TSTP Solution File: ALG201+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n019.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 12:46:17 EDT 2022

% Result   : Theorem 1.77s 1.97s
% Output   : Refutation 1.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   12 (   4 equ;   5 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   :    4 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ( ~ sorti1(A)
    | op1(A,A) != A ),
    file('ALG201+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sorti2(A)
    | sorti1(j(A)) ),
    file('ALG201+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ sorti2(A)
    | ~ sorti2(B)
    | j(op2(A,B)) = op1(j(A),j(B)) ),
    file('ALG201+1.p',unknown),
    [] ).

cnf(11,axiom,
    sorti2(dollar_c1),
    file('ALG201+1.p',unknown),
    [] ).

cnf(13,axiom,
    op2(dollar_c1,dollar_c1) = dollar_c1,
    file('ALG201+1.p',unknown),
    [] ).

cnf(16,plain,
    op1(j(dollar_c1),j(dollar_c1)) = j(dollar_c1),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[11,7,11]),13])]),
    [iquote('hyper,11,7,11,demod,13,flip.1')] ).

cnf(18,plain,
    sorti1(j(dollar_c1)),
    inference(hyper,[status(thm)],[11,5]),
    [iquote('hyper,11,5')] ).

cnf(19,plain,
    $false,
    inference(hyper,[status(thm)],[16,3,18]),
    [iquote('hyper,16,3,18')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 03:48:52 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.77/1.97  ----- Otter 3.3f, August 2004 -----
% 1.77/1.97  The process was started by sandbox on n019.cluster.edu,
% 1.77/1.97  Wed Jul 27 03:48:52 2022
% 1.77/1.97  The command was "./otter".  The process ID is 22478.
% 1.77/1.97  
% 1.77/1.97  set(prolog_style_variables).
% 1.77/1.97  set(auto).
% 1.77/1.97     dependent: set(auto1).
% 1.77/1.97     dependent: set(process_input).
% 1.77/1.97     dependent: clear(print_kept).
% 1.77/1.97     dependent: clear(print_new_demod).
% 1.77/1.97     dependent: clear(print_back_demod).
% 1.77/1.97     dependent: clear(print_back_sub).
% 1.77/1.97     dependent: set(control_memory).
% 1.77/1.97     dependent: assign(max_mem, 12000).
% 1.77/1.97     dependent: assign(pick_given_ratio, 4).
% 1.77/1.97     dependent: assign(stats_level, 1).
% 1.77/1.97     dependent: assign(max_seconds, 10800).
% 1.77/1.97  clear(print_given).
% 1.77/1.97  
% 1.77/1.97  formula_list(usable).
% 1.77/1.97  all A (A=A).
% 1.77/1.97  all U (sorti1(U)-> (all V (sorti1(V)->sorti1(op1(U,V))))).
% 1.77/1.97  all U (sorti2(U)-> (all V (sorti2(V)->sorti2(op2(U,V))))).
% 1.77/1.97  all U (sorti1(U)->op1(U,U)!=U).
% 1.77/1.97  -(all U (sorti2(U)->op2(U,U)!=U)).
% 1.77/1.97  -((all U (sorti1(U)->sorti2(h(U))))& (all V (sorti2(V)->sorti1(j(V))))-> -((all W (sorti1(W)-> (all X (sorti1(X)->h(op1(W,X))=op2(h(W),h(X))))))& (all Y (sorti2(Y)-> (all Z (sorti2(Z)->j(op2(Y,Z))=op1(j(Y),j(Z))))))& (all X1 (sorti2(X1)->h(j(X1))=X1))& (all X2 (sorti1(X2)->j(h(X2))=X2)))).
% 1.77/1.97  end_of_list.
% 1.77/1.97  
% 1.77/1.97  -------> usable clausifies to:
% 1.77/1.97  
% 1.77/1.97  list(usable).
% 1.77/1.97  0 [] A=A.
% 1.77/1.97  0 [] -sorti1(U)| -sorti1(V)|sorti1(op1(U,V)).
% 1.77/1.97  0 [] -sorti2(U)| -sorti2(V)|sorti2(op2(U,V)).
% 1.77/1.97  0 [] -sorti1(U)|op1(U,U)!=U.
% 1.77/1.97  0 [] sorti2($c1).
% 1.77/1.97  0 [] op2($c1,$c1)=$c1.
% 1.77/1.97  0 [] -sorti1(U)|sorti2(h(U)).
% 1.77/1.97  0 [] -sorti2(V)|sorti1(j(V)).
% 1.77/1.97  0 [] -sorti1(W)| -sorti1(X)|h(op1(W,X))=op2(h(W),h(X)).
% 1.77/1.97  0 [] -sorti2(Y)| -sorti2(Z)|j(op2(Y,Z))=op1(j(Y),j(Z)).
% 1.77/1.97  0 [] -sorti2(X1)|h(j(X1))=X1.
% 1.77/1.97  0 [] -sorti1(X2)|j(h(X2))=X2.
% 1.77/1.97  end_of_list.
% 1.77/1.97  
% 1.77/1.97  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.77/1.97  
% 1.77/1.97  This is a Horn set with equality.  The strategy will be
% 1.77/1.97  Knuth-Bendix and hyper_res, with positive clauses in
% 1.77/1.97  sos and nonpositive clauses in usable.
% 1.77/1.97  
% 1.77/1.97     dependent: set(knuth_bendix).
% 1.77/1.97     dependent: set(anl_eq).
% 1.77/1.97     dependent: set(para_from).
% 1.77/1.97     dependent: set(para_into).
% 1.77/1.97     dependent: clear(para_from_right).
% 1.77/1.97     dependent: clear(para_into_right).
% 1.77/1.97     dependent: set(para_from_vars).
% 1.77/1.97     dependent: set(eq_units_both_ways).
% 1.77/1.97     dependent: set(dynamic_demod_all).
% 1.77/1.97     dependent: set(dynamic_demod).
% 1.77/1.97     dependent: set(order_eq).
% 1.77/1.97     dependent: set(back_demod).
% 1.77/1.97     dependent: set(lrpo).
% 1.77/1.97     dependent: set(hyper_res).
% 1.77/1.97     dependent: clear(order_hyper).
% 1.77/1.97  
% 1.77/1.97  ------------> process usable:
% 1.77/1.97  ** KEPT (pick-wt=8): 1 [] -sorti1(A)| -sorti1(B)|sorti1(op1(A,B)).
% 1.77/1.97  ** KEPT (pick-wt=8): 2 [] -sorti2(A)| -sorti2(B)|sorti2(op2(A,B)).
% 1.77/1.97  ** KEPT (pick-wt=7): 3 [] -sorti1(A)|op1(A,A)!=A.
% 1.77/1.97  ** KEPT (pick-wt=5): 4 [] -sorti1(A)|sorti2(h(A)).
% 1.77/1.97  ** KEPT (pick-wt=5): 5 [] -sorti2(A)|sorti1(j(A)).
% 1.77/1.97  ** KEPT (pick-wt=14): 6 [] -sorti1(A)| -sorti1(B)|h(op1(A,B))=op2(h(A),h(B)).
% 1.77/1.97  ** KEPT (pick-wt=14): 7 [] -sorti2(A)| -sorti2(B)|j(op2(A,B))=op1(j(A),j(B)).
% 1.77/1.97  ** KEPT (pick-wt=7): 8 [] -sorti2(A)|h(j(A))=A.
% 1.77/1.97  ** KEPT (pick-wt=7): 9 [] -sorti1(A)|j(h(A))=A.
% 1.77/1.97  
% 1.77/1.97  ------------> process sos:
% 1.77/1.97  ** KEPT (pick-wt=3): 10 [] A=A.
% 1.77/1.97  ** KEPT (pick-wt=2): 11 [] sorti2($c1).
% 1.77/1.97  ** KEPT (pick-wt=5): 12 [] op2($c1,$c1)=$c1.
% 1.77/1.97  ---> New Demodulator: 13 [new_demod,12] op2($c1,$c1)=$c1.
% 1.77/1.97    Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.77/1.97  >>>> Starting back demodulation with 13.
% 1.77/1.97  
% 1.77/1.97  ======= end of input processing =======
% 1.77/1.97  
% 1.77/1.97  =========== start of search ===========
% 1.77/1.97  
% 1.77/1.97  -------- PROOF -------- 
% 1.77/1.97  
% 1.77/1.97  -----> EMPTY CLAUSE at   0.00 sec ----> 19 [hyper,16,3,18] $F.
% 1.77/1.97  
% 1.77/1.97  Length of proof is 2.  Level of proof is 1.
% 1.77/1.97  
% 1.77/1.97  ---------------- PROOF ----------------
% 1.77/1.97  % SZS status Theorem
% 1.77/1.97  % SZS output start Refutation
% See solution above
% 1.77/1.97  ------------ end of proof -------------
% 1.77/1.97  
% 1.77/1.97  
% 1.77/1.97  Search stopped by max_proofs option.
% 1.77/1.97  
% 1.77/1.97  
% 1.77/1.97  Search stopped by max_proofs option.
% 1.77/1.97  
% 1.77/1.97  ============ end of search ============
% 1.77/1.97  
% 1.77/1.97  -------------- statistics -------------
% 1.77/1.97  clauses given                  6
% 1.77/1.97  clauses generated             23
% 1.77/1.97  clauses kept                  15
% 1.77/1.97  clauses forward subsumed      19
% 1.77/1.97  clauses back subsumed          0
% 1.77/1.97  Kbytes malloced              976
% 1.77/1.97  
% 1.77/1.97  ----------- times (seconds) -----------
% 1.77/1.97  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.77/1.97  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.77/1.97  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.77/1.97  
% 1.77/1.97  That finishes the proof of the theorem.
% 1.77/1.97  
% 1.77/1.97  Process 22478 finished Wed Jul 27 03:48:53 2022
% 1.77/1.97  Otter interrupted
% 1.77/1.97  PROOF FOUND
%------------------------------------------------------------------------------