%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : TOP002-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:26:47 EDT 2022
% Result : Unsatisfiable 1.64s 1.84s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 1 nHn; 3 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ element_of_set(A,empty_set),
file('TOP002-2.p',unknown),
[] ).
cnf(2,axiom,
~ element_of_collection(empty_set,top_of_basis(f)),
file('TOP002-2.p',unknown),
[] ).
cnf(3,axiom,
( element_of_collection(A,top_of_basis(B))
| element_of_set(f11(B,A),A) ),
file('TOP002-2.p',unknown),
[] ).
cnf(4,plain,
element_of_collection(empty_set,top_of_basis(A)),
inference(hyper,[status(thm)],[3,1]),
[iquote('hyper,3,1')] ).
cnf(5,plain,
$false,
inference(binary,[status(thm)],[4,2]),
[iquote('binary,4.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : TOP002-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 01:51:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.64/1.84 ----- Otter 3.3f, August 2004 -----
% 1.64/1.84 The process was started by sandbox on n012.cluster.edu,
% 1.64/1.84 Wed Jul 27 01:51:05 2022
% 1.64/1.84 The command was "./otter". The process ID is 7956.
% 1.64/1.84
% 1.64/1.84 set(prolog_style_variables).
% 1.64/1.84 set(auto).
% 1.64/1.84 dependent: set(auto1).
% 1.64/1.84 dependent: set(process_input).
% 1.64/1.84 dependent: clear(print_kept).
% 1.64/1.84 dependent: clear(print_new_demod).
% 1.64/1.84 dependent: clear(print_back_demod).
% 1.64/1.84 dependent: clear(print_back_sub).
% 1.64/1.84 dependent: set(control_memory).
% 1.64/1.84 dependent: assign(max_mem, 12000).
% 1.64/1.84 dependent: assign(pick_given_ratio, 4).
% 1.64/1.84 dependent: assign(stats_level, 1).
% 1.64/1.84 dependent: assign(max_seconds, 10800).
% 1.64/1.84 clear(print_given).
% 1.64/1.84
% 1.64/1.84 list(usable).
% 1.64/1.84 0 [] element_of_collection(U,top_of_basis(Vf))|element_of_set(f11(Vf,U),U).
% 1.64/1.84 0 [] -element_of_set(X,empty_set).
% 1.64/1.84 0 [] -element_of_collection(empty_set,top_of_basis(f)).
% 1.64/1.84 end_of_list.
% 1.64/1.84
% 1.64/1.84 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=2.
% 1.64/1.84
% 1.64/1.84 This is a non-Horn set without equality. The strategy will
% 1.64/1.84 be ordered hyper_res, unit deletion, and factoring, with
% 1.64/1.84 satellites in sos and with nuclei in usable.
% 1.64/1.84
% 1.64/1.84 dependent: set(hyper_res).
% 1.64/1.84 dependent: set(factor).
% 1.64/1.84 dependent: set(unit_deletion).
% 1.64/1.84
% 1.64/1.84 ------------> process usable:
% 1.64/1.84 ** KEPT (pick-wt=3): 1 [] -element_of_set(A,empty_set).
% 1.64/1.84 ** KEPT (pick-wt=4): 2 [] -element_of_collection(empty_set,top_of_basis(f)).
% 1.64/1.84
% 1.64/1.84 ------------> process sos:
% 1.64/1.84 ** KEPT (pick-wt=9): 3 [] element_of_collection(A,top_of_basis(B))|element_of_set(f11(B,A),A).
% 1.64/1.84
% 1.64/1.84 ======= end of input processing =======
% 1.64/1.84
% 1.64/1.84 =========== start of search ===========
% 1.64/1.84
% 1.64/1.84 -------- PROOF --------
% 1.64/1.84
% 1.64/1.84 ----> UNIT CONFLICT at 0.00 sec ----> 5 [binary,4.1,2.1] $F.
% 1.64/1.84
% 1.64/1.84 Length of proof is 1. Level of proof is 1.
% 1.64/1.84
% 1.64/1.84 ---------------- PROOF ----------------
% 1.64/1.84 % SZS status Unsatisfiable
% 1.64/1.84 % SZS output start Refutation
% See solution above
% 1.64/1.84 ------------ end of proof -------------
% 1.64/1.84
% 1.64/1.84
% 1.64/1.84 Search stopped by max_proofs option.
% 1.64/1.84
% 1.64/1.84
% 1.64/1.84 Search stopped by max_proofs option.
% 1.64/1.84
% 1.64/1.84 ============ end of search ============
% 1.64/1.84
% 1.64/1.84 -------------- statistics -------------
% 1.64/1.84 clauses given 1
% 1.64/1.84 clauses generated 1
% 1.64/1.84 clauses kept 4
% 1.64/1.84 clauses forward subsumed 0
% 1.64/1.84 clauses back subsumed 0
% 1.64/1.84 Kbytes malloced 976
% 1.64/1.84
% 1.64/1.84 ----------- times (seconds) -----------
% 1.64/1.84 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.84 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.84 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.64/1.84
% 1.64/1.84 That finishes the proof of the theorem.
% 1.64/1.84
% 1.64/1.84 Process 7956 finished Wed Jul 27 01:51:07 2022
% 1.64/1.84 Otter interrupted
% 1.64/1.84 PROOF FOUND
%------------------------------------------------------------------------------