%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU139+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 13:14:52 EDT 2022
% Result : Theorem 1.98s 2.12s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 12 ( 2 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SEU139+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ proper_subset(A,B)
| subset(A,B) ),
file('SEU139+2.p',unknown),
[] ).
cnf(30,axiom,
~ proper_subset(A,A),
file('SEU139+2.p',unknown),
[] ).
cnf(108,axiom,
subset(dollar_c4,dollar_c3),
file('SEU139+2.p',unknown),
[] ).
cnf(109,axiom,
proper_subset(dollar_c3,dollar_c4),
file('SEU139+2.p',unknown),
[] ).
cnf(216,plain,
subset(dollar_c3,dollar_c4),
inference(hyper,[status(thm)],[109,25]),
[iquote('hyper,109,25')] ).
cnf(267,plain,
dollar_c4 = dollar_c3,
inference(hyper,[status(thm)],[216,5,108]),
[iquote('hyper,216,5,108')] ).
cnf(303,plain,
proper_subset(dollar_c3,dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[109]),267]),
[iquote('back_demod,109,demod,267')] ).
cnf(304,plain,
$false,
inference(binary,[status(thm)],[303,30]),
[iquote('binary,303.1,30.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU139+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n024.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 07:36:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.60/2.11 ----- Otter 3.3f, August 2004 -----
% 1.60/2.11 The process was started by sandbox on n024.cluster.edu,
% 1.60/2.11 Wed Jul 27 07:36:40 2022
% 1.60/2.11 The command was "./otter". The process ID is 2833.
% 1.60/2.11
% 1.60/2.11 set(prolog_style_variables).
% 1.60/2.11 set(auto).
% 1.60/2.11 dependent: set(auto1).
% 1.60/2.11 dependent: set(process_input).
% 1.60/2.11 dependent: clear(print_kept).
% 1.60/2.11 dependent: clear(print_new_demod).
% 1.60/2.11 dependent: clear(print_back_demod).
% 1.60/2.11 dependent: clear(print_back_sub).
% 1.60/2.11 dependent: set(control_memory).
% 1.60/2.11 dependent: assign(max_mem, 12000).
% 1.60/2.11 dependent: assign(pick_given_ratio, 4).
% 1.60/2.11 dependent: assign(stats_level, 1).
% 1.60/2.11 dependent: assign(max_seconds, 10800).
% 1.60/2.11 clear(print_given).
% 1.60/2.11
% 1.60/2.11 formula_list(usable).
% 1.60/2.11 all A (A=A).
% 1.60/2.11 all A B (in(A,B)-> -in(B,A)).
% 1.60/2.11 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 1.60/2.11 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.60/2.11 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.60/2.11 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.60/2.11 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.60/2.11 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.60/2.11 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.60/2.11 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.60/2.11 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.60/2.11 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.60/2.11 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 1.60/2.11 $T.
% 1.60/2.11 $T.
% 1.60/2.11 $T.
% 1.60/2.11 $T.
% 1.60/2.11 empty(empty_set).
% 1.60/2.11 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.60/2.11 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.60/2.11 all A B (set_union2(A,A)=A).
% 1.60/2.11 all A B (set_intersection2(A,A)=A).
% 1.60/2.11 all A B (-proper_subset(A,A)).
% 1.60/2.11 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.60/2.11 exists A empty(A).
% 1.60/2.11 exists A (-empty(A)).
% 1.60/2.11 all A B subset(A,A).
% 1.60/2.11 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.60/2.11 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.60/2.11 all A B subset(set_intersection2(A,B),A).
% 1.60/2.11 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.60/2.11 all A (set_union2(A,empty_set)=A).
% 1.60/2.11 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.60/2.11 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.60/2.11 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.60/2.11 all A (set_intersection2(A,empty_set)=empty_set).
% 1.60/2.11 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.60/2.11 all A subset(empty_set,A).
% 1.60/2.11 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.60/2.11 all A B subset(set_difference(A,B),A).
% 1.60/2.11 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.60/2.11 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 1.60/2.11 all A (set_difference(A,empty_set)=A).
% 1.60/2.11 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))).
% 1.60/2.11 all A (subset(A,empty_set)->A=empty_set).
% 1.60/2.11 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.60/2.11 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 1.60/2.11 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 1.60/2.11 all A (set_difference(empty_set,A)=empty_set).
% 1.60/2.11 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))).
% 1.60/2.11 -(all A B (-(subset(A,B)&proper_subset(B,A)))).
% 1.60/2.11 all A (empty(A)->A=empty_set).
% 1.60/2.11 all A B (-(in(A,B)&empty(B))).
% 1.60/2.11 all A B subset(A,set_union2(A,B)).
% 1.60/2.11 all A B (-(empty(A)&A!=B&empty(B))).
% 1.60/2.11 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.60/2.11 end_of_list.
% 1.60/2.11
% 1.60/2.11 -------> usable clausifies to:
% 1.60/2.11
% 1.60/2.11 list(usable).
% 1.60/2.11 0 [] A=A.
% 1.60/2.11 0 [] -in(A,B)| -in(B,A).
% 1.60/2.11 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.60/2.11 0 [] set_union2(A,B)=set_union2(B,A).
% 1.60/2.11 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.60/2.11 0 [] A!=B|subset(A,B).
% 1.60/2.11 0 [] A!=B|subset(B,A).
% 1.60/2.11 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.60/2.11 0 [] A!=empty_set| -in(B,A).
% 1.60/2.11 0 [] A=empty_set|in($f1(A),A).
% 1.60/2.11 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.60/2.11 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.60/2.11 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.60/2.11 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 1.60/2.11 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 1.60/2.11 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 1.60/2.11 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.60/2.11 0 [] subset(A,B)|in($f3(A,B),A).
% 1.60/2.11 0 [] subset(A,B)| -in($f3(A,B),B).
% 1.60/2.11 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.60/2.11 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.60/2.11 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.60/2.11 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A).
% 1.60/2.11 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),B).
% 1.60/2.11 0 [] C=set_intersection2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A)| -in($f4(A,B,C),B).
% 1.60/2.11 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.60/2.11 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.60/2.11 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.60/2.11 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A).
% 1.60/2.11 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 1.60/2.11 0 [] C=set_difference(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 1.60/2.11 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.60/2.11 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.60/2.11 0 [] -proper_subset(A,B)|subset(A,B).
% 1.60/2.11 0 [] -proper_subset(A,B)|A!=B.
% 1.60/2.11 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.60/2.11 0 [] $T.
% 1.60/2.11 0 [] $T.
% 1.60/2.11 0 [] $T.
% 1.60/2.11 0 [] $T.
% 1.60/2.11 0 [] empty(empty_set).
% 1.60/2.11 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.60/2.11 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.60/2.11 0 [] set_union2(A,A)=A.
% 1.60/2.11 0 [] set_intersection2(A,A)=A.
% 1.60/2.11 0 [] -proper_subset(A,A).
% 1.60/2.11 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.60/2.11 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.60/2.11 0 [] empty($c1).
% 1.60/2.11 0 [] -empty($c2).
% 1.60/2.11 0 [] subset(A,A).
% 1.60/2.11 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.60/2.11 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.60/2.11 0 [] subset(set_intersection2(A,B),A).
% 1.60/2.11 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.60/2.11 0 [] set_union2(A,empty_set)=A.
% 1.60/2.11 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.60/2.11 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.60/2.11 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.60/2.11 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.60/2.11 0 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 1.60/2.11 0 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 1.60/2.11 0 [] subset(empty_set,A).
% 1.60/2.11 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.60/2.11 0 [] subset(set_difference(A,B),A).
% 1.60/2.11 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.60/2.11 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.60/2.11 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.60/2.11 0 [] set_difference(A,empty_set)=A.
% 1.60/2.11 0 [] disjoint(A,B)|in($f7(A,B),A).
% 1.60/2.11 0 [] disjoint(A,B)|in($f7(A,B),B).
% 1.60/2.11 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.60/2.11 0 [] -subset(A,empty_set)|A=empty_set.
% 1.60/2.11 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.60/2.11 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 1.60/2.11 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 1.60/2.11 0 [] set_difference(empty_set,A)=empty_set.
% 1.60/2.11 0 [] disjoint(A,B)|in($f8(A,B),set_intersection2(A,B)).
% 1.60/2.11 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.60/2.11 0 [] subset($c4,$c3).
% 1.60/2.11 0 [] proper_subset($c3,$c4).
% 1.60/2.11 0 [] -empty(A)|A=empty_set.
% 1.60/2.11 0 [] -in(A,B)| -empty(B).
% 1.60/2.11 0 [] subset(A,set_union2(A,B)).
% 1.60/2.11 0 [] -empty(A)|A=B| -empty(B).
% 1.60/2.11 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.60/2.11 end_of_list.
% 1.60/2.11
% 1.60/2.11 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.60/2.11
% 1.60/2.11 This ia a non-Horn set with equality. The strategy will be
% 1.60/2.11 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.60/2.11 deletion, with positive clauses in sos and nonpositive
% 1.60/2.11 clauses in usable.
% 1.60/2.11
% 1.60/2.11 dependent: set(knuth_bendix).
% 1.60/2.11 dependent: set(anl_eq).
% 1.60/2.11 dependent: set(para_from).
% 1.60/2.11 dependent: set(para_into).
% 1.60/2.11 dependent: clear(para_from_right).
% 1.60/2.11 dependent: clear(para_into_right).
% 1.60/2.11 dependent: set(para_from_vars).
% 1.60/2.11 dependent: set(eq_units_both_ways).
% 1.60/2.11 dependent: set(dynamic_demod_all).
% 1.60/2.11 dependent: set(dynamic_demod).
% 1.60/2.11 dependent: set(order_eq).
% 1.60/2.11 dependent: set(back_demod).
% 1.60/2.11 dependent: set(lrpo).
% 1.60/2.11 dependent: set(hyper_res).
% 1.60/2.11 dependent: set(unit_deletion).
% 1.60/2.11 dependent: set(factor).
% 1.60/2.11
% 1.60/2.11 ------------> process usable:
% 1.60/2.11 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.60/2.11 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.60/2.11 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 1.60/2.11 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 1.60/2.11 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 1.60/2.11 ** KEPT (pick-wt=6): 6 [] A!=empty_set| -in(B,A).
% 1.60/2.11 ** KEPT (pick-wt=14): 7 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.60/2.11 ** KEPT (pick-wt=11): 8 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.60/2.11 ** KEPT (pick-wt=11): 9 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.60/2.11 ** KEPT (pick-wt=17): 10 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 1.60/2.11 ** KEPT (pick-wt=17): 11 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 1.60/2.11 ** KEPT (pick-wt=9): 12 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.60/2.11 ** KEPT (pick-wt=8): 13 [] subset(A,B)| -in($f3(A,B),B).
% 1.60/2.11 ** KEPT (pick-wt=11): 14 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.60/2.11 ** KEPT (pick-wt=11): 15 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.60/2.11 ** KEPT (pick-wt=14): 16 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.60/2.11 ** KEPT (pick-wt=23): 17 [] A=set_intersection2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B)| -in($f4(B,C,A),C).
% 1.60/2.11 ** KEPT (pick-wt=11): 18 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.60/2.11 ** KEPT (pick-wt=11): 19 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.60/2.11 ** KEPT (pick-wt=14): 20 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.60/2.11 ** KEPT (pick-wt=17): 21 [] A=set_difference(B,C)|in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 1.60/2.11 ** KEPT (pick-wt=23): 22 [] A=set_difference(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 1.60/2.11 ** KEPT (pick-wt=8): 23 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.60/2.11 ** KEPT (pick-wt=8): 24 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.60/2.11 ** KEPT (pick-wt=6): 25 [] -proper_subset(A,B)|subset(A,B).
% 1.60/2.11 ** KEPT (pick-wt=6): 26 [] -proper_subset(A,B)|A!=B.
% 1.60/2.11 ** KEPT (pick-wt=9): 27 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.60/2.11 ** KEPT (pick-wt=6): 28 [] empty(A)| -empty(set_union2(A,B)).
% 1.60/2.11 ** KEPT (pick-wt=6): 29 [] empty(A)| -empty(set_union2(B,A)).
% 1.60/2.11 ** KEPT (pick-wt=3): 30 [] -proper_subset(A,A).
% 1.60/2.11 ** KEPT (pick-wt=8): 31 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.60/2.11 ** KEPT (pick-wt=8): 32 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.60/2.11 ** KEPT (pick-wt=2): 33 [] -empty($c2).
% 1.60/2.11 ** KEPT (pick-wt=6): 34 [] -disjoint(A,B)|disjoint(B,A).
% 1.60/2.11 ** KEPT (pick-wt=8): 35 [] -subset(A,B)|set_union2(A,B)=B.
% 1.60/2.11 ** KEPT (pick-wt=11): 36 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.60/2.11 ** KEPT (pick-wt=9): 37 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.60/2.11 ** KEPT (pick-wt=10): 38 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.60/2.11 ** KEPT (pick-wt=8): 39 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.60/2.11 ** KEPT (pick-wt=13): 40 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 1.60/2.11 ** KEPT (pick-wt=10): 41 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.60/2.11 Following clause subsumed by 31 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.60/2.11 Following clause subsumed by 32 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.60/2.11 ** KEPT (pick-wt=9): 42 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.60/2.11 ** KEPT (pick-wt=6): 43 [] -subset(A,empty_set)|A=empty_set.
% 1.60/2.11 ** KEPT (pick-wt=10): 45 [copy,44,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 1.60/2.11 ** KEPT (pick-wt=8): 46 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.60/2.11 ** KEPT (pick-wt=5): 47 [] -empty(A)|A=empty_set.
% 1.60/2.11 ** KEPT (pick-wt=5): 48 [] -in(A,B)| -empty(B).
% 1.60/2.11 ** KEPT (pick-wt=7): 49 [] -empty(A)|A=B| -empty(B).
% 1.60/2.11 ** KEPT (pick-wt=11): 50 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.60/2.11
% 1.60/2.11 ------------> process sos:
% 1.60/2.11 ** KEPT (pick-wt=3): 69 [] A=A.
% 1.60/2.11 ** KEPT (pick-wt=7): 70 [] set_union2(A,B)=set_union2(B,A).
% 1.60/2.11 ** KEPT (pick-wt=7): 71 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.60/2.11 ** KEPT (pick-wt=7): 72 [] A=empty_set|in($f1(A),A).
% 1.60/2.11 ** KEPT (pick-wt=23): 73 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 1.60/2.11 ** KEPT (pick-wt=8): 74 [] subset(A,B)|in($f3(A,B),A).
% 1.60/2.11 ** KEPT (pick-wt=17): 75 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B).
% 1.60/2.11 ** KEPT (pick-wt=17): 76 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),C).
% 1.60/2.11 ** KEPT (pick-wt=17): 77 [] A=set_difference(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B).
% 1.60/2.11 ** KEPT (pick-wt=2): 78 [] empty(empty_set).
% 1.60/2.11 ** KEPT (pick-wt=5): 79 [] set_union2(A,A)=A.
% 1.60/2.11 ---> New Demodulator: 80 [new_demod,79] set_union2(A,A)=A.
% 1.60/2.11 ** KEPT (pick-wt=5): 81 [] set_intersection2(A,A)=A.
% 1.60/2.11 ---> New Demodulator: 82 [new_demod,81] set_intersection2(A,A)=A.
% 1.60/2.11 ** KEPT (pick-wt=2): 83 [] empty($c1).
% 1.60/2.11 ** KEPT (pick-wt=3): 84 [] subset(A,A).
% 1.98/2.12 ** KEPT (pick-wt=5): 85 [] subset(set_intersection2(A,B),A).
% 1.98/2.12 ** KEPT (pick-wt=5): 86 [] set_union2(A,empty_set)=A.
% 1.98/2.12 ---> New Demodulator: 87 [new_demod,86] set_union2(A,empty_set)=A.
% 1.98/2.12 ** KEPT (pick-wt=5): 88 [] set_intersection2(A,empty_set)=empty_set.
% 1.98/2.12 ---> New Demodulator: 89 [new_demod,88] set_intersection2(A,empty_set)=empty_set.
% 1.98/2.12 ** KEPT (pick-wt=13): 90 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 1.98/2.12 ** KEPT (pick-wt=3): 91 [] subset(empty_set,A).
% 1.98/2.12 ** KEPT (pick-wt=5): 92 [] subset(set_difference(A,B),A).
% 1.98/2.12 ** KEPT (pick-wt=9): 93 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.98/2.12 ---> New Demodulator: 94 [new_demod,93] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.98/2.12 ** KEPT (pick-wt=5): 95 [] set_difference(A,empty_set)=A.
% 1.98/2.12 ---> New Demodulator: 96 [new_demod,95] set_difference(A,empty_set)=A.
% 1.98/2.12 ** KEPT (pick-wt=8): 97 [] disjoint(A,B)|in($f7(A,B),A).
% 1.98/2.12 ** KEPT (pick-wt=8): 98 [] disjoint(A,B)|in($f7(A,B),B).
% 1.98/2.12 ** KEPT (pick-wt=9): 99 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.98/2.12 ---> New Demodulator: 100 [new_demod,99] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.98/2.12 ** KEPT (pick-wt=9): 102 [copy,101,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.98/2.12 ---> New Demodulator: 103 [new_demod,102] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.98/2.12 ** KEPT (pick-wt=5): 104 [] set_difference(empty_set,A)=empty_set.
% 1.98/2.12 ---> New Demodulator: 105 [new_demod,104] set_difference(empty_set,A)=empty_set.
% 1.98/2.12 ** KEPT (pick-wt=12): 107 [copy,106,demod,103] disjoint(A,B)|in($f8(A,B),set_difference(A,set_difference(A,B))).
% 1.98/2.12 ** KEPT (pick-wt=3): 108 [] subset($c4,$c3).
% 1.98/2.12 ** KEPT (pick-wt=3): 109 [] proper_subset($c3,$c4).
% 1.98/2.12 ** KEPT (pick-wt=5): 110 [] subset(A,set_union2(A,B)).
% 1.98/2.12 Following clause subsumed by 69 during input processing: 0 [copy,69,flip.1] A=A.
% 1.98/2.12 69 back subsumes 66.
% 1.98/2.12 69 back subsumes 64.
% 1.98/2.12 69 back subsumes 52.
% 1.98/2.12 Following clause subsumed by 70 during input processing: 0 [copy,70,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.98/2.12 ** KEPT (pick-wt=11): 111 [copy,71,flip.1,demod,103,103] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.98/2.12 >>>> Starting back demodulation with 80.
% 1.98/2.12 >> back demodulating 67 with 80.
% 1.98/2.12 >> back demodulating 53 with 80.
% 1.98/2.12 >>>> Starting back demodulation with 82.
% 1.98/2.12 >> back demodulating 68 with 82.
% 1.98/2.12 >> back demodulating 63 with 82.
% 1.98/2.12 >> back demodulating 59 with 82.
% 1.98/2.12 >> back demodulating 56 with 82.
% 1.98/2.12 >>>> Starting back demodulation with 87.
% 1.98/2.12 >>>> Starting back demodulation with 89.
% 1.98/2.12 >>>> Starting back demodulation with 94.
% 1.98/2.12 >> back demodulating 45 with 94.
% 1.98/2.12 >>>> Starting back demodulation with 96.
% 1.98/2.12 >>>> Starting back demodulation with 100.
% 1.98/2.12 >>>> Starting back demodulation with 103.
% 1.98/2.12 >> back demodulating 88 with 103.
% 1.98/2.12 >> back demodulating 85 with 103.
% 1.98/2.12 >> back demodulating 81 with 103.
% 1.98/2.12 >> back demodulating 76 with 103.
% 1.98/2.12 >> back demodulating 75 with 103.
% 1.98/2.12 >> back demodulating 71 with 103.
% 1.98/2.12 >> back demodulating 58 with 103.
% 1.98/2.12 >> back demodulating 57 with 103.
% 1.98/2.12 >> back demodulating 46 with 103.
% 1.98/2.12 >> back demodulating 39 with 103.
% 1.98/2.12 >> back demodulating 38 with 103.
% 1.98/2.12 >> back demodulating 36 with 103.
% 1.98/2.12 >> back demodulating 24 with 103.
% 1.98/2.12 >> back demodulating 23 with 103.
% 1.98/2.12 >> back demodulating 17 with 103.
% 1.98/2.12 >> back demodulating 16 with 103.
% 1.98/2.12 >> back demodulating 15 with 103.
% 1.98/2.12 >> back demodulating 14 with 103.
% 1.98/2.12 >>>> Starting back demodulation with 105.
% 1.98/2.12 Following clause subsumed by 111 during input processing: 0 [copy,111,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 1.98/2.12 >>>> Starting back demodulation with 122.
% 1.98/2.12
% 1.98/2.12 ======= end of input processing =======
% 1.98/2.12
% 1.98/2.12 =========== start of search ===========
% 1.98/2.12
% 1.98/2.12 -------- PROOF --------
% 1.98/2.12
% 1.98/2.12 ----> UNIT CONFLICT at 0.01 sec ----> 304 [binary,303.1,30.1] $F.
% 1.98/2.12
% 1.98/2.12 Length of proof is 3. Level of proof is 3.
% 1.98/2.12
% 1.98/2.12 ---------------- PROOF ----------------
% 1.98/2.12 % SZS status Theorem
% 1.98/2.12 % SZS output start Refutation
% See solution above
% 1.98/2.12 ------------ end of proof -------------
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12 ============ end of search ============
% 1.98/2.12
% 1.98/2.12 -------------- statistics -------------
% 1.98/2.12 clauses given 10
% 1.98/2.12 clauses generated 242
% 1.98/2.12 clauses kept 281
% 1.98/2.12 clauses forward subsumed 142
% 1.98/2.12 clauses back subsumed 4
% 1.98/2.12 Kbytes malloced 1953
% 1.98/2.12
% 1.98/2.12 ----------- times (seconds) -----------
% 1.98/2.12 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.12
% 1.98/2.12 That finishes the proof of the theorem.
% 1.98/2.12
% 1.98/2.12 Process 2833 finished Wed Jul 27 07:36:42 2022
% 1.98/2.12 Otter interrupted
% 1.98/2.12 PROOF FOUND
%------------------------------------------------------------------------------