TSTP Solution File: SEU120+2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jul 27 13:14:48 EDT 2022

% Result   : Theorem 2.25s 2.49s
% Output   : Refutation 2.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   21 (  10 unt;   3 nHn;  15 RR)
%            Number of literals    :   33 (   8 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   20 (   4 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    ( ~ disjoint(A,B)
    | set_intersection2(A,B) = empty_set ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( disjoint(A,B)
    | set_intersection2(A,B) != empty_set ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ disjoint(A,B)
    | disjoint(B,A) ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ in(A,B)
    | ~ in(A,C)
    | ~ disjoint(B,C) ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ disjoint(dollar_c5,dollar_c4)
    | in(dollar_c3,set_intersection2(dollar_c5,dollar_c4)) ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ in(A,set_intersection2(dollar_c5,dollar_c4))
    | disjoint(dollar_c5,dollar_c4) ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(20,plain,
    ( ~ in(A,B)
    | ~ disjoint(B,B) ),
    inference(factor,[status(thm)],[11]),
    [iquote('factor,11.1.2')] ).

cnf(23,axiom,
    set_intersection2(A,B) = set_intersection2(B,A),
    file('SEU120+2.p',unknown),
    [] ).

cnf(24,axiom,
    ( A = empty_set
    | in(dollar_f1(A),A) ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(28,axiom,
    set_intersection2(A,A) = A,
    file('SEU120+2.p',unknown),
    [] ).

cnf(31,axiom,
    ( disjoint(A,B)
    | in(dollar_f3(A,B),A) ),
    file('SEU120+2.p',unknown),
    [] ).

cnf(45,plain,
    disjoint(empty_set,empty_set),
    inference(hyper,[status(thm)],[28,8]),
    [iquote('hyper,28,8')] ).

cnf(69,plain,
    ( ~ disjoint(dollar_c5,dollar_c4)
    | in(dollar_c3,set_intersection2(dollar_c4,dollar_c5)) ),
    inference(para_from,[status(thm),theory(equality)],[23,12]),
    [iquote('para_from,23.1.1,12.2.2')] ).

cnf(109,plain,
    ( set_intersection2(dollar_c5,dollar_c4) = empty_set
    | disjoint(dollar_c5,dollar_c4) ),
    inference(hyper,[status(thm)],[24,14]),
    [iquote('hyper,24,14')] ).

cnf(530,plain,
    disjoint(empty_set,A),
    inference(hyper,[status(thm)],[31,20,45]),
    [iquote('hyper,31,20,45')] ).

cnf(545,plain,
    disjoint(A,empty_set),
    inference(hyper,[status(thm)],[530,10]),
    [iquote('hyper,530,10')] ).

cnf(1865,plain,
    set_intersection2(dollar_c5,dollar_c4) = empty_set,
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[109,7])]),
    [iquote('hyper,109,7,factor_simp')] ).

cnf(2002,plain,
    disjoint(dollar_c5,dollar_c4),
    inference(hyper,[status(thm)],[1865,8]),
    [iquote('hyper,1865,8')] ).

cnf(2014,plain,
    set_intersection2(dollar_c4,dollar_c5) = empty_set,
    inference(para_into,[status(thm),theory(equality)],[1865,23]),
    [iquote('para_into,1865.1.1,23.1.1')] ).

cnf(2044,plain,
    in(dollar_c3,empty_set),
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[69]),2014]),2002]),
    [iquote('back_demod,69,demod,2014,unit_del,2002')] ).

cnf(2082,plain,
    $false,
    inference(hyper,[status(thm)],[2044,20,545]),
    [iquote('hyper,2044,20,545')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 07:43:16 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.94/2.14  ----- Otter 3.3f, August 2004 -----
% 1.94/2.14  The process was started by sandbox on n006.cluster.edu,
% 1.94/2.14  Wed Jul 27 07:43:17 2022
% 1.94/2.14  The command was "./otter".  The process ID is 31331.
% 1.94/2.14  
% 1.94/2.14  set(prolog_style_variables).
% 1.94/2.14  set(auto).
% 1.94/2.14     dependent: set(auto1).
% 1.94/2.14     dependent: set(process_input).
% 1.94/2.14     dependent: clear(print_kept).
% 1.94/2.14     dependent: clear(print_new_demod).
% 1.94/2.14     dependent: clear(print_back_demod).
% 1.94/2.14     dependent: clear(print_back_sub).
% 1.94/2.14     dependent: set(control_memory).
% 1.94/2.14     dependent: assign(max_mem, 12000).
% 1.94/2.14     dependent: assign(pick_given_ratio, 4).
% 1.94/2.14     dependent: assign(stats_level, 1).
% 1.94/2.14     dependent: assign(max_seconds, 10800).
% 1.94/2.14  clear(print_given).
% 1.94/2.14  
% 1.94/2.14  formula_list(usable).
% 1.94/2.14  all A (A=A).
% 1.94/2.14  all A B (in(A,B)-> -in(B,A)).
% 1.94/2.14  all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.94/2.14  all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.94/2.14  all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.94/2.14  all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.94/2.14  $T.
% 1.94/2.14  $T.
% 1.94/2.14  empty(empty_set).
% 1.94/2.14  all A B (set_intersection2(A,A)=A).
% 1.94/2.14  exists A empty(A).
% 1.94/2.14  exists A (-empty(A)).
% 1.94/2.14  all A B (disjoint(A,B)->disjoint(B,A)).
% 1.94/2.14  all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B))).
% 1.94/2.14  -(all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B)))).
% 1.94/2.14  end_of_list.
% 1.94/2.14  
% 1.94/2.14  -------> usable clausifies to:
% 1.94/2.14  
% 1.94/2.14  list(usable).
% 1.94/2.14  0 [] A=A.
% 1.94/2.14  0 [] -in(A,B)| -in(B,A).
% 1.94/2.14  0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.94/2.14  0 [] A!=empty_set| -in(B,A).
% 1.94/2.14  0 [] A=empty_set|in($f1(A),A).
% 1.94/2.14  0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.94/2.14  0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.94/2.14  0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.94/2.14  0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A).
% 1.94/2.14  0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),B).
% 1.94/2.14  0 [] C=set_intersection2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A)| -in($f2(A,B,C),B).
% 1.94/2.14  0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.94/2.14  0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.94/2.14  0 [] $T.
% 1.94/2.14  0 [] $T.
% 1.94/2.14  0 [] empty(empty_set).
% 1.94/2.14  0 [] set_intersection2(A,A)=A.
% 1.94/2.14  0 [] empty($c1).
% 1.94/2.14  0 [] -empty($c2).
% 1.94/2.14  0 [] -disjoint(A,B)|disjoint(B,A).
% 1.94/2.14  0 [] disjoint(A,B)|in($f3(A,B),A).
% 1.94/2.14  0 [] disjoint(A,B)|in($f3(A,B),B).
% 1.94/2.14  0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.94/2.14  0 [] -disjoint($c5,$c4)|in($c3,set_intersection2($c5,$c4)).
% 1.94/2.14  0 [] -in(C,set_intersection2($c5,$c4))|in($c3,set_intersection2($c5,$c4)).
% 1.94/2.14  0 [] -in(C,set_intersection2($c5,$c4))|disjoint($c5,$c4).
% 1.94/2.14  end_of_list.
% 1.94/2.14  
% 1.94/2.14  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.94/2.14  
% 1.94/2.14  This ia a non-Horn set with equality.  The strategy will be
% 1.94/2.14  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.94/2.14  deletion, with positive clauses in sos and nonpositive
% 1.94/2.14  clauses in usable.
% 1.94/2.14  
% 1.94/2.14     dependent: set(knuth_bendix).
% 1.94/2.14     dependent: set(anl_eq).
% 1.94/2.14     dependent: set(para_from).
% 1.94/2.14     dependent: set(para_into).
% 1.94/2.14     dependent: clear(para_from_right).
% 1.94/2.14     dependent: clear(para_into_right).
% 1.94/2.14     dependent: set(para_from_vars).
% 1.94/2.14     dependent: set(eq_units_both_ways).
% 1.94/2.14     dependent: set(dynamic_demod_all).
% 1.94/2.14     dependent: set(dynamic_demod).
% 1.94/2.14     dependent: set(order_eq).
% 1.94/2.14     dependent: set(back_demod).
% 1.94/2.14     dependent: set(lrpo).
% 1.94/2.14     dependent: set(hyper_res).
% 1.94/2.14     dependent: set(unit_deletion).
% 1.94/2.14     dependent: set(factor).
% 1.94/2.14  
% 1.94/2.14  ------------> process usable:
% 1.94/2.14  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.94/2.14  ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.94/2.14  ** KEPT (pick-wt=11): 3 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.94/2.14  ** KEPT (pick-wt=11): 4 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.94/2.14  ** KEPT (pick-wt=14): 5 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.94/2.14  ** KEPT (pick-wt=23): 6 [] A=set_intersection2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B)| -in($f2(B,C,A),C).
% 1.94/2.14  ** KEPT (pick-wt=8): 7 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.94/2.14  ** KEPT (pick-wt=8): 8 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.94/2.14  ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.94/2.14  ** KEPT (pick-wt=6): 10 [] -disjoint(A,B)|disjoint(B,A).
% 1.94/2.14  ** KEPT (pick-wt=9): 11 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.94/2.14  ** KEPT (pick-wt=8): 12 [] -disjoint($c5,$c4)|in($c3,set_intersection2($c5,$c4)).
% 1.94/2.14  ** KEPT (pick-wt=10): 13 [] -in(A,set_intersection2($c5,$c4))|in($c3,set_intersection2($c5,$c4)).
% 2.25/2.49  ** KEPT (pick-wt=8): 14 [] -in(A,set_intersection2($c5,$c4))|disjoint($c5,$c4).
% 2.25/2.49  
% 2.25/2.49  ------------> process sos:
% 2.25/2.49  ** KEPT (pick-wt=3): 22 [] A=A.
% 2.25/2.49  ** KEPT (pick-wt=7): 23 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.25/2.49  ** KEPT (pick-wt=7): 24 [] A=empty_set|in($f1(A),A).
% 2.25/2.49  ** KEPT (pick-wt=17): 25 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B).
% 2.25/2.49  ** KEPT (pick-wt=17): 26 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),C).
% 2.25/2.49  ** KEPT (pick-wt=2): 27 [] empty(empty_set).
% 2.25/2.49  ** KEPT (pick-wt=5): 28 [] set_intersection2(A,A)=A.
% 2.25/2.49  ---> New Demodulator: 29 [new_demod,28] set_intersection2(A,A)=A.
% 2.25/2.49  ** KEPT (pick-wt=2): 30 [] empty($c1).
% 2.25/2.49  ** KEPT (pick-wt=8): 31 [] disjoint(A,B)|in($f3(A,B),A).
% 2.25/2.49  ** KEPT (pick-wt=8): 32 [] disjoint(A,B)|in($f3(A,B),B).
% 2.25/2.49    Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 2.25/2.49    Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.25/2.49  >>>> Starting back demodulation with 29.
% 2.25/2.49      >> back demodulating 21 with 29.
% 2.25/2.49      >> back demodulating 19 with 29.
% 2.25/2.49      >> back demodulating 16 with 29.
% 2.25/2.49  
% 2.25/2.49  ======= end of input processing =======
% 2.25/2.49  
% 2.25/2.49  =========== start of search ===========
% 2.25/2.49  
% 2.25/2.49  -------- PROOF -------- 
% 2.25/2.49  
% 2.25/2.49  -----> EMPTY CLAUSE at   0.35 sec ----> 2082 [hyper,2044,20,545] $F.
% 2.25/2.49  
% 2.25/2.49  Length of proof is 10.  Level of proof is 4.
% 2.25/2.49  
% 2.25/2.49  ---------------- PROOF ----------------
% 2.25/2.49  % SZS status Theorem
% 2.25/2.49  % SZS output start Refutation
% See solution above
% 2.25/2.49  ------------ end of proof -------------
% 2.25/2.49  
% 2.25/2.49  
% 2.25/2.49  Search stopped by max_proofs option.
% 2.25/2.49  
% 2.25/2.49  
% 2.25/2.49  Search stopped by max_proofs option.
% 2.25/2.49  
% 2.25/2.49  ============ end of search ============
% 2.25/2.49  
% 2.25/2.49  -------------- statistics -------------
% 2.25/2.49  clauses given                 70
% 2.25/2.49  clauses generated           5903
% 2.25/2.49  clauses kept                2076
% 2.25/2.49  clauses forward subsumed    4055
% 2.25/2.49  clauses back subsumed        364
% 2.25/2.49  Kbytes malloced             2929
% 2.25/2.49  
% 2.25/2.49  ----------- times (seconds) -----------
% 2.25/2.49  user CPU time          0.35          (0 hr, 0 min, 0 sec)
% 2.25/2.49  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.25/2.49  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.25/2.49  
% 2.25/2.49  That finishes the proof of the theorem.
% 2.25/2.49  
% 2.25/2.49  Process 31331 finished Wed Jul 27 07:43:19 2022
% 2.25/2.49  Otter interrupted
% 2.25/2.49  PROOF FOUND
%------------------------------------------------------------------------------