TSTP Solution File: SET077-7 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET077-7 : 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 2.57s 2.74s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 3 RR)
% Number of literals : 6 ( 2 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(77,axiom,
~ member(singleton(x),universal_class),
file('SET077-7.p',unknown),
[] ).
cnf(91,axiom,
member(unordered_pair(A,B),universal_class),
file('SET077-7.p',unknown),
[] ).
cnf(92,axiom,
unordered_pair(A,A) = singleton(A),
file('SET077-7.p',unknown),
[] ).
cnf(94,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[92])]),
[iquote('copy,92,flip.1')] ).
cnf(170,plain,
~ member(unordered_pair(x,x),universal_class),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[77]),94]),
[iquote('back_demod,77,demod,94')] ).
cnf(171,plain,
$false,
inference(binary,[status(thm)],[170,91]),
[iquote('binary,170.1,91.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET077-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 10:33:26 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.57/2.73 ----- Otter 3.3f, August 2004 -----
% 2.57/2.73 The process was started by sandbox2 on n003.cluster.edu,
% 2.57/2.73 Wed Jul 27 10:33:27 2022
% 2.57/2.73 The command was "./otter". The process ID is 9999.
% 2.57/2.73
% 2.57/2.73 set(prolog_style_variables).
% 2.57/2.73 set(auto).
% 2.57/2.73 dependent: set(auto1).
% 2.57/2.73 dependent: set(process_input).
% 2.57/2.73 dependent: clear(print_kept).
% 2.57/2.73 dependent: clear(print_new_demod).
% 2.57/2.73 dependent: clear(print_back_demod).
% 2.57/2.73 dependent: clear(print_back_sub).
% 2.57/2.73 dependent: set(control_memory).
% 2.57/2.73 dependent: assign(max_mem, 12000).
% 2.57/2.73 dependent: assign(pick_given_ratio, 4).
% 2.57/2.73 dependent: assign(stats_level, 1).
% 2.57/2.73 dependent: assign(max_seconds, 10800).
% 2.57/2.73 clear(print_given).
% 2.57/2.73
% 2.57/2.73 list(usable).
% 2.57/2.73 0 [] A=A.
% 2.57/2.73 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 2.57/2.73 0 [] member(not_subclass_element(X,Y),X)|subclass(X,Y).
% 2.57/2.73 0 [] -member(not_subclass_element(X,Y),Y)|subclass(X,Y).
% 2.57/2.73 0 [] subclass(X,universal_class).
% 2.57/2.73 0 [] X!=Y|subclass(X,Y).
% 2.57/2.73 0 [] X!=Y|subclass(Y,X).
% 2.57/2.73 0 [] -subclass(X,Y)| -subclass(Y,X)|X=Y.
% 2.57/2.73 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 2.57/2.73 0 [] -member(X,universal_class)|member(X,unordered_pair(X,Y)).
% 2.57/2.73 0 [] -member(Y,universal_class)|member(Y,unordered_pair(X,Y)).
% 2.57/2.73 0 [] member(unordered_pair(X,Y),universal_class).
% 2.57/2.73 0 [] unordered_pair(X,X)=singleton(X).
% 2.57/2.73 0 [] unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))=ordered_pair(X,Y).
% 2.57/2.73 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 2.57/2.73 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 2.57/2.73 0 [] -member(U,X)| -member(V,Y)|member(ordered_pair(U,V),cross_product(X,Y)).
% 2.57/2.73 0 [] -member(Z,cross_product(X,Y))|ordered_pair(first(Z),second(Z))=Z.
% 2.57/2.73 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 2.57/2.73 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 2.57/2.73 0 [] -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))| -member(X,Y)|member(ordered_pair(X,Y),element_relation).
% 2.57/2.73 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 2.57/2.73 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 2.57/2.73 0 [] -member(Z,X)| -member(Z,Y)|member(Z,intersection(X,Y)).
% 2.57/2.73 0 [] -member(Z,complement(X))| -member(Z,X).
% 2.57/2.73 0 [] -member(Z,universal_class)|member(Z,complement(X))|member(Z,X).
% 2.57/2.73 0 [] complement(intersection(complement(X),complement(Y)))=union(X,Y).
% 2.57/2.73 0 [] intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y))))=symmetric_difference(X,Y).
% 2.57/2.73 0 [] intersection(Xr,cross_product(X,Y))=restrict(Xr,X,Y).
% 2.57/2.73 0 [] intersection(cross_product(X,Y),Xr)=restrict(Xr,X,Y).
% 2.57/2.73 0 [] restrict(X,singleton(Z),universal_class)!=null_class| -member(Z,domain_of(X)).
% 2.57/2.73 0 [] -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class|member(Z,domain_of(X)).
% 2.57/2.73 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.57/2.73 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 2.57/2.73 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)).
% 2.57/2.73 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.57/2.73 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 2.57/2.73 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)).
% 2.57/2.73 0 [] domain_of(flip(cross_product(Y,universal_class)))=inverse(Y).
% 2.57/2.73 0 [] domain_of(inverse(Z))=range_of(Z).
% 2.57/2.73 0 [] first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class))=domain(Z,X,Y).
% 2.57/2.73 0 [] second(not_subclass_element(restrict(Z,singleton(X),Y),null_class))=range(Z,X,Y).
% 2.57/2.73 0 [] range_of(restrict(Xr,X,universal_class))=image(Xr,X).
% 2.57/2.73 0 [] union(X,singleton(X))=successor(X).
% 2.57/2.73 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 2.57/2.73 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 2.57/2.73 0 [] successor(X)!=Y| -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))|member(ordered_pair(X,Y),successor_relation).
% 2.57/2.73 0 [] -inductive(X)|member(null_class,X).
% 2.57/2.73 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 2.57/2.73 0 [] -member(null_class,X)| -subclass(image(successor_relation,X),X)|inductive(X).
% 2.57/2.73 0 [] inductive(omega).
% 2.57/2.73 0 [] -inductive(Y)|subclass(omega,Y).
% 2.57/2.73 0 [] member(omega,universal_class).
% 2.57/2.73 0 [] domain_of(restrict(element_relation,universal_class,X))=sum_class(X).
% 2.57/2.73 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 2.57/2.73 0 [] complement(image(element_relation,complement(X)))=power_class(X).
% 2.57/2.73 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 2.57/2.73 0 [] subclass(compose(Yr,Xr),cross_product(universal_class,universal_class)).
% 2.57/2.73 0 [] -member(ordered_pair(Y,Z),compose(Yr,Xr))|member(Z,image(Yr,image(Xr,singleton(Y)))).
% 2.57/2.73 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)).
% 2.57/2.73 0 [] -single_valued_class(X)|subclass(compose(X,inverse(X)),identity_relation).
% 2.57/2.73 0 [] -subclass(compose(X,inverse(X)),identity_relation)|single_valued_class(X).
% 2.57/2.73 0 [] -function(Xf)|subclass(Xf,cross_product(universal_class,universal_class)).
% 2.57/2.73 0 [] -function(Xf)|subclass(compose(Xf,inverse(Xf)),identity_relation).
% 2.57/2.73 0 [] -subclass(Xf,cross_product(universal_class,universal_class))| -subclass(compose(Xf,inverse(Xf)),identity_relation)|function(Xf).
% 2.57/2.73 0 [] -function(Xf)| -member(X,universal_class)|member(image(Xf,X),universal_class).
% 2.57/2.73 0 [] X=null_class|member(regular(X),X).
% 2.57/2.73 0 [] X=null_class|intersection(X,regular(X))=null_class.
% 2.57/2.73 0 [] sum_class(image(Xf,singleton(Y)))=apply(Xf,Y).
% 2.57/2.73 0 [] function(choice).
% 2.57/2.73 0 [] -member(Y,universal_class)|Y=null_class|member(apply(choice,Y),Y).
% 2.57/2.73 0 [] -one_to_one(Xf)|function(Xf).
% 2.57/2.73 0 [] -one_to_one(Xf)|function(inverse(Xf)).
% 2.57/2.73 0 [] -function(inverse(Xf))| -function(Xf)|one_to_one(Xf).
% 2.57/2.73 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.
% 2.57/2.73 0 [] intersection(inverse(subset_relation),subset_relation)=identity_relation.
% 2.57/2.73 0 [] complement(domain_of(intersection(Xr,identity_relation)))=diagonalise(Xr).
% 2.57/2.73 0 [] intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X)))=cantor(X).
% 2.57/2.73 0 [] -operation(Xf)|function(Xf).
% 2.57/2.73 0 [] -operation(Xf)|cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf)))=domain_of(Xf).
% 2.57/2.73 0 [] -operation(Xf)|subclass(range_of(Xf),domain_of(domain_of(Xf))).
% 2.57/2.73 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).
% 2.57/2.73 0 [] -compatible(Xh,Xf1,Xf2)|function(Xh).
% 2.57/2.73 0 [] -compatible(Xh,Xf1,Xf2)|domain_of(domain_of(Xf1))=domain_of(Xh).
% 2.57/2.73 0 [] -compatible(Xh,Xf1,Xf2)|subclass(range_of(Xh),domain_of(domain_of(Xf2))).
% 2.57/2.73 0 [] -function(Xh)|domain_of(domain_of(Xf1))!=domain_of(Xh)| -subclass(range_of(Xh),domain_of(domain_of(Xf2)))|compatible(Xh,Xf1,Xf2).
% 2.57/2.73 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf1).
% 2.57/2.73 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf2).
% 2.57/2.73 0 [] -homomorphism(Xh,Xf1,Xf2)|compatible(Xh,Xf1,Xf2).
% 2.57/2.73 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))).
% 2.57/2.73 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).
% 2.57/2.73 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).
% 2.57/2.73 0 [] -member(ordered_pair(X,Y),cross_product(U,V))|member(X,unordered_pair(X,Y)).
% 2.57/2.73 0 [] -member(ordered_pair(X,Y),cross_product(U,V))|member(Y,unordered_pair(X,Y)).
% 2.57/2.73 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,universal_class).
% 2.57/2.73 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,universal_class).
% 2.57/2.74 0 [] subclass(X,X).
% 2.57/2.74 0 [] -subclass(X,Y)| -subclass(Y,Z)|subclass(X,Z).
% 2.57/2.74 0 [] X=Y|member(not_subclass_element(X,Y),X)|member(not_subclass_element(Y,X),Y).
% 2.57/2.74 0 [] -member(not_subclass_element(X,Y),Y)|X=Y|member(not_subclass_element(Y,X),Y).
% 2.57/2.74 0 [] -member(not_subclass_element(Y,X),X)|X=Y|member(not_subclass_element(X,Y),X).
% 2.57/2.74 0 [] -member(not_subclass_element(X,Y),Y)| -member(not_subclass_element(Y,X),X)|X=Y.
% 2.57/2.74 0 [] -member(Y,intersection(complement(X),X)).
% 2.57/2.74 0 [] -member(Z,null_class).
% 2.57/2.74 0 [] subclass(null_class,X).
% 2.57/2.74 0 [] -subclass(X,null_class)|X=null_class.
% 2.57/2.74 0 [] Z=null_class|member(not_subclass_element(Z,null_class),Z).
% 2.57/2.74 0 [] member(null_class,universal_class).
% 2.57/2.74 0 [] unordered_pair(X,Y)=unordered_pair(Y,X).
% 2.57/2.74 0 [] subclass(singleton(X),unordered_pair(X,Y)).
% 2.57/2.74 0 [] subclass(singleton(Y),unordered_pair(X,Y)).
% 2.57/2.74 0 [] member(Y,universal_class)|unordered_pair(X,Y)=singleton(X).
% 2.57/2.74 0 [] member(X,universal_class)|unordered_pair(X,Y)=singleton(Y).
% 2.57/2.74 0 [] unordered_pair(X,Y)=null_class|member(X,universal_class)|member(Y,universal_class).
% 2.57/2.74 0 [] unordered_pair(X,Y)!=unordered_pair(X,Z)| -member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))|Y=Z.
% 2.57/2.74 0 [] unordered_pair(X,Z)!=unordered_pair(Y,Z)| -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))|X=Y.
% 2.57/2.74 0 [] -member(X,universal_class)|unordered_pair(X,Y)!=null_class.
% 2.57/2.74 0 [] -member(Y,universal_class)|unordered_pair(X,Y)!=null_class.
% 2.57/2.74 0 [] -member(ordered_pair(X,Y),cross_product(U,V))|unordered_pair(X,Y)!=null_class.
% 2.57/2.74 0 [] -member(X,Z)| -member(Y,Z)|subclass(unordered_pair(X,Y),Z).
% 2.57/2.74 0 [] -member(singleton(x),universal_class).
% 2.57/2.74 end_of_list.
% 2.57/2.74
% 2.57/2.74 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.57/2.74
% 2.57/2.74 This ia a non-Horn set with equality. The strategy will be
% 2.57/2.74 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.57/2.74 deletion, with positive clauses in sos and nonpositive
% 2.57/2.74 clauses in usable.
% 2.57/2.74
% 2.57/2.74 dependent: set(knuth_bendix).
% 2.57/2.74 dependent: set(anl_eq).
% 2.57/2.74 dependent: set(para_from).
% 2.57/2.74 dependent: set(para_into).
% 2.57/2.74 dependent: clear(para_from_right).
% 2.57/2.74 dependent: clear(para_into_right).
% 2.57/2.74 dependent: set(para_from_vars).
% 2.57/2.74 dependent: set(eq_units_both_ways).
% 2.57/2.74 dependent: set(dynamic_demod_all).
% 2.57/2.74 dependent: set(dynamic_demod).
% 2.57/2.74 dependent: set(order_eq).
% 2.57/2.74 dependent: set(back_demod).
% 2.57/2.74 dependent: set(lrpo).
% 2.57/2.74 dependent: set(hyper_res).
% 2.57/2.74 dependent: set(unit_deletion).
% 2.57/2.74 dependent: set(factor).
% 2.57/2.74
% 2.57/2.74 ------------> process usable:
% 2.57/2.74 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 2.57/2.74 ** KEPT (pick-wt=8): 2 [] -member(not_subclass_element(A,B),B)|subclass(A,B).
% 2.57/2.74 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 2.57/2.74 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 2.57/2.74 ** KEPT (pick-wt=9): 5 [] -subclass(A,B)| -subclass(B,A)|A=B.
% 2.57/2.74 ** KEPT (pick-wt=11): 6 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 2.57/2.74 ** KEPT (pick-wt=8): 7 [] -member(A,universal_class)|member(A,unordered_pair(A,B)).
% 2.57/2.74 ** KEPT (pick-wt=8): 8 [] -member(A,universal_class)|member(A,unordered_pair(B,A)).
% 2.57/2.74 ** KEPT (pick-wt=10): 9 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 2.57/2.74 ** KEPT (pick-wt=10): 10 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 2.57/2.74 ** KEPT (pick-wt=13): 11 [] -member(A,B)| -member(C,D)|member(ordered_pair(A,C),cross_product(B,D)).
% 2.57/2.74 ** KEPT (pick-wt=12): 12 [] -member(A,cross_product(B,C))|ordered_pair(first(A),second(A))=A.
% 2.57/2.74 ** KEPT (pick-wt=8): 13 [] -member(ordered_pair(A,B),element_relation)|member(A,B).
% 2.57/2.74 ** 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).
% 2.57/2.74 ** KEPT (pick-wt=8): 15 [] -member(A,intersection(B,C))|member(A,B).
% 2.57/2.74 ** KEPT (pick-wt=8): 16 [] -member(A,intersection(B,C))|member(A,C).
% 2.57/2.74 ** KEPT (pick-wt=11): 17 [] -member(A,B)| -member(A,C)|member(A,intersection(B,C)).
% 2.57/2.74 ** KEPT (pick-wt=7): 18 [] -member(A,complement(B))| -member(A,B).
% 2.57/2.74 ** KEPT (pick-wt=10): 19 [] -member(A,universal_class)|member(A,complement(B))|member(A,B).
% 2.57/2.74 ** KEPT (pick-wt=11): 20 [] restrict(A,singleton(B),universal_class)!=null_class| -member(B,domain_of(A)).
% 2.57/2.74 ** KEPT (pick-wt=14): 21 [] -member(A,universal_class)|restrict(B,singleton(A),universal_class)=null_class|member(A,domain_of(B)).
% 2.57/2.74 ** KEPT (pick-wt=15): 22 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(B,C),A),D).
% 2.57/2.74 ** 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)).
% 2.57/2.74 ** KEPT (pick-wt=15): 24 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(B,A),C),D).
% 2.57/2.74 ** 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)).
% 2.57/2.74 ** KEPT (pick-wt=9): 26 [] -member(ordered_pair(A,B),successor_relation)|successor(A)=B.
% 2.57/2.74 ** 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).
% 2.57/2.74 ** KEPT (pick-wt=5): 28 [] -inductive(A)|member(null_class,A).
% 2.57/2.74 ** KEPT (pick-wt=7): 29 [] -inductive(A)|subclass(image(successor_relation,A),A).
% 2.57/2.74 ** KEPT (pick-wt=10): 30 [] -member(null_class,A)| -subclass(image(successor_relation,A),A)|inductive(A).
% 2.57/2.74 ** KEPT (pick-wt=5): 31 [] -inductive(A)|subclass(omega,A).
% 2.57/2.74 ** KEPT (pick-wt=7): 32 [] -member(A,universal_class)|member(sum_class(A),universal_class).
% 2.57/2.74 ** KEPT (pick-wt=7): 33 [] -member(A,universal_class)|member(power_class(A),universal_class).
% 2.57/2.74 ** KEPT (pick-wt=15): 34 [] -member(ordered_pair(A,B),compose(C,D))|member(B,image(C,image(D,singleton(A)))).
% 2.57/2.74 ** 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)).
% 2.57/2.74 ** KEPT (pick-wt=8): 36 [] -single_valued_class(A)|subclass(compose(A,inverse(A)),identity_relation).
% 2.57/2.74 ** KEPT (pick-wt=8): 37 [] -subclass(compose(A,inverse(A)),identity_relation)|single_valued_class(A).
% 2.57/2.74 ** KEPT (pick-wt=7): 38 [] -function(A)|subclass(A,cross_product(universal_class,universal_class)).
% 2.57/2.74 ** KEPT (pick-wt=8): 39 [] -function(A)|subclass(compose(A,inverse(A)),identity_relation).
% 2.57/2.74 ** KEPT (pick-wt=13): 40 [] -subclass(A,cross_product(universal_class,universal_class))| -subclass(compose(A,inverse(A)),identity_relation)|function(A).
% 2.57/2.74 ** KEPT (pick-wt=10): 41 [] -function(A)| -member(B,universal_class)|member(image(A,B),universal_class).
% 2.57/2.74 ** KEPT (pick-wt=11): 42 [] -member(A,universal_class)|A=null_class|member(apply(choice,A),A).
% 2.57/2.74 ** KEPT (pick-wt=4): 43 [] -one_to_one(A)|function(A).
% 2.57/2.74 ** KEPT (pick-wt=5): 44 [] -one_to_one(A)|function(inverse(A)).
% 2.57/2.74 ** KEPT (pick-wt=7): 45 [] -function(inverse(A))| -function(A)|one_to_one(A).
% 2.57/2.74 ** KEPT (pick-wt=4): 46 [] -operation(A)|function(A).
% 2.57/2.74 ** KEPT (pick-wt=12): 47 [] -operation(A)|cross_product(domain_of(domain_of(A)),domain_of(domain_of(A)))=domain_of(A).
% 2.57/2.74 ** KEPT (pick-wt=8): 48 [] -operation(A)|subclass(range_of(A),domain_of(domain_of(A))).
% 2.57/2.74 ** 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).
% 2.57/2.74 ** KEPT (pick-wt=6): 50 [] -compatible(A,B,C)|function(A).
% 2.57/2.74 ** KEPT (pick-wt=10): 51 [] -compatible(A,B,C)|domain_of(domain_of(B))=domain_of(A).
% 2.57/2.74 ** KEPT (pick-wt=10): 52 [] -compatible(A,B,C)|subclass(range_of(A),domain_of(domain_of(C))).
% 2.57/2.74 ** 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).
% 2.57/2.74 ** KEPT (pick-wt=6): 54 [] -homomorphism(A,B,C)|operation(B).
% 2.57/2.74 ** KEPT (pick-wt=6): 55 [] -homomorphism(A,B,C)|operation(C).
% 2.57/2.74 ** KEPT (pick-wt=8): 56 [] -homomorphism(A,B,C)|compatible(A,B,C).
% 2.57/2.74 ** 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))).
% 2.57/2.74 ** 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).
% 2.57/2.74 ** 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).
% 2.57/2.74 ** KEPT (pick-wt=12): 60 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,unordered_pair(A,B)).
% 2.57/2.74 ** KEPT (pick-wt=12): 61 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,unordered_pair(A,B)).
% 2.57/2.74 ** KEPT (pick-wt=10): 62 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,universal_class).
% 2.57/2.74 ** KEPT (pick-wt=10): 63 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,universal_class).
% 2.57/2.74 ** KEPT (pick-wt=9): 64 [] -subclass(A,B)| -subclass(B,C)|subclass(A,C).
% 2.57/2.74 ** KEPT (pick-wt=13): 65 [] -member(not_subclass_element(A,B),B)|A=B|member(not_subclass_element(B,A),B).
% 2.57/2.74 ** KEPT (pick-wt=13): 66 [] -member(not_subclass_element(A,B),B)|B=A|member(not_subclass_element(B,A),B).
% 2.57/2.74 ** KEPT (pick-wt=13): 67 [] -member(not_subclass_element(A,B),B)| -member(not_subclass_element(B,A),A)|A=B.
% 2.57/2.74 ** KEPT (pick-wt=6): 68 [] -member(A,intersection(complement(B),B)).
% 2.57/2.74 ** KEPT (pick-wt=3): 69 [] -member(A,null_class).
% 2.57/2.74 ** KEPT (pick-wt=6): 70 [] -subclass(A,null_class)|A=null_class.
% 2.57/2.74 ** KEPT (pick-wt=17): 71 [] unordered_pair(A,B)!=unordered_pair(A,C)| -member(ordered_pair(B,C),cross_product(universal_class,universal_class))|B=C.
% 2.57/2.74 ** KEPT (pick-wt=17): 72 [] unordered_pair(A,B)!=unordered_pair(C,B)| -member(ordered_pair(A,C),cross_product(universal_class,universal_class))|A=C.
% 2.57/2.74 ** KEPT (pick-wt=8): 73 [] -member(A,universal_class)|unordered_pair(A,B)!=null_class.
% 2.57/2.74 ** KEPT (pick-wt=8): 74 [] -member(A,universal_class)|unordered_pair(B,A)!=null_class.
% 2.57/2.74 ** KEPT (pick-wt=12): 75 [] -member(ordered_pair(A,B),cross_product(C,D))|unordered_pair(A,B)!=null_class.
% 2.57/2.74 ** KEPT (pick-wt=11): 76 [] -member(A,B)| -member(C,B)|subclass(unordered_pair(A,C),B).
% 2.57/2.74 ** KEPT (pick-wt=4): 77 [] -member(singleton(x),universal_class).
% 2.57/2.74
% 2.57/2.74 ------------> process sos:
% 2.57/2.74 ** KEPT (pick-wt=3): 88 [] A=A.
% 2.57/2.74 ** KEPT (pick-wt=8): 89 [] member(not_subclass_element(A,B),A)|subclass(A,B).
% 2.57/2.74 ** KEPT (pick-wt=3): 90 [] subclass(A,universal_class).
% 2.57/2.74 ** KEPT (pick-wt=5): 91 [] member(unordered_pair(A,B),universal_class).
% 2.57/2.74 ** KEPT (pick-wt=6): 93 [copy,92,flip.1] singleton(A)=unordered_pair(A,A).
% 2.57/2.74 ---> New Demodulator: 94 [new_demod,93] singleton(A)=unordered_pair(A,A).
% 2.57/2.74 ** KEPT (pick-wt=13): 96 [copy,95,demod,94,94] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 2.57/2.74 ---> New Demodulator: 97 [new_demod,96] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 2.57/2.74 ** KEPT (pick-wt=5): 98 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 2.57/2.74 ** KEPT (pick-wt=10): 99 [] complement(intersection(complement(A),complement(B)))=union(A,B).
% 2.57/2.74 ---> New Demodulator: 100 [new_demod,99] complement(intersection(complement(A),complement(B)))=union(A,B).
% 2.57/2.74 ** KEPT (pick-wt=12): 102 [copy,101,demod,100] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 2.57/2.74 ---> New Demodulator: 103 [new_demod,102] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 2.57/2.74 ** KEPT (pick-wt=10): 104 [] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 2.57/2.74 ---> New Demodulator: 105 [new_demod,104] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 2.57/2.74 ** KEPT (pick-wt=10): 106 [] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 2.57/2.74 ---> New Demodulator: 107 [new_demod,106] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 2.57/2.74 ** KEPT (pick-wt=8): 108 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.57/2.74 ** KEPT (pick-wt=8): 109 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 2.57/2.74 ** KEPT (pick-wt=8): 111 [copy,110,flip.1] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 2.57/2.74 ---> New Demodulator: 112 [new_demod,111] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 2.57/2.74 ** KEPT (pick-wt=9): 114 [copy,113,demod,112,flip.1] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 2.57/2.74 ---> New Demodulator: 115 [new_demod,114] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 2.57/2.74 ** KEPT (pick-wt=14): 117 [copy,116,demod,94] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 2.57/2.74 ---> New Demodulator: 118 [new_demod,117] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 2.57/2.74 ** KEPT (pick-wt=14): 120 [copy,119,demod,94] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 2.57/2.74 ---> New Demodulator: 121 [new_demod,120] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 2.57/2.74 ** KEPT (pick-wt=13): 123 [copy,122,demod,115] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 2.57/2.74 ---> New Demodulator: 124 [new_demod,123] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 2.57/2.74 ** KEPT (pick-wt=8): 126 [copy,125,demod,94,flip.1] successor(A)=union(A,unordered_pair(A,A)).
% 2.57/2.74 ---> New Demodulator: 127 [new_demod,126] successor(A)=union(A,unordered_pair(A,A)).
% 2.57/2.74 ** KEPT (pick-wt=5): 128 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 2.57/2.74 ** KEPT (pick-wt=2): 129 [] inductive(omega).
% 2.57/2.74 ** KEPT (pick-wt=3): 130 [] member(omega,universal_class).
% 2.57/2.74 ** KEPT (pick-wt=8): 132 [copy,131,flip.1] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 2.57/2.74 ---> New Demodulator: 133 [new_demod,132] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 2.57/2.74 ** KEPT (pick-wt=8): 135 [copy,134,flip.1] power_class(A)=complement(image(element_relation,complement(A))).
% 2.57/2.74 ---> New Demodulator: 136 [new_demod,135] power_class(A)=complement(image(element_relation,complement(A))).
% 2.57/2.74 ** KEPT (pick-wt=7): 137 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 2.57/2.74 ** KEPT (pick-wt=7): 138 [] A=null_class|member(regular(A),A).
% 2.57/2.74 ** KEPT (pick-wt=9): 139 [] A=null_class|intersection(A,regular(A))=null_class.
% 2.57/2.74 ** KEPT (pick-wt=13): 141 [copy,140,demod,94,133] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 2.57/2.74 ---> New Demodulator: 142 [new_demod,141] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 2.57/2.74 ** KEPT (pick-wt=2): 143 [] function(choice).
% 2.57/2.74 ** KEPT (pick-wt=17): 145 [copy,144,demod,112,107,107] 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.
% 2.57/2.74 ---> New Demodulator: 146 [new_demod,145] 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.
% 2.57/2.74 ** KEPT (pick-wt=9): 148 [copy,147,demod,112] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 2.57/2.74 ---> New Demodulator: 149 [new_demod,148] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 2.57/2.74 ** KEPT (pick-wt=8): 150 [] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 2.57/2.74 ---> New Demodulator: 151 [new_demod,150] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 2.57/2.74 ** KEPT (pick-wt=14): 153 [copy,152,demod,112] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 2.57/2.74 ---> New Demodulator: 154 [new_demod,153] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 2.57/2.74 ** KEPT (pick-wt=3): 155 [] subclass(A,A).
% 2.57/2.74 ** KEPT (pick-wt=13): 156 [] A=B|member(not_subclass_element(A,B),A)|member(not_subclass
% 2.57/2.74 -------- PROOF --------
% 2.57/2.74 _element(B,A),B).
% 2.57/2.74 ** KEPT (pick-wt=3): 157 [] subclass(null_class,A).
% 2.57/2.74 ** KEPT (pick-wt=8): 158 [] A=null_class|member(not_subclass_element(A,null_class),A).
% 2.57/2.74 ** KEPT (pick-wt=3): 159 [] member(null_class,universal_class).
% 2.57/2.74 ** KEPT (pick-wt=7): 160 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.57/2.74 ** KEPT (pick-wt=7): 162 [copy,161,demod,94] subclass(unordered_pair(A,A),unordered_pair(A,B)).
% 2.57/2.74 ** KEPT (pick-wt=7): 164 [copy,163,demod,94] subclass(unordered_pair(A,A),unordered_pair(B,A)).
% 2.57/2.74 ** KEPT (pick-wt=10): 166 [copy,165,demod,94] member(A,universal_class)|unordered_pair(B,A)=unordered_pair(B,B).
% 2.57/2.74 ** KEPT (pick-wt=10): 168 [copy,167,demod,94] member(A,universal_class)|unordered_pair(A,B)=unordered_pair(B,B).
% 2.57/2.74 ** KEPT (pick-wt=11): 169 [] unordered_pair(A,B)=null_class|member(A,universal_class)|member(B,universal_class).
% 2.57/2.74 Following clause subsumed by 88 during input processing: 0 [copy,88,flip.1] A=A.
% 2.57/2.74 88 back subsumes 86.
% 2.57/2.74 88 back subsumes 78.
% 2.57/2.74 >>>> Starting back demodulation with 94.
% 2.57/2.74 >> back demodulating 77 with 94.
% 2.57/2.74
% 2.57/2.74 ----> UNIT CONFLICT at 0.01 sec ----> 171 [binary,170.1,91.1] $F.
% 2.57/2.74
% 2.57/2.74 Length of proof is 2. Level of proof is 2.
% 2.57/2.74
% 2.57/2.74 ---------------- PROOF ----------------
% 2.57/2.74 % SZS status Unsatisfiable
% 2.57/2.74 % SZS output start Refutation
% See solution above
% 2.57/2.74 ------------ end of proof -------------
% 2.57/2.74
% 2.57/2.74
% 2.57/2.74 Search stopped by max_proofs option.
% 2.57/2.74
% 2.57/2.74
% 2.57/2.74 Search stopped by max_proofs option.
% 2.57/2.74
% 2.57/2.74 ============ end of search ============
% 2.57/2.74
% 2.57/2.74 -------------- statistics -------------
% 2.57/2.74 clauses given 0
% 2.57/2.74 clauses generated 11
% 2.57/2.74 clauses kept 132
% 2.57/2.74 clauses forward subsumed 1
% 2.57/2.74 clauses back subsumed 2
% 2.57/2.74 Kbytes malloced 2929
% 2.57/2.74
% 2.57/2.74 ----------- times (seconds) -----------
% 2.57/2.74 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.57/2.74 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.57/2.74 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.57/2.74
% 2.57/2.74 That finishes the proof of the theorem.
% 2.57/2.74
% 2.57/2.74 Process 9999 finished Wed Jul 27 10:33:29 2022
% 2.57/2.74 Otter interrupted
% 2.57/2.74 PROOF FOUND
%------------------------------------------------------------------------------