TSTP Solution File: SET108+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET108+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:13:07 EDT 2022
% Result : Theorem 1.82s 1.99s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 5 unt; 0 nHn; 13 RR)
% Number of literals : 29 ( 18 equ; 17 neg)
% Maximal clause size : 3 ( 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; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(68,axiom,
( ~ member(A,universal_class)
| ~ member(B,universal_class)
| dollar_c3 != ordered_pair(A,B) ),
file('SET108+1.p',unknown),
[] ).
cnf(69,plain,
( ~ member(A,universal_class)
| ~ member(B,universal_class)
| ordered_pair(A,B) != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[68])]),
[iquote('copy,68,flip.3')] ).
cnf(70,axiom,
( member(dollar_f7(A,B),universal_class)
| A != dollar_c3
| B != dollar_c3 ),
file('SET108+1.p',unknown),
[] ).
cnf(71,axiom,
( member(dollar_f6(A,B),universal_class)
| A != dollar_c3
| B != dollar_c3 ),
file('SET108+1.p',unknown),
[] ).
cnf(72,axiom,
( dollar_c3 = ordered_pair(dollar_f7(A,B),dollar_f6(A,B))
| A != dollar_c3
| B != dollar_c3 ),
file('SET108+1.p',unknown),
[] ).
cnf(73,plain,
( ordered_pair(dollar_f7(A,B),dollar_f6(A,B)) = dollar_c3
| A != dollar_c3
| B != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[72])]),
[iquote('copy,72,flip.1')] ).
cnf(88,plain,
( member(dollar_f7(A,A),universal_class)
| A != dollar_c3 ),
inference(factor,[status(thm)],[70]),
[iquote('factor,70.2.3')] ).
cnf(89,plain,
( member(dollar_f6(A,A),universal_class)
| A != dollar_c3 ),
inference(factor,[status(thm)],[71]),
[iquote('factor,71.2.3')] ).
cnf(90,plain,
( ordered_pair(dollar_f7(A,A),dollar_f6(A,A)) = dollar_c3
| A != dollar_c3 ),
inference(factor,[status(thm)],[73]),
[iquote('factor,73.2.3')] ).
cnf(91,axiom,
A = A,
file('SET108+1.p',unknown),
[] ).
cnf(139,plain,
ordered_pair(dollar_f7(dollar_c3,dollar_c3),dollar_f6(dollar_c3,dollar_c3)) = dollar_c3,
inference(hyper,[status(thm)],[91,90]),
[iquote('hyper,91,90')] ).
cnf(141,plain,
member(dollar_f6(dollar_c3,dollar_c3),universal_class),
inference(hyper,[status(thm)],[91,89]),
[iquote('hyper,91,89')] ).
cnf(142,plain,
member(dollar_f7(dollar_c3,dollar_c3),universal_class),
inference(hyper,[status(thm)],[91,88]),
[iquote('hyper,91,88')] ).
cnf(1594,plain,
$false,
inference(hyper,[status(thm)],[139,69,142,141]),
[iquote('hyper,139,69,142,141')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET108+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.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 11:04:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.64/1.84 ----- Otter 3.3f, August 2004 -----
% 1.64/1.84 The process was started by sandbox2 on n029.cluster.edu,
% 1.64/1.84 Wed Jul 27 11:04:29 2022
% 1.64/1.84 The command was "./otter". The process ID is 32628.
% 1.64/1.84
% 1.64/1.84 set(prolog_style_variables).
% 1.64/1.84 set(auto).
% 1.64/1.84 dependent: set(auto1).
% 1.64/1.84 dependent: set(process_input).
% 1.64/1.84 dependent: clear(print_kept).
% 1.64/1.84 dependent: clear(print_new_demod).
% 1.64/1.84 dependent: clear(print_back_demod).
% 1.64/1.84 dependent: clear(print_back_sub).
% 1.64/1.84 dependent: set(control_memory).
% 1.64/1.84 dependent: assign(max_mem, 12000).
% 1.64/1.84 dependent: assign(pick_given_ratio, 4).
% 1.64/1.84 dependent: assign(stats_level, 1).
% 1.64/1.84 dependent: assign(max_seconds, 10800).
% 1.64/1.84 clear(print_given).
% 1.64/1.84
% 1.64/1.84 formula_list(usable).
% 1.64/1.84 all A (A=A).
% 1.64/1.84 all X Y (subclass(X,Y)<-> (all U (member(U,X)->member(U,Y)))).
% 1.64/1.84 all X subclass(X,universal_class).
% 1.64/1.84 all X Y (X=Y<->subclass(X,Y)&subclass(Y,X)).
% 1.64/1.84 all U X Y (member(U,unordered_pair(X,Y))<->member(U,universal_class)& (U=X|U=Y)).
% 1.64/1.84 all X Y member(unordered_pair(X,Y),universal_class).
% 1.64/1.84 all X (singleton(X)=unordered_pair(X,X)).
% 1.64/1.84 all X Y (ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))).
% 1.64/1.84 all U V X Y (member(ordered_pair(U,V),cross_product(X,Y))<->member(U,X)&member(V,Y)).
% 1.64/1.84 all X Y (member(X,universal_class)&member(Y,universal_class)->first(ordered_pair(X,Y))=X&second(ordered_pair(X,Y))=Y).
% 1.64/1.84 all X Y Z (member(Z,cross_product(X,Y))->Z=ordered_pair(first(Z),second(Z))).
% 1.64/1.84 all X Y (member(ordered_pair(X,Y),element_relation)<->member(Y,universal_class)&member(X,Y)).
% 1.64/1.84 subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 all X Y Z (member(Z,intersection(X,Y))<->member(Z,X)&member(Z,Y)).
% 1.64/1.84 all X Z (member(Z,complement(X))<->member(Z,universal_class)& -member(Z,X)).
% 1.64/1.84 all X XR Y (restrict(XR,X,Y)=intersection(XR,cross_product(X,Y))).
% 1.64/1.84 all X (-member(X,null_class)).
% 1.64/1.84 all X Z (member(Z,domain_of(X))<->member(Z,universal_class)&restrict(X,singleton(Z),universal_class)!=null_class).
% 1.64/1.84 all X U V W (member(ordered_pair(ordered_pair(U,V),W),rotate(X))<->member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))&member(ordered_pair(ordered_pair(V,W),U),X)).
% 1.64/1.84 all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 all U V W X (member(ordered_pair(ordered_pair(U,V),W),flip(X))<->member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))&member(ordered_pair(ordered_pair(V,U),W),X)).
% 1.64/1.84 all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 all X Y Z (member(Z,union(X,Y))<->member(Z,X)|member(Z,Y)).
% 1.64/1.84 all X (successor(X)=union(X,singleton(X))).
% 1.64/1.84 subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 all X Y (member(ordered_pair(X,Y),successor_relation)<->member(X,universal_class)&member(Y,universal_class)&successor(X)=Y).
% 1.64/1.84 all Y (inverse(Y)=domain_of(flip(cross_product(Y,universal_class)))).
% 1.64/1.84 all Z (range_of(Z)=domain_of(inverse(Z))).
% 1.64/1.84 all X XR (image(XR,X)=range_of(restrict(XR,X,universal_class))).
% 1.64/1.84 all X (inductive(X)<->member(null_class,X)&subclass(image(successor_relation,X),X)).
% 1.64/1.84 exists X (member(X,universal_class)&inductive(X)& (all Y (inductive(Y)->subclass(X,Y)))).
% 1.64/1.84 all U X (member(U,sum_class(X))<-> (exists Y (member(U,Y)&member(Y,X)))).
% 1.64/1.84 all X (member(X,universal_class)->member(sum_class(X),universal_class)).
% 1.64/1.84 all U X (member(U,power_class(X))<->member(U,universal_class)&subclass(U,X)).
% 1.64/1.84 all U (member(U,universal_class)->member(power_class(U),universal_class)).
% 1.64/1.84 all XR YR subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.64/1.84 all XR YR U V (member(ordered_pair(U,V),compose(YR,XR))<->member(U,universal_class)&member(V,image(YR,image(XR,singleton(U))))).
% 1.64/1.84 all Z (member(Z,identity_relation)<-> (exists X (member(X,universal_class)&Z=ordered_pair(X,X)))).
% 1.64/1.84 all XF (function(XF)<->subclass(XF,cross_product(universal_class,universal_class))&subclass(compose(XF,inverse(XF)),identity_relation)).
% 1.64/1.84 all X XF (member(X,universal_class)&function(XF)->member(image(XF,X),universal_class)).
% 1.64/1.84 all X Y (disjoint(X,Y)<-> (all U (-(member(U,X)&member(U,Y))))).
% 1.64/1.84 all X (X!=null_class-> (exists U (member(U,universal_class)&member(U,X)&disjoint(U,X)))).
% 1.64/1.84 all XF Y (apply(XF,Y)=sum_class(image(XF,singleton(Y)))).
% 1.64/1.84 exists XF (function(XF)& (all Y (member(Y,universal_class)->Y=null_class|member(apply(XF,Y),Y)))).
% 1.64/1.84 -(all X exists U V (member(U,universal_class)&member(V,universal_class)&X=ordered_pair(U,V)| -(exists Y Z (member(Y,universal_class)&member(Z,universal_class)&X=ordered_pair(Y,Z)))&U=X&V=X)).
% 1.64/1.84 end_of_list.
% 1.64/1.84
% 1.64/1.84 -------> usable clausifies to:
% 1.64/1.84
% 1.64/1.84 list(usable).
% 1.64/1.84 0 [] A=A.
% 1.64/1.84 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 1.64/1.84 0 [] subclass(X,Y)|member($f1(X,Y),X).
% 1.64/1.84 0 [] subclass(X,Y)| -member($f1(X,Y),Y).
% 1.64/1.84 0 [] subclass(X,universal_class).
% 1.64/1.84 0 [] X!=Y|subclass(X,Y).
% 1.64/1.84 0 [] X!=Y|subclass(Y,X).
% 1.64/1.84 0 [] X=Y| -subclass(X,Y)| -subclass(Y,X).
% 1.64/1.84 0 [] -member(U,unordered_pair(X,Y))|member(U,universal_class).
% 1.64/1.84 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 1.64/1.84 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=X.
% 1.64/1.84 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=Y.
% 1.64/1.84 0 [] member(unordered_pair(X,Y),universal_class).
% 1.64/1.84 0 [] singleton(X)=unordered_pair(X,X).
% 1.64/1.84 0 [] ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y))).
% 1.64/1.84 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 1.64/1.84 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 1.64/1.84 0 [] member(ordered_pair(U,V),cross_product(X,Y))| -member(U,X)| -member(V,Y).
% 1.64/1.84 0 [] -member(X,universal_class)| -member(Y,universal_class)|first(ordered_pair(X,Y))=X.
% 1.64/1.84 0 [] -member(X,universal_class)| -member(Y,universal_class)|second(ordered_pair(X,Y))=Y.
% 1.64/1.84 0 [] -member(Z,cross_product(X,Y))|Z=ordered_pair(first(Z),second(Z)).
% 1.64/1.84 0 [] -member(ordered_pair(X,Y),element_relation)|member(Y,universal_class).
% 1.64/1.84 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 1.64/1.84 0 [] member(ordered_pair(X,Y),element_relation)| -member(Y,universal_class)| -member(X,Y).
% 1.64/1.84 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 1.64/1.84 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 1.64/1.84 0 [] member(Z,intersection(X,Y))| -member(Z,X)| -member(Z,Y).
% 1.64/1.84 0 [] -member(Z,complement(X))|member(Z,universal_class).
% 1.64/1.84 0 [] -member(Z,complement(X))| -member(Z,X).
% 1.64/1.84 0 [] member(Z,complement(X))| -member(Z,universal_class)|member(Z,X).
% 1.64/1.84 0 [] restrict(XR,X,Y)=intersection(XR,cross_product(X,Y)).
% 1.64/1.84 0 [] -member(X,null_class).
% 1.64/1.84 0 [] -member(Z,domain_of(X))|member(Z,universal_class).
% 1.64/1.84 0 [] -member(Z,domain_of(X))|restrict(X,singleton(Z),universal_class)!=null_class.
% 1.64/1.84 0 [] member(Z,domain_of(X))| -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class.
% 1.64/1.84 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 1.64/1.84 0 [] member(ordered_pair(ordered_pair(U,V),W),rotate(X))| -member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))| -member(ordered_pair(ordered_pair(V,W),U),X).
% 1.64/1.84 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 1.64/1.84 0 [] member(ordered_pair(ordered_pair(U,V),W),flip(X))| -member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))| -member(ordered_pair(ordered_pair(V,U),W),X).
% 1.64/1.84 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 0 [] -member(Z,union(X,Y))|member(Z,X)|member(Z,Y).
% 1.64/1.84 0 [] member(Z,union(X,Y))| -member(Z,X).
% 1.64/1.84 0 [] member(Z,union(X,Y))| -member(Z,Y).
% 1.64/1.84 0 [] successor(X)=union(X,singleton(X)).
% 1.64/1.84 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 0 [] -member(ordered_pair(X,Y),successor_relation)|member(X,universal_class).
% 1.64/1.84 0 [] -member(ordered_pair(X,Y),successor_relation)|member(Y,universal_class).
% 1.64/1.84 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 1.64/1.84 0 [] member(ordered_pair(X,Y),successor_relation)| -member(X,universal_class)| -member(Y,universal_class)|successor(X)!=Y.
% 1.64/1.84 0 [] inverse(Y)=domain_of(flip(cross_product(Y,universal_class))).
% 1.64/1.84 0 [] range_of(Z)=domain_of(inverse(Z)).
% 1.64/1.84 0 [] image(XR,X)=range_of(restrict(XR,X,universal_class)).
% 1.64/1.84 0 [] -inductive(X)|member(null_class,X).
% 1.64/1.84 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 1.64/1.84 0 [] inductive(X)| -member(null_class,X)| -subclass(image(successor_relation,X),X).
% 1.64/1.84 0 [] member($c1,universal_class).
% 1.64/1.84 0 [] inductive($c1).
% 1.64/1.84 0 [] -inductive(Y)|subclass($c1,Y).
% 1.64/1.84 0 [] -member(U,sum_class(X))|member(U,$f2(U,X)).
% 1.64/1.84 0 [] -member(U,sum_class(X))|member($f2(U,X),X).
% 1.64/1.84 0 [] member(U,sum_class(X))| -member(U,Y)| -member(Y,X).
% 1.64/1.84 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 1.64/1.84 0 [] -member(U,power_class(X))|member(U,universal_class).
% 1.64/1.84 0 [] -member(U,power_class(X))|subclass(U,X).
% 1.64/1.84 0 [] member(U,power_class(X))| -member(U,universal_class)| -subclass(U,X).
% 1.64/1.84 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 1.64/1.84 0 [] subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.64/1.84 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(U,universal_class).
% 1.64/1.84 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(V,image(YR,image(XR,singleton(U)))).
% 1.64/1.84 0 [] member(ordered_pair(U,V),compose(YR,XR))| -member(U,universal_class)| -member(V,image(YR,image(XR,singleton(U)))).
% 1.64/1.84 0 [] -member(Z,identity_relation)|member($f3(Z),universal_class).
% 1.64/1.84 0 [] -member(Z,identity_relation)|Z=ordered_pair($f3(Z),$f3(Z)).
% 1.64/1.84 0 [] member(Z,identity_relation)| -member(X,universal_class)|Z!=ordered_pair(X,X).
% 1.64/1.84 0 [] -function(XF)|subclass(XF,cross_product(universal_class,universal_class)).
% 1.64/1.84 0 [] -function(XF)|subclass(compose(XF,inverse(XF)),identity_relation).
% 1.64/1.84 0 [] function(XF)| -subclass(XF,cross_product(universal_class,universal_class))| -subclass(compose(XF,inverse(XF)),identity_relation).
% 1.64/1.84 0 [] -member(X,universal_class)| -function(XF)|member(image(XF,X),universal_class).
% 1.64/1.84 0 [] -disjoint(X,Y)| -member(U,X)| -member(U,Y).
% 1.64/1.84 0 [] disjoint(X,Y)|member($f4(X,Y),X).
% 1.64/1.84 0 [] disjoint(X,Y)|member($f4(X,Y),Y).
% 1.64/1.84 0 [] X=null_class|member($f5(X),universal_class).
% 1.64/1.84 0 [] X=null_class|member($f5(X),X).
% 1.64/1.84 0 [] X=null_class|disjoint($f5(X),X).
% 1.64/1.84 0 [] apply(XF,Y)=sum_class(image(XF,singleton(Y))).
% 1.64/1.84 0 [] function($c2).
% 1.64/1.84 0 [] -member(Y,universal_class)|Y=null_class|member(apply($c2,Y),Y).
% 1.64/1.84 0 [] -member(U,universal_class)| -member(V,universal_class)|$c3!=ordered_pair(U,V).
% 1.64/1.84 0 [] member($f7(U,V),universal_class)|U!=$c3|V!=$c3.
% 1.64/1.84 0 [] member($f6(U,V),universal_class)|U!=$c3|V!=$c3.
% 1.64/1.84 0 [] $c3=ordered_pair($f7(U,V),$f6(U,V))|U!=$c3|V!=$c3.
% 1.64/1.84 end_of_list.
% 1.64/1.84
% 1.64/1.84 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.64/1.84
% 1.64/1.84 This ia a non-Horn set with equality. The strategy will be
% 1.64/1.84 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.64/1.84 deletion, with positive clauses in sos and nonpositive
% 1.64/1.84 clauses in usable.
% 1.64/1.84
% 1.64/1.84 dependent: set(knuth_bendix).
% 1.64/1.84 dependent: set(anl_eq).
% 1.64/1.84 dependent: set(para_from).
% 1.64/1.84 dependent: set(para_into).
% 1.64/1.84 dependent: clear(para_from_right).
% 1.64/1.84 dependent: clear(para_into_right).
% 1.64/1.84 dependent: set(para_from_vars).
% 1.64/1.84 dependent: set(eq_units_both_ways).
% 1.64/1.84 dependent: set(dynamic_demod_all).
% 1.64/1.84 dependent: set(dynamic_demod).
% 1.64/1.84 dependent: set(order_eq).
% 1.64/1.84 dependent: set(back_demod).
% 1.64/1.84 dependent: set(lrpo).
% 1.64/1.84 dependent: set(hyper_res).
% 1.64/1.84 dependent: set(unit_deletion).
% 1.64/1.84 dependent: set(factor).
% 1.64/1.84
% 1.64/1.84 ------------> process usable:
% 1.64/1.84 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 1.64/1.84 ** KEPT (pick-wt=8): 2 [] subclass(A,B)| -member($f1(A,B),B).
% 1.64/1.84 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 1.64/1.84 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 1.64/1.84 ** KEPT (pick-wt=9): 5 [] A=B| -subclass(A,B)| -subclass(B,A).
% 1.64/1.84 ** KEPT (pick-wt=8): 6 [] -member(A,unordered_pair(B,C))|member(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=11): 7 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 1.64/1.84 ** KEPT (pick-wt=11): 8 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=B.
% 1.64/1.84 ** KEPT (pick-wt=11): 9 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=C.
% 1.64/1.84 ** KEPT (pick-wt=10): 10 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 1.64/1.84 ** KEPT (pick-wt=10): 11 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 1.64/1.84 ** KEPT (pick-wt=13): 12 [] member(ordered_pair(A,B),cross_product(C,D))| -member(A,C)| -member(B,D).
% 1.64/1.84 ** KEPT (pick-wt=12): 13 [] -member(A,universal_class)| -member(B,universal_class)|first(ordered_pair(A,B))=A.
% 1.64/1.84 ** KEPT (pick-wt=12): 14 [] -member(A,universal_class)| -member(B,universal_class)|second(ordered_pair(A,B))=B.
% 1.64/1.84 ** KEPT (pick-wt=12): 16 [copy,15,flip.2] -member(A,cross_product(B,C))|ordered_pair(first(A),second(A))=A.
% 1.64/1.84 ** KEPT (pick-wt=8): 17 [] -member(ordered_pair(A,B),element_relation)|member(B,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=8): 18 [] -member(ordered_pair(A,B),element_relation)|member(A,B).
% 1.64/1.84 ** KEPT (pick-wt=11): 19 [] member(ordered_pair(A,B),element_relation)| -member(B,universal_class)| -member(A,B).
% 1.64/1.84 ** KEPT (pick-wt=8): 20 [] -member(A,intersection(B,C))|member(A,B).
% 1.64/1.84 ** KEPT (pick-wt=8): 21 [] -member(A,intersection(B,C))|member(A,C).
% 1.64/1.84 ** KEPT (pick-wt=11): 22 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.64/1.84 ** KEPT (pick-wt=7): 23 [] -member(A,complement(B))|member(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=7): 24 [] -member(A,complement(B))| -member(A,B).
% 1.64/1.84 ** KEPT (pick-wt=10): 25 [] member(A,complement(B))| -member(A,universal_class)|member(A,B).
% 1.64/1.84 ** KEPT (pick-wt=3): 26 [] -member(A,null_class).
% 1.64/1.84 ** KEPT (pick-wt=7): 27 [] -member(A,domain_of(B))|member(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=11): 28 [] -member(A,domain_of(B))|restrict(B,singleton(A),universal_class)!=null_class.
% 1.64/1.84 ** KEPT (pick-wt=14): 29 [] member(A,domain_of(B))| -member(A,universal_class)|restrict(B,singleton(A),universal_class)=null_class.
% 1.64/1.84 ** KEPT (pick-wt=19): 30 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(A,B),C),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=15): 31 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(B,C),A),D).
% 1.64/1.84 ** KEPT (pick-wt=26): 32 [] member(ordered_pair(ordered_pair(A,B),C),rotate(D))| -member(ordered_pair(ordered_pair(A,B),C),cross_product(cross_product(universal_class,universal_class),universal_class))| -member(ordered_pair(ordered_pair(B,C),A),D).
% 1.64/1.84 ** KEPT (pick-wt=19): 33 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(A,B),C),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=15): 34 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(B,A),C),D).
% 1.64/1.84 ** KEPT (pick-wt=26): 35 [] member(ordered_pair(ordered_pair(A,B),C),flip(D))| -member(ordered_pair(ordered_pair(A,B),C),cross_product(cross_product(universal_class,universal_class),universal_class))| -member(ordered_pair(ordered_pair(B,A),C),D).
% 1.64/1.84 ** KEPT (pick-wt=11): 36 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.64/1.84 ** KEPT (pick-wt=8): 37 [] member(A,union(B,C))| -member(A,B).
% 1.64/1.84 ** KEPT (pick-wt=8): 38 [] member(A,union(B,C))| -member(A,C).
% 1.64/1.84 ** KEPT (pick-wt=8): 39 [] -member(ordered_pair(A,B),successor_relation)|member(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=8): 40 [] -member(ordered_pair(A,B),successor_relation)|member(B,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=9): 41 [] -member(ordered_pair(A,B),successor_relation)|successor(A)=B.
% 1.64/1.84 ** KEPT (pick-wt=15): 42 [] member(ordered_pair(A,B),successor_relation)| -member(A,universal_class)| -member(B,universal_class)|successor(A)!=B.
% 1.64/1.84 ** KEPT (pick-wt=5): 43 [] -inductive(A)|member(null_class,A).
% 1.64/1.84 ** KEPT (pick-wt=7): 44 [] -inductive(A)|subclass(image(successor_relation,A),A).
% 1.64/1.84 ** KEPT (pick-wt=10): 45 [] inductive(A)| -member(null_class,A)| -subclass(image(successor_relation,A),A).
% 1.64/1.84 ** KEPT (pick-wt=5): 46 [] -inductive(A)|subclass($c1,A).
% 1.64/1.84 ** KEPT (pick-wt=9): 47 [] -member(A,sum_class(B))|member(A,$f2(A,B)).
% 1.64/1.84 ** KEPT (pick-wt=9): 48 [] -member(A,sum_class(B))|member($f2(A,B),B).
% 1.64/1.84 ** KEPT (pick-wt=10): 49 [] member(A,sum_class(B))| -member(A,C)| -member(C,B).
% 1.64/1.84 ** KEPT (pick-wt=7): 50 [] -member(A,universal_class)|member(sum_class(A),universal_class).
% 1.64/1.84 ** KEPT (pick-wt=7): 51 [] -member(A,power_class(B))|member(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=7): 52 [] -member(A,power_class(B))|subclass(A,B).
% 1.64/1.84 ** KEPT (pick-wt=10): 53 [] member(A,power_class(B))| -member(A,universal_class)| -subclass(A,B).
% 1.64/1.84 ** KEPT (pick-wt=7): 54 [] -member(A,universal_class)|member(power_class(A),universal_class).
% 1.64/1.84 ** KEPT (pick-wt=10): 55 [] -member(ordered_pair(A,B),compose(C,D))|member(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=15): 56 [] -member(ordered_pair(A,B),compose(C,D))|member(B,image(C,image(D,singleton(A)))).
% 1.64/1.84 ** KEPT (pick-wt=18): 57 [] member(ordered_pair(A,B),compose(C,D))| -member(A,universal_class)| -member(B,image(C,image(D,singleton(A)))).
% 1.64/1.84 ** KEPT (pick-wt=7): 58 [] -member(A,identity_relation)|member($f3(A),universal_class).
% 1.64/1.84 ** KEPT (pick-wt=10): 60 [copy,59,flip.2] -member(A,identity_relation)|ordered_pair($f3(A),$f3(A))=A.
% 1.64/1.84 ** KEPT (pick-wt=11): 61 [] member(A,identity_relation)| -member(B,universal_class)|A!=ordered_pair(B,B).
% 1.64/1.84 ** KEPT (pick-wt=7): 62 [] -function(A)|subclass(A,cross_product(universal_class,universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 63 [] -function(A)|subclass(compose(A,inverse(A)),identity_relation).
% 1.64/1.84 ** KEPT (pick-wt=13): 64 [] function(A)| -subclass(A,cross_product(universal_class,universal_class))| -subclass(compose(A,inverse(A)),identity_relation).
% 1.64/1.84 ** KEPT (pick-wt=10): 65 [] -member(A,universal_class)| -function(B)|member(image(B,A),universal_class).
% 1.64/1.84 ** KEPT (pick-wt=9): 66 [] -disjoint(A,B)| -member(C,A)| -member(C,B).
% 1.64/1.84 ** KEPT (pick-wt=11): 67 [] -member(A,universal_class)|A=null_class|member(apply($c2,A),A).
% 1.64/1.84 ** KEPT (pick-wt=11): 69 [copy,68,flip.3] -member(A,universal_class)| -member(B,universal_class)|ordered_pair(A,B)!=$c3.
% 1.64/1.84 ** KEPT (pick-wt=11): 70 [] member($f7(A,B),universal_class)|A!=$c3|B!=$c3.
% 1.64/1.84 ** KEPT (pick-wt=11): 71 [] member($f6(A,B),universal_class)|A!=$c3|B!=$c3.
% 1.64/1.84 ** KEPT (pick-wt=15): 73 [copy,72,flip.1] ordered_pair($f7(A,B),$f6(A,B))=$c3|A!=$c3|B!=$c3.
% 1.64/1.84
% 1.64/1.84 ------------> process sos:
% 1.64/1.84 ** KEPT (pick-wt=3): 91 [] A=A.
% 1.64/1.84 ** KEPT (pick-wt=8): 92 [] subclass(A,B)|member($f1(A,B),A).
% 1.64/1.84 ** KEPT (pick-wt=3): 93 [] subclass(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=5): 94 [] member(unordered_pair(A,B),universal_class).
% 1.64/1.84 ** KEPT (pick-wt=6): 95 [] singleton(A)=unordered_pair(A,A).
% 1.64/1.84 ---> New Demodulator: 96 [new_demod,95] singleton(A)=unordered_pair(A,A).
% 1.64/1.84 ** KEPT (pick-wt=13): 98 [copy,97,demod,96,96,flip.1] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 1.64/1.84 ---> New Demodulator: 99 [new_demod,98] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 1.64/1.84 ** KEPT (pick-wt=5): 100 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=10): 102 [copy,101,flip.1] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.64/1.84 ---> New Demodulator: 103 [new_demod,102] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.64/1.84 ** KEPT (pick-wt=8): 104 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 105 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 107 [copy,106,demod,96] successor(A)=union(A,unordered_pair(A,A)).
% 1.64/1.84 ---> New Demodulator: 108 [new_demod,107] successor(A)=union(A,unordered_pair(A,A)).
% 1.64/1.84 ** KEPT (pick-wt=5): 109 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 110 [] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.64/1.84 ---> New Demodulator: 111 [new_demod,110] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.64/1.84 ** KEPT (pick-wt=9): 113 [copy,112,demod,111] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 1.64/1.84 ---> New Demodulator: 114 [new_demod,113] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 1.82/1.99 ** KEPT (pick-wt=13): 116 [copy,115,demod,114,flip.1] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 1.82/1.99 ---> New Demodulator: 117 [new_demod,116] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 1.82/1.99 ** KEPT (pick-wt=3): 118 [] member($c1,universal_class).
% 1.82/1.99 ** KEPT (pick-wt=2): 119 [] inductive($c1).
% 1.82/1.99 ** KEPT (pick-wt=7): 120 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 1.82/1.99 ** KEPT (pick-wt=8): 121 [] disjoint(A,B)|member($f4(A,B),A).
% 1.82/1.99 ** KEPT (pick-wt=8): 122 [] disjoint(A,B)|member($f4(A,B),B).
% 1.82/1.99 ** KEPT (pick-wt=7): 123 [] A=null_class|member($f5(A),universal_class).
% 1.82/1.99 ** KEPT (pick-wt=7): 124 [] A=null_class|member($f5(A),A).
% 1.82/1.99 ** KEPT (pick-wt=7): 125 [] A=null_class|disjoint($f5(A),A).
% 1.82/1.99 ** KEPT (pick-wt=10): 127 [copy,126,demod,96,flip.1] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 1.82/1.99 ---> New Demodulator: 128 [new_demod,127] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 1.82/1.99 ** KEPT (pick-wt=2): 129 [] function($c2).
% 1.82/1.99 Following clause subsumed by 91 during input processing: 0 [copy,91,flip.1] A=A.
% 1.82/1.99 91 back subsumes 74.
% 1.82/1.99 >>>> Starting back demodulation with 96.
% 1.82/1.99 >> back demodulating 57 with 96.
% 1.82/1.99 >> back demodulating 56 with 96.
% 1.82/1.99 >> back demodulating 29 with 96.
% 1.82/1.99 >> back demodulating 28 with 96.
% 1.82/1.99 >>>> Starting back demodulation with 99.
% 1.82/1.99 >>>> Starting back demodulation with 103.
% 1.82/1.99 >>>> Starting back demodulation with 108.
% 1.82/1.99 >> back demodulating 84 with 108.
% 1.82/1.99 >> back demodulating 42 with 108.
% 1.82/1.99 >> back demodulating 41 with 108.
% 1.82/1.99 >>>> Starting back demodulation with 111.
% 1.82/1.99 >> back demodulating 64 with 111.
% 1.82/1.99 >> back demodulating 63 with 111.
% 1.82/1.99 >>>> Starting back demodulation with 114.
% 1.82/1.99 >>>> Starting back demodulation with 117.
% 1.82/1.99 >>>> Starting back demodulation with 128.
% 1.82/1.99
% 1.82/1.99 ======= end of input processing =======
% 1.82/1.99
% 1.82/1.99 =========== start of search ===========
% 1.82/1.99
% 1.82/1.99
% 1.82/1.99 Resetting weight limit to 6.
% 1.82/1.99
% 1.82/1.99
% 1.82/1.99 Resetting weight limit to 6.
% 1.82/1.99
% 1.82/1.99 sos_size=1006
% 1.82/1.99
% 1.82/1.99 -------- PROOF --------
% 1.82/1.99
% 1.82/1.99 -----> EMPTY CLAUSE at 0.15 sec ----> 1594 [hyper,139,69,142,141] $F.
% 1.82/1.99
% 1.82/1.99 Length of proof is 8. Level of proof is 3.
% 1.82/1.99
% 1.82/1.99 ---------------- PROOF ----------------
% 1.82/1.99 % SZS status Theorem
% 1.82/1.99 % SZS output start Refutation
% See solution above
% 1.82/1.99 ------------ end of proof -------------
% 1.82/1.99
% 1.82/1.99
% 1.82/1.99 Search stopped by max_proofs option.
% 1.82/1.99
% 1.82/1.99
% 1.82/1.99 Search stopped by max_proofs option.
% 1.82/1.99
% 1.82/1.99 ============ end of search ============
% 1.82/1.99
% 1.82/1.99 -------------- statistics -------------
% 1.82/1.99 clauses given 141
% 1.82/1.99 clauses generated 20006
% 1.82/1.99 clauses kept 1396
% 1.82/1.99 clauses forward subsumed 908
% 1.82/1.99 clauses back subsumed 19
% 1.82/1.99 Kbytes malloced 5859
% 1.82/1.99
% 1.82/1.99 ----------- times (seconds) -----------
% 1.82/1.99 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 1.82/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/1.99 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/1.99
% 1.82/1.99 That finishes the proof of the theorem.
% 1.82/1.99
% 1.82/1.99 Process 32628 finished Wed Jul 27 11:04:31 2022
% 1.82/1.99 Otter interrupted
% 1.82/1.99 PROOF FOUND
%------------------------------------------------------------------------------