TSTP Solution File: SEU142+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU142+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 5.08s 5.31s
% Output : Refutation 5.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 7 unt; 4 nHn; 9 RR)
% Number of literals : 31 ( 23 equ; 12 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
( A = singleton(B)
| ~ in(dollar_f1(B,A),A)
| dollar_f1(B,A) != B ),
file('SEU142+2.p',unknown),
[] ).
cnf(10,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU142+2.p',unknown),
[] ).
cnf(11,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU142+2.p',unknown),
[] ).
cnf(57,axiom,
unordered_pair(dollar_c3,dollar_c3) != singleton(dollar_c3),
file('SEU142+2.p',unknown),
[] ).
cnf(58,plain,
singleton(dollar_c3) != unordered_pair(dollar_c3,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[57])]),
[iquote('copy,57,flip.1')] ).
cnf(67,plain,
( A != unordered_pair(B,B)
| ~ in(C,A)
| C = B ),
inference(factor,[status(thm)],[10]),
[iquote('factor,10.3.4')] ).
cnf(84,axiom,
A = A,
file('SEU142+2.p',unknown),
[] ).
cnf(88,axiom,
( A = singleton(B)
| in(dollar_f1(B,A),A)
| dollar_f1(B,A) = B ),
file('SEU142+2.p',unknown),
[] ).
cnf(98,axiom,
set_union2(A,A) = A,
file('SEU142+2.p',unknown),
[] ).
cnf(154,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[84,11,84]),
[iquote('hyper,84,11,84')] ).
cnf(295,plain,
( singleton(A) = B
| ~ in(dollar_f1(A,B),B)
| dollar_f1(A,B) != A ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[98,8]),98,98,98]),
[iquote('para_into,97.1.1,8.1.1,demod,98,98,98')] ).
cnf(430,plain,
( unordered_pair(A,A) = singleton(B)
| dollar_f1(B,unordered_pair(A,A)) = B
| dollar_f1(B,unordered_pair(A,A)) = A ),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[88,67,98]),98,98,98]),
[iquote('hyper,88,67,97,demod,98,98,98')] ).
cnf(439,plain,
( singleton(A) = unordered_pair(A,A)
| dollar_f1(A,unordered_pair(A,A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[430])]),
[iquote('factor,430.2.3,flip.1')] ).
cnf(1783,plain,
dollar_f1(dollar_c3,unordered_pair(dollar_c3,dollar_c3)) = dollar_c3,
inference(hyper,[status(thm)],[439,58]),
[iquote('hyper,439,58')] ).
cnf(1784,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1783,295]),1783]),58,154,84]),
[iquote('para_from,1782.1.1,295.3.1,demod,1783,unit_del,58,154,84')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU142+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 07:30:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.90 ----- Otter 3.3f, August 2004 -----
% 1.70/1.90 The process was started by sandbox2 on n005.cluster.edu,
% 1.70/1.90 Wed Jul 27 07:30:50 2022
% 1.70/1.90 The command was "./otter". The process ID is 12219.
% 1.70/1.90
% 1.70/1.90 set(prolog_style_variables).
% 1.70/1.90 set(auto).
% 1.70/1.90 dependent: set(auto1).
% 1.70/1.90 dependent: set(process_input).
% 1.70/1.90 dependent: clear(print_kept).
% 1.70/1.90 dependent: clear(print_new_demod).
% 1.70/1.90 dependent: clear(print_back_demod).
% 1.70/1.90 dependent: clear(print_back_sub).
% 1.70/1.90 dependent: set(control_memory).
% 1.70/1.90 dependent: assign(max_mem, 12000).
% 1.70/1.90 dependent: assign(pick_given_ratio, 4).
% 1.70/1.90 dependent: assign(stats_level, 1).
% 1.70/1.90 dependent: assign(max_seconds, 10800).
% 1.70/1.90 clear(print_given).
% 1.70/1.90
% 1.70/1.90 formula_list(usable).
% 1.70/1.90 all A (A=A).
% 1.70/1.90 all A B (in(A,B)-> -in(B,A)).
% 1.70/1.90 all A B (proper_subset(A,B)-> -proper_subset(B,A)).
% 1.70/1.90 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.70/1.90 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.70/1.90 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.70/1.90 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.70/1.90 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.70/1.90 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.70/1.90 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.70/1.90 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.70/1.90 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.70/1.90 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.70/1.90 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.70/1.90 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.70/1.90 all A B (proper_subset(A,B)<->subset(A,B)&A!=B).
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 empty(empty_set).
% 1.70/1.90 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.70/1.90 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.70/1.90 all A B (set_union2(A,A)=A).
% 1.70/1.90 all A B (set_intersection2(A,A)=A).
% 1.70/1.90 all A B (-proper_subset(A,A)).
% 1.70/1.90 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.70/1.90 exists A empty(A).
% 1.70/1.90 exists A (-empty(A)).
% 1.70/1.90 all A B subset(A,A).
% 1.70/1.90 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.70/1.90 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.70/1.90 all A B subset(set_intersection2(A,B),A).
% 1.70/1.90 all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C))).
% 1.70/1.90 all A (set_union2(A,empty_set)=A).
% 1.70/1.90 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.70/1.90 all A B C (subset(A,B)->subset(set_intersection2(A,C),set_intersection2(B,C))).
% 1.70/1.90 all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.70/1.90 all A (set_intersection2(A,empty_set)=empty_set).
% 1.70/1.90 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.70/1.90 all A subset(empty_set,A).
% 1.70/1.90 all A B C (subset(A,B)->subset(set_difference(A,C),set_difference(B,C))).
% 1.70/1.90 all A B subset(set_difference(A,B),A).
% 1.70/1.90 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.70/1.90 all A B (set_union2(A,set_difference(B,A))=set_union2(A,B)).
% 1.70/1.90 all A (set_difference(A,empty_set)=A).
% 1.70/1.90 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))).
% 1.70/1.90 all A (subset(A,empty_set)->A=empty_set).
% 1.70/1.90 all A B (set_difference(set_union2(A,B),B)=set_difference(A,B)).
% 1.70/1.90 all A B (subset(A,B)->B=set_union2(A,set_difference(B,A))).
% 1.70/1.90 all A B (set_difference(A,set_difference(A,B))=set_intersection2(A,B)).
% 1.70/1.90 all A (set_difference(empty_set,A)=empty_set).
% 1.70/1.90 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))).
% 1.70/1.90 all A B (-(subset(A,B)&proper_subset(B,A))).
% 1.70/1.90 all A B C (subset(A,B)&disjoint(B,C)->disjoint(A,C)).
% 1.70/1.90 -(all A (unordered_pair(A,A)=singleton(A))).
% 1.70/1.90 all A (empty(A)->A=empty_set).
% 1.70/1.90 all A B (-(in(A,B)&empty(B))).
% 1.70/1.90 all A B subset(A,set_union2(A,B)).
% 1.70/1.90 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.70/1.90 all A B (-(empty(A)&A!=B&empty(B))).
% 1.70/1.90 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 -------> usable clausifies to:
% 1.70/1.90
% 1.70/1.90 list(usable).
% 1.70/1.90 0 [] A=A.
% 1.70/1.90 0 [] -in(A,B)| -in(B,A).
% 1.70/1.90 0 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.70/1.90 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.90 0 [] set_union2(A,B)=set_union2(B,A).
% 1.70/1.90 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.70/1.90 0 [] A!=B|subset(A,B).
% 1.70/1.90 0 [] A!=B|subset(B,A).
% 1.70/1.90 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.70/1.90 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.70/1.90 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.70/1.90 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.70/1.90 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.70/1.90 0 [] A!=empty_set| -in(B,A).
% 1.70/1.90 0 [] A=empty_set|in($f2(A),A).
% 1.70/1.90 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.70/1.90 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.70/1.90 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.70/1.90 0 [] C=unordered_pair(A,B)|in($f3(A,B,C),C)|$f3(A,B,C)=A|$f3(A,B,C)=B.
% 1.70/1.90 0 [] C=unordered_pair(A,B)| -in($f3(A,B,C),C)|$f3(A,B,C)!=A.
% 1.70/1.90 0 [] C=unordered_pair(A,B)| -in($f3(A,B,C),C)|$f3(A,B,C)!=B.
% 1.70/1.90 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.70/1.90 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.70/1.90 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.70/1.90 0 [] C=set_union2(A,B)|in($f4(A,B,C),C)|in($f4(A,B,C),A)|in($f4(A,B,C),B).
% 1.70/1.90 0 [] C=set_union2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),A).
% 1.70/1.90 0 [] C=set_union2(A,B)| -in($f4(A,B,C),C)| -in($f4(A,B,C),B).
% 1.70/1.90 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.70/1.90 0 [] subset(A,B)|in($f5(A,B),A).
% 1.70/1.90 0 [] subset(A,B)| -in($f5(A,B),B).
% 1.70/1.90 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.70/1.90 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.70/1.90 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.70/1.90 0 [] C=set_intersection2(A,B)|in($f6(A,B,C),C)|in($f6(A,B,C),A).
% 1.70/1.90 0 [] C=set_intersection2(A,B)|in($f6(A,B,C),C)|in($f6(A,B,C),B).
% 1.70/1.90 0 [] C=set_intersection2(A,B)| -in($f6(A,B,C),C)| -in($f6(A,B,C),A)| -in($f6(A,B,C),B).
% 1.70/1.90 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.70/1.90 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.70/1.90 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.70/1.90 0 [] C=set_difference(A,B)|in($f7(A,B,C),C)|in($f7(A,B,C),A).
% 1.70/1.90 0 [] C=set_difference(A,B)|in($f7(A,B,C),C)| -in($f7(A,B,C),B).
% 1.70/1.90 0 [] C=set_difference(A,B)| -in($f7(A,B,C),C)| -in($f7(A,B,C),A)|in($f7(A,B,C),B).
% 1.70/1.90 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.70/1.90 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.70/1.90 0 [] -proper_subset(A,B)|subset(A,B).
% 1.70/1.90 0 [] -proper_subset(A,B)|A!=B.
% 1.70/1.90 0 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] empty(empty_set).
% 1.70/1.90 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.70/1.90 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.70/1.90 0 [] set_union2(A,A)=A.
% 1.70/1.90 0 [] set_intersection2(A,A)=A.
% 1.70/1.90 0 [] -proper_subset(A,A).
% 1.70/1.90 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.70/1.90 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.70/1.90 0 [] empty($c1).
% 1.70/1.90 0 [] -empty($c2).
% 1.70/1.90 0 [] subset(A,A).
% 1.70/1.90 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.70/1.90 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.70/1.90 0 [] subset(set_intersection2(A,B),A).
% 1.70/1.90 0 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.70/1.90 0 [] set_union2(A,empty_set)=A.
% 1.70/1.90 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.70/1.90 0 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.70/1.90 0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.70/1.90 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.70/1.90 0 [] in($f8(A,B),A)|in($f8(A,B),B)|A=B.
% 1.70/1.90 0 [] -in($f8(A,B),A)| -in($f8(A,B),B)|A=B.
% 1.70/1.90 0 [] subset(empty_set,A).
% 1.70/1.90 0 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.70/1.90 0 [] subset(set_difference(A,B),A).
% 1.70/1.90 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.70/1.90 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.70/1.90 0 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.70/1.90 0 [] set_difference(A,empty_set)=A.
% 1.70/1.90 0 [] disjoint(A,B)|in($f9(A,B),A).
% 1.70/1.90 0 [] disjoint(A,B)|in($f9(A,B),B).
% 1.70/1.90 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.70/1.90 0 [] -subset(A,empty_set)|A=empty_set.
% 1.70/1.90 0 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.70/1.90 0 [] -subset(A,B)|B=set_union2(A,set_difference(B,A)).
% 1.70/1.90 0 [] set_difference(A,set_difference(A,B))=set_intersection2(A,B).
% 1.70/1.90 0 [] set_difference(empty_set,A)=empty_set.
% 1.70/1.90 0 [] disjoint(A,B)|in($f10(A,B),set_intersection2(A,B)).
% 1.70/1.90 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.70/1.90 0 [] -subset(A,B)| -proper_subset(B,A).
% 1.70/1.90 0 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.70/1.90 0 [] unordered_pair($c3,$c3)!=singleton($c3).
% 1.70/1.90 0 [] -empty(A)|A=empty_set.
% 1.70/1.90 0 [] -in(A,B)| -empty(B).
% 1.70/1.90 0 [] subset(A,set_union2(A,B)).
% 1.70/1.90 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.70/1.90 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.70/1.90 0 [] -empty(A)|A=B| -empty(B).
% 1.70/1.90 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.70/1.90
% 1.70/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.90 deletion, with positive clauses in sos and nonpositive
% 1.70/1.91 clauses in usable.
% 1.70/1.91
% 1.70/1.91 dependent: set(knuth_bendix).
% 1.70/1.91 dependent: set(anl_eq).
% 1.70/1.91 dependent: set(para_from).
% 1.70/1.91 dependent: set(para_into).
% 1.70/1.91 dependent: clear(para_from_right).
% 1.70/1.91 dependent: clear(para_into_right).
% 1.70/1.91 dependent: set(para_from_vars).
% 1.70/1.91 dependent: set(eq_units_both_ways).
% 1.70/1.91 dependent: set(dynamic_demod_all).
% 1.70/1.91 dependent: set(dynamic_demod).
% 1.70/1.91 dependent: set(order_eq).
% 1.70/1.91 dependent: set(back_demod).
% 1.70/1.91 dependent: set(lrpo).
% 1.70/1.91 dependent: set(hyper_res).
% 1.70/1.91 dependent: set(unit_deletion).
% 1.70/1.91 dependent: set(factor).
% 1.70/1.91
% 1.70/1.91 ------------> process usable:
% 1.70/1.91 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.70/1.91 ** KEPT (pick-wt=6): 2 [] -proper_subset(A,B)| -proper_subset(B,A).
% 1.70/1.91 ** KEPT (pick-wt=6): 3 [] A!=B|subset(A,B).
% 1.70/1.91 ** KEPT (pick-wt=6): 4 [] A!=B|subset(B,A).
% 1.70/1.91 ** KEPT (pick-wt=9): 5 [] A=B| -subset(A,B)| -subset(B,A).
% 1.70/1.91 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.70/1.91 ** KEPT (pick-wt=10): 7 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.70/1.91 ** KEPT (pick-wt=14): 8 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.70/1.91 ** KEPT (pick-wt=6): 9 [] A!=empty_set| -in(B,A).
% 1.70/1.91 ** KEPT (pick-wt=14): 10 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.70/1.91 ** KEPT (pick-wt=11): 11 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.70/1.91 ** KEPT (pick-wt=11): 12 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.70/1.91 ** KEPT (pick-wt=17): 13 [] A=unordered_pair(B,C)| -in($f3(B,C,A),A)|$f3(B,C,A)!=B.
% 1.70/1.91 ** KEPT (pick-wt=17): 14 [] A=unordered_pair(B,C)| -in($f3(B,C,A),A)|$f3(B,C,A)!=C.
% 1.70/1.91 ** KEPT (pick-wt=14): 15 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.70/1.91 ** KEPT (pick-wt=11): 16 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.70/1.91 ** KEPT (pick-wt=11): 17 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.70/1.91 ** KEPT (pick-wt=17): 18 [] A=set_union2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),B).
% 1.70/1.91 ** KEPT (pick-wt=17): 19 [] A=set_union2(B,C)| -in($f4(B,C,A),A)| -in($f4(B,C,A),C).
% 1.70/1.91 ** KEPT (pick-wt=9): 20 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.70/1.91 ** KEPT (pick-wt=8): 21 [] subset(A,B)| -in($f5(A,B),B).
% 1.70/1.91 ** KEPT (pick-wt=11): 22 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.70/1.91 ** KEPT (pick-wt=11): 23 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.70/1.91 ** KEPT (pick-wt=14): 24 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.70/1.91 ** KEPT (pick-wt=23): 25 [] A=set_intersection2(B,C)| -in($f6(B,C,A),A)| -in($f6(B,C,A),B)| -in($f6(B,C,A),C).
% 1.70/1.91 ** KEPT (pick-wt=11): 26 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.70/1.91 ** KEPT (pick-wt=11): 27 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.70/1.91 ** KEPT (pick-wt=14): 28 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.70/1.91 ** KEPT (pick-wt=17): 29 [] A=set_difference(B,C)|in($f7(B,C,A),A)| -in($f7(B,C,A),C).
% 1.70/1.91 ** KEPT (pick-wt=23): 30 [] A=set_difference(B,C)| -in($f7(B,C,A),A)| -in($f7(B,C,A),B)|in($f7(B,C,A),C).
% 1.70/1.91 ** KEPT (pick-wt=8): 31 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.70/1.91 ** KEPT (pick-wt=8): 32 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.70/1.91 ** KEPT (pick-wt=6): 33 [] -proper_subset(A,B)|subset(A,B).
% 1.70/1.91 ** KEPT (pick-wt=6): 34 [] -proper_subset(A,B)|A!=B.
% 1.70/1.91 ** KEPT (pick-wt=9): 35 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 1.70/1.91 ** KEPT (pick-wt=6): 36 [] empty(A)| -empty(set_union2(A,B)).
% 1.70/1.91 ** KEPT (pick-wt=6): 37 [] empty(A)| -empty(set_union2(B,A)).
% 1.70/1.91 ** KEPT (pick-wt=3): 38 [] -proper_subset(A,A).
% 1.70/1.91 ** KEPT (pick-wt=8): 39 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.70/1.91 ** KEPT (pick-wt=8): 40 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.70/1.91 ** KEPT (pick-wt=2): 41 [] -empty($c2).
% 1.70/1.91 ** KEPT (pick-wt=6): 42 [] -disjoint(A,B)|disjoint(B,A).
% 1.70/1.91 ** KEPT (pick-wt=8): 43 [] -subset(A,B)|set_union2(A,B)=B.
% 1.70/1.91 ** KEPT (pick-wt=11): 44 [] -subset(A,B)| -subset(A,C)|subset(A,set_intersection2(B,C)).
% 1.70/1.91 ** KEPT (pick-wt=9): 45 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.70/1.91 ** KEPT (pick-wt=10): 46 [] -subset(A,B)|subset(set_intersection2(A,C),set_intersection2(B,C)).
% 1.70/1.91 ** KEPT (pick-wt=8): 47 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.70/1.91 ** KEPT (pick-wt=13): 48 [] -in($f8(A,B),A)| -in($f8(A,B),B)|A=B.
% 1.70/1.91 ** KEPT (pick-wt=10): 49 [] -subset(A,B)|subset(set_difference(A,C),set_difference(B,C)).
% 1.70/1.91 Following clause subsumed by 39 during input processing: 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.70/1.91 Following clause subsumed by 40 during input processing: 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.70/1.91 ** KEPT (pick-wt=9): 50 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.70/1.91 ** KEPT (pick-wt=6): 51 [] -subset(A,empty_set)|A=empty_set.
% 1.70/1.91 ** KEPT (pick-wt=10): 53 [copy,52,flip.2] -subset(A,B)|set_union2(A,set_difference(B,A))=B.
% 1.70/1.91 ** KEPT (pick-wt=8): 54 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.70/1.91 ** KEPT (pick-wt=6): 55 [] -subset(A,B)| -proper_subset(B,A).
% 1.70/1.91 ** KEPT (pick-wt=9): 56 [] -subset(A,B)| -disjoint(B,C)|disjoint(A,C).
% 1.70/1.91 ** KEPT (pick-wt=6): 58 [copy,57,flip.1] singleton($c3)!=unordered_pair($c3,$c3).
% 1.70/1.91 ** KEPT (pick-wt=5): 59 [] -empty(A)|A=empty_set.
% 1.70/1.91 ** KEPT (pick-wt=5): 60 [] -in(A,B)| -empty(B).
% 1.70/1.91 ** KEPT (pick-wt=8): 61 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.70/1.91 ** KEPT (pick-wt=8): 62 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.70/1.91 ** KEPT (pick-wt=7): 63 [] -empty(A)|A=B| -empty(B).
% 1.70/1.91 ** KEPT (pick-wt=11): 64 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 1.70/1.91
% 1.70/1.91 ------------> process sos:
% 1.70/1.91 ** KEPT (pick-wt=3): 84 [] A=A.
% 1.70/1.91 ** KEPT (pick-wt=7): 85 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.91 ** KEPT (pick-wt=7): 86 [] set_union2(A,B)=set_union2(B,A).
% 1.70/1.91 ** KEPT (pick-wt=7): 87 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.70/1.91 ** KEPT (pick-wt=14): 88 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.70/1.91 ** KEPT (pick-wt=7): 89 [] A=empty_set|in($f2(A),A).
% 1.70/1.91 ** KEPT (pick-wt=23): 90 [] A=unordered_pair(B,C)|in($f3(B,C,A),A)|$f3(B,C,A)=B|$f3(B,C,A)=C.
% 1.70/1.91 ** KEPT (pick-wt=23): 91 [] A=set_union2(B,C)|in($f4(B,C,A),A)|in($f4(B,C,A),B)|in($f4(B,C,A),C).
% 1.70/1.91 ** KEPT (pick-wt=8): 92 [] subset(A,B)|in($f5(A,B),A).
% 1.70/1.91 ** KEPT (pick-wt=17): 93 [] A=set_intersection2(B,C)|in($f6(B,C,A),A)|in($f6(B,C,A),B).
% 1.70/1.91 ** KEPT (pick-wt=17): 94 [] A=set_intersection2(B,C)|in($f6(B,C,A),A)|in($f6(B,C,A),C).
% 1.70/1.91 ** KEPT (pick-wt=17): 95 [] A=set_difference(B,C)|in($f7(B,C,A),A)|in($f7(B,C,A),B).
% 1.70/1.91 ** KEPT (pick-wt=2): 96 [] empty(empty_set).
% 1.70/1.91 ** KEPT (pick-wt=5): 97 [] set_union2(A,A)=A.
% 1.70/1.91 ---> New Demodulator: 98 [new_demod,97] set_union2(A,A)=A.
% 1.70/1.91 ** KEPT (pick-wt=5): 99 [] set_intersection2(A,A)=A.
% 1.70/1.91 ---> New Demodulator: 100 [new_demod,99] set_intersection2(A,A)=A.
% 1.70/1.91 ** KEPT (pick-wt=2): 101 [] empty($c1).
% 1.70/1.91 ** KEPT (pick-wt=3): 102 [] subset(A,A).
% 1.70/1.91 ** KEPT (pick-wt=5): 103 [] subset(set_intersection2(A,B),A).
% 1.70/1.91 ** KEPT (pick-wt=5): 104 [] set_union2(A,empty_set)=A.
% 1.70/1.91 ---> New Demodulator: 105 [new_demod,104] set_union2(A,empty_set)=A.
% 1.70/1.91 ** KEPT (pick-wt=5): 106 [] set_intersection2(A,empty_set)=empty_set.
% 1.70/1.91 ---> New Demodulator: 107 [new_demod,106] set_intersection2(A,empty_set)=empty_set.
% 1.70/1.91 ** KEPT (pick-wt=13): 108 [] in($f8(A,B),A)|in($f8(A,B),B)|A=B.
% 1.70/1.91 ** KEPT (pick-wt=3): 109 [] subset(empty_set,A).
% 1.70/1.91 ** KEPT (pick-wt=5): 110 [] subset(set_difference(A,B),A).
% 1.70/1.91 ** KEPT (pick-wt=9): 111 [] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.70/1.91 ---> New Demodulator: 112 [new_demod,111] set_union2(A,set_difference(B,A))=set_union2(A,B).
% 1.70/1.91 ** KEPT (pick-wt=5): 113 [] set_difference(A,empty_set)=A.
% 1.70/1.91 ---> New Demodulator: 114 [new_demod,113] set_difference(A,empty_set)=A.
% 1.70/1.91 ** KEPT (pick-wt=8): 115 [] disjoint(A,B)|in($f9(A,B),A).
% 1.70/1.91 ** KEPT (pick-wt=8): 116 [] disjoint(A,B)|in($f9(A,B),B).
% 1.70/1.91 ** KEPT (pick-wt=9): 117 [] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.70/1.91 ---> New Demodulator: 118 [new_demod,117] set_difference(set_union2(A,B),B)=set_difference(A,B).
% 1.70/1.91 ** KEPT (pick-wt=9): 120 [copy,119,flip.1] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.70/1.91 ---> New Demodulator: 121 [new_demod,120] set_intersection2(A,B)=set_difference(A,set_difference(A,B)).
% 1.70/1.91 ** KEPT (pick-wt=5): 122 [] set_difference(empty_set,A)=empty_set.
% 1.70/1.91 ---> New Demodulator: 123 [new_demod,122] set_difference(empty_set,A)=empty_set.
% 1.70/1.91 ** KEPT (pick-wt=12): 125 [copy,124,demod,121] disjoint(A,B)|in($f10(A,B),set_difference(A,set_difference(A,B))).
% 1.70/1.91 ** KEPT (pick-wt=5): 126 [] subset(A,set_union2(A,B)).
% 1.70/1.91 Following clause subsumed by 84 during input processing: 0 [copy,84,flip.1] A=A.
% 1.70/1.91 84 back subsumes 81.
% 1.70/1.91 84 back subsumes 79.
% 1.70/1.91 84 back subsumes 66.
% 1.70/1.91 Following clause subsumed by 85 during input processing: 0 [copy,85,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 5.08/5.31 Following clause subsumed by 86 during input processing: 0 [copy,86,flip.1] set_union2(A,B)=set_union2(B,A).
% 5.08/5.31 ** KEPT (pick-wt=11): 127 [copy,87,flip.1,demod,121,121] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 5.08/5.31 >>>> Starting back demodulation with 98.
% 5.08/5.31 >> back demodulating 82 with 98.
% 5.08/5.31 >> back demodulating 68 with 98.
% 5.08/5.31 >>>> Starting back demodulation with 100.
% 5.08/5.31 >> back demodulating 83 with 100.
% 5.08/5.31 >> back demodulating 78 with 100.
% 5.08/5.31 >> back demodulating 74 with 100.
% 5.08/5.31 >> back demodulating 71 with 100.
% 5.08/5.31 >>>> Starting back demodulation with 105.
% 5.08/5.31 >>>> Starting back demodulation with 107.
% 5.08/5.31 >>>> Starting back demodulation with 112.
% 5.08/5.31 >> back demodulating 53 with 112.
% 5.08/5.31 >>>> Starting back demodulation with 114.
% 5.08/5.31 >>>> Starting back demodulation with 118.
% 5.08/5.31 >>>> Starting back demodulation with 121.
% 5.08/5.31 >> back demodulating 106 with 121.
% 5.08/5.31 >> back demodulating 103 with 121.
% 5.08/5.31 >> back demodulating 99 with 121.
% 5.08/5.31 >> back demodulating 94 with 121.
% 5.08/5.31 >> back demodulating 93 with 121.
% 5.08/5.31 >> back demodulating 87 with 121.
% 5.08/5.31 >> back demodulating 73 with 121.
% 5.08/5.31 >> back demodulating 72 with 121.
% 5.08/5.31 >> back demodulating 54 with 121.
% 5.08/5.31 >> back demodulating 47 with 121.
% 5.08/5.31 >> back demodulating 46 with 121.
% 5.08/5.31 >> back demodulating 44 with 121.
% 5.08/5.31 >> back demodulating 32 with 121.
% 5.08/5.31 >> back demodulating 31 with 121.
% 5.08/5.31 >> back demodulating 25 with 121.
% 5.08/5.31 >> back demodulating 24 with 121.
% 5.08/5.31 >> back demodulating 23 with 121.
% 5.08/5.31 >> back demodulating 22 with 121.
% 5.08/5.31 >>>> Starting back demodulation with 123.
% 5.08/5.31 Following clause subsumed by 127 during input processing: 0 [copy,127,flip.1] set_difference(A,set_difference(A,B))=set_difference(B,set_difference(B,A)).
% 5.08/5.31 >>>> Starting back demodulation with 139.
% 5.08/5.31
% 5.08/5.31 ======= end of input processing =======
% 5.08/5.31
% 5.08/5.31 =========== start of search ===========
% 5.08/5.31
% 5.08/5.31
% 5.08/5.31 Resetting weight limit to 8.
% 5.08/5.31
% 5.08/5.31
% 5.08/5.31 Resetting weight limit to 8.
% 5.08/5.31
% 5.08/5.31 sos_size=1286
% 5.08/5.31
% 5.08/5.31
% 5.08/5.31 Resetting weight limit to 7.
% 5.08/5.31
% 5.08/5.31
% 5.08/5.31 Resetting weight limit to 7.
% 5.08/5.31
% 5.08/5.31 sos_size=1315
% 5.08/5.31
% 5.08/5.31 -------- PROOF --------
% 5.08/5.31
% 5.08/5.31 -----> EMPTY CLAUSE at 3.41 sec ----> 1784 [para_from,1782.1.1,295.3.1,demod,1783,unit_del,58,154,84] $F.
% 5.08/5.31
% 5.08/5.31 Length of proof is 7. Level of proof is 4.
% 5.08/5.31
% 5.08/5.31 ---------------- PROOF ----------------
% 5.08/5.31 % SZS status Theorem
% 5.08/5.31 % SZS output start Refutation
% See solution above
% 5.08/5.31 ------------ end of proof -------------
% 5.08/5.31
% 5.08/5.31
% 5.08/5.31 Search stopped by max_proofs option.
% 5.08/5.31
% 5.08/5.31
% 5.08/5.31 Search stopped by max_proofs option.
% 5.08/5.31
% 5.08/5.31 ============ end of search ============
% 5.08/5.31
% 5.08/5.31 -------------- statistics -------------
% 5.08/5.31 clauses given 482
% 5.08/5.31 clauses generated 203554
% 5.08/5.31 clauses kept 1747
% 5.08/5.31 clauses forward subsumed 16758
% 5.08/5.31 clauses back subsumed 194
% 5.08/5.31 Kbytes malloced 5859
% 5.08/5.31
% 5.08/5.31 ----------- times (seconds) -----------
% 5.08/5.31 user CPU time 3.41 (0 hr, 0 min, 3 sec)
% 5.08/5.31 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 5.08/5.31 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 5.08/5.31
% 5.08/5.31 That finishes the proof of the theorem.
% 5.08/5.31
% 5.08/5.31 Process 12219 finished Wed Jul 27 07:30:55 2022
% 5.08/5.31 Otter interrupted
% 5.08/5.31 PROOF FOUND
%------------------------------------------------------------------------------