TSTP Solution File: SET877+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n019.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 13:14:27 EDT 2022

% Result   : Theorem 1.68s 1.89s
% Output   : Refutation 1.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   10 (   8 unt;   0 nHn;   8 RR)
%            Number of literals    :   13 (   9 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( A != singleton(B)
    | ~ in(C,A)
    | C = B ),
    file('SET877+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( set_intersection2(A,singleton(B)) != singleton(B)
    | in(B,A) ),
    file('SET877+1.p',unknown),
    [] ).

cnf(7,axiom,
    dollar_c4 != dollar_c3,
    file('SET877+1.p',unknown),
    [] ).

cnf(9,axiom,
    A = A,
    file('SET877+1.p',unknown),
    [] ).

cnf(10,axiom,
    set_intersection2(A,B) = set_intersection2(B,A),
    file('SET877+1.p',unknown),
    [] ).

cnf(15,axiom,
    set_intersection2(singleton(dollar_c4),singleton(dollar_c3)) = singleton(dollar_c4),
    file('SET877+1.p',unknown),
    [] ).

cnf(58,plain,
    set_intersection2(singleton(dollar_c3),singleton(dollar_c4)) = singleton(dollar_c4),
    inference(para_into,[status(thm),theory(equality)],[15,10]),
    [iquote('para_into,15.1.1,10.1.1')] ).

cnf(70,plain,
    in(dollar_c4,singleton(dollar_c3)),
    inference(hyper,[status(thm)],[58,5]),
    [iquote('hyper,58,5')] ).

cnf(83,plain,
    dollar_c4 = dollar_c3,
    inference(hyper,[status(thm)],[70,2,9]),
    [iquote('hyper,70,2,9')] ).

cnf(85,plain,
    $false,
    inference(binary,[status(thm)],[83,7]),
    [iquote('binary,83.1,7.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n019.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 10:47:37 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 1.68/1.89  ----- Otter 3.3f, August 2004 -----
% 1.68/1.89  The process was started by sandbox2 on n019.cluster.edu,
% 1.68/1.89  Wed Jul 27 10:47:37 2022
% 1.68/1.89  The command was "./otter".  The process ID is 20555.
% 1.68/1.89  
% 1.68/1.89  set(prolog_style_variables).
% 1.68/1.89  set(auto).
% 1.68/1.89     dependent: set(auto1).
% 1.68/1.89     dependent: set(process_input).
% 1.68/1.89     dependent: clear(print_kept).
% 1.68/1.89     dependent: clear(print_new_demod).
% 1.68/1.89     dependent: clear(print_back_demod).
% 1.68/1.89     dependent: clear(print_back_sub).
% 1.68/1.89     dependent: set(control_memory).
% 1.68/1.89     dependent: assign(max_mem, 12000).
% 1.68/1.89     dependent: assign(pick_given_ratio, 4).
% 1.68/1.89     dependent: assign(stats_level, 1).
% 1.68/1.89     dependent: assign(max_seconds, 10800).
% 1.68/1.89  clear(print_given).
% 1.68/1.89  
% 1.68/1.89  formula_list(usable).
% 1.68/1.89  all A (A=A).
% 1.68/1.89  all A B (in(A,B)-> -in(B,A)).
% 1.68/1.89  all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.68/1.89  all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.68/1.89  all A B (set_intersection2(A,A)=A).
% 1.68/1.89  all A B (set_intersection2(A,singleton(B))=singleton(B)->in(B,A)).
% 1.68/1.89  exists A empty(A).
% 1.68/1.89  exists A (-empty(A)).
% 1.68/1.89  -(all A B (set_intersection2(singleton(A),singleton(B))=singleton(A)->A=B)).
% 1.68/1.89  end_of_list.
% 1.68/1.89  
% 1.68/1.89  -------> usable clausifies to:
% 1.68/1.89  
% 1.68/1.89  list(usable).
% 1.68/1.89  0 [] A=A.
% 1.68/1.89  0 [] -in(A,B)| -in(B,A).
% 1.68/1.89  0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.68/1.89  0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.68/1.89  0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.68/1.89  0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.68/1.89  0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.68/1.89  0 [] set_intersection2(A,A)=A.
% 1.68/1.89  0 [] set_intersection2(A,singleton(B))!=singleton(B)|in(B,A).
% 1.68/1.89  0 [] empty($c1).
% 1.68/1.89  0 [] -empty($c2).
% 1.68/1.89  0 [] set_intersection2(singleton($c4),singleton($c3))=singleton($c4).
% 1.68/1.89  0 [] $c4!=$c3.
% 1.68/1.89  end_of_list.
% 1.68/1.89  
% 1.68/1.89  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.89  
% 1.68/1.89  This ia a non-Horn set with equality.  The strategy will be
% 1.68/1.89  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.89  deletion, with positive clauses in sos and nonpositive
% 1.68/1.89  clauses in usable.
% 1.68/1.89  
% 1.68/1.89     dependent: set(knuth_bendix).
% 1.68/1.89     dependent: set(anl_eq).
% 1.68/1.89     dependent: set(para_from).
% 1.68/1.89     dependent: set(para_into).
% 1.68/1.89     dependent: clear(para_from_right).
% 1.68/1.89     dependent: clear(para_into_right).
% 1.68/1.89     dependent: set(para_from_vars).
% 1.68/1.89     dependent: set(eq_units_both_ways).
% 1.68/1.89     dependent: set(dynamic_demod_all).
% 1.68/1.89     dependent: set(dynamic_demod).
% 1.68/1.89     dependent: set(order_eq).
% 1.68/1.89     dependent: set(back_demod).
% 1.68/1.89     dependent: set(lrpo).
% 1.68/1.89     dependent: set(hyper_res).
% 1.68/1.89     dependent: set(unit_deletion).
% 1.68/1.89     dependent: set(factor).
% 1.68/1.89  
% 1.68/1.89  ------------> process usable:
% 1.68/1.89  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.68/1.89  ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.68/1.89  ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.68/1.89  ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.68/1.89  ** KEPT (pick-wt=10): 5 [] set_intersection2(A,singleton(B))!=singleton(B)|in(B,A).
% 1.68/1.89  ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.68/1.89  ** KEPT (pick-wt=3): 7 [] $c4!=$c3.
% 1.68/1.89  
% 1.68/1.89  ------------> process sos:
% 1.68/1.89  ** KEPT (pick-wt=3): 9 [] A=A.
% 1.68/1.89  ** KEPT (pick-wt=7): 10 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.68/1.89  ** KEPT (pick-wt=14): 11 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.68/1.89  ** KEPT (pick-wt=5): 12 [] set_intersection2(A,A)=A.
% 1.68/1.89  ---> New Demodulator: 13 [new_demod,12] set_intersection2(A,A)=A.
% 1.68/1.89  ** KEPT (pick-wt=2): 14 [] empty($c1).
% 1.68/1.89  ** KEPT (pick-wt=8): 15 [] set_intersection2(singleton($c4),singleton($c3))=singleton($c4).
% 1.68/1.89  ---> New Demodulator: 16 [new_demod,15] set_intersection2(singleton($c4),singleton($c3))=singleton($c4).
% 1.68/1.89    Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.68/1.89    Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.68/1.89  >>>> Starting back demodulation with 13.
% 1.68/1.89  >>>> Starting back demodulation with 16.
% 1.68/1.89  
% 1.68/1.89  ======= end of input processing =======
% 1.68/1.89  
% 1.68/1.89  =========== start of search ===========
% 1.68/1.89  
% 1.68/1.89  -------- PROOF -------- 
% 1.68/1.89  
% 1.68/1.89  ----> UNIT CONFLICT at   0.00 sec ----> 85 [binary,83.1,7.1] $F.
% 1.68/1.89  
% 1.68/1.89  Length of proof is 3.  Level of proof is 3.
% 1.68/1.89  
% 1.68/1.89  ---------------- PROOF ----------------
% 1.68/1.89  % SZS status Theorem
% 1.68/1.89  % SZS output start Refutation
% See solution above
% 1.68/1.89  ------------ end of proof -------------
% 1.68/1.89  
% 1.68/1.89  
% 1.68/1.89  Search stopped by max_proofs option.
% 1.68/1.89  
% 1.68/1.89  
% 1.68/1.89  Search stopped by max_proofs option.
% 1.68/1.89  
% 1.68/1.89  ============ end of search ============
% 1.68/1.89  
% 1.68/1.89  -------------- statistics -------------
% 1.68/1.89  clauses given                 10
% 1.68/1.89  clauses generated            124
% 1.68/1.89  clauses kept                  80
% 1.68/1.89  clauses forward subsumed      58
% 1.68/1.89  clauses back subsumed          0
% 1.68/1.89  Kbytes malloced              976
% 1.68/1.89  
% 1.68/1.89  ----------- times (seconds) -----------
% 1.68/1.89  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.68/1.89  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.68/1.89  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.68/1.89  
% 1.68/1.89  That finishes the proof of the theorem.
% 1.68/1.89  
% 1.68/1.89  Process 20555 finished Wed Jul 27 10:47:38 2022
% 1.68/1.89  Otter interrupted
% 1.68/1.89  PROOF FOUND
%------------------------------------------------------------------------------