TSTP Solution File: SYN986+1.003 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN986+1.003 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n014.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 13:25:37 EDT 2022

% Result   : Theorem 1.65s 1.83s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   3 RR)
%            Number of literals    :   13 (   0 equ;   6 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :   17 (   4 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   13 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ r(A,B,C)
    | ~ r(C,B,D)
    | r(A,succ(B),D) ),
    file('SYN986+1.003.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ r(zero,zero,A)
    | ~ r(zero,A,B)
    | ~ r(zero,B,C)
    | ~ r(zero,C,D) ),
    file('SYN986+1.003.p',unknown),
    [] ).

cnf(3,axiom,
    r(A,zero,succ(A)),
    file('SYN986+1.003.p',unknown),
    [] ).

cnf(4,plain,
    r(A,succ(zero),succ(succ(A))),
    inference(hyper,[status(thm)],[3,1,3]),
    [iquote('hyper,3,1,3')] ).

cnf(5,plain,
    r(A,succ(succ(zero)),succ(succ(succ(succ(A))))),
    inference(hyper,[status(thm)],[4,1,4]),
    [iquote('hyper,4,1,4')] ).

cnf(6,plain,
    r(A,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(A))))))))),
    inference(hyper,[status(thm)],[5,1,5]),
    [iquote('hyper,5,1,5')] ).

cnf(7,plain,
    r(A,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(A))))))))))))))))),
    inference(hyper,[status(thm)],[6,1,6]),
    [iquote('hyper,6,1,6')] ).

cnf(8,plain,
    $false,
    inference(hyper,[status(thm)],[7,2,3,4,5]),
    [iquote('hyper,7,2,3,4,5')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN986+1.003 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14  % Command  : otter-tptp-script %s
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Jul 27 11:03:24 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.65/1.83  ----- Otter 3.3f, August 2004 -----
% 1.65/1.83  The process was started by sandbox on n014.cluster.edu,
% 1.65/1.83  Wed Jul 27 11:03:24 2022
% 1.65/1.83  The command was "./otter".  The process ID is 15351.
% 1.65/1.83  
% 1.65/1.83  set(prolog_style_variables).
% 1.65/1.83  set(auto).
% 1.65/1.83     dependent: set(auto1).
% 1.65/1.83     dependent: set(process_input).
% 1.65/1.83     dependent: clear(print_kept).
% 1.65/1.83     dependent: clear(print_new_demod).
% 1.65/1.83     dependent: clear(print_back_demod).
% 1.65/1.83     dependent: clear(print_back_sub).
% 1.65/1.83     dependent: set(control_memory).
% 1.65/1.83     dependent: assign(max_mem, 12000).
% 1.65/1.83     dependent: assign(pick_given_ratio, 4).
% 1.65/1.83     dependent: assign(stats_level, 1).
% 1.65/1.83     dependent: assign(max_seconds, 10800).
% 1.65/1.83  clear(print_given).
% 1.65/1.83  
% 1.65/1.83  formula_list(usable).
% 1.65/1.83  all Y r(Y,zero,succ(Y)).
% 1.65/1.83  all Y X Z Z1 (r(Y,X,Z)-> (r(Z,X,Z1)->r(Y,succ(X),Z1))).
% 1.65/1.83  -(exists Z3 Z2 Z1 Z0 (r(zero,zero,Z3)&r(zero,Z3,Z2)&r(zero,Z2,Z1)&r(zero,Z1,Z0))).
% 1.65/1.83  end_of_list.
% 1.65/1.83  
% 1.65/1.83  -------> usable clausifies to:
% 1.65/1.83  
% 1.65/1.83  list(usable).
% 1.65/1.83  0 [] r(Y,zero,succ(Y)).
% 1.65/1.83  0 [] -r(Y,X,Z)| -r(Z,X,Z1)|r(Y,succ(X),Z1).
% 1.65/1.83  0 [] -r(zero,zero,Z3)| -r(zero,Z3,Z2)| -r(zero,Z2,Z1)| -r(zero,Z1,Z0).
% 1.65/1.83  end_of_list.
% 1.65/1.83  
% 1.65/1.83  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.65/1.83  
% 1.65/1.83  This is a Horn set without equality.  The strategy will
% 1.65/1.83  be hyperresolution, with satellites in sos and nuclei
% 1.65/1.83  in usable.
% 1.65/1.83  
% 1.65/1.83     dependent: set(hyper_res).
% 1.65/1.83     dependent: clear(order_hyper).
% 1.65/1.83  
% 1.65/1.83  ------------> process usable:
% 1.65/1.83  ** KEPT (pick-wt=13): 1 [] -r(A,B,C)| -r(C,B,D)|r(A,succ(B),D).
% 1.65/1.83  ** KEPT (pick-wt=16): 2 [] -r(zero,zero,A)| -r(zero,A,B)| -r(zero,B,C)| -r(zero,C,D).
% 1.65/1.83  
% 1.65/1.83  ------------> process sos:
% 1.65/1.83  ** KEPT (pick-wt=5): 3 [] r(A,zero,succ(A)).
% 1.65/1.83  
% 1.65/1.83  ======= end of input processing =======
% 1.65/1.83  
% 1.65/1.83  =========== start of search ===========
% 1.65/1.83  
% 1.65/1.83  -------- PROOF -------- 
% 1.65/1.83  
% 1.65/1.83  -----> EMPTY CLAUSE at   0.00 sec ----> 8 [hyper,7,2,3,4,5] $F.
% 1.65/1.83  
% 1.65/1.83  Length of proof is 4.  Level of proof is 4.
% 1.65/1.83  
% 1.65/1.83  ---------------- PROOF ----------------
% 1.65/1.83  % SZS status Theorem
% 1.65/1.83  % SZS output start Refutation
% See solution above
% 1.65/1.83  ------------ end of proof -------------
% 1.65/1.83  
% 1.65/1.83  
% 1.65/1.83  Search stopped by max_proofs option.
% 1.65/1.83  
% 1.65/1.83  
% 1.65/1.83  Search stopped by max_proofs option.
% 1.65/1.83  
% 1.65/1.83  ============ end of search ============
% 1.65/1.83  
% 1.65/1.83  -------------- statistics -------------
% 1.65/1.83  clauses given                  5
% 1.65/1.83  clauses generated              9
% 1.65/1.83  clauses kept                   7
% 1.65/1.83  clauses forward subsumed       4
% 1.65/1.83  clauses back subsumed          0
% 1.65/1.83  Kbytes malloced              976
% 1.65/1.83  
% 1.65/1.83  ----------- times (seconds) -----------
% 1.65/1.83  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.65/1.83  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.65/1.83  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.65/1.83  
% 1.65/1.83  That finishes the proof of the theorem.
% 1.65/1.83  
% 1.65/1.83  Process 15351 finished Wed Jul 27 11:03:25 2022
% 1.65/1.83  Otter interrupted
% 1.65/1.83  PROOF FOUND
%------------------------------------------------------------------------------