TSTP Solution File: LAT269-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT269-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:02:15 EDT 2022
% Result : Unsatisfiable 1.66s 1.88s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 8 unt; 1 nHn; 10 RR)
% Number of literals : 14 ( 6 equ; 5 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('LAT269-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(A,v_A,t_a)
| ~ c_in(B,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,B,A,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,B,A,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Tarski_Ointerval(v_r,B,A,t_a) = c_emptyset ),
file('LAT269-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(A,v_A,t_a)
| c_Tarski_Ointerval(v_r,A,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ),
file('LAT269-2.p',unknown),
[] ).
cnf(6,axiom,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
file('LAT269-2.p',unknown),
[] ).
cnf(7,axiom,
v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),
file('LAT269-2.p',unknown),
[] ).
cnf(9,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = v_intY1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,axiom,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
file('LAT269-2.p',unknown),
[] ).
cnf(14,plain,
v_intY1 = c_emptyset,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[10,2,6]),9,9,9]),1]),
[iquote('hyper,10,2,6,demod,9,9,9,unit_del,1')] ).
cnf(16,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),14]),
[iquote('back_demod,8,demod,14')] ).
cnf(19,plain,
$false,
inference(hyper,[status(thm)],[16,3,10]),
[iquote('hyper,16,3,10')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LAT269-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 08:51:36 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.66/1.88 ----- Otter 3.3f, August 2004 -----
% 1.66/1.88 The process was started by sandbox2 on n027.cluster.edu,
% 1.66/1.88 Wed Jul 27 08:51:36 2022
% 1.66/1.88 The command was "./otter". The process ID is 21203.
% 1.66/1.88
% 1.66/1.88 set(prolog_style_variables).
% 1.66/1.88 set(auto).
% 1.66/1.88 dependent: set(auto1).
% 1.66/1.88 dependent: set(process_input).
% 1.66/1.88 dependent: clear(print_kept).
% 1.66/1.88 dependent: clear(print_new_demod).
% 1.66/1.88 dependent: clear(print_back_demod).
% 1.66/1.88 dependent: clear(print_back_sub).
% 1.66/1.88 dependent: set(control_memory).
% 1.66/1.88 dependent: assign(max_mem, 12000).
% 1.66/1.88 dependent: assign(pick_given_ratio, 4).
% 1.66/1.88 dependent: assign(stats_level, 1).
% 1.66/1.88 dependent: assign(max_seconds, 10800).
% 1.66/1.88 clear(print_given).
% 1.66/1.88
% 1.66/1.88 list(usable).
% 1.66/1.88 0 [] A=A.
% 1.66/1.88 0 [] -c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.66/1.88 0 [] c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a).
% 1.66/1.88 0 [] -c_in(V_b,v_A,t_a)| -c_in(V_a,v_A,t_a)|c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))|c_Tarski_Ointerval(v_r,V_a,V_b,t_a)=c_emptyset.
% 1.66/1.88 0 [] v_intY1=c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a).
% 1.66/1.88 0 [] c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a).
% 1.66/1.88 0 [] -c_in(V_x,v_A,t_a)|c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a)!=c_emptyset.
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.66/1.88
% 1.66/1.88 This ia a non-Horn set with equality. The strategy will be
% 1.66/1.88 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.66/1.88 deletion, with positive clauses in sos and nonpositive
% 1.66/1.88 clauses in usable.
% 1.66/1.88
% 1.66/1.88 dependent: set(knuth_bendix).
% 1.66/1.88 dependent: set(anl_eq).
% 1.66/1.88 dependent: set(para_from).
% 1.66/1.88 dependent: set(para_into).
% 1.66/1.88 dependent: clear(para_from_right).
% 1.66/1.88 dependent: clear(para_into_right).
% 1.66/1.88 dependent: set(para_from_vars).
% 1.66/1.88 dependent: set(eq_units_both_ways).
% 1.66/1.88 dependent: set(dynamic_demod_all).
% 1.66/1.88 dependent: set(dynamic_demod).
% 1.66/1.88 dependent: set(order_eq).
% 1.66/1.88 dependent: set(back_demod).
% 1.66/1.88 dependent: set(lrpo).
% 1.66/1.88 dependent: set(hyper_res).
% 1.66/1.88 dependent: set(unit_deletion).
% 1.66/1.88 dependent: set(factor).
% 1.66/1.88
% 1.66/1.88 ------------> process usable:
% 1.66/1.88 ** KEPT (pick-wt=14): 1 [] -c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.66/1.88 ** KEPT (pick-wt=37): 2 [] -c_in(A,v_A,t_a)| -c_in(B,v_A,t_a)|c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,B,A,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,B,A,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))|c_Tarski_Ointerval(v_r,B,A,t_a)=c_emptyset.
% 1.66/1.88 ** KEPT (pick-wt=13): 3 [] -c_in(A,v_A,t_a)|c_Tarski_Ointerval(v_r,A,c_Tarski_OTop(v_cl,t_a),t_a)!=c_emptyset.
% 1.66/1.88
% 1.66/1.88 ------------> process sos:
% 1.66/1.88 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.66/1.88 ** KEPT (pick-wt=6): 6 [] c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a).
% 1.66/1.88 ** KEPT (pick-wt=12): 8 [copy,7,flip.1] c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a)=v_intY1.
% 1.66/1.88 ---> New Demodulator: 9 [new_demod,8] c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a)=v_intY1.
% 1.66/1.88 ** KEPT (pick-wt=7): 10 [] c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a).
% 1.66/1.88 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.66/1.88 >>>> Starting back demodulation with 9.
% 1.66/1.88
% 1.66/1.88 ======= end of input processing =======
% 1.66/1.88
% 1.66/1.88 =========== start of search ===========
% 1.66/1.88
% 1.66/1.88 -------- PROOF --------
% 1.66/1.88
% 1.66/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 19 [hyper,16,3,10] $F.
% 1.66/1.88
% 1.66/1.88 Length of proof is 3. Level of proof is 3.
% 1.66/1.88
% 1.66/1.88 ---------------- PROOF ----------------
% 1.66/1.88 % SZS status Unsatisfiable
% 1.66/1.88 % SZS output start Refutation
% See solution above
% 1.66/1.88 ------------ end of proof -------------
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88 ============ end of search ============
% 1.66/1.88
% 1.66/1.88 -------------- statistics -------------
% 1.66/1.88 clauses given 5
% 1.66/1.88 clauses generated 12
% 1.66/1.88 clauses kept 14
% 1.66/1.88 clauses forward subsumed 7
% 1.66/1.88 clauses back subsumed 0
% 1.66/1.88 Kbytes malloced 976
% 1.66/1.88
% 1.66/1.88 ----------- times (seconds) -----------
% 1.66/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.88
% 1.66/1.88 That finishes the proof of the theorem.
% 1.66/1.88
% 1.66/1.88 Process 21203 finished Wed Jul 27 08:51:38 2022
% 1.66/1.88 Otter interrupted
% 1.66/1.88 PROOF FOUND
%------------------------------------------------------------------------------