TSTP Solution File: CAT011-3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : CAT011-3 : 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 12:47:48 EDT 2022

% Result   : Unsatisfiable 2.44s 2.61s
% Output   : Refutation 2.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   18 (  11 unt;   0 nHn;  15 RR)
%            Number of literals    :   26 (  11 equ;   9 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    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ e_quivalent(A,B)
    | A = B ),
    file('CAT011-3.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ there_exists(A)
    | A != B
    | e_quivalent(A,B) ),
    file('CAT011-3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ there_exists(domain(A))
    | there_exists(A) ),
    file('CAT011-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ there_exists(compose(A,B))
    | domain(A) = codomain(B) ),
    file('CAT011-3.p',unknown),
    [] ).

cnf(13,axiom,
    domain(domain(a)) != domain(a),
    file('CAT011-3.p',unknown),
    [] ).

cnf(15,axiom,
    A = A,
    file('CAT011-3.p',unknown),
    [] ).

cnf(20,axiom,
    compose(A,domain(A)) = A,
    file('CAT011-3.p',unknown),
    [] ).

cnf(21,axiom,
    compose(codomain(A),A) = A,
    file('CAT011-3.p',unknown),
    [] ).

cnf(26,axiom,
    there_exists(domain(a)),
    file('CAT011-3.p',unknown),
    [] ).

cnf(27,plain,
    there_exists(a),
    inference(hyper,[status(thm)],[26,4]),
    [iquote('hyper,26,4')] ).

cnf(28,plain,
    e_quivalent(domain(a),domain(a)),
    inference(hyper,[status(thm)],[26,3,15]),
    [iquote('hyper,26,3,15')] ).

cnf(41,plain,
    ( e_quivalent(codomain(A),domain(a))
    | ~ there_exists(compose(a,A)) ),
    inference(para_into,[status(thm),theory(equality)],[28,7]),
    [iquote('para_into,28.1.1,7.2.1')] ).

cnf(61,plain,
    ( A = B
    | ~ e_quivalent(B,A) ),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,2]),20]),
    [iquote('para_into,19.1.1,2.2.1,demod,20')] ).

cnf(89,plain,
    ( ~ there_exists(A)
    | domain(codomain(A)) = codomain(A) ),
    inference(para_from,[status(thm),theory(equality)],[21,7]),
    [iquote('para_from,21.1.1,7.1.1')] ).

cnf(1511,plain,
    e_quivalent(codomain(domain(a)),domain(a)),
    inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[41,20]),27]),
    [iquote('para_into,41.2.1,19.1.1,unit_del,27')] ).

cnf(1516,plain,
    codomain(domain(a)) = domain(a),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1511,61])]),
    [iquote('hyper,1511,61,flip.1')] ).

cnf(2377,plain,
    domain(domain(a)) = domain(a),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[89,26]),1516,1516]),
    [iquote('hyper,89,26,demod,1516,1516')] ).

cnf(2379,plain,
    $false,
    inference(binary,[status(thm)],[2377,13]),
    [iquote('binary,2377.1,13.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : CAT011-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 01:56:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.97/2.15  ----- Otter 3.3f, August 2004 -----
% 1.97/2.15  The process was started by sandbox2 on n020.cluster.edu,
% 1.97/2.15  Wed Jul 27 01:56:38 2022
% 1.97/2.15  The command was "./otter".  The process ID is 23816.
% 1.97/2.15  
% 1.97/2.15  set(prolog_style_variables).
% 1.97/2.15  set(auto).
% 1.97/2.15     dependent: set(auto1).
% 1.97/2.15     dependent: set(process_input).
% 1.97/2.15     dependent: clear(print_kept).
% 1.97/2.15     dependent: clear(print_new_demod).
% 1.97/2.15     dependent: clear(print_back_demod).
% 1.97/2.15     dependent: clear(print_back_sub).
% 1.97/2.15     dependent: set(control_memory).
% 1.97/2.15     dependent: assign(max_mem, 12000).
% 1.97/2.15     dependent: assign(pick_given_ratio, 4).
% 1.97/2.15     dependent: assign(stats_level, 1).
% 1.97/2.15     dependent: assign(max_seconds, 10800).
% 1.97/2.15  clear(print_given).
% 1.97/2.15  
% 1.97/2.15  list(usable).
% 1.97/2.15  0 [] A=A.
% 1.97/2.15  0 [] -e_quivalent(X,Y)|there_exists(X).
% 1.97/2.15  0 [] -e_quivalent(X,Y)|X=Y.
% 1.97/2.15  0 [] -there_exists(X)|X!=Y|e_quivalent(X,Y).
% 1.97/2.15  0 [] -there_exists(domain(X))|there_exists(X).
% 1.97/2.15  0 [] -there_exists(codomain(X))|there_exists(X).
% 1.97/2.15  0 [] -there_exists(compose(X,Y))|there_exists(domain(X)).
% 1.97/2.15  0 [] -there_exists(compose(X,Y))|domain(X)=codomain(Y).
% 1.97/2.15  0 [] -there_exists(domain(X))|domain(X)!=codomain(Y)|there_exists(compose(X,Y)).
% 1.97/2.15  0 [] compose(X,compose(Y,Z))=compose(compose(X,Y),Z).
% 1.97/2.15  0 [] compose(X,domain(X))=X.
% 1.97/2.15  0 [] compose(codomain(X),X)=X.
% 1.97/2.15  0 [] -e_quivalent(X,Y)|there_exists(Y).
% 1.97/2.15  0 [] -there_exists(X)| -there_exists(Y)|X!=Y|e_quivalent(X,Y).
% 1.97/2.15  0 [] -there_exists(compose(X,Y))|there_exists(codomain(X)).
% 1.97/2.15  0 [] there_exists(f1(X,Y))|X=Y.
% 1.97/2.15  0 [] X=f1(X,Y)|Y=f1(X,Y)|X=Y.
% 1.97/2.15  0 [] X!=f1(X,Y)|Y!=f1(X,Y)|X=Y.
% 1.97/2.15  0 [] there_exists(domain(a)).
% 1.97/2.15  0 [] domain(domain(a))!=domain(a).
% 1.97/2.15  end_of_list.
% 1.97/2.15  
% 1.97/2.15  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.97/2.15  
% 1.97/2.15  This ia a non-Horn set with equality.  The strategy will be
% 1.97/2.15  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.15  deletion, with positive clauses in sos and nonpositive
% 1.97/2.15  clauses in usable.
% 1.97/2.15  
% 1.97/2.15     dependent: set(knuth_bendix).
% 1.97/2.15     dependent: set(anl_eq).
% 1.97/2.15     dependent: set(para_from).
% 1.97/2.15     dependent: set(para_into).
% 1.97/2.15     dependent: clear(para_from_right).
% 1.97/2.15     dependent: clear(para_into_right).
% 1.97/2.15     dependent: set(para_from_vars).
% 1.97/2.15     dependent: set(eq_units_both_ways).
% 1.97/2.15     dependent: set(dynamic_demod_all).
% 1.97/2.15     dependent: set(dynamic_demod).
% 1.97/2.15     dependent: set(order_eq).
% 1.97/2.15     dependent: set(back_demod).
% 1.97/2.15     dependent: set(lrpo).
% 1.97/2.15     dependent: set(hyper_res).
% 1.97/2.15     dependent: set(unit_deletion).
% 1.97/2.15     dependent: set(factor).
% 1.97/2.15  
% 1.97/2.15  ------------> process usable:
% 1.97/2.15  ** KEPT (pick-wt=5): 1 [] -e_quivalent(A,B)|there_exists(A).
% 1.97/2.15  ** KEPT (pick-wt=6): 2 [] -e_quivalent(A,B)|A=B.
% 1.97/2.15  ** KEPT (pick-wt=8): 3 [] -there_exists(A)|A!=B|e_quivalent(A,B).
% 1.97/2.15  ** KEPT (pick-wt=5): 4 [] -there_exists(domain(A))|there_exists(A).
% 1.97/2.15  ** KEPT (pick-wt=5): 5 [] -there_exists(codomain(A))|there_exists(A).
% 1.97/2.15  ** KEPT (pick-wt=7): 6 [] -there_exists(compose(A,B))|there_exists(domain(A)).
% 1.97/2.15  ** KEPT (pick-wt=9): 7 [] -there_exists(compose(A,B))|domain(A)=codomain(B).
% 1.97/2.15  ** KEPT (pick-wt=12): 8 [] -there_exists(domain(A))|domain(A)!=codomain(B)|there_exists(compose(A,B)).
% 1.97/2.15  ** KEPT (pick-wt=5): 9 [] -e_quivalent(A,B)|there_exists(B).
% 1.97/2.15    Following clause subsumed by 3 during input processing: 0 [] -there_exists(A)| -there_exists(B)|A!=B|e_quivalent(A,B).
% 1.97/2.15  ** KEPT (pick-wt=7): 10 [] -there_exists(compose(A,B))|there_exists(codomain(A)).
% 1.97/2.15  ** KEPT (pick-wt=13): 12 [copy,11,flip.1,flip.2] f1(A,B)!=A|f1(A,B)!=B|A=B.
% 1.97/2.15  ** KEPT (pick-wt=6): 13 [] domain(domain(a))!=domain(a).
% 1.97/2.15  
% 1.97/2.15  ------------> process sos:
% 1.97/2.15  ** KEPT (pick-wt=3): 15 [] A=A.
% 1.97/2.15  ** KEPT (pick-wt=11): 17 [copy,16,flip.1] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.97/2.15  ---> New Demodulator: 18 [new_demod,17] compose(compose(A,B),C)=compose(A,compose(B,C)).
% 1.97/2.15  ** KEPT (pick-wt=6): 19 [] compose(A,domain(A))=A.
% 1.97/2.15  ---> New Demodulator: 20 [new_demod,19] compose(A,domain(A))=A.
% 1.97/2.15  ** KEPT (pick-wt=6): 21 [] compose(codomain(A),A)=A.
% 1.97/2.15  ---> New Demodulator: 22 [new_demod,21] compose(codomain(A),A)=A.
% 1.97/2.15  ** KEPT (pick-wt=7): 23 [] there_exists(f1(A,B))|A=B.
% 1.97/2.15  ** KEPT (pick-wt=13): 25 [copy,24,flip.1,flip.2] f1(A,B)=A|f1(A,B)=B|A=B.
% 1.97/2.15  ** KEPT (pick-wt=3): 26 [] there_exists(domain(a)).
% 1.97/2.15    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.97/2.15  15 back subsumes 14.
% 1.97/2.15  >>>> Starting back demodulation with 18.
% 1.97/2.15  >>>> Starting back demodulation with 20.
% 2.44/2.61  >>>> Starting back demodulation with 22.
% 2.44/2.61  
% 2.44/2.61  ======= end of input processing =======
% 2.44/2.61  
% 2.44/2.61  =========== start of search ===========
% 2.44/2.61  
% 2.44/2.61  
% 2.44/2.61  Resetting weight limit to 8.
% 2.44/2.61  
% 2.44/2.61  
% 2.44/2.61  Resetting weight limit to 8.
% 2.44/2.61  
% 2.44/2.61  sos_size=2030
% 2.44/2.61  
% 2.44/2.61  -------- PROOF -------- 
% 2.44/2.61  
% 2.44/2.61  ----> UNIT CONFLICT at   0.45 sec ----> 2379 [binary,2377.1,13.1] $F.
% 2.44/2.61  
% 2.44/2.61  Length of proof is 8.  Level of proof is 5.
% 2.44/2.61  
% 2.44/2.61  ---------------- PROOF ----------------
% 2.44/2.61  % SZS status Unsatisfiable
% 2.44/2.61  % SZS output start Refutation
% See solution above
% 2.44/2.61  ------------ end of proof -------------
% 2.44/2.61  
% 2.44/2.61  
% 2.44/2.61  Search stopped by max_proofs option.
% 2.44/2.61  
% 2.44/2.61  
% 2.44/2.61  Search stopped by max_proofs option.
% 2.44/2.61  
% 2.44/2.61  ============ end of search ============
% 2.44/2.61  
% 2.44/2.61  -------------- statistics -------------
% 2.44/2.61  clauses given                154
% 2.44/2.61  clauses generated           7514
% 2.44/2.61  clauses kept                2360
% 2.44/2.61  clauses forward subsumed    2086
% 2.44/2.61  clauses back subsumed          4
% 2.44/2.61  Kbytes malloced             4882
% 2.44/2.61  
% 2.44/2.61  ----------- times (seconds) -----------
% 2.44/2.61  user CPU time          0.45          (0 hr, 0 min, 0 sec)
% 2.44/2.61  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 2.44/2.61  wall-clock time        3             (0 hr, 0 min, 3 sec)
% 2.44/2.61  
% 2.44/2.61  That finishes the proof of the theorem.
% 2.44/2.61  
% 2.44/2.61  Process 23816 finished Wed Jul 27 01:56:41 2022
% 2.44/2.61  Otter interrupted
% 2.44/2.61  PROOF FOUND
%------------------------------------------------------------------------------