TSTP Solution File: NUM412+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM412+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n037.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 15:21:16 EST 2018

% Result   : Theorem 0.06s
% Output   : CNFRefutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   42 (   5 unt;   0 def)
%            Number of atoms       :  149 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  187 (  80   ~;  75   |;  22   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   80 (   3 sgn  40   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(8,axiom,
    ! [X1,X2] :
      ( transfinite_sequence_of(X2,X1)
     => ( relation(X2)
        & function(X2)
        & transfinite_sequence(X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmpA6ZwVl/sel_theBenchmark.p_1',dt_m1_ordinal1) ).

fof(20,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => ! [X3] :
          ( transfinite_sequence_of(X3,X1)
         => transfinite_sequence_of(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmpA6ZwVl/sel_theBenchmark.p_1',t47_ordinal1) ).

fof(27,conjecture,
    ! [X1,X2] :
      ( transfinite_sequence_of(X2,X1)
     => ! [X3] :
          ( ordinal(X3)
         => transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmpA6ZwVl/sel_theBenchmark.p_1',t48_ordinal1) ).

fof(35,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2)
        & transfinite_sequence(X2) )
     => ( transfinite_sequence_of(X2,X1)
      <=> subset(relation_rng(X2),X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmpA6ZwVl/sel_theBenchmark.p_1',d8_ordinal1) ).

fof(48,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1)
        & transfinite_sequence(X1)
        & ordinal(X2) )
     => transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1)) ),
    file('/export/starexec/sandbox2/tmp/tmpA6ZwVl/sel_theBenchmark.p_1',dt_k2_ordinal1) ).

fof(49,negated_conjecture,
    ~ ! [X1,X2] :
        ( transfinite_sequence_of(X2,X1)
       => ! [X3] :
            ( ordinal(X3)
           => transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
    inference(assume_negation,[status(cth)],[27]) ).

fof(86,plain,
    ! [X1,X2] :
      ( ~ transfinite_sequence_of(X2,X1)
      | ( relation(X2)
        & function(X2)
        & transfinite_sequence(X2) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(87,plain,
    ! [X3,X4] :
      ( ~ transfinite_sequence_of(X4,X3)
      | ( relation(X4)
        & function(X4)
        & transfinite_sequence(X4) ) ),
    inference(variable_rename,[status(thm)],[86]) ).

fof(88,plain,
    ! [X3,X4] :
      ( ( relation(X4)
        | ~ transfinite_sequence_of(X4,X3) )
      & ( function(X4)
        | ~ transfinite_sequence_of(X4,X3) )
      & ( transfinite_sequence(X4)
        | ~ transfinite_sequence_of(X4,X3) ) ),
    inference(distribute,[status(thm)],[87]) ).

cnf(89,plain,
    ( transfinite_sequence(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[88]) ).

cnf(90,plain,
    ( function(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[88]) ).

cnf(91,plain,
    ( relation(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[88]) ).

fof(136,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | ! [X3] :
          ( ~ transfinite_sequence_of(X3,X1)
          | transfinite_sequence_of(X3,X2) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(137,plain,
    ! [X4,X5] :
      ( ~ subset(X4,X5)
      | ! [X6] :
          ( ~ transfinite_sequence_of(X6,X4)
          | transfinite_sequence_of(X6,X5) ) ),
    inference(variable_rename,[status(thm)],[136]) ).

fof(138,plain,
    ! [X4,X5,X6] :
      ( ~ transfinite_sequence_of(X6,X4)
      | transfinite_sequence_of(X6,X5)
      | ~ subset(X4,X5) ),
    inference(shift_quantors,[status(thm)],[137]) ).

cnf(139,plain,
    ( transfinite_sequence_of(X3,X2)
    | ~ subset(X1,X2)
    | ~ transfinite_sequence_of(X3,X1) ),
    inference(split_conjunct,[status(thm)],[138]) ).

fof(160,negated_conjecture,
    ? [X1,X2] :
      ( transfinite_sequence_of(X2,X1)
      & ? [X3] :
          ( ordinal(X3)
          & ~ transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
    inference(fof_nnf,[status(thm)],[49]) ).

fof(161,negated_conjecture,
    ? [X4,X5] :
      ( transfinite_sequence_of(X5,X4)
      & ? [X6] :
          ( ordinal(X6)
          & ~ transfinite_sequence_of(tseq_dom_restriction(X5,X6),X4) ) ),
    inference(variable_rename,[status(thm)],[160]) ).

fof(162,negated_conjecture,
    ( transfinite_sequence_of(esk9_0,esk8_0)
    & ordinal(esk10_0)
    & ~ transfinite_sequence_of(tseq_dom_restriction(esk9_0,esk10_0),esk8_0) ),
    inference(skolemize,[status(esa)],[161]) ).

cnf(163,negated_conjecture,
    ~ transfinite_sequence_of(tseq_dom_restriction(esk9_0,esk10_0),esk8_0),
    inference(split_conjunct,[status(thm)],[162]) ).

cnf(164,negated_conjecture,
    ordinal(esk10_0),
    inference(split_conjunct,[status(thm)],[162]) ).

cnf(165,negated_conjecture,
    transfinite_sequence_of(esk9_0,esk8_0),
    inference(split_conjunct,[status(thm)],[162]) ).

fof(195,plain,
    ! [X1,X2] :
      ( ~ relation(X2)
      | ~ function(X2)
      | ~ transfinite_sequence(X2)
      | ( ( ~ transfinite_sequence_of(X2,X1)
          | subset(relation_rng(X2),X1) )
        & ( ~ subset(relation_rng(X2),X1)
          | transfinite_sequence_of(X2,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(196,plain,
    ! [X3,X4] :
      ( ~ relation(X4)
      | ~ function(X4)
      | ~ transfinite_sequence(X4)
      | ( ( ~ transfinite_sequence_of(X4,X3)
          | subset(relation_rng(X4),X3) )
        & ( ~ subset(relation_rng(X4),X3)
          | transfinite_sequence_of(X4,X3) ) ) ),
    inference(variable_rename,[status(thm)],[195]) ).

fof(197,plain,
    ! [X3,X4] :
      ( ( ~ transfinite_sequence_of(X4,X3)
        | subset(relation_rng(X4),X3)
        | ~ relation(X4)
        | ~ function(X4)
        | ~ transfinite_sequence(X4) )
      & ( ~ subset(relation_rng(X4),X3)
        | transfinite_sequence_of(X4,X3)
        | ~ relation(X4)
        | ~ function(X4)
        | ~ transfinite_sequence(X4) ) ),
    inference(distribute,[status(thm)],[196]) ).

cnf(199,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence(X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[197]) ).

fof(246,plain,
    ! [X1,X2] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ~ transfinite_sequence(X1)
      | ~ ordinal(X2)
      | transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1)) ),
    inference(fof_nnf,[status(thm)],[48]) ).

fof(247,plain,
    ! [X3,X4] :
      ( ~ relation(X3)
      | ~ function(X3)
      | ~ transfinite_sequence(X3)
      | ~ ordinal(X4)
      | transfinite_sequence_of(tseq_dom_restriction(X3,X4),relation_rng(X3)) ),
    inference(variable_rename,[status(thm)],[246]) ).

cnf(248,plain,
    ( transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1))
    | ~ ordinal(X2)
    | ~ transfinite_sequence(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[247]) ).

cnf(322,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence_of(X1,X2)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[199,89]) ).

cnf(323,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence_of(X1,X2)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[322,90]) ).

cnf(324,plain,
    ( subset(relation_rng(X1),X2)
    | ~ transfinite_sequence_of(X1,X2) ),
    inference(csr,[status(thm)],[323,91]) ).

cnf(325,plain,
    ( transfinite_sequence_of(X1,X2)
    | ~ transfinite_sequence_of(X1,relation_rng(X3))
    | ~ transfinite_sequence_of(X3,X2) ),
    inference(spm,[status(thm)],[139,324,theory(equality)]) ).

cnf(595,plain,
    ( transfinite_sequence_of(tseq_dom_restriction(X1,X2),X3)
    | ~ transfinite_sequence_of(X1,X3)
    | ~ transfinite_sequence(X1)
    | ~ function(X1)
    | ~ relation(X1)
    | ~ ordinal(X2) ),
    inference(spm,[status(thm)],[325,248,theory(equality)]) ).

cnf(3016,plain,
    ( transfinite_sequence_of(tseq_dom_restriction(X1,X2),X3)
    | ~ transfinite_sequence(X1)
    | ~ transfinite_sequence_of(X1,X3)
    | ~ function(X1)
    | ~ ordinal(X2) ),
    inference(csr,[status(thm)],[595,91]) ).

cnf(3017,plain,
    ( transfinite_sequence_of(tseq_dom_restriction(X1,X2),X3)
    | ~ transfinite_sequence(X1)
    | ~ transfinite_sequence_of(X1,X3)
    | ~ ordinal(X2) ),
    inference(csr,[status(thm)],[3016,90]) ).

cnf(3018,plain,
    ( transfinite_sequence_of(tseq_dom_restriction(X1,X2),X3)
    | ~ transfinite_sequence_of(X1,X3)
    | ~ ordinal(X2) ),
    inference(csr,[status(thm)],[3017,89]) ).

cnf(3019,negated_conjecture,
    ( ~ transfinite_sequence_of(esk9_0,esk8_0)
    | ~ ordinal(esk10_0) ),
    inference(spm,[status(thm)],[163,3018,theory(equality)]) ).

cnf(3041,negated_conjecture,
    ( $false
    | ~ ordinal(esk10_0) ),
    inference(rw,[status(thm)],[3019,165,theory(equality)]) ).

cnf(3042,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[3041,164,theory(equality)]) ).

cnf(3043,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[3042,theory(equality)]) ).

cnf(3044,negated_conjecture,
    $false,
    3043,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM412+1 : TPTP v7.0.0. Released v3.2.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.03/0.23  % Computer : n037.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.625MB
% 0.03/0.23  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Fri Jan  5 03:43:30 CST 2018
% 0.03/0.23  % CPUTime  : 
% 0.06/0.28  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.28  --creating new selector for []
% 0.06/0.39  -running prover on /export/starexec/sandbox2/tmp/tmpA6ZwVl/sel_theBenchmark.p_1 with time limit 29
% 0.06/0.39  -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/tmpA6ZwVl/sel_theBenchmark.p_1']
% 0.06/0.39  -prover status Theorem
% 0.06/0.39  Problem theBenchmark.p solved in phase 0.
% 0.06/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.39  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.39  Solved 1 out of 1.
% 0.06/0.39  # Problem is unsatisfiable (or provable), constructing proof object
% 0.06/0.39  # SZS status Theorem
% 0.06/0.39  # SZS output start CNFRefutation.
% See solution above
% 0.06/0.40  # SZS output end CNFRefutation
%------------------------------------------------------------------------------