TSTP Solution File: SEU120+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:14:48 EDT 2022
% Result : Theorem 2.25s 2.49s
% Output : Refutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 10 unt; 3 nHn; 15 RR)
% Number of literals : 33 ( 8 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
file('SEU120+2.p',unknown),
[] ).
cnf(8,axiom,
( disjoint(A,B)
| set_intersection2(A,B) != empty_set ),
file('SEU120+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ disjoint(A,B)
| disjoint(B,A) ),
file('SEU120+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(A,B)
| ~ in(A,C)
| ~ disjoint(B,C) ),
file('SEU120+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ disjoint(dollar_c5,dollar_c4)
| in(dollar_c3,set_intersection2(dollar_c5,dollar_c4)) ),
file('SEU120+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(A,set_intersection2(dollar_c5,dollar_c4))
| disjoint(dollar_c5,dollar_c4) ),
file('SEU120+2.p',unknown),
[] ).
cnf(20,plain,
( ~ in(A,B)
| ~ disjoint(B,B) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.1.2')] ).
cnf(23,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SEU120+2.p',unknown),
[] ).
cnf(24,axiom,
( A = empty_set
| in(dollar_f1(A),A) ),
file('SEU120+2.p',unknown),
[] ).
cnf(28,axiom,
set_intersection2(A,A) = A,
file('SEU120+2.p',unknown),
[] ).
cnf(31,axiom,
( disjoint(A,B)
| in(dollar_f3(A,B),A) ),
file('SEU120+2.p',unknown),
[] ).
cnf(45,plain,
disjoint(empty_set,empty_set),
inference(hyper,[status(thm)],[28,8]),
[iquote('hyper,28,8')] ).
cnf(69,plain,
( ~ disjoint(dollar_c5,dollar_c4)
| in(dollar_c3,set_intersection2(dollar_c4,dollar_c5)) ),
inference(para_from,[status(thm),theory(equality)],[23,12]),
[iquote('para_from,23.1.1,12.2.2')] ).
cnf(109,plain,
( set_intersection2(dollar_c5,dollar_c4) = empty_set
| disjoint(dollar_c5,dollar_c4) ),
inference(hyper,[status(thm)],[24,14]),
[iquote('hyper,24,14')] ).
cnf(530,plain,
disjoint(empty_set,A),
inference(hyper,[status(thm)],[31,20,45]),
[iquote('hyper,31,20,45')] ).
cnf(545,plain,
disjoint(A,empty_set),
inference(hyper,[status(thm)],[530,10]),
[iquote('hyper,530,10')] ).
cnf(1865,plain,
set_intersection2(dollar_c5,dollar_c4) = empty_set,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[109,7])]),
[iquote('hyper,109,7,factor_simp')] ).
cnf(2002,plain,
disjoint(dollar_c5,dollar_c4),
inference(hyper,[status(thm)],[1865,8]),
[iquote('hyper,1865,8')] ).
cnf(2014,plain,
set_intersection2(dollar_c4,dollar_c5) = empty_set,
inference(para_into,[status(thm),theory(equality)],[1865,23]),
[iquote('para_into,1865.1.1,23.1.1')] ).
cnf(2044,plain,
in(dollar_c3,empty_set),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[69]),2014]),2002]),
[iquote('back_demod,69,demod,2014,unit_del,2002')] ).
cnf(2082,plain,
$false,
inference(hyper,[status(thm)],[2044,20,545]),
[iquote('hyper,2044,20,545')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 07:43:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.94/2.14 ----- Otter 3.3f, August 2004 -----
% 1.94/2.14 The process was started by sandbox on n006.cluster.edu,
% 1.94/2.14 Wed Jul 27 07:43:17 2022
% 1.94/2.14 The command was "./otter". The process ID is 31331.
% 1.94/2.14
% 1.94/2.14 set(prolog_style_variables).
% 1.94/2.14 set(auto).
% 1.94/2.14 dependent: set(auto1).
% 1.94/2.14 dependent: set(process_input).
% 1.94/2.14 dependent: clear(print_kept).
% 1.94/2.14 dependent: clear(print_new_demod).
% 1.94/2.14 dependent: clear(print_back_demod).
% 1.94/2.14 dependent: clear(print_back_sub).
% 1.94/2.14 dependent: set(control_memory).
% 1.94/2.14 dependent: assign(max_mem, 12000).
% 1.94/2.14 dependent: assign(pick_given_ratio, 4).
% 1.94/2.14 dependent: assign(stats_level, 1).
% 1.94/2.14 dependent: assign(max_seconds, 10800).
% 1.94/2.14 clear(print_given).
% 1.94/2.14
% 1.94/2.14 formula_list(usable).
% 1.94/2.14 all A (A=A).
% 1.94/2.14 all A B (in(A,B)-> -in(B,A)).
% 1.94/2.14 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.94/2.14 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.94/2.14 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.94/2.14 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.94/2.14 $T.
% 1.94/2.14 $T.
% 1.94/2.14 empty(empty_set).
% 1.94/2.14 all A B (set_intersection2(A,A)=A).
% 1.94/2.14 exists A empty(A).
% 1.94/2.14 exists A (-empty(A)).
% 1.94/2.14 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.94/2.14 all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B))).
% 1.94/2.14 -(all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B)))).
% 1.94/2.14 end_of_list.
% 1.94/2.14
% 1.94/2.14 -------> usable clausifies to:
% 1.94/2.14
% 1.94/2.14 list(usable).
% 1.94/2.14 0 [] A=A.
% 1.94/2.14 0 [] -in(A,B)| -in(B,A).
% 1.94/2.14 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.94/2.14 0 [] A!=empty_set| -in(B,A).
% 1.94/2.14 0 [] A=empty_set|in($f1(A),A).
% 1.94/2.14 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.94/2.14 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.94/2.14 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.94/2.14 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A).
% 1.94/2.14 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),B).
% 1.94/2.14 0 [] C=set_intersection2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A)| -in($f2(A,B,C),B).
% 1.94/2.14 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.94/2.14 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.94/2.14 0 [] $T.
% 1.94/2.14 0 [] $T.
% 1.94/2.14 0 [] empty(empty_set).
% 1.94/2.14 0 [] set_intersection2(A,A)=A.
% 1.94/2.14 0 [] empty($c1).
% 1.94/2.14 0 [] -empty($c2).
% 1.94/2.14 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.94/2.14 0 [] disjoint(A,B)|in($f3(A,B),A).
% 1.94/2.14 0 [] disjoint(A,B)|in($f3(A,B),B).
% 1.94/2.14 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.94/2.14 0 [] -disjoint($c5,$c4)|in($c3,set_intersection2($c5,$c4)).
% 1.94/2.14 0 [] -in(C,set_intersection2($c5,$c4))|in($c3,set_intersection2($c5,$c4)).
% 1.94/2.14 0 [] -in(C,set_intersection2($c5,$c4))|disjoint($c5,$c4).
% 1.94/2.14 end_of_list.
% 1.94/2.14
% 1.94/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.94/2.14
% 1.94/2.14 This ia a non-Horn set with equality. The strategy will be
% 1.94/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.94/2.14 deletion, with positive clauses in sos and nonpositive
% 1.94/2.14 clauses in usable.
% 1.94/2.14
% 1.94/2.14 dependent: set(knuth_bendix).
% 1.94/2.14 dependent: set(anl_eq).
% 1.94/2.14 dependent: set(para_from).
% 1.94/2.14 dependent: set(para_into).
% 1.94/2.14 dependent: clear(para_from_right).
% 1.94/2.14 dependent: clear(para_into_right).
% 1.94/2.14 dependent: set(para_from_vars).
% 1.94/2.14 dependent: set(eq_units_both_ways).
% 1.94/2.14 dependent: set(dynamic_demod_all).
% 1.94/2.14 dependent: set(dynamic_demod).
% 1.94/2.14 dependent: set(order_eq).
% 1.94/2.14 dependent: set(back_demod).
% 1.94/2.14 dependent: set(lrpo).
% 1.94/2.14 dependent: set(hyper_res).
% 1.94/2.14 dependent: set(unit_deletion).
% 1.94/2.14 dependent: set(factor).
% 1.94/2.14
% 1.94/2.14 ------------> process usable:
% 1.94/2.14 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.94/2.14 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.94/2.14 ** KEPT (pick-wt=11): 3 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.94/2.14 ** KEPT (pick-wt=11): 4 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.94/2.14 ** KEPT (pick-wt=14): 5 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.94/2.14 ** KEPT (pick-wt=23): 6 [] A=set_intersection2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B)| -in($f2(B,C,A),C).
% 1.94/2.14 ** KEPT (pick-wt=8): 7 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.94/2.14 ** KEPT (pick-wt=8): 8 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.94/2.14 ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.94/2.14 ** KEPT (pick-wt=6): 10 [] -disjoint(A,B)|disjoint(B,A).
% 1.94/2.14 ** KEPT (pick-wt=9): 11 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.94/2.14 ** KEPT (pick-wt=8): 12 [] -disjoint($c5,$c4)|in($c3,set_intersection2($c5,$c4)).
% 1.94/2.14 ** KEPT (pick-wt=10): 13 [] -in(A,set_intersection2($c5,$c4))|in($c3,set_intersection2($c5,$c4)).
% 2.25/2.49 ** KEPT (pick-wt=8): 14 [] -in(A,set_intersection2($c5,$c4))|disjoint($c5,$c4).
% 2.25/2.49
% 2.25/2.49 ------------> process sos:
% 2.25/2.49 ** KEPT (pick-wt=3): 22 [] A=A.
% 2.25/2.49 ** KEPT (pick-wt=7): 23 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.25/2.49 ** KEPT (pick-wt=7): 24 [] A=empty_set|in($f1(A),A).
% 2.25/2.49 ** KEPT (pick-wt=17): 25 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B).
% 2.25/2.49 ** KEPT (pick-wt=17): 26 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),C).
% 2.25/2.49 ** KEPT (pick-wt=2): 27 [] empty(empty_set).
% 2.25/2.49 ** KEPT (pick-wt=5): 28 [] set_intersection2(A,A)=A.
% 2.25/2.49 ---> New Demodulator: 29 [new_demod,28] set_intersection2(A,A)=A.
% 2.25/2.49 ** KEPT (pick-wt=2): 30 [] empty($c1).
% 2.25/2.49 ** KEPT (pick-wt=8): 31 [] disjoint(A,B)|in($f3(A,B),A).
% 2.25/2.49 ** KEPT (pick-wt=8): 32 [] disjoint(A,B)|in($f3(A,B),B).
% 2.25/2.49 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 2.25/2.49 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.25/2.49 >>>> Starting back demodulation with 29.
% 2.25/2.49 >> back demodulating 21 with 29.
% 2.25/2.49 >> back demodulating 19 with 29.
% 2.25/2.49 >> back demodulating 16 with 29.
% 2.25/2.49
% 2.25/2.49 ======= end of input processing =======
% 2.25/2.49
% 2.25/2.49 =========== start of search ===========
% 2.25/2.49
% 2.25/2.49 -------- PROOF --------
% 2.25/2.49
% 2.25/2.49 -----> EMPTY CLAUSE at 0.35 sec ----> 2082 [hyper,2044,20,545] $F.
% 2.25/2.49
% 2.25/2.49 Length of proof is 10. Level of proof is 4.
% 2.25/2.49
% 2.25/2.49 ---------------- PROOF ----------------
% 2.25/2.49 % SZS status Theorem
% 2.25/2.49 % SZS output start Refutation
% See solution above
% 2.25/2.49 ------------ end of proof -------------
% 2.25/2.49
% 2.25/2.49
% 2.25/2.49 Search stopped by max_proofs option.
% 2.25/2.49
% 2.25/2.49
% 2.25/2.49 Search stopped by max_proofs option.
% 2.25/2.49
% 2.25/2.49 ============ end of search ============
% 2.25/2.49
% 2.25/2.49 -------------- statistics -------------
% 2.25/2.49 clauses given 70
% 2.25/2.49 clauses generated 5903
% 2.25/2.49 clauses kept 2076
% 2.25/2.49 clauses forward subsumed 4055
% 2.25/2.49 clauses back subsumed 364
% 2.25/2.49 Kbytes malloced 2929
% 2.25/2.49
% 2.25/2.49 ----------- times (seconds) -----------
% 2.25/2.49 user CPU time 0.35 (0 hr, 0 min, 0 sec)
% 2.25/2.49 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.25/2.49 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.25/2.49
% 2.25/2.49 That finishes the proof of the theorem.
% 2.25/2.49
% 2.25/2.49 Process 31331 finished Wed Jul 27 07:43:19 2022
% 2.25/2.49 Otter interrupted
% 2.25/2.49 PROOF FOUND
%------------------------------------------------------------------------------