%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET977+1 : 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 13:14:37 EDT 2022
% Result : Theorem 1.87s 2.06s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 6 unt; 4 nHn; 9 RR)
% Number of literals : 22 ( 13 equ; 8 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SET977+1.p',unknown),
[] ).
cnf(7,axiom,
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
| A != C
| ~ in(B,D) ),
file('SET977+1.p',unknown),
[] ).
cnf(10,axiom,
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| ~ in(A,C)
| B != D ),
file('SET977+1.p',unknown),
[] ).
cnf(11,axiom,
dollar_c4 != empty_set,
file('SET977+1.p',unknown),
[] ).
cnf(12,plain,
empty_set != dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
A = A,
file('SET977+1.p',unknown),
[] ).
cnf(16,axiom,
( A = empty_set
| in(dollar_f1(A),A) ),
file('SET977+1.p',unknown),
[] ).
cnf(22,axiom,
( cartesian_product2(singleton(dollar_c3),dollar_c4) = empty_set
| cartesian_product2(dollar_c4,singleton(dollar_c3)) = empty_set ),
file('SET977+1.p',unknown),
[] ).
cnf(30,plain,
( A = empty_set
| in(ordered_pair(dollar_f1(A),B),cartesian_product2(A,singleton(B))) ),
inference(hyper,[status(thm)],[16,10,14]),
[iquote('hyper,16,10,14')] ).
cnf(32,plain,
( A = empty_set
| in(ordered_pair(B,dollar_f1(A)),cartesian_product2(singleton(B),A)) ),
inference(hyper,[status(thm)],[16,7,14]),
[iquote('hyper,16,7,14')] ).
cnf(772,plain,
cartesian_product2(singleton(dollar_c3),dollar_c4) = empty_set,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[30,2,22]),12]),
[iquote('hyper,30,2,22,unit_del,12')] ).
cnf(1465,plain,
empty_set = dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[32,2,772])]),
[iquote('hyper,32,2,772,flip.1')] ).
cnf(1467,plain,
$false,
inference(binary,[status(thm)],[1465,12]),
[iquote('binary,1465.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% 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 10:38:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.90 ----- Otter 3.3f, August 2004 -----
% 1.68/1.90 The process was started by sandbox2 on n028.cluster.edu,
% 1.68/1.90 Wed Jul 27 10:38:19 2022
% 1.68/1.90 The command was "./otter". The process ID is 19510.
% 1.68/1.90
% 1.68/1.90 set(prolog_style_variables).
% 1.68/1.90 set(auto).
% 1.68/1.90 dependent: set(auto1).
% 1.68/1.90 dependent: set(process_input).
% 1.68/1.90 dependent: clear(print_kept).
% 1.68/1.90 dependent: clear(print_new_demod).
% 1.68/1.90 dependent: clear(print_back_demod).
% 1.68/1.90 dependent: clear(print_back_sub).
% 1.68/1.90 dependent: set(control_memory).
% 1.68/1.90 dependent: assign(max_mem, 12000).
% 1.68/1.90 dependent: assign(pick_given_ratio, 4).
% 1.68/1.90 dependent: assign(stats_level, 1).
% 1.68/1.90 dependent: assign(max_seconds, 10800).
% 1.68/1.90 clear(print_given).
% 1.68/1.90
% 1.68/1.90 formula_list(usable).
% 1.68/1.90 all A (A=A).
% 1.68/1.90 all A B (in(A,B)-> -in(B,A)).
% 1.68/1.90 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.68/1.90 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.68/1.90 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.68/1.90 empty(empty_set).
% 1.68/1.90 all A B (-empty(ordered_pair(A,B))).
% 1.68/1.90 exists A empty(A).
% 1.68/1.90 exists A (-empty(A)).
% 1.68/1.90 all A B C D (in(ordered_pair(A,B),cartesian_product2(singleton(C),D))<->A=C&in(B,D)).
% 1.68/1.90 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))<->in(A,C)&B=D).
% 1.68/1.90 -(all A B (A!=empty_set->cartesian_product2(singleton(B),A)!=empty_set&cartesian_product2(A,singleton(B))!=empty_set)).
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 -------> usable clausifies to:
% 1.68/1.90
% 1.68/1.90 list(usable).
% 1.68/1.90 0 [] A=A.
% 1.68/1.90 0 [] -in(A,B)| -in(B,A).
% 1.68/1.90 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.68/1.90 0 [] A!=empty_set| -in(B,A).
% 1.68/1.90 0 [] A=empty_set|in($f1(A),A).
% 1.68/1.90 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.68/1.90 0 [] empty(empty_set).
% 1.68/1.90 0 [] -empty(ordered_pair(A,B)).
% 1.68/1.90 0 [] empty($c1).
% 1.68/1.90 0 [] -empty($c2).
% 1.68/1.90 0 [] -in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|A=C.
% 1.68/1.90 0 [] -in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|in(B,D).
% 1.68/1.90 0 [] in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|A!=C| -in(B,D).
% 1.68/1.90 0 [] -in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|in(A,C).
% 1.68/1.90 0 [] -in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|B=D.
% 1.68/1.90 0 [] in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))| -in(A,C)|B!=D.
% 1.68/1.90 0 [] $c4!=empty_set.
% 1.68/1.90 0 [] cartesian_product2(singleton($c3),$c4)=empty_set|cartesian_product2($c4,singleton($c3))=empty_set.
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.90
% 1.68/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.90 deletion, with positive clauses in sos and nonpositive
% 1.68/1.90 clauses in usable.
% 1.68/1.90
% 1.68/1.90 dependent: set(knuth_bendix).
% 1.68/1.90 dependent: set(anl_eq).
% 1.68/1.90 dependent: set(para_from).
% 1.68/1.90 dependent: set(para_into).
% 1.68/1.90 dependent: clear(para_from_right).
% 1.68/1.90 dependent: clear(para_into_right).
% 1.68/1.90 dependent: set(para_from_vars).
% 1.68/1.90 dependent: set(eq_units_both_ways).
% 1.68/1.90 dependent: set(dynamic_demod_all).
% 1.68/1.90 dependent: set(dynamic_demod).
% 1.68/1.90 dependent: set(order_eq).
% 1.68/1.90 dependent: set(back_demod).
% 1.68/1.90 dependent: set(lrpo).
% 1.68/1.90 dependent: set(hyper_res).
% 1.68/1.90 dependent: set(unit_deletion).
% 1.68/1.90 dependent: set(factor).
% 1.68/1.90
% 1.68/1.90 ------------> process usable:
% 1.68/1.90 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.68/1.90 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.68/1.90 ** KEPT (pick-wt=4): 3 [] -empty(ordered_pair(A,B)).
% 1.68/1.90 ** KEPT (pick-wt=2): 4 [] -empty($c2).
% 1.68/1.90 ** KEPT (pick-wt=11): 5 [] -in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|A=C.
% 1.68/1.90 ** KEPT (pick-wt=11): 6 [] -in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|in(B,D).
% 1.68/1.90 ** KEPT (pick-wt=14): 7 [] in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|A!=C| -in(B,D).
% 1.68/1.90 ** KEPT (pick-wt=11): 8 [] -in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|in(A,C).
% 1.68/1.90 ** KEPT (pick-wt=11): 9 [] -in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|B=D.
% 1.68/1.90 ** KEPT (pick-wt=14): 10 [] in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))| -in(A,C)|B!=D.
% 1.68/1.90 ** KEPT (pick-wt=3): 12 [copy,11,flip.1] empty_set!=$c4.
% 1.68/1.90
% 1.68/1.90 ------------> process sos:
% 1.68/1.90 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.68/1.90 ** KEPT (pick-wt=7): 15 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.68/1.90 ** KEPT (pick-wt=7): 16 [] A=empty_set|in($f1(A),A).
% 1.68/1.90 ** KEPT (pick-wt=10): 18 [copy,17,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.87/2.06 ---> New Demodulator: 19 [new_demod,18] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.87/2.06 ** KEPT (pick-wt=2): 20 [] empty(empty_set).
% 1.87/2.06 ** KEPT (pick-wt=2): 21 [] empty($c1).
% 1.87/2.06 ** KEPT (pick-wt=12): 22 [] cartesian_product2(singleton($c3),$c4)=empty_set|cartesian_product2($c4,singleton($c3))=empty_set.
% 1.87/2.06 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.87/2.06 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.87/2.06 >>>> Starting back demodulation with 19.
% 1.87/2.06
% 1.87/2.06 ======= end of input processing =======
% 1.87/2.06
% 1.87/2.06 =========== start of search ===========
% 1.87/2.06
% 1.87/2.06 -------- PROOF --------
% 1.87/2.06
% 1.87/2.06 ----> UNIT CONFLICT at 0.16 sec ----> 1467 [binary,1465.1,12.1] $F.
% 1.87/2.06
% 1.87/2.06 Length of proof is 5. Level of proof is 3.
% 1.87/2.06
% 1.87/2.06 ---------------- PROOF ----------------
% 1.87/2.06 % SZS status Theorem
% 1.87/2.06 % SZS output start Refutation
% See solution above
% 1.87/2.06 ------------ end of proof -------------
% 1.87/2.06
% 1.87/2.06
% 1.87/2.06 Search stopped by max_proofs option.
% 1.87/2.06
% 1.87/2.06
% 1.87/2.06 Search stopped by max_proofs option.
% 1.87/2.06
% 1.87/2.06 ============ end of search ============
% 1.87/2.06
% 1.87/2.06 -------------- statistics -------------
% 1.87/2.06 clauses given 41
% 1.87/2.06 clauses generated 2066
% 1.87/2.06 clauses kept 1452
% 1.87/2.06 clauses forward subsumed 706
% 1.87/2.06 clauses back subsumed 57
% 1.87/2.06 Kbytes malloced 3906
% 1.87/2.06
% 1.87/2.06 ----------- times (seconds) -----------
% 1.87/2.06 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 1.87/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.06 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.87/2.06
% 1.87/2.06 That finishes the proof of the theorem.
% 1.87/2.06
% 1.87/2.06 Process 19510 finished Wed Jul 27 10:38:20 2022
% 1.87/2.06 Otter interrupted
% 1.87/2.06 PROOF FOUND
%------------------------------------------------------------------------------