TSTP Solution File: SET075-6 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET075-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:13:01 EDT 2022
% Result : Unsatisfiable 2.42s 2.45s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 8 unt; 2 nHn; 12 RR)
% Number of literals : 25 ( 4 equ; 9 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 15 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET075-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
file('SET075-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(ordered_pair(A,B),cross_product(C,D))
| member(A,C) ),
file('SET075-6.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(A,complement(B))
| ~ member(A,B) ),
file('SET075-6.p',unknown),
[] ).
cnf(70,axiom,
subclass(A,universal_class),
file('SET075-6.p',unknown),
[] ).
cnf(118,axiom,
( A = null_class
| member(regular(A),A) ),
file('SET075-6.p',unknown),
[] ).
cnf(135,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file('SET075-6.p',unknown),
[] ).
cnf(136,axiom,
unordered_pair(x,y) = null_class,
file('SET075-6.p',unknown),
[] ).
cnf(324,plain,
( ~ member(x,universal_class)
| member(x,null_class) ),
inference(para_from,[status(thm),theory(equality)],[136,7]),
[iquote('para_from,136.1.1,7.2.2')] ).
cnf(729,plain,
( A = null_class
| member(regular(A),universal_class) ),
inference(hyper,[status(thm)],[118,1,70]),
[iquote('hyper,118,1,70')] ).
cnf(741,plain,
member(x,u),
inference(hyper,[status(thm)],[135,9]),
[iquote('hyper,135,9')] ).
cnf(762,plain,
member(x,universal_class),
inference(hyper,[status(thm)],[741,1,70]),
[iquote('hyper,741,1,70')] ).
cnf(785,plain,
member(x,null_class),
inference(hyper,[status(thm)],[762,324]),
[iquote('hyper,762,324')] ).
cnf(1021,plain,
complement(universal_class) = null_class,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[729,18,118])]),
[iquote('hyper,729,18,118,factor_simp')] ).
cnf(1042,plain,
( ~ member(A,null_class)
| ~ member(A,universal_class) ),
inference(para_from,[status(thm),theory(equality)],[1021,18]),
[iquote('para_from,1021.1.1,18.1.2')] ).
cnf(1046,plain,
$false,
inference(hyper,[status(thm)],[1042,785,762]),
[iquote('hyper,1042,785,762')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET075-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:42:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.26/2.30 ----- Otter 3.3f, August 2004 -----
% 2.26/2.30 The process was started by sandbox on n003.cluster.edu,
% 2.26/2.30 Wed Jul 27 10:42:41 2022
% 2.26/2.30 The command was "./otter". The process ID is 27424.
% 2.26/2.30
% 2.26/2.30 set(prolog_style_variables).
% 2.26/2.30 set(auto).
% 2.26/2.30 dependent: set(auto1).
% 2.26/2.30 dependent: set(process_input).
% 2.26/2.30 dependent: clear(print_kept).
% 2.26/2.30 dependent: clear(print_new_demod).
% 2.26/2.30 dependent: clear(print_back_demod).
% 2.26/2.30 dependent: clear(print_back_sub).
% 2.26/2.30 dependent: set(control_memory).
% 2.26/2.30 dependent: assign(max_mem, 12000).
% 2.26/2.30 dependent: assign(pick_given_ratio, 4).
% 2.26/2.30 dependent: assign(stats_level, 1).
% 2.26/2.30 dependent: assign(max_seconds, 10800).
% 2.26/2.30 clear(print_given).
% 2.26/2.30
% 2.26/2.30 list(usable).
% 2.26/2.30 0 [] A=A.
% 2.26/2.30 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 2.26/2.30 0 [] member(not_subclass_element(X,Y),X)|subclass(X,Y).
% 2.26/2.30 0 [] -member(not_subclass_element(X,Y),Y)|subclass(X,Y).
% 2.26/2.30 0 [] subclass(X,universal_class).
% 2.26/2.30 0 [] X!=Y|subclass(X,Y).
% 2.26/2.30 0 [] X!=Y|subclass(Y,X).
% 2.26/2.30 0 [] -subclass(X,Y)| -subclass(Y,X)|X=Y.
% 2.26/2.30 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 2.26/2.30 0 [] -member(X,universal_class)|member(X,unordered_pair(X,Y)).
% 2.26/2.30 0 [] -member(Y,universal_class)|member(Y,unordered_pair(X,Y)).
% 2.26/2.30 0 [] member(unordered_pair(X,Y),universal_class).
% 2.26/2.30 0 [] unordered_pair(X,X)=singleton(X).
% 2.26/2.30 0 [] unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))=ordered_pair(X,Y).
% 2.26/2.30 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 2.26/2.30 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 2.26/2.30 0 [] -member(U,X)| -member(V,Y)|member(ordered_pair(U,V),cross_product(X,Y)).
% 2.26/2.30 0 [] -member(Z,cross_product(X,Y))|ordered_pair(first(Z),second(Z))=Z.
% 2.26/2.30 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 2.26/2.30 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 2.26/2.30 0 [] -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))| -member(X,Y)|member(ordered_pair(X,Y),element_relation).
% 2.26/2.30 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 2.26/2.30 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 2.26/2.30 0 [] -member(Z,X)| -member(Z,Y)|member(Z,intersection(X,Y)).
% 2.26/2.30 0 [] -member(Z,complement(X))| -member(Z,X).
% 2.26/2.30 0 [] -member(Z,universal_class)|member(Z,complement(X))|member(Z,X).
% 2.26/2.30 0 [] complement(intersection(complement(X),complement(Y)))=union(X,Y).
% 2.26/2.30 0 [] intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y))))=symmetric_difference(X,Y).
% 2.26/2.30 0 [] intersection(Xr,cross_product(X,Y))=restrict(Xr,X,Y).
% 2.26/2.30 0 [] intersection(cross_product(X,Y),Xr)=restrict(Xr,X,Y).
% 2.26/2.30 0 [] restrict(X,singleton(Z),universal_class)!=null_class| -member(Z,domain_of(X)).
% 2.26/2.30 0 [] -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class|member(Z,domain_of(X)).
% 2.26/2.30 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.26/2.30 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 2.26/2.30 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)).
% 2.26/2.30 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.26/2.30 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 2.26/2.30 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)).
% 2.26/2.30 0 [] domain_of(flip(cross_product(Y,universal_class)))=inverse(Y).
% 2.26/2.30 0 [] domain_of(inverse(Z))=range_of(Z).
% 2.26/2.30 0 [] first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class))=domain(Z,X,Y).
% 2.26/2.30 0 [] second(not_subclass_element(restrict(Z,singleton(X),Y),null_class))=range(Z,X,Y).
% 2.26/2.30 0 [] range_of(restrict(Xr,X,universal_class))=image(Xr,X).
% 2.26/2.30 0 [] union(X,singleton(X))=successor(X).
% 2.26/2.30 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 2.26/2.30 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 2.26/2.30 0 [] successor(X)!=Y| -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))|member(ordered_pair(X,Y),successor_relation).
% 2.26/2.30 0 [] -inductive(X)|member(null_class,X).
% 2.26/2.30 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 2.26/2.30 0 [] -member(null_class,X)| -subclass(image(successor_relation,X),X)|inductive(X).
% 2.26/2.30 0 [] inductive(omega).
% 2.26/2.30 0 [] -inductive(Y)|subclass(omega,Y).
% 2.26/2.30 0 [] member(omega,universal_class).
% 2.26/2.30 0 [] domain_of(restrict(element_relation,universal_class,X))=sum_class(X).
% 2.26/2.30 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 2.26/2.30 0 [] complement(image(element_relation,complement(X)))=power_class(X).
% 2.26/2.30 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 2.26/2.30 0 [] subclass(compose(Yr,Xr),cross_product(universal_class,universal_class)).
% 2.26/2.30 0 [] -member(ordered_pair(Y,Z),compose(Yr,Xr))|member(Z,image(Yr,image(Xr,singleton(Y)))).
% 2.26/2.30 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)).
% 2.26/2.30 0 [] -single_valued_class(X)|subclass(compose(X,inverse(X)),identity_relation).
% 2.26/2.30 0 [] -subclass(compose(X,inverse(X)),identity_relation)|single_valued_class(X).
% 2.26/2.30 0 [] -function(Xf)|subclass(Xf,cross_product(universal_class,universal_class)).
% 2.26/2.30 0 [] -function(Xf)|subclass(compose(Xf,inverse(Xf)),identity_relation).
% 2.26/2.30 0 [] -subclass(Xf,cross_product(universal_class,universal_class))| -subclass(compose(Xf,inverse(Xf)),identity_relation)|function(Xf).
% 2.26/2.30 0 [] -function(Xf)| -member(X,universal_class)|member(image(Xf,X),universal_class).
% 2.26/2.30 0 [] X=null_class|member(regular(X),X).
% 2.26/2.30 0 [] X=null_class|intersection(X,regular(X))=null_class.
% 2.26/2.30 0 [] sum_class(image(Xf,singleton(Y)))=apply(Xf,Y).
% 2.26/2.30 0 [] function(choice).
% 2.26/2.30 0 [] -member(Y,universal_class)|Y=null_class|member(apply(choice,Y),Y).
% 2.26/2.30 0 [] -one_to_one(Xf)|function(Xf).
% 2.26/2.30 0 [] -one_to_one(Xf)|function(inverse(Xf)).
% 2.26/2.30 0 [] -function(inverse(Xf))| -function(Xf)|one_to_one(Xf).
% 2.26/2.30 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.
% 2.26/2.30 0 [] intersection(inverse(subset_relation),subset_relation)=identity_relation.
% 2.26/2.30 0 [] complement(domain_of(intersection(Xr,identity_relation)))=diagonalise(Xr).
% 2.26/2.30 0 [] intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X)))=cantor(X).
% 2.26/2.30 0 [] -operation(Xf)|function(Xf).
% 2.26/2.30 0 [] -operation(Xf)|cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf)))=domain_of(Xf).
% 2.26/2.30 0 [] -operation(Xf)|subclass(range_of(Xf),domain_of(domain_of(Xf))).
% 2.26/2.30 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).
% 2.26/2.30 0 [] -compatible(Xh,Xf1,Xf2)|function(Xh).
% 2.26/2.30 0 [] -compatible(Xh,Xf1,Xf2)|domain_of(domain_of(Xf1))=domain_of(Xh).
% 2.26/2.30 0 [] -compatible(Xh,Xf1,Xf2)|subclass(range_of(Xh),domain_of(domain_of(Xf2))).
% 2.26/2.30 0 [] -function(Xh)|domain_of(domain_of(Xf1))!=domain_of(Xh)| -subclass(range_of(Xh),domain_of(domain_of(Xf2)))|compatible(Xh,Xf1,Xf2).
% 2.26/2.30 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf1).
% 2.26/2.30 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf2).
% 2.26/2.30 0 [] -homomorphism(Xh,Xf1,Xf2)|compatible(Xh,Xf1,Xf2).
% 2.26/2.30 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))).
% 2.26/2.30 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).
% 2.26/2.30 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).
% 2.26/2.30 0 [] member(ordered_pair(x,y),cross_product(u,v)).
% 2.26/2.30 0 [] unordered_pair(x,y)=null_class.
% 2.26/2.30 end_of_list.
% 2.26/2.30
% 2.26/2.30 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.26/2.30
% 2.26/2.30 This ia a non-Horn set with equality. The strategy will be
% 2.26/2.30 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.26/2.30 deletion, with positive clauses in sos and nonpositive
% 2.26/2.30 clauses in usable.
% 2.26/2.30
% 2.26/2.30 dependent: set(knuth_bendix).
% 2.26/2.30 dependent: set(anl_eq).
% 2.26/2.30 dependent: set(para_from).
% 2.26/2.30 dependent: set(para_into).
% 2.26/2.30 dependent: clear(para_from_right).
% 2.26/2.30 dependent: clear(para_into_right).
% 2.26/2.30 dependent: set(para_from_vars).
% 2.26/2.30 dependent: set(eq_units_both_ways).
% 2.26/2.30 dependent: set(dynamic_demod_all).
% 2.26/2.30 dependent: set(dynamic_demod).
% 2.26/2.30 dependent: set(order_eq).
% 2.26/2.30 dependent: set(back_demod).
% 2.26/2.30 dependent: set(lrpo).
% 2.26/2.30 dependent: set(hyper_res).
% 2.26/2.30 dependent: set(unit_deletion).
% 2.26/2.30 dependent: set(factor).
% 2.26/2.30
% 2.26/2.30 ------------> process usable:
% 2.26/2.30 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 2.26/2.30 ** KEPT (pick-wt=8): 2 [] -member(not_subclass_element(A,B),B)|subclass(A,B).
% 2.26/2.30 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 2.26/2.30 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 2.26/2.30 ** KEPT (pick-wt=9): 5 [] -subclass(A,B)| -subclass(B,A)|A=B.
% 2.26/2.30 ** KEPT (pick-wt=11): 6 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 2.26/2.30 ** KEPT (pick-wt=8): 7 [] -member(A,universal_class)|member(A,unordered_pair(A,B)).
% 2.26/2.30 ** KEPT (pick-wt=8): 8 [] -member(A,universal_class)|member(A,unordered_pair(B,A)).
% 2.26/2.30 ** KEPT (pick-wt=10): 9 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 2.26/2.30 ** KEPT (pick-wt=10): 10 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 2.26/2.30 ** KEPT (pick-wt=13): 11 [] -member(A,B)| -member(C,D)|member(ordered_pair(A,C),cross_product(B,D)).
% 2.26/2.30 ** KEPT (pick-wt=12): 12 [] -member(A,cross_product(B,C))|ordered_pair(first(A),second(A))=A.
% 2.26/2.30 ** KEPT (pick-wt=8): 13 [] -member(ordered_pair(A,B),element_relation)|member(A,B).
% 2.26/2.30 ** 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).
% 2.26/2.30 ** KEPT (pick-wt=8): 15 [] -member(A,intersection(B,C))|member(A,B).
% 2.26/2.30 ** KEPT (pick-wt=8): 16 [] -member(A,intersection(B,C))|member(A,C).
% 2.26/2.30 ** KEPT (pick-wt=11): 17 [] -member(A,B)| -member(A,C)|member(A,intersection(B,C)).
% 2.26/2.30 ** KEPT (pick-wt=7): 18 [] -member(A,complement(B))| -member(A,B).
% 2.26/2.30 ** KEPT (pick-wt=10): 19 [] -member(A,universal_class)|member(A,complement(B))|member(A,B).
% 2.26/2.30 ** KEPT (pick-wt=11): 20 [] restrict(A,singleton(B),universal_class)!=null_class| -member(B,domain_of(A)).
% 2.26/2.30 ** KEPT (pick-wt=14): 21 [] -member(A,universal_class)|restrict(B,singleton(A),universal_class)=null_class|member(A,domain_of(B)).
% 2.26/2.30 ** KEPT (pick-wt=15): 22 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(B,C),A),D).
% 2.26/2.30 ** 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)).
% 2.26/2.30 ** KEPT (pick-wt=15): 24 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(B,A),C),D).
% 2.26/2.30 ** 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)).
% 2.26/2.30 ** KEPT (pick-wt=9): 26 [] -member(ordered_pair(A,B),successor_relation)|successor(A)=B.
% 2.26/2.30 ** 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).
% 2.26/2.30 ** KEPT (pick-wt=5): 28 [] -inductive(A)|member(null_class,A).
% 2.26/2.30 ** KEPT (pick-wt=7): 29 [] -inductive(A)|subclass(image(successor_relation,A),A).
% 2.26/2.30 ** KEPT (pick-wt=10): 30 [] -member(null_class,A)| -subclass(image(successor_relation,A),A)|inductive(A).
% 2.26/2.30 ** KEPT (pick-wt=5): 31 [] -inductive(A)|subclass(omega,A).
% 2.26/2.30 ** KEPT (pick-wt=7): 32 [] -member(A,universal_class)|member(sum_class(A),universal_class).
% 2.26/2.30 ** KEPT (pick-wt=7): 33 [] -member(A,universal_class)|member(power_class(A),universal_class).
% 2.26/2.30 ** KEPT (pick-wt=15): 34 [] -member(ordered_pair(A,B),compose(C,D))|member(B,image(C,image(D,singleton(A)))).
% 2.26/2.30 ** 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)).
% 2.26/2.30 ** KEPT (pick-wt=8): 36 [] -single_valued_class(A)|subclass(compose(A,inverse(A)),identity_relation).
% 2.26/2.30 ** KEPT (pick-wt=8): 37 [] -subclass(compose(A,inverse(A)),identity_relation)|single_valued_class(A).
% 2.26/2.30 ** KEPT (pick-wt=7): 38 [] -function(A)|subclass(A,cross_product(universal_class,universal_class)).
% 2.26/2.30 ** KEPT (pick-wt=8): 39 [] -function(A)|subclass(compose(A,inverse(A)),identity_relation).
% 2.26/2.30 ** KEPT (pick-wt=13): 40 [] -subclass(A,cross_product(universal_class,universal_class))| -subclass(compose(A,inverse(A)),identity_relation)|function(A).
% 2.26/2.30 ** KEPT (pick-wt=10): 41 [] -function(A)| -member(B,universal_class)|member(image(A,B),universal_class).
% 2.26/2.30 ** KEPT (pick-wt=11): 42 [] -member(A,universal_class)|A=null_class|member(apply(choice,A),A).
% 2.26/2.30 ** KEPT (pick-wt=4): 43 [] -one_to_one(A)|function(A).
% 2.26/2.30 ** KEPT (pick-wt=5): 44 [] -one_to_one(A)|function(inverse(A)).
% 2.26/2.30 ** KEPT (pick-wt=7): 45 [] -function(inverse(A))| -function(A)|one_to_one(A).
% 2.26/2.30 ** KEPT (pick-wt=4): 46 [] -operation(A)|function(A).
% 2.26/2.30 ** KEPT (pick-wt=12): 47 [] -operation(A)|cross_product(domain_of(domain_of(A)),domain_of(domain_of(A)))=domain_of(A).
% 2.26/2.30 ** KEPT (pick-wt=8): 48 [] -operation(A)|subclass(range_of(A),domain_of(domain_of(A))).
% 2.26/2.30 ** 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).
% 2.26/2.30 ** KEPT (pick-wt=6): 50 [] -compatible(A,B,C)|function(A).
% 2.26/2.30 ** KEPT (pick-wt=10): 51 [] -compatible(A,B,C)|domain_of(domain_of(B))=domain_of(A).
% 2.26/2.30 ** KEPT (pick-wt=10): 52 [] -compatible(A,B,C)|subclass(range_of(A),domain_of(domain_of(C))).
% 2.26/2.30 ** 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).
% 2.26/2.30 ** KEPT (pick-wt=6): 54 [] -homomorphism(A,B,C)|operation(B).
% 2.26/2.30 ** KEPT (pick-wt=6): 55 [] -homomorphism(A,B,C)|operation(C).
% 2.26/2.30 ** KEPT (pick-wt=8): 56 [] -homomorphism(A,B,C)|compatible(A,B,C).
% 2.26/2.30 ** 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))).
% 2.26/2.30 ** 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).
% 2.26/2.30 ** 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).
% 2.26/2.30
% 2.26/2.30 ------------> process sos:
% 2.26/2.30 ** KEPT (pick-wt=3): 68 [] A=A.
% 2.26/2.30 ** KEPT (pick-wt=8): 69 [] member(not_subclass_element(A,B),A)|subclass(A,B).
% 2.26/2.30 ** KEPT (pick-wt=3): 70 [] subclass(A,universal_class).
% 2.26/2.30 ** KEPT (pick-wt=5): 71 [] member(unordered_pair(A,B),universal_class).
% 2.26/2.30 ** KEPT (pick-wt=6): 73 [copy,72,flip.1] singleton(A)=unordered_pair(A,A).
% 2.26/2.30 ---> New Demodulator: 74 [new_demod,73] singleton(A)=unordered_pair(A,A).
% 2.26/2.30 ** KEPT (pick-wt=13): 76 [copy,75,demod,74,74] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 2.26/2.30 ---> New Demodulator: 77 [new_demod,76] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 2.26/2.30 ** KEPT (pick-wt=5): 78 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 2.26/2.30 ** KEPT (pick-wt=10): 79 [] complement(intersection(complement(A),complement(B)))=union(A,B).
% 2.26/2.30 ---> New Demodulator: 80 [new_demod,79] complement(intersection(complement(A),complement(B)))=union(A,B).
% 2.26/2.30 ** KEPT (pick-wt=12): 82 [copy,81,demod,80] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 2.26/2.30 ---> New Demodulator: 83 [new_demod,82] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 2.26/2.30 ** KEPT (pick-wt=10): 84 [] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 2.26/2.30 ---> New Demodulator: 85 [new_demod,84] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 2.26/2.30 ** KEPT (pick-wt=10): 86 [] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 2.26/2.30 ---> New Demodulator: 87 [new_demod,86] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 2.26/2.30 ** KEPT (pick-wt=8): 88 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.26/2.30 ** KEPT (pick-wt=8): 89 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.26/2.30 ** KEPT (pick-wt=8): 91 [copy,90,flip.1] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 2.26/2.30 ---> New Demodulator: 92 [new_demod,91] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 2.26/2.30 ** KEPT (pick-wt=9): 94 [copy,93,demod,92,flip.1] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 2.26/2.30 ---> New Demodulator: 95 [new_demod,94] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 2.26/2.30 ** KEPT (pick-wt=14): 97 [copy,96,demod,74] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 2.26/2.30 ---> New Demodulator: 98 [new_demod,97] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 2.26/2.30 ** KEPT (pick-wt=14): 100 [copy,99,demod,74] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 2.26/2.30 ---> New Demodulator: 101 [new_demod,100] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 2.26/2.30 ** KEPT (pick-wt=13): 103 [copy,102,demod,95] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 2.26/2.30 ---> New Demodulator: 104 [new_demod,103] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 2.26/2.30 ** KEPT (pick-wt=8): 106 [copy,105,demod,74,flip.1] successor(A)=union(A,unordered_pair(A,A)).
% 2.26/2.30 ---> New Demodulator: 107 [new_demod,106] successor(A)=union(A,unordered_pair(A,A)).
% 2.26/2.30 ** KEPT (pick-wt=5): 108 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 2.26/2.30 ** KEPT (pick-wt=2): 109 [] inductive(omega).
% 2.26/2.30 ** KEPT (pick-wt=3): 110 [] member(omega,universal_class).
% 2.26/2.30 ** KEPT (pick-wt=8): 112 [copy,111,flip.1] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 2.26/2.30 ---> New Demodulator: 113 [new_demod,112] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 2.26/2.30 ** KEPT (pick-wt=8): 115 [copy,114,flip.1] power_class(A)=complement(image(element_relation,complement(A))).
% 2.26/2.30 ---> New Demodulator: 116 [new_demod,115] power_class(A)=complement(image(element_relation,complement(A))).
% 2.26/2.30 ** KEPT (pick-wt=7): 117 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 2.26/2.30 ** KEPT (pick-wt=7): 118 [] A=null_class|member(regular(A),A).
% 2.26/2.30 ** KEPT (pick-wt=9): 119 [] A=null_class|intersection(A,regular(A))=null_class.
% 2.26/2.30 ** KEPT (pick-wt=13): 121 [copy,120,demod,74,113] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 2.26/2.30 ---> New Demodulator: 122 [new_demod,121] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 2.26/2.30 ** KEPT (pick-wt=2): 123 [] function(choice).
% 2.26/2.30 ** KEPT (pick-wt=17): 125 [copy,124,demod,92,87,87] 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.
% 2.26/2.30 ---> New Demodulator: 126 [new_demod,125] 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.
% 2.26/2.30 ** KEPT (pick-wt=9): 128 [copy,127,demod,92] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 2.26/2.30 ---> New Demodulator: 129 [new_demod,128] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 2.26/2.30 ** KEPT (pick-wt=8): 130 [] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 2.26/2.30 ---> New Demodulator: 131 [new_demod,130] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 2.42/2.45 ** KEPT (pick-wt=14): 133 [copy,132,demod,92] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 2.42/2.45 ---> New Demodulator: 134 [new_demod,133] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 2.42/2.45 ** KEPT (pick-wt=7): 135 [] member(ordered_pair(x,y),cross_product(u,v)).
% 2.42/2.45 ** KEPT (pick-wt=5): 136 [] unordered_pair(x,y)=null_class.
% 2.42/2.45 ---> New Demodulator: 137 [new_demod,136] unordered_pair(x,y)=null_class.
% 2.42/2.45 Following clause subsumed by 68 during input processing: 0 [copy,68,flip.1] A=A.
% 2.42/2.45 68 back subsumes 60.
% 2.42/2.45 >>>> Starting back demodulation with 74.
% 2.42/2.45 >> back demodulating 35 with 74.
% 2.42/2.45 >> back demodulating 34 with 74.
% 2.42/2.45 >> back demodulating 21 with 74.
% 2.42/2.45 >> back demodulating 20 with 74.
% 2.42/2.45 >>>> Starting back demodulation with 77.
% 2.42/2.45 >>>> Starting back demodulation with 80.
% 2.42/2.45 >>>> Starting back demodulation with 83.
% 2.42/2.45 >>>> Starting back demodulation with 85.
% 2.42/2.45 >>>> Starting back demodulation with 87.
% 2.42/2.45 >>>> Starting back demodulation with 92.
% 2.42/2.45 >> back demodulating 45 with 92.
% 2.42/2.45 >> back demodulating 44 with 92.
% 2.42/2.45 >> back demodulating 40 with 92.
% 2.42/2.45 >> back demodulating 39 with 92.
% 2.42/2.45 >> back demodulating 37 with 92.
% 2.42/2.45 >> back demodulating 36 with 92.
% 2.42/2.45 >>>> Starting back demodulation with 95.
% 2.42/2.45 >> back demodulating 53 with 95.
% 2.42/2.45 >> back demodulating 52 with 95.
% 2.42/2.45 >> back demodulating 49 with 95.
% 2.42/2.45 >> back demodulating 48 with 95.
% 2.42/2.45 >>>> Starting back demodulation with 98.
% 2.42/2.45 >>>> Starting back demodulation with 101.
% 2.42/2.45 >>>> Starting back demodulation with 104.
% 2.42/2.45 >>>> Starting back demodulation with 107.
% 2.42/2.45 >> back demodulating 27 with 107.
% 2.42/2.45 >> back demodulating 26 with 107.
% 2.42/2.45 >>>> Starting back demodulation with 113.
% 2.42/2.45 >> back demodulating 32 with 113.
% 2.42/2.45 >>>> Starting back demodulation with 116.
% 2.42/2.45 >> back demodulating 33 with 116.
% 2.42/2.45 >>>> Starting back demodulation with 122.
% 2.42/2.45 >>>> Starting back demodulation with 126.
% 2.42/2.45 >>>> Starting back demodulation with 129.
% 2.42/2.45 >>>> Starting back demodulation with 131.
% 2.42/2.45 >>>> Starting back demodulation with 134.
% 2.42/2.45 >>>> Starting back demodulation with 137.
% 2.42/2.45
% 2.42/2.45 ======= end of input processing =======
% 2.42/2.45
% 2.42/2.45 =========== start of search ===========
% 2.42/2.45
% 2.42/2.45
% 2.42/2.45 Resetting weight limit to 7.
% 2.42/2.45
% 2.42/2.45
% 2.42/2.45 Resetting weight limit to 7.
% 2.42/2.45
% 2.42/2.45 sos_size=570
% 2.42/2.45
% 2.42/2.45 -------- PROOF --------
% 2.42/2.45
% 2.42/2.45 -----> EMPTY CLAUSE at 0.16 sec ----> 1046 [hyper,1042,785,762] $F.
% 2.42/2.45
% 2.42/2.45 Length of proof is 7. Level of proof is 3.
% 2.42/2.45
% 2.42/2.45 ---------------- PROOF ----------------
% 2.42/2.45 % SZS status Unsatisfiable
% 2.42/2.45 % SZS output start Refutation
% See solution above
% 2.42/2.45 ------------ end of proof -------------
% 2.42/2.45
% 2.42/2.45
% 2.42/2.45 Search stopped by max_proofs option.
% 2.42/2.45
% 2.42/2.45
% 2.42/2.45 Search stopped by max_proofs option.
% 2.42/2.45
% 2.42/2.45 ============ end of search ============
% 2.42/2.45
% 2.42/2.45 -------------- statistics -------------
% 2.42/2.45 clauses given 180
% 2.42/2.45 clauses generated 23810
% 2.42/2.45 clauses kept 1005
% 2.42/2.45 clauses forward subsumed 759
% 2.42/2.45 clauses back subsumed 13
% 2.42/2.45 Kbytes malloced 5859
% 2.42/2.45
% 2.42/2.45 ----------- times (seconds) -----------
% 2.42/2.45 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 2.42/2.45 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.42/2.45 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.42/2.45
% 2.42/2.45 That finishes the proof of the theorem.
% 2.42/2.45
% 2.42/2.45 Process 27424 finished Wed Jul 27 10:42:43 2022
% 2.42/2.45 Otter interrupted
% 2.42/2.45 PROOF FOUND
%------------------------------------------------------------------------------