TSTP Solution File: LCL018-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LCL018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n006.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 13:03:19 EDT 2022

% Result   : Unsatisfiable 4.20s 4.40s
% Output   : Refutation 4.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   46 (  45 unt;   0 nHn;   3 RR)
%            Number of literals    :   48 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  163 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ is_a_theorem(e_quivalent(A,B))
    | ~ is_a_theorem(A)
    | is_a_theorem(B) ),
    file('LCL018-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ is_a_theorem(e_quivalent(e_quivalent(e_quivalent(a,e_quivalent(b,c)),c),e_quivalent(b,a))),
    file('LCL018-1.p',unknown),
    [] ).

cnf(3,axiom,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(B,C)),B),e_quivalent(C,A))),
    file('LCL018-1.p',unknown),
    [] ).

cnf(4,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(B,e_quivalent(e_quivalent(e_quivalent(C,B),A),C)))),
    inference(hyper,[status(thm)],[3,1,3]),
    [iquote('hyper,3,1,3')] ).

cnf(5,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,A),e_quivalent(C,e_quivalent(D,e_quivalent(e_quivalent(e_quivalent(E,D),C),E)))),B))),
    inference(hyper,[status(thm)],[4,1,4]),
    [iquote('hyper,4,1,4')] ).

cnf(6,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,A),e_quivalent(e_quivalent(e_quivalent(C,e_quivalent(D,E)),D),e_quivalent(E,C))),B))),
    inference(hyper,[status(thm)],[4,1,3]),
    [iquote('hyper,4,1,3')] ).

cnf(9,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(B,e_quivalent(C,e_quivalent(e_quivalent(e_quivalent(D,C),B),D)))),e_quivalent(E,e_quivalent(F,e_quivalent(e_quivalent(e_quivalent(G,F),E),G)))),A)),
    inference(hyper,[status(thm)],[5,1,4]),
    [iquote('hyper,5,1,4')] ).

cnf(10,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,e_quivalent(C,D)),C),e_quivalent(D,B))),e_quivalent(E,e_quivalent(F,e_quivalent(e_quivalent(e_quivalent(G,F),E),G)))),A)),
    inference(hyper,[status(thm)],[5,1,3]),
    [iquote('hyper,5,1,3')] ).

cnf(31,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,e_quivalent(B,e_quivalent(e_quivalent(e_quivalent(C,B),A),C))),e_quivalent(D,e_quivalent(E,e_quivalent(e_quivalent(e_quivalent(F,E),D),F))))),
    inference(hyper,[status(thm)],[9,1,9]),
    [iquote('hyper,9,1,9')] ).

cnf(36,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,A),C),B)),e_quivalent(C,e_quivalent(D,e_quivalent(E,e_quivalent(e_quivalent(e_quivalent(F,E),D),F)))))),
    inference(hyper,[status(thm)],[9,1,3]),
    [iquote('hyper,9,1,3')] ).

cnf(43,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(B,e_quivalent(C,e_quivalent(e_quivalent(e_quivalent(D,C),B),D)))),E),A),E)),
    inference(hyper,[status(thm)],[31,1,3]),
    [iquote('hyper,31,1,3')] ).

cnf(56,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(B,C)),B),e_quivalent(C,A)),e_quivalent(D,e_quivalent(E,e_quivalent(e_quivalent(e_quivalent(F,E),D),F))))),
    inference(hyper,[status(thm)],[36,1,6]),
    [iquote('hyper,36,1,6')] ).

cnf(57,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,e_quivalent(B,e_quivalent(e_quivalent(e_quivalent(C,B),A),C))),e_quivalent(e_quivalent(e_quivalent(D,e_quivalent(E,F)),E),e_quivalent(F,D)))),
    inference(hyper,[status(thm)],[10,1,9]),
    [iquote('hyper,10,1,9')] ).

cnf(70,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,B),e_quivalent(C,e_quivalent(e_quivalent(B,e_quivalent(D,A)),D))),C)),
    inference(hyper,[status(thm)],[56,1,10]),
    [iquote('hyper,56,1,10')] ).

cnf(71,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,A),C),B)),e_quivalent(D,C)),D)),
    inference(hyper,[status(thm)],[56,1,9]),
    [iquote('hyper,56,1,9')] ).

cnf(78,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,e_quivalent(C,e_quivalent(e_quivalent(e_quivalent(D,C),B),D))),e_quivalent(E,A)),E))),
    inference(hyper,[status(thm)],[70,1,43]),
    [iquote('hyper,70,1,43')] ).

cnf(145,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,e_quivalent(B,e_quivalent(e_quivalent(C,e_quivalent(e_quivalent(e_quivalent(D,C),E),D)),e_quivalent(A,E)))),B)),
    inference(hyper,[status(thm)],[57,1,70]),
    [iquote('hyper,57,1,70')] ).

cnf(158,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,e_quivalent(B,e_quivalent(e_quivalent(e_quivalent(C,B),A),C))),e_quivalent(e_quivalent(e_quivalent(D,e_quivalent(e_quivalent(e_quivalent(E,D),F),E)),e_quivalent(G,F)),G))),
    inference(hyper,[status(thm)],[145,1,78]),
    [iquote('hyper,145,1,78')] ).

cnf(1242,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,e_quivalent(e_quivalent(e_quivalent(C,B),D),C)),e_quivalent(E,D)),E)),F),A),F)),
    inference(hyper,[status(thm)],[158,1,3]),
    [iquote('hyper,158,1,3')] ).

cnf(1280,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,B),C),A),e_quivalent(B,C))),
    inference(hyper,[status(thm)],[1242,1,71]),
    [iquote('hyper,1242,1,71')] ).

cnf(1287,plain,
    is_a_theorem(e_quivalent(A,A)),
    inference(hyper,[status(thm)],[1280,1,1280]),
    [iquote('hyper,1280,1,1280')] ).

cnf(1319,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(e_quivalent(B,C),A),B),C))),
    inference(hyper,[status(thm)],[1280,1,3]),
    [iquote('hyper,1280,1,3')] ).

cnf(1471,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,B),e_quivalent(C,C)),A),B)),
    inference(hyper,[status(thm)],[1319,1,1287]),
    [iquote('hyper,1319,1,1287')] ).

cnf(1934,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,B),B),A)),
    inference(hyper,[status(thm)],[1471,1,71]),
    [iquote('hyper,1471,1,71')] ).

cnf(1961,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(B,e_quivalent(B,A)))),
    inference(hyper,[status(thm)],[1934,1,3]),
    [iquote('hyper,1934,1,3')] ).

cnf(1963,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,B),A),B)),
    inference(hyper,[status(thm)],[1934,1,1280]),
    [iquote('hyper,1934,1,1280')] ).

cnf(1964,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(B,A),B))),
    inference(hyper,[status(thm)],[1934,1,3]),
    [iquote('hyper,1934,1,3')] ).

cnf(2152,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,B),e_quivalent(e_quivalent(B,e_quivalent(C,A)),C))),
    inference(hyper,[status(thm)],[1963,1,70]),
    [iquote('hyper,1963,1,70')] ).

cnf(2157,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,e_quivalent(B,e_quivalent(e_quivalent(C,B),C))),A)),
    inference(hyper,[status(thm)],[1964,1,1964]),
    [iquote('hyper,1964,1,1964')] ).

cnf(3715,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,B),C),A),e_quivalent(C,B))),
    inference(hyper,[status(thm)],[2152,1,71]),
    [iquote('hyper,2152,1,71')] ).

cnf(3736,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(A,B)),e_quivalent(C,B)),C)),
    inference(hyper,[status(thm)],[2152,1,1961]),
    [iquote('hyper,2152,1,1961')] ).

cnf(3834,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,B),e_quivalent(e_quivalent(C,B),C)),A)),
    inference(hyper,[status(thm)],[2157,1,1280]),
    [iquote('hyper,2157,1,1280')] ).

cnf(5360,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,B),C),A),C),B)),
    inference(hyper,[status(thm)],[3715,1,56]),
    [iquote('hyper,3715,1,56')] ).

cnf(5540,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,B),e_quivalent(B,A))),
    inference(hyper,[status(thm)],[3736,1,2152]),
    [iquote('hyper,3736,1,2152')] ).

cnf(5552,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,B),e_quivalent(C,e_quivalent(B,A))),C)),
    inference(hyper,[status(thm)],[5540,1,2152]),
    [iquote('hyper,5540,1,2152')] ).

cnf(5625,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(A,B),e_quivalent(e_quivalent(C,B),C)))),
    inference(hyper,[status(thm)],[3834,1,5540]),
    [iquote('hyper,3834,1,5540')] ).

cnf(6635,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,C),e_quivalent(C,A)),B))),
    inference(hyper,[status(thm)],[5360,1,3]),
    [iquote('hyper,5360,1,3')] ).

cnf(7256,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,e_quivalent(A,C)),C),B))),
    inference(hyper,[status(thm)],[5625,1,145]),
    [iquote('hyper,5625,1,145')] ).

cnf(8552,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,B),C),e_quivalent(C,e_quivalent(B,A)))),
    inference(hyper,[status(thm)],[6635,1,5552]),
    [iquote('hyper,6635,1,5552')] ).

cnf(8553,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,B),e_quivalent(B,C)),A),C)),
    inference(hyper,[status(thm)],[6635,1,5540]),
    [iquote('hyper,6635,1,5540')] ).

cnf(8699,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(B,C)),C),A),B)),
    inference(hyper,[status(thm)],[7256,1,5540]),
    [iquote('hyper,7256,1,5540')] ).

cnf(12543,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(e_quivalent(e_quivalent(B,A),C),e_quivalent(C,B)))),
    inference(hyper,[status(thm)],[8553,1,3]),
    [iquote('hyper,8553,1,3')] ).

cnf(14288,plain,
    is_a_theorem(e_quivalent(A,e_quivalent(B,e_quivalent(e_quivalent(B,e_quivalent(A,C)),C)))),
    inference(hyper,[status(thm)],[8699,1,8552]),
    [iquote('hyper,8699,1,8552')] ).

cnf(16811,plain,
    is_a_theorem(e_quivalent(e_quivalent(A,e_quivalent(B,C)),e_quivalent(C,e_quivalent(A,B)))),
    inference(hyper,[status(thm)],[12543,1,70]),
    [iquote('hyper,12543,1,70')] ).

cnf(17281,plain,
    is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(B,C)),C),e_quivalent(B,A))),
    inference(hyper,[status(thm)],[16811,1,14288]),
    [iquote('hyper,16811,1,14288')] ).

cnf(17282,plain,
    $false,
    inference(binary,[status(thm)],[17281,2]),
    [iquote('binary,17281.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : LCL018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n006.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 09:13:46 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 4.20/4.40  ----- Otter 3.3f, August 2004 -----
% 4.20/4.40  The process was started by sandbox on n006.cluster.edu,
% 4.20/4.40  Wed Jul 27 09:13:47 2022
% 4.20/4.40  The command was "./otter".  The process ID is 29118.
% 4.20/4.40  
% 4.20/4.40  set(prolog_style_variables).
% 4.20/4.40  set(auto).
% 4.20/4.40     dependent: set(auto1).
% 4.20/4.40     dependent: set(process_input).
% 4.20/4.40     dependent: clear(print_kept).
% 4.20/4.40     dependent: clear(print_new_demod).
% 4.20/4.40     dependent: clear(print_back_demod).
% 4.20/4.40     dependent: clear(print_back_sub).
% 4.20/4.40     dependent: set(control_memory).
% 4.20/4.40     dependent: assign(max_mem, 12000).
% 4.20/4.40     dependent: assign(pick_given_ratio, 4).
% 4.20/4.40     dependent: assign(stats_level, 1).
% 4.20/4.40     dependent: assign(max_seconds, 10800).
% 4.20/4.40  clear(print_given).
% 4.20/4.40  
% 4.20/4.40  list(usable).
% 4.20/4.40  0 [] -is_a_theorem(e_quivalent(X,Y))| -is_a_theorem(X)|is_a_theorem(Y).
% 4.20/4.40  0 [] is_a_theorem(e_quivalent(e_quivalent(e_quivalent(X,e_quivalent(Y,Z)),Y),e_quivalent(Z,X))).
% 4.20/4.40  0 [] -is_a_theorem(e_quivalent(e_quivalent(e_quivalent(a,e_quivalent(b,c)),c),e_quivalent(b,a))).
% 4.20/4.40  end_of_list.
% 4.20/4.40  
% 4.20/4.40  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 4.20/4.40  
% 4.20/4.40  This is a Horn set without equality.  The strategy will
% 4.20/4.40  be hyperresolution, with satellites in sos and nuclei
% 4.20/4.40  in usable.
% 4.20/4.40  
% 4.20/4.40     dependent: set(hyper_res).
% 4.20/4.40     dependent: clear(order_hyper).
% 4.20/4.40  
% 4.20/4.40  ------------> process usable:
% 4.20/4.40  ** KEPT (pick-wt=8): 1 [] -is_a_theorem(e_quivalent(A,B))| -is_a_theorem(A)|is_a_theorem(B).
% 4.20/4.40  ** KEPT (pick-wt=12): 2 [] -is_a_theorem(e_quivalent(e_quivalent(e_quivalent(a,e_quivalent(b,c)),c),e_quivalent(b,a))).
% 4.20/4.40  
% 4.20/4.40  ------------> process sos:
% 4.20/4.40  ** KEPT (pick-wt=12): 3 [] is_a_theorem(e_quivalent(e_quivalent(e_quivalent(A,e_quivalent(B,C)),B),e_quivalent(C,A))).
% 4.20/4.40  
% 4.20/4.40  ======= end of input processing =======
% 4.20/4.40  
% 4.20/4.40  =========== start of search ===========
% 4.20/4.40  
% 4.20/4.40  
% 4.20/4.40  Resetting weight limit to 16.
% 4.20/4.40  
% 4.20/4.40  
% 4.20/4.40  Resetting weight limit to 16.
% 4.20/4.40  
% 4.20/4.40  sos_size=4920
% 4.20/4.40  
% 4.20/4.40  -------- PROOF -------- 
% 4.20/4.40  
% 4.20/4.40  ----> UNIT CONFLICT at   2.31 sec ----> 17282 [binary,17281.1,2.1] $F.
% 4.20/4.40  
% 4.20/4.40  Length of proof is 42.  Level of proof is 22.
% 4.20/4.40  
% 4.20/4.40  ---------------- PROOF ----------------
% 4.20/4.40  % SZS status Unsatisfiable
% 4.20/4.40  % SZS output start Refutation
% See solution above
% 4.20/4.40  ------------ end of proof -------------
% 4.20/4.40  
% 4.20/4.40  
% 4.20/4.40  Search stopped by max_proofs option.
% 4.20/4.40  
% 4.20/4.40  
% 4.20/4.40  Search stopped by max_proofs option.
% 4.20/4.40  
% 4.20/4.40  ============ end of search ============
% 4.20/4.41  
% 4.20/4.41  -------------- statistics -------------
% 4.20/4.41  clauses given                679
% 4.20/4.41  clauses generated         261657
% 4.20/4.41  clauses kept               17281
% 4.20/4.41  clauses forward subsumed   69137
% 4.20/4.41  clauses back subsumed          0
% 4.20/4.41  Kbytes malloced             8789
% 4.20/4.41  
% 4.20/4.41  ----------- times (seconds) -----------
% 4.20/4.41  user CPU time          2.31          (0 hr, 0 min, 2 sec)
% 4.20/4.41  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 4.20/4.41  wall-clock time        4             (0 hr, 0 min, 4 sec)
% 4.20/4.41  
% 4.20/4.41  That finishes the proof of the theorem.
% 4.20/4.41  
% 4.20/4.41  Process 29118 finished Wed Jul 27 09:13:51 2022
% 4.20/4.41  Otter interrupted
% 4.20/4.41  PROOF FOUND
%------------------------------------------------------------------------------