TSTP Solution File: SET637+3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:13:57 EDT 2022
% Result : Theorem 54.98s 55.15s
% Output : Refutation 54.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 29 ( 10 unt; 10 nHn; 18 RR)
% Number of literals : 53 ( 12 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('SET637+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET637+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET637+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),A) ),
file('SET637+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),B) ),
file('SET637+3.p',unknown),
[] ).
cnf(6,axiom,
( intersect(A,B)
| ~ member(C,A)
| ~ member(C,B) ),
file('SET637+3.p',unknown),
[] ).
cnf(7,axiom,
~ member(A,empty_set),
file('SET637+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ not_e_qual(A,B)
| A != B ),
file('SET637+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ intersect(dollar_c2,dollar_c1)
| ~ not_e_qual(intersection(dollar_c2,dollar_c1),empty_set) ),
file('SET637+3.p',unknown),
[] ).
cnf(18,axiom,
A = A,
file('SET637+3.p',unknown),
[] ).
cnf(19,axiom,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),B) ),
file('SET637+3.p',unknown),
[] ).
cnf(20,axiom,
( not_e_qual(A,B)
| A = B ),
file('SET637+3.p',unknown),
[] ).
cnf(21,axiom,
intersection(A,B) = intersection(B,A),
file('SET637+3.p',unknown),
[] ).
cnf(23,axiom,
( intersect(dollar_c2,dollar_c1)
| not_e_qual(intersection(dollar_c2,dollar_c1),empty_set) ),
file('SET637+3.p',unknown),
[] ).
cnf(42,plain,
( A = intersection(B,C)
| not_e_qual(intersection(C,B),A) ),
inference(para_into,[status(thm),theory(equality)],[21,20]),
[iquote('para_into,21.1.1,20.2.1')] ).
cnf(44,plain,
( ~ intersect(dollar_c2,dollar_c1)
| ~ not_e_qual(intersection(dollar_c1,dollar_c2),empty_set) ),
inference(para_from,[status(thm),theory(equality)],[21,14]),
[iquote('para_from,21.1.1,14.2.1')] ).
cnf(50,plain,
( empty_set = A
| member(dollar_f2(empty_set,A),A) ),
inference(hyper,[status(thm)],[19,7]),
[iquote('hyper,19,7')] ).
cnf(60,plain,
( A = intersection(B,C)
| member(dollar_f2(A,intersection(B,C)),A)
| member(dollar_f2(A,intersection(B,C)),B) ),
inference(hyper,[status(thm)],[19,1]),
[iquote('hyper,19,1')] ).
cnf(107,plain,
( intersect(dollar_c2,dollar_c1)
| not_e_qual(intersection(dollar_c2,dollar_c1),A)
| not_e_qual(empty_set,A) ),
inference(para_into,[status(thm),theory(equality)],[23,20]),
[iquote('para_into,23.2.2,20.2.1')] ).
cnf(130,plain,
( intersection(A,B) = empty_set
| member(dollar_f2(empty_set,intersection(A,B)),B) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[50,2])]),
[iquote('hyper,50,2,flip.1')] ).
cnf(5707,plain,
( intersection(A,B) = empty_set
| intersect(A,B) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[130,6,60]),7])]),
[iquote('hyper,130,6,60,unit_del,7,factor_simp')] ).
cnf(5710,plain,
intersection(dollar_c2,dollar_c1) = empty_set,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[5707,44,42])]),
[iquote('hyper,5707,44,42,factor_simp')] ).
cnf(5721,plain,
( intersect(dollar_c2,dollar_c1)
| not_e_qual(empty_set,A) ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[107]),5710])]),
[iquote('back_demod,107,demod,5710,factor_simp')] ).
cnf(5729,plain,
intersection(dollar_c1,dollar_c2) = empty_set,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[5710,11,42])]),
[iquote('hyper,5709,11,42,flip.1')] ).
cnf(5742,plain,
intersect(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[5721,11,18]),
[iquote('hyper,5721,11,18')] ).
cnf(5762,plain,
member(dollar_f1(dollar_c2,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[5742,5]),
[iquote('hyper,5742,5')] ).
cnf(5763,plain,
member(dollar_f1(dollar_c2,dollar_c1),dollar_c2),
inference(hyper,[status(thm)],[5742,4]),
[iquote('hyper,5742,4')] ).
cnf(5788,plain,
member(dollar_f1(dollar_c2,dollar_c1),empty_set),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[5763,3,5762]),5729]),
[iquote('hyper,5763,3,5762,demod,5729')] ).
cnf(5789,plain,
$false,
inference(binary,[status(thm)],[5788,7]),
[iquote('binary,5788.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n022.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 10:49:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.71/1.91 ----- Otter 3.3f, August 2004 -----
% 1.71/1.91 The process was started by sandbox on n022.cluster.edu,
% 1.71/1.91 Wed Jul 27 10:49:50 2022
% 1.71/1.91 The command was "./otter". The process ID is 12377.
% 1.71/1.91
% 1.71/1.91 set(prolog_style_variables).
% 1.71/1.91 set(auto).
% 1.71/1.91 dependent: set(auto1).
% 1.71/1.91 dependent: set(process_input).
% 1.71/1.91 dependent: clear(print_kept).
% 1.71/1.91 dependent: clear(print_new_demod).
% 1.71/1.91 dependent: clear(print_back_demod).
% 1.71/1.91 dependent: clear(print_back_sub).
% 1.71/1.91 dependent: set(control_memory).
% 1.71/1.91 dependent: assign(max_mem, 12000).
% 1.71/1.91 dependent: assign(pick_given_ratio, 4).
% 1.71/1.91 dependent: assign(stats_level, 1).
% 1.71/1.91 dependent: assign(max_seconds, 10800).
% 1.71/1.91 clear(print_given).
% 1.71/1.91
% 1.71/1.91 formula_list(usable).
% 1.71/1.91 all A (A=A).
% 1.71/1.91 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.71/1.91 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.71/1.91 all B (-member(B,empty_set)).
% 1.71/1.91 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.71/1.91 all B C (not_e_qual(B,C)<->B!=C).
% 1.71/1.91 all B C (intersection(B,C)=intersection(C,B)).
% 1.71/1.91 all B C (intersect(B,C)->intersect(C,B)).
% 1.71/1.91 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.71/1.91 -(all B C (intersect(B,C)<->not_e_qual(intersection(B,C),empty_set))).
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 -------> usable clausifies to:
% 1.71/1.91
% 1.71/1.91 list(usable).
% 1.71/1.91 0 [] A=A.
% 1.71/1.91 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.71/1.91 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.71/1.91 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.71/1.91 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.71/1.91 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.71/1.91 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.71/1.91 0 [] -member(B,empty_set).
% 1.71/1.91 0 [] B!=C| -member(D,B)|member(D,C).
% 1.71/1.91 0 [] B!=C|member(D,B)| -member(D,C).
% 1.71/1.91 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.71/1.91 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.71/1.91 0 [] -not_e_qual(B,C)|B!=C.
% 1.71/1.91 0 [] not_e_qual(B,C)|B=C.
% 1.71/1.91 0 [] intersection(B,C)=intersection(C,B).
% 1.71/1.91 0 [] -intersect(B,C)|intersect(C,B).
% 1.71/1.91 0 [] -empty(B)| -member(C,B).
% 1.71/1.91 0 [] empty(B)|member($f3(B),B).
% 1.71/1.91 0 [] intersect($c2,$c1)|not_e_qual(intersection($c2,$c1),empty_set).
% 1.71/1.91 0 [] -intersect($c2,$c1)| -not_e_qual(intersection($c2,$c1),empty_set).
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.71/1.91
% 1.71/1.91 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.91 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.91 deletion, with positive clauses in sos and nonpositive
% 1.71/1.91 clauses in usable.
% 1.71/1.91
% 1.71/1.91 dependent: set(knuth_bendix).
% 1.71/1.91 dependent: set(anl_eq).
% 1.71/1.91 dependent: set(para_from).
% 1.71/1.91 dependent: set(para_into).
% 1.71/1.91 dependent: clear(para_from_right).
% 1.71/1.91 dependent: clear(para_into_right).
% 1.71/1.91 dependent: set(para_from_vars).
% 1.71/1.91 dependent: set(eq_units_both_ways).
% 1.71/1.91 dependent: set(dynamic_demod_all).
% 1.71/1.91 dependent: set(dynamic_demod).
% 1.71/1.91 dependent: set(order_eq).
% 1.71/1.91 dependent: set(back_demod).
% 1.71/1.91 dependent: set(lrpo).
% 1.71/1.91 dependent: set(hyper_res).
% 1.71/1.91 dependent: set(unit_deletion).
% 1.71/1.91 dependent: set(factor).
% 1.71/1.91
% 1.71/1.91 ------------> process usable:
% 1.71/1.91 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.71/1.91 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.71/1.91 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.71/1.91 ** KEPT (pick-wt=8): 4 [] -intersect(A,B)|member($f1(A,B),A).
% 1.71/1.91 ** KEPT (pick-wt=8): 5 [] -intersect(A,B)|member($f1(A,B),B).
% 1.71/1.91 ** KEPT (pick-wt=9): 6 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.71/1.91 ** KEPT (pick-wt=3): 7 [] -member(A,empty_set).
% 1.71/1.91 ** KEPT (pick-wt=9): 8 [] A!=B| -member(C,A)|member(C,B).
% 1.71/1.91 ** KEPT (pick-wt=9): 9 [] A!=B|member(C,A)| -member(C,B).
% 1.71/1.91 ** KEPT (pick-wt=13): 10 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.71/1.91 ** KEPT (pick-wt=6): 11 [] -not_e_qual(A,B)|A!=B.
% 1.71/1.91 ** KEPT (pick-wt=6): 12 [] -intersect(A,B)|intersect(B,A).
% 1.71/1.91 ** KEPT (pick-wt=5): 13 [] -empty(A)| -member(B,A).
% 1.71/1.91 ** KEPT (pick-wt=8): 14 [] -intersect($c2,$c1)| -not_e_qual(intersection($c2,$c1),empty_set).
% 1.71/1.91
% 1.71/1.91 ------------> process sos:
% 1.71/1.91 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.71/1.91 ** KEPT (pick-wt=13): 19 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.71/1.91 ** KEPT (pick-wt=6): 20 [] not_e_qual(A,B)|A=B.
% 1.71/1.91 ** KEPT (pick-wt=7): 21 [] intersection(A,B)=intersection(B,A).
% 1.71/1.91 ** KEPT (pick-wt=6): 22 [] empty(A)|member($f3(A),A).
% 1.71/1.91 ** KEPT (pick-wt=8): 23 [] intersect($c2,$c1)|not_e_qual(intersection($c2,$c1),empty_set).
% 54.98/55.15 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 54.98/55.15 18 back subsumes 17.
% 54.98/55.15 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] intersection(A,B)=intersection(B,A).
% 54.98/55.15
% 54.98/55.15 ======= end of input processing =======
% 54.98/55.15
% 54.98/55.15 =========== start of search ===========
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Resetting weight limit to 11.
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Resetting weight limit to 11.
% 54.98/55.15
% 54.98/55.15 sos_size=4133
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Resetting weight limit to 10.
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Resetting weight limit to 10.
% 54.98/55.15
% 54.98/55.15 sos_size=2472
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Resetting weight limit to 9.
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Resetting weight limit to 9.
% 54.98/55.15
% 54.98/55.15 sos_size=2408
% 54.98/55.15
% 54.98/55.15 -- HEY sandbox, WE HAVE A PROOF!! --
% 54.98/55.15
% 54.98/55.15 ----> UNIT CONFLICT at 53.24 sec ----> 5789 [binary,5788.1,7.1] $F.
% 54.98/55.15
% 54.98/55.15 Length of proof is 14. Level of proof is 8.
% 54.98/55.15
% 54.98/55.15 ---------------- PROOF ----------------
% 54.98/55.15 % SZS status Theorem
% 54.98/55.15 % SZS output start Refutation
% See solution above
% 54.98/55.15 ------------ end of proof -------------
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Search stopped by max_proofs option.
% 54.98/55.15
% 54.98/55.15
% 54.98/55.15 Search stopped by max_proofs option.
% 54.98/55.15
% 54.98/55.15 ============ end of search ============
% 54.98/55.15
% 54.98/55.15 -------------- statistics -------------
% 54.98/55.15 clauses given 482
% 54.98/55.15 clauses generated 434994
% 54.98/55.15 clauses kept 5783
% 54.98/55.15 clauses forward subsumed 17062
% 54.98/55.15 clauses back subsumed 1993
% 54.98/55.15 Kbytes malloced 4882
% 54.98/55.15
% 54.98/55.15 ----------- times (seconds) -----------
% 54.98/55.15 user CPU time 53.24 (0 hr, 0 min, 53 sec)
% 54.98/55.15 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 54.98/55.15 wall-clock time 55 (0 hr, 0 min, 55 sec)
% 54.98/55.15
% 54.98/55.15 That finishes the proof of the theorem.
% 54.98/55.15
% 54.98/55.15 Process 12377 finished Wed Jul 27 10:50:45 2022
% 54.98/55.15 Otter interrupted
% 54.98/55.15 PROOF FOUND
%------------------------------------------------------------------------------