TSTP Solution File: SEU320+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n014.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 13:15:38 EDT 2022

% Result   : Theorem 1.77s 1.96s
% Output   : Refutation 1.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   14 (   7 unt;   1 nHn;  14 RR)
%            Number of literals    :   25 (   2 equ;  11 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ element(A,powerset(B))
    | element(subset_complement(B,A),powerset(B)) ),
    file('SEU320+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ element(A,powerset(B))
    | subset_complement(B,subset_complement(B,A)) = A ),
    file('SEU320+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ top_str(A)
    | ~ element(B,powerset(the_carrier(A)))
    | ~ closed_subset(B,A)
    | open_subset(subset_complement(the_carrier(A),B),A) ),
    file('SEU320+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ top_str(A)
    | ~ element(B,powerset(the_carrier(A)))
    | closed_subset(B,A)
    | ~ open_subset(subset_complement(the_carrier(A),B),A) ),
    file('SEU320+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ open_subset(dollar_c3,dollar_c4)
    | ~ closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4) ),
    file('SEU320+1.p',unknown),
    [] ).

cnf(14,axiom,
    top_str(dollar_c4),
    file('SEU320+1.p',unknown),
    [] ).

cnf(15,axiom,
    element(dollar_c3,powerset(the_carrier(dollar_c4))),
    file('SEU320+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( open_subset(dollar_c3,dollar_c4)
    | closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4) ),
    file('SEU320+1.p',unknown),
    [] ).

cnf(29,plain,
    subset_complement(the_carrier(dollar_c4),subset_complement(the_carrier(dollar_c4),dollar_c3)) = dollar_c3,
    inference(hyper,[status(thm)],[15,3]),
    [iquote('hyper,15,3')] ).

cnf(30,plain,
    element(subset_complement(the_carrier(dollar_c4),dollar_c3),powerset(the_carrier(dollar_c4))),
    inference(hyper,[status(thm)],[15,1]),
    [iquote('hyper,15,1')] ).

cnf(38,plain,
    ( closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4)
    | ~ open_subset(dollar_c3,dollar_c4) ),
    inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[29,5]),14,30]),
    [iquote('para_from,28.1.1,5.4.1,unit_del,14,30')] ).

cnf(40,plain,
    closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[38,16])]),
    [iquote('hyper,38,16,factor_simp')] ).

cnf(41,plain,
    open_subset(dollar_c3,dollar_c4),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[40,4,14,30]),29]),
    [iquote('hyper,40,4,14,30,demod,29')] ).

cnf(42,plain,
    $false,
    inference(hyper,[status(thm)],[41,6,40]),
    [iquote('hyper,41,6,40')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n014.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 08:03:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.77/1.96  ----- Otter 3.3f, August 2004 -----
% 1.77/1.96  The process was started by sandbox2 on n014.cluster.edu,
% 1.77/1.96  Wed Jul 27 08:03:09 2022
% 1.77/1.96  The command was "./otter".  The process ID is 6477.
% 1.77/1.96  
% 1.77/1.96  set(prolog_style_variables).
% 1.77/1.96  set(auto).
% 1.77/1.96     dependent: set(auto1).
% 1.77/1.96     dependent: set(process_input).
% 1.77/1.96     dependent: clear(print_kept).
% 1.77/1.96     dependent: clear(print_new_demod).
% 1.77/1.96     dependent: clear(print_back_demod).
% 1.77/1.96     dependent: clear(print_back_sub).
% 1.77/1.96     dependent: set(control_memory).
% 1.77/1.96     dependent: assign(max_mem, 12000).
% 1.77/1.96     dependent: assign(pick_given_ratio, 4).
% 1.77/1.96     dependent: assign(stats_level, 1).
% 1.77/1.96     dependent: assign(max_seconds, 10800).
% 1.77/1.96  clear(print_given).
% 1.77/1.96  
% 1.77/1.96  formula_list(usable).
% 1.77/1.96  all A (A=A).
% 1.77/1.96  $T.
% 1.77/1.96  all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 1.77/1.96  all A (top_str(A)->one_sorted_str(A)).
% 1.77/1.96  $T.
% 1.77/1.96  $T.
% 1.77/1.96  $T.
% 1.77/1.96  exists A top_str(A).
% 1.77/1.96  exists A one_sorted_str(A).
% 1.77/1.96  all A exists B element(B,A).
% 1.77/1.96  all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 1.77/1.96  all A B subset(A,A).
% 1.77/1.96  all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)<->open_subset(subset_complement(the_carrier(A),B),A))))).
% 1.77/1.96  -(all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (open_subset(B,A)<->closed_subset(subset_complement(the_carrier(A),B),A)))))).
% 1.77/1.96  all A B (element(A,powerset(B))<->subset(A,B)).
% 1.77/1.96  end_of_list.
% 1.77/1.96  
% 1.77/1.96  -------> usable clausifies to:
% 1.77/1.96  
% 1.77/1.96  list(usable).
% 1.77/1.96  0 [] A=A.
% 1.77/1.96  0 [] $T.
% 1.77/1.96  0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 1.77/1.96  0 [] -top_str(A)|one_sorted_str(A).
% 1.77/1.96  0 [] $T.
% 1.77/1.96  0 [] $T.
% 1.77/1.96  0 [] $T.
% 1.77/1.96  0 [] top_str($c1).
% 1.77/1.96  0 [] one_sorted_str($c2).
% 1.77/1.96  0 [] element($f1(A),A).
% 1.77/1.96  0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 1.77/1.96  0 [] subset(A,A).
% 1.77/1.96  0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)|open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96  0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(B,A)| -open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96  0 [] top_str($c4).
% 1.77/1.96  0 [] element($c3,powerset(the_carrier($c4))).
% 1.77/1.96  0 [] open_subset($c3,$c4)|closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96  0 [] -open_subset($c3,$c4)| -closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96  0 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.96  0 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.96  end_of_list.
% 1.77/1.96  
% 1.77/1.96  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.77/1.96  
% 1.77/1.96  This ia a non-Horn set with equality.  The strategy will be
% 1.77/1.96  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.77/1.96  deletion, with positive clauses in sos and nonpositive
% 1.77/1.96  clauses in usable.
% 1.77/1.96  
% 1.77/1.96     dependent: set(knuth_bendix).
% 1.77/1.96     dependent: set(anl_eq).
% 1.77/1.96     dependent: set(para_from).
% 1.77/1.96     dependent: set(para_into).
% 1.77/1.96     dependent: clear(para_from_right).
% 1.77/1.96     dependent: clear(para_into_right).
% 1.77/1.96     dependent: set(para_from_vars).
% 1.77/1.96     dependent: set(eq_units_both_ways).
% 1.77/1.96     dependent: set(dynamic_demod_all).
% 1.77/1.96     dependent: set(dynamic_demod).
% 1.77/1.96     dependent: set(order_eq).
% 1.77/1.96     dependent: set(back_demod).
% 1.77/1.96     dependent: set(lrpo).
% 1.77/1.96     dependent: set(hyper_res).
% 1.77/1.96     dependent: set(unit_deletion).
% 1.77/1.96     dependent: set(factor).
% 1.77/1.96  
% 1.77/1.96  ------------> process usable:
% 1.77/1.96  ** KEPT (pick-wt=10): 1 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 1.77/1.96  ** KEPT (pick-wt=4): 2 [] -top_str(A)|one_sorted_str(A).
% 1.77/1.96  ** KEPT (pick-wt=11): 3 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 1.77/1.96  ** KEPT (pick-wt=16): 4 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)|open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96  ** KEPT (pick-wt=16): 5 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(B,A)| -open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96  ** KEPT (pick-wt=9): 6 [] -open_subset($c3,$c4)| -closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96  ** KEPT (pick-wt=7): 7 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.96  ** KEPT (pick-wt=7): 8 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.96  
% 1.77/1.96  ------------> process sos:
% 1.77/1.96  ** KEPT (pick-wt=3): 9 [] A=A.
% 1.77/1.96  ** KEPT (pick-wt=2): 10 [] top_str($c1).
% 1.77/1.96  ** KEPT (pick-wt=2): 11 [] one_sorted_str($c2).
% 1.77/1.96  ** KEPT (pick-wt=4): 12 [] element($f1(A),A).
% 1.77/1.96  ** KEPT (pick-wt=3): 13 [] subset(A,A).
% 1.77/1.96  ** KEPT (pick-wt=2): 14 [] top_str($c4).
% 1.77/1.96  ** KEPT (pick-wt=5): 15 [] element($c3,powerset(the_carrier($c4))).
% 1.77/1.96  ** KEPT (pick-wt=9): 16 [] open_subset($c3,$c4)|closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96    Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.77/1.96  
% 1.77/1.96  ======= end of input processing =======
% 1.77/1.96  
% 1.77/1.96  =========== start of search ===========
% 1.77/1.96  
% 1.77/1.96  -------- PROOF -------- 
% 1.77/1.96  
% 1.77/1.96  -----> EMPTY CLAUSE at   0.00 sec ----> 42 [hyper,41,6,40] $F.
% 1.77/1.96  
% 1.77/1.96  Length of proof is 5.  Level of proof is 4.
% 1.77/1.96  
% 1.77/1.96  ---------------- PROOF ----------------
% 1.77/1.96  % SZS status Theorem
% 1.77/1.96  % SZS output start Refutation
% See solution above
% 1.77/1.96  ------------ end of proof -------------
% 1.77/1.96  
% 1.77/1.96  
% 1.77/1.96  Search stopped by max_proofs option.
% 1.77/1.96  
% 1.77/1.96  
% 1.77/1.96  Search stopped by max_proofs option.
% 1.77/1.96  
% 1.77/1.96  ============ end of search ============
% 1.77/1.96  
% 1.77/1.96  -------------- statistics -------------
% 1.77/1.96  clauses given                 25
% 1.77/1.96  clauses generated             53
% 1.77/1.97  clauses kept                  38
% 1.77/1.97  clauses forward subsumed      31
% 1.77/1.97  clauses back subsumed          3
% 1.77/1.97  Kbytes malloced              976
% 1.77/1.97  
% 1.77/1.97  ----------- times (seconds) -----------
% 1.77/1.97  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.77/1.97  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.77/1.97  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.77/1.97  
% 1.77/1.97  That finishes the proof of the theorem.
% 1.77/1.97  
% 1.77/1.97  Process 6477 finished Wed Jul 27 08:03:11 2022
% 1.77/1.97  Otter interrupted
% 1.77/1.97  PROOF FOUND
%------------------------------------------------------------------------------