TSTP Solution File: SET962+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 13:14:36 EDT 2022
% Result : Theorem 1.79s 2.00s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 7 unt; 3 nHn; 14 RR)
% Number of literals : 33 ( 7 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
file('SET962+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
file('SET962+1.p',unknown),
[] ).
cnf(5,axiom,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
file('SET962+1.p',unknown),
[] ).
cnf(7,axiom,
dollar_c4 != dollar_c3,
file('SET962+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(dollar_f1(A,B),A)
| ~ in(dollar_f1(A,B),B)
| A = B ),
file('SET962+1.p',unknown),
[] ).
cnf(10,plain,
( in(ordered_pair(A,A),cartesian_product2(B,B))
| ~ in(A,B) ),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.2.3')] ).
cnf(18,axiom,
cartesian_product2(dollar_c4,dollar_c4) = cartesian_product2(dollar_c3,dollar_c3),
file('SET962+1.p',unknown),
[] ).
cnf(20,axiom,
( in(dollar_f1(A,B),A)
| in(dollar_f1(A,B),B)
| A = B ),
file('SET962+1.p',unknown),
[] ).
cnf(27,plain,
( in(ordered_pair(A,B),cartesian_product2(dollar_c3,dollar_c3))
| ~ in(A,dollar_c4)
| ~ in(B,dollar_c4) ),
inference(para_from,[status(thm),theory(equality)],[18,5]),
[iquote('para_from,18.1.1,5.1.2')] ).
cnf(29,plain,
( ~ in(ordered_pair(A,B),cartesian_product2(dollar_c3,dollar_c3))
| in(A,dollar_c4) ),
inference(para_from,[status(thm),theory(equality)],[18,3]),
[iquote('para_from,18.1.1,3.1.2')] ).
cnf(39,plain,
( in(dollar_f1(A,B),B)
| A = B
| in(ordered_pair(dollar_f1(A,B),dollar_f1(A,B)),cartesian_product2(A,A)) ),
inference(hyper,[status(thm)],[20,10]),
[iquote('hyper,20,10')] ).
cnf(1665,plain,
( in(dollar_f1(dollar_c3,A),A)
| dollar_c3 = A
| in(dollar_f1(dollar_c3,A),dollar_c4) ),
inference(hyper,[status(thm)],[39,29]),
[iquote('hyper,39,29')] ).
cnf(1666,plain,
in(dollar_f1(dollar_c3,dollar_c4),dollar_c4),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[1665]),7]),
[iquote('factor,1665.1.3,unit_del,7')] ).
cnf(1670,plain,
in(ordered_pair(dollar_f1(dollar_c3,dollar_c4),dollar_f1(dollar_c3,dollar_c4)),cartesian_product2(dollar_c3,dollar_c3)),
inference(hyper,[status(thm)],[1666,27,1666]),
[iquote('hyper,1666,27,1666')] ).
cnf(1701,plain,
in(dollar_f1(dollar_c3,dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[1670,4]),
[iquote('hyper,1670,4')] ).
cnf(1703,plain,
dollar_c4 = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1701,8,1666])]),
[iquote('hyper,1701,8,1666,flip.1')] ).
cnf(1705,plain,
$false,
inference(binary,[status(thm)],[1703,7]),
[iquote('binary,1703.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.12 % 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 10:36:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.97 ----- Otter 3.3f, August 2004 -----
% 1.71/1.97 The process was started by sandbox on n028.cluster.edu,
% 1.71/1.97 Wed Jul 27 10:36:19 2022
% 1.71/1.97 The command was "./otter". The process ID is 16800.
% 1.71/1.97
% 1.71/1.97 set(prolog_style_variables).
% 1.71/1.97 set(auto).
% 1.71/1.97 dependent: set(auto1).
% 1.71/1.97 dependent: set(process_input).
% 1.71/1.97 dependent: clear(print_kept).
% 1.71/1.97 dependent: clear(print_new_demod).
% 1.71/1.97 dependent: clear(print_back_demod).
% 1.71/1.97 dependent: clear(print_back_sub).
% 1.71/1.97 dependent: set(control_memory).
% 1.71/1.97 dependent: assign(max_mem, 12000).
% 1.71/1.97 dependent: assign(pick_given_ratio, 4).
% 1.71/1.97 dependent: assign(stats_level, 1).
% 1.71/1.97 dependent: assign(max_seconds, 10800).
% 1.71/1.97 clear(print_given).
% 1.71/1.97
% 1.71/1.97 formula_list(usable).
% 1.71/1.97 all A (A=A).
% 1.71/1.97 all A B (in(A,B)-> -in(B,A)).
% 1.71/1.97 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.71/1.97 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.71/1.97 all A B (-empty(ordered_pair(A,B))).
% 1.71/1.97 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 1.71/1.97 exists A empty(A).
% 1.71/1.97 exists A (-empty(A)).
% 1.71/1.97 -(all A B (cartesian_product2(A,A)=cartesian_product2(B,B)->A=B)).
% 1.71/1.97 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.71/1.97 end_of_list.
% 1.71/1.97
% 1.71/1.97 -------> usable clausifies to:
% 1.71/1.97
% 1.71/1.97 list(usable).
% 1.71/1.97 0 [] A=A.
% 1.71/1.97 0 [] -in(A,B)| -in(B,A).
% 1.71/1.97 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.71/1.97 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.71/1.97 0 [] -empty(ordered_pair(A,B)).
% 1.71/1.97 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.71/1.97 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.71/1.97 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.71/1.97 0 [] empty($c1).
% 1.71/1.97 0 [] -empty($c2).
% 1.71/1.97 0 [] cartesian_product2($c4,$c4)=cartesian_product2($c3,$c3).
% 1.71/1.97 0 [] $c4!=$c3.
% 1.71/1.97 0 [] in($f1(A,B),A)|in($f1(A,B),B)|A=B.
% 1.71/1.97 0 [] -in($f1(A,B),A)| -in($f1(A,B),B)|A=B.
% 1.71/1.97 end_of_list.
% 1.71/1.97
% 1.71/1.97 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.71/1.97
% 1.71/1.97 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.97 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.97 deletion, with positive clauses in sos and nonpositive
% 1.71/1.97 clauses in usable.
% 1.71/1.97
% 1.71/1.97 dependent: set(knuth_bendix).
% 1.71/1.97 dependent: set(anl_eq).
% 1.71/1.97 dependent: set(para_from).
% 1.71/1.97 dependent: set(para_into).
% 1.71/1.97 dependent: clear(para_from_right).
% 1.71/1.97 dependent: clear(para_into_right).
% 1.71/1.97 dependent: set(para_from_vars).
% 1.71/1.97 dependent: set(eq_units_both_ways).
% 1.71/1.97 dependent: set(dynamic_demod_all).
% 1.71/1.97 dependent: set(dynamic_demod).
% 1.71/1.97 dependent: set(order_eq).
% 1.71/1.97 dependent: set(back_demod).
% 1.71/1.97 dependent: set(lrpo).
% 1.71/1.97 dependent: set(hyper_res).
% 1.71/1.97 dependent: set(unit_deletion).
% 1.71/1.97 dependent: set(factor).
% 1.71/1.97
% 1.71/1.97 ------------> process usable:
% 1.71/1.97 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.71/1.97 ** KEPT (pick-wt=4): 2 [] -empty(ordered_pair(A,B)).
% 1.71/1.97 ** KEPT (pick-wt=10): 3 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.71/1.97 ** KEPT (pick-wt=10): 4 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.71/1.97 ** KEPT (pick-wt=13): 5 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.71/1.97 ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.71/1.97 ** KEPT (pick-wt=3): 7 [] $c4!=$c3.
% 1.71/1.97 ** KEPT (pick-wt=13): 8 [] -in($f1(A,B),A)| -in($f1(A,B),B)|A=B.
% 1.71/1.97
% 1.71/1.97 ------------> process sos:
% 1.71/1.97 ** KEPT (pick-wt=3): 12 [] A=A.
% 1.71/1.97 ** KEPT (pick-wt=7): 13 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.71/1.97 ** KEPT (pick-wt=10): 15 [copy,14,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.71/1.97 ---> New Demodulator: 16 [new_demod,15] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.71/1.97 ** KEPT (pick-wt=2): 17 [] empty($c1).
% 1.71/1.97 ** KEPT (pick-wt=7): 18 [] cartesian_product2($c4,$c4)=cartesian_product2($c3,$c3).
% 1.71/1.97 ---> New Demodulator: 19 [new_demod,18] cartesian_product2($c4,$c4)=cartesian_product2($c3,$c3).
% 1.71/1.97 ** KEPT (pick-wt=13): 20 [] in($f1(A,B),A)|in($f1(A,B),B)|A=B.
% 1.71/1.97 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 1.71/1.97 12 back subsumes 11.
% 1.71/1.97 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.71/1.97 >>>> Starting back demodulation with 16.
% 1.71/1.97 >>>> Starting back demodulation with 19.
% 1.71/1.97
% 1.71/1.97 ======= end of input processing =======
% 1.71/1.97
% 1.71/1.97 =========== start of search ===========
% 1.71/1.97
% 1.71/1.97
% 1.71/1.97 Resetting weight limit to 20.
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Resetting weight limit to 20.
% 1.79/2.00
% 1.79/2.00 sos_size=1549
% 1.79/2.00
% 1.79/2.00 -------- PROOF --------
% 1.79/2.00
% 1.79/2.00 ----> UNIT CONFLICT at 0.18 sec ----> 1705 [binary,1703.1,7.1] $F.
% 1.79/2.00
% 1.79/2.00 Length of proof is 9. Level of proof is 7.
% 1.79/2.00
% 1.79/2.00 ---------------- PROOF ----------------
% 1.79/2.00 % SZS status Theorem
% 1.79/2.00 % SZS output start Refutation
% See solution above
% 1.79/2.00 ------------ end of proof -------------
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00 ============ end of search ============
% 1.79/2.00
% 1.79/2.00 -------------- statistics -------------
% 1.79/2.00 clauses given 54
% 1.79/2.00 clauses generated 4427
% 1.79/2.00 clauses kept 1676
% 1.79/2.00 clauses forward subsumed 2005
% 1.79/2.00 clauses back subsumed 151
% 1.79/2.00 Kbytes malloced 4882
% 1.79/2.00
% 1.79/2.00 ----------- times (seconds) -----------
% 1.79/2.00 user CPU time 0.18 (0 hr, 0 min, 0 sec)
% 1.79/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.00 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/2.00
% 1.79/2.00 That finishes the proof of the theorem.
% 1.79/2.00
% 1.79/2.00 Process 16800 finished Wed Jul 27 10:36:20 2022
% 1.79/2.00 Otter interrupted
% 1.79/2.00 PROOF FOUND
%------------------------------------------------------------------------------