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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n008.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 02:27:19 PM UTC 2026

% Result   : Theorem 4.45s 21.32s
% Output   : CNFRefutation 4.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   97 (  72 unt;   6 def)
%            Number of atoms       :  174 (  79 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   81 (  37   ~;  34   |;   5   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   87 (   0 sgn  87   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f52,axiom,
    zero_zero(int) = number_number_of(int,pls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).

fof(f62,axiom,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).

fof(f65,axiom,
    ~ ord_less(int,pls,pls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).

fof(f78,axiom,
    ! [X0,X1,X2] : plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zadd__assoc) ).

fof(f79,axiom,
    ! [X0,X1,X2] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_zadd__left__commute) ).

fof(f80,axiom,
    ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zadd__commute) ).

fof(f93,axiom,
    ! [X0,X1] :
      ( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
    <=> ( X0 = X1
        | ord_less(int,X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zless__add1__eq) ).

fof(f94,axiom,
    ! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).

fof(f106,axiom,
    pls = zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).

fof(f108,axiom,
    ! [X0] : plus_plus(int,X0,pls) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).

fof(f109,axiom,
    ! [X0] : plus_plus(int,pls,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__Pls) ).

fof(f111,axiom,
    ! [X0] : bit0(X0) = plus_plus(int,X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Bit0__def) ).

fof(f117,axiom,
    ! [X0] :
      ( number_ring(X0)
     => ! [X1] : plus_plus(X0,number_number_of(X0,pls),X1) = ti(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).

fof(f125,axiom,
    ! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Bit1__def) ).

fof(f128,axiom,
    ! [X0] :
      ( linordered_idom(X0)
     => ! [X1] :
          ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
        <=> ti(X0,X1) != zero_zero(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__less__power2) ).

fof(f134,axiom,
    linordered_idom(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).

fof(f141,axiom,
    number_ring(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).

fof(f153,conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(f154,negated_conjecture,
    ~ ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ),
    inference(negated_conjecture,[status(cth)],[f153]) ).

fof(f155,plain,
    zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
    inference(flattening,[],[f154]) ).

fof(f219,plain,
    ! [X0] :
      ( ~ number_ring(X0)
      | ! [X1] : plus_plus(X0,number_number_of(X0,pls),X1) = ti(X0,X1) ),
    inference(ennf_transformation,[],[f117]) ).

fof(f227,plain,
    ! [X0] :
      ( ~ linordered_idom(X0)
      | ! [X1] :
          ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
        <=> ti(X0,X1) != zero_zero(X0) ) ),
    inference(ennf_transformation,[],[f128]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( ( ~ ord_less(int,X0,plus_plus(int,X1,one_one(int)))
        | X0 = X1
        | ord_less(int,X0,X1) )
      & ( ( X0 != X1
          & ~ ord_less(int,X0,X1) )
        | ord_less(int,X0,plus_plus(int,X1,one_one(int))) ) ),
    inference(nnf_transformation,[],[f93]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( ( ~ ord_less(int,X0,plus_plus(int,X1,one_one(int)))
        | X0 = X1
        | ord_less(int,X0,X1) )
      & ( ( X0 != X1
          & ~ ord_less(int,X0,X1) )
        | ord_less(int,X0,plus_plus(int,X1,one_one(int))) ) ),
    inference(flattening,[],[f259]) ).

fof(f269,plain,
    ! [X0] :
      ( ~ linordered_idom(X0)
      | ! [X1] :
          ( ( ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
            | ti(X0,X1) != zero_zero(X0) )
          & ( zero_zero(X0) = ti(X0,X1)
            | ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ) ),
    inference(nnf_transformation,[],[f227]) ).

fof(f333,plain,
    zero_zero(int) = number_number_of(int,pls),
    inference(cnf_transformation,[],[f52]) ).

fof(f344,plain,
    number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
    inference(cnf_transformation,[],[f62]) ).

fof(f349,plain,
    ~ ord_less(int,pls,pls),
    inference(cnf_transformation,[],[f65]) ).

fof(f371,plain,
    ! [X2,X0,X1] : plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)),
    inference(cnf_transformation,[],[f78]) ).

fof(f372,plain,
    ! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
    inference(cnf_transformation,[],[f79]) ).

fof(f373,plain,
    ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
    inference(cnf_transformation,[],[f80]) ).

fof(f397,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ord_less(int,X0,plus_plus(int,X1,one_one(int))) ),
    inference(cnf_transformation,[],[f260]) ).

fof(f399,plain,
    ! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
    inference(cnf_transformation,[],[f94]) ).

fof(f417,plain,
    pls = zero_zero(int),
    inference(cnf_transformation,[],[f106]) ).

fof(f419,plain,
    ! [X0] : plus_plus(int,X0,pls) = X0,
    inference(cnf_transformation,[],[f108]) ).

fof(f420,plain,
    ! [X0] : plus_plus(int,pls,X0) = X0,
    inference(cnf_transformation,[],[f109]) ).

fof(f422,plain,
    ! [X0] : bit0(X0) = plus_plus(int,X0,X0),
    inference(cnf_transformation,[],[f111]) ).

fof(f428,plain,
    ! [X0,X1] :
      ( ~ number_ring(X0)
      | ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1) ),
    inference(cnf_transformation,[],[f219]) ).

fof(f438,plain,
    ! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
    inference(cnf_transformation,[],[f125]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( ~ linordered_idom(X0)
      | zero_zero(X0) = ti(X0,X1)
      | ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f450,plain,
    linordered_idom(int),
    inference(cnf_transformation,[],[f134]) ).

fof(f457,plain,
    number_ring(int),
    inference(cnf_transformation,[],[f141]) ).

fof(f469,plain,
    zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f155]) ).

fof(f488,plain,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),
    inference(definition_unfolding,[],[f344,f422,f438]) ).

fof(f534,plain,
    ! [X0,X1] :
      ( ~ linordered_idom(X0)
      | zero_zero(X0) = ti(X0,X1)
      | ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) ),
    inference(definition_unfolding,[],[f442,f422,f438]) ).

fof(f540,plain,
    zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),
    inference(definition_unfolding,[],[f469,f422,f438]) ).

fof(f546,plain,
    ! [X1] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
    inference(equality_resolution,[],[f397]) ).

tcf(c_110,plain,
    number_number_of(int,pls) = zero_zero(int),
    inference(cnf_transformation,[],[f333]) ).

tcf(c_121,plain,
    number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
    inference(cnf_transformation,[],[f488]) ).

tcf(c_126,plain,
    ~ ord_less(int,pls,pls),
    inference(cnf_transformation,[],[f349]) ).

tcf(c_143,plain,
    ! [X0: $i,X1: $i,X2: $i] : plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)),
    inference(cnf_transformation,[],[f371]) ).

tcf(c_144,plain,
    ! [X0: $i,X1: $i,X2: $i] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
    inference(cnf_transformation,[],[f372]) ).

tcf(c_145,plain,
    ! [X0: $i,X1: $i] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
    inference(cnf_transformation,[],[f373]) ).

tcf(c_168,plain,
    ! [X0: $i] : ord_less(int,X0,plus_plus(int,X0,one_one(int))),
    inference(cnf_transformation,[],[f546]) ).

tcf(c_170,plain,
    ! [X0: $i] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
    inference(cnf_transformation,[],[f399]) ).

tcf(c_188,plain,
    zero_zero(int) = pls,
    inference(cnf_transformation,[],[f417]) ).

tcf(c_190,plain,
    ! [X0: $i] : plus_plus(int,X0,pls) = X0,
    inference(cnf_transformation,[],[f419]) ).

tcf(c_191,plain,
    ! [X0: $i] : plus_plus(int,pls,X0) = X0,
    inference(cnf_transformation,[],[f420]) ).

tcf(c_198,plain,
    ! [X0: $i,X1: $i] :
      ( ( plus_plus(X0,number_number_of(X0,pls),X1) = ti(X0,X1) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f428]) ).

tcf(c_210,plain,
    ! [X0: $i,X1: $i] :
      ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
      | ( ti(X0,X1) = zero_zero(X0) )
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f534]) ).

tcf(c_219,plain,
    linordered_idom(int),
    inference(cnf_transformation,[],[f450]) ).

tcf(c_226,plain,
    number_ring(int),
    inference(cnf_transformation,[],[f457]) ).

tcf(c_238,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) = zero_zero(int),
    inference(cnf_transformation,[],[f540]) ).

tcf(c_440,plain,
    ! [X0: $i,X1: $i] :
      ( ( plus_plus(X0,number_number_of(X0,pls),X1) = ti(X0,X1) )
      | ~ number_ring(X0) ),
    inference(prop_impl_just,[status(thm)],[c_198]) ).

tcf(c_1471,plain,
    number_number_of(int,pls) = pls,
    inference(light_normalisation,[status(thm)],[c_110,c_188]) ).

tcf(c_1474,plain,
    ! [X0: $i] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls),
    inference(light_normalisation,[status(thm)],[c_170,c_188]) ).

tcf(c_1988,plain,
    number_number_of(nat,plus_plus(int,one_one(int),one_one(int))) = plus_plus(nat,one_one(nat),one_one(nat)),
    inference(demodulation,[status(thm)],[c_121,c_143,c_144,c_190,c_191]) ).

tcf(c_2050,plain,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) = pls,
    inference(light_normalisation,[status(thm)],[c_238,c_188]) ).

tcf(c_2051,plain,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) = pls,
    inference(demodulation,[status(thm)],[c_2050,c_143,c_144,c_190,c_191,c_1988]) ).

tcf(c_2052,plain,
    ! [X0: $i,X1: $i] :
      ( ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
      | ( ti(X0,X1) = zero_zero(X0) )
      | ~ linordered_idom(X0) ),
    inference(demodulation,[status(thm)],[c_210,c_143,c_144,c_190,c_191,c_1988]) ).

tcf(c_2649,plain,
    ! [X0: $i,X1: $i] :
      ( ( plus_plus(X0,number_number_of(X0,pls),X1) = ti(X0,X1) )
      | ( X0 != int ) ),
    inference(resolution_lifted,[status(thm)],[c_440,c_226]) ).

tcf(c_2650,plain,
    ! [X0: $i] : plus_plus(int,number_number_of(int,pls),X0) = ti(int,X0),
    inference(unflattening,[status(thm)],[c_2649]) ).

tcf(c_2825,plain,
    ! [X0: $i,X1: $i] :
      ( ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
      | ( ti(X0,X1) = zero_zero(X0) )
      | ( X0 != int ) ),
    inference(resolution_lifted,[status(thm)],[c_2052,c_219]) ).

tcf(c_2826,plain,
    ! [X0: $i] :
      ( ord_less(int,zero_zero(int),power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))))
      | ( ti(int,X0) = zero_zero(int) ) ),
    inference(unflattening,[status(thm)],[c_2825]) ).

tcf(c_3077,plain,
    ! [X0: $i] :
      ( ( ti(int,X0) = zero_zero(int) )
      | ord_less(int,zero_zero(int),power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat)))) ),
    inference(prop_impl_just,[status(thm)],[c_2826]) ).

tcf(c_3078,plain,
    ! [X0: $i] :
      ( ord_less(int,zero_zero(int),power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))))
      | ( ti(int,X0) = zero_zero(int) ) ),
    inference(renaming,[status(thm)],[c_3077]) ).

tcf(c_3872,plain,
    ! [X0: $i] : ti(int,X0) = X0,
    inference(light_normalisation,[status(thm)],[c_2650,c_191,c_1471]) ).

tcf(c_4088,plain,
    ! [X0: $i] :
      ( ord_less(int,pls,power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))))
      | ( X0 = pls ) ),
    inference(light_normalisation,[status(thm)],[c_3078,c_188,c_3872]) ).

tcf(c_5315,plain,
    ! [X0: $i] :
      ( ord_less(int,pls,power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))))
      | ( X0 = pls ) ),
    inference(prop_impl_just,[status(thm)],[c_4088]) ).

tcf(c_6163,definition,
    iPr_def_10 = one_one(int),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_6164,definition,
    iPr_def_11 = semiring_1_of_nat(int,n),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_6165,definition,
    iPr_def_12 = plus_plus(int,iPr_def_10,iPr_def_11),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_6166,definition,
    iPr_def_13 = one_one(nat),
    introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).

tcf(c_6167,definition,
    iPr_def_14 = plus_plus(nat,iPr_def_13,iPr_def_13),
    introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).

tcf(c_6168,definition,
    iPr_def_15 = power_power(int,iPr_def_12,iPr_def_14),
    introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).

tcf(c_6169,plain,
    iPr_def_15 = pls,
    inference(demodulation,[status(thm)],[c_2051,c_6166,c_6167,c_6164,c_6163,c_6165,c_6168]) ).

tcf(c_7753,plain,
    ~ ord_less(int,iPr_def_15,iPr_def_15),
    inference(light_normalisation,[status(thm)],[c_126,c_6169]) ).

tcf(c_7761,plain,
    ! [X0: $i] : ~ ord_less(int,semiring_1_of_nat(int,X0),iPr_def_15),
    inference(light_normalisation,[status(thm)],[c_1474,c_6169]) ).

tcf(c_7762,plain,
    ~ ord_less(int,iPr_def_11,iPr_def_15),
    inference(superposition,[status(thm)],[c_6164,c_7761]) ).

tcf(c_7771,plain,
    ! [X0: $i] : ord_less(int,X0,plus_plus(int,X0,iPr_def_10)),
    inference(light_normalisation,[status(thm)],[c_168,c_6163]) ).

tcf(c_7786,plain,
    ! [X0: $i] : ord_less(int,X0,plus_plus(int,iPr_def_10,X0)),
    inference(superposition,[status(thm)],[c_145,c_7771]) ).

tcf(c_7791,plain,
    ord_less(int,iPr_def_11,iPr_def_12),
    inference(superposition,[status(thm)],[c_6165,c_7786]) ).

tcf(c_10227,plain,
    ! [X0: $i] :
      ( ord_less(int,iPr_def_15,power_power(int,X0,iPr_def_14))
      | ( X0 = iPr_def_15 ) ),
    inference(light_normalisation,[status(thm)],[c_5315,c_6166,c_6167,c_6169]) ).

tcf(c_10234,plain,
    ( ord_less(int,iPr_def_15,iPr_def_15)
    | ( iPr_def_12 = iPr_def_15 ) ),
    inference(superposition,[status(thm)],[c_6168,c_10227]) ).

tcf(c_10236,plain,
    iPr_def_12 = iPr_def_15,
    inference(forward_subsumption_resolution,[status(thm)],[c_10234,c_7753]) ).

tcf(c_10286,plain,
    ~ ord_less(int,iPr_def_11,iPr_def_12),
    inference(demodulation,[status(thm)],[c_7762,c_10236]) ).

tcf(c_10298,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_10286,c_7791]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/20.39  % Computer : n008.cluster.edu
% 0.09/20.39  % Model    : x86_64 x86_64
% 0.09/20.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/20.39  % Memory   : 8046.5625MB
% 0.09/20.39  % OS       : Linux 6.8.0-71-generic
% 0.09/20.40  % CPULimit : 300
% 0.09/20.40  % WCLimit  : 300
% 0.09/20.40  % DateTime : Thu Sep 24 05:44:46 UTC 2026
% 0.14/20.40  % CPUTime  : 
% 0.14/20.40  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/20.44  Running first-order theorem proving
% 0.14/20.44  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
% 0.14/20.45  
% 0.14/20.45  % ======== iProver multi-core TPTP/SMT =========
% 0.14/20.45  
% 0.14/20.45  % Detected problem language: tptp
% 0.14/20.46  % Proving...
% 4.45/21.32  % SZS status Started for theBenchmark.p
% 4.45/21.32  % SZS status Theorem for theBenchmark.p
% 4.45/21.32  
% 4.45/21.32  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.45/21.32  
% 4.45/21.32  % ------  iProver source info
% 4.45/21.32  
% 4.45/21.32  % git: date: 2026-07-19 20:42:38 +0200
% 4.45/21.32  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.45/21.32  % git: non_committed_changes: false
% 4.45/21.32  
% 4.45/21.32  % ------ Parsing...
% 4.45/21.32  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 4.45/21.32  
% 4.45/21.32  % ------ Preprocessing... sup_sim: 56  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: 59  sf_s  rm: 14 0s  sf_e  pe_s  pe_e  sup_sim: 3  sf_s  rm: 14 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 14 0s  sf_e  pe_s  pe_e % 
% 4.45/21.32  
% 4.45/21.32  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 4.45/21.32  
% 4.45/21.32  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.45/21.32  % ------ Proving...
% 4.45/21.32  % ------ Problem Properties 
% 4.45/21.32  
% 4.45/21.32  % 
% 4.45/21.32  % clauses                               122
% 4.45/21.32  % conjectures                           0
% 4.45/21.32  % EPR                                   3
% 4.45/21.32  % Horn                                  111
% 4.45/21.32  % unary                                 63
% 4.45/21.32  % binary                                53
% 4.45/21.32  % lits                                  187
% 4.45/21.32  % lits eq                               98
% 4.45/21.32  % fd_pure                               0
% 4.45/21.32  % fd_pseudo                             0
% 4.45/21.32  % fd_cond                               3
% 4.45/21.32  % fd_pseudo_cond                        6
% 4.45/21.32  % AC symbols                            0
% 4.45/21.32  
% 4.45/21.32  % ------ Schedule dynamic 5 is on 
% 4.45/21.32  
% 4.45/21.32  % ------ no conjectures: strip conj schedule 
% 4.45/21.32  
% 4.45/21.32  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.45/21.32  
% 4.45/21.32  
% 4.45/21.32  % ------ 
% 4.45/21.32  % Current options:
% 4.45/21.32  % ------ 
% 4.45/21.32  
% 4.45/21.32  
% 4.45/21.32  % 
% 4.45/21.32  
% 4.45/21.32  % ------ Proving...
% 4.45/21.32  % 
% 4.45/21.32  
% 4.45/21.32  % SZS status Theorem for theBenchmark.p
% 4.45/21.32  
% 4.45/21.32  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.45/21.32  
% 4.45/21.32  
%------------------------------------------------------------------------------