%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU134+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:14:51 EDT 2022
% Result : Theorem 2.40s 2.65s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 8 unt; 2 nHn; 19 RR)
% Number of literals : 33 ( 14 equ; 15 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(26,axiom,
( set_difference(A,B) != empty_set
| subset(A,B) ),
file('SEU134+2.p',unknown),
[] ).
cnf(27,axiom,
( set_difference(A,B) = empty_set
| ~ subset(A,B) ),
file('SEU134+2.p',unknown),
[] ).
cnf(37,axiom,
( set_difference(dollar_c4,dollar_c3) != empty_set
| ~ subset(dollar_c4,dollar_c3) ),
file('SEU134+2.p',unknown),
[] ).
cnf(41,axiom,
( ~ empty(A)
| A = empty_set ),
file('SEU134+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU134+2.p',unknown),
[] ).
cnf(63,axiom,
A = A,
file('SEU134+2.p',unknown),
[] ).
cnf(72,axiom,
empty(empty_set),
file('SEU134+2.p',unknown),
[] ).
cnf(77,axiom,
empty(dollar_c1),
file('SEU134+2.p',unknown),
[] ).
cnf(87,axiom,
( set_difference(dollar_c4,dollar_c3) = empty_set
| subset(dollar_c4,dollar_c3) ),
file('SEU134+2.p',unknown),
[] ).
cnf(117,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[77,43,72]),
[iquote('hyper,77,43,72')] ).
cnf(133,plain,
( set_difference(dollar_c4,dollar_c3) = dollar_c1
| subset(dollar_c4,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[87]),117]),
[iquote('back_demod,87,demod,117')] ).
cnf(140,plain,
( ~ empty(A)
| A = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),117]),
[iquote('back_demod,41,demod,117')] ).
cnf(142,plain,
( set_difference(dollar_c4,dollar_c3) != dollar_c1
| ~ subset(dollar_c4,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),117]),
[iquote('back_demod,37,demod,117')] ).
cnf(143,plain,
( set_difference(A,B) = dollar_c1
| ~ subset(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),117]),
[iquote('back_demod,27,demod,117')] ).
cnf(144,plain,
( set_difference(A,B) != dollar_c1
| subset(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),117]),
[iquote('back_demod,26,demod,117')] ).
cnf(1819,plain,
( ~ subset(dollar_c4,dollar_c3)
| ~ empty(set_difference(dollar_c4,dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[142,140]),63]),
[iquote('para_into,142.1.1,140.2.1,unit_del,63')] ).
cnf(1838,plain,
set_difference(dollar_c4,dollar_c3) = dollar_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[143,133])]),
[iquote('hyper,143,133,factor_simp')] ).
cnf(1847,plain,
~ subset(dollar_c4,dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1819]),1838]),77]),
[iquote('back_demod,1819,demod,1838,unit_del,77')] ).
cnf(1882,plain,
subset(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[1838,144]),
[iquote('hyper,1837,144')] ).
cnf(1883,plain,
$false,
inference(binary,[status(thm)],[1882,1847]),
[iquote('binary,1882.1,1847.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU134+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 07:40:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/2.03 ----- Otter 3.3f, August 2004 -----
% 1.80/2.03 The process was started by sandbox2 on n014.cluster.edu,
% 1.80/2.03 Wed Jul 27 07:40:54 2022
% 1.80/2.03 The command was "./otter". The process ID is 1225.
% 1.80/2.03
% 1.80/2.03 set(prolog_style_variables).
% 1.80/2.03 set(auto).
% 1.80/2.03 dependent: set(auto1).
% 1.80/2.03 dependent: set(process_input).
% 1.80/2.03 dependent: clear(print_kept).
% 1.80/2.03 dependent: clear(print_new_demod).
% 1.80/2.03 dependent: clear(print_back_demod).
% 1.80/2.03 dependent: clear(print_back_sub).
% 1.80/2.03 dependent: set(control_memory).
% 1.80/2.03 dependent: assign(max_mem, 12000).
% 1.80/2.03 dependent: assign(pick_given_ratio, 4).
% 1.80/2.03 dependent: assign(stats_level, 1).
% 1.80/2.03 dependent: assign(max_seconds, 10800).
% 1.80/2.03 clear(print_given).
% 1.80/2.03
% 1.80/2.03 formula_list(usable).
% 1.80/2.03 all A (A=A).
% 1.80/2.03 all A B (in(A,B)-> -in(B,A)).
% 1.80/2.03 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.80/2.03 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.80/2.03 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.80/2.03 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.80/2.03 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.80/2.03 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.80/2.03 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.80/2.03 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.80/2.03 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.80/2.03 $T.
% 1.80/2.03 $T.
% 1.80/2.03 $T.
% 1.80/2.03 $T.
% 1.80/2.03 empty(empty_set).
% 1.80/2.03 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.80/2.03 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.80/2.03 all A B (set_union2(A,A)=A).
% 1.80/2.03 all A B (set_intersection2(A,A)=A).
% 1.80/2.03 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.80/2.03 exists A empty(A).
% 1.80/2.03 exists A (-empty(A)).
% 1.80/2.03 all A B subset(A,A).
% 1.80/2.03 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.80/2.03 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.80/2.03 all A B subset(set_intersection2(A,B),A).
% 1.80/2.03 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.80/2.03 all A (set_union2(A,empty_set)=A).
% 1.80/2.03 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.80/2.03 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.80/2.03 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.80/2.03 all A (set_intersection2(A,empty_set)=empty_set).
% 1.80/2.03 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.80/2.03 all A subset(empty_set,A).
% 1.80/2.03 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.80/2.03 all A B subset(set_difference(A,B),A).
% 1.80/2.03 -(all A B (set_difference(A,B)=empty_set<->subset(A,B))).
% 1.80/2.03 all A (set_difference(A,empty_set)=A).
% 1.80/2.03 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))).
% 1.80/2.03 all A (subset(A,empty_set)->A=empty_set).
% 1.80/2.03 all A (set_difference(empty_set,A)=empty_set).
% 1.80/2.03 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))).
% 1.80/2.03 all A (empty(A)->A=empty_set).
% 1.80/2.03 all A B (-(in(A,B)&empty(B))).
% 1.80/2.03 all A B subset(A,set_union2(A,B)).
% 1.80/2.03 all A B (-(empty(A)&A!=B&empty(B))).
% 1.80/2.03 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.80/2.03 end_of_list.
% 1.80/2.03
% 1.80/2.03 -------> usable clausifies to:
% 1.80/2.03
% 1.80/2.03 list(usable).
% 1.80/2.03 0 [] A=A.
% 1.80/2.03 0 [] -in(A,B)| -in(B,A).
% 1.80/2.03 0 [] set_union2(A,B)=set_union2(B,A).
% 1.80/2.03 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.80/2.03 0 [] A!=B|subset(A,B).
% 1.80/2.03 0 [] A!=B|subset(B,A).
% 1.80/2.03 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.80/2.03 0 [] A!=empty_set| -in(B,A).
% 1.80/2.03 0 [] A=empty_set|in($f1(A),A).
% 1.80/2.03 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.80/2.03 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.80/2.03 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.80/2.03 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 1.80/2.03 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 1.80/2.03 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 1.80/2.03 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.80/2.03 0 [] subset(A,B)|in($f3(A,B),A).
% 1.80/2.03 0 [] subset(A,B)| -in($f3(A,B),B).
% 1.80/2.03 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.80/2.03 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.80/2.03 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.80/2.03 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A).
% 1.80/2.03 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),B).
% 1.80/2.03 0 [] C=set_intersection2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A)| -in($f4(A,B,C),B).
% 1.80/2.03 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.80/2.03 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.80/2.03 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.80/2.03 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A).
% 1.80/2.03 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 1.80/2.03 0 [] C=set_difference(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 1.80/2.03 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.80/2.03 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.80/2.03 0 [] $T.
% 1.80/2.03 0 [] $T.
% 1.80/2.03 0 [] $T.
% 1.80/2.03 0 [] $T.
% 1.80/2.03 0 [] empty(empty_set).
% 1.80/2.03 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.80/2.03 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.80/2.03 0 [] set_union2(A,A)=A.
% 1.80/2.03 0 [] set_intersection2(A,A)=A.
% 1.80/2.03 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.80/2.03 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.80/2.03 0 [] empty($c1).
% 1.80/2.03 0 [] -empty($c2).
% 1.80/2.03 0 [] subset(A,A).
% 1.80/2.03 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.80/2.03 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.80/2.03 0 [] subset(set_intersection2(A,B),A).
% 1.80/2.03 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.80/2.03 0 [] set_union2(A,empty_set)=A.
% 1.80/2.03 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.80/2.03 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.80/2.03 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.80/2.03 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.80/2.03 0 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 1.80/2.03 0 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 1.80/2.03 0 [] subset(empty_set,A).
% 1.80/2.03 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.80/2.03 0 [] subset(set_difference(A,B),A).
% 1.80/2.03 0 [] set_difference($c4,$c3)=empty_set|subset($c4,$c3).
% 1.80/2.03 0 [] set_difference($c4,$c3)!=empty_set| -subset($c4,$c3).
% 1.80/2.03 0 [] set_difference(A,empty_set)=A.
% 1.80/2.03 0 [] disjoint(A,B)|in($f7(A,B),A).
% 1.80/2.03 0 [] disjoint(A,B)|in($f7(A,B),B).
% 1.80/2.03 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.80/2.03 0 [] -subset(A,empty_set)|A=empty_set.
% 1.80/2.03 0 [] set_difference(empty_set,A)=empty_set.
% 1.80/2.03 0 [] disjoint(A,B)|in($f8(A,B),set_intersection2(A,B)).
% 1.80/2.03 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.80/2.03 0 [] -empty(A)|A=empty_set.
% 1.80/2.03 0 [] -in(A,B)| -empty(B).
% 1.80/2.03 0 [] subset(A,set_union2(A,B)).
% 1.80/2.03 0 [] -empty(A)|A=B| -empty(B).
% 1.80/2.03 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.80/2.03 end_of_list.
% 1.80/2.03
% 1.80/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.80/2.03
% 1.80/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.80/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.80/2.03 deletion, with positive clauses in sos and nonpositive
% 1.80/2.03 clauses in usable.
% 1.80/2.03
% 1.80/2.03 dependent: set(knuth_bendix).
% 1.80/2.03 dependent: set(anl_eq).
% 1.80/2.03 dependent: set(para_from).
% 1.80/2.03 dependent: set(para_into).
% 1.80/2.03 dependent: clear(para_from_right).
% 1.80/2.03 dependent: clear(para_into_right).
% 1.80/2.03 dependent: set(para_from_vars).
% 1.80/2.03 dependent: set(eq_units_both_ways).
% 1.80/2.03 dependent: set(dynamic_demod_all).
% 1.80/2.03 dependent: set(dynamic_demod).
% 1.80/2.03 dependent: set(order_eq).
% 1.80/2.03 dependent: set(back_demod).
% 1.80/2.03 dependent: set(lrpo).
% 1.80/2.03 dependent: set(hyper_res).
% 1.80/2.03 dependent: set(unit_deletion).
% 1.80/2.03 dependent: set(factor).
% 1.80/2.03
% 1.80/2.03 ------------> process usable:
% 1.80/2.03 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.80/2.03 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.80/2.03 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.80/2.03 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.80/2.03 ** KEPT (pick-wt=6): 5 [] A!=empty_set| -in(B,A).
% 1.80/2.03 ** KEPT (pick-wt=14): 6 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.80/2.03 ** KEPT (pick-wt=11): 7 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.80/2.03 ** KEPT (pick-wt=11): 8 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.80/2.03 ** KEPT (pick-wt=17): 9 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 1.80/2.03 ** KEPT (pick-wt=17): 10 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=9): 11 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.80/2.03 ** KEPT (pick-wt=8): 12 [] subset(A,B)| -in($f3(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=11): 13 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.80/2.03 ** KEPT (pick-wt=11): 14 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.80/2.03 ** KEPT (pick-wt=14): 15 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.80/2.03 ** KEPT (pick-wt=23): 16 [] A=set_intersection2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B)| -in($f4(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=11): 17 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.80/2.03 ** KEPT (pick-wt=11): 18 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.80/2.03 ** KEPT (pick-wt=14): 19 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.80/2.03 ** KEPT (pick-wt=17): 20 [] A=set_difference(B,C)|in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=23): 21 [] A=set_difference(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=8): 22 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=8): 23 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=6): 24 [] empty(A)| -empty(set_union2(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=6): 25 [] empty(A)| -empty(set_union2(B,A)).
% 1.80/2.03 ** KEPT (pick-wt=8): 26 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.80/2.03 ** KEPT (pick-wt=8): 27 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.80/2.03 ** KEPT (pick-wt=2): 28 [] -empty($c2).
% 1.80/2.03 ** KEPT (pick-wt=6): 29 [] -disjoint(A,B)|disjoint(B,A).
% 1.80/2.03 ** KEPT (pick-wt=8): 30 [] -subset(A,B)|set_union2(A,B)=B.
% 1.80/2.03 ** KEPT (pick-wt=11): 31 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.80/2.03 ** KEPT (pick-wt=9): 32 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.80/2.03 ** KEPT (pick-wt=10): 33 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.80/2.03 ** KEPT (pick-wt=8): 34 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.80/2.03 ** KEPT (pick-wt=13): 35 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 1.80/2.03 ** KEPT (pick-wt=10): 36 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.80/2.03 ** KEPT (pick-wt=8): 37 [] set_difference($c4,$c3)!=empty_set| -subset($c4,$c3).
% 1.80/2.03 ** KEPT (pick-wt=9): 38 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.80/2.03 ** KEPT (pick-wt=6): 39 [] -subset(A,empty_set)|A=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=8): 40 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.80/2.03 ** KEPT (pick-wt=5): 41 [] -empty(A)|A=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=5): 42 [] -in(A,B)| -empty(B).
% 1.80/2.03 ** KEPT (pick-wt=7): 43 [] -empty(A)|A=B| -empty(B).
% 1.80/2.03 ** KEPT (pick-wt=11): 44 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.80/2.03
% 1.80/2.03 ------------> process sos:
% 1.80/2.03 ** KEPT (pick-wt=3): 63 [] A=A.
% 1.80/2.03 ** KEPT (pick-wt=7): 64 [] set_union2(A,B)=set_union2(B,A).
% 1.80/2.03 ** KEPT (pick-wt=7): 65 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.80/2.03 ** KEPT (pick-wt=7): 66 [] A=empty_set|in($f1(A),A).
% 1.80/2.03 ** KEPT (pick-wt=23): 67 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=8): 68 [] subset(A,B)|in($f3(A,B),A).
% 1.80/2.03 ** KEPT (pick-wt=17): 69 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B).
% 1.80/2.03 ** KEPT (pick-wt=17): 70 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=17): 71 [] A=set_difference(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B).
% 1.80/2.03 ** KEPT (pick-wt=2): 72 [] empty(empty_set).
% 1.80/2.03 ** KEPT (pick-wt=5): 73 [] set_union2(A,A)=A.
% 1.80/2.03 ---> New Demodulator: 74 [new_demod,73] set_union2(A,A)=A.
% 1.80/2.03 ** KEPT (pick-wt=5): 75 [] set_intersection2(A,A)=A.
% 1.80/2.03 ---> New Demodulator: 76 [new_demod,75] set_intersection2(A,A)=A.
% 1.80/2.03 ** KEPT (pick-wt=2): 77 [] empty($c1).
% 1.80/2.03 ** KEPT (pick-wt=3): 78 [] subset(A,A).
% 1.80/2.03 ** KEPT (pick-wt=5): 79 [] subset(set_intersection2(A,B),A).
% 1.80/2.03 ** KEPT (pick-wt=5): 80 [] set_union2(A,empty_set)=A.
% 1.80/2.03 ---> New Demodulator: 81 [new_demod,80] set_union2(A,empty_set)=A.
% 1.80/2.03 ** KEPT (pick-wt=5): 82 [] set_intersection2(A,empty_set)=empty_set.
% 1.80/2.03 ---> New Demodulator: 83 [new_demod,82] set_intersection2(A,empty_set)=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=13): 84 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 1.80/2.03 ** KEPT (pick-wt=3): 85 [] subset(empty_set,A).
% 1.80/2.03 ** KEPT (pick-wt=5): 86 [] subset(set_difference(A,B),A).
% 1.80/2.03 ** KEPT (pick-wt=8): 87 [] set_difference($c4,$c3)=empty_set|subset($c4,$c3).
% 1.80/2.03 ** KEPT (pick-wt=5): 88 [] set_difference(A,empty_set)=A.
% 1.80/2.03 ---> New Demodulator: 89 [new_demod,88] set_difference(A,empty_set)=A.
% 1.80/2.03 ** KEPT (pick-wt=8): 90 [] disjoint(A,B)|in($f7(A,B),A).
% 1.80/2.03 ** KEPT (pick-wt=8): 91 [] disjoint(A,B)|in($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=5): 92 [] set_difference(empty_set,A)=empty_set.
% 1.80/2.03 ---> New Demodulator: 93 [new_demod,92] set_difference(empty_set,A)=empty_set.
% 1.80/2.03 ** KEPT (pick-wt=10): 94 [] disjoint(A,B)|in($f8(A,B),set_intersection2(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=5): 95 [] subset(A,set_union2(A,B)).
% 1.80/2.03 Following clause subsumed by 63 during input processing: 0 [copy,63,flip.1] A=A.
% 1.80/2.03 63 back subsumes 60.
% 1.80/2.03 63 back subsumes 58.
% 1.80/2.03 63 back subsumes 46.
% 1.80/2.03 Following clause subsumed by 64 during input processing: 0 [copy,64,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.80/2.03 Following clause subsumed by 65 during input processing: 0 [copy,65,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.40/2.65 >>>> Starting back demodulation with 74.
% 2.40/2.65 >> back demodulating 61 with 74.
% 2.40/2.65 >> back demodulating 47 with 74.
% 2.40/2.65 >>>> Starting back demodulation with 76.
% 2.40/2.65 >> back demodulating 62 with 76.
% 2.40/2.65 >> back demodulating 57 with 76.
% 2.40/2.65 >> back demodulating 53 with 76.
% 2.40/2.65 >> back demodulating 50 with 76.
% 2.40/2.65 >>>> Starting back demodulation with 81.
% 2.40/2.65 >>>> Starting back demodulation with 83.
% 2.40/2.65 >>>> Starting back demodulation with 89.
% 2.40/2.65 >>>> Starting back demodulation with 93.
% 2.40/2.65
% 2.40/2.65 ======= end of input processing =======
% 2.40/2.65
% 2.40/2.65 =========== start of search ===========
% 2.40/2.65
% 2.40/2.65
% 2.40/2.65 Resetting weight limit to 8.
% 2.40/2.65
% 2.40/2.65
% 2.40/2.65 Resetting weight limit to 8.
% 2.40/2.65
% 2.40/2.65 sos_size=1492
% 2.40/2.65
% 2.40/2.65 -------- PROOF --------
% 2.40/2.65
% 2.40/2.65 ----> UNIT CONFLICT at 0.61 sec ----> 1883 [binary,1882.1,1847.1] $F.
% 2.40/2.65
% 2.40/2.65 Length of proof is 10. Level of proof is 4.
% 2.40/2.65
% 2.40/2.65 ---------------- PROOF ----------------
% 2.40/2.65 % SZS status Theorem
% 2.40/2.65 % SZS output start Refutation
% See solution above
% 2.40/2.65 ------------ end of proof -------------
% 2.40/2.65
% 2.40/2.65
% 2.40/2.65 Search stopped by max_proofs option.
% 2.40/2.65
% 2.40/2.65
% 2.40/2.65 Search stopped by max_proofs option.
% 2.40/2.65
% 2.40/2.65 ============ end of search ============
% 2.40/2.65
% 2.40/2.65 -------------- statistics -------------
% 2.40/2.65 clauses given 150
% 2.40/2.65 clauses generated 24204
% 2.40/2.65 clauses kept 1845
% 2.40/2.65 clauses forward subsumed 6013
% 2.40/2.65 clauses back subsumed 195
% 2.40/2.65 Kbytes malloced 4882
% 2.40/2.65
% 2.40/2.65 ----------- times (seconds) -----------
% 2.40/2.65 user CPU time 0.61 (0 hr, 0 min, 0 sec)
% 2.40/2.65 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.40/2.65 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.40/2.65
% 2.40/2.65 That finishes the proof of the theorem.
% 2.40/2.65
% 2.40/2.65 Process 1225 finished Wed Jul 27 07:40:56 2022
% 2.40/2.65 Otter interrupted
% 2.40/2.65 PROOF FOUND
%------------------------------------------------------------------------------