TSTP Solution File: SET057-7 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET057-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:12:56 EDT 2022
% Result : Unsatisfiable 2.25s 2.41s
% Output : Refutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 6 unt; 1 nHn; 8 RR)
% Number of literals : 13 ( 3 equ; 6 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(not_subclass_element(A,B),B)
| subclass(A,B) ),
file('SET057-7.p',unknown),
[] ).
cnf(5,axiom,
( ~ subclass(A,B)
| ~ subclass(B,A)
| A = B ),
file('SET057-7.p',unknown),
[] ).
cnf(65,axiom,
x != y,
file('SET057-7.p',unknown),
[] ).
cnf(66,plain,
y != x,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[65])]),
[iquote('copy,65,flip.1')] ).
cnf(67,axiom,
~ member(not_subclass_element(y,x),y),
file('SET057-7.p',unknown),
[] ).
cnf(77,axiom,
( member(not_subclass_element(A,B),A)
| subclass(A,B) ),
file('SET057-7.p',unknown),
[] ).
cnf(144,axiom,
member(not_subclass_element(x,y),y),
file('SET057-7.p',unknown),
[] ).
cnf(332,plain,
subclass(x,y),
inference(hyper,[status(thm)],[144,2]),
[iquote('hyper,144,2')] ).
cnf(357,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[332,5,77]),66,67]),
[iquote('hyper,332,5,77,unit_del,66,67')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET057-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 10:50:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.25/2.40 ----- Otter 3.3f, August 2004 -----
% 2.25/2.40 The process was started by sandbox2 on n018.cluster.edu,
% 2.25/2.40 Wed Jul 27 10:50:16 2022
% 2.25/2.40 The command was "./otter". The process ID is 6226.
% 2.25/2.40
% 2.25/2.40 set(prolog_style_variables).
% 2.25/2.40 set(auto).
% 2.25/2.40 dependent: set(auto1).
% 2.25/2.40 dependent: set(process_input).
% 2.25/2.40 dependent: clear(print_kept).
% 2.25/2.40 dependent: clear(print_new_demod).
% 2.25/2.40 dependent: clear(print_back_demod).
% 2.25/2.40 dependent: clear(print_back_sub).
% 2.25/2.40 dependent: set(control_memory).
% 2.25/2.40 dependent: assign(max_mem, 12000).
% 2.25/2.40 dependent: assign(pick_given_ratio, 4).
% 2.25/2.40 dependent: assign(stats_level, 1).
% 2.25/2.40 dependent: assign(max_seconds, 10800).
% 2.25/2.40 clear(print_given).
% 2.25/2.40
% 2.25/2.40 list(usable).
% 2.25/2.40 0 [] A=A.
% 2.25/2.40 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 2.25/2.40 0 [] member(not_subclass_element(X,Y),X)|subclass(X,Y).
% 2.25/2.40 0 [] -member(not_subclass_element(X,Y),Y)|subclass(X,Y).
% 2.25/2.40 0 [] subclass(X,universal_class).
% 2.25/2.40 0 [] X!=Y|subclass(X,Y).
% 2.25/2.40 0 [] X!=Y|subclass(Y,X).
% 2.25/2.40 0 [] -subclass(X,Y)| -subclass(Y,X)|X=Y.
% 2.25/2.40 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 2.25/2.40 0 [] -member(X,universal_class)|member(X,unordered_pair(X,Y)).
% 2.25/2.40 0 [] -member(Y,universal_class)|member(Y,unordered_pair(X,Y)).
% 2.25/2.40 0 [] member(unordered_pair(X,Y),universal_class).
% 2.25/2.40 0 [] unordered_pair(X,X)=singleton(X).
% 2.25/2.40 0 [] unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))=ordered_pair(X,Y).
% 2.25/2.40 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 2.25/2.40 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 2.25/2.40 0 [] -member(U,X)| -member(V,Y)|member(ordered_pair(U,V),cross_product(X,Y)).
% 2.25/2.40 0 [] -member(Z,cross_product(X,Y))|ordered_pair(first(Z),second(Z))=Z.
% 2.25/2.40 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 2.25/2.40 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 2.25/2.40 0 [] -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))| -member(X,Y)|member(ordered_pair(X,Y),element_relation).
% 2.25/2.40 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 2.25/2.40 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 2.25/2.40 0 [] -member(Z,X)| -member(Z,Y)|member(Z,intersection(X,Y)).
% 2.25/2.40 0 [] -member(Z,complement(X))| -member(Z,X).
% 2.25/2.40 0 [] -member(Z,universal_class)|member(Z,complement(X))|member(Z,X).
% 2.25/2.40 0 [] complement(intersection(complement(X),complement(Y)))=union(X,Y).
% 2.25/2.40 0 [] intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y))))=symmetric_difference(X,Y).
% 2.25/2.40 0 [] intersection(Xr,cross_product(X,Y))=restrict(Xr,X,Y).
% 2.25/2.40 0 [] intersection(cross_product(X,Y),Xr)=restrict(Xr,X,Y).
% 2.25/2.40 0 [] restrict(X,singleton(Z),universal_class)!=null_class| -member(Z,domain_of(X)).
% 2.25/2.40 0 [] -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class|member(Z,domain_of(X)).
% 2.25/2.40 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.25/2.40 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 2.25/2.40 0 [] -member(ordered_pair(ordered_pair(V,W),U),X)| -member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(U,V),W),rotate(X)).
% 2.25/2.40 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.25/2.40 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 2.25/2.40 0 [] -member(ordered_pair(ordered_pair(V,U),W),X)| -member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(U,V),W),flip(X)).
% 2.25/2.40 0 [] domain_of(flip(cross_product(Y,universal_class)))=inverse(Y).
% 2.25/2.40 0 [] domain_of(inverse(Z))=range_of(Z).
% 2.25/2.40 0 [] first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class))=domain(Z,X,Y).
% 2.25/2.40 0 [] second(not_subclass_element(restrict(Z,singleton(X),Y),null_class))=range(Z,X,Y).
% 2.25/2.40 0 [] range_of(restrict(Xr,X,universal_class))=image(Xr,X).
% 2.25/2.40 0 [] union(X,singleton(X))=successor(X).
% 2.25/2.40 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 2.25/2.40 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 2.25/2.40 0 [] successor(X)!=Y| -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))|member(ordered_pair(X,Y),successor_relation).
% 2.25/2.40 0 [] -inductive(X)|member(null_class,X).
% 2.25/2.40 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 2.25/2.40 0 [] -member(null_class,X)| -subclass(image(successor_relation,X),X)|inductive(X).
% 2.25/2.40 0 [] inductive(omega).
% 2.25/2.40 0 [] -inductive(Y)|subclass(omega,Y).
% 2.25/2.40 0 [] member(omega,universal_class).
% 2.25/2.40 0 [] domain_of(restrict(element_relation,universal_class,X))=sum_class(X).
% 2.25/2.40 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 2.25/2.40 0 [] complement(image(element_relation,complement(X)))=power_class(X).
% 2.25/2.40 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 2.25/2.40 0 [] subclass(compose(Yr,Xr),cross_product(universal_class,universal_class)).
% 2.25/2.40 0 [] -member(ordered_pair(Y,Z),compose(Yr,Xr))|member(Z,image(Yr,image(Xr,singleton(Y)))).
% 2.25/2.40 0 [] -member(Z,image(Yr,image(Xr,singleton(Y))))| -member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))|member(ordered_pair(Y,Z),compose(Yr,Xr)).
% 2.25/2.40 0 [] -single_valued_class(X)|subclass(compose(X,inverse(X)),identity_relation).
% 2.25/2.40 0 [] -subclass(compose(X,inverse(X)),identity_relation)|single_valued_class(X).
% 2.25/2.40 0 [] -function(Xf)|subclass(Xf,cross_product(universal_class,universal_class)).
% 2.25/2.40 0 [] -function(Xf)|subclass(compose(Xf,inverse(Xf)),identity_relation).
% 2.25/2.40 0 [] -subclass(Xf,cross_product(universal_class,universal_class))| -subclass(compose(Xf,inverse(Xf)),identity_relation)|function(Xf).
% 2.25/2.40 0 [] -function(Xf)| -member(X,universal_class)|member(image(Xf,X),universal_class).
% 2.25/2.40 0 [] X=null_class|member(regular(X),X).
% 2.25/2.40 0 [] X=null_class|intersection(X,regular(X))=null_class.
% 2.25/2.40 0 [] sum_class(image(Xf,singleton(Y)))=apply(Xf,Y).
% 2.25/2.40 0 [] function(choice).
% 2.25/2.40 0 [] -member(Y,universal_class)|Y=null_class|member(apply(choice,Y),Y).
% 2.25/2.40 0 [] -one_to_one(Xf)|function(Xf).
% 2.25/2.40 0 [] -one_to_one(Xf)|function(inverse(Xf)).
% 2.25/2.40 0 [] -function(inverse(Xf))| -function(Xf)|one_to_one(Xf).
% 2.25/2.40 0 [] intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))))=subset_relation.
% 2.25/2.40 0 [] intersection(inverse(subset_relation),subset_relation)=identity_relation.
% 2.25/2.40 0 [] complement(domain_of(intersection(Xr,identity_relation)))=diagonalise(Xr).
% 2.25/2.40 0 [] intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X)))=cantor(X).
% 2.25/2.40 0 [] -operation(Xf)|function(Xf).
% 2.25/2.40 0 [] -operation(Xf)|cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf)))=domain_of(Xf).
% 2.25/2.40 0 [] -operation(Xf)|subclass(range_of(Xf),domain_of(domain_of(Xf))).
% 2.25/2.40 0 [] -function(Xf)|cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf)))!=domain_of(Xf)| -subclass(range_of(Xf),domain_of(domain_of(Xf)))|operation(Xf).
% 2.25/2.40 0 [] -compatible(Xh,Xf1,Xf2)|function(Xh).
% 2.25/2.40 0 [] -compatible(Xh,Xf1,Xf2)|domain_of(domain_of(Xf1))=domain_of(Xh).
% 2.25/2.40 0 [] -compatible(Xh,Xf1,Xf2)|subclass(range_of(Xh),domain_of(domain_of(Xf2))).
% 2.25/2.40 0 [] -function(Xh)|domain_of(domain_of(Xf1))!=domain_of(Xh)| -subclass(range_of(Xh),domain_of(domain_of(Xf2)))|compatible(Xh,Xf1,Xf2).
% 2.25/2.40 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf1).
% 2.25/2.40 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf2).
% 2.25/2.40 0 [] -homomorphism(Xh,Xf1,Xf2)|compatible(Xh,Xf1,Xf2).
% 2.25/2.40 0 [] -homomorphism(Xh,Xf1,Xf2)| -member(ordered_pair(X,Y),domain_of(Xf1))|apply(Xf2,ordered_pair(apply(Xh,X),apply(Xh,Y)))=apply(Xh,apply(Xf1,ordered_pair(X,Y))).
% 2.25/2.40 0 [] -operation(Xf1)| -operation(Xf2)| -compatible(Xh,Xf1,Xf2)|member(ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2)),domain_of(Xf1))|homomorphism(Xh,Xf1,Xf2).
% 2.25/2.40 0 [] -operation(Xf1)| -operation(Xf2)| -compatible(Xh,Xf1,Xf2)|apply(Xf2,ordered_pair(apply(Xh,not_homomorphism1(Xh,Xf1,Xf2)),apply(Xh,not_homomorphism2(Xh,Xf1,Xf2))))!=apply(Xh,apply(Xf1,ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2))))|homomorphism(Xh,Xf1,Xf2).
% 2.25/2.40 0 [] -member(ordered_pair(X,Y),cross_product(U,V))|member(X,unordered_pair(X,Y)).
% 2.25/2.40 0 [] -member(ordered_pair(X,Y),cross_product(U,V))|member(Y,unordered_pair(X,Y)).
% 2.25/2.40 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,universal_class).
% 2.25/2.40 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,universal_class).
% 2.25/2.41 0 [] subclass(X,X).
% 2.25/2.41 0 [] -subclass(X,Y)| -subclass(Y,Z)|subclass(X,Z).
% 2.25/2.41 0 [] member(not_subclass_element(x,y),y).
% 2.25/2.41 0 [] x!=y.
% 2.25/2.41 0 [] -member(not_subclass_element(y,x),y).
% 2.25/2.41 end_of_list.
% 2.25/2.41
% 2.25/2.41 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.25/2.41
% 2.25/2.41 This ia a non-Horn set with equality. The strategy will be
% 2.25/2.41 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.25/2.41 deletion, with positive clauses in sos and nonpositive
% 2.25/2.41 clauses in usable.
% 2.25/2.41
% 2.25/2.41 dependent: set(knuth_bendix).
% 2.25/2.41 dependent: set(anl_eq).
% 2.25/2.41 dependent: set(para_from).
% 2.25/2.41 dependent: set(para_into).
% 2.25/2.41 dependent: clear(para_from_right).
% 2.25/2.41 dependent: clear(para_into_right).
% 2.25/2.41 dependent: set(para_from_vars).
% 2.25/2.41 dependent: set(eq_units_both_ways).
% 2.25/2.41 dependent: set(dynamic_demod_all).
% 2.25/2.41 dependent: set(dynamic_demod).
% 2.25/2.41 dependent: set(order_eq).
% 2.25/2.41 dependent: set(back_demod).
% 2.25/2.41 dependent: set(lrpo).
% 2.25/2.41 dependent: set(hyper_res).
% 2.25/2.41 dependent: set(unit_deletion).
% 2.25/2.41 dependent: set(factor).
% 2.25/2.41
% 2.25/2.41 ------------> process usable:
% 2.25/2.41 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 2.25/2.41 ** KEPT (pick-wt=8): 2 [] -member(not_subclass_element(A,B),B)|subclass(A,B).
% 2.25/2.41 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 2.25/2.41 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 2.25/2.41 ** KEPT (pick-wt=9): 5 [] -subclass(A,B)| -subclass(B,A)|A=B.
% 2.25/2.41 ** KEPT (pick-wt=11): 6 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 2.25/2.41 ** KEPT (pick-wt=8): 7 [] -member(A,universal_class)|member(A,unordered_pair(A,B)).
% 2.25/2.41 ** KEPT (pick-wt=8): 8 [] -member(A,universal_class)|member(A,unordered_pair(B,A)).
% 2.25/2.41 ** KEPT (pick-wt=10): 9 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 2.25/2.41 ** KEPT (pick-wt=10): 10 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 2.25/2.41 ** KEPT (pick-wt=13): 11 [] -member(A,B)| -member(C,D)|member(ordered_pair(A,C),cross_product(B,D)).
% 2.25/2.41 ** KEPT (pick-wt=12): 12 [] -member(A,cross_product(B,C))|ordered_pair(first(A),second(A))=A.
% 2.25/2.41 ** KEPT (pick-wt=8): 13 [] -member(ordered_pair(A,B),element_relation)|member(A,B).
% 2.25/2.41 ** KEPT (pick-wt=15): 14 [] -member(ordered_pair(A,B),cross_product(universal_class,universal_class))| -member(A,B)|member(ordered_pair(A,B),element_relation).
% 2.25/2.41 ** KEPT (pick-wt=8): 15 [] -member(A,intersection(B,C))|member(A,B).
% 2.25/2.41 ** KEPT (pick-wt=8): 16 [] -member(A,intersection(B,C))|member(A,C).
% 2.25/2.41 ** KEPT (pick-wt=11): 17 [] -member(A,B)| -member(A,C)|member(A,intersection(B,C)).
% 2.25/2.41 ** KEPT (pick-wt=7): 18 [] -member(A,complement(B))| -member(A,B).
% 2.25/2.41 ** KEPT (pick-wt=10): 19 [] -member(A,universal_class)|member(A,complement(B))|member(A,B).
% 2.25/2.41 ** KEPT (pick-wt=11): 20 [] restrict(A,singleton(B),universal_class)!=null_class| -member(B,domain_of(A)).
% 2.25/2.41 ** KEPT (pick-wt=14): 21 [] -member(A,universal_class)|restrict(B,singleton(A),universal_class)=null_class|member(A,domain_of(B)).
% 2.25/2.41 ** KEPT (pick-wt=15): 22 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(B,C),A),D).
% 2.25/2.41 ** KEPT (pick-wt=26): 23 [] -member(ordered_pair(ordered_pair(A,B),C),D)| -member(ordered_pair(ordered_pair(C,A),B),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(C,A),B),rotate(D)).
% 2.25/2.41 ** KEPT (pick-wt=15): 24 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(B,A),C),D).
% 2.25/2.41 ** KEPT (pick-wt=26): 25 [] -member(ordered_pair(ordered_pair(A,B),C),D)| -member(ordered_pair(ordered_pair(B,A),C),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(B,A),C),flip(D)).
% 2.25/2.41 ** KEPT (pick-wt=9): 26 [] -member(ordered_pair(A,B),successor_relation)|successor(A)=B.
% 2.25/2.41 ** KEPT (pick-wt=16): 27 [] successor(A)!=B| -member(ordered_pair(A,B),cross_product(universal_class,universal_class))|member(ordered_pair(A,B),successor_relation).
% 2.25/2.41 ** KEPT (pick-wt=5): 28 [] -inductive(A)|member(null_class,A).
% 2.25/2.41 ** KEPT (pick-wt=7): 29 [] -inductive(A)|subclass(image(successor_relation,A),A).
% 2.25/2.41 ** KEPT (pick-wt=10): 30 [] -member(null_class,A)| -subclass(image(successor_relation,A),A)|inductive(A).
% 2.25/2.41 ** KEPT (pick-wt=5): 31 [] -inductive(A)|subclass(omega,A).
% 2.25/2.41 ** KEPT (pick-wt=7): 32 [] -member(A,universal_class)|member(sum_class(A),universal_class).
% 2.25/2.41 ** KEPT (pick-wt=7): 33 [] -member(A,universal_class)|member(power_class(A),universal_class).
% 2.25/2.41 ** KEPT (pick-wt=15): 34 [] -member(ordered_pair(A,B),compose(C,D))|member(B,image(C,image(D,singleton(A)))).
% 2.25/2.41 ** KEPT (pick-wt=22): 35 [] -member(A,image(B,image(C,singleton(D))))| -member(ordered_pair(D,A),cross_product(universal_class,universal_class))|member(ordered_pair(D,A),compose(B,C)).
% 2.25/2.41 ** KEPT (pick-wt=8): 36 [] -single_valued_class(A)|subclass(compose(A,inverse(A)),identity_relation).
% 2.25/2.41 ** KEPT (pick-wt=8): 37 [] -subclass(compose(A,inverse(A)),identity_relation)|single_valued_class(A).
% 2.25/2.41 ** KEPT (pick-wt=7): 38 [] -function(A)|subclass(A,cross_product(universal_class,universal_class)).
% 2.25/2.41 ** KEPT (pick-wt=8): 39 [] -function(A)|subclass(compose(A,inverse(A)),identity_relation).
% 2.25/2.41 ** KEPT (pick-wt=13): 40 [] -subclass(A,cross_product(universal_class,universal_class))| -subclass(compose(A,inverse(A)),identity_relation)|function(A).
% 2.25/2.41 ** KEPT (pick-wt=10): 41 [] -function(A)| -member(B,universal_class)|member(image(A,B),universal_class).
% 2.25/2.41 ** KEPT (pick-wt=11): 42 [] -member(A,universal_class)|A=null_class|member(apply(choice,A),A).
% 2.25/2.41 ** KEPT (pick-wt=4): 43 [] -one_to_one(A)|function(A).
% 2.25/2.41 ** KEPT (pick-wt=5): 44 [] -one_to_one(A)|function(inverse(A)).
% 2.25/2.41 ** KEPT (pick-wt=7): 45 [] -function(inverse(A))| -function(A)|one_to_one(A).
% 2.25/2.41 ** KEPT (pick-wt=4): 46 [] -operation(A)|function(A).
% 2.25/2.41 ** KEPT (pick-wt=12): 47 [] -operation(A)|cross_product(domain_of(domain_of(A)),domain_of(domain_of(A)))=domain_of(A).
% 2.25/2.41 ** KEPT (pick-wt=8): 48 [] -operation(A)|subclass(range_of(A),domain_of(domain_of(A))).
% 2.25/2.41 ** KEPT (pick-wt=20): 49 [] -function(A)|cross_product(domain_of(domain_of(A)),domain_of(domain_of(A)))!=domain_of(A)| -subclass(range_of(A),domain_of(domain_of(A)))|operation(A).
% 2.25/2.41 ** KEPT (pick-wt=6): 50 [] -compatible(A,B,C)|function(A).
% 2.25/2.41 ** KEPT (pick-wt=10): 51 [] -compatible(A,B,C)|domain_of(domain_of(B))=domain_of(A).
% 2.25/2.41 ** KEPT (pick-wt=10): 52 [] -compatible(A,B,C)|subclass(range_of(A),domain_of(domain_of(C))).
% 2.25/2.41 ** KEPT (pick-wt=18): 53 [] -function(A)|domain_of(domain_of(B))!=domain_of(A)| -subclass(range_of(A),domain_of(domain_of(C)))|compatible(A,B,C).
% 2.25/2.41 ** KEPT (pick-wt=6): 54 [] -homomorphism(A,B,C)|operation(B).
% 2.25/2.41 ** KEPT (pick-wt=6): 55 [] -homomorphism(A,B,C)|operation(C).
% 2.25/2.41 ** KEPT (pick-wt=8): 56 [] -homomorphism(A,B,C)|compatible(A,B,C).
% 2.25/2.41 ** KEPT (pick-wt=27): 57 [] -homomorphism(A,B,C)| -member(ordered_pair(D,E),domain_of(B))|apply(C,ordered_pair(apply(A,D),apply(A,E)))=apply(A,apply(B,ordered_pair(D,E))).
% 2.25/2.41 ** KEPT (pick-wt=24): 58 [] -operation(A)| -operation(B)| -compatible(C,A,B)|member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A))|homomorphism(C,A,B).
% 2.25/2.41 ** KEPT (pick-wt=41): 59 [] -operation(A)| -operation(B)| -compatible(C,A,B)|apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B))))!=apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B))))|homomorphism(C,A,B).
% 2.25/2.41 ** KEPT (pick-wt=12): 60 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,unordered_pair(A,B)).
% 2.25/2.41 ** KEPT (pick-wt=12): 61 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,unordered_pair(A,B)).
% 2.25/2.41 ** KEPT (pick-wt=10): 62 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,universal_class).
% 2.25/2.41 ** KEPT (pick-wt=10): 63 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,universal_class).
% 2.25/2.41 ** KEPT (pick-wt=9): 64 [] -subclass(A,B)| -subclass(B,C)|subclass(A,C).
% 2.25/2.41 ** KEPT (pick-wt=3): 66 [copy,65,flip.1] y!=x.
% 2.25/2.41 ** KEPT (pick-wt=5): 67 [] -member(not_subclass_element(y,x),y).
% 2.25/2.41
% 2.25/2.41 ------------> process sos:
% 2.25/2.41 ** KEPT (pick-wt=3): 76 [] A=A.
% 2.25/2.41 ** KEPT (pick-wt=8): 77 [] member(not_subclass_element(A,B),A)|subclass(A,B).
% 2.25/2.41 ** KEPT (pick-wt=3): 78 [] subclass(A,universal_class).
% 2.25/2.41 ** KEPT (pick-wt=5): 79 [] member(unordered_pair(A,B),universal_class).
% 2.25/2.41 ** KEPT (pick-wt=6): 81 [copy,80,flip.1] singleton(A)=unordered_pair(A,A).
% 2.25/2.41 ---> New Demodulator: 82 [new_demod,81] singleton(A)=unordered_pair(A,A).
% 2.25/2.41 ** KEPT (pick-wt=13): 84 [copy,83,demod,82,82] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 2.25/2.41 ---> New Demodulator: 85 [new_demod,84] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 2.25/2.41 ** KEPT (pick-wt=5): 86 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 2.25/2.41 ** KEPT (pick-wt=10): 87 [] complement(intersection(complement(A),complement(B)))=union(A,B).
% 2.25/2.41 ---> New Demodulator: 88 [new_demod,87] complement(intersection(complement(A),complement(B)))=union(A,B).
% 2.25/2.41 ** KEPT (pick-wt=12): 90 [copy,89,demod,88] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 2.25/2.41 ---> New Demodulator: 91 [new_demod,90] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 2.25/2.41 ** KEPT (pick-wt=10): 92 [] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 2.25/2.41 ---> New Demodulator: 93 [new_demod,92] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 2.25/2.41 ** KEPT (pick-wt=10): 94 [] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 2.25/2.41 ---> New Demodulator: 95 [new_demod,94] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 2.25/2.41 ** KEPT (pick-wt=8): 96 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.25/2.41 ** KEPT (pick-wt=8): 97 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.25/2.41 ** KEPT (pick-wt=8): 99 [copy,98,flip.1] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 2.25/2.41 ---> New Demodulator: 100 [new_demod,99] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 2.25/2.41 ** KEPT (pick-wt=9): 102 [copy,101,demod,100,flip.1] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 2.25/2.41 ---> New Demodulator: 103 [new_demod,102] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 2.25/2.41 ** KEPT (pick-wt=14): 105 [copy,104,demod,82] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 2.25/2.41 ---> New Demodulator: 106 [new_demod,105] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 2.25/2.41 ** KEPT (pick-wt=14): 108 [copy,107,demod,82] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 2.25/2.41 ---> New Demodulator: 109 [new_demod,108] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 2.25/2.41 ** KEPT (pick-wt=13): 111 [copy,110,demod,103] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 2.25/2.41 ---> New Demodulator: 112 [new_demod,111] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 2.25/2.41 ** KEPT (pick-wt=8): 114 [copy,113,demod,82,flip.1] successor(A)=union(A,unordered_pair(A,A)).
% 2.25/2.41 ---> New Demodulator: 115 [new_demod,114] successor(A)=union(A,unordered_pair(A,A)).
% 2.25/2.41 ** KEPT (pick-wt=5): 116 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 2.25/2.41 ** KEPT (pick-wt=2): 117 [] inductive(omega).
% 2.25/2.41 ** KEPT (pick-wt=3): 118 [] member(omega,universal_class).
% 2.25/2.41 ** KEPT (pick-wt=8): 120 [copy,119,flip.1] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 2.25/2.41 ---> New Demodulator: 121 [new_demod,120] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 2.25/2.41 ** KEPT (pick-wt=8): 123 [copy,122,flip.1] power_class(A)=complement(image(element_relation,complement(A))).
% 2.25/2.41 ---> New Demodulator: 124 [new_demod,123] power_class(A)=complement(image(element_relation,complement(A))).
% 2.25/2.41 ** KEPT (pick-wt=7): 125 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 2.25/2.41 ** KEPT (pick-wt=7): 126 [] A=null_class|member(regular(A),A).
% 2.25/2.41 ** KEPT (pick-wt=9): 127 [] A=null_class|intersection(A,regular(A))=null_class.
% 2.25/2.41 ** KEPT (pick-wt=13): 129 [copy,128,demod,82,121] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 2.25/2.41 ---> New Demodulator: 130 [new_demod,129] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 2.25/2.41 ** KEPT (pick-wt=2): 131 [] function(choice).
% 2.25/2.41 ** KEPT (pick-wt=17): 133 [copy,132,demod,100,95,95] restrict(restrict(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),universal_class,universal_class),universal_class,universal_class)=subset_relation.
% 2.25/2.41 ---> New Demodulator: 134 [new_demod,133] restrict(restrict(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),universal_class,universal_class),universal_class,universal_class)=subset_relation.
% 2.25/2.41 ** KEPT (pick-wt=9): 136 [copy,135,demod,100] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 2.25/2.41 ---> New Demodulator: 137 [new_demod,136] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 2.25/2.41 ** KEPT (pick-wt=8): 138 [] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 2.25/2.41 ---> New Demodulator: 139 [new_demod,138] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 2.25/2.41 ** KEPT (pick-wt=14): 141 [copy,140,demod,100] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 2.25/2.41 ---> New Demodulator: 142 [new_demod,141] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 2.25/2.41 ** KEPT (pick-wt=3): 143 [] subclass(A,A).
% 2.25/2.41 ** KEPT (pick-wt=5): 144 [] member(not_subclass_element(x,y),y).
% 2.25/2.41 Following clause subsumed by 76 during input processing: 0 [copy,76,flip.1] A=A.
% 2.25/2.41 76 back subsumes 68.
% 2.25/2.41 >>>> Starting back demodulation with 82.
% 2.25/2.41 >> back demodulating 35 with 82.
% 2.25/2.41 >> back demodulating 34 with 82.
% 2.25/2.41 >> back demodulating 21 with 82.
% 2.25/2.41 >> back demodulating 20 with 82.
% 2.25/2.41 >>>> Starting back demodulation with 85.
% 2.25/2.41 >>>> Starting back demodulation with 88.
% 2.25/2.41 >>>> Starting back demodulation with 91.
% 2.25/2.41 >>>> Starting back demodulation with 93.
% 2.25/2.41 >>>> Starting back demodulation with 95.
% 2.25/2.41 >>>> Starting back demodulation with 100.
% 2.25/2.41 >> back demodulating 45 with 100.
% 2.25/2.41 >> back demodulating 44 with 100.
% 2.25/2.41 >> back demodulating 40 with 100.
% 2.25/2.41 >> back demodulating 39 with 100.
% 2.25/2.41 >> back demodulating 37 with 100.
% 2.25/2.41 >> back demodulating 36 with 100.
% 2.25/2.41 >>>> Starting back demodulation with 103.
% 2.25/2.41 >> back demodulating 53 with 103.
% 2.25/2.41 >> back demodulating 52 with 103.
% 2.25/2.41 >> back demodulating 49 with 103.
% 2.25/2.41 >> back demodulating 48 with 103.
% 2.25/2.41 >>>> Starting back demodulation with 106.
% 2.25/2.41 >>>> Starting back demodulation with 109.
% 2.25/2.41 >>>> Starting back demodulation with 112.
% 2.25/2.41 >>>> Starting back demodulation with 115.
% 2.25/2.41 >> back demodulating 27 with 115.
% 2.25/2.41 >> back demodulating 26 with 115.
% 2.25/2.41 >>>> Starting back demodulation with 121.
% 2.25/2.41 >> back demodulating 32 with 121.
% 2.25/2.41 >>>> Starting back demodulation with 124.
% 2.25/2.41 >> back demodulating 33 with 124.
% 2.25/2.41 >>>> Starting back demodulation with 130.
% 2.25/2.41 >>>> Starting back demodulation with 134.
% 2.25/2.41 >>>> Starting back demodulation with 137.
% 2.25/2.41 >>>> Starting back demodulation with 139.
% 2.25/2.41 >>>> Starting back demodulation with 142.
% 2.25/2.41
% 2.25/2.41 ======= end of input processing =======
% 2.25/2.41
% 2.25/2.41 =========== start of search ===========
% 2.25/2.41
% 2.25/2.41 -------- PROOF --------
% 2.25/2.41
% 2.25/2.41 -----> EMPTY CLAUSE at 0.01 sec ----> 357 [hyper,332,5,77,unit_del,66,67] $F.
% 2.25/2.41
% 2.25/2.41 Length of proof is 2. Level of proof is 1.
% 2.25/2.41
% 2.25/2.41 ---------------- PROOF ----------------
% 2.25/2.41 % SZS status Unsatisfiable
% 2.25/2.41 % SZS output start Refutation
% See solution above
% 2.25/2.41 ------------ end of proof -------------
% 2.25/2.41
% 2.25/2.41
% 2.25/2.41 Search stopped by max_proofs option.
% 2.25/2.41
% 2.25/2.41
% 2.25/2.41 Search stopped by max_proofs option.
% 2.25/2.41
% 2.25/2.41 ============ end of search ============
% 2.25/2.41
% 2.25/2.41 -------------- statistics -------------
% 2.25/2.41 clauses given 15
% 2.25/2.41 clauses generated 291
% 2.25/2.41 clauses kept 321
% 2.25/2.41 clauses forward subsumed 88
% 2.25/2.41 clauses back subsumed 3
% 2.25/2.41 Kbytes malloced 2929
% 2.25/2.41
% 2.25/2.41 ----------- times (seconds) -----------
% 2.25/2.41 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.25/2.41 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.25/2.41 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.25/2.41
% 2.25/2.41 That finishes the proof of the theorem.
% 2.25/2.41
% 2.25/2.41 Process 6226 finished Wed Jul 27 10:50:18 2022
% 2.25/2.42 Otter interrupted
% 2.25/2.42 PROOF FOUND
%------------------------------------------------------------------------------