## TSTP Solution File: LCL666+1.001 by Otter---3.3

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n022.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 13:04:59 EDT 2022

% Result   : Theorem 1.66s 1.87s
% Output   : Refutation 1.66s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    1
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   4 RR)
%            Number of literals    :    7 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :    2 (   0 sgn)

% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r1(dollar_c1,A)
| ~ p201(A)
| ~ p101(A) ),
file('LCL666+1.001.p',unknown),
[] ).

cnf(2,axiom,
r1(A,A),
file('LCL666+1.001.p',unknown),
[] ).

cnf(3,axiom,
p201(dollar_c1),
file('LCL666+1.001.p',unknown),
[] ).

cnf(4,axiom,
p101(dollar_c1),
file('LCL666+1.001.p',unknown),
[] ).

cnf(5,plain,
\$false,
inference(hyper,[status(thm)],[4,1,2,3]),
[iquote('hyper,4,1,2,3')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n022.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 09:31:05 EDT 2022
% 0.13/0.34  % CPUTime  :
% 1.66/1.87  ----- Otter 3.3f, August 2004 -----
% 1.66/1.87  The process was started by sandbox on n022.cluster.edu,
% 1.66/1.87  Wed Jul 27 09:31:05 2022
% 1.66/1.87  The command was "./otter".  The process ID is 13814.
% 1.66/1.87
% 1.66/1.87  set(prolog_style_variables).
% 1.66/1.87  set(auto).
% 1.66/1.87     dependent: set(auto1).
% 1.66/1.87     dependent: set(process_input).
% 1.66/1.87     dependent: clear(print_kept).
% 1.66/1.87     dependent: clear(print_new_demod).
% 1.66/1.87     dependent: clear(print_back_demod).
% 1.66/1.87     dependent: clear(print_back_sub).
% 1.66/1.87     dependent: set(control_memory).
% 1.66/1.87     dependent: assign(max_mem, 12000).
% 1.66/1.87     dependent: assign(pick_given_ratio, 4).
% 1.66/1.87     dependent: assign(stats_level, 1).
% 1.66/1.87     dependent: assign(max_seconds, 10800).
% 1.66/1.87  clear(print_given).
% 1.66/1.87
% 1.66/1.87  formula_list(usable).
% 1.66/1.87  all X r1(X,X).
% 1.66/1.87  -(-(exists X (-(-(all Y (-r1(X,Y)| -(p201(Y)&p101(Y))))| -(p201(X)&p101(X)))))).
% 1.66/1.87  end_of_list.
% 1.66/1.87
% 1.66/1.87  -------> usable clausifies to:
% 1.66/1.87
% 1.66/1.87  list(usable).
% 1.66/1.87  0 [] r1(X,X).
% 1.66/1.87  0 [] -r1(\$c1,Y)| -p201(Y)| -p101(Y).
% 1.66/1.87  0 [] p201(\$c1).
% 1.66/1.87  0 [] p101(\$c1).
% 1.66/1.87  end_of_list.
% 1.66/1.87
% 1.66/1.87  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.66/1.87
% 1.66/1.87  This is a Horn set without equality.  The strategy will
% 1.66/1.87  be hyperresolution, with satellites in sos and nuclei
% 1.66/1.87  in usable.
% 1.66/1.87
% 1.66/1.87     dependent: set(hyper_res).
% 1.66/1.87     dependent: clear(order_hyper).
% 1.66/1.87
% 1.66/1.87  ------------> process usable:
% 1.66/1.87  ** KEPT (pick-wt=7): 1 [] -r1(\$c1,A)| -p201(A)| -p101(A).
% 1.66/1.87
% 1.66/1.87  ------------> process sos:
% 1.66/1.87  ** KEPT (pick-wt=3): 2 [] r1(A,A).
% 1.66/1.87  ** KEPT (pick-wt=2): 3 [] p201(\$c1).
% 1.66/1.87  ** KEPT (pick-wt=2): 4 [] p101(\$c1).
% 1.66/1.87
% 1.66/1.87  ======= end of input processing =======
% 1.66/1.87
% 1.66/1.87  =========== start of search ===========
% 1.66/1.87
% 1.66/1.87  -------- PROOF --------
% 1.66/1.87
% 1.66/1.87  -----> EMPTY CLAUSE at   0.00 sec ----> 5 [hyper,4,1,2,3] \$F.
% 1.66/1.87
% 1.66/1.87  Length of proof is 0.  Level of proof is 0.
% 1.66/1.87
% 1.66/1.87  ---------------- PROOF ----------------
% 1.66/1.87  % SZS status Theorem
% 1.66/1.87  % SZS output start Refutation
% See solution above
% 1.66/1.87  ------------ end of proof -------------
% 1.66/1.87
% 1.66/1.87
% 1.66/1.87  Search stopped by max_proofs option.
% 1.66/1.87
% 1.66/1.87
% 1.66/1.87  Search stopped by max_proofs option.
% 1.66/1.87
% 1.66/1.87  ============ end of search ============
% 1.66/1.87
% 1.66/1.87  -------------- statistics -------------
% 1.66/1.87  clauses given                  3
% 1.66/1.87  clauses generated              1
% 1.66/1.87  clauses kept                   4
% 1.66/1.87  clauses forward subsumed       0
% 1.66/1.87  clauses back subsumed          0
% 1.66/1.87  Kbytes malloced              976
% 1.66/1.87
% 1.66/1.87  ----------- times (seconds) -----------
% 1.66/1.87  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.87  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.87  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.66/1.87
% 1.66/1.87  That finishes the proof of the theorem.
% 1.66/1.87
% 1.66/1.87  Process 13814 finished Wed Jul 27 09:31:07 2022
% 1.66/1.87  Otter interrupted
% 1.66/1.87  PROOF FOUND
%------------------------------------------------------------------------------
```