%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET044-5 : TPTP v8.1.0. Released v1.0.0.
% 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 13:12:55 EDT 2022
% Result : Unsatisfiable 1.90s 2.09s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 3 unt; 3 nHn; 6 RR)
% Number of literals : 15 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element(A,a)
| element(A,A) ),
file('SET044-5.p',unknown),
[] ).
cnf(2,axiom,
( ~ element(A,A)
| element(A,a) ),
file('SET044-5.p',unknown),
[] ).
cnf(3,axiom,
( ~ element(A,f(B))
| ~ element(A,B) ),
file('SET044-5.p',unknown),
[] ).
cnf(4,axiom,
( element(A,B)
| element(A,f(B)) ),
file('SET044-5.p',unknown),
[] ).
cnf(7,plain,
( element(A,f(a))
| element(A,A) ),
inference(hyper,[status(thm)],[4,1]),
[iquote('hyper,4,1')] ).
cnf(8,plain,
( element(f(A),A)
| element(f(A),a) ),
inference(hyper,[status(thm)],[4,2]),
[iquote('hyper,4,2')] ).
cnf(9,plain,
element(f(a),f(a)),
inference(factor,[status(thm)],[7]),
[iquote('factor,7.1.2')] ).
cnf(10,plain,
element(f(a),a),
inference(factor,[status(thm)],[8]),
[iquote('factor,8.1.2')] ).
cnf(13,plain,
$false,
inference(hyper,[status(thm)],[9,3,10]),
[iquote('hyper,9,3,10')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET044-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:34:01 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.90/2.09 ----- Otter 3.3f, August 2004 -----
% 1.90/2.09 The process was started by sandbox on n006.cluster.edu,
% 1.90/2.09 Wed Jul 27 10:34:02 2022
% 1.90/2.09 The command was "./otter". The process ID is 15557.
% 1.90/2.09
% 1.90/2.09 set(prolog_style_variables).
% 1.90/2.09 set(auto).
% 1.90/2.09 dependent: set(auto1).
% 1.90/2.09 dependent: set(process_input).
% 1.90/2.09 dependent: clear(print_kept).
% 1.90/2.09 dependent: clear(print_new_demod).
% 1.90/2.09 dependent: clear(print_back_demod).
% 1.90/2.09 dependent: clear(print_back_sub).
% 1.90/2.09 dependent: set(control_memory).
% 1.90/2.09 dependent: assign(max_mem, 12000).
% 1.90/2.09 dependent: assign(pick_given_ratio, 4).
% 1.90/2.09 dependent: assign(stats_level, 1).
% 1.90/2.09 dependent: assign(max_seconds, 10800).
% 1.90/2.09 clear(print_given).
% 1.90/2.09
% 1.90/2.09 list(usable).
% 1.90/2.09 0 [] -element(X,a)|element(X,X).
% 1.90/2.09 0 [] -element(X,X)|element(X,a).
% 1.90/2.09 0 [] -element(Y,f(X))| -element(Y,X).
% 1.90/2.09 0 [] element(Y,X)|element(Y,f(X)).
% 1.90/2.09 end_of_list.
% 1.90/2.09
% 1.90/2.09 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=2.
% 1.90/2.09
% 1.90/2.09 This is a non-Horn set without equality. The strategy will
% 1.90/2.09 be ordered hyper_res, unit deletion, and factoring, with
% 1.90/2.09 satellites in sos and with nuclei in usable.
% 1.90/2.09
% 1.90/2.09 dependent: set(hyper_res).
% 1.90/2.09 dependent: set(factor).
% 1.90/2.09 dependent: set(unit_deletion).
% 1.90/2.09
% 1.90/2.09 ------------> process usable:
% 1.90/2.09 ** KEPT (pick-wt=6): 1 [] -element(A,a)|element(A,A).
% 1.90/2.09 ** KEPT (pick-wt=6): 2 [] -element(A,A)|element(A,a).
% 1.90/2.09 ** KEPT (pick-wt=7): 3 [] -element(A,f(B))| -element(A,B).
% 1.90/2.09
% 1.90/2.09 ------------> process sos:
% 1.90/2.09 ** KEPT (pick-wt=7): 4 [] element(A,B)|element(A,f(B)).
% 1.90/2.09
% 1.90/2.09 ======= end of input processing =======
% 1.90/2.09
% 1.90/2.09 =========== start of search ===========
% 1.90/2.09
% 1.90/2.09 -------- PROOF --------
% 1.90/2.09
% 1.90/2.09 -----> EMPTY CLAUSE at 0.00 sec ----> 13 [hyper,9,3,10] $F.
% 1.90/2.09
% 1.90/2.09 Length of proof is 4. Level of proof is 2.
% 1.90/2.09
% 1.90/2.09 ---------------- PROOF ----------------
% 1.90/2.09 % SZS status Unsatisfiable
% 1.90/2.09 % SZS output start Refutation
% See solution above
% 1.90/2.09 ------------ end of proof -------------
% 1.90/2.09
% 1.90/2.09
% 1.90/2.09 Search stopped by max_proofs option.
% 1.90/2.09
% 1.90/2.09
% 1.90/2.09 Search stopped by max_proofs option.
% 1.90/2.09
% 1.90/2.09 ============ end of search ============
% 1.90/2.09
% 1.90/2.09 -------------- statistics -------------
% 1.90/2.09 clauses given 3
% 1.90/2.09 clauses generated 19
% 1.90/2.09 clauses kept 12
% 1.90/2.09 clauses forward subsumed 10
% 1.90/2.09 clauses back subsumed 0
% 1.90/2.09 Kbytes malloced 976
% 1.90/2.09
% 1.90/2.09 ----------- times (seconds) -----------
% 1.90/2.09 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.09 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.90/2.09
% 1.90/2.09 That finishes the proof of the theorem.
% 1.90/2.09
% 1.90/2.09 Process 15557 finished Wed Jul 27 10:34:03 2022
% 1.90/2.09 Otter interrupted
% 1.90/2.09 PROOF FOUND
%------------------------------------------------------------------------------