TSTP Solution File: LDA007-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n003.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 13:05:48 EDT 2022

% Result   : Unsatisfiable 1.73s 1.94s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   19 (  19 unt;   0 nHn;  15 RR)
%            Number of literals    :   19 (  18 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    f(t,tsk) != f(tt_ts,tk),
    file('LDA007-2.p',unknown),
    [] ).

cnf(6,plain,
    f(tt_ts,tk) != f(t,tsk),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
    [iquote('copy,5,flip.1')] ).

cnf(8,axiom,
    f(A,f(B,C)) = f(f(A,B),f(A,C)),
    file('LDA007-2.p',unknown),
    [] ).

cnf(9,plain,
    f(f(A,B),f(A,C)) = f(A,f(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
    [iquote('copy,8,flip.1')] ).

cnf(19,axiom,
    tt = f(t,t),
    file('LDA007-2.p',unknown),
    [] ).

cnf(20,plain,
    f(t,t) = tt,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
    [iquote('copy,19,flip.1')] ).

cnf(25,axiom,
    ts = f(t,s),
    file('LDA007-2.p',unknown),
    [] ).

cnf(27,plain,
    f(t,s) = ts,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
    [iquote('copy,25,flip.1')] ).

cnf(28,axiom,
    tt_ts = f(tt,ts),
    file('LDA007-2.p',unknown),
    [] ).

cnf(30,plain,
    f(tt,ts) = tt_ts,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[28])]),
    [iquote('copy,28,flip.1')] ).

cnf(37,axiom,
    tk = f(t,k),
    file('LDA007-2.p',unknown),
    [] ).

cnf(38,plain,
    f(t,k) = tk,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[37])]),
    [iquote('copy,37,flip.1')] ).

cnf(43,axiom,
    tsk = f(ts,k),
    file('LDA007-2.p',unknown),
    [] ).

cnf(45,plain,
    f(ts,k) = tsk,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[43])]),
    [iquote('copy,43,flip.1')] ).

cnf(57,plain,
    f(tt,f(t,A)) = f(t,f(t,A)),
    inference(para_into,[status(thm),theory(equality)],[9,20]),
    [iquote('para_into,9.1.1.1,20.1.1')] ).

cnf(80,plain,
    f(f(t,A),tk) = f(t,f(A,k)),
    inference(para_from,[status(thm),theory(equality)],[38,9]),
    [iquote('para_from,38.1.1,9.1.1.2')] ).

cnf(332,plain,
    f(t,ts) = tt_ts,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,27]),30,27])]),
    [iquote('para_into,57.1.1.2,26.1.1,demod,30,27,flip.1')] ).

cnf(1103,plain,
    f(tt_ts,tk) = f(t,tsk),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[80,332]),45]),
    [iquote('para_into,80.1.1.1,332.1.1,demod,45')] ).

cnf(1105,plain,
    $false,
    inference(binary,[status(thm)],[1103,6]),
    [iquote('binary,1103.1,6.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n003.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 02:06:11 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.68/1.90  ----- Otter 3.3f, August 2004 -----
% 1.68/1.90  The process was started by sandbox on n003.cluster.edu,
% 1.68/1.90  Wed Jul 27 02:06:11 2022
% 1.68/1.90  The command was "./otter".  The process ID is 29827.
% 1.68/1.90  
% 1.68/1.90  set(prolog_style_variables).
% 1.68/1.90  set(auto).
% 1.68/1.90     dependent: set(auto1).
% 1.68/1.90     dependent: set(process_input).
% 1.68/1.90     dependent: clear(print_kept).
% 1.68/1.90     dependent: clear(print_new_demod).
% 1.68/1.90     dependent: clear(print_back_demod).
% 1.68/1.90     dependent: clear(print_back_sub).
% 1.68/1.90     dependent: set(control_memory).
% 1.68/1.90     dependent: assign(max_mem, 12000).
% 1.68/1.90     dependent: assign(pick_given_ratio, 4).
% 1.68/1.90     dependent: assign(stats_level, 1).
% 1.68/1.90     dependent: assign(max_seconds, 10800).
% 1.68/1.90  clear(print_given).
% 1.68/1.90  
% 1.68/1.90  list(usable).
% 1.68/1.90  0 [] A=A.
% 1.68/1.90  0 [] f(X,f(Y,Z))=f(f(X,Y),f(X,Z)).
% 1.68/1.90  0 [] a(X,a(Y,Z))=a(f(X,Y),a(X,Z)).
% 1.68/1.90  0 [] critical_point(f(U,V))=a(U,critical_point(V)).
% 1.68/1.90  0 [] -less(X,X).
% 1.68/1.90  0 [] -less(X,Y)|less(a(U,X),a(U,Y)).
% 1.68/1.90  0 [] X=a(U,X)|less(X,a(U,X)).
% 1.68/1.90  0 [] -less(X,critical_point(U))|a(U,X)=X.
% 1.68/1.90  0 [] less(X,critical_point(U))|less(X,a(U,X)).
% 1.68/1.90  0 [] a(U,X)!=X|a(f(V,U),X)=X.
% 1.68/1.90  0 [] tt=f(t,t).
% 1.68/1.90  0 [] st=f(s,t).
% 1.68/1.90  0 [] ts=f(t,s).
% 1.68/1.90  0 [] tt_ts=f(tt,ts).
% 1.68/1.90  0 [] k=critical_point(t).
% 1.68/1.90  0 [] sk=f(s,k).
% 1.68/1.90  0 [] tk=f(t,k).
% 1.68/1.90  0 [] stk=f(st,k).
% 1.68/1.90  0 [] tsk=f(ts,k).
% 1.68/1.90  0 [] ttk=f(tt,k).
% 1.68/1.90  0 [] f(t,tsk)!=f(tt_ts,tk).
% 1.68/1.90  end_of_list.
% 1.68/1.90  
% 1.68/1.90  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.68/1.90  
% 1.68/1.90  This ia a non-Horn set with equality.  The strategy will be
% 1.68/1.90  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.90  deletion, with positive clauses in sos and nonpositive
% 1.68/1.90  clauses in usable.
% 1.68/1.90  
% 1.68/1.90     dependent: set(knuth_bendix).
% 1.68/1.90     dependent: set(anl_eq).
% 1.68/1.90     dependent: set(para_from).
% 1.68/1.90     dependent: set(para_into).
% 1.68/1.90     dependent: clear(para_from_right).
% 1.68/1.90     dependent: clear(para_into_right).
% 1.68/1.90     dependent: set(para_from_vars).
% 1.68/1.90     dependent: set(eq_units_both_ways).
% 1.68/1.90     dependent: set(dynamic_demod_all).
% 1.68/1.90     dependent: set(dynamic_demod).
% 1.68/1.90     dependent: set(order_eq).
% 1.68/1.90     dependent: set(back_demod).
% 1.68/1.90     dependent: set(lrpo).
% 1.68/1.90     dependent: set(hyper_res).
% 1.68/1.90     dependent: set(unit_deletion).
% 1.68/1.90     dependent: set(factor).
% 1.68/1.90  
% 1.68/1.90  ------------> process usable:
% 1.68/1.90  ** KEPT (pick-wt=3): 1 [] -less(A,A).
% 1.68/1.90  ** KEPT (pick-wt=10): 2 [] -less(A,B)|less(a(C,A),a(C,B)).
% 1.68/1.90  ** KEPT (pick-wt=9): 3 [] -less(A,critical_point(B))|a(B,A)=A.
% 1.68/1.90  ** KEPT (pick-wt=12): 4 [] a(A,B)!=B|a(f(C,A),B)=B.
% 1.68/1.90  ** KEPT (pick-wt=7): 6 [copy,5,flip.1] f(tt_ts,tk)!=f(t,tsk).
% 1.68/1.90  
% 1.68/1.90  ------------> process sos:
% 1.68/1.90  ** KEPT (pick-wt=3): 7 [] A=A.
% 1.68/1.90  ** KEPT (pick-wt=13): 9 [copy,8,flip.1] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.68/1.90  ---> New Demodulator: 10 [new_demod,9] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.68/1.90  ** KEPT (pick-wt=13): 12 [copy,11,flip.1] a(f(A,B),a(A,C))=a(A,a(B,C)).
% 1.68/1.90  ---> New Demodulator: 13 [new_demod,12] a(f(A,B),a(A,C))=a(A,a(B,C)).
% 1.68/1.90  ** KEPT (pick-wt=9): 14 [] critical_point(f(A,B))=a(A,critical_point(B)).
% 1.68/1.90  ---> New Demodulator: 15 [new_demod,14] critical_point(f(A,B))=a(A,critical_point(B)).
% 1.68/1.90  ** KEPT (pick-wt=10): 17 [copy,16,flip.1] a(A,B)=B|less(B,a(A,B)).
% 1.68/1.90  ** KEPT (pick-wt=9): 18 [] less(A,critical_point(B))|less(A,a(B,A)).
% 1.68/1.90  ** KEPT (pick-wt=5): 20 [copy,19,flip.1] f(t,t)=tt.
% 1.68/1.90  ---> New Demodulator: 21 [new_demod,20] f(t,t)=tt.
% 1.68/1.90  ** KEPT (pick-wt=5): 23 [copy,22,flip.1] f(s,t)=st.
% 1.68/1.90  ---> New Demodulator: 24 [new_demod,23] f(s,t)=st.
% 1.68/1.90  ** KEPT (pick-wt=5): 26 [copy,25,flip.1] f(t,s)=ts.
% 1.68/1.90  ---> New Demodulator: 27 [new_demod,26] f(t,s)=ts.
% 1.68/1.90  ** KEPT (pick-wt=5): 29 [copy,28,flip.1] f(tt,ts)=tt_ts.
% 1.68/1.90  ---> New Demodulator: 30 [new_demod,29] f(tt,ts)=tt_ts.
% 1.68/1.90  ** KEPT (pick-wt=4): 32 [copy,31,flip.1] critical_point(t)=k.
% 1.68/1.90  ---> New Demodulator: 33 [new_demod,32] critical_point(t)=k.
% 1.68/1.90  ** KEPT (pick-wt=5): 35 [copy,34,flip.1] f(s,k)=sk.
% 1.68/1.90  ---> New Demodulator: 36 [new_demod,35] f(s,k)=sk.
% 1.68/1.90  ** KEPT (pick-wt=5): 38 [copy,37,flip.1] f(t,k)=tk.
% 1.68/1.90  ---> New Demodulator: 39 [new_demod,38] f(t,k)=tk.
% 1.68/1.90  ** KEPT (pick-wt=5): 41 [copy,40,flip.1] f(st,k)=stk.
% 1.68/1.90  ---> New Demodulator: 42 [new_demod,41] f(st,k)=stk.
% 1.68/1.90  ** KEPT (pick-wt=5): 44 [copy,43,flip.1] f(ts,k)=tsk.
% 1.68/1.90  ---> New Demodulator: 45 [new_demod,44] f(ts,k)=tsk.
% 1.68/1.90  ** KEPT (pick-wt=5): 47 [copy,46,flip.1] f(tt,k)=ttk.
% 1.68/1.90  ---> New Demodulator: 48 [new_demod,47] f(tt,k)=ttk.
% 1.68/1.90    Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.68/1.90  >>>> Starting back demodulation with 10.
% 1.73/1.94  >>>> Starting back demodulation with 13.
% 1.73/1.94  >>>> Starting back demodulation with 15.
% 1.73/1.94  >>>> Starting back demodulation with 21.
% 1.73/1.94  >>>> Starting back demodulation with 24.
% 1.73/1.94  >>>> Starting back demodulation with 27.
% 1.73/1.94  >>>> Starting back demodulation with 30.
% 1.73/1.94  >>>> Starting back demodulation with 33.
% 1.73/1.94  >>>> Starting back demodulation with 36.
% 1.73/1.94  >>>> Starting back demodulation with 39.
% 1.73/1.94  >>>> Starting back demodulation with 42.
% 1.73/1.94  >>>> Starting back demodulation with 45.
% 1.73/1.94  >>>> Starting back demodulation with 48.
% 1.73/1.94  
% 1.73/1.94  ======= end of input processing =======
% 1.73/1.94  
% 1.73/1.94  =========== start of search ===========
% 1.73/1.94  
% 1.73/1.94  -------- PROOF -------- 
% 1.73/1.94  
% 1.73/1.94  ----> UNIT CONFLICT at   0.04 sec ----> 1105 [binary,1103.1,6.1] $F.
% 1.73/1.94  
% 1.73/1.94  Length of proof is 11.  Level of proof is 4.
% 1.73/1.94  
% 1.73/1.94  ---------------- PROOF ----------------
% 1.73/1.94  % SZS status Unsatisfiable
% 1.73/1.94  % SZS output start Refutation
% See solution above
% 1.73/1.94  ------------ end of proof -------------
% 1.73/1.94  
% 1.73/1.94  
% 1.73/1.94  Search stopped by max_proofs option.
% 1.73/1.94  
% 1.73/1.94  
% 1.73/1.94  Search stopped by max_proofs option.
% 1.73/1.94  
% 1.73/1.94  ============ end of search ============
% 1.73/1.94  
% 1.73/1.94  -------------- statistics -------------
% 1.73/1.94  clauses given                111
% 1.73/1.94  clauses generated           1571
% 1.73/1.94  clauses kept                 778
% 1.73/1.94  clauses forward subsumed     800
% 1.73/1.94  clauses back subsumed         75
% 1.73/1.94  Kbytes malloced             3906
% 1.73/1.94  
% 1.73/1.94  ----------- times (seconds) -----------
% 1.73/1.94  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.73/1.94  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.94  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.73/1.94  
% 1.73/1.94  That finishes the proof of the theorem.
% 1.73/1.94  
% 1.73/1.94  Process 29827 finished Wed Jul 27 02:06:13 2022
% 1.73/1.94  Otter interrupted
% 1.73/1.94  PROOF FOUND
%------------------------------------------------------------------------------