## TSTP Solution File: SYN969+1 by Otter---3.3

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 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 13:25:35 EDT 2022

% Result   : Theorem 1.59s 1.78s
% Output   : Refutation 1.59s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :    9 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :    2 (   0 sgn)

%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ p(A)
| q(A) ),
file('SYN969+1.p',unknown),
[] ).

cnf(2,axiom,
( ~ r(A)
| p(A) ),
file('SYN969+1.p',unknown),
[] ).

cnf(3,axiom,
~ q(dollar_c1),
file('SYN969+1.p',unknown),
[] ).

cnf(4,axiom,
r(dollar_c1),
file('SYN969+1.p',unknown),
[] ).

cnf(5,plain,
p(dollar_c1),
inference(hyper,[status(thm)],[4,2]),
[iquote('hyper,4,2')] ).

cnf(6,plain,
q(dollar_c1),
inference(hyper,[status(thm)],[5,1]),
[iquote('hyper,5,1')] ).

cnf(7,plain,
\$false,
inference(binary,[status(thm)],[6,3]),
[iquote('binary,6.1,3.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n019.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 11:00:52 EDT 2022
% 0.18/0.33  % CPUTime  :
% 1.59/1.78  ----- Otter 3.3f, August 2004 -----
% 1.59/1.78  The process was started by sandbox on n019.cluster.edu,
% 1.59/1.78  Wed Jul 27 11:00:52 2022
% 1.59/1.78  The command was "./otter".  The process ID is 14731.
% 1.59/1.78
% 1.59/1.78  set(prolog_style_variables).
% 1.59/1.78  set(auto).
% 1.59/1.78     dependent: set(auto1).
% 1.59/1.78     dependent: set(process_input).
% 1.59/1.78     dependent: clear(print_kept).
% 1.59/1.78     dependent: clear(print_new_demod).
% 1.59/1.78     dependent: clear(print_back_demod).
% 1.59/1.78     dependent: clear(print_back_sub).
% 1.59/1.78     dependent: set(control_memory).
% 1.59/1.78     dependent: assign(max_mem, 12000).
% 1.59/1.78     dependent: assign(pick_given_ratio, 4).
% 1.59/1.78     dependent: assign(stats_level, 1).
% 1.59/1.78     dependent: assign(max_seconds, 10800).
% 1.59/1.78  clear(print_given).
% 1.59/1.78
% 1.59/1.78  formula_list(usable).
% 1.59/1.78  -(all B ((all X (p(X)->q(X)))&r(B)-> ((all Y (r(Y)->p(Y)))->q(B)))).
% 1.59/1.78  end_of_list.
% 1.59/1.78
% 1.59/1.78  -------> usable clausifies to:
% 1.59/1.78
% 1.59/1.78  list(usable).
% 1.59/1.78  0 [] -p(X)|q(X).
% 1.59/1.78  0 [] r(\$c1).
% 1.59/1.78  0 [] -r(Y)|p(Y).
% 1.59/1.78  0 [] -q(\$c1).
% 1.59/1.78  end_of_list.
% 1.59/1.78
% 1.59/1.78  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=2.
% 1.59/1.78
% 1.59/1.78  This is a Horn set without equality.  The strategy will
% 1.59/1.78  be hyperresolution, with satellites in sos and nuclei
% 1.59/1.78  in usable.
% 1.59/1.78
% 1.59/1.78     dependent: set(hyper_res).
% 1.59/1.78     dependent: clear(order_hyper).
% 1.59/1.78
% 1.59/1.78  ------------> process usable:
% 1.59/1.78  ** KEPT (pick-wt=4): 1 [] -p(A)|q(A).
% 1.59/1.78  ** KEPT (pick-wt=4): 2 [] -r(A)|p(A).
% 1.59/1.78  ** KEPT (pick-wt=2): 3 [] -q(\$c1).
% 1.59/1.78
% 1.59/1.78  ------------> process sos:
% 1.59/1.78  ** KEPT (pick-wt=2): 4 [] r(\$c1).
% 1.59/1.78
% 1.59/1.78  ======= end of input processing =======
% 1.59/1.78
% 1.59/1.78  =========== start of search ===========
% 1.59/1.78
% 1.59/1.78  -------- PROOF --------
% 1.59/1.78
% 1.59/1.78  ----> UNIT CONFLICT at   0.00 sec ----> 7 [binary,6.1,3.1] \$F.
% 1.59/1.78
% 1.59/1.78  Length of proof is 2.  Level of proof is 2.
% 1.59/1.78
% 1.59/1.78  ---------------- PROOF ----------------
% 1.59/1.78  % SZS status Theorem
% 1.59/1.78  % SZS output start Refutation
% See solution above
% 1.59/1.78  ------------ end of proof -------------
% 1.59/1.78
% 1.59/1.78
% 1.59/1.78  Search stopped by max_proofs option.
% 1.59/1.78
% 1.59/1.78
% 1.59/1.78  Search stopped by max_proofs option.
% 1.59/1.78
% 1.59/1.78  ============ end of search ============
% 1.59/1.78
% 1.59/1.78  -------------- statistics -------------
% 1.59/1.78  clauses given                  2
% 1.59/1.78  clauses generated              2
% 1.59/1.78  clauses kept                   6
% 1.59/1.78  clauses forward subsumed       0
% 1.59/1.78  clauses back subsumed          0
% 1.59/1.78  Kbytes malloced              976
% 1.59/1.78
% 1.59/1.78  ----------- times (seconds) -----------
% 1.59/1.78  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.59/1.78  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.59/1.78  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.59/1.78
% 1.59/1.78  That finishes the proof of the theorem.
% 1.59/1.78
% 1.59/1.78  Process 14731 finished Wed Jul 27 11:00:53 2022
% 1.59/1.78  Otter interrupted
% 1.59/1.78  PROOF FOUND
%------------------------------------------------------------------------------
```