%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET103-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 : Mon Jun 24 14:20:45 EDT 2024
% Result : Unsatisfiable 0.60s 0.66s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET103-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n021.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 : Sun Jun 23 17:56:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.52 start to proof:theBenchmark
% 0.60/0.65 %-------------------------------------------
% 0.60/0.65 % File :CSE---1.7
% 0.60/0.65 % Problem :theBenchmark
% 0.60/0.65 % Transform :cnf
% 0.60/0.65 % Format :tptp:raw
% 0.60/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.60/0.65
% 0.60/0.65 % Result :Theorem 0.050000s
% 0.60/0.65 % Output :CNFRefutation 0.050000s
% 0.60/0.65 %-------------------------------------------
% 0.60/0.65 %--------------------------------------------------------------------------
% 0.60/0.65 % File : SET103-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.60/0.65 % Domain : Set Theory
% 0.60/0.65 % Problem : Special member 1 of an ordered pair
% 0.60/0.65 % Version : [Qua92] axioms : Augmented.
% 0.60/0.65 % English :
% 0.60/0.65
% 0.60/0.65 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.60/0.65 % Source : [Quaife]
% 0.60/0.65 % Names : OP3.1 [Qua92]
% 0.60/0.65
% 0.60/0.65 % Status : Unsatisfiable
% 0.60/0.65 % Rating : 0.20 v8.2.0, 0.19 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.18 v7.3.0, 0.33 v7.1.0, 0.25 v7.0.0, 0.40 v6.4.0, 0.33 v6.3.0, 0.36 v6.2.0, 0.50 v6.1.0, 0.43 v6.0.0, 0.50 v5.5.0, 0.55 v5.4.0, 0.50 v5.2.0, 0.38 v5.1.0, 0.35 v5.0.0, 0.29 v4.1.0, 0.38 v4.0.1, 0.45 v3.7.0, 0.30 v3.5.0, 0.36 v3.4.0, 0.33 v3.3.0, 0.29 v3.2.0, 0.31 v3.1.0, 0.27 v2.7.0, 0.25 v2.6.0, 0.22 v2.5.0, 0.27 v2.4.0, 0.25 v2.3.0, 0.12 v2.2.1, 0.50 v2.2.0, 0.33 v2.1.0
% 0.60/0.65 % Syntax : Number of clauses : 149 ( 46 unt; 25 nHn; 97 RR)
% 0.60/0.65 % Number of literals : 298 ( 88 equ; 130 neg)
% 0.60/0.65 % Maximal clause size : 5 ( 2 avg)
% 0.60/0.65 % Maximal term depth : 6 ( 1 avg)
% 0.60/0.65 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.60/0.65 % Number of functors : 42 ( 42 usr; 10 con; 0-3 aty)
% 0.60/0.65 % Number of variables : 279 ( 49 sgn)
% 0.60/0.65 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.60/0.65
% 0.60/0.65 % Comments : Preceding lemmas are added.
% 0.60/0.65 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.60/0.65 %--------------------------------------------------------------------------
% 0.60/0.65 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.60/0.65 include('Axioms/SET004-0.ax').
% 0.60/0.65 %--------------------------------------------------------------------------
% 0.60/0.65 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.60/0.65 cnf(corollary_1_to_unordered_pair,axiom,
% 0.60/0.65 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.60/0.65 | member(X,unordered_pair(X,Y)) ) ).
% 0.60/0.65
% 0.60/0.65 cnf(corollary_2_to_unordered_pair,axiom,
% 0.60/0.65 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.60/0.65 | member(Y,unordered_pair(X,Y)) ) ).
% 0.60/0.65
% 0.60/0.65 %----Corollaries to Cartesian product axiom.
% 0.60/0.65 cnf(corollary_1_to_cartesian_product,axiom,
% 0.60/0.65 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.60/0.65 | member(U,universal_class) ) ).
% 0.60/0.65
% 0.60/0.65 cnf(corollary_2_to_cartesian_product,axiom,
% 0.60/0.65 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.60/0.65 | member(V,universal_class) ) ).
% 0.60/0.65
% 0.60/0.65 %---- PARTIAL ORDER.
% 0.60/0.65 %----(PO1): reflexive.
% 0.60/0.65 cnf(subclass_is_reflexive,axiom,
% 0.60/0.65 subclass(X,X) ).
% 0.60/0.65
% 0.60/0.65 %----(PO2): antisymmetry is part of A-3.
% 0.60/0.65 %----(x < y), (y < x) --> (x = y).
% 0.60/0.65
% 0.60/0.65 %----(PO3): transitivity.
% 0.60/0.65 cnf(transitivity_of_subclass,axiom,
% 0.60/0.65 ( ~ subclass(X,Y)
% 0.60/0.65 | ~ subclass(Y,Z)
% 0.60/0.65 | subclass(X,Z) ) ).
% 0.60/0.65
% 0.60/0.65 %---- EQUALITY.
% 0.60/0.65 %----(EQ1): equality axiom.
% 0.60/0.65 %----a:x:(x = x).
% 0.60/0.65 %----This is always an axiom in the TPTP presentation.
% 0.60/0.65
% 0.60/0.65 %----(EQ2): expanded equality definition.
% 0.60/0.65 cnf(equality1,axiom,
% 0.60/0.65 ( X = Y
% 0.60/0.65 | member(not_subclass_element(X,Y),X)
% 0.60/0.65 | member(not_subclass_element(Y,X),Y) ) ).
% 0.60/0.65
% 0.60/0.65 cnf(equality2,axiom,
% 0.60/0.65 ( ~ member(not_subclass_element(X,Y),Y)
% 0.60/0.65 | X = Y
% 0.60/0.65 | member(not_subclass_element(Y,X),Y) ) ).
% 0.60/0.65
% 0.60/0.65 cnf(equality3,axiom,
% 0.60/0.65 ( ~ member(not_subclass_element(Y,X),X)
% 0.60/0.65 | X = Y
% 0.60/0.65 | member(not_subclass_element(X,Y),X) ) ).
% 0.60/0.65
% 0.60/0.65 cnf(equality4,axiom,
% 0.60/0.65 ( ~ member(not_subclass_element(X,Y),Y)
% 0.60/0.65 | ~ member(not_subclass_element(Y,X),X)
% 0.60/0.65 | X = Y ) ).
% 0.60/0.65
% 0.60/0.65 %---- SPECIAL CLASSES.
% 0.60/0.65 %----(SP1): lemma.
% 0.60/0.65 cnf(special_classes_lemma,axiom,
% 0.60/0.65 ~ member(Y,intersection(complement(X),X)) ).
% 0.60/0.65
% 0.60/0.65 %----(SP2): Existence of O (null class).
% 0.60/0.65 %----e:x:a:z:(-(z e x)).
% 0.60/0.65 cnf(existence_of_null_class,axiom,
% 0.60/0.65 ~ member(Z,null_class) ).
% 0.60/0.65
% 0.60/0.65 %----(SP3): O is a subclass of every class.
% 0.60/0.65 cnf(null_class_is_subclass,axiom,
% 0.60/0.65 subclass(null_class,X) ).
% 0.60/0.65
% 0.60/0.65 %----corollary.
% 0.60/0.65 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.60/0.65 ( ~ subclass(X,null_class)
% 0.60/0.65 | X = null_class ) ).
% 0.60/0.65
% 0.60/0.65 %----(SP4): uniqueness of null class.
% 0.60/0.65 cnf(null_class_is_unique,axiom,
% 0.60/0.65 ( Z = null_class
% 0.60/0.65 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.60/0.65
% 0.60/0.65 %----(SP5): O is a set (follows from axiom of infinity).
% 0.60/0.65 cnf(null_class_is_a_set,axiom,
% 0.60/0.65 member(null_class,universal_class) ).
% 0.60/0.65
% 0.60/0.65 %---- UNORDERED PAIRS.
% 0.60/0.65 %----(UP1): unordered pair is commutative.
% 0.60/0.65 cnf(commutativity_of_unordered_pair,axiom,
% 0.60/0.65 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.60/0.65
% 0.60/0.65 %----(UP2): if one argument is a proper class, pair contains only the
% 0.60/0.65 %----other. In a slightly different form to the paper
% 0.60/0.65 cnf(singleton_in_unordered_pair1,axiom,
% 0.60/0.65 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.60/0.66
% 0.60/0.66 cnf(singleton_in_unordered_pair2,axiom,
% 0.60/0.66 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.60/0.66
% 0.60/0.66 cnf(unordered_pair_equals_singleton1,axiom,
% 0.60/0.66 ( member(Y,universal_class)
% 0.60/0.66 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.60/0.66
% 0.60/0.66 cnf(unordered_pair_equals_singleton2,axiom,
% 0.60/0.66 ( member(X,universal_class)
% 0.60/0.66 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.60/0.66
% 0.60/0.66 %----(UP3): if both arguments are proper classes, pair is null.
% 0.60/0.66 cnf(null_unordered_pair,axiom,
% 0.60/0.66 ( unordered_pair(X,Y) = null_class
% 0.60/0.66 | member(X,universal_class)
% 0.60/0.66 | member(Y,universal_class) ) ).
% 0.60/0.66
% 0.60/0.66 %----(UP4): left cancellation for unordered pairs.
% 0.60/0.66 cnf(left_cancellation,axiom,
% 0.60/0.66 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.60/0.66 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.60/0.66 | Y = Z ) ).
% 0.60/0.66
% 0.60/0.66 %----(UP5): right cancellation for unordered pairs.
% 0.60/0.66 cnf(right_cancellation,axiom,
% 0.60/0.66 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.60/0.66 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.60/0.66 | X = Y ) ).
% 0.60/0.66
% 0.60/0.66 %----(UP6): corollary to (A-4).
% 0.60/0.66 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.60/0.66 ( ~ member(X,universal_class)
% 0.60/0.66 | unordered_pair(X,Y) != null_class ) ).
% 0.60/0.66
% 0.60/0.66 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.60/0.66 ( ~ member(Y,universal_class)
% 0.60/0.66 | unordered_pair(X,Y) != null_class ) ).
% 0.60/0.66
% 0.60/0.66 %----corollary to instantiate variables.
% 0.60/0.66 %----Not in the paper
% 0.60/0.66 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.60/0.66 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.60/0.66 | unordered_pair(X,Y) != null_class ) ).
% 0.60/0.66
% 0.60/0.66 %----(UP7): if both members of a pair belong to a set, the pair
% 0.60/0.66 %----is a subset.
% 0.60/0.66 cnf(unordered_pair_is_subset,axiom,
% 0.60/0.66 ( ~ member(X,Z)
% 0.60/0.66 | ~ member(Y,Z)
% 0.60/0.66 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.60/0.66
% 0.60/0.66 %---- SINGLETONS.
% 0.60/0.66 %----(SS1): every singleton is a set.
% 0.60/0.66 cnf(singletons_are_sets,axiom,
% 0.60/0.66 member(singleton(X),universal_class) ).
% 0.60/0.66
% 0.60/0.66 %----corollary, not in the paper.
% 0.60/0.66 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.60/0.66 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.60/0.66
% 0.60/0.66 %----(SS2): a set belongs to its singleton.
% 0.60/0.66 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.60/0.66 cnf(set_in_its_singleton,axiom,
% 0.60/0.66 ( ~ member(X,universal_class)
% 0.60/0.66 | member(X,singleton(X)) ) ).
% 0.60/0.66
% 0.60/0.66 %----corollary
% 0.60/0.66 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.60/0.66 ( ~ member(X,universal_class)
% 0.60/0.66 | singleton(X) != null_class ) ).
% 0.60/0.66
% 0.60/0.66 %----Not in the paper
% 0.60/0.66 cnf(null_class_in_its_singleton,axiom,
% 0.60/0.66 member(null_class,singleton(null_class)) ).
% 0.60/0.66
% 0.60/0.66 %----(SS3): only x can belong to {x}.
% 0.60/0.66 cnf(only_member_in_singleton,axiom,
% 0.60/0.66 ( ~ member(Y,singleton(X))
% 0.60/0.66 | Y = X ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS4): if x is not a set, {x} = O.
% 0.60/0.66 cnf(singleton_is_null_class,axiom,
% 0.60/0.66 ( member(X,universal_class)
% 0.60/0.66 | singleton(X) = null_class ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS5): a singleton set is determined by its element.
% 0.60/0.66 cnf(singleton_identified_by_element1,axiom,
% 0.60/0.66 ( singleton(X) != singleton(Y)
% 0.60/0.66 | ~ member(X,universal_class)
% 0.60/0.66 | X = Y ) ).
% 0.60/0.66
% 0.60/0.66 cnf(singleton_identified_by_element2,axiom,
% 0.60/0.66 ( singleton(X) != singleton(Y)
% 0.60/0.66 | ~ member(Y,universal_class)
% 0.60/0.66 | X = Y ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS5.5).
% 0.60/0.66 %----Not in the paper
% 0.60/0.66 cnf(singleton_in_unordered_pair3,axiom,
% 0.60/0.66 ( unordered_pair(Y,Z) != singleton(X)
% 0.60/0.66 | ~ member(X,universal_class)
% 0.60/0.66 | X = Y
% 0.60/0.66 | X = Z ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS6): existence of memb.
% 0.60/0.66 %----a:x:e:u:(((u e universal_class) & x = {u}) | (-e:y:((y
% 0.60/0.66 %----e universal_class) & x = {y}) & u = x)).
% 0.60/0.66 cnf(member_exists1,axiom,
% 0.60/0.66 ( ~ member(Y,universal_class)
% 0.60/0.66 | member(member_of(singleton(Y)),universal_class) ) ).
% 0.60/0.66
% 0.60/0.66 cnf(member_exists2,axiom,
% 0.60/0.66 ( ~ member(Y,universal_class)
% 0.60/0.66 | singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.60/0.66
% 0.60/0.66 cnf(member_exists3,axiom,
% 0.60/0.66 ( member(member_of(X),universal_class)
% 0.60/0.66 | member_of(X) = X ) ).
% 0.60/0.66
% 0.60/0.66 cnf(member_exists4,axiom,
% 0.60/0.66 ( singleton(member_of(X)) = X
% 0.60/0.66 | member_of(X) = X ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS7): uniqueness of memb of a singleton set.
% 0.60/0.66 %----a:x:a:u:(((u e universal_class) & x = {u}) ==> member_of(x) = u)
% 0.60/0.66 cnf(member_of_singleton_is_unique,axiom,
% 0.60/0.66 ( ~ member(U,universal_class)
% 0.60/0.66 | member_of(singleton(U)) = U ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS8): uniqueness of memb when x is not a singleton of a set.
% 0.60/0.66 %----a:x:a:u:((e:y:((y e universal_class) & x = {y})
% 0.60/0.66 %----& u = x) | member_of(x) = u)
% 0.60/0.66 cnf(member_of_non_singleton_unique1,axiom,
% 0.60/0.66 ( member(member_of1(X),universal_class)
% 0.60/0.66 | member_of(X) = X ) ).
% 0.60/0.66
% 0.60/0.66 cnf(member_of_non_singleton_unique2,axiom,
% 0.60/0.66 ( singleton(member_of1(X)) = X
% 0.60/0.66 | member_of(X) = X ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS9): corollary to (SS1).
% 0.60/0.66 cnf(corollary_2_to_singletons_are_sets,axiom,
% 0.60/0.66 ( singleton(member_of(X)) != X
% 0.60/0.66 | member(X,universal_class) ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS10).
% 0.60/0.66 cnf(property_of_singletons1,axiom,
% 0.60/0.66 ( singleton(member_of(X)) != X
% 0.60/0.66 | ~ member(Y,X)
% 0.60/0.66 | member_of(X) = Y ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS11).
% 0.60/0.66 cnf(property_of_singletons2,axiom,
% 0.60/0.66 ( ~ member(X,Y)
% 0.60/0.66 | subclass(singleton(X),Y) ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS12): there are at most two subsets of a singleton.
% 0.60/0.66 cnf(two_subsets_of_singleton,axiom,
% 0.60/0.66 ( ~ subclass(X,singleton(Y))
% 0.60/0.66 | X = null_class
% 0.60/0.66 | singleton(Y) = X ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS13): a class contains 0, 1, or at least 2 members.
% 0.60/0.66 cnf(number_of_elements_in_class,axiom,
% 0.60/0.66 ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
% 0.60/0.66 | singleton(not_subclass_element(X,null_class)) = X
% 0.60/0.66 | X = null_class ) ).
% 0.60/0.66
% 0.60/0.66 %----corollaries.
% 0.60/0.66 cnf(corollary_2_to_number_of_elements_in_class,axiom,
% 0.60/0.66 ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),X)
% 0.60/0.66 | singleton(not_subclass_element(X,null_class)) = X
% 0.60/0.66 | X = null_class ) ).
% 0.60/0.66
% 0.60/0.66 cnf(corollary_1_to_number_of_elements_in_class,axiom,
% 0.60/0.66 ( not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class) != not_subclass_element(X,null_class)
% 0.60/0.66 | singleton(not_subclass_element(X,null_class)) = X
% 0.60/0.66 | X = null_class ) ).
% 0.60/0.66
% 0.60/0.66 %----(SS14): relation to ordered pair.
% 0.60/0.66 %----It looks like we could simplify Godel's axioms by taking singleton
% 0.60/0.66 %----as a primitive and using the next as a definition. Not in the paper
% 0.60/0.66 cnf(unordered_pairs_and_singletons,axiom,
% 0.60/0.66 unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ).
% 0.60/0.66
% 0.60/0.66 %---- ORDERED PAIRS.
% 0.60/0.66 %----(OP1): an ordered pair is a set.
% 0.60/0.66 cnf(ordered_pair_is_set,axiom,
% 0.60/0.66 member(ordered_pair(X,Y),universal_class) ).
% 0.60/0.66
% 0.60/0.66 %----(OP2): members of ordered pair.
% 0.60/0.66 cnf(singleton_member_of_ordered_pair,axiom,
% 0.60/0.66 member(singleton(X),ordered_pair(X,Y)) ).
% 0.60/0.66
% 0.60/0.66 cnf(unordered_pair_member_of_ordered_pair,axiom,
% 0.60/0.66 member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)) ).
% 0.60/0.66
% 0.60/0.66 cnf(prove_property_1_of_ordered_pair_1,negated_conjecture,
% 0.60/0.66 unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y) ).
% 0.60/0.66
% 0.60/0.66 cnf(prove_property_1_of_ordered_pair_2,negated_conjecture,
% 0.60/0.66 ~ member(y,universal_class) ).
% 0.60/0.66
% 0.60/0.66 %--------------------------------------------------------------------------
% 0.60/0.66 %-------------------------------------------
% 0.60/0.66 % Proof found
% 0.60/0.66 % SZS status Theorem for theBenchmark
% 0.60/0.66 % SZS output start Proof
% 0.60/0.66 %ClaNum:178(EqnAxiom:44)
% 0.60/0.66 %VarNum:1002(SingletonVarNum:246)
% 0.60/0.66 %MaxLitNum:5
% 0.60/0.66 %MaxfuncDepth:24
% 0.60/0.66 %SharedTerms:42
% 0.60/0.66 %goalClause: 72 75
% 0.60/0.66 %singleGoalClaCount:2
% 0.60/0.66 [45]P1(a1)
% 0.60/0.66 [46]P2(a2)
% 0.60/0.66 [47]P5(a4,a19)
% 0.60/0.66 [48]P5(a1,a19)
% 0.60/0.66 [72]~P5(a26,a19)
% 0.60/0.66 [53]P6(a5,f6(a19,a19))
% 0.60/0.66 [54]P6(a20,f6(a19,a19))
% 0.60/0.66 [55]P5(a4,f25(a4,a4))
% 0.60/0.66 [75]~E(f25(f25(a27,a27),f25(a27,f25(a26,a26))),f25(f25(a27,a27),f25(a27,a4)))
% 0.60/0.66 [64]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.60/0.66 [70]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.60/0.66 [49]P6(x491,a19)
% 0.60/0.66 [50]P6(a4,x501)
% 0.60/0.66 [51]P6(x511,x511)
% 0.60/0.66 [73]~P5(x731,a4)
% 0.60/0.66 [62]P6(f21(x621),f6(f6(a19,a19),a19))
% 0.60/0.66 [63]P6(f11(x631),f6(f6(a19,a19),a19))
% 0.60/0.66 [71]E(f10(f9(x711),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x711),a13)))),f3(x711))
% 0.60/0.66 [52]E(f25(x521,x522),f25(x522,x521))
% 0.60/0.66 [56]P5(f25(x561,x562),a19)
% 0.60/0.66 [58]P6(f7(x581,x582),f6(a19,a19))
% 0.60/0.66 [59]P6(f25(x591,x591),f25(x592,x591))
% 0.60/0.66 [60]P6(f25(x601,x601),f25(x601,x602))
% 0.60/0.66 [65]P5(f25(x651,x651),f25(x652,f25(x651,x651)))
% 0.60/0.66 [74]~P5(x741,f10(f8(x742),x742))
% 0.60/0.66 [67]P5(f25(x671,x671),f25(f25(x671,x671),f25(x671,f25(x672,x672))))
% 0.60/0.66 [69]P5(f25(x691,f25(x692,x692)),f25(f25(x691,x691),f25(x691,f25(x692,x692))))
% 0.60/0.66 [68]E(f8(f10(f8(f25(x681,x681)),f8(f25(x682,x682)))),f25(x681,x682))
% 0.60/0.66 [61]E(f10(f6(x611,x612),x613),f10(x613,f6(x611,x612)))
% 0.60/0.66 [76]~P7(x761)+P2(x761)
% 0.60/0.66 [77]~P8(x771)+P2(x771)
% 0.60/0.66 [80]~P1(x801)+P6(a1,x801)
% 0.60/0.66 [81]~P1(x811)+P5(a4,x811)
% 0.60/0.66 [82]~P6(x821,a4)+E(x821,a4)
% 0.60/0.66 [84]P5(f22(x841),x841)+E(x841,a4)
% 0.60/0.66 [85]E(f14(x851),x851)+P5(f14(x851),a19)
% 0.60/0.66 [86]E(f14(x861),x861)+P5(f15(x861),a19)
% 0.60/0.66 [87]P5(x871,a19)+E(f25(x871,x871),a4)
% 0.60/0.67 [90]E(x901,a4)+P5(f16(x901,a4),x901)
% 0.60/0.67 [94]~P2(x941)+P6(x941,f6(a19,a19))
% 0.60/0.67 [83]E(x831,a4)+E(f10(x831,f22(x831)),a4)
% 0.60/0.67 [88]E(f14(x881),x881)+E(f25(f14(x881),f14(x881)),x881)
% 0.60/0.67 [89]E(f14(x891),x891)+E(f25(f15(x891),f15(x891)),x891)
% 0.60/0.67 [99]~P5(x991,a19)+E(f14(f25(x991,x991)),x991)
% 0.60/0.67 [103]P5(x1031,a19)+~E(f25(f14(x1031),f14(x1031)),x1031)
% 0.60/0.67 [127]~P5(x1271,a19)+P5(f14(f25(x1271,x1271)),a19)
% 0.60/0.67 [109]~P8(x1091)+E(f6(f9(f9(x1091)),f9(f9(x1091))),f9(x1091))
% 0.60/0.67 [131]~P7(x1311)+P2(f9(f11(f6(x1311,a19))))
% 0.60/0.67 [135]~P5(x1351,a19)+E(f25(f14(f25(x1351,x1351)),f14(f25(x1351,x1351))),f25(x1351,x1351))
% 0.60/0.67 [137]~P5(x1371,a19)+P5(f9(f10(a5,f6(a19,x1371))),a19)
% 0.60/0.67 [139]~P9(x1391)+P6(f7(x1391,f9(f11(f6(x1391,a19)))),a13)
% 0.60/0.67 [140]~P2(x1401)+P6(f7(x1401,f9(f11(f6(x1401,a19)))),a13)
% 0.60/0.67 [141]~P8(x1411)+P6(f9(f9(f11(f6(x1411,a19)))),f9(f9(x1411)))
% 0.60/0.67 [146]P9(x1461)+~P6(f7(x1461,f9(f11(f6(x1461,a19)))),a13)
% 0.60/0.67 [164]~P1(x1641)+P6(f9(f9(f11(f6(f10(a20,f6(x1641,a19)),a19)))),x1641)
% 0.60/0.67 [169]~P5(x1691,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1691),a19)),a19))))),a19)
% 0.60/0.67 [78]~E(x782,x781)+P6(x781,x782)
% 0.60/0.67 [79]~E(x791,x792)+P6(x791,x792)
% 0.60/0.67 [92]P5(x922,a19)+E(f25(x921,x922),f25(x921,x921))
% 0.60/0.67 [93]P5(x931,a19)+E(f25(x931,x932),f25(x932,x932))
% 0.60/0.67 [95]~P5(x952,a19)+~E(f25(x951,x952),a4)
% 0.60/0.67 [96]~P5(x961,a19)+~E(f25(x961,x962),a4)
% 0.60/0.67 [100]P6(x1001,x1002)+P5(f16(x1001,x1002),x1001)
% 0.60/0.67 [101]~P5(x1011,x1012)+~P5(x1011,f8(x1012))
% 0.60/0.67 [106]~P5(x1061,a19)+P5(x1061,f25(x1062,x1061))
% 0.60/0.67 [107]~P5(x1071,a19)+P5(x1071,f25(x1071,x1072))
% 0.60/0.67 [110]~P5(x1101,x1102)+P6(f25(x1101,x1101),x1102)
% 0.60/0.67 [111]E(x1111,x1112)+~P5(x1111,f25(x1112,x1112))
% 0.60/0.67 [119]P6(x1191,x1192)+~P5(f16(x1191,x1192),x1192)
% 0.60/0.67 [136]~P5(x1362,f9(x1361))+~E(f10(x1361,f6(f25(x1362,x1362),a19)),a4)
% 0.60/0.67 [145]P5(x1451,x1452)+~P5(f25(f25(x1451,x1451),f25(x1451,f25(x1452,x1452))),a5)
% 0.60/0.67 [159]~P5(f25(f25(x1591,x1591),f25(x1591,f25(x1592,x1592))),a20)+E(f8(f10(f8(x1591),f8(f25(x1591,x1591)))),x1592)
% 0.60/0.67 [124]P2(x1241)+~P3(x1241,x1242,x1243)
% 0.60/0.67 [125]P8(x1251)+~P4(x1252,x1253,x1251)
% 0.60/0.67 [126]P8(x1261)+~P4(x1262,x1261,x1263)
% 0.60/0.67 [134]~P4(x1341,x1342,x1343)+P3(x1341,x1342,x1343)
% 0.60/0.67 [117]P5(x1171,x1172)+~P5(x1171,f10(x1173,x1172))
% 0.60/0.67 [118]P5(x1181,x1182)+~P5(x1181,f10(x1182,x1183))
% 0.60/0.67 [128]~P3(x1282,x1281,x1283)+E(f9(f9(x1281)),f9(x1282))
% 0.60/0.67 [142]~P5(x1421,f6(x1422,x1423))+E(f25(f25(f12(x1421),f12(x1421)),f25(f12(x1421),f25(f24(x1421),f24(x1421)))),x1421)
% 0.60/0.67 [144]~P3(x1441,x1443,x1442)+P6(f9(f9(f11(f6(x1441,a19)))),f9(f9(x1442)))
% 0.60/0.67 [147]P5(x1471,a19)+~P5(f25(f25(x1472,x1472),f25(x1472,f25(x1471,x1471))),f6(x1473,x1474))
% 0.60/0.67 [148]P5(x1481,a19)+~P5(f25(f25(x1481,x1481),f25(x1481,f25(x1482,x1482))),f6(x1483,x1484))
% 0.60/0.67 [149]P5(x1491,x1492)+~P5(f25(f25(x1493,x1493),f25(x1493,f25(x1491,x1491))),f6(x1494,x1492))
% 0.60/0.67 [150]P5(x1501,x1502)+~P5(f25(f25(x1501,x1501),f25(x1501,f25(x1503,x1503))),f6(x1502,x1504))
% 0.60/0.67 [151]~E(f25(x1511,x1512),a4)+~P5(f25(f25(x1511,x1511),f25(x1511,f25(x1512,x1512))),f6(x1513,x1514))
% 0.60/0.67 [155]P5(x1551,f25(x1552,x1551))+~P5(f25(f25(x1552,x1552),f25(x1552,f25(x1551,x1551))),f6(x1553,x1554))
% 0.60/0.67 [156]P5(x1561,f25(x1561,x1562))+~P5(f25(f25(x1561,x1561),f25(x1561,f25(x1562,x1562))),f6(x1563,x1564))
% 0.60/0.67 [170]~P5(f25(f25(f25(f25(x1703,x1703),f25(x1703,f25(x1701,x1701))),f25(f25(x1703,x1703),f25(x1703,f25(x1701,x1701)))),f25(f25(f25(x1703,x1703),f25(x1703,f25(x1701,x1701))),f25(x1702,x1702))),f21(x1704))+P5(f25(f25(f25(f25(x1701,x1701),f25(x1701,f25(x1702,x1702))),f25(f25(x1701,x1701),f25(x1701,f25(x1702,x1702)))),f25(f25(f25(x1701,x1701),f25(x1701,f25(x1702,x1702))),f25(x1703,x1703))),x1704)
% 0.60/0.67 [171]~P5(f25(f25(f25(f25(x1712,x1712),f25(x1712,f25(x1711,x1711))),f25(f25(x1712,x1712),f25(x1712,f25(x1711,x1711)))),f25(f25(f25(x1712,x1712),f25(x1712,f25(x1711,x1711))),f25(x1713,x1713))),f11(x1714))+P5(f25(f25(f25(f25(x1711,x1711),f25(x1711,f25(x1712,x1712))),f25(f25(x1711,x1711),f25(x1711,f25(x1712,x1712)))),f25(f25(f25(x1711,x1711),f25(x1711,f25(x1712,x1712))),f25(x1713,x1713))),x1714)
% 0.60/0.67 [175]~P5(f25(f25(x1754,x1754),f25(x1754,f25(x1751,x1751))),f7(x1752,x1753))+P5(x1751,f9(f9(f11(f6(f10(x1752,f6(f9(f9(f11(f6(f10(x1753,f6(f25(x1754,x1754),a19)),a19)))),a19)),a19)))))
% 0.60/0.67 [138]~P2(x1381)+P7(x1381)+~P2(f9(f11(f6(x1381,a19))))
% 0.60/0.67 [152]P2(x1521)+~P6(x1521,f6(a19,a19))+~P6(f7(x1521,f9(f11(f6(x1521,a19)))),a13)
% 0.60/0.67 [161]E(x1611,a4)+E(f25(f16(x1611,a4),f16(x1611,a4)),x1611)+~E(f16(f10(f8(f25(f16(x1611,a4),f16(x1611,a4))),x1611),a4),f16(x1611,a4))
% 0.60/0.67 [163]E(x1631,a4)+E(f25(f16(x1631,a4),f16(x1631,a4)),x1631)+P5(f16(f10(f8(f25(f16(x1631,a4),f16(x1631,a4))),x1631),a4),x1631)
% 0.60/0.67 [166]E(x1661,a4)+E(f25(f16(x1661,a4),f16(x1661,a4)),x1661)+P5(f16(f10(f8(f25(f16(x1661,a4),f16(x1661,a4))),x1661),a4),f10(f8(f25(f16(x1661,a4),f16(x1661,a4))),x1661))
% 0.60/0.67 [167]P1(x1671)+~P5(a4,x1671)+~P6(f9(f9(f11(f6(f10(a20,f6(x1671,a19)),a19)))),x1671)
% 0.60/0.67 [174]~P5(x1741,a19)+E(x1741,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f25(x1741,x1741),a19)),a19))))))),x1741)
% 0.60/0.67 [98]~P6(x982,x981)+~P6(x981,x982)+E(x981,x982)
% 0.60/0.67 [91]P5(x912,a19)+P5(x911,a19)+E(f25(x911,x912),a4)
% 0.60/0.67 [102]P5(x1021,x1022)+P5(x1021,f8(x1022))+~P5(x1021,a19)
% 0.60/0.67 [112]E(x1121,x1122)+~E(f25(x1121,x1121),f25(x1122,x1122))+~P5(x1122,a19)
% 0.60/0.67 [113]E(x1131,x1132)+~E(f25(x1131,x1131),f25(x1132,x1132))+~P5(x1131,a19)
% 0.60/0.67 [120]E(f25(x1202,x1202),x1201)+~P6(x1201,f25(x1202,x1202))+E(x1201,a4)
% 0.60/0.67 [121]E(x1211,x1212)+P5(f16(x1212,x1211),x1212)+P5(f16(x1211,x1212),x1211)
% 0.60/0.67 [130]E(x1301,x1302)+P5(f16(x1302,x1301),x1302)+~P5(f16(x1301,x1302),x1302)
% 0.60/0.67 [132]E(x1321,x1322)+~P5(f16(x1322,x1321),x1321)+~P5(f16(x1321,x1322),x1322)
% 0.60/0.67 [116]~P5(x1162,x1161)+E(f14(x1161),x1162)+~E(f25(f14(x1161),f14(x1161)),x1161)
% 0.60/0.67 [133]P5(x1332,f9(x1331))+~P5(x1332,a19)+E(f10(x1331,f6(f25(x1332,x1332),a19)),a4)
% 0.60/0.67 [160]~P5(x1601,x1602)+~P5(f25(f25(x1601,x1601),f25(x1601,f25(x1602,x1602))),f6(a19,a19))+P5(f25(f25(x1601,x1601),f25(x1601,f25(x1602,x1602))),a5)
% 0.60/0.67 [162]~P5(f25(f25(x1621,x1621),f25(x1621,f25(x1622,x1622))),f6(a19,a19))+~E(f8(f10(f8(x1621),f8(f25(x1621,x1621)))),x1622)+P5(f25(f25(x1621,x1621),f25(x1621,f25(x1622,x1622))),a20)
% 0.60/0.67 [165]~P2(x1651)+~P5(x1652,a19)+P5(f9(f9(f11(f6(f10(x1651,f6(x1652,a19)),a19)))),a19)
% 0.60/0.67 [104]~P6(x1041,x1043)+P6(x1041,x1042)+~P6(x1043,x1042)
% 0.60/0.67 [105]~P5(x1051,x1053)+P5(x1051,x1052)+~P6(x1053,x1052)
% 0.60/0.67 [114]E(x1141,x1142)+E(x1141,x1143)+~P5(x1141,f25(x1143,x1142))
% 0.60/0.67 [122]~P5(x1221,x1223)+~P5(x1221,x1222)+P5(x1221,f10(x1222,x1223))
% 0.60/0.67 [123]~P5(x1232,x1233)+~P5(x1231,x1233)+P6(f25(x1231,x1232),x1233)
% 0.60/0.67 [153]E(x1531,x1532)+~E(f25(x1533,x1531),f25(x1533,x1532))+~P5(f25(f25(x1531,x1531),f25(x1531,f25(x1532,x1532))),f6(a19,a19))
% 0.60/0.67 [154]E(x1541,x1542)+~E(f25(x1541,x1543),f25(x1542,x1543))+~P5(f25(f25(x1541,x1541),f25(x1541,f25(x1542,x1542))),f6(a19,a19))
% 0.60/0.67 [143]~P5(x1432,x1434)+~P5(x1431,x1433)+P5(f25(f25(x1431,x1431),f25(x1431,f25(x1432,x1432))),f6(x1433,x1434))
% 0.60/0.67 [172]~P5(f25(f25(f25(f25(x1722,x1722),f25(x1722,f25(x1723,x1723))),f25(f25(x1722,x1722),f25(x1722,f25(x1723,x1723)))),f25(f25(f25(x1722,x1722),f25(x1722,f25(x1723,x1723))),f25(x1721,x1721))),x1724)+P5(f25(f25(f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722))),f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722)))),f25(f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722))),f25(x1723,x1723))),f21(x1724))+~P5(f25(f25(f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722))),f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722)))),f25(f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722))),f25(x1723,x1723))),f6(f6(a19,a19),a19))
% 0.60/0.67 [173]~P5(f25(f25(f25(f25(x1732,x1732),f25(x1732,f25(x1731,x1731))),f25(f25(x1732,x1732),f25(x1732,f25(x1731,x1731)))),f25(f25(f25(x1732,x1732),f25(x1732,f25(x1731,x1731))),f25(x1733,x1733))),x1734)+P5(f25(f25(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732)))),f25(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f25(x1733,x1733))),f11(x1734))+~P5(f25(f25(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732)))),f25(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f25(x1733,x1733))),f6(f6(a19,a19),a19))
% 0.60/0.67 [176]P5(f25(f25(x1761,x1761),f25(x1761,f25(x1762,x1762))),f7(x1763,x1764))+~P5(f25(f25(x1761,x1761),f25(x1761,f25(x1762,x1762))),f6(a19,a19))+~P5(x1762,f9(f9(f11(f6(f10(x1763,f6(f9(f9(f11(f6(f10(x1764,f6(f25(x1761,x1761),a19)),a19)))),a19)),a19)))))
% 0.60/0.67 [177]~P4(x1772,x1775,x1771)+~P5(f25(f25(x1773,x1773),f25(x1773,f25(x1774,x1774))),f9(x1775))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1771,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1773,x1773),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1773,x1773),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1773,x1773),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1774,x1774),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1774,x1774),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1773,x1773),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1773,x1773),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1773,x1773),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1774,x1774),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(x1774,x1774),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1772,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1775,f6(f25(f25(f25(x1773,x1773),f25(x1773,f25(x1774,x1774))),f25(f25(x1773,x1773),f25(x1773,f25(x1774,x1774)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1775,f6(f25(f25(f25(x1773,x1773),f25(x1773,f25(x1774,x1774))),f25(f25(x1773,x1773),f25(x1773,f25(x1774,x1774)))),a19)),a19)))))))),a19)),a19))))))))
% 0.60/0.67 [158]~P2(x1581)+P8(x1581)+~E(f6(f9(f9(x1581)),f9(f9(x1581))),f9(x1581))+~P6(f9(f9(f11(f6(x1581,a19)))),f9(f9(x1581)))
% 0.60/0.67 [115]E(x1151,x1152)+E(x1153,x1152)+~E(f25(x1153,x1151),f25(x1152,x1152))+~P5(x1152,a19)
% 0.60/0.67 [157]~P2(x1571)+P3(x1571,x1572,x1573)+~E(f9(f9(x1572)),f9(x1571))+~P6(f9(f9(f11(f6(x1571,a19)))),f9(f9(x1573)))
% 0.60/0.67 [168]~P8(x1683)+~P8(x1682)+~P3(x1681,x1682,x1683)+P4(x1681,x1682,x1683)+P5(f25(f25(f17(x1681,x1682,x1683),f17(x1681,x1682,x1683)),f25(f17(x1681,x1682,x1683),f25(f18(x1681,x1682,x1683),f18(x1681,x1682,x1683)))),f9(x1682))
% 0.60/0.67 [178]~P8(x1783)+~P8(x1782)+~P3(x1781,x1782,x1783)+P4(x1781,x1782,x1783)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1783,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783)),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1781,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1782,f6(f25(f25(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),f25(f17(x1781,x1782,x1783),f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783)))),f25(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),f25(f17(x1781,x1782,x1783),f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1782,f6(f25(f25(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),f25(f17(x1781,x1782,x1783),f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783)))),f25(f25(f17(x1781,x1782,x1783),f17(x1781,x1782,x1783)),f25(f17(x1781,x1782,x1783),f25(f18(x1781,x1782,x1783),f18(x1781,x1782,x1783))))),a19)),a19)))))))),a19)),a19))))))))
% 0.60/0.67 %EqnAxiom
% 0.60/0.67 [1]E(x11,x11)
% 0.60/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.60/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.60/0.67 [4]~E(x41,x42)+E(f25(x41,x43),f25(x42,x43))
% 0.60/0.67 [5]~E(x51,x52)+E(f25(x53,x51),f25(x53,x52))
% 0.60/0.67 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.60/0.67 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.60/0.67 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.60/0.67 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.60/0.67 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.60/0.67 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.60/0.67 [12]~E(x121,x122)+E(f16(x121,x123),f16(x122,x123))
% 0.60/0.67 [13]~E(x131,x132)+E(f16(x133,x131),f16(x133,x132))
% 0.60/0.67 [14]~E(x141,x142)+E(f18(x141,x143,x144),f18(x142,x143,x144))
% 0.60/0.67 [15]~E(x151,x152)+E(f18(x153,x151,x154),f18(x153,x152,x154))
% 0.60/0.67 [16]~E(x161,x162)+E(f18(x163,x164,x161),f18(x163,x164,x162))
% 0.60/0.67 [17]~E(x171,x172)+E(f7(x171,x173),f7(x172,x173))
% 0.60/0.67 [18]~E(x181,x182)+E(f7(x183,x181),f7(x183,x182))
% 0.60/0.67 [19]~E(x191,x192)+E(f14(x191),f14(x192))
% 0.60/0.67 [20]~E(x201,x202)+E(f17(x201,x203,x204),f17(x202,x203,x204))
% 0.60/0.67 [21]~E(x211,x212)+E(f17(x213,x211,x214),f17(x213,x212,x214))
% 0.60/0.67 [22]~E(x221,x222)+E(f17(x223,x224,x221),f17(x223,x224,x222))
% 0.60/0.67 [23]~E(x231,x232)+E(f15(x231),f15(x232))
% 0.60/0.67 [24]~E(x241,x242)+E(f8(x241),f8(x242))
% 0.60/0.67 [25]~E(x251,x252)+E(f21(x251),f21(x252))
% 0.60/0.67 [26]~E(x261,x262)+E(f3(x261),f3(x262))
% 0.60/0.67 [27]~E(x271,x272)+E(f22(x271),f22(x272))
% 0.60/0.67 [28]~E(x281,x282)+E(f24(x281),f24(x282))
% 0.60/0.67 [29]~E(x291,x292)+E(f12(x291),f12(x292))
% 0.60/0.67 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.60/0.67 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.60/0.67 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.60/0.67 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.60/0.67 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.60/0.67 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.60/0.67 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.60/0.67 [37]P6(x372,x373)+~E(x371,x372)+~P6(x371,x373)
% 0.60/0.67 [38]P6(x383,x382)+~E(x381,x382)+~P6(x383,x381)
% 0.60/0.67 [39]~P8(x391)+P8(x392)+~E(x391,x392)
% 0.60/0.67 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.60/0.67 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.60/0.67 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.60/0.67 [43]~P7(x431)+P7(x432)+~E(x431,x432)
% 0.60/0.67 [44]~P9(x441)+P9(x442)+~E(x441,x442)
% 0.60/0.67
% 0.60/0.67 %-------------------------------------------
% 0.60/0.67 cnf(189,plain,
% 0.60/0.67 (~E(f25(a27,f25(a26,a26)),f25(a27,a4))),
% 0.60/0.67 inference(scs_inference,[],[75,61,2,5])).
% 0.60/0.67 cnf(191,plain,
% 0.60/0.67 (~P5(x1911,a4)),
% 0.60/0.67 inference(rename_variables,[],[73])).
% 0.60/0.67 cnf(194,plain,
% 0.60/0.67 (~P5(x1941,f10(f8(x1942),x1942))),
% 0.60/0.67 inference(rename_variables,[],[74])).
% 0.60/0.67 cnf(197,plain,
% 0.60/0.67 (~P5(x1971,f10(f8(x1972),x1972))),
% 0.60/0.67 inference(rename_variables,[],[74])).
% 0.60/0.67 cnf(201,plain,
% 0.60/0.67 (~P5(f25(f25(f25(f25(x2011,x2011),f25(x2011,f25(x2012,x2012))),f25(f25(x2011,x2011),f25(x2011,f25(x2012,x2012)))),f25(f25(f25(x2011,x2011),f25(x2011,f25(x2012,x2012))),f25(x2013,x2013))),f21(a4))),
% 0.60/0.67 inference(scs_inference,[],[75,73,191,61,74,194,2,5,81,90,100,136,170])).
% 0.60/0.67 cnf(202,plain,
% 0.60/0.67 (~P5(x2021,a4)),
% 0.60/0.67 inference(rename_variables,[],[73])).
% 0.60/0.67 cnf(205,plain,
% 0.60/0.67 (~P5(x2051,a4)),
% 0.60/0.67 inference(rename_variables,[],[73])).
% 0.60/0.67 cnf(212,plain,
% 0.60/0.67 (~P5(x2121,f10(f8(x2122),x2122))),
% 0.60/0.67 inference(rename_variables,[],[74])).
% 0.60/0.67 cnf(213,plain,
% 0.60/0.67 (~P5(x2131,a4)),
% 0.60/0.67 inference(rename_variables,[],[73])).
% 0.60/0.67 cnf(216,plain,
% 0.60/0.67 (E(f25(x2161,x2162),f25(x2162,x2161))),
% 0.60/0.67 inference(rename_variables,[],[52])).
% 0.60/0.67 cnf(220,plain,
% 0.60/0.67 (~P5(a4,f8(a19))),
% 0.60/0.67 inference(scs_inference,[],[72,75,73,191,202,205,213,52,60,47,65,61,74,194,197,212,2,5,81,90,100,136,170,171,105,121,3,32,33,122])).
% 0.60/0.67 cnf(239,plain,
% 0.60/0.67 (~E(a26,a4)),
% 0.60/0.67 inference(scs_inference,[],[72,75,51,49,50,73,191,202,205,213,52,216,60,47,65,61,74,194,197,212,2,5,81,90,100,136,170,171,105,121,3,32,33,122,167,30,37,82,84,98,31,78,79])).
% 0.60/0.67 cnf(266,plain,
% 0.60/0.67 ($false),
% 0.60/0.67 inference(scs_inference,[],[72,189,220,239,201,68,81,171,170,84,5,2,91]),
% 0.60/0.67 ['proof']).
% 0.60/0.67 % SZS output end Proof
% 0.60/0.67 % Total time :0.050000s
%------------------------------------------------------------------------------