TSTP Solution File: SEU121+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU121+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 13:14:49 EDT 2022
% Result : Theorem 1.80s 2.03s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 8 unt; 1 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU121+2.p',unknown),
[] ).
cnf(4,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SEU121+2.p',unknown),
[] ).
cnf(13,axiom,
~ subset(dollar_c5,dollar_c3),
file('SEU121+2.p',unknown),
[] ).
cnf(30,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SEU121+2.p',unknown),
[] ).
cnf(38,axiom,
subset(dollar_c5,dollar_c4),
file('SEU121+2.p',unknown),
[] ).
cnf(39,axiom,
subset(dollar_c4,dollar_c3),
file('SEU121+2.p',unknown),
[] ).
cnf(114,plain,
in(dollar_f2(dollar_c5,dollar_c3),dollar_c5),
inference(hyper,[status(thm)],[30,13]),
[iquote('hyper,30,13')] ).
cnf(469,plain,
in(dollar_f2(dollar_c5,dollar_c3),dollar_c4),
inference(hyper,[status(thm)],[114,3,38]),
[iquote('hyper,114,3,38')] ).
cnf(513,plain,
in(dollar_f2(dollar_c5,dollar_c3),dollar_c3),
inference(hyper,[status(thm)],[469,3,39]),
[iquote('hyper,469,3,39')] ).
cnf(559,plain,
subset(dollar_c5,dollar_c3),
inference(hyper,[status(thm)],[513,4]),
[iquote('hyper,513,4')] ).
cnf(560,plain,
$false,
inference(binary,[status(thm)],[559,13]),
[iquote('binary,559.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU121+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 07:06:48 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.80/1.99 ----- Otter 3.3f, August 2004 -----
% 1.80/1.99 The process was started by sandbox on n017.cluster.edu,
% 1.80/1.99 Wed Jul 27 07:06:48 2022
% 1.80/1.99 The command was "./otter". The process ID is 24480.
% 1.80/1.99
% 1.80/1.99 set(prolog_style_variables).
% 1.80/1.99 set(auto).
% 1.80/1.99 dependent: set(auto1).
% 1.80/1.99 dependent: set(process_input).
% 1.80/1.99 dependent: clear(print_kept).
% 1.80/1.99 dependent: clear(print_new_demod).
% 1.80/1.99 dependent: clear(print_back_demod).
% 1.80/1.99 dependent: clear(print_back_sub).
% 1.80/1.99 dependent: set(control_memory).
% 1.80/1.99 dependent: assign(max_mem, 12000).
% 1.80/1.99 dependent: assign(pick_given_ratio, 4).
% 1.80/1.99 dependent: assign(stats_level, 1).
% 1.80/1.99 dependent: assign(max_seconds, 10800).
% 1.80/1.99 clear(print_given).
% 1.80/1.99
% 1.80/1.99 formula_list(usable).
% 1.80/1.99 all A (A=A).
% 1.80/1.99 all A B (in(A,B)-> -in(B,A)).
% 1.80/1.99 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.80/1.99 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.80/1.99 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.80/1.99 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.80/1.99 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.80/1.99 $T.
% 1.80/1.99 $T.
% 1.80/1.99 empty(empty_set).
% 1.80/1.99 all A B (set_intersection2(A,A)=A).
% 1.80/1.99 exists A empty(A).
% 1.80/1.99 exists A (-empty(A)).
% 1.80/1.99 all A B subset(A,A).
% 1.80/1.99 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.80/1.99 -(all A B C (subset(A,B)&subset(B,C)->subset(A,C))).
% 1.80/1.99 all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B))).
% 1.80/1.99 all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B))).
% 1.80/1.99 all A (empty(A)->A=empty_set).
% 1.80/1.99 all A B (-(in(A,B)&empty(B))).
% 1.80/1.99 all A B (-(empty(A)&A!=B&empty(B))).
% 1.80/1.99 end_of_list.
% 1.80/1.99
% 1.80/1.99 -------> usable clausifies to:
% 1.80/1.99
% 1.80/1.99 list(usable).
% 1.80/1.99 0 [] A=A.
% 1.80/1.99 0 [] -in(A,B)| -in(B,A).
% 1.80/1.99 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.80/1.99 0 [] A!=empty_set| -in(B,A).
% 1.80/1.99 0 [] A=empty_set|in($f1(A),A).
% 1.80/1.99 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.80/1.99 0 [] subset(A,B)|in($f2(A,B),A).
% 1.80/1.99 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.80/1.99 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.80/1.99 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.80/1.99 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.80/1.99 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A).
% 1.80/1.99 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),B).
% 1.80/1.99 0 [] C=set_intersection2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A)| -in($f3(A,B,C),B).
% 1.80/1.99 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.80/1.99 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.80/1.99 0 [] $T.
% 1.80/1.99 0 [] $T.
% 1.80/1.99 0 [] empty(empty_set).
% 1.80/1.99 0 [] set_intersection2(A,A)=A.
% 1.80/1.99 0 [] empty($c1).
% 1.80/1.99 0 [] -empty($c2).
% 1.80/1.99 0 [] subset(A,A).
% 1.80/1.99 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.80/1.99 0 [] subset($c5,$c4).
% 1.80/1.99 0 [] subset($c4,$c3).
% 1.80/1.99 0 [] -subset($c5,$c3).
% 1.80/1.99 0 [] disjoint(A,B)|in($f4(A,B),A).
% 1.80/1.99 0 [] disjoint(A,B)|in($f4(A,B),B).
% 1.80/1.99 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.80/1.99 0 [] disjoint(A,B)|in($f5(A,B),set_intersection2(A,B)).
% 1.80/1.99 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.80/1.99 0 [] -empty(A)|A=empty_set.
% 1.80/1.99 0 [] -in(A,B)| -empty(B).
% 1.80/1.99 0 [] -empty(A)|A=B| -empty(B).
% 1.80/1.99 end_of_list.
% 1.80/1.99
% 1.80/1.99 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.80/1.99
% 1.80/1.99 This ia a non-Horn set with equality. The strategy will be
% 1.80/1.99 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.80/1.99 deletion, with positive clauses in sos and nonpositive
% 1.80/1.99 clauses in usable.
% 1.80/1.99
% 1.80/1.99 dependent: set(knuth_bendix).
% 1.80/1.99 dependent: set(anl_eq).
% 1.80/1.99 dependent: set(para_from).
% 1.80/1.99 dependent: set(para_into).
% 1.80/1.99 dependent: clear(para_from_right).
% 1.80/1.99 dependent: clear(para_into_right).
% 1.80/1.99 dependent: set(para_from_vars).
% 1.80/1.99 dependent: set(eq_units_both_ways).
% 1.80/1.99 dependent: set(dynamic_demod_all).
% 1.80/1.99 dependent: set(dynamic_demod).
% 1.80/1.99 dependent: set(order_eq).
% 1.80/1.99 dependent: set(back_demod).
% 1.80/1.99 dependent: set(lrpo).
% 1.80/1.99 dependent: set(hyper_res).
% 1.80/1.99 dependent: set(unit_deletion).
% 1.80/1.99 dependent: set(factor).
% 1.80/1.99
% 1.80/1.99 ------------> process usable:
% 1.80/1.99 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.80/1.99 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.80/1.99 ** KEPT (pick-wt=9): 3 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.80/1.99 ** KEPT (pick-wt=8): 4 [] subset(A,B)| -in($f2(A,B),B).
% 1.80/1.99 ** KEPT (pick-wt=11): 5 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.80/1.99 ** KEPT (pick-wt=11): 6 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.80/1.99 ** KEPT (pick-wt=14): 7 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.80/2.03 ** KEPT (pick-wt=23): 8 [] A=set_intersection2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B)| -in($f3(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=8): 9 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=8): 10 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=2): 11 [] -empty($c2).
% 1.80/2.03 ** KEPT (pick-wt=6): 12 [] -disjoint(A,B)|disjoint(B,A).
% 1.80/2.03 ** KEPT (pick-wt=3): 13 [] -subset($c5,$c3).
% 1.80/2.03 ** KEPT (pick-wt=9): 14 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.80/2.03 ** KEPT (pick-wt=8): 15 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.80/2.03 ** KEPT (pick-wt=5): 16 [] -empty(A)|A=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=5): 17 [] -in(A,B)| -empty(B).
% 1.80/2.03 ** KEPT (pick-wt=7): 18 [] -empty(A)|A=B| -empty(B).
% 1.80/2.03
% 1.80/2.03 ------------> process sos:
% 1.80/2.03 ** KEPT (pick-wt=3): 27 [] A=A.
% 1.80/2.03 ** KEPT (pick-wt=7): 28 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.80/2.03 ** KEPT (pick-wt=7): 29 [] A=empty_set|in($f1(A),A).
% 1.80/2.03 ** KEPT (pick-wt=8): 30 [] subset(A,B)|in($f2(A,B),A).
% 1.80/2.03 ** KEPT (pick-wt=17): 31 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B).
% 1.80/2.03 ** KEPT (pick-wt=17): 32 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=2): 33 [] empty(empty_set).
% 1.80/2.03 ** KEPT (pick-wt=5): 34 [] set_intersection2(A,A)=A.
% 1.80/2.03 ---> New Demodulator: 35 [new_demod,34] set_intersection2(A,A)=A.
% 1.80/2.03 ** KEPT (pick-wt=2): 36 [] empty($c1).
% 1.80/2.03 ** KEPT (pick-wt=3): 37 [] subset(A,A).
% 1.80/2.03 ** KEPT (pick-wt=3): 38 [] subset($c5,$c4).
% 1.80/2.03 ** KEPT (pick-wt=3): 39 [] subset($c4,$c3).
% 1.80/2.03 ** KEPT (pick-wt=8): 40 [] disjoint(A,B)|in($f4(A,B),A).
% 1.80/2.03 ** KEPT (pick-wt=8): 41 [] disjoint(A,B)|in($f4(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=10): 42 [] disjoint(A,B)|in($f5(A,B),set_intersection2(A,B)).
% 1.80/2.03 Following clause subsumed by 27 during input processing: 0 [copy,27,flip.1] A=A.
% 1.80/2.03 27 back subsumes 25.
% 1.80/2.03 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.80/2.03 >>>> Starting back demodulation with 35.
% 1.80/2.03 >> back demodulating 26 with 35.
% 1.80/2.03 >> back demodulating 23 with 35.
% 1.80/2.03 >> back demodulating 20 with 35.
% 1.80/2.03
% 1.80/2.03 ======= end of input processing =======
% 1.80/2.03
% 1.80/2.03 =========== start of search ===========
% 1.80/2.03
% 1.80/2.03 -------- PROOF --------
% 1.80/2.03
% 1.80/2.03 ----> UNIT CONFLICT at 0.04 sec ----> 560 [binary,559.1,13.1] $F.
% 1.80/2.03
% 1.80/2.03 Length of proof is 4. Level of proof is 4.
% 1.80/2.03
% 1.80/2.03 ---------------- PROOF ----------------
% 1.80/2.03 % SZS status Theorem
% 1.80/2.03 % SZS output start Refutation
% See solution above
% 1.80/2.03 ------------ end of proof -------------
% 1.80/2.03
% 1.80/2.03
% 1.80/2.03 Search stopped by max_proofs option.
% 1.80/2.03
% 1.80/2.03
% 1.80/2.03 Search stopped by max_proofs option.
% 1.80/2.03
% 1.80/2.03 ============ end of search ============
% 1.80/2.03
% 1.80/2.03 -------------- statistics -------------
% 1.80/2.03 clauses given 24
% 1.80/2.03 clauses generated 1081
% 1.80/2.03 clauses kept 557
% 1.80/2.03 clauses forward subsumed 569
% 1.80/2.03 clauses back subsumed 3
% 1.80/2.03 Kbytes malloced 1953
% 1.80/2.03
% 1.80/2.03 ----------- times (seconds) -----------
% 1.80/2.03 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.80/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.03 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.80/2.03
% 1.80/2.03 That finishes the proof of the theorem.
% 1.80/2.03
% 1.80/2.03 Process 24480 finished Wed Jul 27 07:06:49 2022
% 1.80/2.03 Otter interrupted
% 1.80/2.03 PROOF FOUND
%------------------------------------------------------------------------------