TSTP Solution File: SEU162+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:15:00 EDT 2022
% Result : Theorem 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 6 unt; 3 nHn; 13 RR)
% Number of literals : 24 ( 7 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
file('SEU162+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ disjoint(A,B)
| disjoint(B,A) ),
file('SEU162+3.p',unknown),
[] ).
cnf(5,axiom,
( set_difference(dollar_c4,singleton(dollar_c3)) = dollar_c4
| ~ in(dollar_c3,dollar_c4) ),
file('SEU162+3.p',unknown),
[] ).
cnf(6,axiom,
( set_difference(dollar_c4,singleton(dollar_c3)) != dollar_c4
| in(dollar_c3,dollar_c4) ),
file('SEU162+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
file('SEU162+3.p',unknown),
[] ).
cnf(8,axiom,
( disjoint(A,B)
| set_difference(A,B) != A ),
file('SEU162+3.p',unknown),
[] ).
cnf(10,axiom,
A = A,
file('SEU162+3.p',unknown),
[] ).
cnf(11,axiom,
( in(A,B)
| disjoint(singleton(A),B) ),
file('SEU162+3.p',unknown),
[] ).
cnf(14,plain,
( disjoint(singleton(dollar_c3),dollar_c4)
| set_difference(dollar_c4,singleton(dollar_c3)) = dollar_c4 ),
inference(hyper,[status(thm)],[11,5]),
[iquote('hyper,11,5')] ).
cnf(23,plain,
( disjoint(dollar_c4,singleton(dollar_c3))
| disjoint(singleton(dollar_c3),dollar_c4) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[14,8]),10]),
[iquote('para_from,14.2.1,8.2.1,unit_del,10')] ).
cnf(26,plain,
disjoint(singleton(dollar_c3),dollar_c4),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[23,4])]),
[iquote('hyper,23,4,factor_simp')] ).
cnf(28,plain,
disjoint(dollar_c4,singleton(dollar_c3)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[23,4])]),
[iquote('hyper,23,4,factor_simp')] ).
cnf(33,plain,
set_difference(dollar_c4,singleton(dollar_c3)) = dollar_c4,
inference(hyper,[status(thm)],[28,7]),
[iquote('hyper,28,7')] ).
cnf(34,plain,
in(dollar_c3,dollar_c4),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),33]),10]),
[iquote('back_demod,6,demod,33,unit_del,10')] ).
cnf(35,plain,
$false,
inference(hyper,[status(thm)],[34,2,26]),
[iquote('hyper,34,2,26')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 07:59:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox2 on n027.cluster.edu,
% 1.68/1.89 Wed Jul 27 07:59:51 2022
% 1.68/1.89 The command was "./otter". The process ID is 28523.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 formula_list(usable).
% 1.68/1.89 all A (A=A).
% 1.68/1.89 all A B (in(A,B)-> -in(B,A)).
% 1.68/1.89 all A B (-(disjoint(singleton(A),B)&in(A,B))).
% 1.68/1.89 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 1.68/1.89 exists A empty(A).
% 1.68/1.89 exists A (-empty(A)).
% 1.68/1.89 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.68/1.89 -(all A B (set_difference(A,singleton(B))=A<-> -in(B,A))).
% 1.68/1.89 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 -------> usable clausifies to:
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] -in(A,B)| -in(B,A).
% 1.68/1.89 0 [] -disjoint(singleton(A),B)| -in(A,B).
% 1.68/1.89 0 [] in(A,B)|disjoint(singleton(A),B).
% 1.68/1.89 0 [] empty($c1).
% 1.68/1.89 0 [] -empty($c2).
% 1.68/1.89 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.68/1.89 0 [] set_difference($c4,singleton($c3))=$c4| -in($c3,$c4).
% 1.68/1.89 0 [] set_difference($c4,singleton($c3))!=$c4|in($c3,$c4).
% 1.68/1.89 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.68/1.89 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.68/1.89
% 1.68/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.89 deletion, with positive clauses in sos and nonpositive
% 1.68/1.89 clauses in usable.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89 dependent: set(hyper_res).
% 1.68/1.89 dependent: set(unit_deletion).
% 1.68/1.89 dependent: set(factor).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.68/1.89 ** KEPT (pick-wt=7): 2 [] -disjoint(singleton(A),B)| -in(A,B).
% 1.68/1.89 ** KEPT (pick-wt=2): 3 [] -empty($c2).
% 1.68/1.89 ** KEPT (pick-wt=6): 4 [] -disjoint(A,B)|disjoint(B,A).
% 1.68/1.89 ** KEPT (pick-wt=9): 5 [] set_difference($c4,singleton($c3))=$c4| -in($c3,$c4).
% 1.68/1.89 ** KEPT (pick-wt=9): 6 [] set_difference($c4,singleton($c3))!=$c4|in($c3,$c4).
% 1.68/1.89 ** KEPT (pick-wt=8): 7 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.68/1.89 ** KEPT (pick-wt=8): 8 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=7): 11 [] in(A,B)|disjoint(singleton(A),B).
% 1.68/1.89 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.68/1.89 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 -----> EMPTY CLAUSE at 0.00 sec ----> 35 [hyper,34,2,26] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 6. Level of proof is 5.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Theorem
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 14
% 1.68/1.89 clauses generated 68
% 1.68/1.89 clauses kept 30
% 1.68/1.89 clauses forward subsumed 53
% 1.68/1.89 clauses back subsumed 4
% 1.68/1.89 Kbytes malloced 976
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 28523 finished Wed Jul 27 07:59:53 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------