TSTP Solution File: SET985+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:14:38 EDT 2022
% Result : Theorem 1.65s 1.88s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 7 unt; 8 nHn; 13 RR)
% Number of literals : 27 ( 14 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( cartesian_product2(A,B) != empty_set
| A = empty_set
| B = empty_set ),
file('SET985+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(A,C) ),
file('SET985+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(B,D) ),
file('SET985+1.p',unknown),
[] ).
cnf(7,axiom,
~ empty(dollar_c6),
file('SET985+1.p',unknown),
[] ).
cnf(8,axiom,
~ subset(dollar_c5,dollar_c3),
file('SET985+1.p',unknown),
[] ).
cnf(11,axiom,
empty(empty_set),
file('SET985+1.p',unknown),
[] ).
cnf(14,axiom,
( subset(cartesian_product2(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3))
| subset(cartesian_product2(dollar_c5,dollar_c6),cartesian_product2(dollar_c3,dollar_c4)) ),
file('SET985+1.p',unknown),
[] ).
cnf(15,axiom,
subset(empty_set,A),
file('SET985+1.p',unknown),
[] ).
cnf(20,plain,
( subset(cartesian_product2(dollar_c5,dollar_c6),cartesian_product2(dollar_c3,dollar_c4))
| cartesian_product2(dollar_c6,dollar_c5) = empty_set ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[14,6]),8]),
[iquote('hyper,14,6,unit_del,8')] ).
cnf(53,plain,
( cartesian_product2(dollar_c6,dollar_c5) = empty_set
| cartesian_product2(dollar_c5,dollar_c6) = empty_set ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[20,5]),8]),
[iquote('hyper,20,5,unit_del,8')] ).
cnf(76,plain,
( cartesian_product2(dollar_c5,dollar_c6) = empty_set
| empty_set = dollar_c6
| empty_set = dollar_c5 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[53,2])])]),
[iquote('hyper,53,2,flip.2,flip.3')] ).
cnf(102,plain,
( empty_set = dollar_c6
| empty_set = dollar_c5 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[76,2])])]),
[iquote('hyper,76,2,factor_simp,factor_simp')] ).
cnf(107,plain,
empty_set = dollar_c5,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[102,11]),7]),
[iquote('para_from,102.1.1,11.1.1,unit_del,7')] ).
cnf(189,plain,
subset(dollar_c5,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),107]),
[iquote('back_demod,15,demod,107')] ).
cnf(190,plain,
$false,
inference(binary,[status(thm)],[189,8]),
[iquote('binary,189.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 10:56:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.88 ----- Otter 3.3f, August 2004 -----
% 1.65/1.88 The process was started by sandbox on n018.cluster.edu,
% 1.65/1.88 Wed Jul 27 10:56:01 2022
% 1.65/1.88 The command was "./otter". The process ID is 18398.
% 1.65/1.88
% 1.65/1.88 set(prolog_style_variables).
% 1.65/1.88 set(auto).
% 1.65/1.88 dependent: set(auto1).
% 1.65/1.88 dependent: set(process_input).
% 1.65/1.88 dependent: clear(print_kept).
% 1.65/1.88 dependent: clear(print_new_demod).
% 1.65/1.88 dependent: clear(print_back_demod).
% 1.65/1.88 dependent: clear(print_back_sub).
% 1.65/1.88 dependent: set(control_memory).
% 1.65/1.88 dependent: assign(max_mem, 12000).
% 1.65/1.88 dependent: assign(pick_given_ratio, 4).
% 1.65/1.88 dependent: assign(stats_level, 1).
% 1.65/1.88 dependent: assign(max_seconds, 10800).
% 1.65/1.88 clear(print_given).
% 1.65/1.88
% 1.65/1.88 formula_list(usable).
% 1.65/1.88 all A (A=A).
% 1.65/1.88 empty(empty_set).
% 1.65/1.88 exists A empty(A).
% 1.65/1.88 exists A (-empty(A)).
% 1.65/1.88 all A B subset(A,A).
% 1.65/1.88 all A B (cartesian_product2(A,B)=empty_set<->A=empty_set|B=empty_set).
% 1.65/1.88 all A B C D (subset(cartesian_product2(A,B),cartesian_product2(C,D))->cartesian_product2(A,B)=empty_set|subset(A,C)&subset(B,D)).
% 1.65/1.88 -(all A (-empty(A)-> (all B C D (subset(cartesian_product2(A,B),cartesian_product2(C,D))|subset(cartesian_product2(B,A),cartesian_product2(D,C))->subset(B,D))))).
% 1.65/1.88 all A subset(empty_set,A).
% 1.65/1.88 end_of_list.
% 1.65/1.88
% 1.65/1.88 -------> usable clausifies to:
% 1.65/1.88
% 1.65/1.88 list(usable).
% 1.65/1.88 0 [] A=A.
% 1.65/1.88 0 [] empty(empty_set).
% 1.65/1.88 0 [] empty($c1).
% 1.65/1.88 0 [] -empty($c2).
% 1.65/1.88 0 [] subset(A,A).
% 1.65/1.88 0 [] cartesian_product2(A,B)!=empty_set|A=empty_set|B=empty_set.
% 1.65/1.88 0 [] cartesian_product2(A,B)=empty_set|A!=empty_set.
% 1.65/1.88 0 [] cartesian_product2(A,B)=empty_set|B!=empty_set.
% 1.65/1.88 0 [] -subset(cartesian_product2(A,B),cartesian_product2(C,D))|cartesian_product2(A,B)=empty_set|subset(A,C).
% 1.65/1.88 0 [] -subset(cartesian_product2(A,B),cartesian_product2(C,D))|cartesian_product2(A,B)=empty_set|subset(B,D).
% 1.65/1.88 0 [] -empty($c6).
% 1.65/1.88 0 [] subset(cartesian_product2($c6,$c5),cartesian_product2($c4,$c3))|subset(cartesian_product2($c5,$c6),cartesian_product2($c3,$c4)).
% 1.65/1.88 0 [] -subset($c5,$c3).
% 1.65/1.88 0 [] subset(empty_set,A).
% 1.65/1.88 end_of_list.
% 1.65/1.88
% 1.65/1.88 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.65/1.88
% 1.65/1.88 This ia a non-Horn set with equality. The strategy will be
% 1.65/1.88 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.65/1.88 deletion, with positive clauses in sos and nonpositive
% 1.65/1.88 clauses in usable.
% 1.65/1.88
% 1.65/1.88 dependent: set(knuth_bendix).
% 1.65/1.88 dependent: set(anl_eq).
% 1.65/1.88 dependent: set(para_from).
% 1.65/1.88 dependent: set(para_into).
% 1.65/1.88 dependent: clear(para_from_right).
% 1.65/1.88 dependent: clear(para_into_right).
% 1.65/1.88 dependent: set(para_from_vars).
% 1.65/1.88 dependent: set(eq_units_both_ways).
% 1.65/1.88 dependent: set(dynamic_demod_all).
% 1.65/1.88 dependent: set(dynamic_demod).
% 1.65/1.88 dependent: set(order_eq).
% 1.65/1.88 dependent: set(back_demod).
% 1.65/1.88 dependent: set(lrpo).
% 1.65/1.88 dependent: set(hyper_res).
% 1.65/1.88 dependent: set(unit_deletion).
% 1.65/1.88 dependent: set(factor).
% 1.65/1.88
% 1.65/1.88 ------------> process usable:
% 1.65/1.88 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.65/1.88 ** KEPT (pick-wt=11): 2 [] cartesian_product2(A,B)!=empty_set|A=empty_set|B=empty_set.
% 1.65/1.88 ** KEPT (pick-wt=8): 3 [] cartesian_product2(A,B)=empty_set|A!=empty_set.
% 1.65/1.88 ** KEPT (pick-wt=8): 4 [] cartesian_product2(A,B)=empty_set|B!=empty_set.
% 1.65/1.88 ** KEPT (pick-wt=15): 5 [] -subset(cartesian_product2(A,B),cartesian_product2(C,D))|cartesian_product2(A,B)=empty_set|subset(A,C).
% 1.65/1.88 ** KEPT (pick-wt=15): 6 [] -subset(cartesian_product2(A,B),cartesian_product2(C,D))|cartesian_product2(A,B)=empty_set|subset(B,D).
% 1.65/1.88 ** KEPT (pick-wt=2): 7 [] -empty($c6).
% 1.65/1.88 ** KEPT (pick-wt=3): 8 [] -subset($c5,$c3).
% 1.65/1.88
% 1.65/1.88 ------------> process sos:
% 1.65/1.88 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.65/1.88 ** KEPT (pick-wt=2): 11 [] empty(empty_set).
% 1.65/1.88 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.65/1.88 ** KEPT (pick-wt=3): 13 [] subset(A,A).
% 1.65/1.88 ** KEPT (pick-wt=14): 14 [] subset(cartesian_product2($c6,$c5),cartesian_product2($c4,$c3))|subset(cartesian_product2($c5,$c6),cartesian_product2($c3,$c4)).
% 1.65/1.88 ** KEPT (pick-wt=3): 15 [] subset(empty_set,A).
% 1.65/1.88 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.65/1.88
% 1.65/1.88 ======= end of input processing =======
% 1.65/1.88
% 1.65/1.88 =========== start of search ===========
% 1.65/1.88
% 1.65/1.88 -------- PROOF --------
% 1.65/1.88
% 1.65/1.88 ----> UNIT CONFLICT at 0.01 sec ----> 190 [binary,189.1,8.1] $F.
% 1.65/1.88
% 1.65/1.88 Length of proof is 6. Level of proof is 6.
% 1.65/1.88
% 1.65/1.88 ---------------- PROOF ----------------
% 1.65/1.88 % SZS status Theorem
% 1.65/1.88 % SZS output start Refutation
% See solution above
% 1.65/1.88 ------------ end of proof -------------
% 1.65/1.88
% 1.65/1.88
% 1.65/1.88 Search stopped by max_proofs option.
% 1.65/1.88
% 1.65/1.88
% 1.65/1.88 Search stopped by max_proofs option.
% 1.65/1.88
% 1.65/1.88 ============ end of search ============
% 1.65/1.88
% 1.65/1.88 -------------- statistics -------------
% 1.65/1.88 clauses given 13
% 1.65/1.88 clauses generated 331
% 1.65/1.88 clauses kept 184
% 1.65/1.88 clauses forward subsumed 242
% 1.65/1.88 clauses back subsumed 9
% 1.65/1.88 Kbytes malloced 976
% 1.65/1.88
% 1.65/1.88 ----------- times (seconds) -----------
% 1.65/1.88 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.88
% 1.65/1.88 That finishes the proof of the theorem.
% 1.65/1.88
% 1.65/1.88 Process 18398 finished Wed Jul 27 10:56:03 2022
% 1.65/1.88 Otter interrupted
% 1.65/1.88 PROOF FOUND
%------------------------------------------------------------------------------