TSTP Solution File: SEU147+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU147+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n022.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 13:14:54 EDT 2022

% Result   : Theorem 2.06s 2.23s
% Output   : Refutation 2.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   14 (   7 unt;   3 nHn;   8 RR)
%            Number of literals    :   27 (  16 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   17 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ( A = singleton(B)
    | ~ in(dollar_f1(B,A),A)
    | dollar_f1(B,A) != B ),
    file('SEU147+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( A != powerset(B)
    | ~ in(C,A)
    | subset(C,B) ),
    file('SEU147+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( A != powerset(B)
    | in(C,A)
    | ~ subset(C,B) ),
    file('SEU147+1.p',unknown),
    [] ).

cnf(9,axiom,
    powerset(empty_set) != singleton(empty_set),
    file('SEU147+1.p',unknown),
    [] ).

cnf(10,plain,
    singleton(empty_set) != powerset(empty_set),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
    [iquote('copy,9,flip.1')] ).

cnf(12,axiom,
    ( ~ subset(A,empty_set)
    | A = empty_set ),
    file('SEU147+1.p',unknown),
    [] ).

cnf(15,axiom,
    A = A,
    file('SEU147+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( A = singleton(B)
    | in(dollar_f1(B,A),A)
    | dollar_f1(B,A) = B ),
    file('SEU147+1.p',unknown),
    [] ).

cnf(20,axiom,
    subset(A,A),
    file('SEU147+1.p',unknown),
    [] ).

cnf(31,plain,
    in(A,powerset(A)),
    inference(hyper,[status(thm)],[20,6,15]),
    [iquote('hyper,20,6,15')] ).

cnf(37,plain,
    ( powerset(A) = singleton(B)
    | dollar_f1(B,powerset(A)) = B
    | subset(dollar_f1(B,powerset(A)),A) ),
    inference(hyper,[status(thm)],[16,5,15]),
    [iquote('hyper,16,5,15')] ).

cnf(2089,plain,
    ( singleton(A) = powerset(empty_set)
    | dollar_f1(A,powerset(empty_set)) = A
    | dollar_f1(A,powerset(empty_set)) = empty_set ),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[37,12])]),
    [iquote('hyper,37,12,flip.1')] ).

cnf(2091,plain,
    dollar_f1(empty_set,powerset(empty_set)) = empty_set,
    inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[2089]),10]),
    [iquote('factor,2089.2.3,unit_del,10')] ).

cnf(2174,plain,
    $false,
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2091,4]),2091]),10,31,15]),
    [iquote('para_from,2090.1.1,4.3.1,demod,2091,unit_del,10,31,15')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU147+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 07:56:05 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.06/2.22  ----- Otter 3.3f, August 2004 -----
% 2.06/2.22  The process was started by sandbox on n022.cluster.edu,
% 2.06/2.22  Wed Jul 27 07:56:05 2022
% 2.06/2.22  The command was "./otter".  The process ID is 14689.
% 2.06/2.22  
% 2.06/2.22  set(prolog_style_variables).
% 2.06/2.22  set(auto).
% 2.06/2.22     dependent: set(auto1).
% 2.06/2.22     dependent: set(process_input).
% 2.06/2.22     dependent: clear(print_kept).
% 2.06/2.22     dependent: clear(print_new_demod).
% 2.06/2.22     dependent: clear(print_back_demod).
% 2.06/2.22     dependent: clear(print_back_sub).
% 2.06/2.22     dependent: set(control_memory).
% 2.06/2.22     dependent: assign(max_mem, 12000).
% 2.06/2.22     dependent: assign(pick_given_ratio, 4).
% 2.06/2.22     dependent: assign(stats_level, 1).
% 2.06/2.22     dependent: assign(max_seconds, 10800).
% 2.06/2.22  clear(print_given).
% 2.06/2.22  
% 2.06/2.22  formula_list(usable).
% 2.06/2.22  all A (A=A).
% 2.06/2.22  all A B (in(A,B)-> -in(B,A)).
% 2.06/2.22  all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.06/2.22  all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 2.06/2.22  $T.
% 2.06/2.22  $T.
% 2.06/2.22  $T.
% 2.06/2.22  empty(empty_set).
% 2.06/2.22  exists A empty(A).
% 2.06/2.22  exists A (-empty(A)).
% 2.06/2.22  all A B subset(A,A).
% 2.06/2.22  powerset(empty_set)!=singleton(empty_set).
% 2.06/2.22  all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.06/2.22  all A (subset(A,empty_set)->A=empty_set).
% 2.06/2.23  end_of_list.
% 2.06/2.23  
% 2.06/2.23  -------> usable clausifies to:
% 2.06/2.23  
% 2.06/2.23  list(usable).
% 2.06/2.23  0 [] A=A.
% 2.06/2.23  0 [] -in(A,B)| -in(B,A).
% 2.06/2.23  0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.06/2.23  0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.06/2.23  0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 2.06/2.23  0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 2.06/2.23  0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 2.06/2.23  0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 2.06/2.23  0 [] B=powerset(A)|in($f2(A,B),B)|subset($f2(A,B),A).
% 2.06/2.23  0 [] B=powerset(A)| -in($f2(A,B),B)| -subset($f2(A,B),A).
% 2.06/2.23  0 [] $T.
% 2.06/2.23  0 [] $T.
% 2.06/2.23  0 [] $T.
% 2.06/2.23  0 [] empty(empty_set).
% 2.06/2.23  0 [] empty($c1).
% 2.06/2.23  0 [] -empty($c2).
% 2.06/2.23  0 [] subset(A,A).
% 2.06/2.23  0 [] powerset(empty_set)!=singleton(empty_set).
% 2.06/2.23  0 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 2.06/2.23  0 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 2.06/2.23  0 [] -subset(A,empty_set)|A=empty_set.
% 2.06/2.23  end_of_list.
% 2.06/2.23  
% 2.06/2.23  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.06/2.23  
% 2.06/2.23  This ia a non-Horn set with equality.  The strategy will be
% 2.06/2.23  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.06/2.23  deletion, with positive clauses in sos and nonpositive
% 2.06/2.23  clauses in usable.
% 2.06/2.23  
% 2.06/2.23     dependent: set(knuth_bendix).
% 2.06/2.23     dependent: set(anl_eq).
% 2.06/2.23     dependent: set(para_from).
% 2.06/2.23     dependent: set(para_into).
% 2.06/2.23     dependent: clear(para_from_right).
% 2.06/2.23     dependent: clear(para_into_right).
% 2.06/2.23     dependent: set(para_from_vars).
% 2.06/2.23     dependent: set(eq_units_both_ways).
% 2.06/2.23     dependent: set(dynamic_demod_all).
% 2.06/2.23     dependent: set(dynamic_demod).
% 2.06/2.23     dependent: set(order_eq).
% 2.06/2.23     dependent: set(back_demod).
% 2.06/2.23     dependent: set(lrpo).
% 2.06/2.23     dependent: set(hyper_res).
% 2.06/2.23     dependent: set(unit_deletion).
% 2.06/2.23     dependent: set(factor).
% 2.06/2.23  
% 2.06/2.23  ------------> process usable:
% 2.06/2.23  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.06/2.23  ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.06/2.23  ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.06/2.23  ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 2.06/2.23  ** KEPT (pick-wt=10): 5 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 2.06/2.23  ** KEPT (pick-wt=10): 6 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 2.06/2.23  ** KEPT (pick-wt=14): 7 [] A=powerset(B)| -in($f2(B,A),A)| -subset($f2(B,A),B).
% 2.06/2.23  ** KEPT (pick-wt=2): 8 [] -empty($c2).
% 2.06/2.23  ** KEPT (pick-wt=5): 10 [copy,9,flip.1] singleton(empty_set)!=powerset(empty_set).
% 2.06/2.23  ** KEPT (pick-wt=13): 11 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 2.06/2.23  ** KEPT (pick-wt=6): 12 [] -subset(A,empty_set)|A=empty_set.
% 2.06/2.23  
% 2.06/2.23  ------------> process sos:
% 2.06/2.23  ** KEPT (pick-wt=3): 15 [] A=A.
% 2.06/2.23  ** KEPT (pick-wt=14): 16 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 2.06/2.23  ** KEPT (pick-wt=14): 17 [] A=powerset(B)|in($f2(B,A),A)|subset($f2(B,A),B).
% 2.06/2.23  ** KEPT (pick-wt=2): 18 [] empty(empty_set).
% 2.06/2.23  ** KEPT (pick-wt=2): 19 [] empty($c1).
% 2.06/2.23  ** KEPT (pick-wt=3): 20 [] subset(A,A).
% 2.06/2.23  ** KEPT (pick-wt=13): 21 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 2.06/2.23    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 2.06/2.23  15 back subsumes 14.
% 2.06/2.23  
% 2.06/2.23  ======= end of input processing =======
% 2.06/2.23  
% 2.06/2.23  =========== start of search ===========
% 2.06/2.23  
% 2.06/2.23  -------- PROOF -------- 
% 2.06/2.23  
% 2.06/2.23  -----> EMPTY CLAUSE at   0.33 sec ----> 2174 [para_from,2090.1.1,4.3.1,demod,2091,unit_del,10,31,15] $F.
% 2.06/2.23  
% 2.06/2.23  Length of proof is 5.  Level of proof is 3.
% 2.06/2.23  
% 2.06/2.23  ---------------- PROOF ----------------
% 2.06/2.23  % SZS status Theorem
% 2.06/2.23  % SZS output start Refutation
% See solution above
% 2.06/2.23  ------------ end of proof -------------
% 2.06/2.23  
% 2.06/2.23  
% 2.06/2.23  Search stopped by max_proofs option.
% 2.06/2.23  
% 2.06/2.23  
% 2.06/2.23  Search stopped by max_proofs option.
% 2.06/2.23  
% 2.06/2.23  ============ end of search ============
% 2.06/2.23  
% 2.06/2.23  -------------- statistics -------------
% 2.06/2.23  clauses given                 57
% 2.06/2.23  clauses generated           3344
% 2.06/2.23  clauses kept                2171
% 2.06/2.23  clauses forward subsumed    1161
% 2.06/2.23  clauses back subsumed         11
% 2.06/2.23  Kbytes malloced             3906
% 2.06/2.23  
% 2.06/2.23  ----------- times (seconds) -----------
% 2.06/2.23  user CPU time          0.33          (0 hr, 0 min, 0 sec)
% 2.06/2.23  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 2.06/2.23  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.06/2.23  
% 2.06/2.23  That finishes the proof of the theorem.
% 2.06/2.23  
% 2.06/2.23  Process 14689 finished Wed Jul 27 07:56:07 2022
% 2.06/2.23  Otter interrupted
% 2.06/2.23  PROOF FOUND
%------------------------------------------------------------------------------