TSTP Solution File: SET851-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET851-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:14:24 EDT 2022
% Result : Unsatisfiable 1.70s 1.94s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 11 ( 7 unt; 3 nHn; 8 RR)
% Number of literals : 17 ( 2 equ; 5 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; 4 con; 0-3 aty)
% Number of variables : 8 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_lesse_quals(A,B,tc_set(tc_set(C)))
| c_lesse_quals(A,c_Zorn_Osucc(D,B,C),tc_set(tc_set(C))) ),
file('SET851-2.p',unknown),
[] ).
cnf(2,axiom,
~ c_lesse_quals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('SET851-2.p',unknown),
[] ).
cnf(3,axiom,
~ c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('SET851-2.p',unknown),
[] ).
cnf(4,axiom,
( c_lesse_quals(c_Zorn_Osucc(v_S,A,t_a),v_m,tc_set(tc_set(t_a)))
| A = v_m
| ~ c_lesse_quals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
file('SET851-2.p',unknown),
[] ).
cnf(6,axiom,
c_lesse_quals(A,A,tc_set(B)),
file('SET851-2.p',unknown),
[] ).
cnf(7,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET851-2.p',unknown),
[] ).
cnf(8,axiom,
( c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lesse_quals(v_x,v_m,tc_set(tc_set(t_a))) ),
file('SET851-2.p',unknown),
[] ).
cnf(28,plain,
( c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = v_m ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[8,4,7]),2]),
[iquote('hyper,8,4,7,unit_del,2')] ).
cnf(47,plain,
c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[28,3]),6]),
[iquote('para_from,28.2.1,3.1.2.2,unit_del,6')] ).
cnf(48,plain,
c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(A,v_x,t_a),tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[47,1]),
[iquote('hyper,47,1')] ).
cnf(49,plain,
$false,
inference(binary,[status(thm)],[48,3]),
[iquote('binary,48.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET851-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.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 10:43:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.70/1.94 ----- Otter 3.3f, August 2004 -----
% 1.70/1.94 The process was started by sandbox on n003.cluster.edu,
% 1.70/1.94 Wed Jul 27 10:43:11 2022
% 1.70/1.94 The command was "./otter". The process ID is 29187.
% 1.70/1.94
% 1.70/1.94 set(prolog_style_variables).
% 1.70/1.94 set(auto).
% 1.70/1.94 dependent: set(auto1).
% 1.70/1.94 dependent: set(process_input).
% 1.70/1.94 dependent: clear(print_kept).
% 1.70/1.94 dependent: clear(print_new_demod).
% 1.70/1.94 dependent: clear(print_back_demod).
% 1.70/1.94 dependent: clear(print_back_sub).
% 1.70/1.94 dependent: set(control_memory).
% 1.70/1.94 dependent: assign(max_mem, 12000).
% 1.70/1.94 dependent: assign(pick_given_ratio, 4).
% 1.70/1.94 dependent: assign(stats_level, 1).
% 1.70/1.94 dependent: assign(max_seconds, 10800).
% 1.70/1.94 clear(print_given).
% 1.70/1.94
% 1.70/1.94 list(usable).
% 1.70/1.94 0 [] A=A.
% 1.70/1.94 0 [] c_lesse_quals(V_A,V_A,tc_set(T_a)).
% 1.70/1.94 0 [] -c_lesse_quals(V_x,V_y,tc_set(tc_set(T_a)))|c_lesse_quals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))).
% 1.70/1.94 0 [] c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.70/1.94 0 [] -c_lesse_quals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))).
% 1.70/1.94 0 [] -c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))).
% 1.70/1.94 0 [] c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))|c_lesse_quals(v_x,v_m,tc_set(tc_set(t_a))).
% 1.70/1.94 0 [] c_lesse_quals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))|V_U=v_m| -c_lesse_quals(V_U,v_m,tc_set(tc_set(t_a)))| -c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.70/1.94 end_of_list.
% 1.70/1.94
% 1.70/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.70/1.94
% 1.70/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.94 deletion, with positive clauses in sos and nonpositive
% 1.70/1.94 clauses in usable.
% 1.70/1.94
% 1.70/1.94 dependent: set(knuth_bendix).
% 1.70/1.94 dependent: set(anl_eq).
% 1.70/1.94 dependent: set(para_from).
% 1.70/1.94 dependent: set(para_into).
% 1.70/1.94 dependent: clear(para_from_right).
% 1.70/1.94 dependent: clear(para_into_right).
% 1.70/1.94 dependent: set(para_from_vars).
% 1.70/1.94 dependent: set(eq_units_both_ways).
% 1.70/1.94 dependent: set(dynamic_demod_all).
% 1.70/1.94 dependent: set(dynamic_demod).
% 1.70/1.94 dependent: set(order_eq).
% 1.70/1.94 dependent: set(back_demod).
% 1.70/1.94 dependent: set(lrpo).
% 1.70/1.94 dependent: set(hyper_res).
% 1.70/1.94 dependent: set(unit_deletion).
% 1.70/1.94 dependent: set(factor).
% 1.70/1.94
% 1.70/1.94 ------------> process usable:
% 1.70/1.94 ** KEPT (pick-wt=15): 1 [] -c_lesse_quals(A,B,tc_set(tc_set(C)))|c_lesse_quals(A,c_Zorn_Osucc(D,B,C),tc_set(tc_set(C))).
% 1.70/1.94 ** KEPT (pick-wt=9): 2 [] -c_lesse_quals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))).
% 1.70/1.94 ** KEPT (pick-wt=12): 3 [] -c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))).
% 1.70/1.94 ** KEPT (pick-wt=26): 4 [] c_lesse_quals(c_Zorn_Osucc(v_S,A,t_a),v_m,tc_set(tc_set(t_a)))|A=v_m| -c_lesse_quals(A,v_m,tc_set(tc_set(t_a)))| -c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.70/1.94
% 1.70/1.94 ------------> process sos:
% 1.70/1.94 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.70/1.94 ** KEPT (pick-wt=5): 6 [] c_lesse_quals(A,A,tc_set(B)).
% 1.70/1.94 ** KEPT (pick-wt=8): 7 [] c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.70/1.94 ** KEPT (pick-wt=15): 8 [] c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))|c_lesse_quals(v_x,v_m,tc_set(tc_set(t_a))).
% 1.70/1.94 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.70/1.94
% 1.70/1.94 ======= end of input processing =======
% 1.70/1.94
% 1.70/1.94 =========== start of search ===========
% 1.70/1.94
% 1.70/1.94 -------- PROOF --------
% 1.70/1.94
% 1.70/1.94 ----> UNIT CONFLICT at 0.00 sec ----> 49 [binary,48.1,3.1] $F.
% 1.70/1.94
% 1.70/1.94 Length of proof is 3. Level of proof is 3.
% 1.70/1.94
% 1.70/1.94 ---------------- PROOF ----------------
% 1.70/1.94 % SZS status Unsatisfiable
% 1.70/1.94 % SZS output start Refutation
% See solution above
% 1.70/1.94 ------------ end of proof -------------
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Search stopped by max_proofs option.
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Search stopped by max_proofs option.
% 1.70/1.94
% 1.70/1.94 ============ end of search ============
% 1.70/1.94
% 1.70/1.94 -------------- statistics -------------
% 1.70/1.94 clauses given 8
% 1.70/1.94 clauses generated 53
% 1.70/1.94 clauses kept 48
% 1.70/1.94 clauses forward subsumed 13
% 1.70/1.94 clauses back subsumed 7
% 1.70/1.94 Kbytes malloced 976
% 1.70/1.94
% 1.70/1.94 ----------- times (seconds) -----------
% 1.70/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.94
% 1.70/1.94 That finishes the proof of the theorem.
% 1.70/1.94
% 1.70/1.94 Process 29187 finished Wed Jul 27 10:43:13 2022
% 1.70/1.94 Otter interrupted
% 1.70/1.94 PROOF FOUND
%------------------------------------------------------------------------------