TSTP Solution File: SET825-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:14:19 EDT 2022
% Result : Unsatisfiable 1.66s 1.89s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 8 unt; 2 nHn; 12 RR)
% Number of literals : 20 ( 2 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(c_Pair(A,B,C,C),c_Relation_OId,tc_prod(C,C))
| A = B ),
file('SET825-2.p',unknown),
[] ).
cnf(2,axiom,
~ v_Q(v_m),
file('SET825-2.p',unknown),
[] ).
cnf(3,axiom,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
file('SET825-2.p',unknown),
[] ).
cnf(4,axiom,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(A)),c_Suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
file('SET825-2.p',unknown),
[] ).
cnf(6,axiom,
c_in(c_Pair(A,A,B,B),c_Relation_OId,tc_prod(B,B)),
file('SET825-2.p',unknown),
[] ).
cnf(7,axiom,
v_Q(v_n),
file('SET825-2.p',unknown),
[] ).
cnf(8,plain,
( v_Q(A)
| ~ c_in(c_Pair(v_n,A,B,B),c_Relation_OId,tc_prod(B,B)) ),
inference(para_into,[status(thm),theory(equality)],[7,1]),
[iquote('para_into,7.1.1,1.2.1')] ).
cnf(9,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(hyper,[status(thm)],[6,3]),
[iquote('hyper,6,3')] ).
cnf(23,plain,
c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[9,8]),2]),
[iquote('hyper,9,8,unit_del,2')] ).
cnf(25,plain,
v_xa(c_Relation_OId) = v_x(c_Relation_OId),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[23,1])]),
[iquote('hyper,23,1,flip.1')] ).
cnf(29,plain,
c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[25,4]),6,6]),
[iquote('para_from,25.1.1,4.2.1.2.1,unit_del,6,6')] ).
cnf(30,plain,
v_Q(v_m),
inference(hyper,[status(thm)],[29,8]),
[iquote('hyper,29,8')] ).
cnf(31,plain,
$false,
inference(binary,[status(thm)],[30,2]),
[iquote('binary,30.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 10:44:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.89 ----- Otter 3.3f, August 2004 -----
% 1.66/1.89 The process was started by sandbox on n028.cluster.edu,
% 1.66/1.89 Wed Jul 27 10:44:04 2022
% 1.66/1.89 The command was "./otter". The process ID is 26330.
% 1.66/1.89
% 1.66/1.89 set(prolog_style_variables).
% 1.66/1.89 set(auto).
% 1.66/1.89 dependent: set(auto1).
% 1.66/1.89 dependent: set(process_input).
% 1.66/1.89 dependent: clear(print_kept).
% 1.66/1.89 dependent: clear(print_new_demod).
% 1.66/1.89 dependent: clear(print_back_demod).
% 1.66/1.89 dependent: clear(print_back_sub).
% 1.66/1.89 dependent: set(control_memory).
% 1.66/1.89 dependent: assign(max_mem, 12000).
% 1.66/1.89 dependent: assign(pick_given_ratio, 4).
% 1.66/1.89 dependent: assign(stats_level, 1).
% 1.66/1.89 dependent: assign(max_seconds, 10800).
% 1.66/1.89 clear(print_given).
% 1.66/1.89
% 1.66/1.89 list(usable).
% 1.66/1.89 0 [] A=A.
% 1.66/1.89 0 [] c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)).
% 1.66/1.89 0 [] -c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a))|V_a=V_b.
% 1.66/1.89 0 [] v_Q(v_n).
% 1.66/1.89 0 [] -v_Q(v_m).
% 1.66/1.89 0 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))|c_in(c_Pair(v_x(V_U),v_xa(V_U),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89 0 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_Suc(v_x(V_U)),c_Suc(v_xa(V_U)),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89 end_of_list.
% 1.66/1.89
% 1.66/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.66/1.89
% 1.66/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.66/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.66/1.89 deletion, with positive clauses in sos and nonpositive
% 1.66/1.89 clauses in usable.
% 1.66/1.89
% 1.66/1.89 dependent: set(knuth_bendix).
% 1.66/1.89 dependent: set(anl_eq).
% 1.66/1.89 dependent: set(para_from).
% 1.66/1.89 dependent: set(para_into).
% 1.66/1.89 dependent: clear(para_from_right).
% 1.66/1.89 dependent: clear(para_into_right).
% 1.66/1.89 dependent: set(para_from_vars).
% 1.66/1.89 dependent: set(eq_units_both_ways).
% 1.66/1.89 dependent: set(dynamic_demod_all).
% 1.66/1.89 dependent: set(dynamic_demod).
% 1.66/1.89 dependent: set(order_eq).
% 1.66/1.89 dependent: set(back_demod).
% 1.66/1.89 dependent: set(lrpo).
% 1.66/1.89 dependent: set(hyper_res).
% 1.66/1.89 dependent: set(unit_deletion).
% 1.66/1.89 dependent: set(factor).
% 1.66/1.89
% 1.66/1.89 ------------> process usable:
% 1.66/1.89 ** KEPT (pick-wt=13): 1 [] -c_in(c_Pair(A,B,C,C),c_Relation_OId,tc_prod(C,C))|A=B.
% 1.66/1.89 ** KEPT (pick-wt=2): 2 [] -v_Q(v_m).
% 1.66/1.89 ** KEPT (pick-wt=32): 3 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|c_in(c_Pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89 ** KEPT (pick-wt=34): 4 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_Suc(v_x(A)),c_Suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89
% 1.66/1.89 ------------> process sos:
% 1.66/1.89 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.66/1.89 ** KEPT (pick-wt=10): 6 [] c_in(c_Pair(A,A,B,B),c_Relation_OId,tc_prod(B,B)).
% 1.66/1.89 ** KEPT (pick-wt=2): 7 [] v_Q(v_n).
% 1.66/1.89 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.66/1.89
% 1.66/1.89 ======= end of input processing =======
% 1.66/1.89
% 1.66/1.89 =========== start of search ===========
% 1.66/1.89
% 1.66/1.89 -------- PROOF --------
% 1.66/1.89
% 1.66/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,30.1,2.1] $F.
% 1.66/1.89
% 1.66/1.89 Length of proof is 6. Level of proof is 5.
% 1.66/1.89
% 1.66/1.89 ---------------- PROOF ----------------
% 1.66/1.89 % SZS status Unsatisfiable
% 1.66/1.89 % SZS output start Refutation
% See solution above
% 1.66/1.89 ------------ end of proof -------------
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89 ============ end of search ============
% 1.66/1.89
% 1.66/1.89 -------------- statistics -------------
% 1.66/1.89 clauses given 9
% 1.66/1.89 clauses generated 31
% 1.66/1.89 clauses kept 29
% 1.66/1.89 clauses forward subsumed 12
% 1.66/1.89 clauses back subsumed 1
% 1.66/1.89 Kbytes malloced 976
% 1.66/1.89
% 1.66/1.89 ----------- times (seconds) -----------
% 1.66/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.89
% 1.66/1.89 That finishes the proof of the theorem.
% 1.66/1.89
% 1.66/1.89 Process 26330 finished Wed Jul 27 10:44:05 2022
% 1.66/1.89 Otter interrupted
% 1.66/1.89 PROOF FOUND
%------------------------------------------------------------------------------