TSTP Solution File: SET907+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET907+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 13:14:30 EDT 2022

% Result   : Theorem 1.62s 1.83s
% Output   : Refutation 1.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   8 RR)
%            Number of literals    :   11 (   3 equ;   4 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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    5 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    ( ~ subset(A,B)
    | set_union2(A,B) = B ),
    file('SET907+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( subset(unordered_pair(A,B),C)
    | ~ in(A,C)
    | ~ in(B,C) ),
    file('SET907+1.p',unknown),
    [] ).

cnf(9,axiom,
    set_union2(unordered_pair(dollar_c5,dollar_c3),dollar_c4) != dollar_c4,
    file('SET907+1.p',unknown),
    [] ).

cnf(17,axiom,
    in(dollar_c5,dollar_c4),
    file('SET907+1.p',unknown),
    [] ).

cnf(18,axiom,
    in(dollar_c3,dollar_c4),
    file('SET907+1.p',unknown),
    [] ).

cnf(23,plain,
    subset(unordered_pair(dollar_c5,dollar_c3),dollar_c4),
    inference(hyper,[status(thm)],[18,8,17]),
    [iquote('hyper,18,8,17')] ).

cnf(35,plain,
    set_union2(unordered_pair(dollar_c5,dollar_c3),dollar_c4) = dollar_c4,
    inference(hyper,[status(thm)],[23,5]),
    [iquote('hyper,23,5')] ).

cnf(37,plain,
    $false,
    inference(binary,[status(thm)],[35,9]),
    [iquote('binary,35.1,9.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 10:31:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.62/1.83  ----- Otter 3.3f, August 2004 -----
% 1.62/1.83  The process was started by sandbox on n019.cluster.edu,
% 1.62/1.83  Wed Jul 27 10:31:22 2022
% 1.62/1.83  The command was "./otter".  The process ID is 25033.
% 1.62/1.83  
% 1.62/1.83  set(prolog_style_variables).
% 1.62/1.83  set(auto).
% 1.62/1.83     dependent: set(auto1).
% 1.62/1.83     dependent: set(process_input).
% 1.62/1.83     dependent: clear(print_kept).
% 1.62/1.83     dependent: clear(print_new_demod).
% 1.62/1.83     dependent: clear(print_back_demod).
% 1.62/1.83     dependent: clear(print_back_sub).
% 1.62/1.83     dependent: set(control_memory).
% 1.62/1.83     dependent: assign(max_mem, 12000).
% 1.62/1.83     dependent: assign(pick_given_ratio, 4).
% 1.62/1.83     dependent: assign(stats_level, 1).
% 1.62/1.83     dependent: assign(max_seconds, 10800).
% 1.62/1.83  clear(print_given).
% 1.62/1.83  
% 1.62/1.83  formula_list(usable).
% 1.62/1.83  all A (A=A).
% 1.62/1.83  all A B (in(A,B)-> -in(B,A)).
% 1.62/1.83  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.62/1.83  all A B (set_union2(A,B)=set_union2(B,A)).
% 1.62/1.83  all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.62/1.83  all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.62/1.83  all A B (set_union2(A,A)=A).
% 1.62/1.83  exists A empty(A).
% 1.62/1.83  exists A (-empty(A)).
% 1.62/1.83  all A B subset(A,A).
% 1.62/1.83  all A B (subset(A,B)->set_union2(A,B)=B).
% 1.62/1.83  all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C)).
% 1.62/1.83  -(all A B C (in(A,B)&in(C,B)->set_union2(unordered_pair(A,C),B)=B)).
% 1.62/1.83  end_of_list.
% 1.62/1.83  
% 1.62/1.83  -------> usable clausifies to:
% 1.62/1.83  
% 1.62/1.83  list(usable).
% 1.62/1.83  0 [] A=A.
% 1.62/1.83  0 [] -in(A,B)| -in(B,A).
% 1.62/1.83  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.62/1.83  0 [] set_union2(A,B)=set_union2(B,A).
% 1.62/1.83  0 [] empty(A)| -empty(set_union2(A,B)).
% 1.62/1.83  0 [] empty(A)| -empty(set_union2(B,A)).
% 1.62/1.83  0 [] set_union2(A,A)=A.
% 1.62/1.83  0 [] empty($c1).
% 1.62/1.83  0 [] -empty($c2).
% 1.62/1.83  0 [] subset(A,A).
% 1.62/1.83  0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.62/1.83  0 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 1.62/1.83  0 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 1.62/1.83  0 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 1.62/1.83  0 [] in($c5,$c4).
% 1.62/1.83  0 [] in($c3,$c4).
% 1.62/1.83  0 [] set_union2(unordered_pair($c5,$c3),$c4)!=$c4.
% 1.62/1.83  end_of_list.
% 1.62/1.83  
% 1.62/1.83  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.62/1.83  
% 1.62/1.83  This is a Horn set with equality.  The strategy will be
% 1.62/1.83  Knuth-Bendix and hyper_res, with positive clauses in
% 1.62/1.83  sos and nonpositive clauses in usable.
% 1.62/1.83  
% 1.62/1.83     dependent: set(knuth_bendix).
% 1.62/1.83     dependent: set(anl_eq).
% 1.62/1.83     dependent: set(para_from).
% 1.62/1.83     dependent: set(para_into).
% 1.62/1.83     dependent: clear(para_from_right).
% 1.62/1.83     dependent: clear(para_into_right).
% 1.62/1.83     dependent: set(para_from_vars).
% 1.62/1.83     dependent: set(eq_units_both_ways).
% 1.62/1.83     dependent: set(dynamic_demod_all).
% 1.62/1.83     dependent: set(dynamic_demod).
% 1.62/1.83     dependent: set(order_eq).
% 1.62/1.83     dependent: set(back_demod).
% 1.62/1.83     dependent: set(lrpo).
% 1.62/1.83     dependent: set(hyper_res).
% 1.62/1.83     dependent: clear(order_hyper).
% 1.62/1.83  
% 1.62/1.83  ------------> process usable:
% 1.62/1.83  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.62/1.83  ** KEPT (pick-wt=6): 2 [] empty(A)| -empty(set_union2(A,B)).
% 1.62/1.83  ** KEPT (pick-wt=6): 3 [] empty(A)| -empty(set_union2(B,A)).
% 1.62/1.83  ** KEPT (pick-wt=2): 4 [] -empty($c2).
% 1.62/1.83  ** KEPT (pick-wt=8): 5 [] -subset(A,B)|set_union2(A,B)=B.
% 1.62/1.83  ** KEPT (pick-wt=8): 6 [] -subset(unordered_pair(A,B),C)|in(A,C).
% 1.62/1.83  ** KEPT (pick-wt=8): 7 [] -subset(unordered_pair(A,B),C)|in(B,C).
% 1.62/1.83  ** KEPT (pick-wt=11): 8 [] subset(unordered_pair(A,B),C)| -in(A,C)| -in(B,C).
% 1.62/1.83  ** KEPT (pick-wt=7): 9 [] set_union2(unordered_pair($c5,$c3),$c4)!=$c4.
% 1.62/1.83  
% 1.62/1.83  ------------> process sos:
% 1.62/1.83  ** KEPT (pick-wt=3): 10 [] A=A.
% 1.62/1.83  ** KEPT (pick-wt=7): 11 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.62/1.83  ** KEPT (pick-wt=7): 12 [] set_union2(A,B)=set_union2(B,A).
% 1.62/1.83  ** KEPT (pick-wt=5): 13 [] set_union2(A,A)=A.
% 1.62/1.83  ---> New Demodulator: 14 [new_demod,13] set_union2(A,A)=A.
% 1.62/1.83  ** KEPT (pick-wt=2): 15 [] empty($c1).
% 1.62/1.83  ** KEPT (pick-wt=3): 16 [] subset(A,A).
% 1.62/1.83  ** KEPT (pick-wt=3): 17 [] in($c5,$c4).
% 1.62/1.83  ** KEPT (pick-wt=3): 18 [] in($c3,$c4).
% 1.62/1.83    Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.62/1.83    Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.62/1.83    Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.62/1.83  >>>> Starting back demodulation with 14.
% 1.62/1.83  
% 1.62/1.83  ======= end of input processing =======
% 1.62/1.83  
% 1.62/1.83  =========== start of search ===========
% 1.62/1.83  
% 1.62/1.83  -------- PROOF -------- 
% 1.62/1.83  
% 1.62/1.83  ----> UNIT CONFLICT at   0.00 sec ----> 37 [binary,35.1,9.1] $F.
% 1.62/1.83  
% 1.62/1.83  Length of proof is 2.  Level of proof is 2.
% 1.62/1.83  
% 1.62/1.83  ---------------- PROOF ----------------
% 1.62/1.83  % SZS status Theorem
% 1.62/1.83  % SZS output start Refutation
% See solution above
% 1.62/1.83  ------------ end of proof -------------
% 1.62/1.83  
% 1.62/1.83  
% 1.62/1.83  Search stopped by max_proofs option.
% 1.62/1.83  
% 1.62/1.83  
% 1.62/1.83  Search stopped by max_proofs option.
% 1.62/1.83  
% 1.62/1.83  ============ end of search ============
% 1.62/1.83  
% 1.62/1.83  -------------- statistics -------------
% 1.62/1.83  clauses given                 13
% 1.62/1.83  clauses generated             49
% 1.62/1.83  clauses kept                  32
% 1.62/1.83  clauses forward subsumed      35
% 1.62/1.83  clauses back subsumed          0
% 1.62/1.83  Kbytes malloced              976
% 1.62/1.83  
% 1.62/1.83  ----------- times (seconds) -----------
% 1.62/1.83  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.62/1.83  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.62/1.83  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.62/1.83  
% 1.62/1.83  That finishes the proof of the theorem.
% 1.62/1.83  
% 1.62/1.83  Process 25033 finished Wed Jul 27 10:31:23 2022
% 1.62/1.83  Otter interrupted
% 1.62/1.83  PROOF FOUND
%------------------------------------------------------------------------------