TSTP Solution File: NUM925+5 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM925+5 : TPTP v7.0.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n058.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan  8 15:22:42 EST 2018

% Result   : Theorem 0.06s
% Output   : CNFRefutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   62 (  44 unt;   0 def)
%            Number of atoms       :  102 (  34 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   76 (  36   ~;  33   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   39 (   0 sgn  24   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    equal(pls,zero_zero(int)),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_73_Pls__def) ).

fof(17,axiom,
    ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_0_n1pos) ).

fof(33,axiom,
    ! [X1] :
      ( number_ring(X1)
     => ! [X22] : equal(plus_plus(X1,X22,number_number_of(X1,pls)),ti(X1,X22)) ),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_85_add__numeral__0__right) ).

fof(42,axiom,
    ! [X1] :
      ( ring_11004092258visors(X1)
     => ! [X23] :
          ( equal(power_power(X1,X23,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X1))
        <=> equal(ti(X1,X23),zero_zero(X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_5_zero__eq__power2) ).

fof(58,axiom,
    equal(zero_zero(int),number_number_of(int,pls)),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_19_zero__is__num__zero) ).

fof(91,axiom,
    ring_11004092258visors(int),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).

fof(114,conjecture,
    ~ equal(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/tmp/tmpYdWFRS/sel_theBenchmark.p_1',conj_0) ).

fof(121,axiom,
    ! [X4] : equal(plus_plus(int,X4,pls),X4),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_75_add__Pls__right) ).

fof(122,axiom,
    ! [X4] : equal(bit0(X4),plus_plus(int,X4,X4)),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_78_Bit0__def) ).

fof(124,axiom,
    ! [X4] : equal(bit1(X4),plus_plus(int,plus_plus(int,one_one(int),X4),X4)),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_92_Bit1__def) ).

fof(146,axiom,
    ~ ord_less(int,pls,pls),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_32_rel__simps_I2_J) ).

fof(147,axiom,
    equal(plus_plus(nat,one_one(nat),one_one(nat)),number_number_of(nat,bit0(bit1(pls)))),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',fact_29_nat__1__add__1) ).

fof(153,axiom,
    number_ring(int),
    file('/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1',arity_Int_Oint___Int_Onumber__ring) ).

fof(154,negated_conjecture,
    ~ ~ equal(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(assume_negation,[status(cth)],[114]) ).

fof(159,negated_conjecture,
    equal(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(fof_simplification,[status(thm)],[154,theory(equality)]) ).

fof(160,plain,
    ~ ord_less(int,pls,pls),
    inference(fof_simplification,[status(thm)],[146,theory(equality)]) ).

cnf(175,plain,
    pls = zero_zero(int),
    inference(split_conjunct,[status(thm)],[6]) ).

cnf(201,plain,
    ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(247,plain,
    ! [X1] :
      ( ~ number_ring(X1)
      | ! [X22] : equal(plus_plus(X1,X22,number_number_of(X1,pls)),ti(X1,X22)) ),
    inference(fof_nnf,[status(thm)],[33]) ).

fof(248,plain,
    ! [X23] :
      ( ~ number_ring(X23)
      | ! [X24] : equal(plus_plus(X23,X24,number_number_of(X23,pls)),ti(X23,X24)) ),
    inference(variable_rename,[status(thm)],[247]) ).

fof(249,plain,
    ! [X23,X24] :
      ( equal(plus_plus(X23,X24,number_number_of(X23,pls)),ti(X23,X24))
      | ~ number_ring(X23) ),
    inference(shift_quantors,[status(thm)],[248]) ).

cnf(250,plain,
    ( plus_plus(X1,X2,number_number_of(X1,pls)) = ti(X1,X2)
    | ~ number_ring(X1) ),
    inference(split_conjunct,[status(thm)],[249]) ).

fof(273,plain,
    ! [X1] :
      ( ~ ring_11004092258visors(X1)
      | ! [X23] :
          ( ( ~ equal(power_power(X1,X23,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X1))
            | equal(ti(X1,X23),zero_zero(X1)) )
          & ( ~ equal(ti(X1,X23),zero_zero(X1))
            | equal(power_power(X1,X23,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X1)) ) ) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(274,plain,
    ! [X24] :
      ( ~ ring_11004092258visors(X24)
      | ! [X25] :
          ( ( ~ equal(power_power(X24,X25,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X24))
            | equal(ti(X24,X25),zero_zero(X24)) )
          & ( ~ equal(ti(X24,X25),zero_zero(X24))
            | equal(power_power(X24,X25,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X24)) ) ) ),
    inference(variable_rename,[status(thm)],[273]) ).

fof(275,plain,
    ! [X24,X25] :
      ( ( ( ~ equal(power_power(X24,X25,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X24))
          | equal(ti(X24,X25),zero_zero(X24)) )
        & ( ~ equal(ti(X24,X25),zero_zero(X24))
          | equal(power_power(X24,X25,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X24)) ) )
      | ~ ring_11004092258visors(X24) ),
    inference(shift_quantors,[status(thm)],[274]) ).

fof(276,plain,
    ! [X24,X25] :
      ( ( ~ equal(power_power(X24,X25,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X24))
        | equal(ti(X24,X25),zero_zero(X24))
        | ~ ring_11004092258visors(X24) )
      & ( ~ equal(ti(X24,X25),zero_zero(X24))
        | equal(power_power(X24,X25,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X24))
        | ~ ring_11004092258visors(X24) ) ),
    inference(distribute,[status(thm)],[275]) ).

cnf(278,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ ring_11004092258visors(X1)
    | power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[276]) ).

cnf(314,plain,
    zero_zero(int) = number_number_of(int,pls),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(411,plain,
    ring_11004092258visors(int),
    inference(split_conjunct,[status(thm)],[91]) ).

cnf(472,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(split_conjunct,[status(thm)],[159]) ).

fof(498,plain,
    ! [X5] : equal(plus_plus(int,X5,pls),X5),
    inference(variable_rename,[status(thm)],[121]) ).

cnf(499,plain,
    plus_plus(int,X1,pls) = X1,
    inference(split_conjunct,[status(thm)],[498]) ).

fof(500,plain,
    ! [X5] : equal(bit0(X5),plus_plus(int,X5,X5)),
    inference(variable_rename,[status(thm)],[122]) ).

cnf(501,plain,
    bit0(X1) = plus_plus(int,X1,X1),
    inference(split_conjunct,[status(thm)],[500]) ).

fof(504,plain,
    ! [X5] : equal(bit1(X5),plus_plus(int,plus_plus(int,one_one(int),X5),X5)),
    inference(variable_rename,[status(thm)],[124]) ).

cnf(505,plain,
    bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
    inference(split_conjunct,[status(thm)],[504]) ).

cnf(575,plain,
    ~ ord_less(int,pls,pls),
    inference(split_conjunct,[status(thm)],[160]) ).

cnf(576,plain,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
    inference(split_conjunct,[status(thm)],[147]) ).

cnf(590,plain,
    number_ring(int),
    inference(split_conjunct,[status(thm)],[153]) ).

cnf(597,plain,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),
    inference(rw,[status(thm)],[576,501,theory(equality)]),
    [unfolding] ).

cnf(598,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = zero_zero(int),
    inference(rw,[status(thm)],[472,501,theory(equality)]),
    [unfolding] ).

cnf(626,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | power_power(X1,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) != zero_zero(X1)
    | ~ ring_11004092258visors(X1) ),
    inference(rw,[status(thm)],[278,501,theory(equality)]),
    [unfolding] ).

cnf(643,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(rw,[status(thm)],[inference(rw,[status(thm)],[597,505,theory(equality)]),505,theory(equality)]),
    [unfolding] ).

cnf(644,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(rw,[status(thm)],[inference(rw,[status(thm)],[598,505,theory(equality)]),505,theory(equality)]),
    [unfolding] ).

cnf(670,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | power_power(X1,X2,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(X1)
    | ~ ring_11004092258visors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[626,505,theory(equality)]),505,theory(equality)]),
    [unfolding] ).

cnf(687,plain,
    number_number_of(int,pls) = pls,
    inference(rw,[status(thm)],[314,175,theory(equality)]) ).

cnf(716,plain,
    number_number_of(nat,plus_plus(int,one_one(int),one_one(int))) = plus_plus(nat,one_one(nat),one_one(nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[643,499,theory(equality)]),499,theory(equality)]),499,theory(equality)]),499,theory(equality)]) ).

cnf(717,plain,
    ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    inference(rw,[status(thm)],[201,175,theory(equality)]) ).

cnf(728,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[644,499,theory(equality)]),499,theory(equality)]),499,theory(equality)]),499,theory(equality)]),716,theory(equality)]) ).

cnf(729,negated_conjecture,
    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(rw,[status(thm)],[728,175,theory(equality)]) ).

cnf(1478,plain,
    plus_plus(int,X1,number_number_of(int,pls)) = ti(int,X1),
    inference(spm,[status(thm)],[250,590,theory(equality)]) ).

cnf(1479,plain,
    X1 = ti(int,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1478,687,theory(equality)]),499,theory(equality)]) ).

cnf(1900,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | power_power(X1,X2,plus_plus(nat,one_one(nat),one_one(nat))) != zero_zero(X1)
    | ~ ring_11004092258visors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[670,499,theory(equality)]),499,theory(equality)]),499,theory(equality)]),499,theory(equality)]),716,theory(equality)]) ).

cnf(1901,negated_conjecture,
    ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int)
    | pls != zero_zero(int)
    | ~ ring_11004092258visors(int) ),
    inference(spm,[status(thm)],[1900,729,theory(equality)]) ).

cnf(1904,negated_conjecture,
    ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = pls
    | pls != zero_zero(int)
    | ~ ring_11004092258visors(int) ),
    inference(rw,[status(thm)],[1901,175,theory(equality)]) ).

cnf(1905,negated_conjecture,
    ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = pls
    | $false
    | ~ ring_11004092258visors(int) ),
    inference(rw,[status(thm)],[1904,175,theory(equality)]) ).

cnf(1906,negated_conjecture,
    ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = pls
    | $false
    | $false ),
    inference(rw,[status(thm)],[1905,411,theory(equality)]) ).

cnf(1907,negated_conjecture,
    ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = pls,
    inference(cn,[status(thm)],[1906,theory(equality)]) ).

cnf(4808,negated_conjecture,
    plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls,
    inference(rw,[status(thm)],[1907,1479,theory(equality)]) ).

cnf(4853,plain,
    ord_less(int,pls,pls),
    inference(rw,[status(thm)],[717,4808,theory(equality)]) ).

cnf(4854,plain,
    $false,
    inference(sr,[status(thm)],[4853,575,theory(equality)]) ).

cnf(4855,plain,
    $false,
    4854,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : NUM925+5 : TPTP v7.0.0. Released v5.3.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.03/0.24  % Computer : n058.star.cs.uiowa.edu
% 0.03/0.24  % Model    : x86_64 x86_64
% 0.03/0.24  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.24  % Memory   : 32218.625MB
% 0.03/0.24  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.24  % CPULimit : 300
% 0.03/0.24  % DateTime : Fri Jan  5 16:17:34 CST 2018
% 0.06/0.24  % CPUTime  : 
% 0.06/0.29  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.29  --creating new selector for []
% 0.06/0.47  -running prover on /export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1 with time limit 29
% 0.06/0.47  -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpYdWFRS/sel_theBenchmark.p_1']
% 0.06/0.47  -prover status Theorem
% 0.06/0.47  Problem theBenchmark.p solved in phase 0.
% 0.06/0.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.47  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.47  Solved 1 out of 1.
% 0.06/0.47  # Problem is unsatisfiable (or provable), constructing proof object
% 0.06/0.47  # SZS status Theorem
% 0.06/0.47  # SZS output start CNFRefutation.
% See solution above
% 0.06/0.47  # SZS output end CNFRefutation
%------------------------------------------------------------------------------