## TSTP Solution File: GRP125-1.003 by Otter---3.3

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n011.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 12:56:10 EDT 2022

% Result   : Unsatisfiable 1.96s 2.14s
% Output   : Refutation 1.96s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   20 (  11 unt;   5 nHn;  19 RR)
%            Number of literals    :   38 (   0 equ;  13 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   19 (   0 sgn)

%------------------------------------------------------------------------------
cnf(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP125-1.003.p',unknown),
[] ).

cnf(3,axiom,
~ e_qualish(e_2,e_1),
file('GRP125-1.003.p',unknown),
[] ).

cnf(5,axiom,
~ e_qualish(e_3,e_1),
file('GRP125-1.003.p',unknown),
[] ).

cnf(7,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
file('GRP125-1.003.p',unknown),
[] ).

cnf(17,axiom,
group_element(e_1),
file('GRP125-1.003.p',unknown),
[] ).

cnf(18,axiom,
group_element(e_2),
file('GRP125-1.003.p',unknown),
[] ).

cnf(20,axiom,
product(A,A,A),
file('GRP125-1.003.p',unknown),
[] ).

cnf(21,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(hyper,[status(thm)],[18,7,17]),
[iquote('hyper,18,7,17')] ).

cnf(22,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(hyper,[status(thm)],[18,7,17]),
[iquote('hyper,18,7,17')] ).

cnf(28,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[21,9,20]),1]),
[iquote('hyper,21,9,20,unit_del,1')] ).

cnf(30,plain,
product(e_1,e_2,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,10,20]),3]),
[iquote('hyper,28,10,20,unit_del,3')] ).

cnf(33,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[22,10,20]),1]),
[iquote('hyper,22,10,20,unit_del,1')] ).

cnf(41,plain,
product(e_2,e_1,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[33,9,20]),3]),
[iquote('hyper,33,9,20,unit_del,3')] ).

cnf(46,plain,
product(e_3,e_3,e_1),
inference(hyper,[status(thm)],[41,11,30]),
[iquote('hyper,41,11,30')] ).

cnf(51,plain,
e_qualish(e_3,e_1),
inference(hyper,[status(thm)],[46,8,20]),
[iquote('hyper,46,8,20')] ).

cnf(52,plain,
\$false,
inference(binary,[status(thm)],[51,5]),
[iquote('binary,51.1,5.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.00/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n011.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 05:13:55 EDT 2022
% 0.12/0.33  % CPUTime  :
% 1.96/2.14  ----- Otter 3.3f, August 2004 -----
% 1.96/2.14  The process was started by sandbox2 on n011.cluster.edu,
% 1.96/2.14  Wed Jul 27 05:13:55 2022
% 1.96/2.14  The command was "./otter".  The process ID is 7465.
% 1.96/2.14
% 1.96/2.14  set(prolog_style_variables).
% 1.96/2.14  set(auto).
% 1.96/2.14     dependent: set(auto1).
% 1.96/2.14     dependent: set(process_input).
% 1.96/2.14     dependent: clear(print_kept).
% 1.96/2.14     dependent: clear(print_new_demod).
% 1.96/2.14     dependent: clear(print_back_demod).
% 1.96/2.14     dependent: clear(print_back_sub).
% 1.96/2.14     dependent: set(control_memory).
% 1.96/2.14     dependent: assign(max_mem, 12000).
% 1.96/2.14     dependent: assign(pick_given_ratio, 4).
% 1.96/2.14     dependent: assign(stats_level, 1).
% 1.96/2.14     dependent: assign(max_seconds, 10800).
% 1.96/2.14  clear(print_given).
% 1.96/2.14
% 1.96/2.14  list(usable).
% 1.96/2.14  0 [] group_element(e_1).
% 1.96/2.14  0 [] group_element(e_2).
% 1.96/2.14  0 [] group_element(e_3).
% 1.96/2.14  0 [] -e_qualish(e_1,e_2).
% 1.96/2.14  0 [] -e_qualish(e_1,e_3).
% 1.96/2.14  0 [] -e_qualish(e_2,e_1).
% 1.96/2.14  0 [] -e_qualish(e_2,e_3).
% 1.96/2.14  0 [] -e_qualish(e_3,e_1).
% 1.96/2.14  0 [] -e_qualish(e_3,e_2).
% 1.96/2.14  0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.96/2.14  0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.96/2.14  0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.96/2.14  0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.96/2.14  0 [] product(X,X,X).
% 1.96/2.14  0 [] -product(X,Y,Z1)| -product(Y,X,Z2)|product(Z1,Z2,X).
% 1.96/2.14  end_of_list.
% 1.96/2.14
% 1.96/2.14  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.96/2.14
% 1.96/2.14  This is a non-Horn set without equality.  The strategy will
% 1.96/2.14  be ordered hyper_res, unit deletion, and factoring, with
% 1.96/2.14  satellites in sos and with nuclei in usable.
% 1.96/2.14
% 1.96/2.14     dependent: set(hyper_res).
% 1.96/2.14     dependent: set(factor).
% 1.96/2.14     dependent: set(unit_deletion).
% 1.96/2.14
% 1.96/2.14  ------------> process usable:
% 1.96/2.14  ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 1.96/2.14  ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_3).
% 1.96/2.14  ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.96/2.14  ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_3).
% 1.96/2.14  ** KEPT (pick-wt=3): 5 [] -e_qualish(e_3,e_1).
% 1.96/2.14  ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_2).
% 1.96/2.14  ** KEPT (pick-wt=16): 7 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 1.96/2.14  ** KEPT (pick-wt=11): 8 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.96/2.14  ** KEPT (pick-wt=11): 9 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.96/2.14  ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.96/2.14  ** KEPT (pick-wt=12): 11 [] -product(A,B,C)| -product(B,A,D)|product(C,D,A).
% 1.96/2.14
% 1.96/2.14  ------------> process sos:
% 1.96/2.14  ** KEPT (pick-wt=2): 17 [] group_element(e_1).
% 1.96/2.14  ** KEPT (pick-wt=2): 18 [] group_element(e_2).
% 1.96/2.14  ** KEPT (pick-wt=2): 19 [] group_element(e_3).
% 1.96/2.14  ** KEPT (pick-wt=4): 20 [] product(A,A,A).
% 1.96/2.14
% 1.96/2.14  ======= end of input processing =======
% 1.96/2.14
% 1.96/2.14  =========== start of search ===========
% 1.96/2.14
% 1.96/2.14  -------- PROOF --------
% 1.96/2.14
% 1.96/2.14  ----> UNIT CONFLICT at   0.00 sec ----> 52 [binary,51.1,5.1] \$F.
% 1.96/2.14
% 1.96/2.14  Length of proof is 8.  Level of proof is 5.
% 1.96/2.14
% 1.96/2.14  ---------------- PROOF ----------------
% 1.96/2.14  % SZS status Unsatisfiable
% 1.96/2.14  % SZS output start Refutation
% See solution above
% 1.96/2.14  ------------ end of proof -------------
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14  Search stopped by max_proofs option.
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14  Search stopped by max_proofs option.
% 1.96/2.14
% 1.96/2.14  ============ end of search ============
% 1.96/2.14
% 1.96/2.14  -------------- statistics -------------
% 1.96/2.14  clauses given                 13
% 1.96/2.14  clauses generated            205
% 1.96/2.14  clauses kept                  51
% 1.96/2.14  clauses forward subsumed     169
% 1.96/2.14  clauses back subsumed         20
% 1.96/2.14  Kbytes malloced              976
% 1.96/2.14
% 1.96/2.14  ----------- times (seconds) -----------
% 1.96/2.14  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.96/2.14  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.96/2.14  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.96/2.14
% 1.96/2.14  That finishes the proof of the theorem.
% 1.96/2.14
% 1.96/2.14  Process 7465 finished Wed Jul 27 05:13:57 2022
% 1.96/2.14  Otter interrupted
% 1.96/2.14  PROOF FOUND
%------------------------------------------------------------------------------
```