TSTP Solution File: NUN055+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUN055+2 : TPTP v7.3.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : sine.py -e eprover -t %d %s

% Computer : n185.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.5MB
% OS       : Linux 3.10.0-862.11.6.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Feb 27 14:27:03 EST 2019

% Result   : Theorem 0.08s
% Output   : CNFRefutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   72 (  25 unt;   0 def)
%            Number of atoms       :  238 (  14 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  289 ( 123   ~;  97   |;  67   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  181 (   6 sgn  65   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( ( ~ r2(X1,X3)
        & ~ equal(X3,X2) )
      | ( r2(X1,X3)
        & equal(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmpGKNcTY/sel_theBenchmark.p_1',axiom_2) ).

fof(4,axiom,
    ! [X12,X13] :
    ? [X14] :
    ! [X15] :
      ( ( ~ r3(X12,X13,X15)
        & ~ equal(X15,X14) )
      | ( r3(X12,X13,X15)
        & equal(X15,X14) ) ),
    file('/export/starexec/sandbox2/tmp/tmpGKNcTY/sel_theBenchmark.p_1',axiom_3) ).

fof(5,axiom,
    ? [X16] :
    ! [X17] :
      ( ( ~ r1(X17)
        & ~ equal(X17,X16) )
      | ( r1(X17)
        & equal(X17,X16) ) ),
    file('/export/starexec/sandbox2/tmp/tmpGKNcTY/sel_theBenchmark.p_1',axiom_1) ).

fof(6,axiom,
    ! [X18,X19] :
    ? [X20] :
      ( ? [X21] :
          ( ? [X22] :
              ( r2(X19,X22)
              & r3(X18,X22,X21) )
          & equal(X21,X20) )
      & ? [X23] :
          ( r2(X23,X20)
          & r3(X18,X19,X23) ) ),
    file('/export/starexec/sandbox2/tmp/tmpGKNcTY/sel_theBenchmark.p_1',axiom_1a) ).

fof(7,axiom,
    ! [X24] :
    ? [X25] :
      ( ? [X26] :
          ( r1(X26)
          & r3(X24,X26,X25) )
      & equal(X25,X24) ),
    file('/export/starexec/sandbox2/tmp/tmpGKNcTY/sel_theBenchmark.p_1',axiom_4a) ).

fof(9,conjecture,
    ? [X10] :
      ( ? [X30] :
          ( ? [X20] :
              ( r2(X20,X30)
              & ? [X31] :
                  ( r1(X31)
                  & r2(X31,X20) ) )
          & ? [X23] :
              ( r1(X23)
              & r3(X23,X30,X10) ) )
      & ? [X32] :
          ( equal(X10,X32)
          & ? [X21] :
              ( r2(X21,X32)
              & ? [X33] :
                  ( r1(X33)
                  & r2(X33,X21) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmpGKNcTY/sel_theBenchmark.p_1',zeroplustwoeqtwo) ).

fof(10,negated_conjecture,
    ~ ? [X10] :
        ( ? [X30] :
            ( ? [X20] :
                ( r2(X20,X30)
                & ? [X31] :
                    ( r1(X31)
                    & r2(X31,X20) ) )
            & ? [X23] :
                ( r1(X23)
                & r3(X23,X30,X10) ) )
        & ? [X32] :
            ( equal(X10,X32)
            & ? [X21] :
                ( r2(X21,X32)
                & ? [X33] :
                    ( r1(X33)
                    & r2(X33,X21) ) ) ) ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(11,plain,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( ( ~ r2(X1,X3)
        & ~ equal(X3,X2) )
      | ( r2(X1,X3)
        & equal(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).

fof(13,plain,
    ! [X12,X13] :
    ? [X14] :
    ! [X15] :
      ( ( ~ r3(X12,X13,X15)
        & ~ equal(X15,X14) )
      | ( r3(X12,X13,X15)
        & equal(X15,X14) ) ),
    inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).

fof(14,plain,
    ? [X16] :
    ! [X17] :
      ( ( ~ r1(X17)
        & ~ equal(X17,X16) )
      | ( r1(X17)
        & equal(X17,X16) ) ),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(16,plain,
    ! [X4] :
    ? [X5] :
    ! [X6] :
      ( ( ~ r2(X4,X6)
        & ~ equal(X6,X5) )
      | ( r2(X4,X6)
        & equal(X6,X5) ) ),
    inference(variable_rename,[status(thm)],[11]) ).

fof(17,plain,
    ! [X4,X6] :
      ( ( ~ r2(X4,X6)
        & ~ equal(X6,esk1_1(X4)) )
      | ( r2(X4,X6)
        & equal(X6,esk1_1(X4)) ) ),
    inference(skolemize,[status(esa)],[16]) ).

fof(18,plain,
    ! [X4,X6] :
      ( ( r2(X4,X6)
        | ~ r2(X4,X6) )
      & ( equal(X6,esk1_1(X4))
        | ~ r2(X4,X6) )
      & ( r2(X4,X6)
        | ~ equal(X6,esk1_1(X4)) )
      & ( equal(X6,esk1_1(X4))
        | ~ equal(X6,esk1_1(X4)) ) ),
    inference(distribute,[status(thm)],[17]) ).

cnf(20,plain,
    ( r2(X2,X1)
    | X1 != esk1_1(X2) ),
    inference(split_conjunct,[status(thm)],[18]) ).

cnf(21,plain,
    ( X2 = esk1_1(X1)
    | ~ r2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(33,plain,
    ! [X16,X17] :
    ? [X18] :
    ! [X19] :
      ( ( ~ r3(X16,X17,X19)
        & ~ equal(X19,X18) )
      | ( r3(X16,X17,X19)
        & equal(X19,X18) ) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(34,plain,
    ! [X16,X17,X19] :
      ( ( ~ r3(X16,X17,X19)
        & ~ equal(X19,esk5_2(X16,X17)) )
      | ( r3(X16,X17,X19)
        & equal(X19,esk5_2(X16,X17)) ) ),
    inference(skolemize,[status(esa)],[33]) ).

fof(35,plain,
    ! [X16,X17,X19] :
      ( ( r3(X16,X17,X19)
        | ~ r3(X16,X17,X19) )
      & ( equal(X19,esk5_2(X16,X17))
        | ~ r3(X16,X17,X19) )
      & ( r3(X16,X17,X19)
        | ~ equal(X19,esk5_2(X16,X17)) )
      & ( equal(X19,esk5_2(X16,X17))
        | ~ equal(X19,esk5_2(X16,X17)) ) ),
    inference(distribute,[status(thm)],[34]) ).

cnf(38,plain,
    ( X3 = esk5_2(X1,X2)
    | ~ r3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(40,plain,
    ? [X18] :
    ! [X19] :
      ( ( ~ r1(X19)
        & ~ equal(X19,X18) )
      | ( r1(X19)
        & equal(X19,X18) ) ),
    inference(variable_rename,[status(thm)],[14]) ).

fof(41,plain,
    ! [X19] :
      ( ( ~ r1(X19)
        & ~ equal(X19,esk6_0) )
      | ( r1(X19)
        & equal(X19,esk6_0) ) ),
    inference(skolemize,[status(esa)],[40]) ).

fof(42,plain,
    ! [X19] :
      ( ( r1(X19)
        | ~ r1(X19) )
      & ( equal(X19,esk6_0)
        | ~ r1(X19) )
      & ( r1(X19)
        | ~ equal(X19,esk6_0) )
      & ( equal(X19,esk6_0)
        | ~ equal(X19,esk6_0) ) ),
    inference(distribute,[status(thm)],[41]) ).

cnf(45,plain,
    ( X1 = esk6_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[42]) ).

fof(47,plain,
    ! [X24,X25] :
    ? [X26] :
      ( ? [X27] :
          ( ? [X28] :
              ( r2(X25,X28)
              & r3(X24,X28,X27) )
          & equal(X27,X26) )
      & ? [X29] :
          ( r2(X29,X26)
          & r3(X24,X25,X29) ) ),
    inference(variable_rename,[status(thm)],[6]) ).

fof(48,plain,
    ! [X24,X25] :
      ( r2(X25,esk9_2(X24,X25))
      & r3(X24,esk9_2(X24,X25),esk8_2(X24,X25))
      & equal(esk8_2(X24,X25),esk7_2(X24,X25))
      & r2(esk10_2(X24,X25),esk7_2(X24,X25))
      & r3(X24,X25,esk10_2(X24,X25)) ),
    inference(skolemize,[status(esa)],[47]) ).

cnf(49,plain,
    r3(X1,X2,esk10_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,plain,
    r2(esk10_2(X1,X2),esk7_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(51,plain,
    esk8_2(X1,X2) = esk7_2(X1,X2),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(52,plain,
    r3(X1,esk9_2(X1,X2),esk8_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(53,plain,
    r2(X1,esk9_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(54,plain,
    ! [X27] :
    ? [X28] :
      ( ? [X29] :
          ( r1(X29)
          & r3(X27,X29,X28) )
      & equal(X28,X27) ),
    inference(variable_rename,[status(thm)],[7]) ).

fof(55,plain,
    ! [X27] :
      ( r1(esk12_1(X27))
      & r3(X27,esk12_1(X27),esk11_1(X27))
      & equal(esk11_1(X27),X27) ),
    inference(skolemize,[status(esa)],[54]) ).

cnf(56,plain,
    esk11_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(57,plain,
    r3(X1,esk12_1(X1),esk11_1(X1)),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(58,plain,
    r1(esk12_1(X1)),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(62,negated_conjecture,
    ! [X10] :
      ( ! [X30] :
          ( ! [X20] :
              ( ~ r2(X20,X30)
              | ! [X31] :
                  ( ~ r1(X31)
                  | ~ r2(X31,X20) ) )
          | ! [X23] :
              ( ~ r1(X23)
              | ~ r3(X23,X30,X10) ) )
      | ! [X32] :
          ( ~ equal(X10,X32)
          | ! [X21] :
              ( ~ r2(X21,X32)
              | ! [X33] :
                  ( ~ r1(X33)
                  | ~ r2(X33,X21) ) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(63,negated_conjecture,
    ! [X34] :
      ( ! [X35] :
          ( ! [X36] :
              ( ~ r2(X36,X35)
              | ! [X37] :
                  ( ~ r1(X37)
                  | ~ r2(X37,X36) ) )
          | ! [X38] :
              ( ~ r1(X38)
              | ~ r3(X38,X35,X34) ) )
      | ! [X39] :
          ( ~ equal(X34,X39)
          | ! [X40] :
              ( ~ r2(X40,X39)
              | ! [X41] :
                  ( ~ r1(X41)
                  | ~ r2(X41,X40) ) ) ) ),
    inference(variable_rename,[status(thm)],[62]) ).

fof(64,negated_conjecture,
    ! [X34,X35,X36,X37,X38,X39,X40,X41] :
      ( ~ r1(X41)
      | ~ r2(X41,X40)
      | ~ r2(X40,X39)
      | ~ equal(X34,X39)
      | ~ r1(X38)
      | ~ r3(X38,X35,X34)
      | ~ r1(X37)
      | ~ r2(X37,X36)
      | ~ r2(X36,X35) ),
    inference(shift_quantors,[status(thm)],[63]) ).

cnf(65,negated_conjecture,
    ( ~ r2(X1,X2)
    | ~ r2(X3,X1)
    | ~ r1(X3)
    | ~ r3(X4,X2,X5)
    | ~ r1(X4)
    | X5 != X6
    | ~ r2(X7,X6)
    | ~ r2(X8,X7)
    | ~ r1(X8) ),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(66,plain,
    r3(X1,esk12_1(X1),X1),
    inference(rw,[status(thm)],[57,56,theory(equality)]),
    [unfolding] ).

cnf(67,plain,
    r3(X1,esk9_2(X1,X2),esk7_2(X1,X2)),
    inference(rw,[status(thm)],[52,51,theory(equality)]),
    [unfolding] ).

cnf(68,plain,
    esk6_0 = esk12_1(X1),
    inference(spm,[status(thm)],[45,58,theory(equality)]) ).

cnf(70,plain,
    r2(X1,esk1_1(X1)),
    inference(er,[status(thm)],[20,theory(equality)]) ).

cnf(71,plain,
    esk1_1(X1) = esk9_2(X2,X1),
    inference(spm,[status(thm)],[21,53,theory(equality)]) ).

cnf(77,plain,
    esk5_2(X1,X2) = esk10_2(X1,X2),
    inference(spm,[status(thm)],[38,49,theory(equality)]) ).

cnf(84,negated_conjecture,
    ( ~ r3(X1,X2,X3)
    | ~ r1(X4)
    | ~ r1(X1)
    | ~ r1(X5)
    | ~ r2(X4,X6)
    | ~ r2(X6,X3)
    | ~ r2(X5,X7)
    | ~ r2(X7,X2) ),
    inference(er,[status(thm)],[65,theory(equality)]) ).

cnf(91,plain,
    r3(X1,esk6_0,X1),
    inference(rw,[status(thm)],[66,68,theory(equality)]) ).

cnf(92,plain,
    r1(esk6_0),
    inference(rw,[status(thm)],[58,68,theory(equality)]) ).

cnf(94,plain,
    esk5_2(X1,esk6_0) = X1,
    inference(spm,[status(thm)],[38,91,theory(equality)]) ).

cnf(95,plain,
    r3(X1,esk1_1(X2),esk7_2(X1,X2)),
    inference(rw,[status(thm)],[67,71,theory(equality)]) ).

cnf(106,plain,
    esk10_2(X1,esk6_0) = X1,
    inference(rw,[status(thm)],[94,77,theory(equality)]) ).

cnf(107,plain,
    ( esk10_2(X1,X2) = X3
    | ~ r3(X1,X2,X3) ),
    inference(rw,[status(thm)],[38,77,theory(equality)]) ).

cnf(136,plain,
    esk10_2(X1,esk1_1(X2)) = esk7_2(X1,X2),
    inference(spm,[status(thm)],[107,95,theory(equality)]) ).

cnf(170,plain,
    r2(esk7_2(X1,X2),esk7_2(X1,esk1_1(X2))),
    inference(spm,[status(thm)],[50,136,theory(equality)]) ).

cnf(245,negated_conjecture,
    ( ~ r1(X3)
    | ~ r1(X1)
    | ~ r1(X4)
    | ~ r2(X3,X5)
    | ~ r2(X5,esk7_2(X1,X2))
    | ~ r2(X4,X6)
    | ~ r2(X6,esk1_1(X2)) ),
    inference(spm,[status(thm)],[84,95,theory(equality)]) ).

cnf(298,negated_conjecture,
    ( ~ r1(X1)
    | ~ r1(X2)
    | ~ r1(X3)
    | ~ r2(X5,esk1_1(esk1_1(X4)))
    | ~ r2(X1,esk7_2(X2,X4))
    | ~ r2(X3,X5) ),
    inference(spm,[status(thm)],[245,170,theory(equality)]) ).

cnf(319,negated_conjecture,
    ( ~ r1(X1)
    | ~ r1(X2)
    | ~ r1(X3)
    | ~ r2(X1,esk7_2(X2,X4))
    | ~ r2(X3,esk1_1(X4)) ),
    inference(spm,[status(thm)],[298,70,theory(equality)]) ).

cnf(327,negated_conjecture,
    ( ~ r1(esk10_2(X1,X2))
    | ~ r1(X1)
    | ~ r1(X3)
    | ~ r2(X3,esk1_1(X2)) ),
    inference(spm,[status(thm)],[319,50,theory(equality)]) ).

cnf(333,negated_conjecture,
    ( ~ r1(X1)
    | ~ r1(X2)
    | ~ r2(X2,esk1_1(esk6_0)) ),
    inference(spm,[status(thm)],[327,106,theory(equality)]) ).

fof(389,plain,
    ( ~ epred1_0
  <=> ! [X1] : ~ r1(X1) ),
    introduced(definition),
    [split] ).

cnf(390,plain,
    ( epred1_0
    | ~ r1(X1) ),
    inference(split_equiv,[status(thm)],[389]) ).

fof(391,plain,
    ( ~ epred2_0
  <=> ! [X2] :
        ( ~ r2(X2,esk1_1(esk6_0))
        | ~ r1(X2) ) ),
    introduced(definition),
    [split] ).

cnf(392,plain,
    ( epred2_0
    | ~ r2(X2,esk1_1(esk6_0))
    | ~ r1(X2) ),
    inference(split_equiv,[status(thm)],[391]) ).

cnf(393,negated_conjecture,
    ( ~ epred2_0
    | ~ epred1_0 ),
    inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[333,389,theory(equality)]),391,theory(equality)]),
    [split] ).

cnf(394,negated_conjecture,
    epred1_0,
    inference(spm,[status(thm)],[390,92,theory(equality)]) ).

cnf(402,negated_conjecture,
    ( epred2_0
    | ~ r1(esk6_0) ),
    inference(spm,[status(thm)],[392,70,theory(equality)]) ).

cnf(406,negated_conjecture,
    ( epred2_0
    | $false ),
    inference(rw,[status(thm)],[402,92,theory(equality)]) ).

cnf(407,negated_conjecture,
    epred2_0,
    inference(cn,[status(thm)],[406,theory(equality)]) ).

cnf(414,negated_conjecture,
    ( $false
    | ~ epred1_0 ),
    inference(rw,[status(thm)],[393,407,theory(equality)]) ).

cnf(415,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[414,394,theory(equality)]) ).

cnf(416,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[415,theory(equality)]) ).

cnf(417,negated_conjecture,
    $false,
    416,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : NUN055+2 : TPTP v7.3.0. Released v7.3.0.
% 0.00/0.05  % Command  : sine.py -e eprover -t %d %s
% 0.03/0.25  % Computer : n185.star.cs.uiowa.edu
% 0.03/0.25  % Model    : x86_64 x86_64
% 0.03/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.25  % Memory   : 32218.5MB
% 0.03/0.25  % OS       : Linux 3.10.0-862.11.6.el7.x86_64
% 0.03/0.25  % CPULimit : 300
% 0.03/0.25  % DateTime : Sat Feb 23 16:34:57 CST 2019
% 0.03/0.26  % CPUTime  : 
% 0.08/0.30  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.30  --creating new selector for [NUM008+0.ax]
% 0.08/0.38  -running prover on /export/starexec/sandbox2/tmp/tmpGKNcTY/sel_theBenchmark.p_1 with time limit 29
% 0.08/0.38  -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/tmpGKNcTY/sel_theBenchmark.p_1']
% 0.08/0.38  -prover status Theorem
% 0.08/0.38  Problem theBenchmark.p solved in phase 0.
% 0.08/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.38  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.38  Solved 1 out of 1.
% 0.08/0.38  # Problem is unsatisfiable (or provable), constructing proof object
% 0.08/0.38  # SZS status Theorem
% 0.08/0.38  # SZS output start CNFRefutation.
% See solution above
% 0.08/0.39  # SZS output end CNFRefutation
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