TSTP Solution File: SEU119+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU119+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 5.26s 5.43s
% Output : Refutation 5.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 24 ( 9 unt; 5 nHn; 17 RR)
% Number of literals : 43 ( 15 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SEU119+2.p',unknown),
[] ).
cnf(4,axiom,
( A != set_intersection2(B,C)
| ~ in(D,A)
| in(D,C) ),
file('SEU119+2.p',unknown),
[] ).
cnf(5,axiom,
( A != set_intersection2(B,C)
| in(D,A)
| ~ in(D,B)
| ~ in(D,C) ),
file('SEU119+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
file('SEU119+2.p',unknown),
[] ).
cnf(8,axiom,
( disjoint(A,B)
| set_intersection2(A,B) != empty_set ),
file('SEU119+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ disjoint(dollar_c5,dollar_c4)
| in(dollar_c3,dollar_c5) ),
file('SEU119+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ disjoint(dollar_c5,dollar_c4)
| in(dollar_c3,dollar_c4) ),
file('SEU119+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(A,dollar_c5)
| ~ in(A,dollar_c4)
| disjoint(dollar_c5,dollar_c4) ),
file('SEU119+2.p',unknown),
[] ).
cnf(22,axiom,
A = A,
file('SEU119+2.p',unknown),
[] ).
cnf(23,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SEU119+2.p',unknown),
[] ).
cnf(24,axiom,
( A = empty_set
| in(dollar_f1(A),A) ),
file('SEU119+2.p',unknown),
[] ).
cnf(29,axiom,
set_intersection2(A,A) = A,
file('SEU119+2.p',unknown),
[] ).
cnf(59,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,7])]),
[iquote('para_into,23.1.1,7.2.1,flip.1')] ).
cnf(64,plain,
( disjoint(A,B)
| set_intersection2(B,A) != empty_set ),
inference(para_from,[status(thm),theory(equality)],[23,8]),
[iquote('para_from,23.1.1,8.2.1')] ).
cnf(106,plain,
( set_intersection2(A,B) = empty_set
| in(dollar_f1(set_intersection2(A,B)),B) ),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,4,29]),29,29]),
[iquote('hyper,24,4,28,demod,29,29')] ).
cnf(107,plain,
( set_intersection2(A,B) = empty_set
| in(dollar_f1(set_intersection2(A,B)),A) ),
inference(hyper,[status(thm)],[24,4,23]),
[iquote('hyper,24,4,23')] ).
cnf(4390,plain,
( disjoint(A,B)
| in(dollar_f1(set_intersection2(B,A)),A) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[106,64]),22]),
[iquote('para_from,106.1.1,64.2.1,unit_del,22')] ).
cnf(4397,plain,
( set_intersection2(dollar_c4,dollar_c5) = empty_set
| disjoint(dollar_c5,dollar_c4) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[107,15,4390])]),
[iquote('hyper,107,15,4390,factor_simp')] ).
cnf(4408,plain,
set_intersection2(dollar_c4,dollar_c5) = empty_set,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4397,59])]),
[iquote('hyper,4397,59,factor_simp')] ).
cnf(4412,plain,
disjoint(dollar_c5,dollar_c4),
inference(hyper,[status(thm)],[4408,64]),
[iquote('hyper,4407,64')] ).
cnf(4420,plain,
in(dollar_c3,dollar_c4),
inference(hyper,[status(thm)],[4412,12]),
[iquote('hyper,4412,12')] ).
cnf(4421,plain,
in(dollar_c3,dollar_c5),
inference(hyper,[status(thm)],[4412,11]),
[iquote('hyper,4412,11')] ).
cnf(4431,plain,
in(dollar_c3,empty_set),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4421,5,29,4420]),4408,4408,29]),
[iquote('hyper,4421,5,28,4420,demod,4408,4408,29')] ).
cnf(4437,plain,
$false,
inference(hyper,[status(thm)],[4431,2,22]),
[iquote('hyper,4431,2,22')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU119+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 08:11:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.18 ----- Otter 3.3f, August 2004 -----
% 1.97/2.18 The process was started by sandbox on n025.cluster.edu,
% 1.97/2.18 Wed Jul 27 08:11:30 2022
% 1.97/2.18 The command was "./otter". The process ID is 6287.
% 1.97/2.18
% 1.97/2.18 set(prolog_style_variables).
% 1.97/2.18 set(auto).
% 1.97/2.18 dependent: set(auto1).
% 1.97/2.18 dependent: set(process_input).
% 1.97/2.18 dependent: clear(print_kept).
% 1.97/2.18 dependent: clear(print_new_demod).
% 1.97/2.18 dependent: clear(print_back_demod).
% 1.97/2.18 dependent: clear(print_back_sub).
% 1.97/2.18 dependent: set(control_memory).
% 1.97/2.18 dependent: assign(max_mem, 12000).
% 1.97/2.18 dependent: assign(pick_given_ratio, 4).
% 1.97/2.18 dependent: assign(stats_level, 1).
% 1.97/2.18 dependent: assign(max_seconds, 10800).
% 1.97/2.18 clear(print_given).
% 1.97/2.18
% 1.97/2.18 formula_list(usable).
% 1.97/2.18 all A (A=A).
% 1.97/2.18 all A B (in(A,B)-> -in(B,A)).
% 1.97/2.18 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.97/2.18 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.97/2.18 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.97/2.18 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.97/2.18 $T.
% 1.97/2.18 $T.
% 1.97/2.18 empty(empty_set).
% 1.97/2.18 all A B (set_intersection2(A,A)=A).
% 1.97/2.18 exists A empty(A).
% 1.97/2.18 exists A (-empty(A)).
% 1.97/2.18 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.97/2.18 -(all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B)))).
% 1.97/2.18 end_of_list.
% 1.97/2.18
% 1.97/2.18 -------> usable clausifies to:
% 1.97/2.18
% 1.97/2.18 list(usable).
% 1.97/2.18 0 [] A=A.
% 1.97/2.18 0 [] -in(A,B)| -in(B,A).
% 1.97/2.18 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.97/2.18 0 [] A!=empty_set| -in(B,A).
% 1.97/2.18 0 [] A=empty_set|in($f1(A),A).
% 1.97/2.18 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.97/2.18 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.97/2.18 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.97/2.18 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A).
% 1.97/2.18 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),B).
% 1.97/2.18 0 [] C=set_intersection2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A)| -in($f2(A,B,C),B).
% 1.97/2.18 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.97/2.18 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.97/2.18 0 [] $T.
% 1.97/2.18 0 [] $T.
% 1.97/2.18 0 [] empty(empty_set).
% 1.97/2.18 0 [] set_intersection2(A,A)=A.
% 1.97/2.18 0 [] empty($c1).
% 1.97/2.18 0 [] -empty($c2).
% 1.97/2.18 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.97/2.18 0 [] -disjoint($c5,$c4)|in($c3,$c5).
% 1.97/2.18 0 [] -disjoint($c5,$c4)|in($c3,$c4).
% 1.97/2.18 0 [] -in(C,$c5)| -in(C,$c4)|in($c3,$c5).
% 1.97/2.18 0 [] -in(C,$c5)| -in(C,$c4)|in($c3,$c4).
% 1.97/2.18 0 [] -in(C,$c5)| -in(C,$c4)|disjoint($c5,$c4).
% 1.97/2.18 end_of_list.
% 1.97/2.18
% 1.97/2.18 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.97/2.18
% 1.97/2.18 This ia a non-Horn set with equality. The strategy will be
% 1.97/2.18 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.18 deletion, with positive clauses in sos and nonpositive
% 1.97/2.18 clauses in usable.
% 1.97/2.18
% 1.97/2.18 dependent: set(knuth_bendix).
% 1.97/2.18 dependent: set(anl_eq).
% 1.97/2.18 dependent: set(para_from).
% 1.97/2.18 dependent: set(para_into).
% 1.97/2.18 dependent: clear(para_from_right).
% 1.97/2.18 dependent: clear(para_into_right).
% 1.97/2.18 dependent: set(para_from_vars).
% 1.97/2.18 dependent: set(eq_units_both_ways).
% 1.97/2.18 dependent: set(dynamic_demod_all).
% 1.97/2.18 dependent: set(dynamic_demod).
% 1.97/2.18 dependent: set(order_eq).
% 1.97/2.18 dependent: set(back_demod).
% 1.97/2.18 dependent: set(lrpo).
% 1.97/2.18 dependent: set(hyper_res).
% 1.97/2.18 dependent: set(unit_deletion).
% 1.97/2.18 dependent: set(factor).
% 1.97/2.18
% 1.97/2.18 ------------> process usable:
% 1.97/2.18 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.97/2.18 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.97/2.18 ** KEPT (pick-wt=11): 3 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.97/2.18 ** KEPT (pick-wt=11): 4 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.97/2.18 ** KEPT (pick-wt=14): 5 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.97/2.18 ** KEPT (pick-wt=23): 6 [] A=set_intersection2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B)| -in($f2(B,C,A),C).
% 1.97/2.18 ** KEPT (pick-wt=8): 7 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.97/2.18 ** KEPT (pick-wt=8): 8 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.97/2.18 ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.97/2.18 ** KEPT (pick-wt=6): 10 [] -disjoint(A,B)|disjoint(B,A).
% 1.97/2.18 ** KEPT (pick-wt=6): 11 [] -disjoint($c5,$c4)|in($c3,$c5).
% 1.97/2.18 ** KEPT (pick-wt=6): 12 [] -disjoint($c5,$c4)|in($c3,$c4).
% 1.97/2.18 ** KEPT (pick-wt=9): 13 [] -in(A,$c5)| -in(A,$c4)|in($c3,$c5).
% 1.97/2.18 ** KEPT (pick-wt=9): 14 [] -in(A,$c5)| -in(A,$c4)|in($c3,$c4).
% 1.97/2.18 ** KEPT (pick-wt=9): 15 [] -in(A,$c5)| -in(A,$c4)|disjoint($c5,$c4).
% 1.97/2.18
% 1.97/2.18 ------------> process sos:
% 1.97/2.18 ** KEPT (pick-wt=3): 22 [] A=A.
% 1.97/2.18 ** KEPT (pick-wt=7): 23 [] set_intersection2(A,B)=set_intersection2(B,A).
% 5.26/5.43 ** KEPT (pick-wt=7): 24 [] A=empty_set|in($f1(A),A).
% 5.26/5.43 ** KEPT (pick-wt=17): 25 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B).
% 5.26/5.43 ** KEPT (pick-wt=17): 26 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),C).
% 5.26/5.43 ** KEPT (pick-wt=2): 27 [] empty(empty_set).
% 5.26/5.43 ** KEPT (pick-wt=5): 28 [] set_intersection2(A,A)=A.
% 5.26/5.43 ---> New Demodulator: 29 [new_demod,28] set_intersection2(A,A)=A.
% 5.26/5.43 ** KEPT (pick-wt=2): 30 [] empty($c1).
% 5.26/5.43 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 5.26/5.43 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 5.26/5.43 >>>> Starting back demodulation with 29.
% 5.26/5.43 >> back demodulating 21 with 29.
% 5.26/5.43 >> back demodulating 20 with 29.
% 5.26/5.43 >> back demodulating 17 with 29.
% 5.26/5.43
% 5.26/5.43 ======= end of input processing =======
% 5.26/5.43
% 5.26/5.43 =========== start of search ===========
% 5.26/5.43
% 5.26/5.43
% 5.26/5.43 Resetting weight limit to 13.
% 5.26/5.43
% 5.26/5.43
% 5.26/5.43 Resetting weight limit to 13.
% 5.26/5.43
% 5.26/5.43 sos_size=3582
% 5.26/5.43
% 5.26/5.43
% 5.26/5.43 Resetting weight limit to 12.
% 5.26/5.43
% 5.26/5.43
% 5.26/5.43 Resetting weight limit to 12.
% 5.26/5.43
% 5.26/5.43 sos_size=3678
% 5.26/5.43
% 5.26/5.43 -------- PROOF --------
% 5.26/5.43
% 5.26/5.43 -----> EMPTY CLAUSE at 3.25 sec ----> 4437 [hyper,4431,2,22] $F.
% 5.26/5.43
% 5.26/5.43 Length of proof is 11. Level of proof is 7.
% 5.26/5.43
% 5.26/5.43 ---------------- PROOF ----------------
% 5.26/5.43 % SZS status Theorem
% 5.26/5.43 % SZS output start Refutation
% See solution above
% 5.26/5.43 ------------ end of proof -------------
% 5.26/5.43
% 5.26/5.43
% 5.26/5.43 Search stopped by max_proofs option.
% 5.26/5.43
% 5.26/5.43
% 5.26/5.43 Search stopped by max_proofs option.
% 5.26/5.43
% 5.26/5.43 ============ end of search ============
% 5.26/5.43
% 5.26/5.43 -------------- statistics -------------
% 5.26/5.43 clauses given 204
% 5.26/5.43 clauses generated 45452
% 5.26/5.43 clauses kept 4431
% 5.26/5.43 clauses forward subsumed 26496
% 5.26/5.43 clauses back subsumed 757
% 5.26/5.43 Kbytes malloced 4882
% 5.26/5.43
% 5.26/5.43 ----------- times (seconds) -----------
% 5.26/5.43 user CPU time 3.25 (0 hr, 0 min, 3 sec)
% 5.26/5.43 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 5.26/5.43 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 5.26/5.43
% 5.26/5.43 That finishes the proof of the theorem.
% 5.26/5.43
% 5.26/5.43 Process 6287 finished Wed Jul 27 08:11:35 2022
% 5.26/5.43 Otter interrupted
% 5.26/5.43 PROOF FOUND
%------------------------------------------------------------------------------