%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:12:46 EDT 2022
% Result : Theorem 2.56s 2.74s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 9 unt; 5 nHn; 10 RR)
% Number of literals : 26 ( 9 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET008+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(A,difference(B,C))
| ~ member(A,C) ),
file('SET008+3.p',unknown),
[] ).
cnf(7,axiom,
~ member(A,empty_set),
file('SET008+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ empty(A)
| ~ member(B,A) ),
file('SET008+3.p',unknown),
[] ).
cnf(17,axiom,
intersection(difference(dollar_c2,dollar_c1),dollar_c1) != empty_set,
file('SET008+3.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('SET008+3.p',unknown),
[] ).
cnf(22,axiom,
intersection(A,B) = intersection(B,A),
file('SET008+3.p',unknown),
[] ).
cnf(25,axiom,
( empty(A)
| member(dollar_f2(A),A) ),
file('SET008+3.p',unknown),
[] ).
cnf(26,axiom,
( A = B
| member(dollar_f3(A,B),A)
| member(dollar_f3(A,B),B) ),
file('SET008+3.p',unknown),
[] ).
cnf(32,plain,
intersection(dollar_c1,difference(dollar_c2,dollar_c1)) != empty_set,
inference(para_from,[status(thm),theory(equality)],[22,17]),
[iquote('para_from,22.1.1,17.1.1')] ).
cnf(54,plain,
( empty_set = A
| member(dollar_f3(empty_set,A),A) ),
inference(hyper,[status(thm)],[26,7]),
[iquote('hyper,26,7')] ).
cnf(119,plain,
( empty_set = A
| member(dollar_f2(A),A) ),
inference(hyper,[status(thm)],[54,13,25]),
[iquote('hyper,54,13,25')] ).
cnf(138,plain,
( intersection(A,B) = empty_set
| member(dollar_f2(intersection(A,B)),B) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[119,2])]),
[iquote('hyper,119,2,flip.1')] ).
cnf(1904,plain,
member(dollar_f2(intersection(difference(dollar_c2,dollar_c1),dollar_c1)),dollar_c1),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[138,17]),21]),
[iquote('para_from,138.1.1,17.1.1,unit_del,21')] ).
cnf(2476,plain,
member(dollar_f2(intersection(dollar_c1,difference(dollar_c2,dollar_c1))),dollar_c1),
inference(para_into,[status(thm),theory(equality)],[1904,22]),
[iquote('para_into,1904.1.1.1,22.1.1')] ).
cnf(2531,plain,
intersection(dollar_c1,difference(dollar_c2,dollar_c1)) = empty_set,
inference(hyper,[status(thm)],[2476,5,138]),
[iquote('hyper,2476,5,138')] ).
cnf(2533,plain,
$false,
inference(binary,[status(thm)],[2531,32]),
[iquote('binary,2531.1,32.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 10:50:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.13 ----- Otter 3.3f, August 2004 -----
% 1.95/2.13 The process was started by sandbox2 on n020.cluster.edu,
% 1.95/2.13 Wed Jul 27 10:50:53 2022
% 1.95/2.13 The command was "./otter". The process ID is 30577.
% 1.95/2.13
% 1.95/2.13 set(prolog_style_variables).
% 1.95/2.13 set(auto).
% 1.95/2.13 dependent: set(auto1).
% 1.95/2.13 dependent: set(process_input).
% 1.95/2.13 dependent: clear(print_kept).
% 1.95/2.13 dependent: clear(print_new_demod).
% 1.95/2.13 dependent: clear(print_back_demod).
% 1.95/2.13 dependent: clear(print_back_sub).
% 1.95/2.13 dependent: set(control_memory).
% 1.95/2.13 dependent: assign(max_mem, 12000).
% 1.95/2.13 dependent: assign(pick_given_ratio, 4).
% 1.95/2.13 dependent: assign(stats_level, 1).
% 1.95/2.13 dependent: assign(max_seconds, 10800).
% 1.95/2.13 clear(print_given).
% 1.95/2.13
% 1.95/2.13 formula_list(usable).
% 1.95/2.13 all A (A=A).
% 1.95/2.13 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.95/2.13 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.95/2.13 all B (-member(B,empty_set)).
% 1.95/2.13 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.95/2.13 all B C (intersection(B,C)=intersection(C,B)).
% 1.95/2.13 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.95/2.13 all B subset(B,B).
% 1.95/2.13 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.95/2.13 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.95/2.13 -(all B C (intersection(difference(B,C),C)=empty_set)).
% 1.95/2.13 end_of_list.
% 1.95/2.13
% 1.95/2.13 -------> usable clausifies to:
% 1.95/2.13
% 1.95/2.13 list(usable).
% 1.95/2.13 0 [] A=A.
% 1.95/2.13 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.95/2.13 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.95/2.13 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.95/2.13 0 [] -member(D,difference(B,C))|member(D,B).
% 1.95/2.13 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.95/2.13 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.95/2.13 0 [] -member(B,empty_set).
% 1.95/2.13 0 [] B!=C|subset(B,C).
% 1.95/2.13 0 [] B!=C|subset(C,B).
% 1.95/2.13 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.95/2.13 0 [] intersection(B,C)=intersection(C,B).
% 1.95/2.13 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.95/2.13 0 [] subset(B,C)|member($f1(B,C),B).
% 1.95/2.13 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.95/2.13 0 [] subset(B,B).
% 1.95/2.13 0 [] -empty(B)| -member(C,B).
% 1.95/2.13 0 [] empty(B)|member($f2(B),B).
% 1.95/2.13 0 [] B!=C| -member(D,B)|member(D,C).
% 1.95/2.13 0 [] B!=C|member(D,B)| -member(D,C).
% 1.95/2.13 0 [] B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 1.95/2.13 0 [] B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 1.95/2.13 0 [] intersection(difference($c2,$c1),$c1)!=empty_set.
% 1.95/2.13 end_of_list.
% 1.95/2.13
% 1.95/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.95/2.13
% 1.95/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.95/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.95/2.13 deletion, with positive clauses in sos and nonpositive
% 1.95/2.13 clauses in usable.
% 1.95/2.13
% 1.95/2.13 dependent: set(knuth_bendix).
% 1.95/2.13 dependent: set(anl_eq).
% 1.95/2.13 dependent: set(para_from).
% 1.95/2.13 dependent: set(para_into).
% 1.95/2.13 dependent: clear(para_from_right).
% 1.95/2.13 dependent: clear(para_into_right).
% 1.95/2.13 dependent: set(para_from_vars).
% 1.95/2.13 dependent: set(eq_units_both_ways).
% 1.95/2.13 dependent: set(dynamic_demod_all).
% 1.95/2.13 dependent: set(dynamic_demod).
% 1.95/2.13 dependent: set(order_eq).
% 1.95/2.13 dependent: set(back_demod).
% 1.95/2.13 dependent: set(lrpo).
% 1.95/2.13 dependent: set(hyper_res).
% 1.95/2.13 dependent: set(unit_deletion).
% 1.95/2.13 dependent: set(factor).
% 1.95/2.13
% 1.95/2.13 ------------> process usable:
% 1.95/2.13 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.95/2.13 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.95/2.13 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.95/2.13 ** KEPT (pick-wt=8): 4 [] -member(A,difference(B,C))|member(A,B).
% 1.95/2.13 ** KEPT (pick-wt=8): 5 [] -member(A,difference(B,C))| -member(A,C).
% 1.95/2.13 ** KEPT (pick-wt=11): 6 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.95/2.13 ** KEPT (pick-wt=3): 7 [] -member(A,empty_set).
% 1.95/2.13 ** KEPT (pick-wt=6): 8 [] A!=B|subset(A,B).
% 1.95/2.13 ** KEPT (pick-wt=6): 9 [] A!=B|subset(B,A).
% 1.95/2.13 ** KEPT (pick-wt=9): 10 [] A=B| -subset(A,B)| -subset(B,A).
% 1.95/2.13 ** KEPT (pick-wt=9): 11 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.95/2.13 ** KEPT (pick-wt=8): 12 [] subset(A,B)| -member($f1(A,B),B).
% 1.95/2.13 ** KEPT (pick-wt=5): 13 [] -empty(A)| -member(B,A).
% 1.95/2.13 ** KEPT (pick-wt=9): 14 [] A!=B| -member(C,A)|member(C,B).
% 1.95/2.13 ** KEPT (pick-wt=9): 15 [] A!=B|member(C,A)| -member(C,B).
% 1.95/2.13 ** KEPT (pick-wt=13): 16 [] A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 1.95/2.13 ** KEPT (pick-wt=7): 17 [] intersection(difference($c2,$c1),$c1)!=empty_set.
% 1.95/2.13
% 1.95/2.13 ------------> process sos:
% 1.95/2.13 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.95/2.13 ** KEPT (pick-wt=7): 22 [] intersection(A,B)=intersection(B,A).
% 2.56/2.74 ** KEPT (pick-wt=8): 23 [] subset(A,B)|member($f1(A,B),A).
% 2.56/2.74 ** KEPT (pick-wt=3): 24 [] subset(A,A).
% 2.56/2.74 ** KEPT (pick-wt=6): 25 [] empty(A)|member($f2(A),A).
% 2.56/2.74 ** KEPT (pick-wt=13): 26 [] A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 2.56/2.74 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 2.56/2.74 21 back subsumes 20.
% 2.56/2.74 21 back subsumes 19.
% 2.56/2.74 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] intersection(A,B)=intersection(B,A).
% 2.56/2.74
% 2.56/2.74 ======= end of input processing =======
% 2.56/2.74
% 2.56/2.74 =========== start of search ===========
% 2.56/2.74
% 2.56/2.74
% 2.56/2.74 Resetting weight limit to 11.
% 2.56/2.74
% 2.56/2.74
% 2.56/2.74 Resetting weight limit to 11.
% 2.56/2.74
% 2.56/2.74 sos_size=1634
% 2.56/2.74
% 2.56/2.74
% 2.56/2.74 Resetting weight limit to 10.
% 2.56/2.74
% 2.56/2.74
% 2.56/2.74 Resetting weight limit to 10.
% 2.56/2.74
% 2.56/2.74 sos_size=1685
% 2.56/2.74
% 2.56/2.74 -------- PROOF --------
% 2.56/2.74
% 2.56/2.74 ----> UNIT CONFLICT at 0.61 sec ----> 2533 [binary,2531.1,32.1] $F.
% 2.56/2.74
% 2.56/2.74 Length of proof is 7. Level of proof is 6.
% 2.56/2.74
% 2.56/2.74 ---------------- PROOF ----------------
% 2.56/2.74 % SZS status Theorem
% 2.56/2.74 % SZS output start Refutation
% See solution above
% 2.56/2.74 ------------ end of proof -------------
% 2.56/2.74
% 2.56/2.74
% 2.56/2.74 Search stopped by max_proofs option.
% 2.56/2.74
% 2.56/2.74
% 2.56/2.74 Search stopped by max_proofs option.
% 2.56/2.74
% 2.56/2.74 ============ end of search ============
% 2.56/2.74
% 2.56/2.74 -------------- statistics -------------
% 2.56/2.74 clauses given 94
% 2.56/2.74 clauses generated 8944
% 2.56/2.74 clauses kept 2527
% 2.56/2.74 clauses forward subsumed 4323
% 2.56/2.74 clauses back subsumed 543
% 2.56/2.74 Kbytes malloced 4882
% 2.56/2.74
% 2.56/2.74 ----------- times (seconds) -----------
% 2.56/2.74 user CPU time 0.61 (0 hr, 0 min, 0 sec)
% 2.56/2.74 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.56/2.74 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.56/2.74
% 2.56/2.74 That finishes the proof of the theorem.
% 2.56/2.74
% 2.56/2.74 Process 30577 finished Wed Jul 27 10:50:56 2022
% 2.56/2.74 Otter interrupted
% 2.56/2.74 PROOF FOUND
%------------------------------------------------------------------------------