%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM925+4 : TPTP v7.0.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n101.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 97.69s
% Output   : CNFRefutation 97.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   53 (  40 unt;   0 def)
%            Number of atoms       :   89 (  24 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   69 (  33   ~;  26   |;   7   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  15 con; 0-2 aty)
%            Number of variables   :   39 (   6 sgn  23   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(332,conjecture,
    ~ equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),zero_zero_int),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',conj_0) ).

fof(591,axiom,
    ! [X2] : equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X2))),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_3105_int__Suc) ).

fof(1124,axiom,
    ! [X47] : equal(hAPP_int_int(succ,X47),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X47),one_one_int)),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_857_succ__def) ).

fof(1434,axiom,
    ! [X7,X1] : equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,X7)),X1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X7),X1))),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_390_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

fof(1472,axiom,
    equal(pls,zero_zero_int),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_151_Pls__def) ).

fof(2044,axiom,
    ! [X47] :
      ( is_int(X47)
     => equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X47),X47) ),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_154_add__Pls) ).

fof(2214,axiom,
    is_int(one_one_int),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).

fof(3135,axiom,
    equal(hAPP_int_int(succ,pls),hAPP_int_int(bit1,pls)),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_772_succ__Pls) ).

fof(3406,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_0_n1pos) ).

fof(3431,axiom,
    ! [X63,X64] : is_int(hAPP_nat_int(X63,X64)),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).

fof(3752,axiom,
    ! [X27,X75] :
      ( is_int(X27)
     => ( equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X27),X75),zero_zero_int)
      <=> ( equal(X27,zero_zero_int)
          & ~ equal(X75,zero_zero_nat) ) ) ),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_451_power__eq__0__iff) ).

fof(4494,axiom,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    file('/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2',fact_76_rel__simps_I2_J) ).

fof(5488,negated_conjecture,
    ~ ~ equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),zero_zero_int),
    inference(assume_negation,[status(cth)],[332]) ).

fof(5513,negated_conjecture,
    equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),zero_zero_int),
    inference(fof_simplification,[status(thm)],[5488,theory(equality)]) ).

fof(5831,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    inference(fof_simplification,[status(thm)],[4494,theory(equality)]) ).

cnf(7003,negated_conjecture,
    hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
    inference(split_conjunct,[status(thm)],[5513]) ).

fof(7894,plain,
    ! [X3] : equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X3))),
    inference(variable_rename,[status(thm)],[591]) ).

cnf(7895,plain,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X1)),
    inference(split_conjunct,[status(thm)],[7894]) ).

fof(9537,plain,
    ! [X48] : equal(hAPP_int_int(succ,X48),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X48),one_one_int)),
    inference(variable_rename,[status(thm)],[1124]) ).

cnf(9538,plain,
    hAPP_int_int(succ,X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int),
    inference(split_conjunct,[status(thm)],[9537]) ).

fof(10546,plain,
    ! [X8,X9] : equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,X8)),X9),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X8),X9))),
    inference(variable_rename,[status(thm)],[1434]) ).

cnf(10547,plain,
    hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X1),X2)),
    inference(split_conjunct,[status(thm)],[10546]) ).

cnf(10676,plain,
    pls = zero_zero_int,
    inference(split_conjunct,[status(thm)],[1472]) ).

fof(12604,plain,
    ! [X47] :
      ( ~ is_int(X47)
      | equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X47),X47) ),
    inference(fof_nnf,[status(thm)],[2044]) ).

fof(12605,plain,
    ! [X48] :
      ( ~ is_int(X48)
      | equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X48),X48) ),
    inference(variable_rename,[status(thm)],[12604]) ).

cnf(12606,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X1) = X1
    | ~ is_int(X1) ),
    inference(split_conjunct,[status(thm)],[12605]) ).

cnf(13138,plain,
    is_int(one_one_int),
    inference(split_conjunct,[status(thm)],[2214]) ).

cnf(16019,plain,
    hAPP_int_int(succ,pls) = hAPP_int_int(bit1,pls),
    inference(split_conjunct,[status(thm)],[3135]) ).

cnf(16894,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(split_conjunct,[status(thm)],[3406]) ).

fof(16960,plain,
    ! [X65,X66] : is_int(hAPP_nat_int(X65,X66)),
    inference(variable_rename,[status(thm)],[3431]) ).

cnf(16961,plain,
    is_int(hAPP_nat_int(X1,X2)),
    inference(split_conjunct,[status(thm)],[16960]) ).

fof(17999,plain,
    ! [X27,X75] :
      ( ~ is_int(X27)
      | ( ( ~ equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X27),X75),zero_zero_int)
          | ( equal(X27,zero_zero_int)
            & ~ equal(X75,zero_zero_nat) ) )
        & ( ~ equal(X27,zero_zero_int)
          | equal(X75,zero_zero_nat)
          | equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X27),X75),zero_zero_int) ) ) ),
    inference(fof_nnf,[status(thm)],[3752]) ).

fof(18000,plain,
    ! [X76,X77] :
      ( ~ is_int(X76)
      | ( ( ~ equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X76),X77),zero_zero_int)
          | ( equal(X76,zero_zero_int)
            & ~ equal(X77,zero_zero_nat) ) )
        & ( ~ equal(X76,zero_zero_int)
          | equal(X77,zero_zero_nat)
          | equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X76),X77),zero_zero_int) ) ) ),
    inference(variable_rename,[status(thm)],[17999]) ).

fof(18001,plain,
    ! [X76,X77] :
      ( ( equal(X76,zero_zero_int)
        | ~ equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X76),X77),zero_zero_int)
        | ~ is_int(X76) )
      & ( ~ equal(X77,zero_zero_nat)
        | ~ equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X76),X77),zero_zero_int)
        | ~ is_int(X76) )
      & ( ~ equal(X76,zero_zero_int)
        | equal(X77,zero_zero_nat)
        | equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X76),X77),zero_zero_int)
        | ~ is_int(X76) ) ),
    inference(distribute,[status(thm)],[18000]) ).

cnf(18004,plain,
    ( X1 = zero_zero_int
    | ~ is_int(X1)
    | hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),X2) != zero_zero_int ),
    inference(split_conjunct,[status(thm)],[18001]) ).

cnf(20342,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    inference(split_conjunct,[status(thm)],[5831]) ).

cnf(24093,negated_conjecture,
    hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int)))) = zero_zero_int,
    inference(rw,[status(thm)],[7003,10676,theory(equality)]) ).

cnf(24109,plain,
    hAPP_int_int(bit1,zero_zero_int) = hAPP_int_int(succ,pls),
    inference(rw,[status(thm)],[16019,10676,theory(equality)]) ).

cnf(24110,plain,
    hAPP_int_int(bit1,zero_zero_int) = hAPP_int_int(succ,zero_zero_int),
    inference(rw,[status(thm)],[24109,10676,theory(equality)]) ).

cnf(24270,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[20342,10676,theory(equality)]),10676,theory(equality)]) ).

cnf(24501,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X1) = X1
    | ~ is_int(X1) ),
    inference(rw,[status(thm)],[12606,10676,theory(equality)]) ).

cnf(24503,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),one_one_int) = one_one_int,
    inference(spm,[status(thm)],[24501,13138,theory(equality)]) ).

cnf(24542,plain,
    hAPP_int_int(bit1,zero_zero_int) = one_one_int,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[24503,9538,theory(equality)]),24110,theory(equality)]) ).

cnf(24743,negated_conjecture,
    hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int)))) = zero_zero_int,
    inference(rw,[status(thm)],[24093,7895,theory(equality)]) ).

cnf(25682,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))),
    inference(rw,[status(thm)],[16894,7895,theory(equality)]) ).

cnf(28618,plain,
    ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X1)
    | hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X1),X2)) != zero_zero_int
    | ~ is_int(hAPP_nat_int(semiri1621563631at_int,X1)) ),
    inference(spm,[status(thm)],[18004,10547,theory(equality)]) ).

cnf(28640,plain,
    ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X1)
    | hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X1),X2)) != zero_zero_int
    | $false ),
    inference(rw,[status(thm)],[28618,16961,theory(equality)]) ).

cnf(28641,plain,
    ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X1)
    | hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X1),X2)) != zero_zero_int ),
    inference(cn,[status(thm)],[28640,theory(equality)]) ).

cnf(382168,negated_conjecture,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)))) = zero_zero_int,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[24743,24542,theory(equality)]),10547,theory(equality)]) ).

cnf(598757,negated_conjecture,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) = zero_zero_int,
    inference(spm,[status(thm)],[28641,382168,theory(equality)]) ).

cnf(602613,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
    inference(rw,[status(thm)],[25682,598757,theory(equality)]) ).

cnf(602614,plain,
    $false,
    inference(sr,[status(thm)],[602613,24270,theory(equality)]) ).

cnf(602615,plain,
    $false,
    602614,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM925+4 : TPTP v7.0.0. Released v5.3.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.23  % Computer : n101.star.cs.uiowa.edu
% 0.02/0.23  % Model    : x86_64 x86_64
% 0.02/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23  % Memory   : 32218.625MB
% 0.02/0.23  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23  % CPULimit : 300
% 0.02/0.23  % DateTime : Fri Jan  5 16:35:34 CST 2018
% 0.02/0.23  % CPUTime  : 
% 0.02/0.28  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.31  --creating new selector for []
% 29.51/29.86  eprover: CPU time limit exceeded, terminating
% 97.69/98.67  -running prover on /export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_1 with time limit 29
% 97.69/98.67  -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_1']
% 97.69/98.67  -prover status ResourceOut
% 97.69/98.67  -running prover on /export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2 with time limit 80
% 97.69/98.67  -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=80', '/export/starexec/sandbox/tmp/tmptg5Xim/sel_theBenchmark.p_2']
% 97.69/98.67  -prover status Theorem
% 97.69/98.67  Problem theBenchmark.p solved in phase 1.
% 97.69/98.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.69/98.67  % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.69/98.67  Solved 1 out of 1.
% 97.69/98.67  # Problem is unsatisfiable (or provable), constructing proof object
% 97.69/98.67  # SZS status Theorem
% 97.69/98.67  # SZS output start CNFRefutation.
% See solution above
% 97.69/98.69  # SZS output end CNFRefutation
%------------------------------------------------------------------------------