TSTP Solution File: SET926+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET926+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:14:32 EDT 2022
% Result : Theorem 1.69s 1.90s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 6 unt; 1 nHn; 6 RR)
% Number of literals : 10 ( 6 equ; 3 neg)
% Maximal clause size : 2 ( 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; 3 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ),
file('SET926+1.p',unknown),
[] ).
cnf(6,axiom,
set_difference(singleton(dollar_c4),dollar_c3) != empty_set,
file('SET926+1.p',unknown),
[] ).
cnf(7,axiom,
set_difference(singleton(dollar_c4),dollar_c3) != singleton(dollar_c4),
file('SET926+1.p',unknown),
[] ).
cnf(9,axiom,
A = A,
file('SET926+1.p',unknown),
[] ).
cnf(11,axiom,
( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ),
file('SET926+1.p',unknown),
[] ).
cnf(17,plain,
in(dollar_c4,dollar_c3),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[11,7]),9]),
[iquote('para_from,11.1.1,7.1.1,unit_del,9')] ).
cnf(19,plain,
set_difference(singleton(dollar_c4),dollar_c3) = empty_set,
inference(hyper,[status(thm)],[17,4]),
[iquote('hyper,17,4')] ).
cnf(21,plain,
$false,
inference(binary,[status(thm)],[19,6]),
[iquote('binary,19.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET926+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.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 10:42:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.90 ----- Otter 3.3f, August 2004 -----
% 1.69/1.90 The process was started by sandbox on n008.cluster.edu,
% 1.69/1.90 Wed Jul 27 10:42:08 2022
% 1.69/1.90 The command was "./otter". The process ID is 22256.
% 1.69/1.90
% 1.69/1.90 set(prolog_style_variables).
% 1.69/1.90 set(auto).
% 1.69/1.90 dependent: set(auto1).
% 1.69/1.90 dependent: set(process_input).
% 1.69/1.90 dependent: clear(print_kept).
% 1.69/1.90 dependent: clear(print_new_demod).
% 1.69/1.90 dependent: clear(print_back_demod).
% 1.69/1.90 dependent: clear(print_back_sub).
% 1.69/1.90 dependent: set(control_memory).
% 1.69/1.90 dependent: assign(max_mem, 12000).
% 1.69/1.90 dependent: assign(pick_given_ratio, 4).
% 1.69/1.90 dependent: assign(stats_level, 1).
% 1.69/1.90 dependent: assign(max_seconds, 10800).
% 1.69/1.90 clear(print_given).
% 1.69/1.90
% 1.69/1.90 formula_list(usable).
% 1.69/1.90 all A (A=A).
% 1.69/1.90 all A B (in(A,B)-> -in(B,A)).
% 1.69/1.90 empty(empty_set).
% 1.69/1.90 all A B (set_difference(singleton(A),B)=singleton(A)<-> -in(A,B)).
% 1.69/1.90 all A B (set_difference(singleton(A),B)=empty_set<->in(A,B)).
% 1.69/1.90 exists A empty(A).
% 1.69/1.90 exists A (-empty(A)).
% 1.69/1.90 -(all A B (set_difference(singleton(A),B)=empty_set|set_difference(singleton(A),B)=singleton(A))).
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 -------> usable clausifies to:
% 1.69/1.90
% 1.69/1.90 list(usable).
% 1.69/1.90 0 [] A=A.
% 1.69/1.90 0 [] -in(A,B)| -in(B,A).
% 1.69/1.90 0 [] empty(empty_set).
% 1.69/1.90 0 [] set_difference(singleton(A),B)!=singleton(A)| -in(A,B).
% 1.69/1.90 0 [] set_difference(singleton(A),B)=singleton(A)|in(A,B).
% 1.69/1.90 0 [] set_difference(singleton(A),B)!=empty_set|in(A,B).
% 1.69/1.90 0 [] set_difference(singleton(A),B)=empty_set| -in(A,B).
% 1.69/1.90 0 [] empty($c1).
% 1.69/1.90 0 [] -empty($c2).
% 1.69/1.90 0 [] set_difference(singleton($c4),$c3)!=empty_set.
% 1.69/1.90 0 [] set_difference(singleton($c4),$c3)!=singleton($c4).
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.69/1.90
% 1.69/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.90 deletion, with positive clauses in sos and nonpositive
% 1.69/1.90 clauses in usable.
% 1.69/1.90
% 1.69/1.90 dependent: set(knuth_bendix).
% 1.69/1.90 dependent: set(anl_eq).
% 1.69/1.90 dependent: set(para_from).
% 1.69/1.90 dependent: set(para_into).
% 1.69/1.90 dependent: clear(para_from_right).
% 1.69/1.90 dependent: clear(para_into_right).
% 1.69/1.90 dependent: set(para_from_vars).
% 1.69/1.90 dependent: set(eq_units_both_ways).
% 1.69/1.90 dependent: set(dynamic_demod_all).
% 1.69/1.90 dependent: set(dynamic_demod).
% 1.69/1.90 dependent: set(order_eq).
% 1.69/1.90 dependent: set(back_demod).
% 1.69/1.90 dependent: set(lrpo).
% 1.69/1.90 dependent: set(hyper_res).
% 1.69/1.90 dependent: set(unit_deletion).
% 1.69/1.90 dependent: set(factor).
% 1.69/1.90
% 1.69/1.90 ------------> process usable:
% 1.69/1.90 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.69/1.90 ** KEPT (pick-wt=10): 2 [] set_difference(singleton(A),B)!=singleton(A)| -in(A,B).
% 1.69/1.90 ** KEPT (pick-wt=9): 3 [] set_difference(singleton(A),B)!=empty_set|in(A,B).
% 1.69/1.90 ** KEPT (pick-wt=9): 4 [] set_difference(singleton(A),B)=empty_set| -in(A,B).
% 1.69/1.90 ** KEPT (pick-wt=2): 5 [] -empty($c2).
% 1.69/1.90 ** KEPT (pick-wt=6): 6 [] set_difference(singleton($c4),$c3)!=empty_set.
% 1.69/1.90 ** KEPT (pick-wt=7): 7 [] set_difference(singleton($c4),$c3)!=singleton($c4).
% 1.69/1.90
% 1.69/1.90 ------------> process sos:
% 1.69/1.90 ** KEPT (pick-wt=3): 9 [] A=A.
% 1.69/1.90 ** KEPT (pick-wt=2): 10 [] empty(empty_set).
% 1.69/1.90 ** KEPT (pick-wt=10): 11 [] set_difference(singleton(A),B)=singleton(A)|in(A,B).
% 1.69/1.90 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.69/1.90 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.69/1.90
% 1.69/1.90 ======= end of input processing =======
% 1.69/1.90
% 1.69/1.90 =========== start of search ===========
% 1.69/1.90
% 1.69/1.90 -------- PROOF --------
% 1.69/1.90
% 1.69/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 21 [binary,19.1,6.1] $F.
% 1.69/1.90
% 1.69/1.90 Length of proof is 2. Level of proof is 2.
% 1.69/1.90
% 1.69/1.90 ---------------- PROOF ----------------
% 1.69/1.90 % SZS status Theorem
% 1.69/1.90 % SZS output start Refutation
% See solution above
% 1.69/1.90 ------------ end of proof -------------
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90 ============ end of search ============
% 1.69/1.90
% 1.69/1.90 -------------- statistics -------------
% 1.69/1.90 clauses given 5
% 1.69/1.90 clauses generated 15
% 1.69/1.90 clauses kept 18
% 1.69/1.90 clauses forward subsumed 6
% 1.69/1.90 clauses back subsumed 0
% 1.69/1.90 Kbytes malloced 976
% 1.69/1.90
% 1.69/1.90 ----------- times (seconds) -----------
% 1.69/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.69/1.90
% 1.69/1.90 That finishes the proof of the theorem.
% 1.69/1.90
% 1.69/1.90 Process 22256 finished Wed Jul 27 10:42:10 2022
% 1.69/1.90 Otter interrupted
% 1.69/1.90 PROOF FOUND
%------------------------------------------------------------------------------