TSTP Solution File: SET978+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET978+1 : 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 13:14:37 EDT 2022
% Result : Theorem 1.70s 1.91s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 2 unt; 3 nHn; 3 RR)
% Number of literals : 14 ( 4 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ disjoint(A,B)
| disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('SET978+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ disjoint(A,B)
| disjoint(cartesian_product2(C,A),cartesian_product2(D,B)) ),
file('SET978+1.p',unknown),
[] ).
cnf(5,axiom,
dollar_c6 != dollar_c5,
file('SET978+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ disjoint(cartesian_product2(singleton(dollar_c6),dollar_c4),cartesian_product2(singleton(dollar_c5),dollar_c3))
| ~ disjoint(cartesian_product2(dollar_c4,singleton(dollar_c6)),cartesian_product2(dollar_c3,singleton(dollar_c5))) ),
file('SET978+1.p',unknown),
[] ).
cnf(9,axiom,
( A = B
| disjoint(singleton(A),singleton(B)) ),
file('SET978+1.p',unknown),
[] ).
cnf(10,plain,
( A = B
| disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ),
inference(hyper,[status(thm)],[9,4]),
[iquote('hyper,9,4')] ).
cnf(11,plain,
( A = B
| disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ),
inference(hyper,[status(thm)],[9,3]),
[iquote('hyper,9,3')] ).
cnf(172,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[11,6,10]),5,5]),
[iquote('hyper,11,6,10,unit_del,5,5')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 10:26:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.91 ----- Otter 3.3f, August 2004 -----
% 1.70/1.91 The process was started by sandbox on n003.cluster.edu,
% 1.70/1.91 Wed Jul 27 10:26:26 2022
% 1.70/1.91 The command was "./otter". The process ID is 1463.
% 1.70/1.91
% 1.70/1.91 set(prolog_style_variables).
% 1.70/1.91 set(auto).
% 1.70/1.91 dependent: set(auto1).
% 1.70/1.91 dependent: set(process_input).
% 1.70/1.91 dependent: clear(print_kept).
% 1.70/1.91 dependent: clear(print_new_demod).
% 1.70/1.91 dependent: clear(print_back_demod).
% 1.70/1.91 dependent: clear(print_back_sub).
% 1.70/1.91 dependent: set(control_memory).
% 1.70/1.91 dependent: assign(max_mem, 12000).
% 1.70/1.91 dependent: assign(pick_given_ratio, 4).
% 1.70/1.91 dependent: assign(stats_level, 1).
% 1.70/1.91 dependent: assign(max_seconds, 10800).
% 1.70/1.91 clear(print_given).
% 1.70/1.91
% 1.70/1.91 formula_list(usable).
% 1.70/1.91 all A (A=A).
% 1.70/1.91 exists A empty(A).
% 1.70/1.91 exists A (-empty(A)).
% 1.70/1.91 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.70/1.91 all A B C D (disjoint(A,B)|disjoint(C,D)->disjoint(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.70/1.91 -(all A B C D (A!=B->disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))&disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))))).
% 1.70/1.91 all A B (A!=B->disjoint(singleton(A),singleton(B))).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 -------> usable clausifies to:
% 1.70/1.91
% 1.70/1.91 list(usable).
% 1.70/1.91 0 [] A=A.
% 1.70/1.91 0 [] empty($c1).
% 1.70/1.91 0 [] -empty($c2).
% 1.70/1.91 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.70/1.91 0 [] -disjoint(A,B)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.91 0 [] -disjoint(C,D)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.91 0 [] $c6!=$c5.
% 1.70/1.91 0 [] -disjoint(cartesian_product2(singleton($c6),$c4),cartesian_product2(singleton($c5),$c3))| -disjoint(cartesian_product2($c4,singleton($c6)),cartesian_product2($c3,singleton($c5))).
% 1.70/1.91 0 [] A=B|disjoint(singleton(A),singleton(B)).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.70/1.91
% 1.70/1.91 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.91 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.91 deletion, with positive clauses in sos and nonpositive
% 1.70/1.91 clauses in usable.
% 1.70/1.91
% 1.70/1.91 dependent: set(knuth_bendix).
% 1.70/1.91 dependent: set(anl_eq).
% 1.70/1.91 dependent: set(para_from).
% 1.70/1.91 dependent: set(para_into).
% 1.70/1.91 dependent: clear(para_from_right).
% 1.70/1.91 dependent: clear(para_into_right).
% 1.70/1.91 dependent: set(para_from_vars).
% 1.70/1.91 dependent: set(eq_units_both_ways).
% 1.70/1.91 dependent: set(dynamic_demod_all).
% 1.70/1.91 dependent: set(dynamic_demod).
% 1.70/1.91 dependent: set(order_eq).
% 1.70/1.91 dependent: set(back_demod).
% 1.70/1.91 dependent: set(lrpo).
% 1.70/1.91 dependent: set(hyper_res).
% 1.70/1.91 dependent: set(unit_deletion).
% 1.70/1.91 dependent: set(factor).
% 1.70/1.91
% 1.70/1.91 ------------> process usable:
% 1.70/1.91 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.70/1.91 ** KEPT (pick-wt=6): 2 [] -disjoint(A,B)|disjoint(B,A).
% 1.70/1.91 ** KEPT (pick-wt=10): 3 [] -disjoint(A,B)|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.91 ** KEPT (pick-wt=10): 4 [] -disjoint(A,B)|disjoint(cartesian_product2(C,A),cartesian_product2(D,B)).
% 1.70/1.91 ** KEPT (pick-wt=3): 5 [] $c6!=$c5.
% 1.70/1.91 ** KEPT (pick-wt=18): 6 [] -disjoint(cartesian_product2(singleton($c6),$c4),cartesian_product2(singleton($c5),$c3))| -disjoint(cartesian_product2($c4,singleton($c6)),cartesian_product2($c3,singleton($c5))).
% 1.70/1.91
% 1.70/1.91 ------------> process sos:
% 1.70/1.91 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.70/1.91 ** KEPT (pick-wt=2): 8 [] empty($c1).
% 1.70/1.91 ** KEPT (pick-wt=8): 9 [] A=B|disjoint(singleton(A),singleton(B)).
% 1.70/1.91 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.70/1.91
% 1.70/1.91 ======= end of input processing =======
% 1.70/1.91
% 1.70/1.91 =========== start of search ===========
% 1.70/1.91
% 1.70/1.91 -------- PROOF --------
% 1.70/1.91
% 1.70/1.91 -----> EMPTY CLAUSE at 0.01 sec ----> 172 [hyper,11,6,10,unit_del,5,5] $F.
% 1.70/1.91
% 1.70/1.91 Length of proof is 2. Level of proof is 1.
% 1.70/1.91
% 1.70/1.91 ---------------- PROOF ----------------
% 1.70/1.91 % SZS status Theorem
% 1.70/1.91 % SZS output start Refutation
% See solution above
% 1.70/1.91 ------------ end of proof -------------
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 Search stopped by max_proofs option.
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 Search stopped by max_proofs option.
% 1.70/1.91
% 1.70/1.91 ============ end of search ============
% 1.70/1.91
% 1.70/1.91 -------------- statistics -------------
% 1.70/1.91 clauses given 11
% 1.70/1.91 clauses generated 190
% 1.70/1.91 clauses kept 171
% 1.70/1.91 clauses forward subsumed 28
% 1.70/1.91 clauses back subsumed 0
% 1.70/1.91 Kbytes malloced 976
% 1.70/1.91
% 1.70/1.91 ----------- times (seconds) -----------
% 1.70/1.91 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.70/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.91
% 1.70/1.91 That finishes the proof of the theorem.
% 1.70/1.91
% 1.70/1.91 Process 1463 finished Wed Jul 27 10:26:28 2022
% 1.70/1.91 Otter interrupted
% 1.70/1.91 PROOF FOUND
%------------------------------------------------------------------------------