%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:13:16 EDT 2022
% Result : Theorem 2.05s 2.27s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 11 unt; 1 nHn; 16 RR)
% Number of literals : 25 ( 0 equ; 8 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('SET201+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET201+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET201+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET201+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET201+3.p',unknown),
[] ).
cnf(9,axiom,
~ subset(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),
file('SET201+3.p',unknown),
[] ).
cnf(13,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET201+3.p',unknown),
[] ).
cnf(17,axiom,
subset(dollar_c4,dollar_c3),
file('SET201+3.p',unknown),
[] ).
cnf(18,axiom,
subset(dollar_c2,dollar_c1),
file('SET201+3.p',unknown),
[] ).
cnf(26,plain,
member(dollar_f1(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),intersection(dollar_c4,dollar_c2)),
inference(hyper,[status(thm)],[13,9]),
[iquote('hyper,13,9')] ).
cnf(53,plain,
member(dollar_f1(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),dollar_c2),
inference(hyper,[status(thm)],[26,2]),
[iquote('hyper,26,2')] ).
cnf(54,plain,
member(dollar_f1(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),dollar_c4),
inference(hyper,[status(thm)],[26,1]),
[iquote('hyper,26,1')] ).
cnf(234,plain,
member(dollar_f1(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),dollar_c1),
inference(hyper,[status(thm)],[53,4,18]),
[iquote('hyper,53,4,18')] ).
cnf(261,plain,
member(dollar_f1(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),dollar_c3),
inference(hyper,[status(thm)],[54,4,17]),
[iquote('hyper,54,4,17')] ).
cnf(381,plain,
member(dollar_f1(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),intersection(dollar_c3,dollar_c1)),
inference(hyper,[status(thm)],[261,3,234]),
[iquote('hyper,261,3,234')] ).
cnf(2385,plain,
subset(intersection(dollar_c4,dollar_c2),intersection(dollar_c3,dollar_c1)),
inference(hyper,[status(thm)],[381,5]),
[iquote('hyper,381,5')] ).
cnf(2386,plain,
$false,
inference(binary,[status(thm)],[2385,9]),
[iquote('binary,2385.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 10:49:18 EDT 2022
% 0.18/0.33 % CPUTime :
% 2.05/2.27 ----- Otter 3.3f, August 2004 -----
% 2.05/2.27 The process was started by sandbox on n023.cluster.edu,
% 2.05/2.27 Wed Jul 27 10:49:18 2022
% 2.05/2.27 The command was "./otter". The process ID is 24936.
% 2.05/2.27
% 2.05/2.27 set(prolog_style_variables).
% 2.05/2.27 set(auto).
% 2.05/2.27 dependent: set(auto1).
% 2.05/2.27 dependent: set(process_input).
% 2.05/2.27 dependent: clear(print_kept).
% 2.05/2.27 dependent: clear(print_new_demod).
% 2.05/2.27 dependent: clear(print_back_demod).
% 2.05/2.27 dependent: clear(print_back_sub).
% 2.05/2.27 dependent: set(control_memory).
% 2.05/2.27 dependent: assign(max_mem, 12000).
% 2.05/2.27 dependent: assign(pick_given_ratio, 4).
% 2.05/2.27 dependent: assign(stats_level, 1).
% 2.05/2.27 dependent: assign(max_seconds, 10800).
% 2.05/2.27 clear(print_given).
% 2.05/2.27
% 2.05/2.27 formula_list(usable).
% 2.05/2.27 all A (A=A).
% 2.05/2.27 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 2.05/2.27 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 2.05/2.27 all B C (intersection(B,C)=intersection(C,B)).
% 2.05/2.27 all B subset(B,B).
% 2.05/2.27 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 2.05/2.27 -(all B C D E (subset(B,C)&subset(D,E)->subset(intersection(B,D),intersection(C,E)))).
% 2.05/2.27 end_of_list.
% 2.05/2.27
% 2.05/2.27 -------> usable clausifies to:
% 2.05/2.27
% 2.05/2.27 list(usable).
% 2.05/2.27 0 [] A=A.
% 2.05/2.27 0 [] -member(D,intersection(B,C))|member(D,B).
% 2.05/2.27 0 [] -member(D,intersection(B,C))|member(D,C).
% 2.05/2.27 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 2.05/2.27 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 2.05/2.27 0 [] subset(B,C)|member($f1(B,C),B).
% 2.05/2.27 0 [] subset(B,C)| -member($f1(B,C),C).
% 2.05/2.27 0 [] intersection(B,C)=intersection(C,B).
% 2.05/2.27 0 [] subset(B,B).
% 2.05/2.27 0 [] B!=C| -member(D,B)|member(D,C).
% 2.05/2.27 0 [] B!=C|member(D,B)| -member(D,C).
% 2.05/2.27 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 2.05/2.27 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 2.05/2.27 0 [] subset($c4,$c3).
% 2.05/2.27 0 [] subset($c2,$c1).
% 2.05/2.27 0 [] -subset(intersection($c4,$c2),intersection($c3,$c1)).
% 2.05/2.27 end_of_list.
% 2.05/2.27
% 2.05/2.27 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.05/2.27
% 2.05/2.27 This ia a non-Horn set with equality. The strategy will be
% 2.05/2.27 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.05/2.27 deletion, with positive clauses in sos and nonpositive
% 2.05/2.27 clauses in usable.
% 2.05/2.27
% 2.05/2.27 dependent: set(knuth_bendix).
% 2.05/2.27 dependent: set(anl_eq).
% 2.05/2.27 dependent: set(para_from).
% 2.05/2.27 dependent: set(para_into).
% 2.05/2.27 dependent: clear(para_from_right).
% 2.05/2.27 dependent: clear(para_into_right).
% 2.05/2.27 dependent: set(para_from_vars).
% 2.05/2.27 dependent: set(eq_units_both_ways).
% 2.05/2.27 dependent: set(dynamic_demod_all).
% 2.05/2.27 dependent: set(dynamic_demod).
% 2.05/2.27 dependent: set(order_eq).
% 2.05/2.27 dependent: set(back_demod).
% 2.05/2.27 dependent: set(lrpo).
% 2.05/2.27 dependent: set(hyper_res).
% 2.05/2.27 dependent: set(unit_deletion).
% 2.05/2.27 dependent: set(factor).
% 2.05/2.27
% 2.05/2.27 ------------> process usable:
% 2.05/2.27 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 2.05/2.27 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 2.05/2.27 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 2.05/2.27 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.05/2.27 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f1(A,B),B).
% 2.05/2.27 ** KEPT (pick-wt=9): 6 [] A!=B| -member(C,A)|member(C,B).
% 2.05/2.27 ** KEPT (pick-wt=9): 7 [] A!=B|member(C,A)| -member(C,B).
% 2.05/2.27 ** KEPT (pick-wt=13): 8 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 2.05/2.27 ** KEPT (pick-wt=7): 9 [] -subset(intersection($c4,$c2),intersection($c3,$c1)).
% 2.05/2.27
% 2.05/2.27 ------------> process sos:
% 2.05/2.27 ** KEPT (pick-wt=3): 12 [] A=A.
% 2.05/2.27 ** KEPT (pick-wt=8): 13 [] subset(A,B)|member($f1(A,B),A).
% 2.05/2.27 ** KEPT (pick-wt=7): 14 [] intersection(A,B)=intersection(B,A).
% 2.05/2.27 ** KEPT (pick-wt=3): 15 [] subset(A,A).
% 2.05/2.27 ** KEPT (pick-wt=13): 16 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 2.05/2.27 ** KEPT (pick-wt=3): 17 [] subset($c4,$c3).
% 2.05/2.27 ** KEPT (pick-wt=3): 18 [] subset($c2,$c1).
% 2.05/2.27 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.05/2.27 12 back subsumes 11.
% 2.05/2.27 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] intersection(A,B)=intersection(B,A).
% 2.05/2.27
% 2.05/2.27 ======= end of input processing =======
% 2.05/2.27
% 2.05/2.27 =========== start of search ===========
% 2.05/2.27
% 2.05/2.27 -------- PROOF --------
% 2.05/2.27
% 2.05/2.27 ----> UNIT CONFLICT at 0.18 sec ----> 2386 [binary,2385.1,9.1] $F.
% 2.05/2.27
% 2.05/2.27 Length of proof is 7. Level of proof is 5.
% 2.05/2.27
% 2.05/2.27 ---------------- PROOF ----------------
% 2.05/2.27 % SZS status Theorem
% 2.05/2.27 % SZS output start Refutation
% See solution above
% 2.05/2.27 ------------ end of proof -------------
% 2.05/2.27
% 2.05/2.27
% 2.05/2.27 Search stopped by max_proofs option.
% 2.05/2.27
% 2.05/2.27
% 2.05/2.27 Search stopped by max_proofs option.
% 2.05/2.27
% 2.05/2.27 ============ end of search ============
% 2.05/2.27
% 2.05/2.27 -------------- statistics -------------
% 2.05/2.27 clauses given 64
% 2.05/2.27 clauses generated 4628
% 2.05/2.27 clauses kept 2385
% 2.05/2.27 clauses forward subsumed 2225
% 2.05/2.27 clauses back subsumed 6
% 2.05/2.27 Kbytes malloced 2929
% 2.05/2.27
% 2.05/2.27 ----------- times (seconds) -----------
% 2.05/2.27 user CPU time 0.18 (0 hr, 0 min, 0 sec)
% 2.05/2.27 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.05/2.27 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.05/2.27
% 2.05/2.27 That finishes the proof of the theorem.
% 2.05/2.27
% 2.05/2.27 Process 24936 finished Wed Jul 27 10:49:20 2022
% 2.05/2.27 Otter interrupted
% 2.05/2.27 PROOF FOUND
%------------------------------------------------------------------------------