TSTP Solution File: SEU217+3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU217+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n013.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 13:15:12 EDT 2022

% Result   : Theorem 2.05s 2.24s
% Output   : Refutation 2.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    6
% Syntax   : Number of clauses     :    8 (   7 unt;   0 nHn;   5 RR)
%            Number of literals    :   12 (   5 equ;   5 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(20,axiom,
    apply(identity_relation(dollar_c8),dollar_c7) != dollar_c7,
    file('SEU217+3.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ relation(A)
    | ~ function(A)
    | A != identity_relation(B)
    | ~ in(C,B)
    | apply(A,C) = C ),
    file('SEU217+3.p',unknown),
    [] ).

cnf(27,axiom,
    A = A,
    file('SEU217+3.p',unknown),
    [] ).

cnf(33,axiom,
    relation(identity_relation(A)),
    file('SEU217+3.p',unknown),
    [] ).

cnf(34,axiom,
    function(identity_relation(A)),
    file('SEU217+3.p',unknown),
    [] ).

cnf(46,axiom,
    in(dollar_c7,dollar_c8),
    file('SEU217+3.p',unknown),
    [] ).

cnf(84,plain,
    apply(identity_relation(dollar_c8),dollar_c7) = dollar_c7,
    inference(hyper,[status(thm)],[46,22,33,34,27]),
    [iquote('hyper,46,22,33,34,27')] ).

cnf(86,plain,
    $false,
    inference(binary,[status(thm)],[84,20]),
    [iquote('binary,84.1,20.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU217+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 07:47:00 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 2.05/2.24  ----- Otter 3.3f, August 2004 -----
% 2.05/2.24  The process was started by sandbox on n013.cluster.edu,
% 2.05/2.24  Wed Jul 27 07:47:00 2022
% 2.05/2.24  The command was "./otter".  The process ID is 6734.
% 2.05/2.24  
% 2.05/2.24  set(prolog_style_variables).
% 2.05/2.24  set(auto).
% 2.05/2.24     dependent: set(auto1).
% 2.05/2.24     dependent: set(process_input).
% 2.05/2.24     dependent: clear(print_kept).
% 2.05/2.24     dependent: clear(print_new_demod).
% 2.05/2.24     dependent: clear(print_back_demod).
% 2.05/2.24     dependent: clear(print_back_sub).
% 2.05/2.24     dependent: set(control_memory).
% 2.05/2.24     dependent: assign(max_mem, 12000).
% 2.05/2.24     dependent: assign(pick_given_ratio, 4).
% 2.05/2.24     dependent: assign(stats_level, 1).
% 2.05/2.24     dependent: assign(max_seconds, 10800).
% 2.05/2.24  clear(print_given).
% 2.05/2.24  
% 2.05/2.24  formula_list(usable).
% 2.05/2.24  all A (A=A).
% 2.05/2.24  all A B subset(A,A).
% 2.05/2.24  empty(empty_set).
% 2.05/2.24  relation(empty_set).
% 2.05/2.24  empty(empty_set).
% 2.05/2.24  relation(empty_set).
% 2.05/2.24  relation_empty_yielding(empty_set).
% 2.05/2.24  empty(empty_set).
% 2.05/2.24  all A exists B element(B,A).
% 2.05/2.24  all A (empty(A)->function(A)).
% 2.05/2.24  all A (-empty(powerset(A))).
% 2.05/2.24  all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 2.05/2.24  all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 2.05/2.24  all A (empty(A)->relation(A)).
% 2.05/2.24  all A B (element(A,B)->empty(B)|in(A,B)).
% 2.05/2.24  all A B (element(A,powerset(B))<->subset(A,B)).
% 2.05/2.24  all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.05/2.24  all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.05/2.24  all A (empty(A)->A=empty_set).
% 2.05/2.24  all A B (-(empty(A)&A!=B&empty(B))).
% 2.05/2.24  all A B (in(A,B)-> -in(B,A)).
% 2.05/2.24  all A relation(identity_relation(A)).
% 2.05/2.24  all A (relation(identity_relation(A))&function(identity_relation(A))).
% 2.05/2.24  exists A (relation(A)&function(A)).
% 2.05/2.24  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.05/2.24  all A exists B (element(B,powerset(A))&empty(B)).
% 2.05/2.24  exists A (empty(A)&relation(A)).
% 2.05/2.24  exists A (-empty(A)&relation(A)).
% 2.05/2.24  exists A (relation(A)&relation_empty_yielding(A)).
% 2.05/2.24  exists A empty(A).
% 2.05/2.24  exists A (-empty(A)).
% 2.05/2.24  all A B (in(A,B)->element(A,B)).
% 2.05/2.24  all A B (-(in(A,B)&empty(B))).
% 2.05/2.24  -(all A B (in(B,A)->apply(identity_relation(A),B)=B)).
% 2.05/2.24  all A B (relation(B)&function(B)-> (B=identity_relation(A)<->relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=C)))).
% 2.05/2.24  end_of_list.
% 2.05/2.24  
% 2.05/2.24  -------> usable clausifies to:
% 2.05/2.24  
% 2.05/2.24  list(usable).
% 2.05/2.24  0 [] A=A.
% 2.05/2.24  0 [] subset(A,A).
% 2.05/2.24  0 [] empty(empty_set).
% 2.05/2.24  0 [] relation(empty_set).
% 2.05/2.24  0 [] empty(empty_set).
% 2.05/2.24  0 [] relation(empty_set).
% 2.05/2.24  0 [] relation_empty_yielding(empty_set).
% 2.05/2.24  0 [] empty(empty_set).
% 2.05/2.24  0 [] element($f1(A),A).
% 2.05/2.24  0 [] -empty(A)|function(A).
% 2.05/2.24  0 [] -empty(powerset(A)).
% 2.05/2.24  0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.05/2.24  0 [] -empty(A)|empty(relation_dom(A)).
% 2.05/2.24  0 [] -empty(A)|relation(relation_dom(A)).
% 2.05/2.24  0 [] -empty(A)|relation(A).
% 2.05/2.24  0 [] -element(A,B)|empty(B)|in(A,B).
% 2.05/2.24  0 [] -element(A,powerset(B))|subset(A,B).
% 2.05/2.24  0 [] element(A,powerset(B))| -subset(A,B).
% 2.05/2.24  0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.05/2.24  0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.05/2.24  0 [] -empty(A)|A=empty_set.
% 2.05/2.24  0 [] -empty(A)|A=B| -empty(B).
% 2.05/2.24  0 [] -in(A,B)| -in(B,A).
% 2.05/2.24  0 [] relation(identity_relation(A)).
% 2.05/2.24  0 [] relation(identity_relation(A)).
% 2.05/2.24  0 [] function(identity_relation(A)).
% 2.05/2.24  0 [] relation($c1).
% 2.05/2.24  0 [] function($c1).
% 2.05/2.24  0 [] empty(A)|element($f2(A),powerset(A)).
% 2.05/2.24  0 [] empty(A)| -empty($f2(A)).
% 2.05/2.24  0 [] element($f3(A),powerset(A)).
% 2.05/2.24  0 [] empty($f3(A)).
% 2.05/2.24  0 [] empty($c2).
% 2.05/2.24  0 [] relation($c2).
% 2.05/2.24  0 [] -empty($c3).
% 2.05/2.24  0 [] relation($c3).
% 2.05/2.24  0 [] relation($c4).
% 2.05/2.24  0 [] relation_empty_yielding($c4).
% 2.05/2.24  0 [] empty($c5).
% 2.05/2.24  0 [] -empty($c6).
% 2.05/2.24  0 [] -in(A,B)|element(A,B).
% 2.05/2.24  0 [] -in(A,B)| -empty(B).
% 2.05/2.24  0 [] in($c7,$c8).
% 2.05/2.24  0 [] apply(identity_relation($c8),$c7)!=$c7.
% 2.05/2.24  0 [] -relation(B)| -function(B)|B!=identity_relation(A)|relation_dom(B)=A.
% 2.05/2.24  0 [] -relation(B)| -function(B)|B!=identity_relation(A)| -in(C,A)|apply(B,C)=C.
% 2.05/2.24  0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|in($f4(A,B),A).
% 2.05/2.24  0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|apply(B,$f4(A,B))!=$f4(A,B).
% 2.05/2.24  end_of_list.
% 2.05/2.24  
% 2.05/2.24  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.05/2.24  
% 2.05/2.24  This ia a non-Horn set with equality.  The strategy will be
% 2.05/2.24  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.05/2.24  deletion, with positive clauses in sos and nonpositive
% 2.05/2.24  clauses in usable.
% 2.05/2.24  
% 2.05/2.24     dependent: set(knuth_bendix).
% 2.05/2.24     dependent: set(anl_eq).
% 2.05/2.24     dependent: set(para_from).
% 2.05/2.24     dependent: set(para_into).
% 2.05/2.24     dependent: clear(para_from_right).
% 2.05/2.24     dependent: clear(para_into_right).
% 2.05/2.24     dependent: set(para_from_vars).
% 2.05/2.24     dependent: set(eq_units_both_ways).
% 2.05/2.24     dependent: set(dynamic_demod_all).
% 2.05/2.24     dependent: set(dynamic_demod).
% 2.05/2.24     dependent: set(order_eq).
% 2.05/2.24     dependent: set(back_demod).
% 2.05/2.24     dependent: set(lrpo).
% 2.05/2.24     dependent: set(hyper_res).
% 2.05/2.24     dependent: set(unit_deletion).
% 2.05/2.24     dependent: set(factor).
% 2.05/2.24  
% 2.05/2.24  ------------> process usable:
% 2.05/2.24  ** KEPT (pick-wt=4): 1 [] -empty(A)|function(A).
% 2.05/2.24  ** KEPT (pick-wt=3): 2 [] -empty(powerset(A)).
% 2.05/2.24  ** KEPT (pick-wt=7): 3 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.05/2.24  ** KEPT (pick-wt=5): 4 [] -empty(A)|empty(relation_dom(A)).
% 2.05/2.24  ** KEPT (pick-wt=5): 5 [] -empty(A)|relation(relation_dom(A)).
% 2.05/2.24  ** KEPT (pick-wt=4): 6 [] -empty(A)|relation(A).
% 2.05/2.24  ** KEPT (pick-wt=8): 7 [] -element(A,B)|empty(B)|in(A,B).
% 2.05/2.24  ** KEPT (pick-wt=7): 8 [] -element(A,powerset(B))|subset(A,B).
% 2.05/2.24  ** KEPT (pick-wt=7): 9 [] element(A,powerset(B))| -subset(A,B).
% 2.05/2.24  ** KEPT (pick-wt=10): 10 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.05/2.24  ** KEPT (pick-wt=9): 11 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.05/2.24  ** KEPT (pick-wt=5): 12 [] -empty(A)|A=empty_set.
% 2.05/2.24  ** KEPT (pick-wt=7): 13 [] -empty(A)|A=B| -empty(B).
% 2.05/2.24  ** KEPT (pick-wt=6): 14 [] -in(A,B)| -in(B,A).
% 2.05/2.24  ** KEPT (pick-wt=5): 15 [] empty(A)| -empty($f2(A)).
% 2.05/2.24  ** KEPT (pick-wt=2): 16 [] -empty($c3).
% 2.05/2.24  ** KEPT (pick-wt=2): 17 [] -empty($c6).
% 2.05/2.24  ** KEPT (pick-wt=6): 18 [] -in(A,B)|element(A,B).
% 2.05/2.24  ** KEPT (pick-wt=5): 19 [] -in(A,B)| -empty(B).
% 2.05/2.24  ** KEPT (pick-wt=6): 20 [] apply(identity_relation($c8),$c7)!=$c7.
% 2.05/2.24  ** KEPT (pick-wt=12): 21 [] -relation(A)| -function(A)|A!=identity_relation(B)|relation_dom(A)=B.
% 2.05/2.24  ** KEPT (pick-wt=16): 22 [] -relation(A)| -function(A)|A!=identity_relation(B)| -in(C,B)|apply(A,C)=C.
% 2.05/2.24  ** KEPT (pick-wt=17): 23 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|in($f4(B,A),B).
% 2.05/2.24  ** KEPT (pick-wt=21): 24 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|apply(A,$f4(B,A))!=$f4(B,A).
% 2.05/2.24  
% 2.05/2.24  ------------> process sos:
% 2.05/2.24  ** KEPT (pick-wt=3): 27 [] A=A.
% 2.05/2.24  ** KEPT (pick-wt=3): 28 [] subset(A,A).
% 2.05/2.24  ** KEPT (pick-wt=2): 29 [] empty(empty_set).
% 2.05/2.24  ** KEPT (pick-wt=2): 30 [] relation(empty_set).
% 2.05/2.24    Following clause subsumed by 29 during input processing: 0 [] empty(empty_set).
% 2.05/2.24    Following clause subsumed by 30 during input processing: 0 [] relation(empty_set).
% 2.05/2.24  ** KEPT (pick-wt=2): 31 [] relation_empty_yielding(empty_set).
% 2.05/2.24    Following clause subsumed by 29 during input processing: 0 [] empty(empty_set).
% 2.05/2.24  ** KEPT (pick-wt=4): 32 [] element($f1(A),A).
% 2.05/2.24  ** KEPT (pick-wt=3): 33 [] relation(identity_relation(A)).
% 2.05/2.24    Following clause subsumed by 33 during input processing: 0 [] relation(identity_relation(A)).
% 2.05/2.24  ** KEPT (pick-wt=3): 34 [] function(identity_relation(A)).
% 2.05/2.24  ** KEPT (pick-wt=2): 35 [] relation($c1).
% 2.05/2.24  ** KEPT (pick-wt=2): 36 [] function($c1).
% 2.05/2.24  ** KEPT (pick-wt=7): 37 [] empty(A)|element($f2(A),powerset(A)).
% 2.05/2.24  ** KEPT (pick-wt=5): 38 [] element($f3(A),powerset(A)).
% 2.05/2.24  ** KEPT (pick-wt=3): 39 [] empty($f3(A)).
% 2.05/2.24  ** KEPT (pick-wt=2): 40 [] empty($c2).
% 2.05/2.24  ** KEPT (pick-wt=2): 41 [] relation($c2).
% 2.05/2.24  ** KEPT (pick-wt=2): 42 [] relation($c3).
% 2.05/2.24  ** KEPT (pick-wt=2): 43 [] relation($c4).
% 2.05/2.24  ** KEPT (pick-wt=2): 44 [] relation_empty_yielding($c4).
% 2.05/2.24  ** KEPT (pick-wt=2): 45 [] empty($c5).
% 2.05/2.24  ** KEPT (pick-wt=3): 46 [] in($c7,$c8).
% 2.05/2.24    Following clause subsumed by 27 during input processing: 0 [copy,27,flip.1] A=A.
% 2.05/2.24  27 back subsumes 25.
% 2.05/2.24  
% 2.05/2.24  ======= end of input processing =======
% 2.05/2.24  
% 2.05/2.24  =========== start of search ===========
% 2.05/2.24  
% 2.05/2.24  -------- PROOF -------- 
% 2.05/2.24  
% 2.05/2.24  ----> UNIT CONFLICT at   0.00 sec ----> 86 [binary,84.1,20.1] $F.
% 2.05/2.24  
% 2.05/2.24  Length of proof is 1.  Level of proof is 1.
% 2.05/2.24  
% 2.05/2.24  ---------------- PROOF ----------------
% 2.05/2.24  % SZS status Theorem
% 2.05/2.24  % SZS output start Refutation
% See solution above
% 2.05/2.24  ------------ end of proof -------------
% 2.05/2.24  
% 2.05/2.24  
% 2.05/2.24  Search stopped by max_proofs option.
% 2.05/2.24  
% 2.05/2.24  
% 2.05/2.24  Search stopped by max_proofs option.
% 2.05/2.24  
% 2.05/2.24  ============ end of search ============
% 2.05/2.24  
% 2.05/2.24  -------------- statistics -------------
% 2.05/2.24  clauses given                 20
% 2.05/2.24  clauses generated             93
% 2.05/2.24  clauses kept                  80
% 2.05/2.24  clauses forward subsumed      75
% 2.05/2.24  clauses back subsumed          1
% 2.05/2.24  Kbytes malloced              976
% 2.05/2.24  
% 2.05/2.24  ----------- times (seconds) -----------
% 2.05/2.24  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 2.05/2.24  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.05/2.24  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.05/2.24  
% 2.05/2.24  That finishes the proof of the theorem.
% 2.05/2.24  
% 2.05/2.24  Process 6734 finished Wed Jul 27 07:47:02 2022
% 2.05/2.24  Otter interrupted
% 2.05/2.24  PROOF FOUND
%------------------------------------------------------------------------------