt0_0 != X1_iProver_smndt0_0 ) ),
    theory(equality) ).

tcf(c_334,plain,
    ( ~ iPr_def_10
    | ~ aScalar0(sz0z00) ),
    inference(instantiation,[status(thm)],[c_297]) ).

tcf(c_344,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ~ aScalar0(X0_iProver_smndt0_0)
      | ~ aScalar0(X1_iProver_smndt0_0)
      | ( sdtasdt0(X0_iProver_smndt0_0,X1_iProver_smndt0_0) = sdtasdt0(X1_iProver_smndt0_0,X0_iProver_smndt0_0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_300,c_55,c_334,c_300,c_301]) ).

tcf(c_345,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(X0_iProver_smndt0_0,X1_iProver_smndt0_0) = sdtasdt0(X1_iProver_smndt0_0,X0_iProver_smndt0_0) )
      | ~ aScalar0(X1_iProver_smndt0_0)
      | ~ aScalar0(X0_iProver_smndt0_0) ),
    inference(renaming,[status(thm)],[c_344]) ).

tcf(c_810,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(xx,xy) != X0_iProver_smndt0_0 )
      | ( sdtasdt0(smndt0(xx),smndt0(xy)) != X0_iProver_smndt0_0 ) ),
    inference(resolution,[status(thm)],[c_305,c_268]) ).

tcf(c_821,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( X1_iProver_smndt0_0 != X0_iProver_smndt0_0 )
      | ( sdtasdt0(xx,xy) != X1_iProver_smndt0_0 )
      | ( sdtasdt0(smndt0(xx),smndt0(xy)) != X0_iProver_smndt0_0 ) ),
    inference(resolution,[status(thm)],[c_810,c_305]) ).

tcf(c_902,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( X1_iProver_smndt0_0 != X0_iProver_smndt0_0 )
      | ( sdtasdt0(xx,xy) != smndt0(X1_iProver_smndt0_0) )
      | ( sdtasdt0(smndt0(xx),smndt0(xy)) != smndt0(X0_iProver_smndt0_0) ) ),
    inference(resolution,[status(thm)],[c_821,c_312]) ).

tcf(c_940,plain,
    ( ( sdtasdt0(xx,xy) = sdtasdt0(xy,xx) )
    | ~ aScalar0(xy)
    | ~ aScalar0(xx) ),
    inference(instantiation,[status(thm)],[c_345]) ).

tcf(c_942,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0,X1_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(xx,xy) = X1_iProver_smndt0_0 )
      | ( X1_iProver_smndt0_0 != X0_iProver_smndt0_0 )
      | ( sdtasdt0(xx,xy) != X0_iProver_smndt0_0 ) ),
    inference(instantiation,[status(thm)],[c_305]) ).

tcf(c_1003,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(xx,xy) = X0_iProver_smndt0_0 )
      | ( X0_iProver_smndt0_0 != sdtasdt0(xy,xx) )
      | ( sdtasdt0(xx,xy) != sdtasdt0(xy,xx) ) ),
    inference(instantiation,[status(thm)],[c_942]) ).

tcf(c_1183,plain,
    ( aScalar0(smndt0(xy))
    | ~ aScalar0(xy) ),
    inference(instantiation,[status(thm)],[c_287]) ).

tcf(c_1317,plain,
    ( ( sdtasdt0(xx,xy) = smndt0(smndt0(sdtasdt0(xy,xx))) )
    | ( sdtasdt0(xx,xy) != sdtasdt0(xy,xx) )
    | ( smndt0(smndt0(sdtasdt0(xy,xx))) != sdtasdt0(xy,xx) ) ),
    inference(instantiation,[status(thm)],[c_1003]) ).

tcf(c_1318,plain,
    ( ( smndt0(smndt0(sdtasdt0(xy,xx))) = sdtasdt0(xy,xx) )
    | ~ aScalar0(sdtasdt0(xy,xx)) ),
    inference(instantiation,[status(thm)],[c_280]) ).

tcf(c_1474,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ~ aScalar0(xx)
      | ~ aScalar0(smndt0(xy))
      | ( X0_iProver_smndt0_0 != sdtasdt0(xx,smndt0(xy)) )
      | ( sdtasdt0(xx,xy) != smndt0(X0_iProver_smndt0_0) ) ),
    inference(resolution,[status(thm)],[c_902,c_271]) ).

tcf(c_1476,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( X0_iProver_smndt0_0 != sdtasdt0(xx,smndt0(xy)) )
      | ( sdtasdt0(xx,xy) != smndt0(X0_iProver_smndt0_0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_1474,c_77,c_76,c_1183,c_1474]) ).

tcf(c_1640,plain,
    ( ~ aScalar0(xx)
    | ~ aScalar0(smndt0(xy))
    | ( sdtasdt0(xx,xy) != smndt0(sdtasdt0(smndt0(xy),xx)) ) ),
    inference(resolution,[status(thm)],[c_1476,c_345]) ).

tcf(c_1641,plain,
    sdtasdt0(xx,xy) != smndt0(sdtasdt0(smndt0(xy),xx)),
    inference(global_subsumption_just,[status(thm)],[c_1640,c_77,c_76,c_1183,c_1640]) ).

tcf(c_1665,plain,
    ( aScalar0(sdtasdt0(xy,xx))
    | ~ aScalar0(xy)
    | ~ aScalar0(xx) ),
    inference(instantiation,[status(thm)],[c_288]) ).

tcf(c_1700,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(xx,xy) != X0_iProver_smndt0_0 )
      | ( smndt0(sdtasdt0(smndt0(xy),xx)) != X0_iProver_smndt0_0 ) ),
    inference(resolution,[status(thm)],[c_1641,c_305]) ).

tcf(c_1771,plain,
    ! [X0_iProver_smndt0_0: iProver_smndt0_0] :
      ( ( sdtasdt0(xx,xy) != smndt0(X0_iProver_smndt0_0) )
      | ( sdtasdt0(smndt0(xy),xx) != X0_iProver_smndt0_0 ) ),
    inference(resolution,[status(thm)],[c_1700,c_312]) ).

tcf(c_1798,plain,
    ( ~ aScalar0(xy)
    | ~ aScalar0(xx)
    | ( sdtasdt0(xx,xy) != smndt0(smndt0(sdtasdt0(xy,xx))) ) ),
    inference(resolution,[status(thm)],[c_1771,c_271]) ).

tcf(c_1799,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1798,c_1665,c_1318,c_1317,c_940,c_76,c_77]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : RNG046+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38  % Computer : n015.cluster.edu
% 0.11/0.38  % Model    : x86_64 x86_64
% 0.11/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38  % Memory   : 8046.5625MB
% 0.11/0.38  % OS       : Linux 6.8.0-71-generic
% 0.11/0.38  % CPULimit : 300
% 0.11/0.38  % WCLimit  : 300
% 0.11/0.38  % DateTime : Thu Sep 24 08:00:41 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42  Running first-order theorem proving
% 0.11/0.42  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43  
% 0.11/0.43  % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43  
% 0.11/0.43  % Detected problem language: tptp
% 0.11/0.44  % Proving...
% 3.94/1.30  % SZS status Started for theBenchmark.p
% 3.94/1.30  % SZS status Theorem for theBenchmark.p
% 3.94/1.30  
% 3.94/1.30  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.94/1.30  
% 3.94/1.30  % ------  iProver source info
% 3.94/1.30  
% 3.94/1.30  % git: date: 2026-07-19 20:42:38 +0200
% 3.94/1.30  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.94/1.30  % git: non_committed_changes: false
% 3.94/1.30  
% 3.94/1.30  % ------ Parsing...
% 3.94/1.30  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.94/1.30  
% 3.94/1.30  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 3.94/1.30  
% 3.94/1.30  % ------ Preprocessing... gs_s  sp: 4 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 3.94/1.30  
% 3.94/1.30  % ------ Preprocessing... sf_s  rm: 4 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.94/1.30  % ------ Proving...
% 3.94/1.30  % ------ Problem Properties 
% 3.94/1.30  
% 3.94/1.30  % 
% 3.94/1.30  % clauses                               33
% 3.94/1.30  % conjectures                           1
% 3.94/1.30  % EPR                                   7
% 3.94/1.30  % Horn                                  29
% 3.94/1.30  % unary                                 6
% 3.94/1.30  % binary                                13
% 3.94/1.30  % lits                                  83
% 3.94/1.30  % lits eq                               24
% 3.94/1.30  % fd_pure                               0
% 3.94/1.30  % fd_pseudo                             0
% 3.94/1.30  % fd_cond                               1
% 3.94/1.30  % fd_pseudo_cond                        1
% 3.94/1.30  % AC symbols                            0
% 3.94/1.30  
% 3.94/1.30  % ------ Input Options Time Limit: Unbounded
% 3.94/1.30  
% 3.94/1.30  
% 3.94/1.30  % ------ 
% 3.94/1.30  % Current options:
% 3.94/1.30  % ------ 
% 3.94/1.30  
% 3.94/1.30  
% 3.94/1.30  % 
% 3.94/1.30  
% 3.94/1.30  % ------ Proving...
% 3.94/1.30  % 
% 3.94/1.30  
% 3.94/1.30  % SZS status Theorem for theBenchmark.p
% 3.94/1.30  
% 3.94/1.30  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/1.31  
% 3.94/1.31  
%------------------------------------------------------------------------------