TSTP Solution File: SET064+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET064+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:12:58 EDT 2022
% Result : Theorem 1.97s 2.13s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 7 unt; 3 nHn; 7 RR)
% Number of literals : 18 ( 4 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(66,axiom,
( ~ disjoint(A,B)
| ~ member(C,A)
| ~ member(C,B) ),
file('SET064+1.p',unknown),
[] ).
cnf(68,axiom,
dollar_c3 != null_class,
file('SET064+1.p',unknown),
[] ).
cnf(69,plain,
null_class != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[68])]),
[iquote('copy,68,flip.1')] ).
cnf(70,axiom,
~ member(A,dollar_c3),
file('SET064+1.p',unknown),
[] ).
cnf(83,plain,
( ~ disjoint(A,A)
| ~ member(B,A) ),
inference(factor,[status(thm)],[66]),
[iquote('factor,66.2.3')] ).
cnf(114,axiom,
( disjoint(A,B)
| member(dollar_f4(A,B),A) ),
file('SET064+1.p',unknown),
[] ).
cnf(115,axiom,
( disjoint(A,B)
| member(dollar_f4(A,B),B) ),
file('SET064+1.p',unknown),
[] ).
cnf(117,axiom,
( A = null_class
| member(dollar_f5(A),A) ),
file('SET064+1.p',unknown),
[] ).
cnf(1389,plain,
disjoint(dollar_c3,A),
inference(hyper,[status(thm)],[114,70]),
[iquote('hyper,114,70')] ).
cnf(1396,plain,
disjoint(A,dollar_c3),
inference(hyper,[status(thm)],[115,83,1389]),
[iquote('hyper,115,83,1389')] ).
cnf(1456,plain,
null_class = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[117,83,1396])]),
[iquote('hyper,117,83,1396,flip.1')] ).
cnf(1458,plain,
$false,
inference(binary,[status(thm)],[1456,69]),
[iquote('binary,1456.1,69.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET064+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.04/0.14 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 10:41:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.87/2.05 ----- Otter 3.3f, August 2004 -----
% 1.87/2.05 The process was started by sandbox2 on n022.cluster.edu,
% 1.87/2.05 Wed Jul 27 10:41:35 2022
% 1.87/2.05 The command was "./otter". The process ID is 19610.
% 1.87/2.05
% 1.87/2.05 set(prolog_style_variables).
% 1.87/2.05 set(auto).
% 1.87/2.05 dependent: set(auto1).
% 1.87/2.05 dependent: set(process_input).
% 1.87/2.05 dependent: clear(print_kept).
% 1.87/2.05 dependent: clear(print_new_demod).
% 1.87/2.05 dependent: clear(print_back_demod).
% 1.87/2.05 dependent: clear(print_back_sub).
% 1.87/2.05 dependent: set(control_memory).
% 1.87/2.05 dependent: assign(max_mem, 12000).
% 1.87/2.05 dependent: assign(pick_given_ratio, 4).
% 1.87/2.05 dependent: assign(stats_level, 1).
% 1.87/2.05 dependent: assign(max_seconds, 10800).
% 1.87/2.05 clear(print_given).
% 1.87/2.05
% 1.87/2.05 formula_list(usable).
% 1.87/2.05 all A (A=A).
% 1.87/2.05 all X Y (subclass(X,Y)<-> (all U (member(U,X)->member(U,Y)))).
% 1.87/2.05 all X subclass(X,universal_class).
% 1.87/2.05 all X Y (X=Y<->subclass(X,Y)&subclass(Y,X)).
% 1.87/2.05 all U X Y (member(U,unordered_pair(X,Y))<->member(U,universal_class)& (U=X|U=Y)).
% 1.87/2.05 all X Y member(unordered_pair(X,Y),universal_class).
% 1.87/2.05 all X (singleton(X)=unordered_pair(X,X)).
% 1.87/2.05 all X Y (ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))).
% 1.87/2.05 all U V X Y (member(ordered_pair(U,V),cross_product(X,Y))<->member(U,X)&member(V,Y)).
% 1.87/2.05 all X Y (member(X,universal_class)&member(Y,universal_class)->first(ordered_pair(X,Y))=X&second(ordered_pair(X,Y))=Y).
% 1.87/2.05 all X Y Z (member(Z,cross_product(X,Y))->Z=ordered_pair(first(Z),second(Z))).
% 1.87/2.05 all X Y (member(ordered_pair(X,Y),element_relation)<->member(Y,universal_class)&member(X,Y)).
% 1.87/2.05 subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.87/2.05 all X Y Z (member(Z,intersection(X,Y))<->member(Z,X)&member(Z,Y)).
% 1.87/2.05 all X Z (member(Z,complement(X))<->member(Z,universal_class)& -member(Z,X)).
% 1.87/2.05 all X XR Y (restrict(XR,X,Y)=intersection(XR,cross_product(X,Y))).
% 1.87/2.05 all X (-member(X,null_class)).
% 1.87/2.05 all X Z (member(Z,domain_of(X))<->member(Z,universal_class)&restrict(X,singleton(Z),universal_class)!=null_class).
% 1.87/2.05 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)).
% 1.87/2.05 all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.87/2.05 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)).
% 1.87/2.05 all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.87/2.05 all X Y Z (member(Z,union(X,Y))<->member(Z,X)|member(Z,Y)).
% 1.87/2.05 all X (successor(X)=union(X,singleton(X))).
% 1.87/2.05 subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.87/2.05 all X Y (member(ordered_pair(X,Y),successor_relation)<->member(X,universal_class)&member(Y,universal_class)&successor(X)=Y).
% 1.87/2.05 all Y (inverse(Y)=domain_of(flip(cross_product(Y,universal_class)))).
% 1.87/2.05 all Z (range_of(Z)=domain_of(inverse(Z))).
% 1.87/2.05 all X XR (image(XR,X)=range_of(restrict(XR,X,universal_class))).
% 1.87/2.05 all X (inductive(X)<->member(null_class,X)&subclass(image(successor_relation,X),X)).
% 1.87/2.05 exists X (member(X,universal_class)&inductive(X)& (all Y (inductive(Y)->subclass(X,Y)))).
% 1.87/2.05 all U X (member(U,sum_class(X))<-> (exists Y (member(U,Y)&member(Y,X)))).
% 1.87/2.05 all X (member(X,universal_class)->member(sum_class(X),universal_class)).
% 1.87/2.05 all U X (member(U,power_class(X))<->member(U,universal_class)&subclass(U,X)).
% 1.87/2.05 all U (member(U,universal_class)->member(power_class(U),universal_class)).
% 1.87/2.05 all XR YR subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.87/2.05 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))))).
% 1.87/2.05 all Z (member(Z,identity_relation)<-> (exists X (member(X,universal_class)&Z=ordered_pair(X,X)))).
% 1.87/2.05 all XF (function(XF)<->subclass(XF,cross_product(universal_class,universal_class))&subclass(compose(XF,inverse(XF)),identity_relation)).
% 1.87/2.05 all X XF (member(X,universal_class)&function(XF)->member(image(XF,X),universal_class)).
% 1.87/2.05 all X Y (disjoint(X,Y)<-> (all U (-(member(U,X)&member(U,Y))))).
% 1.87/2.05 all X (X!=null_class-> (exists U (member(U,universal_class)&member(U,X)&disjoint(U,X)))).
% 1.87/2.05 all XF Y (apply(XF,Y)=sum_class(image(XF,singleton(Y)))).
% 1.87/2.05 exists XF (function(XF)& (all Y (member(Y,universal_class)->Y=null_class|member(apply(XF,Y),Y)))).
% 1.87/2.05 -(all Z (Z=null_class| (exists Y member(Y,Z)))).
% 1.87/2.05 end_of_list.
% 1.87/2.05
% 1.87/2.05 -------> usable clausifies to:
% 1.87/2.05
% 1.87/2.05 list(usable).
% 1.87/2.05 0 [] A=A.
% 1.87/2.05 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 1.87/2.05 0 [] subclass(X,Y)|member($f1(X,Y),X).
% 1.87/2.05 0 [] subclass(X,Y)| -member($f1(X,Y),Y).
% 1.87/2.05 0 [] subclass(X,universal_class).
% 1.87/2.05 0 [] X!=Y|subclass(X,Y).
% 1.87/2.05 0 [] X!=Y|subclass(Y,X).
% 1.87/2.05 0 [] X=Y| -subclass(X,Y)| -subclass(Y,X).
% 1.87/2.05 0 [] -member(U,unordered_pair(X,Y))|member(U,universal_class).
% 1.87/2.05 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 1.87/2.05 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=X.
% 1.87/2.05 0 [] member(U,unordered_pair(X,Y))| -member(U,universal_class)|U!=Y.
% 1.87/2.05 0 [] member(unordered_pair(X,Y),universal_class).
% 1.87/2.05 0 [] singleton(X)=unordered_pair(X,X).
% 1.87/2.05 0 [] ordered_pair(X,Y)=unordered_pair(singleton(X),unordered_pair(X,singleton(Y))).
% 1.87/2.05 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 1.87/2.05 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 1.87/2.05 0 [] member(ordered_pair(U,V),cross_product(X,Y))| -member(U,X)| -member(V,Y).
% 1.87/2.05 0 [] -member(X,universal_class)| -member(Y,universal_class)|first(ordered_pair(X,Y))=X.
% 1.87/2.05 0 [] -member(X,universal_class)| -member(Y,universal_class)|second(ordered_pair(X,Y))=Y.
% 1.87/2.05 0 [] -member(Z,cross_product(X,Y))|Z=ordered_pair(first(Z),second(Z)).
% 1.87/2.05 0 [] -member(ordered_pair(X,Y),element_relation)|member(Y,universal_class).
% 1.87/2.05 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 1.87/2.05 0 [] member(ordered_pair(X,Y),element_relation)| -member(Y,universal_class)| -member(X,Y).
% 1.87/2.05 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.87/2.05 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 1.87/2.05 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 1.87/2.05 0 [] member(Z,intersection(X,Y))| -member(Z,X)| -member(Z,Y).
% 1.87/2.05 0 [] -member(Z,complement(X))|member(Z,universal_class).
% 1.87/2.05 0 [] -member(Z,complement(X))| -member(Z,X).
% 1.87/2.05 0 [] member(Z,complement(X))| -member(Z,universal_class)|member(Z,X).
% 1.87/2.05 0 [] restrict(XR,X,Y)=intersection(XR,cross_product(X,Y)).
% 1.87/2.05 0 [] -member(X,null_class).
% 1.87/2.05 0 [] -member(Z,domain_of(X))|member(Z,universal_class).
% 1.87/2.05 0 [] -member(Z,domain_of(X))|restrict(X,singleton(Z),universal_class)!=null_class.
% 1.87/2.05 0 [] member(Z,domain_of(X))| -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class.
% 1.87/2.05 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)).
% 1.87/2.05 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 1.87/2.05 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).
% 1.87/2.05 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.87/2.05 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)).
% 1.87/2.05 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 1.87/2.05 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).
% 1.87/2.05 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.87/2.05 0 [] -member(Z,union(X,Y))|member(Z,X)|member(Z,Y).
% 1.87/2.05 0 [] member(Z,union(X,Y))| -member(Z,X).
% 1.87/2.05 0 [] member(Z,union(X,Y))| -member(Z,Y).
% 1.87/2.05 0 [] successor(X)=union(X,singleton(X)).
% 1.87/2.05 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.87/2.05 0 [] -member(ordered_pair(X,Y),successor_relation)|member(X,universal_class).
% 1.87/2.05 0 [] -member(ordered_pair(X,Y),successor_relation)|member(Y,universal_class).
% 1.87/2.05 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 1.87/2.05 0 [] member(ordered_pair(X,Y),successor_relation)| -member(X,universal_class)| -member(Y,universal_class)|successor(X)!=Y.
% 1.87/2.05 0 [] inverse(Y)=domain_of(flip(cross_product(Y,universal_class))).
% 1.87/2.05 0 [] range_of(Z)=domain_of(inverse(Z)).
% 1.87/2.05 0 [] image(XR,X)=range_of(restrict(XR,X,universal_class)).
% 1.87/2.05 0 [] -inductive(X)|member(null_class,X).
% 1.87/2.05 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 1.87/2.05 0 [] inductive(X)| -member(null_class,X)| -subclass(image(successor_relation,X),X).
% 1.87/2.05 0 [] member($c1,universal_class).
% 1.87/2.05 0 [] inductive($c1).
% 1.87/2.05 0 [] -inductive(Y)|subclass($c1,Y).
% 1.87/2.05 0 [] -member(U,sum_class(X))|member(U,$f2(U,X)).
% 1.87/2.05 0 [] -member(U,sum_class(X))|member($f2(U,X),X).
% 1.87/2.05 0 [] member(U,sum_class(X))| -member(U,Y)| -member(Y,X).
% 1.87/2.05 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 1.87/2.05 0 [] -member(U,power_class(X))|member(U,universal_class).
% 1.87/2.05 0 [] -member(U,power_class(X))|subclass(U,X).
% 1.87/2.05 0 [] member(U,power_class(X))| -member(U,universal_class)| -subclass(U,X).
% 1.87/2.05 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 1.87/2.05 0 [] subclass(compose(YR,XR),cross_product(universal_class,universal_class)).
% 1.87/2.05 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(U,universal_class).
% 1.87/2.05 0 [] -member(ordered_pair(U,V),compose(YR,XR))|member(V,image(YR,image(XR,singleton(U)))).
% 1.87/2.05 0 [] member(ordered_pair(U,V),compose(YR,XR))| -member(U,universal_class)| -member(V,image(YR,image(XR,singleton(U)))).
% 1.87/2.05 0 [] -member(Z,identity_relation)|member($f3(Z),universal_class).
% 1.87/2.05 0 [] -member(Z,identity_relation)|Z=ordered_pair($f3(Z),$f3(Z)).
% 1.87/2.05 0 [] member(Z,identity_relation)| -member(X,universal_class)|Z!=ordered_pair(X,X).
% 1.87/2.05 0 [] -function(XF)|subclass(XF,cross_product(universal_class,universal_class)).
% 1.87/2.05 0 [] -function(XF)|subclass(compose(XF,inverse(XF)),identity_relation).
% 1.87/2.05 0 [] function(XF)| -subclass(XF,cross_product(universal_class,universal_class))| -subclass(compose(XF,inverse(XF)),identity_relation).
% 1.87/2.05 0 [] -member(X,universal_class)| -function(XF)|member(image(XF,X),universal_class).
% 1.87/2.05 0 [] -disjoint(X,Y)| -member(U,X)| -member(U,Y).
% 1.87/2.05 0 [] disjoint(X,Y)|member($f4(X,Y),X).
% 1.87/2.05 0 [] disjoint(X,Y)|member($f4(X,Y),Y).
% 1.87/2.05 0 [] X=null_class|member($f5(X),universal_class).
% 1.87/2.05 0 [] X=null_class|member($f5(X),X).
% 1.87/2.05 0 [] X=null_class|disjoint($f5(X),X).
% 1.87/2.05 0 [] apply(XF,Y)=sum_class(image(XF,singleton(Y))).
% 1.87/2.05 0 [] function($c2).
% 1.87/2.05 0 [] -member(Y,universal_class)|Y=null_class|member(apply($c2,Y),Y).
% 1.87/2.05 0 [] $c3!=null_class.
% 1.87/2.05 0 [] -member(Y,$c3).
% 1.87/2.05 end_of_list.
% 1.87/2.05
% 1.87/2.05 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.87/2.05
% 1.87/2.05 This ia a non-Horn set with equality. The strategy will be
% 1.87/2.05 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.87/2.05 deletion, with positive clauses in sos and nonpositive
% 1.87/2.05 clauses in usable.
% 1.87/2.05
% 1.87/2.05 dependent: set(knuth_bendix).
% 1.87/2.05 dependent: set(anl_eq).
% 1.87/2.05 dependent: set(para_from).
% 1.87/2.05 dependent: set(para_into).
% 1.87/2.05 dependent: clear(para_from_right).
% 1.87/2.05 dependent: clear(para_into_right).
% 1.87/2.05 dependent: set(para_from_vars).
% 1.87/2.05 dependent: set(eq_units_both_ways).
% 1.87/2.05 dependent: set(dynamic_demod_all).
% 1.87/2.05 dependent: set(dynamic_demod).
% 1.87/2.05 dependent: set(order_eq).
% 1.87/2.05 dependent: set(back_demod).
% 1.87/2.05 dependent: set(lrpo).
% 1.87/2.05 dependent: set(hyper_res).
% 1.87/2.05 dependent: set(unit_deletion).
% 1.87/2.05 dependent: set(factor).
% 1.87/2.05
% 1.87/2.05 ------------> process usable:
% 1.87/2.05 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 1.87/2.05 ** KEPT (pick-wt=8): 2 [] subclass(A,B)| -member($f1(A,B),B).
% 1.87/2.05 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 1.87/2.05 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 1.87/2.05 ** KEPT (pick-wt=9): 5 [] A=B| -subclass(A,B)| -subclass(B,A).
% 1.87/2.05 ** KEPT (pick-wt=8): 6 [] -member(A,unordered_pair(B,C))|member(A,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=11): 7 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 1.87/2.05 ** KEPT (pick-wt=11): 8 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=B.
% 1.87/2.05 ** KEPT (pick-wt=11): 9 [] member(A,unordered_pair(B,C))| -member(A,universal_class)|A!=C.
% 1.87/2.05 ** KEPT (pick-wt=10): 10 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 1.87/2.05 ** KEPT (pick-wt=10): 11 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 1.87/2.05 ** KEPT (pick-wt=13): 12 [] member(ordered_pair(A,B),cross_product(C,D))| -member(A,C)| -member(B,D).
% 1.87/2.05 ** KEPT (pick-wt=12): 13 [] -member(A,universal_class)| -member(B,universal_class)|first(ordered_pair(A,B))=A.
% 1.87/2.05 ** KEPT (pick-wt=12): 14 [] -member(A,universal_class)| -member(B,universal_class)|second(ordered_pair(A,B))=B.
% 1.87/2.05 ** KEPT (pick-wt=12): 16 [copy,15,flip.2] -member(A,cross_product(B,C))|ordered_pair(first(A),second(A))=A.
% 1.87/2.05 ** KEPT (pick-wt=8): 17 [] -member(ordered_pair(A,B),element_relation)|member(B,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=8): 18 [] -member(ordered_pair(A,B),element_relation)|member(A,B).
% 1.87/2.05 ** KEPT (pick-wt=11): 19 [] member(ordered_pair(A,B),element_relation)| -member(B,universal_class)| -member(A,B).
% 1.87/2.05 ** KEPT (pick-wt=8): 20 [] -member(A,intersection(B,C))|member(A,B).
% 1.87/2.05 ** KEPT (pick-wt=8): 21 [] -member(A,intersection(B,C))|member(A,C).
% 1.87/2.05 ** KEPT (pick-wt=11): 22 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.87/2.05 ** KEPT (pick-wt=7): 23 [] -member(A,complement(B))|member(A,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=7): 24 [] -member(A,complement(B))| -member(A,B).
% 1.87/2.05 ** KEPT (pick-wt=10): 25 [] member(A,complement(B))| -member(A,universal_class)|member(A,B).
% 1.87/2.05 ** KEPT (pick-wt=3): 26 [] -member(A,null_class).
% 1.87/2.05 ** KEPT (pick-wt=7): 27 [] -member(A,domain_of(B))|member(A,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=11): 28 [] -member(A,domain_of(B))|restrict(B,singleton(A),universal_class)!=null_class.
% 1.87/2.05 ** KEPT (pick-wt=14): 29 [] member(A,domain_of(B))| -member(A,universal_class)|restrict(B,singleton(A),universal_class)=null_class.
% 1.87/2.05 ** 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)).
% 1.87/2.05 ** KEPT (pick-wt=15): 31 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(B,C),A),D).
% 1.87/2.05 ** 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).
% 1.87/2.05 ** 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)).
% 1.87/2.05 ** KEPT (pick-wt=15): 34 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(B,A),C),D).
% 1.87/2.05 ** 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).
% 1.87/2.05 ** KEPT (pick-wt=11): 36 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.87/2.05 ** KEPT (pick-wt=8): 37 [] member(A,union(B,C))| -member(A,B).
% 1.87/2.05 ** KEPT (pick-wt=8): 38 [] member(A,union(B,C))| -member(A,C).
% 1.87/2.05 ** KEPT (pick-wt=8): 39 [] -member(ordered_pair(A,B),successor_relation)|member(A,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=8): 40 [] -member(ordered_pair(A,B),successor_relation)|member(B,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=9): 41 [] -member(ordered_pair(A,B),successor_relation)|successor(A)=B.
% 1.87/2.05 ** KEPT (pick-wt=15): 42 [] member(ordered_pair(A,B),successor_relation)| -member(A,universal_class)| -member(B,universal_class)|successor(A)!=B.
% 1.87/2.05 ** KEPT (pick-wt=5): 43 [] -inductive(A)|member(null_class,A).
% 1.87/2.05 ** KEPT (pick-wt=7): 44 [] -inductive(A)|subclass(image(successor_relation,A),A).
% 1.87/2.05 ** KEPT (pick-wt=10): 45 [] inductive(A)| -member(null_class,A)| -subclass(image(successor_relation,A),A).
% 1.87/2.05 ** KEPT (pick-wt=5): 46 [] -inductive(A)|subclass($c1,A).
% 1.87/2.05 ** KEPT (pick-wt=9): 47 [] -member(A,sum_class(B))|member(A,$f2(A,B)).
% 1.87/2.05 ** KEPT (pick-wt=9): 48 [] -member(A,sum_class(B))|member($f2(A,B),B).
% 1.87/2.05 ** KEPT (pick-wt=10): 49 [] member(A,sum_class(B))| -member(A,C)| -member(C,B).
% 1.87/2.05 ** KEPT (pick-wt=7): 50 [] -member(A,universal_class)|member(sum_class(A),universal_class).
% 1.87/2.05 ** KEPT (pick-wt=7): 51 [] -member(A,power_class(B))|member(A,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=7): 52 [] -member(A,power_class(B))|subclass(A,B).
% 1.87/2.05 ** KEPT (pick-wt=10): 53 [] member(A,power_class(B))| -member(A,universal_class)| -subclass(A,B).
% 1.87/2.05 ** KEPT (pick-wt=7): 54 [] -member(A,universal_class)|member(power_class(A),universal_class).
% 1.87/2.05 ** KEPT (pick-wt=10): 55 [] -member(ordered_pair(A,B),compose(C,D))|member(A,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=15): 56 [] -member(ordered_pair(A,B),compose(C,D))|member(B,image(C,image(D,singleton(A)))).
% 1.87/2.05 ** 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)))).
% 1.87/2.05 ** KEPT (pick-wt=7): 58 [] -member(A,identity_relation)|member($f3(A),universal_class).
% 1.87/2.05 ** KEPT (pick-wt=10): 60 [copy,59,flip.2] -member(A,identity_relation)|ordered_pair($f3(A),$f3(A))=A.
% 1.87/2.05 ** KEPT (pick-wt=11): 61 [] member(A,identity_relation)| -member(B,universal_class)|A!=ordered_pair(B,B).
% 1.87/2.05 ** KEPT (pick-wt=7): 62 [] -function(A)|subclass(A,cross_product(universal_class,universal_class)).
% 1.87/2.05 ** KEPT (pick-wt=8): 63 [] -function(A)|subclass(compose(A,inverse(A)),identity_relation).
% 1.87/2.05 ** KEPT (pick-wt=13): 64 [] function(A)| -subclass(A,cross_product(universal_class,universal_class))| -subclass(compose(A,inverse(A)),identity_relation).
% 1.87/2.05 ** KEPT (pick-wt=10): 65 [] -member(A,universal_class)| -function(B)|member(image(B,A),universal_class).
% 1.87/2.05 ** KEPT (pick-wt=9): 66 [] -disjoint(A,B)| -member(C,A)| -member(C,B).
% 1.87/2.05 ** KEPT (pick-wt=11): 67 [] -member(A,universal_class)|A=null_class|member(apply($c2,A),A).
% 1.87/2.05 ** KEPT (pick-wt=3): 69 [copy,68,flip.1] null_class!=$c3.
% 1.87/2.05 ** KEPT (pick-wt=3): 70 [] -member(A,$c3).
% 1.87/2.05
% 1.87/2.05 ------------> process sos:
% 1.87/2.05 ** KEPT (pick-wt=3): 84 [] A=A.
% 1.87/2.05 ** KEPT (pick-wt=8): 85 [] subclass(A,B)|member($f1(A,B),A).
% 1.87/2.05 ** KEPT (pick-wt=3): 86 [] subclass(A,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=5): 87 [] member(unordered_pair(A,B),universal_class).
% 1.87/2.05 ** KEPT (pick-wt=6): 88 [] singleton(A)=unordered_pair(A,A).
% 1.87/2.05 ---> New Demodulator: 89 [new_demod,88] singleton(A)=unordered_pair(A,A).
% 1.87/2.05 ** 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).
% 1.87/2.05 ---> New Demodulator: 92 [new_demod,91] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 1.87/2.05 ** KEPT (pick-wt=5): 93 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 1.87/2.05 ** KEPT (pick-wt=10): 95 [copy,94,flip.1] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.87/2.05 ---> New Demodulator: 96 [new_demod,95] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 1.87/2.05 ** KEPT (pick-wt=8): 97 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.87/2.05 ** KEPT (pick-wt=8): 98 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 1.87/2.05 ** KEPT (pick-wt=8): 100 [copy,99,demod,89] successor(A)=union(A,unordered_pair(A,A)).
% 1.87/2.05 ---> New Demodulator: 101 [new_demod,100] successor(A)=union(A,unordered_pair(A,A)).
% 1.87/2.05 ** KEPT (pick-wt=5): 102 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 1.87/2.05 ** KEPT (pick-wt=8): 103 [] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.87/2.05 ---> New Demodulator: 104 [new_demod,103] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 1.87/2.05 ** KEPT (pick-wt=9): 106 [copy,105,demod,104] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 1.87/2.05 ---> New Demodulator: 107 [new_demod,106] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 1.87/2.05 ** 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).
% 1.87/2.05 ---> New Demodulator: 110 [new_demod,109] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 1.87/2.05 ** KEPT (pick-wt=3): 111 [] member($c1,universal_class).
% 1.87/2.05 ** KEPT (pick-wt=2): 112 [] inductive($c1).
% 1.87/2.05 ** KEPT (pick-wt=7): 113 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 1.87/2.05 ** KEPT (pick-wt=8): 114 [] disjoint(A,B)|member($f4(A,B),A).
% 1.87/2.05 ** KEPT (pick-wt=8): 115 [] disjoint(A,B)|member($f4(A,B),B).
% 1.97/2.13 ** KEPT (pick-wt=7): 116 [] A=null_class|member($f5(A),universal_class).
% 1.97/2.13 ** KEPT (pick-wt=7): 117 [] A=null_class|member($f5(A),A).
% 1.97/2.13 ** KEPT (pick-wt=7): 118 [] A=null_class|disjoint($f5(A),A).
% 1.97/2.13 ** KEPT (pick-wt=10): 120 [copy,119,demod,89,flip.1] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 1.97/2.13 ---> New Demodulator: 121 [new_demod,120] sum_class(image(A,unordered_pair(B,B)))=apply(A,B).
% 1.97/2.13 ** KEPT (pick-wt=2): 122 [] function($c2).
% 1.97/2.13 Following clause subsumed by 84 during input processing: 0 [copy,84,flip.1] A=A.
% 1.97/2.13 84 back subsumes 71.
% 1.97/2.13 >>>> Starting back demodulation with 89.
% 1.97/2.13 >> back demodulating 57 with 89.
% 1.97/2.13 >> back demodulating 56 with 89.
% 1.97/2.13 >> back demodulating 29 with 89.
% 1.97/2.13 >> back demodulating 28 with 89.
% 1.97/2.13 >>>> Starting back demodulation with 92.
% 1.97/2.13 >>>> Starting back demodulation with 96.
% 1.97/2.13 >>>> Starting back demodulation with 101.
% 1.97/2.13 >> back demodulating 81 with 101.
% 1.97/2.13 >> back demodulating 42 with 101.
% 1.97/2.13 >> back demodulating 41 with 101.
% 1.97/2.13 >>>> Starting back demodulation with 104.
% 1.97/2.13 >> back demodulating 64 with 104.
% 1.97/2.13 >> back demodulating 63 with 104.
% 1.97/2.13 >>>> Starting back demodulation with 107.
% 1.97/2.13 >>>> Starting back demodulation with 110.
% 1.97/2.13 >>>> Starting back demodulation with 121.
% 1.97/2.13
% 1.97/2.13 ======= end of input processing =======
% 1.97/2.13
% 1.97/2.13 =========== start of search ===========
% 1.97/2.13
% 1.97/2.13
% 1.97/2.13 Resetting weight limit to 6.
% 1.97/2.13
% 1.97/2.13
% 1.97/2.13 Resetting weight limit to 6.
% 1.97/2.13
% 1.97/2.13 sos_size=1083
% 1.97/2.13
% 1.97/2.13 -------- PROOF --------
% 1.97/2.13
% 1.97/2.13 ----> UNIT CONFLICT at 0.08 sec ----> 1458 [binary,1456.1,69.1] $F.
% 1.97/2.13
% 1.97/2.13 Length of proof is 5. Level of proof is 3.
% 1.97/2.13
% 1.97/2.13 ---------------- PROOF ----------------
% 1.97/2.13 % SZS status Theorem
% 1.97/2.13 % SZS output start Refutation
% See solution above
% 1.97/2.13 ------------ end of proof -------------
% 1.97/2.13
% 1.97/2.13
% 1.97/2.13 Search stopped by max_proofs option.
% 1.97/2.13
% 1.97/2.13
% 1.97/2.13 Search stopped by max_proofs option.
% 1.97/2.13
% 1.97/2.13 ============ end of search ============
% 1.97/2.13
% 1.97/2.13 -------------- statistics -------------
% 1.97/2.13 clauses given 81
% 1.97/2.13 clauses generated 6774
% 1.97/2.13 clauses kept 1306
% 1.97/2.13 clauses forward subsumed 522
% 1.97/2.13 clauses back subsumed 18
% 1.97/2.13 Kbytes malloced 4882
% 1.97/2.13
% 1.97/2.13 ----------- times (seconds) -----------
% 1.97/2.13 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.97/2.13 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.97/2.13 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.13
% 1.97/2.13 That finishes the proof of the theorem.
% 1.97/2.13
% 1.97/2.13 Process 19610 finished Wed Jul 27 10:41:37 2022
% 1.97/2.13 Otter interrupted
% 1.97/2.13 PROOF FOUND
%------------------------------------------------------------------------------