## TSTP Solution File: SYN721+1 by Otter---3.3

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n006.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 13:25:11 EDT 2022

% Result   : Theorem 1.78s 1.99s
% Output   : Refutation 1.78s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   4 unt;   0 nHn;   5 RR)
%            Number of literals    :   10 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :    7 (   4 sgn)

%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r(A,B)
| q(A,A) ),
file('SYN721+1.p',unknown),
[] ).

cnf(2,axiom,
( ~ q(A,B)
| r(C,B) ),
file('SYN721+1.p',unknown),
[] ).

cnf(3,axiom,
( ~ r(b,A)
| ~ q(A,a) ),
file('SYN721+1.p',unknown),
[] ).

cnf(4,axiom,
r(a,b),
file('SYN721+1.p',unknown),
[] ).

cnf(5,plain,
q(a,a),
inference(hyper,[status(thm)],[4,1]),
[iquote('hyper,4,1')] ).

cnf(6,plain,
r(A,a),
inference(hyper,[status(thm)],[5,2]),
[iquote('hyper,5,2')] ).

cnf(7,plain,
\$false,
inference(hyper,[status(thm)],[6,3,5]),
[iquote('hyper,6,3,5')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n006.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 11:09:46 EDT 2022
% 0.12/0.33  % CPUTime  :
% 1.78/1.99  ----- Otter 3.3f, August 2004 -----
% 1.78/1.99  The process was started by sandbox on n006.cluster.edu,
% 1.78/1.99  Wed Jul 27 11:09:47 2022
% 1.78/1.99  The command was "./otter".  The process ID is 3233.
% 1.78/1.99
% 1.78/1.99  set(prolog_style_variables).
% 1.78/1.99  set(auto).
% 1.78/1.99     dependent: set(auto1).
% 1.78/1.99     dependent: set(process_input).
% 1.78/1.99     dependent: clear(print_kept).
% 1.78/1.99     dependent: clear(print_new_demod).
% 1.78/1.99     dependent: clear(print_back_demod).
% 1.78/1.99     dependent: clear(print_back_sub).
% 1.78/1.99     dependent: set(control_memory).
% 1.78/1.99     dependent: assign(max_mem, 12000).
% 1.78/1.99     dependent: assign(pick_given_ratio, 4).
% 1.78/1.99     dependent: assign(stats_level, 1).
% 1.78/1.99     dependent: assign(max_seconds, 10800).
% 1.78/1.99  clear(print_given).
% 1.78/1.99
% 1.78/1.99  formula_list(usable).
% 1.78/1.99  -(r(a,b)& (all X ((exists Y r(X,Y))->q(X,X)))& (all U V (q(U,V)-> (all Z r(Z,V))))-> (exists W (r(b,W)&q(W,a)))).
% 1.78/1.99  end_of_list.
% 1.78/1.99
% 1.78/1.99  -------> usable clausifies to:
% 1.78/1.99
% 1.78/1.99  list(usable).
% 1.78/1.99  0 [] r(a,b).
% 1.78/1.99  0 [] -r(X,Y)|q(X,X).
% 1.78/1.99  0 [] -q(U,V)|r(Z,V).
% 1.78/1.99  0 [] -r(b,W)| -q(W,a).
% 1.78/1.99  end_of_list.
% 1.78/1.99
% 1.78/1.99  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=2.
% 1.78/1.99
% 1.78/1.99  This is a Horn set without equality.  The strategy will
% 1.78/1.99  be hyperresolution, with satellites in sos and nuclei
% 1.78/1.99  in usable.
% 1.78/1.99
% 1.78/1.99     dependent: set(hyper_res).
% 1.78/1.99     dependent: clear(order_hyper).
% 1.78/1.99
% 1.78/1.99  ------------> process usable:
% 1.78/1.99  ** KEPT (pick-wt=6): 1 [] -r(A,B)|q(A,A).
% 1.78/1.99  ** KEPT (pick-wt=6): 2 [] -q(A,B)|r(C,B).
% 1.78/1.99  ** KEPT (pick-wt=6): 3 [] -r(b,A)| -q(A,a).
% 1.78/1.99
% 1.78/1.99  ------------> process sos:
% 1.78/1.99  ** KEPT (pick-wt=3): 4 [] r(a,b).
% 1.78/1.99
% 1.78/1.99  ======= end of input processing =======
% 1.78/1.99
% 1.78/1.99  =========== start of search ===========
% 1.78/1.99
% 1.78/1.99  -------- PROOF --------
% 1.78/1.99
% 1.78/1.99  -----> EMPTY CLAUSE at   0.00 sec ----> 7 [hyper,6,3,5] \$F.
% 1.78/1.99
% 1.78/1.99  Length of proof is 2.  Level of proof is 2.
% 1.78/1.99
% 1.78/1.99  ---------------- PROOF ----------------
% 1.78/1.99  % SZS status Theorem
% 1.78/1.99  % SZS output start Refutation
% See solution above
% 1.78/1.99  ------------ end of proof -------------
% 1.78/1.99
% 1.78/1.99
% 1.78/1.99  Search stopped by max_proofs option.
% 1.78/1.99
% 1.78/1.99
% 1.78/1.99  Search stopped by max_proofs option.
% 1.78/1.99
% 1.78/1.99  ============ end of search ============
% 1.78/1.99
% 1.78/1.99  -------------- statistics -------------
% 1.78/1.99  clauses given                  3
% 1.78/1.99  clauses generated              3
% 1.78/1.99  clauses kept                   6
% 1.78/1.99  clauses forward subsumed       0
% 1.78/1.99  clauses back subsumed          0
% 1.78/1.99  Kbytes malloced              976
% 1.78/1.99
% 1.78/1.99  ----------- times (seconds) -----------
% 1.78/1.99  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.78/1.99  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.78/1.99  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.78/1.99
% 1.78/1.99  That finishes the proof of the theorem.
% 1.78/1.99
% 1.78/1.99  Process 3233 finished Wed Jul 27 11:09:48 2022
% 1.78/1.99  Otter interrupted
% 1.78/1.99  PROOF FOUND
%------------------------------------------------------------------------------
```