TSTP Solution File: SET626+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:13:54 EDT 2022
% Result : Theorem 1.73s 1.96s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 11 RR)
% Number of literals : 16 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('SET626+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),A) ),
file('SET626+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),B) ),
file('SET626+3.p',unknown),
[] ).
cnf(6,axiom,
( intersect(A,B)
| ~ member(C,A)
| ~ member(C,B) ),
file('SET626+3.p',unknown),
[] ).
cnf(11,axiom,
~ intersect(dollar_c3,dollar_c2),
file('SET626+3.p',unknown),
[] ).
cnf(18,axiom,
intersect(dollar_c3,intersection(dollar_c2,dollar_c1)),
file('SET626+3.p',unknown),
[] ).
cnf(20,plain,
member(dollar_f1(dollar_c3,intersection(dollar_c2,dollar_c1)),intersection(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[18,5]),
[iquote('hyper,18,5')] ).
cnf(21,plain,
member(dollar_f1(dollar_c3,intersection(dollar_c2,dollar_c1)),dollar_c3),
inference(hyper,[status(thm)],[18,4]),
[iquote('hyper,18,4')] ).
cnf(126,plain,
member(dollar_f1(dollar_c3,intersection(dollar_c2,dollar_c1)),dollar_c2),
inference(hyper,[status(thm)],[20,1]),
[iquote('hyper,20,1')] ).
cnf(460,plain,
intersect(dollar_c3,dollar_c2),
inference(hyper,[status(thm)],[126,6,21]),
[iquote('hyper,126,6,21')] ).
cnf(461,plain,
$false,
inference(binary,[status(thm)],[460,11]),
[iquote('binary,460.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:57:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.73/1.96 ----- Otter 3.3f, August 2004 -----
% 1.73/1.96 The process was started by sandbox2 on n019.cluster.edu,
% 1.73/1.96 Wed Jul 27 10:57:07 2022
% 1.73/1.96 The command was "./otter". The process ID is 7021.
% 1.73/1.96
% 1.73/1.96 set(prolog_style_variables).
% 1.73/1.96 set(auto).
% 1.73/1.96 dependent: set(auto1).
% 1.73/1.96 dependent: set(process_input).
% 1.73/1.96 dependent: clear(print_kept).
% 1.73/1.96 dependent: clear(print_new_demod).
% 1.73/1.96 dependent: clear(print_back_demod).
% 1.73/1.96 dependent: clear(print_back_sub).
% 1.73/1.96 dependent: set(control_memory).
% 1.73/1.96 dependent: assign(max_mem, 12000).
% 1.73/1.96 dependent: assign(pick_given_ratio, 4).
% 1.73/1.96 dependent: assign(stats_level, 1).
% 1.73/1.96 dependent: assign(max_seconds, 10800).
% 1.73/1.96 clear(print_given).
% 1.73/1.96
% 1.73/1.96 formula_list(usable).
% 1.73/1.96 all A (A=A).
% 1.73/1.96 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.73/1.96 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.73/1.96 all B C (intersection(B,C)=intersection(C,B)).
% 1.73/1.96 all B C (intersect(B,C)->intersect(C,B)).
% 1.73/1.96 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.73/1.96 -(all B C D (intersect(B,intersection(C,D))->intersect(B,C))).
% 1.73/1.96 end_of_list.
% 1.73/1.96
% 1.73/1.96 -------> usable clausifies to:
% 1.73/1.96
% 1.73/1.96 list(usable).
% 1.73/1.96 0 [] A=A.
% 1.73/1.96 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.73/1.96 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.73/1.96 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.73/1.96 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.73/1.96 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.73/1.96 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.73/1.96 0 [] intersection(B,C)=intersection(C,B).
% 1.73/1.96 0 [] -intersect(B,C)|intersect(C,B).
% 1.73/1.96 0 [] B!=C| -member(D,B)|member(D,C).
% 1.73/1.96 0 [] B!=C|member(D,B)| -member(D,C).
% 1.73/1.96 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.73/1.96 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.73/1.96 0 [] intersect($c3,intersection($c2,$c1)).
% 1.73/1.96 0 [] -intersect($c3,$c2).
% 1.73/1.96 end_of_list.
% 1.73/1.96
% 1.73/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.73/1.96
% 1.73/1.96 This ia a non-Horn set with equality. The strategy will be
% 1.73/1.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.96 deletion, with positive clauses in sos and nonpositive
% 1.73/1.96 clauses in usable.
% 1.73/1.96
% 1.73/1.96 dependent: set(knuth_bendix).
% 1.73/1.96 dependent: set(anl_eq).
% 1.73/1.96 dependent: set(para_from).
% 1.73/1.96 dependent: set(para_into).
% 1.73/1.96 dependent: clear(para_from_right).
% 1.73/1.96 dependent: clear(para_into_right).
% 1.73/1.96 dependent: set(para_from_vars).
% 1.73/1.96 dependent: set(eq_units_both_ways).
% 1.73/1.96 dependent: set(dynamic_demod_all).
% 1.73/1.96 dependent: set(dynamic_demod).
% 1.73/1.96 dependent: set(order_eq).
% 1.73/1.96 dependent: set(back_demod).
% 1.73/1.96 dependent: set(lrpo).
% 1.73/1.96 dependent: set(hyper_res).
% 1.73/1.96 dependent: set(unit_deletion).
% 1.73/1.96 dependent: set(factor).
% 1.73/1.96
% 1.73/1.96 ------------> process usable:
% 1.73/1.96 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.73/1.96 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.73/1.96 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.73/1.96 ** KEPT (pick-wt=8): 4 [] -intersect(A,B)|member($f1(A,B),A).
% 1.73/1.96 ** KEPT (pick-wt=8): 5 [] -intersect(A,B)|member($f1(A,B),B).
% 1.73/1.96 ** KEPT (pick-wt=9): 6 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.73/1.96 ** KEPT (pick-wt=6): 7 [] -intersect(A,B)|intersect(B,A).
% 1.73/1.96 ** KEPT (pick-wt=9): 8 [] A!=B| -member(C,A)|member(C,B).
% 1.73/1.96 ** KEPT (pick-wt=9): 9 [] A!=B|member(C,A)| -member(C,B).
% 1.73/1.96 ** KEPT (pick-wt=13): 10 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.73/1.96 ** KEPT (pick-wt=3): 11 [] -intersect($c3,$c2).
% 1.73/1.96
% 1.73/1.96 ------------> process sos:
% 1.73/1.96 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.73/1.96 ** KEPT (pick-wt=7): 16 [] intersection(A,B)=intersection(B,A).
% 1.73/1.96 ** KEPT (pick-wt=13): 17 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.73/1.96 ** KEPT (pick-wt=5): 18 [] intersect($c3,intersection($c2,$c1)).
% 1.73/1.96 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.73/1.96 15 back subsumes 14.
% 1.73/1.96 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] intersection(A,B)=intersection(B,A).
% 1.73/1.96
% 1.73/1.96 ======= end of input processing =======
% 1.73/1.96
% 1.73/1.96 =========== start of search ===========
% 1.73/1.96
% 1.73/1.96 -------- PROOF --------
% 1.73/1.96
% 1.73/1.96 ----> UNIT CONFLICT at 0.03 sec ----> 461 [binary,460.1,11.1] $F.
% 1.73/1.96
% 1.73/1.96 Length of proof is 4. Level of proof is 3.
% 1.73/1.96
% 1.73/1.96 ---------------- PROOF ----------------
% 1.73/1.96 % SZS status Theorem
% 1.73/1.96 % SZS output start Refutation
% See solution above
% 1.73/1.96 ------------ end of proof -------------
% 1.73/1.96
% 1.73/1.96
% 1.73/1.96 Search stopped by max_proofs option.
% 1.73/1.96
% 1.73/1.96
% 1.73/1.96 Search stopped by max_proofs option.
% 1.73/1.96
% 1.73/1.96 ============ end of search ============
% 1.73/1.96
% 1.73/1.96 -------------- statistics -------------
% 1.73/1.96 clauses given 37
% 1.73/1.96 clauses generated 1124
% 1.73/1.96 clauses kept 460
% 1.73/1.96 clauses forward subsumed 667
% 1.73/1.96 clauses back subsumed 1
% 1.73/1.96 Kbytes malloced 1953
% 1.73/1.96
% 1.73/1.96 ----------- times (seconds) -----------
% 1.73/1.96 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.73/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.96 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.73/1.96
% 1.73/1.96 That finishes the proof of the theorem.
% 1.73/1.96
% 1.73/1.96 Process 7021 finished Wed Jul 27 10:57:08 2022
% 1.73/1.96 Otter interrupted
% 1.73/1.96 PROOF FOUND
%------------------------------------------------------------------------------