TSTP Solution File: LCL171-3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LCL171-3 : TPTP v8.1.0. Released v2.3.0.
% 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 13:03:45 EDT 2022

% Result   : Unsatisfiable 1.66s 1.83s
% Output   : Refutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   8 unt;   0 nHn;   3 RR)
%            Number of literals    :   10 (   2 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   13 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( theorem(A)
    | ~ axiom(A) ),
    file('LCL171-3.p',unknown),
    [] ).

cnf(3,axiom,
    ~ theorem(implies(implies(p,not(q)),implies(q,not(p)))),
    file('LCL171-3.p',unknown),
    [] ).

cnf(7,axiom,
    axiom(implies(or(A,B),or(B,A))),
    file('LCL171-3.p',unknown),
    [] ).

cnf(10,axiom,
    implies(A,B) = or(not(A),B),
    file('LCL171-3.p',unknown),
    [] ).

cnf(11,plain,
    or(not(A),B) = implies(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
    [iquote('copy,10,flip.1')] ).

cnf(17,plain,
    theorem(implies(or(A,B),or(B,A))),
    inference(hyper,[status(thm)],[7,1]),
    [iquote('hyper,7,1')] ).

cnf(40,plain,
    theorem(implies(implies(A,B),or(B,not(A)))),
    inference(para_into,[status(thm),theory(equality)],[17,11]),
    [iquote('para_into,17.1.1.1,11.1.1')] ).

cnf(73,plain,
    theorem(implies(implies(A,not(B)),implies(B,not(A)))),
    inference(para_into,[status(thm),theory(equality)],[40,11]),
    [iquote('para_into,40.1.1.2,11.1.1')] ).

cnf(74,plain,
    $false,
    inference(binary,[status(thm)],[73,3]),
    [iquote('binary,73.1,3.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL171-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n022.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 09:31:35 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.66/1.83  ----- Otter 3.3f, August 2004 -----
% 1.66/1.83  The process was started by sandbox on n022.cluster.edu,
% 1.66/1.83  Wed Jul 27 09:31:35 2022
% 1.66/1.83  The command was "./otter".  The process ID is 15588.
% 1.66/1.83  
% 1.66/1.83  set(prolog_style_variables).
% 1.66/1.83  set(auto).
% 1.66/1.83     dependent: set(auto1).
% 1.66/1.83     dependent: set(process_input).
% 1.66/1.83     dependent: clear(print_kept).
% 1.66/1.83     dependent: clear(print_new_demod).
% 1.66/1.83     dependent: clear(print_back_demod).
% 1.66/1.83     dependent: clear(print_back_sub).
% 1.66/1.83     dependent: set(control_memory).
% 1.66/1.83     dependent: assign(max_mem, 12000).
% 1.66/1.83     dependent: assign(pick_given_ratio, 4).
% 1.66/1.83     dependent: assign(stats_level, 1).
% 1.66/1.83     dependent: assign(max_seconds, 10800).
% 1.66/1.83  clear(print_given).
% 1.66/1.83  
% 1.66/1.83  list(usable).
% 1.66/1.83  0 [] A=A.
% 1.66/1.83  0 [] axiom(implies(or(A,A),A)).
% 1.66/1.83  0 [] axiom(implies(A,or(B,A))).
% 1.66/1.83  0 [] axiom(implies(or(A,B),or(B,A))).
% 1.66/1.83  0 [] axiom(implies(or(A,or(B,C)),or(B,or(A,C)))).
% 1.66/1.83  0 [] axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))).
% 1.66/1.83  0 [] implies(X,Y)=or(not(X),Y).
% 1.66/1.83  0 [] theorem(X)| -axiom(X).
% 1.66/1.83  0 [] theorem(X)| -theorem(implies(Y,X))| -theorem(Y).
% 1.66/1.83  0 [] -theorem(implies(implies(p,not(q)),implies(q,not(p)))).
% 1.66/1.83  end_of_list.
% 1.66/1.83  
% 1.66/1.83  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.66/1.83  
% 1.66/1.83  This is a Horn set with equality.  The strategy will be
% 1.66/1.83  Knuth-Bendix and hyper_res, with positive clauses in
% 1.66/1.83  sos and nonpositive clauses in usable.
% 1.66/1.83  
% 1.66/1.83     dependent: set(knuth_bendix).
% 1.66/1.83     dependent: set(anl_eq).
% 1.66/1.83     dependent: set(para_from).
% 1.66/1.83     dependent: set(para_into).
% 1.66/1.83     dependent: clear(para_from_right).
% 1.66/1.83     dependent: clear(para_into_right).
% 1.66/1.83     dependent: set(para_from_vars).
% 1.66/1.83     dependent: set(eq_units_both_ways).
% 1.66/1.83     dependent: set(dynamic_demod_all).
% 1.66/1.83     dependent: set(dynamic_demod).
% 1.66/1.83     dependent: set(order_eq).
% 1.66/1.83     dependent: set(back_demod).
% 1.66/1.83     dependent: set(lrpo).
% 1.66/1.83     dependent: set(hyper_res).
% 1.66/1.83     dependent: clear(order_hyper).
% 1.66/1.83  
% 1.66/1.83  ------------> process usable:
% 1.66/1.83  ** KEPT (pick-wt=4): 1 [] theorem(A)| -axiom(A).
% 1.66/1.83  ** KEPT (pick-wt=8): 2 [] theorem(A)| -theorem(implies(B,A))| -theorem(B).
% 1.66/1.83  ** KEPT (pick-wt=10): 3 [] -theorem(implies(implies(p,not(q)),implies(q,not(p)))).
% 1.66/1.83  
% 1.66/1.83  ------------> process sos:
% 1.66/1.83  ** KEPT (pick-wt=3): 4 [] A=A.
% 1.66/1.83  ** KEPT (pick-wt=6): 5 [] axiom(implies(or(A,A),A)).
% 1.66/1.83  ** KEPT (pick-wt=6): 6 [] axiom(implies(A,or(B,A))).
% 1.66/1.83  ** KEPT (pick-wt=8): 7 [] axiom(implies(or(A,B),or(B,A))).
% 1.66/1.83  ** KEPT (pick-wt=12): 8 [] axiom(implies(or(A,or(B,C)),or(B,or(A,C)))).
% 1.66/1.83  ** KEPT (pick-wt=12): 9 [] axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))).
% 1.66/1.83  ** KEPT (pick-wt=8): 11 [copy,10,flip.1] or(not(A),B)=implies(A,B).
% 1.66/1.83  ---> New Demodulator: 12 [new_demod,11] or(not(A),B)=implies(A,B).
% 1.66/1.83    Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.66/1.83  >>>> Starting back demodulation with 12.
% 1.66/1.83  
% 1.66/1.83  ======= end of input processing =======
% 1.66/1.83  
% 1.66/1.83  =========== start of search ===========
% 1.66/1.83  
% 1.66/1.83  -------- PROOF -------- 
% 1.66/1.83  
% 1.66/1.83  ----> UNIT CONFLICT at   0.00 sec ----> 74 [binary,73.1,3.1] $F.
% 1.66/1.83  
% 1.66/1.83  Length of proof is 4.  Level of proof is 3.
% 1.66/1.83  
% 1.66/1.83  ---------------- PROOF ----------------
% 1.66/1.83  % SZS status Unsatisfiable
% 1.66/1.83  % SZS output start Refutation
% See solution above
% 1.66/1.83  ------------ end of proof -------------
% 1.66/1.83  
% 1.66/1.83  
% 1.66/1.83  Search stopped by max_proofs option.
% 1.66/1.83  
% 1.66/1.83  
% 1.66/1.83  Search stopped by max_proofs option.
% 1.66/1.83  
% 1.66/1.83  ============ end of search ============
% 1.66/1.83  
% 1.66/1.83  -------------- statistics -------------
% 1.66/1.83  clauses given                 27
% 1.66/1.83  clauses generated            164
% 1.66/1.83  clauses kept                  71
% 1.66/1.83  clauses forward subsumed     104
% 1.66/1.83  clauses back subsumed          0
% 1.66/1.83  Kbytes malloced             1953
% 1.66/1.83  
% 1.66/1.83  ----------- times (seconds) -----------
% 1.66/1.83  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.83  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.83  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.66/1.83  
% 1.66/1.83  That finishes the proof of the theorem.
% 1.66/1.83  
% 1.66/1.83  Process 15588 finished Wed Jul 27 09:31:36 2022
% 1.66/1.83  Otter interrupted
% 1.66/1.83  PROOF FOUND
%------------------------------------------------------------------------------