TSTP Solution File: SET581+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:13:44 EDT 2022
% Result : Theorem 1.76s 1.92s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 8 unt; 1 nHn; 9 RR)
% Number of literals : 13 ( 2 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET581+3.p',unknown),
[] ).
cnf(4,axiom,
~ member(A,empty_set),
file('SET581+3.p',unknown),
[] ).
cnf(10,axiom,
~ not_e_qual(intersection(dollar_c2,dollar_c1),empty_set),
file('SET581+3.p',unknown),
[] ).
cnf(15,axiom,
( not_e_qual(A,B)
| A = B ),
file('SET581+3.p',unknown),
[] ).
cnf(18,axiom,
member(dollar_c3,dollar_c2),
file('SET581+3.p',unknown),
[] ).
cnf(19,axiom,
member(dollar_c3,dollar_c1),
file('SET581+3.p',unknown),
[] ).
cnf(24,plain,
member(dollar_c3,intersection(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[19,3,18]),
[iquote('hyper,19,3,18')] ).
cnf(126,plain,
intersection(dollar_c2,dollar_c1) = empty_set,
inference(hyper,[status(thm)],[15,10]),
[iquote('hyper,15,10')] ).
cnf(143,plain,
member(dollar_c3,empty_set),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),126]),
[iquote('back_demod,24,demod,126')] ).
cnf(144,plain,
$false,
inference(binary,[status(thm)],[143,4]),
[iquote('binary,143.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 10:29:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.76/1.92 ----- Otter 3.3f, August 2004 -----
% 1.76/1.92 The process was started by sandbox on n018.cluster.edu,
% 1.76/1.92 Wed Jul 27 10:29:01 2022
% 1.76/1.92 The command was "./otter". The process ID is 20672.
% 1.76/1.92
% 1.76/1.92 set(prolog_style_variables).
% 1.76/1.92 set(auto).
% 1.76/1.92 dependent: set(auto1).
% 1.76/1.92 dependent: set(process_input).
% 1.76/1.92 dependent: clear(print_kept).
% 1.76/1.92 dependent: clear(print_new_demod).
% 1.76/1.92 dependent: clear(print_back_demod).
% 1.76/1.92 dependent: clear(print_back_sub).
% 1.76/1.92 dependent: set(control_memory).
% 1.76/1.92 dependent: assign(max_mem, 12000).
% 1.76/1.92 dependent: assign(pick_given_ratio, 4).
% 1.76/1.92 dependent: assign(stats_level, 1).
% 1.76/1.92 dependent: assign(max_seconds, 10800).
% 1.76/1.92 clear(print_given).
% 1.76/1.92
% 1.76/1.92 formula_list(usable).
% 1.76/1.92 all A (A=A).
% 1.76/1.92 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.76/1.92 all B (-member(B,empty_set)).
% 1.76/1.92 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.76/1.92 all B C (not_e_qual(B,C)<->B!=C).
% 1.76/1.92 all B C (intersection(B,C)=intersection(C,B)).
% 1.76/1.92 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.76/1.92 -(all B C D (member(B,C)&member(B,D)->not_e_qual(intersection(C,D),empty_set))).
% 1.76/1.92 end_of_list.
% 1.76/1.92
% 1.76/1.92 -------> usable clausifies to:
% 1.76/1.92
% 1.76/1.92 list(usable).
% 1.76/1.92 0 [] A=A.
% 1.76/1.92 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.76/1.92 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.76/1.92 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.76/1.92 0 [] -member(B,empty_set).
% 1.76/1.92 0 [] B!=C| -member(D,B)|member(D,C).
% 1.76/1.92 0 [] B!=C|member(D,B)| -member(D,C).
% 1.76/1.92 0 [] B=C|member($f1(B,C),B)|member($f1(B,C),C).
% 1.76/1.92 0 [] B=C| -member($f1(B,C),B)| -member($f1(B,C),C).
% 1.76/1.92 0 [] -not_e_qual(B,C)|B!=C.
% 1.76/1.92 0 [] not_e_qual(B,C)|B=C.
% 1.76/1.92 0 [] intersection(B,C)=intersection(C,B).
% 1.76/1.92 0 [] -empty(B)| -member(C,B).
% 1.76/1.92 0 [] empty(B)|member($f2(B),B).
% 1.76/1.92 0 [] member($c3,$c2).
% 1.76/1.92 0 [] member($c3,$c1).
% 1.76/1.92 0 [] -not_e_qual(intersection($c2,$c1),empty_set).
% 1.76/1.92 end_of_list.
% 1.76/1.92
% 1.76/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.76/1.92
% 1.76/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.76/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.76/1.92 deletion, with positive clauses in sos and nonpositive
% 1.76/1.92 clauses in usable.
% 1.76/1.92
% 1.76/1.92 dependent: set(knuth_bendix).
% 1.76/1.92 dependent: set(anl_eq).
% 1.76/1.92 dependent: set(para_from).
% 1.76/1.92 dependent: set(para_into).
% 1.76/1.92 dependent: clear(para_from_right).
% 1.76/1.92 dependent: clear(para_into_right).
% 1.76/1.92 dependent: set(para_from_vars).
% 1.76/1.92 dependent: set(eq_units_both_ways).
% 1.76/1.92 dependent: set(dynamic_demod_all).
% 1.76/1.92 dependent: set(dynamic_demod).
% 1.76/1.92 dependent: set(order_eq).
% 1.76/1.92 dependent: set(back_demod).
% 1.76/1.92 dependent: set(lrpo).
% 1.76/1.92 dependent: set(hyper_res).
% 1.76/1.92 dependent: set(unit_deletion).
% 1.76/1.92 dependent: set(factor).
% 1.76/1.92
% 1.76/1.92 ------------> process usable:
% 1.76/1.92 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.76/1.92 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.76/1.92 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.76/1.92 ** KEPT (pick-wt=3): 4 [] -member(A,empty_set).
% 1.76/1.92 ** KEPT (pick-wt=9): 5 [] A!=B| -member(C,A)|member(C,B).
% 1.76/1.92 ** KEPT (pick-wt=9): 6 [] A!=B|member(C,A)| -member(C,B).
% 1.76/1.92 ** KEPT (pick-wt=13): 7 [] A=B| -member($f1(A,B),A)| -member($f1(A,B),B).
% 1.76/1.92 ** KEPT (pick-wt=6): 8 [] -not_e_qual(A,B)|A!=B.
% 1.76/1.92 ** KEPT (pick-wt=5): 9 [] -empty(A)| -member(B,A).
% 1.76/1.92 ** KEPT (pick-wt=5): 10 [] -not_e_qual(intersection($c2,$c1),empty_set).
% 1.76/1.92
% 1.76/1.92 ------------> process sos:
% 1.76/1.92 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.76/1.92 ** KEPT (pick-wt=13): 14 [] A=B|member($f1(A,B),A)|member($f1(A,B),B).
% 1.76/1.92 ** KEPT (pick-wt=6): 15 [] not_e_qual(A,B)|A=B.
% 1.76/1.92 ** KEPT (pick-wt=7): 16 [] intersection(A,B)=intersection(B,A).
% 1.76/1.92 ** KEPT (pick-wt=6): 17 [] empty(A)|member($f2(A),A).
% 1.76/1.92 ** KEPT (pick-wt=3): 18 [] member($c3,$c2).
% 1.76/1.92 ** KEPT (pick-wt=3): 19 [] member($c3,$c1).
% 1.76/1.92 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.76/1.92 13 back subsumes 12.
% 1.76/1.92 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] intersection(A,B)=intersection(B,A).
% 1.76/1.92
% 1.76/1.92 ======= end of input processing =======
% 1.76/1.92
% 1.76/1.92 =========== start of search ===========
% 1.76/1.92
% 1.76/1.92 -------- PROOF --------
% 1.76/1.92
% 1.76/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 144 [binary,143.1,4.1] $F.
% 1.76/1.92
% 1.76/1.92 Length of proof is 3. Level of proof is 2.
% 1.76/1.92
% 1.76/1.92 ---------------- PROOF ----------------
% 1.76/1.92 % SZS status Theorem
% 1.76/1.92 % SZS output start Refutation
% See solution above
% 1.76/1.92 ------------ end of proof -------------
% 1.76/1.92
% 1.76/1.92
% 1.76/1.92 Search stopped by max_proofs option.
% 1.76/1.92
% 1.76/1.92
% 1.76/1.92 Search stopped by max_proofs option.
% 1.76/1.92
% 1.76/1.92 ============ end of search ============
% 1.76/1.92
% 1.76/1.92 -------------- statistics -------------
% 1.76/1.92 clauses given 9
% 1.76/1.92 clauses generated 230
% 1.76/1.92 clauses kept 142
% 1.76/1.92 clauses forward subsumed 123
% 1.76/1.92 clauses back subsumed 1
% 1.76/1.92 Kbytes malloced 976
% 1.76/1.92
% 1.76/1.92 ----------- times (seconds) -----------
% 1.76/1.92 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.76/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.92 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.76/1.92
% 1.76/1.92 That finishes the proof of the theorem.
% 1.76/1.92
% 1.76/1.92 Process 20672 finished Wed Jul 27 10:29:03 2022
% 1.76/1.92 Otter interrupted
% 1.76/1.92 PROOF FOUND
%------------------------------------------------------------------------------