TSTP Solution File: SET987+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 1.70s 1.91s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 6 unt; 1 nHn; 5 RR)
% Number of literals : 8 ( 5 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 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 : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
~ in(dollar_c4,dollar_c3),
file('SET987+1.p',unknown),
[] ).
cnf(6,axiom,
set_difference(set_union2(dollar_c3,singleton(dollar_c4)),singleton(dollar_c4)) != dollar_c3,
file('SET987+1.p',unknown),
[] ).
cnf(15,axiom,
set_difference(set_union2(A,B),B) = set_difference(A,B),
file('SET987+1.p',unknown),
[] ).
cnf(16,axiom,
( set_difference(A,singleton(B)) = A
| in(B,A) ),
file('SET987+1.p',unknown),
[] ).
cnf(17,plain,
set_difference(dollar_c3,singleton(dollar_c4)) != dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),15]),
[iquote('back_demod,6,demod,15')] ).
cnf(23,plain,
set_difference(dollar_c3,singleton(dollar_c4)) = dollar_c3,
inference(hyper,[status(thm)],[16,5]),
[iquote('hyper,16,5')] ).
cnf(25,plain,
$false,
inference(binary,[status(thm)],[23,17]),
[iquote('binary,23.1,17.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:34:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.70/1.91 ----- Otter 3.3f, August 2004 -----
% 1.70/1.91 The process was started by sandbox2 on n021.cluster.edu,
% 1.70/1.91 Wed Jul 27 10:34:53 2022
% 1.70/1.91 The command was "./otter". The process ID is 30055.
% 1.70/1.91
% 1.70/1.91 set(prolog_style_variables).
% 1.70/1.91 set(auto).
% 1.70/1.91 dependent: set(auto1).
% 1.70/1.91 dependent: set(process_input).
% 1.70/1.91 dependent: clear(print_kept).
% 1.70/1.91 dependent: clear(print_new_demod).
% 1.70/1.91 dependent: clear(print_back_demod).
% 1.70/1.91 dependent: clear(print_back_sub).
% 1.70/1.91 dependent: set(control_memory).
% 1.70/1.91 dependent: assign(max_mem, 12000).
% 1.70/1.91 dependent: assign(pick_given_ratio, 4).
% 1.70/1.91 dependent: assign(stats_level, 1).
% 1.70/1.91 dependent: assign(max_seconds, 10800).
% 1.70/1.91 clear(print_given).
% 1.70/1.91
% 1.70/1.91 formula_list(usable).
% 1.70/1.91 all A (A=A).
% 1.70/1.91 all A B (in(A,B)-> -in(B,A)).
% 1.70/1.91 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.70/1.91 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.70/1.91 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.70/1.91 all A B (set_union2(A,A)=A).
% 1.70/1.91 exists A empty(A).
% 1.70/1.91 exists A (-empty(A)).
% 1.70/1.91 -(all A B (-in(A,B)->set_difference(set_union2(B,singleton(A)),singleton(A))=B)).
% 1.70/1.91 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.70/1.91 all A B (set_difference(A,singleton(B))=A<-> -in(B,A)).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 -------> usable clausifies to:
% 1.70/1.91
% 1.70/1.91 list(usable).
% 1.70/1.91 0 [] A=A.
% 1.70/1.91 0 [] -in(A,B)| -in(B,A).
% 1.70/1.91 0 [] set_union2(A,B)=set_union2(B,A).
% 1.70/1.91 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.70/1.91 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.70/1.91 0 [] set_union2(A,A)=A.
% 1.70/1.91 0 [] empty($c1).
% 1.70/1.91 0 [] -empty($c2).
% 1.70/1.91 0 [] -in($c4,$c3).
% 1.70/1.91 0 [] set_difference(set_union2($c3,singleton($c4)),singleton($c4))!=$c3.
% 1.70/1.91 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.70/1.91 0 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 1.70/1.91 0 [] set_difference(A,singleton(B))=A|in(B,A).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.70/1.91
% 1.70/1.91 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.91 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.91 deletion, with positive clauses in sos and nonpositive
% 1.70/1.91 clauses in usable.
% 1.70/1.91
% 1.70/1.91 dependent: set(knuth_bendix).
% 1.70/1.91 dependent: set(anl_eq).
% 1.70/1.91 dependent: set(para_from).
% 1.70/1.91 dependent: set(para_into).
% 1.70/1.91 dependent: clear(para_from_right).
% 1.70/1.91 dependent: clear(para_into_right).
% 1.70/1.91 dependent: set(para_from_vars).
% 1.70/1.91 dependent: set(eq_units_both_ways).
% 1.70/1.91 dependent: set(dynamic_demod_all).
% 1.70/1.91 dependent: set(dynamic_demod).
% 1.70/1.91 dependent: set(order_eq).
% 1.70/1.91 dependent: set(back_demod).
% 1.70/1.91 dependent: set(lrpo).
% 1.70/1.91 dependent: set(hyper_res).
% 1.70/1.91 dependent: set(unit_deletion).
% 1.70/1.91 dependent: set(factor).
% 1.70/1.91
% 1.70/1.91 ------------> process usable:
% 1.70/1.91 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.70/1.91 ** KEPT (pick-wt=6): 2 [] empty(A)| -empty(set_union2(A,B)).
% 1.70/1.91 ** KEPT (pick-wt=6): 3 [] empty(A)| -empty(set_union2(B,A)).
% 1.70/1.91 ** KEPT (pick-wt=2): 4 [] -empty($c2).
% 1.70/1.91 ** KEPT (pick-wt=3): 5 [] -in($c4,$c3).
% 1.70/1.91 ** KEPT (pick-wt=9): 6 [] set_difference(set_union2($c3,singleton($c4)),singleton($c4))!=$c3.
% 1.70/1.91 ** KEPT (pick-wt=9): 7 [] set_difference(A,singleton(B))!=A| -in(B,A).
% 1.70/1.91
% 1.70/1.91 ------------> process sos:
% 1.70/1.91 ** KEPT (pick-wt=3): 9 [] A=A.
% 1.70/1.91 ** KEPT (pick-wt=7): 10 [] set_union2(A,B)=set_union2(B,A).
% 1.70/1.91 ** KEPT (pick-wt=5): 11 [] set_union2(A,A)=A.
% 1.70/1.91 ---> New Demodulator: 12 [new_demod,11] set_union2(A,A)=A.
% 1.70/1.91 ** KEPT (pick-wt=2): 13 [] empty($c1).
% 1.70/1.91 ** KEPT (pick-wt=9): 14 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.70/1.91 ---> New Demodulator: 15 [new_demod,14] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.70/1.91 ** KEPT (pick-wt=9): 16 [] set_difference(A,singleton(B))=A|in(B,A).
% 1.70/1.91 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.70/1.91 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.70/1.91 >>>> Starting back demodulation with 12.
% 1.70/1.91 >>>> Starting back demodulation with 15.
% 1.70/1.91 >> back demodulating 6 with 15.
% 1.70/1.91
% 1.70/1.91 ======= end of input processing =======
% 1.70/1.91
% 1.70/1.91 =========== start of search ===========
% 1.70/1.91
% 1.70/1.91 -------- PROOF --------
% 1.70/1.91
% 1.70/1.91 ----> UNIT CONFLICT at 0.00 sec ----> 25 [binary,23.1,17.1] $F.
% 1.70/1.91
% 1.70/1.91 Length of proof is 2. Level of proof is 1.
% 1.70/1.91
% 1.70/1.91 ---------------- PROOF ----------------
% 1.70/1.91 % SZS status Theorem
% 1.70/1.91 % SZS output start Refutation
% See solution above
% 1.70/1.91 ------------ end of proof -------------
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 Search stopped by max_proofs option.
% 1.70/1.91
% 1.70/1.91
% 1.70/1.91 Search stopped by max_proofs option.
% 1.70/1.91
% 1.70/1.91 ============ end of search ============
% 1.70/1.91
% 1.70/1.91 -------------- statistics -------------
% 1.70/1.91 clauses given 7
% 1.70/1.91 clauses generated 18
% 1.70/1.91 clauses kept 19
% 1.70/1.91 clauses forward subsumed 13
% 1.70/1.91 clauses back subsumed 0
% 1.70/1.91 Kbytes malloced 976
% 1.70/1.91
% 1.70/1.91 ----------- times (seconds) -----------
% 1.70/1.91 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.70/1.91
% 1.70/1.91 That finishes the proof of the theorem.
% 1.70/1.91
% 1.70/1.91 Process 30055 finished Wed Jul 27 10:34:54 2022
% 1.70/1.91 Otter interrupted
% 1.70/1.91 PROOF FOUND
%------------------------------------------------------------------------------