TSTP Solution File: SEU126+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:14:50 EDT 2022
% Result : Theorem 1.90s 2.07s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 8 RR)
% Number of literals : 15 ( 5 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SEU126+2.p',unknown),
[] ).
cnf(23,axiom,
set_union2(dollar_c4,dollar_c3) != dollar_c3,
file('SEU126+2.p',unknown),
[] ).
cnf(31,axiom,
( ~ subset(A,B)
| ~ subset(C,B)
| subset(set_union2(A,C),B) ),
file('SEU126+2.p',unknown),
[] ).
cnf(46,axiom,
set_union2(A,B) = set_union2(B,A),
file('SEU126+2.p',unknown),
[] ).
cnf(59,axiom,
subset(A,A),
file('SEU126+2.p',unknown),
[] ).
cnf(60,axiom,
subset(dollar_c4,dollar_c3),
file('SEU126+2.p',unknown),
[] ).
cnf(67,axiom,
subset(A,set_union2(A,B)),
file('SEU126+2.p',unknown),
[] ).
cnf(105,plain,
subset(set_union2(dollar_c3,dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[60,31,59]),
[iquote('hyper,60,31,59')] ).
cnf(140,plain,
set_union2(dollar_c3,dollar_c4) != dollar_c3,
inference(para_from,[status(thm),theory(equality)],[46,23]),
[iquote('para_from,46.1.1,23.1.1')] ).
cnf(611,plain,
set_union2(dollar_c3,dollar_c4) = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[105,4,67])]),
[iquote('hyper,105,4,67,flip.1')] ).
cnf(613,plain,
$false,
inference(binary,[status(thm)],[611,140]),
[iquote('binary,611.1,140.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n024.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 08:03:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.79/2.00 ----- Otter 3.3f, August 2004 -----
% 1.79/2.00 The process was started by sandbox on n024.cluster.edu,
% 1.79/2.00 Wed Jul 27 08:03:25 2022
% 1.79/2.00 The command was "./otter". The process ID is 26991.
% 1.79/2.00
% 1.79/2.00 set(prolog_style_variables).
% 1.79/2.00 set(auto).
% 1.79/2.00 dependent: set(auto1).
% 1.79/2.00 dependent: set(process_input).
% 1.79/2.00 dependent: clear(print_kept).
% 1.79/2.00 dependent: clear(print_new_demod).
% 1.79/2.00 dependent: clear(print_back_demod).
% 1.79/2.00 dependent: clear(print_back_sub).
% 1.79/2.00 dependent: set(control_memory).
% 1.79/2.00 dependent: assign(max_mem, 12000).
% 1.79/2.00 dependent: assign(pick_given_ratio, 4).
% 1.79/2.00 dependent: assign(stats_level, 1).
% 1.79/2.00 dependent: assign(max_seconds, 10800).
% 1.79/2.00 clear(print_given).
% 1.79/2.00
% 1.79/2.00 formula_list(usable).
% 1.79/2.00 all A (A=A).
% 1.79/2.00 all A B (in(A,B)-> -in(B,A)).
% 1.79/2.00 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.79/2.00 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.79/2.00 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.79/2.00 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.79/2.00 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.79/2.00 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.79/2.00 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.79/2.00 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.79/2.00 $T.
% 1.79/2.00 $T.
% 1.79/2.00 $T.
% 1.79/2.00 empty(empty_set).
% 1.79/2.00 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.79/2.00 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.79/2.00 all A B (set_union2(A,A)=A).
% 1.79/2.00 all A B (set_intersection2(A,A)=A).
% 1.79/2.00 exists A empty(A).
% 1.79/2.00 exists A (-empty(A)).
% 1.79/2.00 all A B subset(A,A).
% 1.79/2.00 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.79/2.00 -(all A B (subset(A,B)->set_union2(A,B)=B)).
% 1.79/2.00 all A (set_union2(A,empty_set)=A).
% 1.79/2.00 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.79/2.00 all A subset(empty_set,A).
% 1.79/2.00 all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B))).
% 1.79/2.00 all A (subset(A,empty_set)->A=empty_set).
% 1.79/2.00 all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B))).
% 1.79/2.00 all A (empty(A)->A=empty_set).
% 1.79/2.00 all A B (-(in(A,B)&empty(B))).
% 1.79/2.00 all A B subset(A,set_union2(A,B)).
% 1.79/2.00 all A B (-(empty(A)&A!=B&empty(B))).
% 1.79/2.00 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.79/2.00 end_of_list.
% 1.79/2.00
% 1.79/2.00 -------> usable clausifies to:
% 1.79/2.00
% 1.79/2.00 list(usable).
% 1.79/2.00 0 [] A=A.
% 1.79/2.00 0 [] -in(A,B)| -in(B,A).
% 1.79/2.00 0 [] set_union2(A,B)=set_union2(B,A).
% 1.79/2.00 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.79/2.00 0 [] A!=B|subset(A,B).
% 1.79/2.00 0 [] A!=B|subset(B,A).
% 1.79/2.00 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.79/2.00 0 [] A!=empty_set| -in(B,A).
% 1.79/2.00 0 [] A=empty_set|in($f1(A),A).
% 1.79/2.00 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.79/2.00 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.79/2.00 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.79/2.00 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 1.79/2.00 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 1.79/2.00 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 1.79/2.00 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.79/2.00 0 [] subset(A,B)|in($f3(A,B),A).
% 1.79/2.00 0 [] subset(A,B)| -in($f3(A,B),B).
% 1.79/2.00 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.79/2.00 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.79/2.00 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.79/2.00 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A).
% 1.79/2.00 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),B).
% 1.79/2.00 0 [] C=set_intersection2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A)| -in($f4(A,B,C),B).
% 1.79/2.00 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.79/2.00 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.79/2.00 0 [] $T.
% 1.79/2.00 0 [] $T.
% 1.79/2.00 0 [] $T.
% 1.79/2.00 0 [] empty(empty_set).
% 1.79/2.00 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.79/2.00 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.79/2.00 0 [] set_union2(A,A)=A.
% 1.79/2.00 0 [] set_intersection2(A,A)=A.
% 1.79/2.00 0 [] empty($c1).
% 1.79/2.00 0 [] -empty($c2).
% 1.79/2.00 0 [] subset(A,A).
% 1.79/2.00 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.79/2.00 0 [] subset($c4,$c3).
% 1.79/2.00 0 [] set_union2($c4,$c3)!=$c3.
% 1.79/2.00 0 [] set_union2(A,empty_set)=A.
% 1.79/2.00 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.79/2.00 0 [] subset(empty_set,A).
% 1.79/2.00 0 [] disjoint(A,B)|in($f5(A,B),A).
% 1.79/2.00 0 [] disjoint(A,B)|in($f5(A,B),B).
% 1.79/2.00 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.79/2.00 0 [] -subset(A,empty_set)|A=empty_set.
% 1.79/2.00 0 [] disjoint(A,B)|in($f6(A,B),set_intersection2(A,B)).
% 1.79/2.00 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.79/2.00 0 [] -empty(A)|A=empty_set.
% 1.79/2.00 0 [] -in(A,B)| -empty(B).
% 1.79/2.00 0 [] subset(A,set_union2(A,B)).
% 1.79/2.00 0 [] -empty(A)|A=B| -empty(B).
% 1.79/2.00 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.79/2.00 end_of_list.
% 1.79/2.00
% 1.79/2.00 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.79/2.00
% 1.79/2.00 This ia a non-Horn set with equality. The strategy will be
% 1.79/2.00 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.79/2.00 deletion, with positive clauses in sos and nonpositive
% 1.79/2.00 clauses in usable.
% 1.79/2.00
% 1.79/2.00 dependent: set(knuth_bendix).
% 1.79/2.00 dependent: set(anl_eq).
% 1.79/2.00 dependent: set(para_from).
% 1.79/2.00 dependent: set(para_into).
% 1.79/2.00 dependent: clear(para_from_right).
% 1.79/2.00 dependent: clear(para_into_right).
% 1.79/2.00 dependent: set(para_from_vars).
% 1.79/2.00 dependent: set(eq_units_both_ways).
% 1.79/2.00 dependent: set(dynamic_demod_all).
% 1.79/2.00 dependent: set(dynamic_demod).
% 1.79/2.00 dependent: set(order_eq).
% 1.79/2.00 dependent: set(back_demod).
% 1.79/2.00 dependent: set(lrpo).
% 1.79/2.00 dependent: set(hyper_res).
% 1.79/2.00 dependent: set(unit_deletion).
% 1.79/2.00 dependent: set(factor).
% 1.79/2.00
% 1.79/2.00 ------------> process usable:
% 1.79/2.00 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.79/2.00 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.79/2.00 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.79/2.00 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.79/2.00 ** KEPT (pick-wt=6): 5 [] A!=empty_set| -in(B,A).
% 1.79/2.00 ** KEPT (pick-wt=14): 6 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.79/2.00 ** KEPT (pick-wt=11): 7 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.79/2.00 ** KEPT (pick-wt=11): 8 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.79/2.00 ** KEPT (pick-wt=17): 9 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 1.79/2.00 ** KEPT (pick-wt=17): 10 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 1.79/2.00 ** KEPT (pick-wt=9): 11 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.79/2.00 ** KEPT (pick-wt=8): 12 [] subset(A,B)| -in($f3(A,B),B).
% 1.79/2.00 ** KEPT (pick-wt=11): 13 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.79/2.00 ** KEPT (pick-wt=11): 14 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.79/2.00 ** KEPT (pick-wt=14): 15 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.79/2.00 ** KEPT (pick-wt=23): 16 [] A=set_intersection2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B)| -in($f4(B,C,A),C).
% 1.79/2.00 ** KEPT (pick-wt=8): 17 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.79/2.00 ** KEPT (pick-wt=8): 18 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.79/2.00 ** KEPT (pick-wt=6): 19 [] empty(A)| -empty(set_union2(A,B)).
% 1.79/2.00 ** KEPT (pick-wt=6): 20 [] empty(A)| -empty(set_union2(B,A)).
% 1.79/2.00 ** KEPT (pick-wt=2): 21 [] -empty($c2).
% 1.79/2.00 ** KEPT (pick-wt=6): 22 [] -disjoint(A,B)|disjoint(B,A).
% 1.79/2.00 ** KEPT (pick-wt=5): 23 [] set_union2($c4,$c3)!=$c3.
% 1.79/2.00 ** KEPT (pick-wt=9): 24 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.79/2.00 ** KEPT (pick-wt=9): 25 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.79/2.00 ** KEPT (pick-wt=6): 26 [] -subset(A,empty_set)|A=empty_set.
% 1.79/2.00 ** KEPT (pick-wt=8): 27 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.79/2.00 ** KEPT (pick-wt=5): 28 [] -empty(A)|A=empty_set.
% 1.79/2.00 ** KEPT (pick-wt=5): 29 [] -in(A,B)| -empty(B).
% 1.79/2.00 ** KEPT (pick-wt=7): 30 [] -empty(A)|A=B| -empty(B).
% 1.79/2.00 ** KEPT (pick-wt=11): 31 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.79/2.00
% 1.79/2.00 ------------> process sos:
% 1.79/2.00 ** KEPT (pick-wt=3): 45 [] A=A.
% 1.79/2.00 ** KEPT (pick-wt=7): 46 [] set_union2(A,B)=set_union2(B,A).
% 1.79/2.00 ** KEPT (pick-wt=7): 47 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.79/2.00 ** KEPT (pick-wt=7): 48 [] A=empty_set|in($f1(A),A).
% 1.79/2.00 ** KEPT (pick-wt=23): 49 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 1.79/2.00 ** KEPT (pick-wt=8): 50 [] subset(A,B)|in($f3(A,B),A).
% 1.79/2.00 ** KEPT (pick-wt=17): 51 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B).
% 1.79/2.00 ** KEPT (pick-wt=17): 52 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),C).
% 1.79/2.00 ** KEPT (pick-wt=2): 53 [] empty(empty_set).
% 1.79/2.00 ** KEPT (pick-wt=5): 54 [] set_union2(A,A)=A.
% 1.79/2.00 ---> New Demodulator: 55 [new_demod,54] set_union2(A,A)=A.
% 1.79/2.00 ** KEPT (pick-wt=5): 56 [] set_intersection2(A,A)=A.
% 1.79/2.00 ---> New Demodulator: 57 [new_demod,56] set_intersection2(A,A)=A.
% 1.79/2.00 ** KEPT (pick-wt=2): 58 [] empty($c1).
% 1.79/2.00 ** KEPT (pick-wt=3): 59 [] subset(A,A).
% 1.79/2.00 ** KEPT (pick-wt=3): 60 [] subset($c4,$c3).
% 1.79/2.00 ** KEPT (pick-wt=5): 61 [] set_union2(A,empty_set)=A.
% 1.79/2.00 ---> New Demodulator: 62 [new_demod,61] set_union2(A,empty_set)=A.
% 1.79/2.00 ** KEPT (pick-wt=3): 63 [] subset(empty_set,A).
% 1.79/2.00 ** KEPT (pick-wt=8): 64 [] disjoint(A,B)|in($f5(A,B),A).
% 1.79/2.00 ** KEPT (pick-wt=8): 65 [] disjoint(A,B)|in($f5(A,B),B).
% 1.90/2.07 ** KEPT (pick-wt=10): 66 [] disjoint(A,B)|in($f6(A,B),set_intersection2(A,B)).
% 1.90/2.07 ** KEPT (pick-wt=5): 67 [] subset(A,set_union2(A,B)).
% 1.90/2.07 Following clause subsumed by 45 during input processing: 0 [copy,45,flip.1] A=A.
% 1.90/2.07 45 back subsumes 42.
% 1.90/2.07 45 back subsumes 33.
% 1.90/2.07 Following clause subsumed by 46 during input processing: 0 [copy,46,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.90/2.07 Following clause subsumed by 47 during input processing: 0 [copy,47,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.90/2.07 >>>> Starting back demodulation with 55.
% 1.90/2.07 >> back demodulating 43 with 55.
% 1.90/2.07 >> back demodulating 34 with 55.
% 1.90/2.07 >>>> Starting back demodulation with 57.
% 1.90/2.07 >> back demodulating 44 with 57.
% 1.90/2.07 >> back demodulating 40 with 57.
% 1.90/2.07 >> back demodulating 37 with 57.
% 1.90/2.07 >>>> Starting back demodulation with 62.
% 1.90/2.07
% 1.90/2.07 ======= end of input processing =======
% 1.90/2.07
% 1.90/2.07 =========== start of search ===========
% 1.90/2.07
% 1.90/2.07 -------- PROOF --------
% 1.90/2.07
% 1.90/2.07 ----> UNIT CONFLICT at 0.07 sec ----> 613 [binary,611.1,140.1] $F.
% 1.90/2.07
% 1.90/2.07 Length of proof is 3. Level of proof is 2.
% 1.90/2.07
% 1.90/2.07 ---------------- PROOF ----------------
% 1.90/2.07 % SZS status Theorem
% 1.90/2.07 % SZS output start Refutation
% See solution above
% 1.90/2.07 ------------ end of proof -------------
% 1.90/2.07
% 1.90/2.07
% 1.90/2.07 Search stopped by max_proofs option.
% 1.90/2.07
% 1.90/2.07
% 1.90/2.07 Search stopped by max_proofs option.
% 1.90/2.07
% 1.90/2.07 ============ end of search ============
% 1.90/2.07
% 1.90/2.07 -------------- statistics -------------
% 1.90/2.07 clauses given 18
% 1.90/2.07 clauses generated 1296
% 1.90/2.07 clauses kept 605
% 1.90/2.07 clauses forward subsumed 762
% 1.90/2.07 clauses back subsumed 8
% 1.90/2.07 Kbytes malloced 1953
% 1.90/2.07
% 1.90/2.07 ----------- times (seconds) -----------
% 1.90/2.07 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.90/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.90/2.07
% 1.90/2.07 That finishes the proof of the theorem.
% 1.90/2.07
% 1.90/2.07 Process 26991 finished Wed Jul 27 08:03:27 2022
% 1.90/2.07 Otter interrupted
% 1.90/2.07 PROOF FOUND
%------------------------------------------------------------------------------