TSTP Solution File: SET094+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET094+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 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 13:13:05 EDT 2022
% Result : Theorem 6.61s 6.84s
% Output : Refutation 6.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 16 unt; 1 nHn; 21 RR)
% Number of literals : 38 ( 11 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET094+1.p',unknown),
[] ).
cnf(4,axiom,
( A != B
| subclass(B,A) ),
file('SET094+1.p',unknown),
[] ).
cnf(5,axiom,
( A = B
| ~ subclass(A,B)
| ~ subclass(B,A) ),
file('SET094+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(A,unordered_pair(B,C))
| A = B
| A = C ),
file('SET094+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ member(A,power_class(B))
| subclass(A,B) ),
file('SET094+1.p',unknown),
[] ).
cnf(53,axiom,
( member(A,power_class(B))
| ~ member(A,universal_class)
| ~ subclass(A,B) ),
file('SET094+1.p',unknown),
[] ).
cnf(70,axiom,
member_of(dollar_c4) != dollar_c3,
file('SET094+1.p',unknown),
[] ).
cnf(72,plain,
( ~ member(A,unordered_pair(B,B))
| A = B ),
inference(factor,[status(thm)],[7]),
[iquote('factor,7.2.3')] ).
cnf(84,axiom,
A = A,
file('SET094+1.p',unknown),
[] ).
cnf(86,axiom,
subclass(A,universal_class),
file('SET094+1.p',unknown),
[] ).
cnf(89,axiom,
singleton(A) = unordered_pair(A,A),
file('SET094+1.p',unknown),
[] ).
cnf(126,axiom,
singleton(member_of(dollar_c4)) = dollar_c4,
file('SET094+1.p',unknown),
[] ).
cnf(127,plain,
unordered_pair(member_of(dollar_c4),member_of(dollar_c4)) = dollar_c4,
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[126]),89]),
[iquote('copy,126,demod,89')] ).
cnf(129,axiom,
member(dollar_c3,dollar_c4),
file('SET094+1.p',unknown),
[] ).
cnf(141,plain,
subclass(A,A),
inference(hyper,[status(thm)],[84,4]),
[iquote('hyper,84,4')] ).
cnf(203,plain,
member(dollar_c3,universal_class),
inference(hyper,[status(thm)],[129,1,86]),
[iquote('hyper,129,1,86')] ).
cnf(247,plain,
member(dollar_c3,power_class(dollar_c3)),
inference(hyper,[status(thm)],[203,53,141]),
[iquote('hyper,203,53,141')] ).
cnf(867,plain,
( member(A,power_class(dollar_c3))
| ~ member(dollar_c3,unordered_pair(A,A)) ),
inference(para_into,[status(thm),theory(equality)],[247,72]),
[iquote('para_into,247.1.1,72.2.1')] ).
cnf(871,plain,
( member(dollar_c3,power_class(A))
| ~ member(dollar_c3,unordered_pair(A,A)) ),
inference(para_into,[status(thm),theory(equality)],[247,72]),
[iquote('para_into,247.1.2.1,72.2.1')] ).
cnf(2523,plain,
member(member_of(dollar_c4),power_class(dollar_c3)),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[867,127]),129]),
[iquote('para_into,867.2.2,127.1.1,unit_del,129')] ).
cnf(2524,plain,
subclass(member_of(dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[2523,52]),
[iquote('hyper,2523,52')] ).
cnf(2597,plain,
member(dollar_c3,power_class(member_of(dollar_c4))),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[871,127]),129]),
[iquote('para_into,871.2.2,127.1.1,unit_del,129')] ).
cnf(2598,plain,
subclass(dollar_c3,member_of(dollar_c4)),
inference(hyper,[status(thm)],[2597,52]),
[iquote('hyper,2597,52')] ).
cnf(2599,plain,
member_of(dollar_c4) = dollar_c3,
inference(hyper,[status(thm)],[2598,5,2524]),
[iquote('hyper,2598,5,2524')] ).
cnf(2601,plain,
$false,
inference(binary,[status(thm)],[2599,70]),
[iquote('binary,2599.1,70.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET094+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.03/0.12 % 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 10:51:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.77/1.98 ----- Otter 3.3f, August 2004 -----
% 1.77/1.98 The process was started by sandbox on n005.cluster.edu,
% 1.77/1.98 Wed Jul 27 10:51:50 2022
% 1.77/1.98 The command was "./otter". The process ID is 2999.
% 1.77/1.98
% 1.77/1.98 set(prolog_style_variables).
% 1.77/1.98 set(auto).
% 1.77/1.98 dependent: set(auto1).
% 1.77/1.98 dependent: set(process_input).
% 1.77/1.98 dependent: clear(print_kept).
% 1.77/1.98 dependent: clear(print_new_demod).
% 1.77/1.98 dependent: clear(print_back_demod).
% 1.77/1.98 dependent: clear(print_back_sub).
% 1.77/1.98 dependent: set(control_memory).
% 1.77/1.98 dependent: assign(max_mem, 12000).
% 1.77/1.98 dependent: assign(pick_given_ratio, 4).
% 1.77/1.98 dependent: assign(stats_level, 1).
% 1.77/1.98 dependent: assign(max_seconds, 10800).
% 1.77/1.98 clear(print_given).
% 1.77/1.98
% 1.77/1.98 formula_list(usable).
% 1.77/1.98 all A (A=A).
% 1.77/1.98 all X Y (subclass(X,Y)<-> (all U (member(U,X)->member(U,Y)))).
% 1.77/1.98 all X subclass(X,universal_class).
% 1.77/1.98 all X Y (X=Y<->subclass(X,Y)&subclass(Y,X)).
% 1.77/1.98 all U X Y (member(U,unordered_pair(X,Y))<->member(U,universal_class)& (U=X|U=Y)).
% 1.77/1.98 all X Y member(unordered_pair(X,Y),universal_class).
% 1.77/1.98 all X (singleton(X)=unordered_pair(X,X)).
% 1.77/1.98 all X Y (ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))).
% 1.77/1.98 all U V X Y (member(ordered_pair(U,V),cross_product(X,Y))<->member(U,X)&member(V,Y)).
% 1.77/1.98 all X Y (member(X,universal_class)&member(Y,universal_class)->first(ordered_pair(X,Y))=X&second(ordered_pair(X,Y))=Y).
% 1.77/1.98 all X Y Z (member(Z,cross_product(X,Y))->Z=ordered_pair(first(Z),second(Z))).
% 1.77/1.98 all X Y (member(ordered_pair(X,Y),element_relation)<->member(Y,universal_class)&member(X,Y)).
% 1.77/1.98 subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.77/1.98 all X Y Z (member(Z,intersection(X,Y))<->member(Z,X)&member(Z,Y)).
% 1.77/1.98 all X Z (member(Z,complement(X))<->member(Z,universal_class)& -member(Z,X)).
% 1.77/1.98 all X XR Y (restrict(XR,X,Y)=intersection(XR,cross_product(X,Y))).
% 1.77/1.98 all X (-member(X,null_class)).
% 1.77/1.98 all X Z (member(Z,domain_of(X))<->member(Z,universal_class)&restrict(X,singleton(Z),universal_class)!=null_class).
% 1.77/1.98 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)).
% 1.77/1.98 all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.77/1.98 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)).
% 1.77/1.98 all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.77/1.98 all X Y Z (member(Z,union(X,Y))<->member(Z,X)|member(Z,Y)).
% 1.77/1.98 all X (successor(X)=union(X,singleton(X))).
% 1.77/1.98 subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.77/1.98 all X Y (member(ordered_pair(X,Y),successor_relation)<->member(X,universal_class)&member(Y,universal_class)&successor(X)=Y).
% 1.77/1.98 all Y (inverse(Y)=domain_of(flip(cross_product(Y,universal_class)))).
% 1.77/1.98 all Z (range_of(Z)=domain_of(inverse(Z))).
% 1.77/1.98 all X XR (image(XR,X)=range_of(restrict(XR,X,universal_class))).
% 1.77/1.98 all X (inductive(X)<->member(null_class,X)&subclass(image(successor_relation,X),X)).
% 1.77/1.98 exists X (member(X,universal_class)&inductive(X)& (all Y (inductive(Y)->subclass(X,Y)))).
% 1.77/1.98 all U X (member(U,sum_class(X))<-> (exists Y (member(U,Y)&member(Y,X)))).
% 1.77/1.98 all X (member(X,universal_class)->member(sum_class(X),universal_class)).
% 1.77/1.98 all U X (member(U,power_class(X))<->member(U,universal_class)&subclass(U,X)).
% 1.77/1.98 all U (member(U,universal_class)->member(power_class(U),universal_class)).
% 1.77/1.98 all XR YR subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.77/1.98 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))))).
% 1.77/1.98 all Z (member(Z,identity_relation)<-> (exists X (member(X,universal_class)&Z=ordered_pair(X,X)))).
% 1.77/1.98 all XF (function(XF)<->subclass(XF,cross_product(universal_class,universal_class))&subclass(compose(XF,inverse(XF)),identity_relation)).
% 1.77/1.98 all X XF (member(X,universal_class)&function(XF)->member(image(XF,X),universal_class)).
% 1.77/1.98 all X Y (disjoint(X,Y)<-> (all U (-(member(U,X)&member(U,Y))))).
% 1.77/1.98 all X (X!=null_class-> (exists U (member(U,universal_class)&member(U,X)&disjoint(U,X)))).
% 1.77/1.98 all XF Y (apply(XF,Y)=sum_class(image(XF,singleton(Y)))).
% 1.77/1.98 exists XF (function(XF)& (all Y (member(Y,universal_class)->Y=null_class|member(apply(XF,Y),Y)))).
% 1.77/1.98 all Y (member(Y,universal_class)->member(member_of(singleton(Y)),universal_class)).
% 1.77/1.98 all Y (member(Y,universal_class)->singleton(member_of(singleton(Y)))=singleton(Y)).
% 1.77/1.98 all X (member(member_of(X),universal_class)|member_of(X)=X).
% 1.77/1.98 all X (singleton(member_of(X))=X|member_of(X)=X).
% 1.77/1.98 -(all X Y (singleton(member_of(X))=X&member(Y,X)->member_of(X)=Y)).
% 1.77/1.98 end_of_list.
% 1.77/1.98
% 1.77/1.98 -------> usable clausifies to:
% 1.77/1.98
% 1.77/1.98 list(usable).
% 1.77/1.98 0 [] A=A.
% 1.77/1.98 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 1.77/1.98 0 [] subclass(X,Y)|member($f1(X,Y),X).
% 1.77/1.98 0 [] subclass(X,Y)| -member($f1(X,Y),Y).
% 1.77/1.98 0 [] subclass(X,universal_class).
% 1.77/1.98 0 [] X!=Y|subclass(X,Y).
% 1.77/1.98 0 [] X!=Y|subclass(Y,X).
% 1.77/1.98 0 [] X=Y| -subclass(X,Y)| -subclass(Y,X).
% 1.77/1.98 0 [] -member(U,unordered_pair(X,Y))|member(U,universal_class).
% 1.77/1.98 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 1.77/1.98 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=X.
% 1.77/1.98 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=Y.
% 1.77/1.98 0 [] member(unordered_pair(X,Y),universal_class).
% 1.77/1.98 0 [] singleton(X)=unordered_pair(X,X).
% 1.77/1.98 0 [] ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y))).
% 1.77/1.98 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 1.77/1.98 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 1.77/1.98 0 [] member(ordered_pair(U,V),cross_product(X,Y))| -member(U,X)| -member(V,Y).
% 1.77/1.98 0 [] -member(X,universal_class)| -member(Y,universal_class)|first(ordered_pair(X,Y))=X.
% 1.77/1.98 0 [] -member(X,universal_class)| -member(Y,universal_class)|second(ordered_pair(X,Y))=Y.
% 1.77/1.98 0 [] -member(Z,cross_product(X,Y))|Z=ordered_pair(first(Z),second(Z)).
% 1.77/1.98 0 [] -member(ordered_pair(X,Y),element_relation)|member(Y,universal_class).
% 1.77/1.98 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 1.77/1.98 0 [] member(ordered_pair(X,Y),element_relation)| -member(Y,universal_class)| -member(X,Y).
% 1.77/1.98 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.77/1.98 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 1.77/1.98 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 1.77/1.98 0 [] member(Z,intersection(X,Y))| -member(Z,X)| -member(Z,Y).
% 1.77/1.98 0 [] -member(Z,complement(X))|member(Z,universal_class).
% 1.77/1.98 0 [] -member(Z,complement(X))| -member(Z,X).
% 1.77/1.98 0 [] member(Z,complement(X))| -member(Z,universal_class)|member(Z,X).
% 1.77/1.98 0 [] restrict(XR,X,Y)=intersection(XR,cross_product(X,Y)).
% 1.77/1.98 0 [] -member(X,null_class).
% 1.77/1.98 0 [] -member(Z,domain_of(X))|member(Z,universal_class).
% 1.77/1.98 0 [] -member(Z,domain_of(X))|restrict(X,singleton(Z),universal_class)!=null_class.
% 1.77/1.98 0 [] member(Z,domain_of(X))| -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class.
% 1.77/1.98 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)).
% 1.77/1.98 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 1.77/1.98 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).
% 1.77/1.98 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.77/1.98 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)).
% 1.77/1.98 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 1.77/1.98 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).
% 1.77/1.98 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.77/1.98 0 [] -member(Z,union(X,Y))|member(Z,X)|member(Z,Y).
% 1.77/1.98 0 [] member(Z,union(X,Y))| -member(Z,X).
% 1.77/1.98 0 [] member(Z,union(X,Y))| -member(Z,Y).
% 1.82/1.98 0 [] successor(X)=union(X,singleton(X)).
% 1.82/1.98 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.82/1.98 0 [] -member(ordered_pair(X,Y),successor_relation)|member(X,universal_class).
% 1.82/1.98 0 [] -member(ordered_pair(X,Y),successor_relation)|member(Y,universal_class).
% 1.82/1.98 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 1.82/1.98 0 [] member(ordered_pair(X,Y),successor_relation)| -member(X,universal_class)| -member(Y,universal_class)|successor(X)!=Y.
% 1.82/1.98 0 [] inverse(Y)=domain_of(flip(cross_product(Y,universal_class))).
% 1.82/1.98 0 [] range_of(Z)=domain_of(inverse(Z)).
% 1.82/1.98 0 [] image(XR,X)=range_of(restrict(XR,X,universal_class)).
% 1.82/1.98 0 [] -inductive(X)|member(null_class,X).
% 1.82/1.98 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 1.82/1.98 0 [] inductive(X)| -member(null_class,X)| -subclass(image(successor_relation,X),X).
% 1.82/1.98 0 [] member($c1,universal_class).
% 1.82/1.98 0 [] inductive($c1).
% 1.82/1.98 0 [] -inductive(Y)|subclass($c1,Y).
% 1.82/1.98 0 [] -member(U,sum_class(X))|member(U,$f2(U,X)).
% 1.82/1.98 0 [] -member(U,sum_class(X))|member($f2(U,X),X).
% 1.82/1.98 0 [] member(U,sum_class(X))| -member(U,Y)| -member(Y,X).
% 1.82/1.98 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 1.82/1.98 0 [] -member(U,power_class(X))|member(U,universal_class).
% 1.82/1.98 0 [] -member(U,power_class(X))|subclass(U,X).
% 1.82/1.98 0 [] member(U,power_class(X))| -member(U,universal_class)| -subclass(U,X).
% 1.82/1.98 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 1.82/1.98 0 [] subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.82/1.98 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(U,universal_class).
% 1.82/1.98 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(V,image(YR,image(XR,singleton(U)))).
% 1.82/1.98 0 [] member(ordered_pair(U,V),compose(YR,XR))| -member(U,universal_class)| -member(V,image(YR,image(XR,singleton(U)))).
% 1.82/1.98 0 [] -member(Z,identity_relation)|member($f3(Z),universal_class).
% 1.82/1.98 0 [] -member(Z,identity_relation)|Z=ordered_pair($f3(Z),$f3(Z)).
% 1.82/1.98 0 [] member(Z,identity_relation)| -member(X,universal_class)|Z!=ordered_pair(X,X).
% 1.82/1.98 0 [] -function(XF)|subclass(XF,cross_product(universal_class,universal_class)).
% 1.82/1.98 0 [] -function(XF)|subclass(compose(XF,inverse(XF)),identity_relation).
% 1.82/1.98 0 [] function(XF)| -subclass(XF,cross_product(universal_class,universal_class))| -subclass(compose(XF,inverse(XF)),identity_relation).
% 1.82/1.98 0 [] -member(X,universal_class)| -function(XF)|member(image(XF,X),universal_class).
% 1.82/1.98 0 [] -disjoint(X,Y)| -member(U,X)| -member(U,Y).
% 1.82/1.98 0 [] disjoint(X,Y)|member($f4(X,Y),X).
% 1.82/1.98 0 [] disjoint(X,Y)|member($f4(X,Y),Y).
% 1.82/1.98 0 [] X=null_class|member($f5(X),universal_class).
% 1.82/1.98 0 [] X=null_class|member($f5(X),X).
% 1.82/1.98 0 [] X=null_class|disjoint($f5(X),X).
% 1.82/1.98 0 [] apply(XF,Y)=sum_class(image(XF,singleton(Y))).
% 1.82/1.98 0 [] function($c2).
% 1.82/1.98 0 [] -member(Y,universal_class)|Y=null_class|member(apply($c2,Y),Y).
% 1.82/1.98 0 [] -member(Y,universal_class)|member(member_of(singleton(Y)),universal_class).
% 1.82/1.98 0 [] -member(Y,universal_class)|singleton(member_of(singleton(Y)))=singleton(Y).
% 1.82/1.98 0 [] member(member_of(X),universal_class)|member_of(X)=X.
% 1.82/1.98 0 [] singleton(member_of(X))=X|member_of(X)=X.
% 1.82/1.98 0 [] singleton(member_of($c4))=$c4.
% 1.82/1.98 0 [] member($c3,$c4).
% 1.82/1.98 0 [] member_of($c4)!=$c3.
% 1.82/1.98 end_of_list.
% 1.82/1.98
% 1.82/1.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.82/1.98
% 1.82/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.82/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.82/1.98 deletion, with positive clauses in sos and nonpositive
% 1.82/1.98 clauses in usable.
% 1.82/1.98
% 1.82/1.98 dependent: set(knuth_bendix).
% 1.82/1.98 dependent: set(anl_eq).
% 1.82/1.98 dependent: set(para_from).
% 1.82/1.98 dependent: set(para_into).
% 1.82/1.98 dependent: clear(para_from_right).
% 1.82/1.98 dependent: clear(para_into_right).
% 1.82/1.98 dependent: set(para_from_vars).
% 1.82/1.98 dependent: set(eq_units_both_ways).
% 1.82/1.98 dependent: set(dynamic_demod_all).
% 1.82/1.98 dependent: set(dynamic_demod).
% 1.82/1.98 dependent: set(order_eq).
% 1.82/1.98 dependent: set(back_demod).
% 1.82/1.98 dependent: set(lrpo).
% 1.82/1.98 dependent: set(hyper_res).
% 1.82/1.98 dependent: set(unit_deletion).
% 1.82/1.98 dependent: set(factor).
% 1.82/1.98
% 1.82/1.98 ------------> process usable:
% 1.82/1.98 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 1.82/1.98 ** KEPT (pick-wt=8): 2 [] subclass(A,B)| -member($f1(A,B),B).
% 1.82/1.98 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 1.82/1.98 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 1.82/1.98 ** KEPT (pick-wt=9): 5 [] A=B| -subclass(A,B)| -subclass(B,A).
% 1.82/1.98 ** KEPT (pick-wt=8): 6 [] -member(A,unordered_pair(B,C))|member(A,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=11): 7 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 1.82/1.98 ** KEPT (pick-wt=11): 8 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=B.
% 1.82/1.98 ** KEPT (pick-wt=11): 9 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=C.
% 1.82/1.98 ** KEPT (pick-wt=10): 10 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 1.82/1.98 ** KEPT (pick-wt=10): 11 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 1.82/1.98 ** KEPT (pick-wt=13): 12 [] member(ordered_pair(A,B),cross_product(C,D))| -member(A,C)| -member(B,D).
% 1.82/1.98 ** KEPT (pick-wt=12): 13 [] -member(A,universal_class)| -member(B,universal_class)|first(ordered_pair(A,B))=A.
% 1.82/1.98 ** KEPT (pick-wt=12): 14 [] -member(A,universal_class)| -member(B,universal_class)|second(ordered_pair(A,B))=B.
% 1.82/1.98 ** KEPT (pick-wt=12): 16 [copy,15,flip.2] -member(A,cross_product(B,C))|ordered_pair(first(A),second(A))=A.
% 1.82/1.98 ** KEPT (pick-wt=8): 17 [] -member(ordered_pair(A,B),element_relation)|member(B,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=8): 18 [] -member(ordered_pair(A,B),element_relation)|member(A,B).
% 1.82/1.98 ** KEPT (pick-wt=11): 19 [] member(ordered_pair(A,B),element_relation)| -member(B,universal_class)| -member(A,B).
% 1.82/1.98 ** KEPT (pick-wt=8): 20 [] -member(A,intersection(B,C))|member(A,B).
% 1.82/1.98 ** KEPT (pick-wt=8): 21 [] -member(A,intersection(B,C))|member(A,C).
% 1.82/1.98 ** KEPT (pick-wt=11): 22 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.82/1.98 ** KEPT (pick-wt=7): 23 [] -member(A,complement(B))|member(A,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=7): 24 [] -member(A,complement(B))| -member(A,B).
% 1.82/1.98 ** KEPT (pick-wt=10): 25 [] member(A,complement(B))| -member(A,universal_class)|member(A,B).
% 1.82/1.98 ** KEPT (pick-wt=3): 26 [] -member(A,null_class).
% 1.82/1.98 ** KEPT (pick-wt=7): 27 [] -member(A,domain_of(B))|member(A,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=11): 28 [] -member(A,domain_of(B))|restrict(B,singleton(A),universal_class)!=null_class.
% 1.82/1.98 ** KEPT (pick-wt=14): 29 [] member(A,domain_of(B))| -member(A,universal_class)|restrict(B,singleton(A),universal_class)=null_class.
% 1.82/1.98 ** 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)).
% 1.82/1.98 ** KEPT (pick-wt=15): 31 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(B,C),A),D).
% 1.82/1.98 ** 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).
% 1.82/1.98 ** 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)).
% 1.82/1.98 ** KEPT (pick-wt=15): 34 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(B,A),C),D).
% 1.82/1.98 ** 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).
% 1.82/1.98 ** KEPT (pick-wt=11): 36 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.82/1.98 ** KEPT (pick-wt=8): 37 [] member(A,union(B,C))| -member(A,B).
% 1.82/1.98 ** KEPT (pick-wt=8): 38 [] member(A,union(B,C))| -member(A,C).
% 1.82/1.98 ** KEPT (pick-wt=8): 39 [] -member(ordered_pair(A,B),successor_relation)|member(A,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=8): 40 [] -member(ordered_pair(A,B),successor_relation)|member(B,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=9): 41 [] -member(ordered_pair(A,B),successor_relation)|successor(A)=B.
% 1.82/1.98 ** KEPT (pick-wt=15): 42 [] member(ordered_pair(A,B),successor_relation)| -member(A,universal_class)| -member(B,universal_class)|successor(A)!=B.
% 1.82/1.98 ** KEPT (pick-wt=5): 43 [] -inductive(A)|member(null_class,A).
% 1.82/1.98 ** KEPT (pick-wt=7): 44 [] -inductive(A)|subclass(image(successor_relation,A),A).
% 1.82/1.98 ** KEPT (pick-wt=10): 45 [] inductive(A)| -member(null_class,A)| -subclass(image(successor_relation,A),A).
% 1.82/1.98 ** KEPT (pick-wt=5): 46 [] -inductive(A)|subclass($c1,A).
% 1.82/1.98 ** KEPT (pick-wt=9): 47 [] -member(A,sum_class(B))|member(A,$f2(A,B)).
% 1.82/1.98 ** KEPT (pick-wt=9): 48 [] -member(A,sum_class(B))|member($f2(A,B),B).
% 1.82/1.98 ** KEPT (pick-wt=10): 49 [] member(A,sum_class(B))| -member(A,C)| -member(C,B).
% 1.82/1.98 ** KEPT (pick-wt=7): 50 [] -member(A,universal_class)|member(sum_class(A),universal_class).
% 1.82/1.98 ** KEPT (pick-wt=7): 51 [] -member(A,power_class(B))|member(A,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=7): 52 [] -member(A,power_class(B))|subclass(A,B).
% 1.82/1.98 ** KEPT (pick-wt=10): 53 [] member(A,power_class(B))| -member(A,universal_class)| -subclass(A,B).
% 1.82/1.98 ** KEPT (pick-wt=7): 54 [] -member(A,universal_class)|member(power_class(A),universal_class).
% 1.82/1.98 ** KEPT (pick-wt=10): 55 [] -member(ordered_pair(A,B),compose(C,D))|member(A,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=15): 56 [] -member(ordered_pair(A,B),compose(C,D))|member(B,image(C,image(D,singleton(A)))).
% 1.82/1.98 ** 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)))).
% 1.82/1.98 ** KEPT (pick-wt=7): 58 [] -member(A,identity_relation)|member($f3(A),universal_class).
% 1.82/1.98 ** KEPT (pick-wt=10): 60 [copy,59,flip.2] -member(A,identity_relation)|ordered_pair($f3(A),$f3(A))=A.
% 1.82/1.98 ** KEPT (pick-wt=11): 61 [] member(A,identity_relation)| -member(B,universal_class)|A!=ordered_pair(B,B).
% 1.82/1.98 ** KEPT (pick-wt=7): 62 [] -function(A)|subclass(A,cross_product(universal_class,universal_class)).
% 1.82/1.98 ** KEPT (pick-wt=8): 63 [] -function(A)|subclass(compose(A,inverse(A)),identity_relation).
% 1.82/1.98 ** KEPT (pick-wt=13): 64 [] function(A)| -subclass(A,cross_product(universal_class,universal_class))| -subclass(compose(A,inverse(A)),identity_relation).
% 1.82/1.98 ** KEPT (pick-wt=10): 65 [] -member(A,universal_class)| -function(B)|member(image(B,A),universal_class).
% 1.82/1.98 ** KEPT (pick-wt=9): 66 [] -disjoint(A,B)| -member(C,A)| -member(C,B).
% 1.82/1.98 ** KEPT (pick-wt=11): 67 [] -member(A,universal_class)|A=null_class|member(apply($c2,A),A).
% 1.82/1.98 ** KEPT (pick-wt=8): 68 [] -member(A,universal_class)|member(member_of(singleton(A)),universal_class).
% 1.82/1.98 ** KEPT (pick-wt=10): 69 [] -member(A,universal_class)|singleton(member_of(singleton(A)))=singleton(A).
% 1.82/1.98 ** KEPT (pick-wt=4): 70 [] member_of($c4)!=$c3.
% 1.82/1.98
% 1.82/1.98 ------------> process sos:
% 1.82/1.98 ** KEPT (pick-wt=3): 84 [] A=A.
% 1.82/1.98 ** KEPT (pick-wt=8): 85 [] subclass(A,B)|member($f1(A,B),A).
% 1.82/1.98 ** KEPT (pick-wt=3): 86 [] subclass(A,universal_class).
% 1.82/1.98 ** KEPT (pick-wt=5): 87 [] member(unordered_pair(A,B),universal_class).
% 1.82/1.98 ** KEPT (pick-wt=6): 88 [] singleton(A)=unordered_pair(A,A).
% 1.82/1.98 ---> New Demodulator: 89 [new_demod,88] singleton(A)=unordered_pair(A,A).
% 1.82/1.98 ** KEPT (pick-wt=13): 91 [copy,90,demod,89,89,flip.1] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 1.82/1.98 ---> New Demodulator: 92 [new_demod,91] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 1.82/1.98 ** KEPT (pick-wt=5): 93 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.82/1.98 ** KEPT (pick-wt=10): 95 [copy,94,flip.1] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.82/1.98 ---> New Demodulator: 96 [new_demod,95] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.82/1.98 ** KEPT (pick-wt=8): 97 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.82/1.98 ** KEPT (pick-wt=8): 98 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.82/1.98 ** KEPT (pick-wt=8): 100 [copy,99,demod,89] successor(A)=union(A,unordered_pair(A,A)).
% 1.82/1.98 ---> New Demodulator: 101 [new_demod,100] successor(A)=union(A,unordered_pair(A,A)).
% 1.82/1.98 ** KEPT (pick-wt=5): 102 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.82/1.98 ** KEPT (pick-wt=8): 103 [] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.82/1.98 ---> New Demodulator: 104 [new_demod,103] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.82/1.98 ** KEPT (pick-wt=9): 106 [copy,105,demod,104] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 6.61/6.84 ---> New Demodulator: 107 [new_demod,106] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 6.61/6.84 ** KEPT (pick-wt=13): 109 [copy,108,demod,107,flip.1] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 6.61/6.84 ---> New Demodulator: 110 [new_demod,109] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 6.61/6.84 ** KEPT (pick-wt=3): 111 [] member($c1,universal_class).
% 6.61/6.84 ** KEPT (pick-wt=2): 112 [] inductive($c1).
% 6.61/6.84 ** KEPT (pick-wt=7): 113 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 6.61/6.84 ** KEPT (pick-wt=8): 114 [] disjoint(A,B)|member($f4(A,B),A).
% 6.61/6.84 ** KEPT (pick-wt=8): 115 [] disjoint(A,B)|member($f4(A,B),B).
% 6.61/6.84 ** KEPT (pick-wt=7): 116 [] A=null_class|member($f5(A),universal_class).
% 6.61/6.84 ** KEPT (pick-wt=7): 117 [] A=null_class|member($f5(A),A).
% 6.61/6.84 ** KEPT (pick-wt=7): 118 [] A=null_class|disjoint($f5(A),A).
% 6.61/6.84 ** KEPT (pick-wt=10): 120 [copy,119,demod,89,flip.1] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 6.61/6.84 ---> New Demodulator: 121 [new_demod,120] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 6.61/6.84 ** KEPT (pick-wt=2): 122 [] function($c2).
% 6.61/6.84 ** KEPT (pick-wt=8): 123 [] member(member_of(A),universal_class)|member_of(A)=A.
% 6.61/6.84 ** KEPT (pick-wt=11): 125 [copy,124,demod,89] unordered_pair(member_of(A),member_of(A))=A|member_of(A)=A.
% 6.61/6.84 ** KEPT (pick-wt=7): 127 [copy,126,demod,89] unordered_pair(member_of($c4),member_of($c4))=$c4.
% 6.61/6.84 ---> New Demodulator: 128 [new_demod,127] unordered_pair(member_of($c4),member_of($c4))=$c4.
% 6.61/6.84 ** KEPT (pick-wt=3): 129 [] member($c3,$c4).
% 6.61/6.84 Following clause subsumed by 84 during input processing: 0 [copy,84,flip.1] A=A.
% 6.61/6.84 84 back subsumes 71.
% 6.61/6.84 >>>> Starting back demodulation with 89.
% 6.61/6.84 >> back demodulating 69 with 89.
% 6.61/6.84 >> back demodulating 68 with 89.
% 6.61/6.84 >> back demodulating 57 with 89.
% 6.61/6.84 >> back demodulating 56 with 89.
% 6.61/6.84 >> back demodulating 29 with 89.
% 6.61/6.84 >> back demodulating 28 with 89.
% 6.61/6.84 >>>> Starting back demodulation with 92.
% 6.61/6.84 >>>> Starting back demodulation with 96.
% 6.61/6.84 >>>> Starting back demodulation with 101.
% 6.61/6.84 >> back demodulating 81 with 101.
% 6.61/6.84 >> back demodulating 42 with 101.
% 6.61/6.84 >> back demodulating 41 with 101.
% 6.61/6.84 >>>> Starting back demodulation with 104.
% 6.61/6.84 >> back demodulating 64 with 104.
% 6.61/6.84 >> back demodulating 63 with 104.
% 6.61/6.84 >>>> Starting back demodulation with 107.
% 6.61/6.84 >>>> Starting back demodulation with 110.
% 6.61/6.84 >>>> Starting back demodulation with 121.
% 6.61/6.84 >>>> Starting back demodulation with 128.
% 6.61/6.84
% 6.61/6.84 ======= end of input processing =======
% 6.61/6.84
% 6.61/6.84 =========== start of search ===========
% 6.61/6.84
% 6.61/6.84
% 6.61/6.84 Resetting weight limit to 6.
% 6.61/6.84
% 6.61/6.84
% 6.61/6.84 Resetting weight limit to 6.
% 6.61/6.84
% 6.61/6.84 sos_size=1327
% 6.61/6.84
% 6.61/6.84 -------- PROOF --------
% 6.61/6.84
% 6.61/6.84 ----> UNIT CONFLICT at 4.86 sec ----> 2601 [binary,2599.1,70.1] $F.
% 6.61/6.84
% 6.61/6.84 Length of proof is 12. Level of proof is 6.
% 6.61/6.84
% 6.61/6.84 ---------------- PROOF ----------------
% 6.61/6.84 % SZS status Theorem
% 6.61/6.84 % SZS output start Refutation
% See solution above
% 6.61/6.84 ------------ end of proof -------------
% 6.61/6.84
% 6.61/6.84
% 6.61/6.84 Search stopped by max_proofs option.
% 6.61/6.84
% 6.61/6.84
% 6.61/6.84 Search stopped by max_proofs option.
% 6.61/6.84
% 6.61/6.84 ============ end of search ============
% 6.61/6.84
% 6.61/6.84 -------------- statistics -------------
% 6.61/6.84 clauses given 1694
% 6.61/6.84 clauses generated 1803757
% 6.61/6.84 clauses kept 2359
% 6.61/6.84 clauses forward subsumed 13588
% 6.61/6.84 clauses back subsumed 73
% 6.61/6.84 Kbytes malloced 9765
% 6.61/6.84
% 6.61/6.84 ----------- times (seconds) -----------
% 6.61/6.84 user CPU time 4.86 (0 hr, 0 min, 4 sec)
% 6.61/6.84 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 6.61/6.84 wall-clock time 7 (0 hr, 0 min, 7 sec)
% 6.61/6.84
% 6.61/6.84 That finishes the proof of the theorem.
% 6.61/6.84
% 6.61/6.84 Process 2999 finished Wed Jul 27 10:51:57 2022
% 6.61/6.84 Otter interrupted
% 6.61/6.84 PROOF FOUND
%------------------------------------------------------------------------------