TSTP Solution File: SET864-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:14:26 EDT 2022
% Result : Unsatisfiable 2.02s 2.16s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 6 unt; 0 nHn; 11 RR)
% Number of literals : 18 ( 4 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(A,B,tc_set(C))
| ~ c_in(D,c_Zorn_Omaxchain(B,C),tc_set(tc_set(C)))
| ~ c_lesse_quals(c_Union(D,C),A,tc_set(C))
| c_Union(D,C) = A ),
file('SET864-2.p',unknown),
[] ).
cnf(2,axiom,
( c_in(v_x(A),v_S,tc_set(t_a))
| ~ c_in(A,v_S,tc_set(t_a)) ),
file('SET864-2.p',unknown),
[] ).
cnf(3,axiom,
( c_lesse_quals(A,v_x(A),tc_set(t_a))
| ~ c_in(A,v_S,tc_set(t_a)) ),
file('SET864-2.p',unknown),
[] ).
cnf(4,axiom,
( A != v_x(A)
| ~ c_in(A,v_S,tc_set(t_a)) ),
file('SET864-2.p',unknown),
[] ).
cnf(5,plain,
( v_x(A) != A
| ~ c_in(A,v_S,tc_set(t_a)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(7,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET864-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('SET864-2.p',unknown),
[] ).
cnf(9,plain,
c_lesse_quals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)),
inference(hyper,[status(thm)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(10,plain,
c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
inference(hyper,[status(thm)],[8,2]),
[iquote('hyper,8,2')] ).
cnf(18,plain,
v_x(c_Union(v_c,t_a)) = c_Union(v_c,t_a),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[9,1,10,7])]),
[iquote('hyper,9,1,10,7,flip.1')] ).
cnf(21,plain,
$false,
inference(hyper,[status(thm)],[18,5,8]),
[iquote('hyper,18,5,8')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 11:01:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.02/2.16 ----- Otter 3.3f, August 2004 -----
% 2.02/2.16 The process was started by sandbox2 on n015.cluster.edu,
% 2.02/2.16 Wed Jul 27 11:01:27 2022
% 2.02/2.16 The command was "./otter". The process ID is 3130.
% 2.02/2.16
% 2.02/2.16 set(prolog_style_variables).
% 2.02/2.16 set(auto).
% 2.02/2.16 dependent: set(auto1).
% 2.02/2.16 dependent: set(process_input).
% 2.02/2.16 dependent: clear(print_kept).
% 2.02/2.16 dependent: clear(print_new_demod).
% 2.02/2.16 dependent: clear(print_back_demod).
% 2.02/2.16 dependent: clear(print_back_sub).
% 2.02/2.16 dependent: set(control_memory).
% 2.02/2.16 dependent: assign(max_mem, 12000).
% 2.02/2.16 dependent: assign(pick_given_ratio, 4).
% 2.02/2.16 dependent: assign(stats_level, 1).
% 2.02/2.16 dependent: assign(max_seconds, 10800).
% 2.02/2.16 clear(print_given).
% 2.02/2.16
% 2.02/2.16 list(usable).
% 2.02/2.16 0 [] A=A.
% 2.02/2.16 0 [] -c_in(V_u,V_S,tc_set(T_a))| -c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(c_Union(V_c,T_a),V_u,tc_set(T_a))|c_Union(V_c,T_a)=V_u.
% 2.02/2.16 0 [] c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 2.02/2.16 0 [] c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)).
% 2.02/2.16 0 [] c_in(v_x(V_U),v_S,tc_set(t_a))| -c_in(V_U,v_S,tc_set(t_a)).
% 2.02/2.16 0 [] c_lesse_quals(V_U,v_x(V_U),tc_set(t_a))| -c_in(V_U,v_S,tc_set(t_a)).
% 2.02/2.16 0 [] V_U!=v_x(V_U)| -c_in(V_U,v_S,tc_set(t_a)).
% 2.02/2.16 end_of_list.
% 2.02/2.16
% 2.02/2.16 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.02/2.16
% 2.02/2.16 This is a Horn set with equality. The strategy will be
% 2.02/2.16 Knuth-Bendix and hyper_res, with positive clauses in
% 2.02/2.16 sos and nonpositive clauses in usable.
% 2.02/2.16
% 2.02/2.16 dependent: set(knuth_bendix).
% 2.02/2.16 dependent: set(anl_eq).
% 2.02/2.16 dependent: set(para_from).
% 2.02/2.16 dependent: set(para_into).
% 2.02/2.16 dependent: clear(para_from_right).
% 2.02/2.16 dependent: clear(para_into_right).
% 2.02/2.16 dependent: set(para_from_vars).
% 2.02/2.16 dependent: set(eq_units_both_ways).
% 2.02/2.16 dependent: set(dynamic_demod_all).
% 2.02/2.16 dependent: set(dynamic_demod).
% 2.02/2.16 dependent: set(order_eq).
% 2.02/2.16 dependent: set(back_demod).
% 2.02/2.16 dependent: set(lrpo).
% 2.02/2.16 dependent: set(hyper_res).
% 2.02/2.16 dependent: clear(order_hyper).
% 2.02/2.16
% 2.02/2.16 ------------> process usable:
% 2.02/2.16 ** KEPT (pick-wt=25): 1 [] -c_in(A,B,tc_set(C))| -c_in(D,c_Zorn_Omaxchain(B,C),tc_set(tc_set(C)))| -c_lesse_quals(c_Union(D,C),A,tc_set(C))|c_Union(D,C)=A.
% 2.02/2.16 ** KEPT (pick-wt=11): 2 [] c_in(v_x(A),v_S,tc_set(t_a))| -c_in(A,v_S,tc_set(t_a)).
% 2.02/2.16 ** KEPT (pick-wt=11): 3 [] c_lesse_quals(A,v_x(A),tc_set(t_a))| -c_in(A,v_S,tc_set(t_a)).
% 2.02/2.16 ** KEPT (pick-wt=9): 5 [copy,4,flip.1] v_x(A)!=A| -c_in(A,v_S,tc_set(t_a)).
% 2.02/2.16
% 2.02/2.16 ------------> process sos:
% 2.02/2.16 ** KEPT (pick-wt=3): 6 [] A=A.
% 2.02/2.16 ** KEPT (pick-wt=8): 7 [] c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 2.02/2.16 ** KEPT (pick-wt=7): 8 [] c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)).
% 2.02/2.16 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 2.02/2.16
% 2.02/2.16 ======= end of input processing =======
% 2.02/2.16
% 2.02/2.16 =========== start of search ===========
% 2.02/2.16
% 2.02/2.16 -------- PROOF --------
% 2.02/2.16
% 2.02/2.16 -----> EMPTY CLAUSE at 0.00 sec ----> 21 [hyper,18,5,8] $F.
% 2.02/2.16
% 2.02/2.16 Length of proof is 4. Level of proof is 2.
% 2.02/2.16
% 2.02/2.16 ---------------- PROOF ----------------
% 2.02/2.16 % SZS status Unsatisfiable
% 2.02/2.16 % SZS output start Refutation
% See solution above
% 2.02/2.16 ------------ end of proof -------------
% 2.02/2.16
% 2.02/2.16
% 2.02/2.16 Search stopped by max_proofs option.
% 2.02/2.16
% 2.02/2.16
% 2.02/2.16 Search stopped by max_proofs option.
% 2.02/2.16
% 2.02/2.16 ============ end of search ============
% 2.02/2.16
% 2.02/2.16 -------------- statistics -------------
% 2.02/2.16 clauses given 7
% 2.02/2.16 clauses generated 11
% 2.02/2.16 clauses kept 18
% 2.02/2.16 clauses forward subsumed 6
% 2.02/2.16 clauses back subsumed 0
% 2.02/2.16 Kbytes malloced 976
% 2.02/2.16
% 2.02/2.16 ----------- times (seconds) -----------
% 2.02/2.16 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.16 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.02/2.16
% 2.02/2.16 That finishes the proof of the theorem.
% 2.02/2.16
% 2.02/2.16 Process 3130 finished Wed Jul 27 11:01:28 2022
% 2.02/2.16 Otter interrupted
% 2.02/2.16 PROOF FOUND
%------------------------------------------------------------------------------