## TSTP Solution File: SEU163+1 by Otter---3.3

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU163+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n021.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 13:15:00 EDT 2022

% Result   : Theorem 1.74s 1.94s
% Output   : Refutation 1.74s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   5 RR)
%            Number of literals    :    6 (   0 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    2 (   0 sgn)

%------------------------------------------------------------------------------
cnf(2,axiom,
~ subset(dollar_c2,union(dollar_c1)),
file('SEU163+1.p',unknown),
[] ).

cnf(3,axiom,
( ~ in(A,B)
| subset(A,union(B)) ),
file('SEU163+1.p',unknown),
[] ).

cnf(5,axiom,
in(dollar_c2,dollar_c1),
file('SEU163+1.p',unknown),
[] ).

cnf(6,plain,
subset(dollar_c2,union(dollar_c1)),
inference(hyper,[status(thm)],[5,3]),
[iquote('hyper,5,3')] ).

cnf(7,plain,
\$false,
inference(binary,[status(thm)],[6,2]),
[iquote('binary,6.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEU163+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14  % Command  : otter-tptp-script %s
% 0.13/0.35  % Computer : n021.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 07:29:23 EDT 2022
% 0.13/0.35  % CPUTime  :
% 1.74/1.94  ----- Otter 3.3f, August 2004 -----
% 1.74/1.94  The process was started by sandbox on n021.cluster.edu,
% 1.74/1.94  Wed Jul 27 07:29:23 2022
% 1.74/1.94  The command was "./otter".  The process ID is 14060.
% 1.74/1.94
% 1.74/1.94  set(prolog_style_variables).
% 1.74/1.94  set(auto).
% 1.74/1.94     dependent: set(auto1).
% 1.74/1.94     dependent: set(process_input).
% 1.74/1.94     dependent: clear(print_kept).
% 1.74/1.94     dependent: clear(print_new_demod).
% 1.74/1.94     dependent: clear(print_back_demod).
% 1.74/1.94     dependent: clear(print_back_sub).
% 1.74/1.94     dependent: set(control_memory).
% 1.74/1.94     dependent: assign(max_mem, 12000).
% 1.74/1.94     dependent: assign(pick_given_ratio, 4).
% 1.74/1.94     dependent: assign(stats_level, 1).
% 1.74/1.94     dependent: assign(max_seconds, 10800).
% 1.74/1.94  clear(print_given).
% 1.74/1.94
% 1.74/1.94  formula_list(usable).
% 1.74/1.94  all A B subset(A,A).
% 1.74/1.94  all A B (in(A,B)-> -in(B,A)).
% 1.74/1.94  \$T.
% 1.74/1.94  -(all A B (in(A,B)->subset(A,union(B)))).
% 1.74/1.94  all A B (in(A,B)->subset(A,union(B))).
% 1.74/1.94  end_of_list.
% 1.74/1.94
% 1.74/1.94  -------> usable clausifies to:
% 1.74/1.94
% 1.74/1.94  list(usable).
% 1.74/1.94  0 [] subset(A,A).
% 1.74/1.94  0 [] -in(A,B)| -in(B,A).
% 1.74/1.94  0 [] \$T.
% 1.74/1.94  0 [] in(\$c2,\$c1).
% 1.74/1.94  0 [] -subset(\$c2,union(\$c1)).
% 1.74/1.94  0 [] -in(A,B)|subset(A,union(B)).
% 1.74/1.94  end_of_list.
% 1.74/1.94
% 1.74/1.94  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=2.
% 1.74/1.94
% 1.74/1.94  This is a Horn set without equality.  The strategy will
% 1.74/1.94  be hyperresolution, with satellites in sos and nuclei
% 1.74/1.94  in usable.
% 1.74/1.94
% 1.74/1.94     dependent: set(hyper_res).
% 1.74/1.94     dependent: clear(order_hyper).
% 1.74/1.94
% 1.74/1.94  ------------> process usable:
% 1.74/1.94  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.74/1.94  ** KEPT (pick-wt=4): 2 [] -subset(\$c2,union(\$c1)).
% 1.74/1.94  ** KEPT (pick-wt=7): 3 [] -in(A,B)|subset(A,union(B)).
% 1.74/1.94
% 1.74/1.94  ------------> process sos:
% 1.74/1.94  ** KEPT (pick-wt=3): 4 [] subset(A,A).
% 1.74/1.94  ** KEPT (pick-wt=3): 5 [] in(\$c2,\$c1).
% 1.74/1.94
% 1.74/1.94  ======= end of input processing =======
% 1.74/1.94
% 1.74/1.94  =========== start of search ===========
% 1.74/1.94
% 1.74/1.94  -------- PROOF --------
% 1.74/1.94
% 1.74/1.94  ----> UNIT CONFLICT at   0.00 sec ----> 7 [binary,6.1,2.1] \$F.
% 1.74/1.94
% 1.74/1.94  Length of proof is 1.  Level of proof is 1.
% 1.74/1.94
% 1.74/1.94  ---------------- PROOF ----------------
% 1.74/1.94  % SZS status Theorem
% 1.74/1.94  % SZS output start Refutation
% See solution above
% 1.74/1.94  ------------ end of proof -------------
% 1.74/1.94
% 1.74/1.94
% 1.74/1.94  Search stopped by max_proofs option.
% 1.74/1.94
% 1.74/1.94
% 1.74/1.94  Search stopped by max_proofs option.
% 1.74/1.94
% 1.74/1.94  ============ end of search ============
% 1.74/1.94
% 1.74/1.94  -------------- statistics -------------
% 1.74/1.94  clauses given                  2
% 1.74/1.94  clauses generated              1
% 1.74/1.94  clauses kept                   6
% 1.74/1.94  clauses forward subsumed       0
% 1.74/1.94  clauses back subsumed          0
% 1.74/1.94  Kbytes malloced              976
% 1.74/1.94
% 1.74/1.94  ----------- times (seconds) -----------
% 1.74/1.94  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.74/1.94  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.74/1.94  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.74/1.94
% 1.74/1.94  That finishes the proof of the theorem.
% 1.74/1.94
% 1.74/1.94  Process 14060 finished Wed Jul 27 07:29:24 2022
% 1.74/1.94  Otter interrupted
% 1.74/1.95  PROOF FOUND
%------------------------------------------------------------------------------
```