TSTP Solution File: SET117+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET117+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:13:08 EDT 2022
% Result : Theorem 1.64s 1.88s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 4 RR)
% Number of literals : 9 ( 4 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(68,axiom,
~ member(dollar_c3,universal_class),
file('SET117+1.p',unknown),
[] ).
cnf(85,axiom,
member(unordered_pair(A,B),universal_class),
file('SET117+1.p',unknown),
[] ).
cnf(87,axiom,
singleton(A) = unordered_pair(A,A),
file('SET117+1.p',unknown),
[] ).
cnf(88,axiom,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
file('SET117+1.p',unknown),
[] ).
cnf(89,plain,
unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))) = ordered_pair(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[88]),87,87])]),
[iquote('copy,88,demod,87,87,flip.1')] ).
cnf(121,axiom,
ordered_pair(first(dollar_c3),second(dollar_c3)) = dollar_c3,
file('SET117+1.p',unknown),
[] ).
cnf(733,plain,
member(ordered_pair(A,B),universal_class),
inference(para_from,[status(thm),theory(equality)],[89,85]),
[iquote('para_from,89.1.1,85.1.1')] ).
cnf(1463,plain,
member(dollar_c3,universal_class),
inference(para_into,[status(thm),theory(equality)],[733,121]),
[iquote('para_into,733.1.1,121.1.1')] ).
cnf(1464,plain,
$false,
inference(binary,[status(thm)],[1463,68]),
[iquote('binary,1463.1,68.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET117+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 10:19:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.64/1.83 ----- Otter 3.3f, August 2004 -----
% 1.64/1.83 The process was started by sandbox2 on n007.cluster.edu,
% 1.64/1.83 Wed Jul 27 10:19:01 2022
% 1.64/1.83 The command was "./otter". The process ID is 8142.
% 1.64/1.83
% 1.64/1.83 set(prolog_style_variables).
% 1.64/1.83 set(auto).
% 1.64/1.83 dependent: set(auto1).
% 1.64/1.83 dependent: set(process_input).
% 1.64/1.83 dependent: clear(print_kept).
% 1.64/1.83 dependent: clear(print_new_demod).
% 1.64/1.83 dependent: clear(print_back_demod).
% 1.64/1.83 dependent: clear(print_back_sub).
% 1.64/1.83 dependent: set(control_memory).
% 1.64/1.83 dependent: assign(max_mem, 12000).
% 1.64/1.83 dependent: assign(pick_given_ratio, 4).
% 1.64/1.83 dependent: assign(stats_level, 1).
% 1.64/1.83 dependent: assign(max_seconds, 10800).
% 1.64/1.83 clear(print_given).
% 1.64/1.83
% 1.64/1.83 formula_list(usable).
% 1.64/1.83 all A (A=A).
% 1.64/1.83 all X Y (subclass(X,Y)<-> (all U (member(U,X)->member(U,Y)))).
% 1.64/1.83 all X subclass(X,universal_class).
% 1.64/1.83 all X Y (X=Y<->subclass(X,Y)&subclass(Y,X)).
% 1.64/1.83 all U X Y (member(U,unordered_pair(X,Y))<->member(U,universal_class)& (U=X|U=Y)).
% 1.64/1.83 all X Y member(unordered_pair(X,Y),universal_class).
% 1.64/1.83 all X (singleton(X)=unordered_pair(X,X)).
% 1.64/1.83 all X Y (ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))).
% 1.64/1.83 all U V X Y (member(ordered_pair(U,V),cross_product(X,Y))<->member(U,X)&member(V,Y)).
% 1.64/1.83 all X Y (member(X,universal_class)&member(Y,universal_class)->first(ordered_pair(X,Y))=X&second(ordered_pair(X,Y))=Y).
% 1.64/1.83 all X Y Z (member(Z,cross_product(X,Y))->Z=ordered_pair(first(Z),second(Z))).
% 1.64/1.83 all X Y (member(ordered_pair(X,Y),element_relation)<->member(Y,universal_class)&member(X,Y)).
% 1.64/1.83 subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.64/1.83 all X Y Z (member(Z,intersection(X,Y))<->member(Z,X)&member(Z,Y)).
% 1.64/1.83 all X Z (member(Z,complement(X))<->member(Z,universal_class)& -member(Z,X)).
% 1.64/1.83 all X XR Y (restrict(XR,X,Y)=intersection(XR,cross_product(X,Y))).
% 1.64/1.83 all X (-member(X,null_class)).
% 1.64/1.83 all X Z (member(Z,domain_of(X))<->member(Z,universal_class)&restrict(X,singleton(Z),universal_class)!=null_class).
% 1.64/1.83 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)).
% 1.64/1.83 all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.83 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)).
% 1.64/1.83 all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.83 all X Y Z (member(Z,union(X,Y))<->member(Z,X)|member(Z,Y)).
% 1.64/1.83 all X (successor(X)=union(X,singleton(X))).
% 1.64/1.83 subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.64/1.83 all X Y (member(ordered_pair(X,Y),successor_relation)<->member(X,universal_class)&member(Y,universal_class)&successor(X)=Y).
% 1.64/1.83 all Y (inverse(Y)=domain_of(flip(cross_product(Y,universal_class)))).
% 1.64/1.83 all Z (range_of(Z)=domain_of(inverse(Z))).
% 1.64/1.83 all X XR (image(XR,X)=range_of(restrict(XR,X,universal_class))).
% 1.64/1.83 all X (inductive(X)<->member(null_class,X)&subclass(image(successor_relation,X),X)).
% 1.64/1.83 exists X (member(X,universal_class)&inductive(X)& (all Y (inductive(Y)->subclass(X,Y)))).
% 1.64/1.83 all U X (member(U,sum_class(X))<-> (exists Y (member(U,Y)&member(Y,X)))).
% 1.64/1.83 all X (member(X,universal_class)->member(sum_class(X),universal_class)).
% 1.64/1.83 all U X (member(U,power_class(X))<->member(U,universal_class)&subclass(U,X)).
% 1.64/1.83 all U (member(U,universal_class)->member(power_class(U),universal_class)).
% 1.64/1.83 all XR YR subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.64/1.83 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))))).
% 1.64/1.83 all Z (member(Z,identity_relation)<-> (exists X (member(X,universal_class)&Z=ordered_pair(X,X)))).
% 1.64/1.83 all XF (function(XF)<->subclass(XF,cross_product(universal_class,universal_class))&subclass(compose(XF,inverse(XF)),identity_relation)).
% 1.64/1.83 all X XF (member(X,universal_class)&function(XF)->member(image(XF,X),universal_class)).
% 1.64/1.83 all X Y (disjoint(X,Y)<-> (all U (-(member(U,X)&member(U,Y))))).
% 1.64/1.83 all X (X!=null_class-> (exists U (member(U,universal_class)&member(U,X)&disjoint(U,X)))).
% 1.64/1.83 all XF Y (apply(XF,Y)=sum_class(image(XF,singleton(Y)))).
% 1.64/1.83 exists XF (function(XF)& (all Y (member(Y,universal_class)->Y=null_class|member(apply(XF,Y),Y)))).
% 1.64/1.83 -(all X (ordered_pair(first(X),second(X))=X->member(X,universal_class))).
% 1.64/1.83 end_of_list.
% 1.64/1.83
% 1.64/1.83 -------> usable clausifies to:
% 1.64/1.83
% 1.64/1.83 list(usable).
% 1.64/1.83 0 [] A=A.
% 1.64/1.83 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 1.64/1.83 0 [] subclass(X,Y)|member($f1(X,Y),X).
% 1.64/1.83 0 [] subclass(X,Y)| -member($f1(X,Y),Y).
% 1.64/1.83 0 [] subclass(X,universal_class).
% 1.64/1.83 0 [] X!=Y|subclass(X,Y).
% 1.64/1.83 0 [] X!=Y|subclass(Y,X).
% 1.64/1.83 0 [] X=Y| -subclass(X,Y)| -subclass(Y,X).
% 1.64/1.83 0 [] -member(U,unordered_pair(X,Y))|member(U,universal_class).
% 1.64/1.83 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 1.64/1.83 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=X.
% 1.64/1.83 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=Y.
% 1.64/1.83 0 [] member(unordered_pair(X,Y),universal_class).
% 1.64/1.83 0 [] singleton(X)=unordered_pair(X,X).
% 1.64/1.83 0 [] ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y))).
% 1.64/1.83 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 1.64/1.83 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 1.64/1.83 0 [] member(ordered_pair(U,V),cross_product(X,Y))| -member(U,X)| -member(V,Y).
% 1.64/1.83 0 [] -member(X,universal_class)| -member(Y,universal_class)|first(ordered_pair(X,Y))=X.
% 1.64/1.83 0 [] -member(X,universal_class)| -member(Y,universal_class)|second(ordered_pair(X,Y))=Y.
% 1.64/1.83 0 [] -member(Z,cross_product(X,Y))|Z=ordered_pair(first(Z),second(Z)).
% 1.64/1.83 0 [] -member(ordered_pair(X,Y),element_relation)|member(Y,universal_class).
% 1.64/1.83 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 1.64/1.83 0 [] member(ordered_pair(X,Y),element_relation)| -member(Y,universal_class)| -member(X,Y).
% 1.64/1.83 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.64/1.83 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 1.64/1.83 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 1.64/1.83 0 [] member(Z,intersection(X,Y))| -member(Z,X)| -member(Z,Y).
% 1.64/1.83 0 [] -member(Z,complement(X))|member(Z,universal_class).
% 1.64/1.83 0 [] -member(Z,complement(X))| -member(Z,X).
% 1.64/1.83 0 [] member(Z,complement(X))| -member(Z,universal_class)|member(Z,X).
% 1.64/1.83 0 [] restrict(XR,X,Y)=intersection(XR,cross_product(X,Y)).
% 1.64/1.83 0 [] -member(X,null_class).
% 1.64/1.83 0 [] -member(Z,domain_of(X))|member(Z,universal_class).
% 1.64/1.83 0 [] -member(Z,domain_of(X))|restrict(X,singleton(Z),universal_class)!=null_class.
% 1.64/1.83 0 [] member(Z,domain_of(X))| -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class.
% 1.64/1.83 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)).
% 1.64/1.83 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 1.64/1.83 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).
% 1.64/1.83 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.83 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)).
% 1.64/1.83 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 1.64/1.83 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).
% 1.64/1.83 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.83 0 [] -member(Z,union(X,Y))|member(Z,X)|member(Z,Y).
% 1.64/1.83 0 [] member(Z,union(X,Y))| -member(Z,X).
% 1.64/1.83 0 [] member(Z,union(X,Y))| -member(Z,Y).
% 1.64/1.83 0 [] successor(X)=union(X,singleton(X)).
% 1.64/1.83 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.64/1.83 0 [] -member(ordered_pair(X,Y),successor_relation)|member(X,universal_class).
% 1.64/1.83 0 [] -member(ordered_pair(X,Y),successor_relation)|member(Y,universal_class).
% 1.64/1.83 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 1.64/1.83 0 [] member(ordered_pair(X,Y),successor_relation)| -member(X,universal_class)| -member(Y,universal_class)|successor(X)!=Y.
% 1.64/1.83 0 [] inverse(Y)=domain_of(flip(cross_product(Y,universal_class))).
% 1.64/1.83 0 [] range_of(Z)=domain_of(inverse(Z)).
% 1.64/1.83 0 [] image(XR,X)=range_of(restrict(XR,X,universal_class)).
% 1.64/1.83 0 [] -inductive(X)|member(null_class,X).
% 1.64/1.83 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 1.64/1.83 0 [] inductive(X)| -member(null_class,X)| -subclass(image(successor_relation,X),X).
% 1.64/1.83 0 [] member($c1,universal_class).
% 1.64/1.83 0 [] inductive($c1).
% 1.64/1.83 0 [] -inductive(Y)|subclass($c1,Y).
% 1.64/1.83 0 [] -member(U,sum_class(X))|member(U,$f2(U,X)).
% 1.64/1.83 0 [] -member(U,sum_class(X))|member($f2(U,X),X).
% 1.64/1.83 0 [] member(U,sum_class(X))| -member(U,Y)| -member(Y,X).
% 1.64/1.83 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 1.64/1.83 0 [] -member(U,power_class(X))|member(U,universal_class).
% 1.64/1.83 0 [] -member(U,power_class(X))|subclass(U,X).
% 1.64/1.83 0 [] member(U,power_class(X))| -member(U,universal_class)| -subclass(U,X).
% 1.64/1.83 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 1.64/1.83 0 [] subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.64/1.83 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(U,universal_class).
% 1.64/1.83 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(V,image(YR,image(XR,singleton(U)))).
% 1.64/1.83 0 [] member(ordered_pair(U,V),compose(YR,XR))| -member(U,universal_class)| -member(V,image(YR,image(XR,singleton(U)))).
% 1.64/1.83 0 [] -member(Z,identity_relation)|member($f3(Z),universal_class).
% 1.64/1.83 0 [] -member(Z,identity_relation)|Z=ordered_pair($f3(Z),$f3(Z)).
% 1.64/1.83 0 [] member(Z,identity_relation)| -member(X,universal_class)|Z!=ordered_pair(X,X).
% 1.64/1.83 0 [] -function(XF)|subclass(XF,cross_product(universal_class,universal_class)).
% 1.64/1.83 0 [] -function(XF)|subclass(compose(XF,inverse(XF)),identity_relation).
% 1.64/1.83 0 [] function(XF)| -subclass(XF,cross_product(universal_class,universal_class))| -subclass(compose(XF,inverse(XF)),identity_relation).
% 1.64/1.83 0 [] -member(X,universal_class)| -function(XF)|member(image(XF,X),universal_class).
% 1.64/1.83 0 [] -disjoint(X,Y)| -member(U,X)| -member(U,Y).
% 1.64/1.83 0 [] disjoint(X,Y)|member($f4(X,Y),X).
% 1.64/1.83 0 [] disjoint(X,Y)|member($f4(X,Y),Y).
% 1.64/1.83 0 [] X=null_class|member($f5(X),universal_class).
% 1.64/1.83 0 [] X=null_class|member($f5(X),X).
% 1.64/1.83 0 [] X=null_class|disjoint($f5(X),X).
% 1.64/1.83 0 [] apply(XF,Y)=sum_class(image(XF,singleton(Y))).
% 1.64/1.83 0 [] function($c2).
% 1.64/1.83 0 [] -member(Y,universal_class)|Y=null_class|member(apply($c2,Y),Y).
% 1.64/1.83 0 [] ordered_pair(first($c3),second($c3))=$c3.
% 1.64/1.83 0 [] -member($c3,universal_class).
% 1.64/1.83 end_of_list.
% 1.64/1.83
% 1.64/1.83 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.64/1.83
% 1.64/1.83 This ia a non-Horn set with equality. The strategy will be
% 1.64/1.83 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.64/1.83 deletion, with positive clauses in sos and nonpositive
% 1.64/1.83 clauses in usable.
% 1.64/1.83
% 1.64/1.83 dependent: set(knuth_bendix).
% 1.64/1.83 dependent: set(anl_eq).
% 1.64/1.83 dependent: set(para_from).
% 1.64/1.83 dependent: set(para_into).
% 1.64/1.83 dependent: clear(para_from_right).
% 1.64/1.83 dependent: clear(para_into_right).
% 1.64/1.83 dependent: set(para_from_vars).
% 1.64/1.83 dependent: set(eq_units_both_ways).
% 1.64/1.83 dependent: set(dynamic_demod_all).
% 1.64/1.83 dependent: set(dynamic_demod).
% 1.64/1.83 dependent: set(order_eq).
% 1.64/1.83 dependent: set(back_demod).
% 1.64/1.83 dependent: set(lrpo).
% 1.64/1.83 dependent: set(hyper_res).
% 1.64/1.83 dependent: set(unit_deletion).
% 1.64/1.83 dependent: set(factor).
% 1.64/1.83
% 1.64/1.83 ------------> process usable:
% 1.64/1.83 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 1.64/1.83 ** KEPT (pick-wt=8): 2 [] subclass(A,B)| -member($f1(A,B),B).
% 1.64/1.83 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 1.64/1.83 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 1.64/1.83 ** KEPT (pick-wt=9): 5 [] A=B| -subclass(A,B)| -subclass(B,A).
% 1.64/1.83 ** KEPT (pick-wt=8): 6 [] -member(A,unordered_pair(B,C))|member(A,universal_class).
% 1.64/1.83 ** KEPT (pick-wt=11): 7 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 1.64/1.83 ** KEPT (pick-wt=11): 8 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=B.
% 1.64/1.83 ** KEPT (pick-wt=11): 9 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=C.
% 1.64/1.83 ** 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=3): 68 [] -member($c3,universal_class).
% 1.64/1.84
% 1.64/1.84 ------------> process sos:
% 1.64/1.84 ** KEPT (pick-wt=3): 82 [] A=A.
% 1.64/1.84 ** KEPT (pick-wt=8): 83 [] subclass(A,B)|member($f1(A,B),A).
% 1.64/1.84 ** KEPT (pick-wt=3): 84 [] subclass(A,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=5): 85 [] member(unordered_pair(A,B),universal_class).
% 1.64/1.84 ** KEPT (pick-wt=6): 86 [] singleton(A)=unordered_pair(A,A).
% 1.64/1.84 ---> New Demodulator: 87 [new_demod,86] singleton(A)=unordered_pair(A,A).
% 1.64/1.84 ** KEPT (pick-wt=13): 89 [copy,88,demod,87,87,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: 90 [new_demod,89] 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): 91 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=10): 93 [copy,92,flip.1] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.64/1.84 ---> New Demodulator: 94 [new_demod,93] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.64/1.84 ** KEPT (pick-wt=8): 95 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 96 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 98 [copy,97,demod,87] successor(A)=union(A,unordered_pair(A,A)).
% 1.64/1.84 ---> New Demodulator: 99 [new_demod,98] successor(A)=union(A,unordered_pair(A,A)).
% 1.64/1.84 ** KEPT (pick-wt=5): 100 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 101 [] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.64/1.84 ---> New Demodulator: 102 [new_demod,101] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.64/1.84 ** KEPT (pick-wt=9): 104 [copy,103,demod,102] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 1.64/1.84 ---> New Demodulator: 105 [new_demod,104] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 1.64/1.84 ** KEPT (pick-wt=13): 107 [copy,106,demod,105,flip.1] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 1.64/1.84 ---> New Demodulator: 108 [new_demod,107] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 1.64/1.84 ** KEPT (pick-wt=3): 109 [] member($c1,universal_class).
% 1.64/1.84 ** KEPT (pick-wt=2): 110 [] inductive($c1).
% 1.64/1.84 ** KEPT (pick-wt=7): 111 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 1.64/1.84 ** KEPT (pick-wt=8): 112 [] disjoint(A,B)|member($f4(A,B),A).
% 1.64/1.84 ** KEPT (pick-wt=8): 113 [] disjoint(A,B)|member($f4(A,B),B).
% 1.64/1.88 ** KEPT (pick-wt=7): 114 [] A=null_class|member($f5(A),universal_class).
% 1.64/1.88 ** KEPT (pick-wt=7): 115 [] A=null_class|member($f5(A),A).
% 1.64/1.88 ** KEPT (pick-wt=7): 116 [] A=null_class|disjoint($f5(A),A).
% 1.64/1.88 ** KEPT (pick-wt=10): 118 [copy,117,demod,87,flip.1] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 1.64/1.88 ---> New Demodulator: 119 [new_demod,118] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 1.64/1.88 ** KEPT (pick-wt=2): 120 [] function($c2).
% 1.64/1.88 ** KEPT (pick-wt=7): 121 [] ordered_pair(first($c3),second($c3))=$c3.
% 1.64/1.88 ---> New Demodulator: 122 [new_demod,121] ordered_pair(first($c3),second($c3))=$c3.
% 1.64/1.88 Following clause subsumed by 82 during input processing: 0 [copy,82,flip.1] A=A.
% 1.64/1.88 82 back subsumes 69.
% 1.64/1.88 >>>> Starting back demodulation with 87.
% 1.64/1.88 >> back demodulating 57 with 87.
% 1.64/1.88 >> back demodulating 56 with 87.
% 1.64/1.88 >> back demodulating 29 with 87.
% 1.64/1.88 >> back demodulating 28 with 87.
% 1.64/1.88 >>>> Starting back demodulation with 90.
% 1.64/1.88 >>>> Starting back demodulation with 94.
% 1.64/1.88 >>>> Starting back demodulation with 99.
% 1.64/1.88 >> back demodulating 79 with 99.
% 1.64/1.88 >> back demodulating 42 with 99.
% 1.64/1.88 >> back demodulating 41 with 99.
% 1.64/1.88 >>>> Starting back demodulation with 102.
% 1.64/1.88 >> back demodulating 64 with 102.
% 1.64/1.88 >> back demodulating 63 with 102.
% 1.64/1.88 >>>> Starting back demodulation with 105.
% 1.64/1.88 >>>> Starting back demodulation with 108.
% 1.64/1.88 >>>> Starting back demodulation with 119.
% 1.64/1.88 >>>> Starting back demodulation with 122.
% 1.64/1.88
% 1.64/1.88 ======= end of input processing =======
% 1.64/1.88
% 1.64/1.88 =========== start of search ===========
% 1.64/1.88
% 1.64/1.88
% 1.64/1.88 Resetting weight limit to 6.
% 1.64/1.88
% 1.64/1.88
% 1.64/1.88 Resetting weight limit to 6.
% 1.64/1.88
% 1.64/1.88 sos_size=1020
% 1.64/1.88
% 1.64/1.88 -------- PROOF --------
% 1.64/1.88
% 1.64/1.88 ----> UNIT CONFLICT at 0.05 sec ----> 1464 [binary,1463.1,68.1] $F.
% 1.64/1.88
% 1.64/1.88 Length of proof is 3. Level of proof is 3.
% 1.64/1.88
% 1.64/1.88 ---------------- PROOF ----------------
% 1.64/1.88 % SZS status Theorem
% 1.64/1.88 % SZS output start Refutation
% See solution above
% 1.64/1.88 ------------ end of proof -------------
% 1.64/1.88
% 1.64/1.88
% 1.64/1.88 Search stopped by max_proofs option.
% 1.64/1.88
% 1.64/1.88
% 1.64/1.88 Search stopped by max_proofs option.
% 1.64/1.88
% 1.64/1.88 ============ end of search ============
% 1.64/1.88
% 1.64/1.88 -------------- statistics -------------
% 1.64/1.88 clauses given 103
% 1.64/1.88 clauses generated 10308
% 1.64/1.88 clauses kept 1311
% 1.64/1.88 clauses forward subsumed 707
% 1.64/1.88 clauses back subsumed 20
% 1.64/1.88 Kbytes malloced 4882
% 1.64/1.88
% 1.64/1.88 ----------- times (seconds) -----------
% 1.64/1.88 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.64/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.64/1.88
% 1.64/1.88 That finishes the proof of the theorem.
% 1.64/1.88
% 1.64/1.88 Process 8142 finished Wed Jul 27 10:19:02 2022
% 1.64/1.88 Otter interrupted
% 1.64/1.88 PROOF FOUND
%------------------------------------------------------------------------------