TSTP Solution File: SET984+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 175.21s 175.44s
% Output : Refutation 175.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 24 ( 15 unt; 4 nHn; 18 RR)
% Number of literals : 41 ( 30 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( cartesian_product2(A,B) = empty_set
| A != empty_set ),
file('SET984+1.p',unknown),
[] ).
cnf(4,axiom,
( cartesian_product2(A,B) = empty_set
| B != empty_set ),
file('SET984+1.p',unknown),
[] ).
cnf(5,axiom,
( cartesian_product2(A,B) != cartesian_product2(C,D)
| A = empty_set
| B = empty_set
| A = C ),
file('SET984+1.p',unknown),
[] ).
cnf(6,axiom,
( cartesian_product2(A,B) != cartesian_product2(C,D)
| A = empty_set
| B = empty_set
| B = D ),
file('SET984+1.p',unknown),
[] ).
cnf(7,axiom,
cartesian_product2(dollar_c6,dollar_c5) != empty_set,
file('SET984+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(dollar_c6,dollar_c4)
| ~ subset(dollar_c5,dollar_c3) ),
file('SET984+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
file('SET984+1.p',unknown),
[] ).
cnf(18,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SET984+1.p',unknown),
[] ).
cnf(24,axiom,
cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('SET984+1.p',unknown),
[] ).
cnf(26,plain,
set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D)) = cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24])]),
[iquote('copy,24,flip.1')] ).
cnf(27,axiom,
subset(cartesian_product2(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3)),
file('SET984+1.p',unknown),
[] ).
cnf(28,axiom,
subset(set_intersection2(A,B),A),
file('SET984+1.p',unknown),
[] ).
cnf(55,plain,
( set_intersection2(A,B) = B
| ~ subset(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,9])]),
[iquote('para_into,18.1.1,9.2.1,flip.1')] ).
cnf(78,plain,
( subset(A,B)
| cartesian_product2(C,set_intersection2(B,D)) != cartesian_product2(E,A)
| C = empty_set
| set_intersection2(B,D) = empty_set ),
inference(para_into,[status(thm),theory(equality)],[28,6]),
[iquote('para_into,28.1.1,6.4.1')] ).
cnf(81,plain,
( subset(A,B)
| cartesian_product2(set_intersection2(B,C),D) != cartesian_product2(A,E)
| set_intersection2(B,C) = empty_set
| D = empty_set ),
inference(para_into,[status(thm),theory(equality)],[28,5]),
[iquote('para_into,28.1.1,5.4.1')] ).
cnf(147,plain,
cartesian_product2(set_intersection2(dollar_c6,dollar_c4),set_intersection2(dollar_c5,dollar_c3)) = cartesian_product2(dollar_c6,dollar_c5),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[27,9]),26]),
[iquote('hyper,27,9,demod,26')] ).
cnf(294,plain,
cartesian_product2(set_intersection2(dollar_c4,dollar_c6),set_intersection2(dollar_c3,dollar_c5)) = cartesian_product2(dollar_c6,dollar_c5),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[55,27]),26]),
[iquote('hyper,55,27,demod,26')] ).
cnf(4516,plain,
set_intersection2(dollar_c5,dollar_c3) != empty_set,
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[147,4]),7]),
[iquote('para_into,147.1.1,4.1.1,unit_del,7')] ).
cnf(4517,plain,
set_intersection2(dollar_c6,dollar_c4) != empty_set,
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[147,3]),7]),
[iquote('para_into,147.1.1,3.1.1,unit_del,7')] ).
cnf(4636,plain,
set_intersection2(dollar_c3,dollar_c5) != empty_set,
inference(para_into,[status(thm),theory(equality)],[4516,18]),
[iquote('para_into,4516.1.1,18.1.1')] ).
cnf(4637,plain,
set_intersection2(dollar_c4,dollar_c6) != empty_set,
inference(para_into,[status(thm),theory(equality)],[4517,18]),
[iquote('para_into,4517.1.1,18.1.1')] ).
cnf(7459,plain,
subset(dollar_c6,dollar_c4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[294,81]),4637,4636]),
[iquote('hyper,294,81,unit_del,4637,4636')] ).
cnf(7462,plain,
subset(dollar_c5,dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[294,78]),4637,4636]),
[iquote('hyper,294,78,unit_del,4637,4636')] ).
cnf(7473,plain,
$false,
inference(hyper,[status(thm)],[7462,8,7459]),
[iquote('hyper,7462,8,7459')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 10:34:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.91 ----- Otter 3.3f, August 2004 -----
% 1.68/1.91 The process was started by sandbox on n012.cluster.edu,
% 1.68/1.91 Wed Jul 27 10:34:50 2022
% 1.68/1.91 The command was "./otter". The process ID is 13481.
% 1.68/1.91
% 1.68/1.91 set(prolog_style_variables).
% 1.68/1.91 set(auto).
% 1.68/1.91 dependent: set(auto1).
% 1.68/1.91 dependent: set(process_input).
% 1.68/1.91 dependent: clear(print_kept).
% 1.68/1.91 dependent: clear(print_new_demod).
% 1.68/1.91 dependent: clear(print_back_demod).
% 1.68/1.91 dependent: clear(print_back_sub).
% 1.68/1.91 dependent: set(control_memory).
% 1.68/1.91 dependent: assign(max_mem, 12000).
% 1.68/1.91 dependent: assign(pick_given_ratio, 4).
% 1.68/1.91 dependent: assign(stats_level, 1).
% 1.68/1.91 dependent: assign(max_seconds, 10800).
% 1.68/1.91 clear(print_given).
% 1.68/1.91
% 1.68/1.91 formula_list(usable).
% 1.68/1.91 all A (A=A).
% 1.68/1.91 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.68/1.91 empty(empty_set).
% 1.68/1.91 all A B (set_intersection2(A,A)=A).
% 1.68/1.91 exists A empty(A).
% 1.68/1.91 exists A (-empty(A)).
% 1.68/1.91 all A B subset(A,A).
% 1.68/1.91 all A B (cartesian_product2(A,B)=empty_set<->A=empty_set|B=empty_set).
% 1.68/1.91 all A B C D (cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.68/1.91 all A B C D (cartesian_product2(A,B)=cartesian_product2(C,D)->A=empty_set|B=empty_set|A=C&B=D).
% 1.68/1.91 -(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))).
% 1.68/1.91 all A B subset(set_intersection2(A,B),A).
% 1.68/1.91 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.68/1.91 end_of_list.
% 1.68/1.91
% 1.68/1.91 -------> usable clausifies to:
% 1.68/1.91
% 1.68/1.91 list(usable).
% 1.68/1.91 0 [] A=A.
% 1.68/1.91 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.68/1.91 0 [] empty(empty_set).
% 1.68/1.91 0 [] set_intersection2(A,A)=A.
% 1.68/1.91 0 [] empty($c1).
% 1.68/1.91 0 [] -empty($c2).
% 1.68/1.91 0 [] subset(A,A).
% 1.68/1.91 0 [] cartesian_product2(A,B)!=empty_set|A=empty_set|B=empty_set.
% 1.68/1.91 0 [] cartesian_product2(A,B)=empty_set|A!=empty_set.
% 1.68/1.91 0 [] cartesian_product2(A,B)=empty_set|B!=empty_set.
% 1.68/1.91 0 [] cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.68/1.91 0 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|A=C.
% 1.68/1.91 0 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|B=D.
% 1.68/1.91 0 [] subset(cartesian_product2($c6,$c5),cartesian_product2($c4,$c3)).
% 1.68/1.91 0 [] cartesian_product2($c6,$c5)!=empty_set.
% 1.68/1.91 0 [] -subset($c6,$c4)| -subset($c5,$c3).
% 1.68/1.91 0 [] subset(set_intersection2(A,B),A).
% 1.68/1.91 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.68/1.91 end_of_list.
% 1.68/1.91
% 1.68/1.91 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.68/1.91
% 1.68/1.91 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.91 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.91 deletion, with positive clauses in sos and nonpositive
% 1.68/1.91 clauses in usable.
% 1.68/1.91
% 1.68/1.91 dependent: set(knuth_bendix).
% 1.68/1.91 dependent: set(anl_eq).
% 1.68/1.91 dependent: set(para_from).
% 1.68/1.91 dependent: set(para_into).
% 1.68/1.91 dependent: clear(para_from_right).
% 1.68/1.91 dependent: clear(para_into_right).
% 1.68/1.91 dependent: set(para_from_vars).
% 1.68/1.91 dependent: set(eq_units_both_ways).
% 1.68/1.91 dependent: set(dynamic_demod_all).
% 1.68/1.91 dependent: set(dynamic_demod).
% 1.68/1.91 dependent: set(order_eq).
% 1.68/1.91 dependent: set(back_demod).
% 1.68/1.91 dependent: set(lrpo).
% 1.68/1.91 dependent: set(hyper_res).
% 1.68/1.91 dependent: set(unit_deletion).
% 1.68/1.91 dependent: set(factor).
% 1.68/1.91
% 1.68/1.91 ------------> process usable:
% 1.68/1.91 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.68/1.91 ** KEPT (pick-wt=11): 2 [] cartesian_product2(A,B)!=empty_set|A=empty_set|B=empty_set.
% 1.68/1.91 ** KEPT (pick-wt=8): 3 [] cartesian_product2(A,B)=empty_set|A!=empty_set.
% 1.68/1.91 ** KEPT (pick-wt=8): 4 [] cartesian_product2(A,B)=empty_set|B!=empty_set.
% 1.68/1.91 ** KEPT (pick-wt=16): 5 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|A=C.
% 1.68/1.91 ** KEPT (pick-wt=16): 6 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|B=D.
% 1.68/1.91 ** KEPT (pick-wt=5): 7 [] cartesian_product2($c6,$c5)!=empty_set.
% 1.68/1.91 ** KEPT (pick-wt=6): 8 [] -subset($c6,$c4)| -subset($c5,$c3).
% 1.68/1.91 ** KEPT (pick-wt=8): 9 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.68/1.91
% 1.68/1.91 ------------> process sos:
% 1.68/1.91 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.68/1.91 ** KEPT (pick-wt=7): 18 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.68/1.91 ** KEPT (pick-wt=2): 19 [] empty(empty_set).
% 1.68/1.91 ** KEPT (pick-wt=5): 20 [] set_intersection2(A,A)=A.
% 1.68/1.91 ---> New Demodulator: 21 [new_demod,20] set_intersection2(A,A)=A.
% 175.21/175.44 ** KEPT (pick-wt=2): 22 [] empty($c1).
% 175.21/175.44 ** KEPT (pick-wt=3): 23 [] subset(A,A).
% 175.21/175.44 ** KEPT (pick-wt=15): 25 [copy,24,flip.1] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 175.21/175.44 ---> New Demodulator: 26 [new_demod,25] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 175.21/175.44 ** KEPT (pick-wt=7): 27 [] subset(cartesian_product2($c6,$c5),cartesian_product2($c4,$c3)).
% 175.21/175.44 ** KEPT (pick-wt=5): 28 [] subset(set_intersection2(A,B),A).
% 175.21/175.44 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 175.21/175.44 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 175.21/175.44 >>>> Starting back demodulation with 21.
% 175.21/175.44 >>>> Starting back demodulation with 26.
% 175.21/175.44
% 175.21/175.44 ======= end of input processing =======
% 175.21/175.44
% 175.21/175.44 =========== start of search ===========
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Resetting weight limit to 12.
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Resetting weight limit to 12.
% 175.21/175.44
% 175.21/175.44 sos_size=3150
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Resetting weight limit to 10.
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Resetting weight limit to 10.
% 175.21/175.44
% 175.21/175.44 sos_size=3319
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Resetting weight limit to 9.
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Resetting weight limit to 9.
% 175.21/175.44
% 175.21/175.44 sos_size=3396
% 175.21/175.44
% 175.21/175.44 -- HEY sandbox, WE HAVE A PROOF!! --
% 175.21/175.44
% 175.21/175.44 -----> EMPTY CLAUSE at 173.53 sec ----> 7473 [hyper,7462,8,7459] $F.
% 175.21/175.44
% 175.21/175.44 Length of proof is 12. Level of proof is 5.
% 175.21/175.44
% 175.21/175.44 ---------------- PROOF ----------------
% 175.21/175.44 % SZS status Theorem
% 175.21/175.44 % SZS output start Refutation
% See solution above
% 175.21/175.44 ------------ end of proof -------------
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Search stopped by max_proofs option.
% 175.21/175.44
% 175.21/175.44
% 175.21/175.44 Search stopped by max_proofs option.
% 175.21/175.44
% 175.21/175.44 ============ end of search ============
% 175.21/175.44
% 175.21/175.44 -------------- statistics -------------
% 175.21/175.44 clauses given 818
% 175.21/175.44 clauses generated 638114
% 175.21/175.44 clauses kept 7450
% 175.21/175.44 clauses forward subsumed 51432
% 175.21/175.44 clauses back subsumed 872
% 175.21/175.44 Kbytes malloced 5859
% 175.21/175.44
% 175.21/175.44 ----------- times (seconds) -----------
% 175.21/175.44 user CPU time 173.53 (0 hr, 2 min, 53 sec)
% 175.21/175.44 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 175.21/175.44 wall-clock time 175 (0 hr, 2 min, 55 sec)
% 175.21/175.44
% 175.21/175.44 That finishes the proof of the theorem.
% 175.21/175.44
% 175.21/175.44 Process 13481 finished Wed Jul 27 10:37:45 2022
% 175.21/175.44 Otter interrupted
% 175.21/175.44 PROOF FOUND
%------------------------------------------------------------------------------