TSTP Solution File: SEU140+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU140+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 13:14:53 EDT 2022
% Result : Theorem 17.41s 17.59s
% Output : Refutation 17.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 11 ( 5 unt; 3 nHn; 8 RR)
% Number of literals : 19 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(12,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU140+2.p',unknown),
[] ).
cnf(34,axiom,
( ~ disjoint(A,B)
| disjoint(B,A) ),
file('SEU140+2.p',unknown),
[] ).
cnf(42,axiom,
( ~ in(A,B)
| ~ in(A,C)
| ~ disjoint(B,C) ),
file('SEU140+2.p',unknown),
[] ).
cnf(48,axiom,
~ disjoint(dollar_c5,dollar_c3),
file('SEU140+2.p',unknown),
[] ).
cnf(99,axiom,
( disjoint(A,B)
| in(dollar_f7(A,B),A) ),
file('SEU140+2.p',unknown),
[] ).
cnf(100,axiom,
( disjoint(A,B)
| in(dollar_f7(A,B),B) ),
file('SEU140+2.p',unknown),
[] ).
cnf(110,axiom,
subset(dollar_c5,dollar_c4),
file('SEU140+2.p',unknown),
[] ).
cnf(111,axiom,
disjoint(dollar_c4,dollar_c3),
file('SEU140+2.p',unknown),
[] ).
cnf(218,plain,
disjoint(dollar_c3,dollar_c4),
inference(hyper,[status(thm)],[111,34]),
[iquote('hyper,111,34')] ).
cnf(1704,plain,
( disjoint(dollar_c5,A)
| in(dollar_f7(dollar_c5,A),dollar_c4) ),
inference(hyper,[status(thm)],[99,12,110]),
[iquote('hyper,99,12,110')] ).
cnf(2345,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1704,42,100,218]),48,48]),
[iquote('hyper,1704,42,100,218,unit_del,48,48')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU140+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 08:10:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.12/2.32 ----- Otter 3.3f, August 2004 -----
% 2.12/2.32 The process was started by sandbox on n025.cluster.edu,
% 2.12/2.32 Wed Jul 27 08:10:15 2022
% 2.12/2.32 The command was "./otter". The process ID is 3732.
% 2.12/2.32
% 2.12/2.32 set(prolog_style_variables).
% 2.12/2.32 set(auto).
% 2.12/2.32 dependent: set(auto1).
% 2.12/2.32 dependent: set(process_input).
% 2.12/2.32 dependent: clear(print_kept).
% 2.12/2.32 dependent: clear(print_new_demod).
% 2.12/2.32 dependent: clear(print_back_demod).
% 2.12/2.32 dependent: clear(print_back_sub).
% 2.12/2.32 dependent: set(control_memory).
% 2.12/2.32 dependent: assign(max_mem, 12000).
% 2.12/2.32 dependent: assign(pick_given_ratio, 4).
% 2.12/2.32 dependent: assign(stats_level, 1).
% 2.12/2.32 dependent: assign(max_seconds, 10800).
% 2.12/2.32 clear(print_given).
% 2.12/2.32
% 2.12/2.32 formula_list(usable).
% 2.12/2.32 all A (A=A).
% 2.12/2.32 all A B (in(A,B)-> -in(B,A)).
% 2.12/2.32 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 2.12/2.32 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.12/2.32 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.12/2.32 all A B (A=B<->subset(A,B)&subset(B,A)).
% 2.12/2.32 all A (A=empty_set<-> (all B (-in(B,A)))).
% 2.12/2.32 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 2.12/2.32 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.12/2.32 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 2.12/2.32 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 2.12/2.32 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 2.12/2.32 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 2.12/2.32 $T.
% 2.12/2.32 $T.
% 2.12/2.32 $T.
% 2.12/2.32 $T.
% 2.12/2.32 empty(empty_set).
% 2.12/2.32 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.12/2.32 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.12/2.32 all A B (set_union2(A,A)=A).
% 2.12/2.32 all A B (set_intersection2(A,A)=A).
% 2.12/2.32 all A B (-proper_subset(A,A)).
% 2.12/2.32 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.12/2.32 exists A empty(A).
% 2.12/2.32 exists A (-empty(A)).
% 2.12/2.32 all A B subset(A,A).
% 2.12/2.32 all A B (disjoint(A,B)->disjoint(B,A)).
% 2.12/2.32 all A B (subset(A,B)->set_union2(A,B)=B).
% 2.12/2.32 all A B subset(set_intersection2(A,B),A).
% 2.12/2.32 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 2.12/2.32 all A (set_union2(A,empty_set)=A).
% 2.12/2.32 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 2.12/2.32 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 2.12/2.32 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 2.12/2.32 all A (set_intersection2(A,empty_set)=empty_set).
% 2.12/2.32 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.12/2.32 all A subset(empty_set,A).
% 2.12/2.32 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 2.12/2.32 all A B subset(set_difference(A,B),A).
% 2.12/2.32 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.12/2.32 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 2.12/2.32 all A (set_difference(A,empty_set)=A).
% 2.12/2.32 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))).
% 2.12/2.32 all A (subset(A,empty_set)->A=empty_set).
% 2.12/2.32 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 2.12/2.32 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 2.12/2.32 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 2.12/2.32 all A (set_difference(empty_set,A)=empty_set).
% 2.12/2.32 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))).
% 2.12/2.32 all A B (-(subset(A,B)&proper_subset(B,A))).
% 2.12/2.32 -(all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C))).
% 2.12/2.32 all A (empty(A)->A=empty_set).
% 2.12/2.32 all A B (-(in(A,B)&empty(B))).
% 2.12/2.32 all A B subset(A,set_union2(A,B)).
% 2.12/2.32 all A B (-(empty(A)&A!=B&empty(B))).
% 2.12/2.32 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 2.12/2.32 end_of_list.
% 2.12/2.32
% 2.12/2.32 -------> usable clausifies to:
% 2.12/2.32
% 2.12/2.32 list(usable).
% 2.12/2.32 0 [] A=A.
% 2.12/2.32 0 [] -in(A,B)| -in(B,A).
% 2.12/2.32 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.12/2.32 0 [] set_union2(A,B)=set_union2(B,A).
% 2.12/2.32 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.12/2.32 0 [] A!=B|subset(A,B).
% 2.12/2.32 0 [] A!=B|subset(B,A).
% 2.12/2.32 0 [] A=B| -subset(A,B)| -subset(B,A).
% 2.12/2.32 0 [] A!=empty_set| -in(B,A).
% 2.12/2.32 0 [] A=empty_set|in($f1(A),A).
% 2.12/2.32 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 2.12/2.32 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 2.12/2.32 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 2.12/2.32 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 2.12/2.32 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 2.12/2.32 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 2.12/2.32 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.12/2.32 0 [] subset(A,B)|in($f3(A,B),A).
% 2.12/2.32 0 [] subset(A,B)| -in($f3(A,B),B).
% 2.12/2.32 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 2.12/2.32 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 2.12/2.32 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 2.12/2.32 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A).
% 2.12/2.32 0 [] C=set_intersection2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),B).
% 2.12/2.32 0 [] C=set_intersection2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A)| -in($f4(A,B,C),B).
% 2.12/2.32 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 2.12/2.32 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 2.12/2.32 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 2.12/2.32 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)|in($f5(A,B,C),A).
% 2.12/2.32 0 [] C=set_difference(A,B)|in($f5(A,B,C),C)| -in($f5(A,B,C),B).
% 2.12/2.32 0 [] C=set_difference(A,B)| -in($f5(A,B,C),C)| -in($f5(A,B,C),A)|in($f5(A,B,C),B).
% 2.12/2.32 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.12/2.32 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.12/2.32 0 [] -proper_subset(A,B)|subset(A,B).
% 2.12/2.32 0 [] -proper_subset(A,B)|A!=B.
% 2.12/2.32 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.12/2.32 0 [] $T.
% 2.12/2.32 0 [] $T.
% 2.12/2.32 0 [] $T.
% 2.12/2.32 0 [] $T.
% 2.12/2.32 0 [] empty(empty_set).
% 2.12/2.32 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.12/2.32 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.12/2.32 0 [] set_union2(A,A)=A.
% 2.12/2.32 0 [] set_intersection2(A,A)=A.
% 2.12/2.32 0 [] -proper_subset(A,A).
% 2.12/2.32 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.12/2.32 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.12/2.32 0 [] empty($c1).
% 2.12/2.32 0 [] -empty($c2).
% 2.12/2.32 0 [] subset(A,A).
% 2.12/2.32 0 [] -disjoint(A,B)|disjoint(B,A).
% 2.12/2.32 0 [] -subset(A,B)|set_union2(A,B)=B.
% 2.12/2.32 0 [] subset(set_intersection2(A,B),A).
% 2.12/2.32 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.12/2.32 0 [] set_union2(A,empty_set)=A.
% 2.12/2.32 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.12/2.32 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.12/2.32 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.12/2.32 0 [] set_intersection2(A,empty_set)=empty_set.
% 2.12/2.32 0 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 2.12/2.32 0 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 2.12/2.32 0 [] subset(empty_set,A).
% 2.12/2.32 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.12/2.32 0 [] subset(set_difference(A,B),A).
% 2.12/2.32 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.12/2.32 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.12/2.32 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 2.12/2.32 0 [] set_difference(A,empty_set)=A.
% 2.12/2.32 0 [] disjoint(A,B)|in($f7(A,B),A).
% 2.12/2.32 0 [] disjoint(A,B)|in($f7(A,B),B).
% 2.12/2.32 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 2.12/2.32 0 [] -subset(A,empty_set)|A=empty_set.
% 2.12/2.32 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 2.12/2.32 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 2.12/2.32 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 2.12/2.32 0 [] set_difference(empty_set,A)=empty_set.
% 2.12/2.32 0 [] disjoint(A,B)|in($f8(A,B),set_intersection2(A,B)).
% 2.12/2.32 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.12/2.32 0 [] -subset(A,B)| -proper_subset(B,A).
% 2.12/2.32 0 [] subset($c5,$c4).
% 2.12/2.32 0 [] disjoint($c4,$c3).
% 2.12/2.32 0 [] -disjoint($c5,$c3).
% 2.12/2.32 0 [] -empty(A)|A=empty_set.
% 2.12/2.32 0 [] -in(A,B)| -empty(B).
% 2.12/2.32 0 [] subset(A,set_union2(A,B)).
% 2.12/2.32 0 [] -empty(A)|A=B| -empty(B).
% 2.12/2.32 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.12/2.32 end_of_list.
% 2.12/2.32
% 2.12/2.32 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.12/2.32
% 2.12/2.32 This ia a non-Horn set with equality. The strategy will be
% 2.12/2.32 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.12/2.32 deletion, with positive clauses in sos and nonpositive
% 2.12/2.32 clauses in usable.
% 2.12/2.32
% 2.12/2.32 dependent: set(knuth_bendix).
% 2.12/2.32 dependent: set(anl_eq).
% 2.12/2.32 dependent: set(para_from).
% 2.12/2.32 dependent: set(para_into).
% 2.12/2.32 dependent: clear(para_from_right).
% 2.12/2.32 dependent: clear(para_into_right).
% 2.12/2.32 dependent: set(para_from_vars).
% 2.12/2.32 dependent: set(eq_units_both_ways).
% 2.12/2.32 dependent: set(dynamic_demod_all).
% 2.12/2.32 dependent: set(dynamic_demod).
% 2.12/2.32 dependent: set(order_eq).
% 2.12/2.32 dependent: set(back_demod).
% 2.12/2.32 dependent: set(lrpo).
% 2.12/2.32 dependent: set(hyper_res).
% 2.12/2.32 dependent: set(unit_deletion).
% 2.12/2.32 dependent: set(factor).
% 2.12/2.32
% 2.12/2.32 ------------> process usable:
% 2.12/2.32 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.12/2.32 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 2.12/2.32 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 2.12/2.32 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 2.12/2.32 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 2.12/2.32 ** KEPT (pick-wt=6): 6 [] A!=empty_set| -in(B,A).
% 2.12/2.32 ** KEPT (pick-wt=14): 7 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 2.12/2.32 ** KEPT (pick-wt=11): 8 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 2.12/2.32 ** KEPT (pick-wt=11): 9 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 2.12/2.32 ** KEPT (pick-wt=17): 10 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 2.12/2.32 ** KEPT (pick-wt=17): 11 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 2.12/2.32 ** KEPT (pick-wt=9): 12 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.12/2.32 ** KEPT (pick-wt=8): 13 [] subset(A,B)| -in($f3(A,B),B).
% 2.12/2.32 ** KEPT (pick-wt=11): 14 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 2.12/2.32 ** KEPT (pick-wt=11): 15 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 2.12/2.32 ** KEPT (pick-wt=14): 16 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 2.12/2.32 ** KEPT (pick-wt=23): 17 [] A=set_intersection2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B)| -in($f4(B,C,A),C).
% 2.12/2.32 ** KEPT (pick-wt=11): 18 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 2.12/2.32 ** KEPT (pick-wt=11): 19 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 2.12/2.32 ** KEPT (pick-wt=14): 20 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 2.12/2.32 ** KEPT (pick-wt=17): 21 [] A=set_difference(B,C)|in($f5(B,C,A),A)| -in($f5(B,C,A),C).
% 2.12/2.32 ** KEPT (pick-wt=23): 22 [] A=set_difference(B,C)| -in($f5(B,C,A),A)| -in($f5(B,C,A),B)|in($f5(B,C,A),C).
% 2.12/2.32 ** KEPT (pick-wt=8): 23 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.12/2.32 ** KEPT (pick-wt=8): 24 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.12/2.32 ** KEPT (pick-wt=6): 25 [] -proper_subset(A,B)|subset(A,B).
% 2.12/2.32 ** KEPT (pick-wt=6): 26 [] -proper_subset(A,B)|A!=B.
% 2.12/2.32 ** KEPT (pick-wt=9): 27 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 2.12/2.32 ** KEPT (pick-wt=6): 28 [] empty(A)| -empty(set_union2(A,B)).
% 2.12/2.32 ** KEPT (pick-wt=6): 29 [] empty(A)| -empty(set_union2(B,A)).
% 2.12/2.32 ** KEPT (pick-wt=3): 30 [] -proper_subset(A,A).
% 2.12/2.32 ** KEPT (pick-wt=8): 31 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.12/2.32 ** KEPT (pick-wt=8): 32 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.12/2.32 ** KEPT (pick-wt=2): 33 [] -empty($c2).
% 2.12/2.32 ** KEPT (pick-wt=6): 34 [] -disjoint(A,B)|disjoint(B,A).
% 2.12/2.32 ** KEPT (pick-wt=8): 35 [] -subset(A,B)|set_union2(A,B)=B.
% 2.12/2.32 ** KEPT (pick-wt=11): 36 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 2.12/2.32 ** KEPT (pick-wt=9): 37 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.12/2.32 ** KEPT (pick-wt=10): 38 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 2.12/2.32 ** KEPT (pick-wt=8): 39 [] -subset(A,B)|set_intersection2(A,B)=A.
% 2.12/2.32 ** KEPT (pick-wt=13): 40 [] -in($f6(A,B),A)| -in($f6(A,B),B)|A=B.
% 2.12/2.32 ** KEPT (pick-wt=10): 41 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 2.12/2.32 Following clause subsumed by 31 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.12/2.32 Following clause subsumed by 32 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.12/2.32 ** KEPT (pick-wt=9): 42 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 2.12/2.32 ** KEPT (pick-wt=6): 43 [] -subset(A,empty_set)|A=empty_set.
% 2.12/2.32 ** KEPT (pick-wt=10): 45 [copy,44,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 2.12/2.32 ** KEPT (pick-wt=8): 46 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.12/2.32 ** KEPT (pick-wt=6): 47 [] -subset(A,B)| -proper_subset(B,A).
% 2.12/2.32 ** KEPT (pick-wt=3): 48 [] -disjoint($c5,$c3).
% 2.12/2.32 ** KEPT (pick-wt=5): 49 [] -empty(A)|A=empty_set.
% 2.12/2.32 ** KEPT (pick-wt=5): 50 [] -in(A,B)| -empty(B).
% 2.12/2.32 ** KEPT (pick-wt=7): 51 [] -empty(A)|A=B| -empty(B).
% 2.12/2.32 ** KEPT (pick-wt=11): 52 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.12/2.32
% 2.12/2.32 ------------> process sos:
% 2.12/2.32 ** KEPT (pick-wt=3): 71 [] A=A.
% 2.12/2.32 ** KEPT (pick-wt=7): 72 [] set_union2(A,B)=set_union2(B,A).
% 2.12/2.32 ** KEPT (pick-wt=7): 73 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.12/2.32 ** KEPT (pick-wt=7): 74 [] A=empty_set|in($f1(A),A).
% 2.12/2.32 ** KEPT (pick-wt=23): 75 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 2.12/2.32 ** KEPT (pick-wt=8): 76 [] subset(A,B)|in($f3(A,B),A).
% 2.12/2.32 ** KEPT (pick-wt=17): 77 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B).
% 2.12/2.32 ** KEPT (pick-wt=17): 78 [] A=set_intersection2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),C).
% 2.12/2.32 ** KEPT (pick-wt=17): 79 [] A=set_difference(B,C)|in($f5(B,C,A),A)|in($f5(B,C,A),B).
% 2.12/2.32 ** KEPT (pick-wt=2): 80 [] empty(empty_set).
% 2.12/2.32 ** KEPT (pick-wt=5): 81 [] set_union2(A,A)=A.
% 2.12/2.32 ---> New Demodulator: 82 [new_demod,81] set_union2(A,A)=A.
% 17.41/17.59 ** KEPT (pick-wt=5): 83 [] set_intersection2(A,A)=A.
% 17.41/17.59 ---> New Demodulator: 84 [new_demod,83] set_intersection2(A,A)=A.
% 17.41/17.59 ** KEPT (pick-wt=2): 85 [] empty($c1).
% 17.41/17.59 ** KEPT (pick-wt=3): 86 [] subset(A,A).
% 17.41/17.59 ** KEPT (pick-wt=5): 87 [] subset(set_intersection2(A,B),A).
% 17.41/17.59 ** KEPT (pick-wt=5): 88 [] set_union2(A,empty_set)=A.
% 17.41/17.59 ---> New Demodulator: 89 [new_demod,88] set_union2(A,empty_set)=A.
% 17.41/17.59 ** KEPT (pick-wt=5): 90 [] set_intersection2(A,empty_set)=empty_set.
% 17.41/17.59 ---> New Demodulator: 91 [new_demod,90] set_intersection2(A,empty_set)=empty_set.
% 17.41/17.59 ** KEPT (pick-wt=13): 92 [] in($f6(A,B),A)|in($f6(A,B),B)|A=B.
% 17.41/17.59 ** KEPT (pick-wt=3): 93 [] subset(empty_set,A).
% 17.41/17.59 ** KEPT (pick-wt=5): 94 [] subset(set_difference(A,B),A).
% 17.41/17.59 ** KEPT (pick-wt=9): 95 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 17.41/17.59 ---> New Demodulator: 96 [new_demod,95] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 17.41/17.59 ** KEPT (pick-wt=5): 97 [] set_difference(A,empty_set)=A.
% 17.41/17.59 ---> New Demodulator: 98 [new_demod,97] set_difference(A,empty_set)=A.
% 17.41/17.59 ** KEPT (pick-wt=8): 99 [] disjoint(A,B)|in($f7(A,B),A).
% 17.41/17.59 ** KEPT (pick-wt=8): 100 [] disjoint(A,B)|in($f7(A,B),B).
% 17.41/17.59 ** KEPT (pick-wt=9): 101 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 17.41/17.59 ---> New Demodulator: 102 [new_demod,101] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 17.41/17.59 ** KEPT (pick-wt=9): 104 [copy,103,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 17.41/17.59 ---> New Demodulator: 105 [new_demod,104] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 17.41/17.59 ** KEPT (pick-wt=5): 106 [] set_difference(empty_set,A)=empty_set.
% 17.41/17.59 ---> New Demodulator: 107 [new_demod,106] set_difference(empty_set,A)=empty_set.
% 17.41/17.59 ** KEPT (pick-wt=12): 109 [copy,108,demod,105] disjoint(A,B)|in($f8(A,B),set_difference(A,set_difference(A,B))).
% 17.41/17.59 ** KEPT (pick-wt=3): 110 [] subset($c5,$c4).
% 17.41/17.59 ** KEPT (pick-wt=3): 111 [] disjoint($c4,$c3).
% 17.41/17.59 ** KEPT (pick-wt=5): 112 [] subset(A,set_union2(A,B)).
% 17.41/17.59 Following clause subsumed by 71 during input processing: 0 [copy,71,flip.1] A=A.
% 17.41/17.59 71 back subsumes 68.
% 17.41/17.59 71 back subsumes 66.
% 17.41/17.59 71 back subsumes 54.
% 17.41/17.59 Following clause subsumed by 72 during input processing: 0 [copy,72,flip.1] set_union2(A,B)=set_union2(B,A).
% 17.41/17.59 ** KEPT (pick-wt=11): 113 [copy,73,flip.1,demod,105,105] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 17.41/17.59 >>>> Starting back demodulation with 82.
% 17.41/17.59 >> back demodulating 69 with 82.
% 17.41/17.59 >> back demodulating 55 with 82.
% 17.41/17.59 >>>> Starting back demodulation with 84.
% 17.41/17.59 >> back demodulating 70 with 84.
% 17.41/17.59 >> back demodulating 65 with 84.
% 17.41/17.59 >> back demodulating 61 with 84.
% 17.41/17.59 >> back demodulating 58 with 84.
% 17.41/17.59 >>>> Starting back demodulation with 89.
% 17.41/17.59 >>>> Starting back demodulation with 91.
% 17.41/17.59 >>>> Starting back demodulation with 96.
% 17.41/17.59 >> back demodulating 45 with 96.
% 17.41/17.59 >>>> Starting back demodulation with 98.
% 17.41/17.59 >>>> Starting back demodulation with 102.
% 17.41/17.59 >>>> Starting back demodulation with 105.
% 17.41/17.59 >> back demodulating 90 with 105.
% 17.41/17.59 >> back demodulating 87 with 105.
% 17.41/17.59 >> back demodulating 83 with 105.
% 17.41/17.59 >> back demodulating 78 with 105.
% 17.41/17.59 >> back demodulating 77 with 105.
% 17.41/17.59 >> back demodulating 73 with 105.
% 17.41/17.59 >> back demodulating 60 with 105.
% 17.41/17.59 >> back demodulating 59 with 105.
% 17.41/17.59 >> back demodulating 46 with 105.
% 17.41/17.59 >> back demodulating 39 with 105.
% 17.41/17.59 >> back demodulating 38 with 105.
% 17.41/17.59 >> back demodulating 36 with 105.
% 17.41/17.59 >> back demodulating 24 with 105.
% 17.41/17.59 >> back demodulating 23 with 105.
% 17.41/17.59 >> back demodulating 17 with 105.
% 17.41/17.59 >> back demodulating 16 with 105.
% 17.41/17.59 >> back demodulating 15 with 105.
% 17.41/17.59 >> back demodulating 14 with 105.
% 17.41/17.59 >>>> Starting back demodulation with 107.
% 17.41/17.59 Following clause subsumed by 113 during input processing: 0 [copy,113,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 17.41/17.59 >>>> Starting back demodulation with 124.
% 17.41/17.59
% 17.41/17.59 ======= end of input processing =======
% 17.41/17.59
% 17.41/17.59 =========== start of search ===========
% 17.41/17.59
% 17.41/17.59
% 17.41/17.59 Resetting weight limit to 8.
% 17.41/17.59
% 17.41/17.59
% 17.41/17.59 Resetting weight limit to 8.
% 17.41/17.59
% 17.41/17.59 sos_size=1558
% 17.41/17.59
% 17.41/17.59
% 17.41/17.59 Resetting weight limit to 7.
% 17.41/17.59
% 17.41/17.59
% 17.41/17.59 Resetting weight limit to 7.
% 17.41/17.59
% 17.41/17.59 sos_size=1552
% 17.41/17.59
% 17.41/17.59 -- HEY sandbox, WE HAVE A PROOF!! --
% 17.41/17.59
% 17.41/17.59 -----> EMPTY CLAUSE at 15.27 sec ----> 2345 [hyper,1704,42,100,218,unit_del,48,48] $F.
% 17.41/17.59
% 17.41/17.59 Length of proof is 2. Level of proof is 1.
% 17.41/17.59
% 17.41/17.59 ---------------- PROOF ----------------
% 17.41/17.59 % SZS status Theorem
% 17.41/17.59 % SZS output start Refutation
% See solution above
% 17.41/17.59 ------------ end of proof -------------
% 17.41/17.59
% 17.41/17.59
% 17.41/17.59 Search stopped by max_proofs option.
% 17.41/17.59
% 17.41/17.59
% 17.41/17.59 Search stopped by max_proofs option.
% 17.41/17.59
% 17.41/17.59 ============ end of search ============
% 17.41/17.59
% 17.41/17.59 -------------- statistics -------------
% 17.41/17.59 clauses given 730
% 17.41/17.59 clauses generated 491575
% 17.41/17.59 clauses kept 2302
% 17.41/17.59 clauses forward subsumed 31228
% 17.41/17.59 clauses back subsumed 240
% 17.41/17.59 Kbytes malloced 5859
% 17.41/17.59
% 17.41/17.59 ----------- times (seconds) -----------
% 17.41/17.59 user CPU time 15.27 (0 hr, 0 min, 15 sec)
% 17.41/17.59 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 17.41/17.59 wall-clock time 17 (0 hr, 0 min, 17 sec)
% 17.41/17.59
% 17.41/17.59 That finishes the proof of the theorem.
% 17.41/17.59
% 17.41/17.59 Process 3732 finished Wed Jul 27 08:10:32 2022
% 17.41/17.59 Otter interrupted
% 17.41/17.59 PROOF FOUND
%------------------------------------------------------------------------------