TSTP Solution File: SYN075-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN075-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n020.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 13:23:30 EDT 2022

% Result   : Unsatisfiable 1.95s 2.12s
% Output   : Refutation 1.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   17 (   6 unt;   5 nHn;  10 RR)
%            Number of literals    :   33 (  20 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   25 (   4 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ big_f(A,B)
    | A = a ),
    file('SYN075-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( A != a
    | B != b
    | big_f(A,B) ),
    file('SYN075-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ big_f(A,f(B))
    | A != g(B)
    | f(B) = B ),
    file('SYN075-1.p',unknown),
    [] ).

cnf(5,axiom,
    ( A != g(B)
    | big_f(A,f(B))
    | f(B) = B ),
    file('SYN075-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( f(A) != A
    | big_f(h(A,B),f(A))
    | h(A,B) = B ),
    file('SYN075-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( f(A) != A
    | h(A,B) != B
    | ~ big_f(h(A,B),f(A)) ),
    file('SYN075-1.p',unknown),
    [] ).

cnf(11,axiom,
    A = A,
    file('SYN075-1.p',unknown),
    [] ).

cnf(13,plain,
    ( big_f(g(A),f(A))
    | f(A) = A ),
    inference(hyper,[status(thm)],[11,5]),
    [iquote('hyper,11,5')] ).

cnf(14,plain,
    big_f(a,b),
    inference(hyper,[status(thm)],[11,3,11]),
    [iquote('hyper,11,3,11')] ).

cnf(19,plain,
    f(A) = A,
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[13,4,11])]),
    [iquote('hyper,13,4,11,factor_simp')] ).

cnf(22,plain,
    ( h(A,B) != B
    | ~ big_f(h(A,B),A) ),
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),19,19]),11]),
    [iquote('back_demod,9,demod,19,19,unit_del,11')] ).

cnf(23,plain,
    ( big_f(h(A,B),A)
    | h(A,B) = B ),
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[8]),19,19]),11]),
    [iquote('back_demod,8,demod,19,19,unit_del,11')] ).

cnf(25,plain,
    ( a = A
    | ~ big_f(A,B) ),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,1]),19]),
    [iquote('para_into,18.1.1,1.2.1,demod,19')] ).

cnf(75,plain,
    ( h(A,B) = B
    | h(A,B) = a ),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[23,25])]),
    [iquote('hyper,23,25,flip.2')] ).

cnf(82,plain,
    h(A,a) = a,
    inference(factor,[status(thm)],[75]),
    [iquote('factor,75.1.2')] ).

cnf(104,plain,
    ~ big_f(a,A),
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[82,22]),82]),11]),
    [iquote('para_from,81.1.1,22.2.1,demod,82,unit_del,11')] ).

cnf(105,plain,
    $false,
    inference(binary,[status(thm)],[104,14]),
    [iquote('binary,104.1,14.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYN075-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n020.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 11:22:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.95/2.12  ----- Otter 3.3f, August 2004 -----
% 1.95/2.12  The process was started by sandbox on n020.cluster.edu,
% 1.95/2.12  Wed Jul 27 11:22:38 2022
% 1.95/2.12  The command was "./otter".  The process ID is 7548.
% 1.95/2.12  
% 1.95/2.12  set(prolog_style_variables).
% 1.95/2.12  set(auto).
% 1.95/2.12     dependent: set(auto1).
% 1.95/2.12     dependent: set(process_input).
% 1.95/2.12     dependent: clear(print_kept).
% 1.95/2.12     dependent: clear(print_new_demod).
% 1.95/2.12     dependent: clear(print_back_demod).
% 1.95/2.12     dependent: clear(print_back_sub).
% 1.95/2.12     dependent: set(control_memory).
% 1.95/2.12     dependent: assign(max_mem, 12000).
% 1.95/2.12     dependent: assign(pick_given_ratio, 4).
% 1.95/2.12     dependent: assign(stats_level, 1).
% 1.95/2.12     dependent: assign(max_seconds, 10800).
% 1.95/2.12  clear(print_given).
% 1.95/2.12  
% 1.95/2.12  list(usable).
% 1.95/2.12  0 [] A=A.
% 1.95/2.12  0 [] -big_f(X,Y)|X=a.
% 1.95/2.12  0 [] -big_f(X,Y)|Y=b.
% 1.95/2.12  0 [] X!=a|Y!=b|big_f(X,Y).
% 1.95/2.12  0 [] -big_f(Y,f(X))|Y!=g(X)|f(X)=X.
% 1.95/2.12  0 [] -big_f(Y,f(X))|Y=g(X)|big_f(h(X,Z),f(X))| -big_f(h(X,Z),f(X)).
% 1.95/2.12  0 [] Y!=g(X)|big_f(Y,f(X))|f(X)=X.
% 1.95/2.12  0 [] Y!=g(X)|big_f(Y,f(X))|big_f(h(X,Z),f(X))|h(X,Z)=Z.
% 1.95/2.12  0 [] Y!=g(X)|big_f(Y,f(X))|h(X,Z)!=Z| -big_f(h(X,Z),f(X)).
% 1.95/2.12  0 [] f(X)!=X|big_f(h(X,Z),f(X))|h(X,Z)=Z.
% 1.95/2.12  0 [] f(X)!=X|h(X,Z)!=Z| -big_f(h(X,Z),f(X)).
% 1.95/2.12  end_of_list.
% 1.95/2.12  
% 1.95/2.12  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.95/2.12  
% 1.95/2.12  This ia a non-Horn set with equality.  The strategy will be
% 1.95/2.12  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.95/2.12  deletion, with positive clauses in sos and nonpositive
% 1.95/2.12  clauses in usable.
% 1.95/2.12  
% 1.95/2.12     dependent: set(knuth_bendix).
% 1.95/2.12     dependent: set(anl_eq).
% 1.95/2.12     dependent: set(para_from).
% 1.95/2.12     dependent: set(para_into).
% 1.95/2.12     dependent: clear(para_from_right).
% 1.95/2.12     dependent: clear(para_into_right).
% 1.95/2.12     dependent: set(para_from_vars).
% 1.95/2.12     dependent: set(eq_units_both_ways).
% 1.95/2.12     dependent: set(dynamic_demod_all).
% 1.95/2.12     dependent: set(dynamic_demod).
% 1.95/2.12     dependent: set(order_eq).
% 1.95/2.12     dependent: set(back_demod).
% 1.95/2.12     dependent: set(lrpo).
% 1.95/2.12     dependent: set(hyper_res).
% 1.95/2.12     dependent: set(unit_deletion).
% 1.95/2.12     dependent: set(factor).
% 1.95/2.12  
% 1.95/2.12  ------------> process usable:
% 1.95/2.12  ** KEPT (pick-wt=6): 1 [] -big_f(A,B)|A=a.
% 1.95/2.12  ** KEPT (pick-wt=6): 2 [] -big_f(A,B)|B=b.
% 1.95/2.12  ** KEPT (pick-wt=9): 3 [] A!=a|B!=b|big_f(A,B).
% 1.95/2.12  ** KEPT (pick-wt=12): 4 [] -big_f(A,f(B))|A!=g(B)|f(B)=B.
% 1.95/2.12  ** KEPT (pick-wt=12): 5 [] A!=g(B)|big_f(A,f(B))|f(B)=B.
% 1.95/2.12  ** KEPT (pick-wt=19): 6 [] A!=g(B)|big_f(A,f(B))|big_f(h(B,C),f(B))|h(B,C)=C.
% 1.95/2.12  ** KEPT (pick-wt=19): 7 [] A!=g(B)|big_f(A,f(B))|h(B,C)!=C| -big_f(h(B,C),f(B)).
% 1.95/2.12  ** KEPT (pick-wt=15): 8 [] f(A)!=A|big_f(h(A,B),f(A))|h(A,B)=B.
% 1.95/2.12  ** KEPT (pick-wt=15): 9 [] f(A)!=A|h(A,B)!=B| -big_f(h(A,B),f(A)).
% 1.95/2.12  
% 1.95/2.12  ------------> process sos:
% 1.95/2.12  ** KEPT (pick-wt=3): 11 [] A=A.
% 1.95/2.12    Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.95/2.12  
% 1.95/2.12  ======= end of input processing =======
% 1.95/2.12  
% 1.95/2.12  =========== start of search ===========
% 1.95/2.12  
% 1.95/2.12  -------- PROOF -------- 
% 1.95/2.12  
% 1.95/2.12  ----> UNIT CONFLICT at   0.00 sec ----> 105 [binary,104.1,14.1] $F.
% 1.95/2.12  
% 1.95/2.12  Length of proof is 9.  Level of proof is 6.
% 1.95/2.12  
% 1.95/2.12  ---------------- PROOF ----------------
% 1.95/2.12  % SZS status Unsatisfiable
% 1.95/2.12  % SZS output start Refutation
% See solution above
% 1.95/2.12  ------------ end of proof -------------
% 1.95/2.12  
% 1.95/2.12  
% 1.95/2.12  Search stopped by max_proofs option.
% 1.95/2.12  
% 1.95/2.12  
% 1.95/2.12  Search stopped by max_proofs option.
% 1.95/2.12  
% 1.95/2.12  ============ end of search ============
% 1.95/2.12  
% 1.95/2.12  -------------- statistics -------------
% 1.95/2.12  clauses given                 23
% 1.95/2.12  clauses generated            244
% 1.95/2.12  clauses kept                 100
% 1.95/2.12  clauses forward subsumed     163
% 1.95/2.12  clauses back subsumed         48
% 1.95/2.12  Kbytes malloced              976
% 1.95/2.12  
% 1.95/2.12  ----------- times (seconds) -----------
% 1.95/2.12  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.95/2.12  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.95/2.12  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.95/2.12  
% 1.95/2.12  That finishes the proof of the theorem.
% 1.95/2.12  
% 1.95/2.12  Process 7548 finished Wed Jul 27 11:22:40 2022
% 1.95/2.12  Otter interrupted
% 1.95/2.12  PROOF FOUND
%------------------------------------------------------------------------------