TSTP Solution File: SET101-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET101-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n008.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 : Thu Aug 31 14:28:44 EDT 2023
% Result : Unsatisfiable 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET101-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 08:26:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % File :CSE---1.6
% 0.20/0.63 % Problem :theBenchmark
% 0.20/0.63 % Transform :cnf
% 0.20/0.63 % Format :tptp:raw
% 0.20/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.63
% 0.20/0.63 % Result :Theorem 0.000000s
% 0.20/0.63 % Output :CNFRefutation 0.000000s
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 % File : SET101-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.20/0.63 % Domain : Set Theory
% 0.20/0.63 % Problem : Singleton of the first is a member of an ordered pair
% 0.20/0.63 % Version : [Qua92] axioms : Augmented.
% 0.20/0.63 % English :
% 0.20/0.63
% 0.20/0.63 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.20/0.63 % Source : [Quaife]
% 0.20/0.64 % Names : OP2.1 [Qua92]
% 0.20/0.64
% 0.20/0.64 % Status : Unsatisfiable
% 0.20/0.64 % Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.20 v6.4.0, 0.33 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.21 v6.0.0, 0.00 v5.5.0, 0.20 v5.3.0, 0.28 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.31 v4.0.1, 0.27 v4.0.0, 0.36 v3.7.0, 0.20 v3.5.0, 0.27 v3.4.0, 0.25 v3.3.0, 0.21 v3.2.0, 0.15 v3.1.0, 0.18 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.18 v2.4.0, 0.12 v2.3.0, 0.00 v2.2.1, 0.17 v2.2.0, 0.00 v2.1.0
% 0.20/0.64 % Syntax : Number of clauses : 146 ( 43 unt; 25 nHn; 96 RR)
% 0.20/0.64 % Number of literals : 295 ( 87 equ; 129 neg)
% 0.20/0.64 % Maximal clause size : 5 ( 2 avg)
% 0.20/0.64 % Maximal term depth : 6 ( 1 avg)
% 0.20/0.64 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.20/0.64 % Number of functors : 42 ( 42 usr; 10 con; 0-3 aty)
% 0.20/0.64 % Number of variables : 275 ( 48 sgn)
% 0.20/0.64 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.20/0.64
% 0.20/0.64 % Comments : Preceding lemmas are added.
% 0.20/0.64 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.20/0.64 include('Axioms/SET004-0.ax').
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.20/0.64 cnf(corollary_1_to_unordered_pair,axiom,
% 0.20/0.64 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.64 | member(X,unordered_pair(X,Y)) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(corollary_2_to_unordered_pair,axiom,
% 0.20/0.64 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.64 | member(Y,unordered_pair(X,Y)) ) ).
% 0.20/0.64
% 0.20/0.64 %----Corollaries to Cartesian product axiom.
% 0.20/0.64 cnf(corollary_1_to_cartesian_product,axiom,
% 0.20/0.64 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.64 | member(U,universal_class) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(corollary_2_to_cartesian_product,axiom,
% 0.20/0.64 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.64 | member(V,universal_class) ) ).
% 0.20/0.64
% 0.20/0.64 %---- PARTIAL ORDER.
% 0.20/0.64 %----(PO1): reflexive.
% 0.20/0.64 cnf(subclass_is_reflexive,axiom,
% 0.20/0.64 subclass(X,X) ).
% 0.20/0.64
% 0.20/0.64 %----(PO2): antisymmetry is part of A-3.
% 0.20/0.64 %----(x < y), (y < x) --> (x = y).
% 0.20/0.64
% 0.20/0.64 %----(PO3): transitivity.
% 0.20/0.64 cnf(transitivity_of_subclass,axiom,
% 0.20/0.64 ( ~ subclass(X,Y)
% 0.20/0.64 | ~ subclass(Y,Z)
% 0.20/0.64 | subclass(X,Z) ) ).
% 0.20/0.64
% 0.20/0.64 %---- EQUALITY.
% 0.20/0.64 %----(EQ1): equality axiom.
% 0.20/0.64 %----a:x:(x = x).
% 0.20/0.64 %----This is always an axiom in the TPTP presentation.
% 0.20/0.64
% 0.20/0.64 %----(EQ2): expanded equality definition.
% 0.20/0.64 cnf(equality1,axiom,
% 0.20/0.64 ( X = Y
% 0.20/0.64 | member(not_subclass_element(X,Y),X)
% 0.20/0.64 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(equality2,axiom,
% 0.20/0.64 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.64 | X = Y
% 0.20/0.64 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(equality3,axiom,
% 0.20/0.64 ( ~ member(not_subclass_element(Y,X),X)
% 0.20/0.64 | X = Y
% 0.20/0.64 | member(not_subclass_element(X,Y),X) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(equality4,axiom,
% 0.20/0.64 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.64 | ~ member(not_subclass_element(Y,X),X)
% 0.20/0.64 | X = Y ) ).
% 0.20/0.64
% 0.20/0.64 %---- SPECIAL CLASSES.
% 0.20/0.64 %----(SP1): lemma.
% 0.20/0.64 cnf(special_classes_lemma,axiom,
% 0.20/0.64 ~ member(Y,intersection(complement(X),X)) ).
% 0.20/0.64
% 0.20/0.64 %----(SP2): Existence of O (null class).
% 0.20/0.64 %----e:x:a:z:(-(z e x)).
% 0.20/0.64 cnf(existence_of_null_class,axiom,
% 0.20/0.64 ~ member(Z,null_class) ).
% 0.20/0.64
% 0.20/0.64 %----(SP3): O is a subclass of every class.
% 0.20/0.64 cnf(null_class_is_subclass,axiom,
% 0.20/0.64 subclass(null_class,X) ).
% 0.20/0.64
% 0.20/0.64 %----corollary.
% 0.20/0.64 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.20/0.64 ( ~ subclass(X,null_class)
% 0.20/0.64 | X = null_class ) ).
% 0.20/0.64
% 0.20/0.64 %----(SP4): uniqueness of null class.
% 0.20/0.64 cnf(null_class_is_unique,axiom,
% 0.20/0.64 ( Z = null_class
% 0.20/0.64 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.20/0.64
% 0.20/0.64 %----(SP5): O is a set (follows from axiom of infinity).
% 0.20/0.64 cnf(null_class_is_a_set,axiom,
% 0.20/0.64 member(null_class,universal_class) ).
% 0.20/0.64
% 0.20/0.64 %---- UNORDERED PAIRS.
% 0.20/0.64 %----(UP1): unordered pair is commutative.
% 0.20/0.64 cnf(commutativity_of_unordered_pair,axiom,
% 0.20/0.64 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.20/0.64
% 0.20/0.64 %----(UP2): if one argument is a proper class, pair contains only the
% 0.20/0.64 %----other. In a slightly different form to the paper
% 0.20/0.64 cnf(singleton_in_unordered_pair1,axiom,
% 0.20/0.64 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.20/0.64
% 0.20/0.64 cnf(singleton_in_unordered_pair2,axiom,
% 0.20/0.64 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.20/0.64
% 0.20/0.64 cnf(unordered_pair_equals_singleton1,axiom,
% 0.20/0.64 ( member(Y,universal_class)
% 0.20/0.64 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(unordered_pair_equals_singleton2,axiom,
% 0.20/0.64 ( member(X,universal_class)
% 0.20/0.64 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.20/0.64
% 0.20/0.64 %----(UP3): if both arguments are proper classes, pair is null.
% 0.20/0.64 cnf(null_unordered_pair,axiom,
% 0.20/0.64 ( unordered_pair(X,Y) = null_class
% 0.20/0.64 | member(X,universal_class)
% 0.20/0.64 | member(Y,universal_class) ) ).
% 0.20/0.64
% 0.20/0.64 %----(UP4): left cancellation for unordered pairs.
% 0.20/0.64 cnf(left_cancellation,axiom,
% 0.20/0.64 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.20/0.64 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.20/0.64 | Y = Z ) ).
% 0.20/0.64
% 0.20/0.64 %----(UP5): right cancellation for unordered pairs.
% 0.20/0.64 cnf(right_cancellation,axiom,
% 0.20/0.64 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.20/0.64 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.20/0.64 | X = Y ) ).
% 0.20/0.64
% 0.20/0.64 %----(UP6): corollary to (A-4).
% 0.20/0.64 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.20/0.64 ( ~ member(X,universal_class)
% 0.20/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.64
% 0.20/0.64 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.20/0.64 ( ~ member(Y,universal_class)
% 0.20/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.64
% 0.20/0.64 %----corollary to instantiate variables.
% 0.20/0.64 %----Not in the paper
% 0.20/0.64 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.20/0.64 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.64
% 0.20/0.64 %----(UP7): if both members of a pair belong to a set, the pair
% 0.20/0.64 %----is a subset.
% 0.20/0.64 cnf(unordered_pair_is_subset,axiom,
% 0.20/0.64 ( ~ member(X,Z)
% 0.20/0.64 | ~ member(Y,Z)
% 0.20/0.64 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.20/0.64
% 0.20/0.64 %---- SINGLETONS.
% 0.20/0.64 %----(SS1): every singleton is a set.
% 0.20/0.64 cnf(singletons_are_sets,axiom,
% 0.20/0.64 member(singleton(X),universal_class) ).
% 0.20/0.64
% 0.20/0.64 %----corollary, not in the paper.
% 0.20/0.64 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.20/0.64 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.20/0.64
% 0.20/0.64 %----(SS2): a set belongs to its singleton.
% 0.20/0.64 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.20/0.64 cnf(set_in_its_singleton,axiom,
% 0.20/0.64 ( ~ member(X,universal_class)
% 0.20/0.64 | member(X,singleton(X)) ) ).
% 0.20/0.64
% 0.20/0.64 %----corollary
% 0.20/0.64 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.20/0.64 ( ~ member(X,universal_class)
% 0.20/0.64 | singleton(X) != null_class ) ).
% 0.20/0.64
% 0.20/0.64 %----Not in the paper
% 0.20/0.64 cnf(null_class_in_its_singleton,axiom,
% 0.20/0.64 member(null_class,singleton(null_class)) ).
% 0.20/0.64
% 0.20/0.64 %----(SS3): only x can belong to {x}.
% 0.20/0.64 cnf(only_member_in_singleton,axiom,
% 0.20/0.64 ( ~ member(Y,singleton(X))
% 0.20/0.64 | Y = X ) ).
% 0.20/0.64
% 0.20/0.64 %----(SS4): if x is not a set, {x} = O.
% 0.20/0.64 cnf(singleton_is_null_class,axiom,
% 0.20/0.64 ( member(X,universal_class)
% 0.20/0.64 | singleton(X) = null_class ) ).
% 0.20/0.64
% 0.20/0.64 %----(SS5): a singleton set is determined by its element.
% 0.20/0.64 cnf(singleton_identified_by_element1,axiom,
% 0.20/0.64 ( singleton(X) != singleton(Y)
% 0.20/0.64 | ~ member(X,universal_class)
% 0.20/0.64 | X = Y ) ).
% 0.20/0.64
% 0.20/0.64 cnf(singleton_identified_by_element2,axiom,
% 0.20/0.64 ( singleton(X) != singleton(Y)
% 0.20/0.64 | ~ member(Y,universal_class)
% 0.20/0.64 | X = Y ) ).
% 0.20/0.64
% 0.20/0.64 %----(SS5.5).
% 0.20/0.64 %----Not in the paper
% 0.20/0.64 cnf(singleton_in_unordered_pair3,axiom,
% 0.20/0.64 ( unordered_pair(Y,Z) != singleton(X)
% 0.20/0.64 | ~ member(X,universal_class)
% 0.20/0.64 | X = Y
% 0.20/0.64 | X = Z ) ).
% 0.20/0.64
% 0.20/0.64 %----(SS6): existence of memb.
% 0.20/0.64 %----a:x:e:u:(((u e universal_class) & x = {u}) | (-e:y:((y
% 0.20/0.64 %----e universal_class) & x = {y}) & u = x)).
% 0.20/0.64 cnf(member_exists1,axiom,
% 0.20/0.64 ( ~ member(Y,universal_class)
% 0.20/0.64 | member(member_of(singleton(Y)),universal_class) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(member_exists2,axiom,
% 0.20/0.64 ( ~ member(Y,universal_class)
% 0.20/0.64 | singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(member_exists3,axiom,
% 0.20/0.64 ( member(member_of(X),universal_class)
% 0.20/0.64 | member_of(X) = X ) ).
% 0.20/0.64
% 0.20/0.64 cnf(member_exists4,axiom,
% 0.20/0.65 ( singleton(member_of(X)) = X
% 0.20/0.65 | member_of(X) = X ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS7): uniqueness of memb of a singleton set.
% 0.20/0.65 %----a:x:a:u:(((u e universal_class) & x = {u}) ==> member_of(x) = u)
% 0.20/0.65 cnf(member_of_singleton_is_unique,axiom,
% 0.20/0.65 ( ~ member(U,universal_class)
% 0.20/0.65 | member_of(singleton(U)) = U ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS8): uniqueness of memb when x is not a singleton of a set.
% 0.20/0.65 %----a:x:a:u:((e:y:((y e universal_class) & x = {y})
% 0.20/0.65 %----& u = x) | member_of(x) = u)
% 0.20/0.65 cnf(member_of_non_singleton_unique1,axiom,
% 0.20/0.65 ( member(member_of1(X),universal_class)
% 0.20/0.65 | member_of(X) = X ) ).
% 0.20/0.65
% 0.20/0.65 cnf(member_of_non_singleton_unique2,axiom,
% 0.20/0.65 ( singleton(member_of1(X)) = X
% 0.20/0.65 | member_of(X) = X ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS9): corollary to (SS1).
% 0.20/0.65 cnf(corollary_2_to_singletons_are_sets,axiom,
% 0.20/0.65 ( singleton(member_of(X)) != X
% 0.20/0.65 | member(X,universal_class) ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS10).
% 0.20/0.65 cnf(property_of_singletons1,axiom,
% 0.20/0.65 ( singleton(member_of(X)) != X
% 0.20/0.65 | ~ member(Y,X)
% 0.20/0.65 | member_of(X) = Y ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS11).
% 0.20/0.65 cnf(property_of_singletons2,axiom,
% 0.20/0.65 ( ~ member(X,Y)
% 0.20/0.65 | subclass(singleton(X),Y) ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS12): there are at most two subsets of a singleton.
% 0.20/0.65 cnf(two_subsets_of_singleton,axiom,
% 0.20/0.65 ( ~ subclass(X,singleton(Y))
% 0.20/0.65 | X = null_class
% 0.20/0.65 | singleton(Y) = X ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS13): a class contains 0, 1, or at least 2 members.
% 0.20/0.65 cnf(number_of_elements_in_class,axiom,
% 0.20/0.65 ( 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))
% 0.20/0.65 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.65 | X = null_class ) ).
% 0.20/0.65
% 0.20/0.65 %----corollaries.
% 0.20/0.65 cnf(corollary_2_to_number_of_elements_in_class,axiom,
% 0.20/0.65 ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),X)
% 0.20/0.65 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.65 | X = null_class ) ).
% 0.20/0.65
% 0.20/0.65 cnf(corollary_1_to_number_of_elements_in_class,axiom,
% 0.20/0.65 ( not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class) != not_subclass_element(X,null_class)
% 0.20/0.65 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.65 | X = null_class ) ).
% 0.20/0.65
% 0.20/0.65 %----(SS14): relation to ordered pair.
% 0.20/0.65 %----It looks like we could simplify Godel's axioms by taking singleton
% 0.20/0.65 %----as a primitive and using the next as a definition. Not in the paper
% 0.20/0.65 cnf(unordered_pairs_and_singletons,axiom,
% 0.20/0.65 unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ).
% 0.20/0.65
% 0.20/0.65 %---- ORDERED PAIRS.
% 0.20/0.65 %----(OP1): an ordered pair is a set.
% 0.20/0.65 cnf(ordered_pair_is_set,axiom,
% 0.20/0.65 member(ordered_pair(X,Y),universal_class) ).
% 0.20/0.65
% 0.20/0.65 cnf(prove_singleton_member_of_ordered_pair_1,negated_conjecture,
% 0.20/0.65 ~ member(singleton(x),ordered_pair(x,y)) ).
% 0.20/0.65
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark
% 0.20/0.65 % SZS output start Proof
% 0.20/0.65 %ClaNum:175(EqnAxiom:44)
% 0.20/0.65 %VarNum:987(SingletonVarNum:242)
% 0.20/0.65 %MaxLitNum:5
% 0.20/0.65 %MaxfuncDepth:24
% 0.20/0.65 %SharedTerms:39
% 0.20/0.65 %goalClause: 72
% 0.20/0.65 %singleGoalClaCount:1
% 0.20/0.65 [45]P1(a1)
% 0.20/0.65 [46]P2(a2)
% 0.20/0.65 [47]P5(a4,a19)
% 0.20/0.65 [48]P5(a1,a19)
% 0.20/0.65 [53]P6(a5,f6(a19,a19))
% 0.20/0.65 [54]P6(a20,f6(a19,a19))
% 0.20/0.65 [55]P5(a4,f25(a4,a4))
% 0.20/0.65 [72]~P5(f25(a26,a26),f25(f25(a26,a26),f25(a26,f25(a27,a27))))
% 0.20/0.65 [64]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.20/0.65 [68]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.20/0.65 [49]P6(x491,a19)
% 0.20/0.65 [50]P6(a4,x501)
% 0.20/0.65 [51]P6(x511,x511)
% 0.20/0.65 [70]~P5(x701,a4)
% 0.20/0.65 [62]P6(f21(x621),f6(f6(a19,a19),a19))
% 0.20/0.65 [63]P6(f11(x631),f6(f6(a19,a19),a19))
% 0.20/0.65 [69]E(f10(f9(x691),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x691),a13)))),f3(x691))
% 0.20/0.65 [52]E(f25(x521,x522),f25(x522,x521))
% 0.20/0.65 [56]P5(f25(x561,x562),a19)
% 0.20/0.65 [58]P6(f7(x581,x582),f6(a19,a19))
% 0.20/0.65 [59]P6(f25(x591,x591),f25(x592,x591))
% 0.20/0.65 [60]P6(f25(x601,x601),f25(x601,x602))
% 0.20/0.65 [65]P5(f25(x651,x651),f25(x652,f25(x651,x651)))
% 0.20/0.65 [71]~P5(x711,f10(f8(x712),x712))
% 0.20/0.65 [67]E(f8(f10(f8(f25(x671,x671)),f8(f25(x672,x672)))),f25(x671,x672))
% 0.20/0.65 [61]E(f10(f6(x611,x612),x613),f10(x613,f6(x611,x612)))
% 0.20/0.65 [73]~P7(x731)+P2(x731)
% 0.20/0.65 [74]~P8(x741)+P2(x741)
% 0.20/0.65 [77]~P1(x771)+P6(a1,x771)
% 0.20/0.65 [78]~P1(x781)+P5(a4,x781)
% 0.20/0.65 [79]~P6(x791,a4)+E(x791,a4)
% 0.20/0.65 [81]P5(f22(x811),x811)+E(x811,a4)
% 0.20/0.65 [82]E(f14(x821),x821)+P5(f14(x821),a19)
% 0.20/0.65 [83]E(f14(x831),x831)+P5(f15(x831),a19)
% 0.20/0.65 [84]P5(x841,a19)+E(f25(x841,x841),a4)
% 0.20/0.65 [87]E(x871,a4)+P5(f16(x871,a4),x871)
% 0.20/0.65 [91]~P2(x911)+P6(x911,f6(a19,a19))
% 0.20/0.65 [80]E(x801,a4)+E(f10(x801,f22(x801)),a4)
% 0.20/0.65 [85]E(f14(x851),x851)+E(f25(f14(x851),f14(x851)),x851)
% 0.20/0.65 [86]E(f14(x861),x861)+E(f25(f15(x861),f15(x861)),x861)
% 0.20/0.65 [96]~P5(x961,a19)+E(f14(f25(x961,x961)),x961)
% 0.20/0.65 [100]P5(x1001,a19)+~E(f25(f14(x1001),f14(x1001)),x1001)
% 0.20/0.65 [124]~P5(x1241,a19)+P5(f14(f25(x1241,x1241)),a19)
% 0.20/0.65 [106]~P8(x1061)+E(f6(f9(f9(x1061)),f9(f9(x1061))),f9(x1061))
% 0.20/0.65 [128]~P7(x1281)+P2(f9(f11(f6(x1281,a19))))
% 0.20/0.65 [132]~P5(x1321,a19)+E(f25(f14(f25(x1321,x1321)),f14(f25(x1321,x1321))),f25(x1321,x1321))
% 0.20/0.65 [134]~P5(x1341,a19)+P5(f9(f10(a5,f6(a19,x1341))),a19)
% 0.20/0.65 [136]~P9(x1361)+P6(f7(x1361,f9(f11(f6(x1361,a19)))),a13)
% 0.20/0.65 [137]~P2(x1371)+P6(f7(x1371,f9(f11(f6(x1371,a19)))),a13)
% 0.20/0.65 [138]~P8(x1381)+P6(f9(f9(f11(f6(x1381,a19)))),f9(f9(x1381)))
% 0.20/0.65 [143]P9(x1431)+~P6(f7(x1431,f9(f11(f6(x1431,a19)))),a13)
% 0.20/0.65 [161]~P1(x1611)+P6(f9(f9(f11(f6(f10(a20,f6(x1611,a19)),a19)))),x1611)
% 0.20/0.65 [166]~P5(x1661,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1661),a19)),a19))))),a19)
% 0.20/0.65 [75]~E(x752,x751)+P6(x751,x752)
% 0.20/0.65 [76]~E(x761,x762)+P6(x761,x762)
% 0.20/0.65 [89]P5(x892,a19)+E(f25(x891,x892),f25(x891,x891))
% 0.20/0.65 [90]P5(x901,a19)+E(f25(x901,x902),f25(x902,x902))
% 0.20/0.65 [92]~P5(x922,a19)+~E(f25(x921,x922),a4)
% 0.20/0.65 [93]~P5(x931,a19)+~E(f25(x931,x932),a4)
% 0.20/0.65 [97]P6(x971,x972)+P5(f16(x971,x972),x971)
% 0.20/0.65 [98]~P5(x981,x982)+~P5(x981,f8(x982))
% 0.20/0.65 [103]~P5(x1031,a19)+P5(x1031,f25(x1032,x1031))
% 0.20/0.65 [104]~P5(x1041,a19)+P5(x1041,f25(x1041,x1042))
% 0.20/0.65 [107]~P5(x1071,x1072)+P6(f25(x1071,x1071),x1072)
% 0.20/0.65 [108]E(x1081,x1082)+~P5(x1081,f25(x1082,x1082))
% 0.20/0.65 [116]P6(x1161,x1162)+~P5(f16(x1161,x1162),x1162)
% 0.20/0.65 [133]~P5(x1332,f9(x1331))+~E(f10(x1331,f6(f25(x1332,x1332),a19)),a4)
% 0.20/0.65 [142]P5(x1421,x1422)+~P5(f25(f25(x1421,x1421),f25(x1421,f25(x1422,x1422))),a5)
% 0.20/0.65 [156]~P5(f25(f25(x1561,x1561),f25(x1561,f25(x1562,x1562))),a20)+E(f8(f10(f8(x1561),f8(f25(x1561,x1561)))),x1562)
% 0.20/0.65 [121]P2(x1211)+~P3(x1211,x1212,x1213)
% 0.20/0.65 [122]P8(x1221)+~P4(x1222,x1223,x1221)
% 0.20/0.65 [123]P8(x1231)+~P4(x1232,x1231,x1233)
% 0.20/0.65 [131]~P4(x1311,x1312,x1313)+P3(x1311,x1312,x1313)
% 0.20/0.65 [114]P5(x1141,x1142)+~P5(x1141,f10(x1143,x1142))
% 0.20/0.65 [115]P5(x1151,x1152)+~P5(x1151,f10(x1152,x1153))
% 0.20/0.65 [125]~P3(x1252,x1251,x1253)+E(f9(f9(x1251)),f9(x1252))
% 0.20/0.65 [139]~P5(x1391,f6(x1392,x1393))+E(f25(f25(f12(x1391),f12(x1391)),f25(f12(x1391),f25(f24(x1391),f24(x1391)))),x1391)
% 0.20/0.65 [141]~P3(x1411,x1413,x1412)+P6(f9(f9(f11(f6(x1411,a19)))),f9(f9(x1412)))
% 0.20/0.65 [144]P5(x1441,a19)+~P5(f25(f25(x1442,x1442),f25(x1442,f25(x1441,x1441))),f6(x1443,x1444))
% 0.20/0.65 [145]P5(x1451,a19)+~P5(f25(f25(x1451,x1451),f25(x1451,f25(x1452,x1452))),f6(x1453,x1454))
% 0.20/0.65 [146]P5(x1461,x1462)+~P5(f25(f25(x1463,x1463),f25(x1463,f25(x1461,x1461))),f6(x1464,x1462))
% 0.20/0.65 [147]P5(x1471,x1472)+~P5(f25(f25(x1471,x1471),f25(x1471,f25(x1473,x1473))),f6(x1472,x1474))
% 0.20/0.65 [148]~E(f25(x1481,x1482),a4)+~P5(f25(f25(x1481,x1481),f25(x1481,f25(x1482,x1482))),f6(x1483,x1484))
% 0.20/0.65 [152]P5(x1521,f25(x1522,x1521))+~P5(f25(f25(x1522,x1522),f25(x1522,f25(x1521,x1521))),f6(x1523,x1524))
% 0.20/0.65 [153]P5(x1531,f25(x1531,x1532))+~P5(f25(f25(x1531,x1531),f25(x1531,f25(x1532,x1532))),f6(x1533,x1534))
% 0.20/0.65 [167]~P5(f25(f25(f25(f25(x1673,x1673),f25(x1673,f25(x1671,x1671))),f25(f25(x1673,x1673),f25(x1673,f25(x1671,x1671)))),f25(f25(f25(x1673,x1673),f25(x1673,f25(x1671,x1671))),f25(x1672,x1672))),f21(x1674))+P5(f25(f25(f25(f25(x1671,x1671),f25(x1671,f25(x1672,x1672))),f25(f25(x1671,x1671),f25(x1671,f25(x1672,x1672)))),f25(f25(f25(x1671,x1671),f25(x1671,f25(x1672,x1672))),f25(x1673,x1673))),x1674)
% 0.20/0.65 [168]~P5(f25(f25(f25(f25(x1682,x1682),f25(x1682,f25(x1681,x1681))),f25(f25(x1682,x1682),f25(x1682,f25(x1681,x1681)))),f25(f25(f25(x1682,x1682),f25(x1682,f25(x1681,x1681))),f25(x1683,x1683))),f11(x1684))+P5(f25(f25(f25(f25(x1681,x1681),f25(x1681,f25(x1682,x1682))),f25(f25(x1681,x1681),f25(x1681,f25(x1682,x1682)))),f25(f25(f25(x1681,x1681),f25(x1681,f25(x1682,x1682))),f25(x1683,x1683))),x1684)
% 0.20/0.65 [172]~P5(f25(f25(x1724,x1724),f25(x1724,f25(x1721,x1721))),f7(x1722,x1723))+P5(x1721,f9(f9(f11(f6(f10(x1722,f6(f9(f9(f11(f6(f10(x1723,f6(f25(x1724,x1724),a19)),a19)))),a19)),a19)))))
% 0.20/0.65 [135]~P2(x1351)+P7(x1351)+~P2(f9(f11(f6(x1351,a19))))
% 0.20/0.65 [149]P2(x1491)+~P6(x1491,f6(a19,a19))+~P6(f7(x1491,f9(f11(f6(x1491,a19)))),a13)
% 0.20/0.65 [158]E(x1581,a4)+E(f25(f16(x1581,a4),f16(x1581,a4)),x1581)+~E(f16(f10(f8(f25(f16(x1581,a4),f16(x1581,a4))),x1581),a4),f16(x1581,a4))
% 0.20/0.65 [160]E(x1601,a4)+E(f25(f16(x1601,a4),f16(x1601,a4)),x1601)+P5(f16(f10(f8(f25(f16(x1601,a4),f16(x1601,a4))),x1601),a4),x1601)
% 0.20/0.65 [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),f10(f8(f25(f16(x1631,a4),f16(x1631,a4))),x1631))
% 0.20/0.65 [164]P1(x1641)+~P5(a4,x1641)+~P6(f9(f9(f11(f6(f10(a20,f6(x1641,a19)),a19)))),x1641)
% 0.20/0.65 [171]~P5(x1711,a19)+E(x1711,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f25(x1711,x1711),a19)),a19))))))),x1711)
% 0.20/0.65 [95]~P6(x952,x951)+~P6(x951,x952)+E(x951,x952)
% 0.20/0.65 [88]P5(x882,a19)+P5(x881,a19)+E(f25(x881,x882),a4)
% 0.20/0.65 [99]P5(x991,x992)+P5(x991,f8(x992))+~P5(x991,a19)
% 0.20/0.65 [109]E(x1091,x1092)+~E(f25(x1091,x1091),f25(x1092,x1092))+~P5(x1092,a19)
% 0.20/0.65 [110]E(x1101,x1102)+~E(f25(x1101,x1101),f25(x1102,x1102))+~P5(x1101,a19)
% 0.20/0.65 [117]E(f25(x1172,x1172),x1171)+~P6(x1171,f25(x1172,x1172))+E(x1171,a4)
% 0.20/0.65 [118]E(x1181,x1182)+P5(f16(x1182,x1181),x1182)+P5(f16(x1181,x1182),x1181)
% 0.20/0.65 [127]E(x1271,x1272)+P5(f16(x1272,x1271),x1272)+~P5(f16(x1271,x1272),x1272)
% 0.20/0.65 [129]E(x1291,x1292)+~P5(f16(x1292,x1291),x1291)+~P5(f16(x1291,x1292),x1292)
% 0.20/0.65 [113]~P5(x1132,x1131)+E(f14(x1131),x1132)+~E(f25(f14(x1131),f14(x1131)),x1131)
% 0.20/0.65 [130]P5(x1302,f9(x1301))+~P5(x1302,a19)+E(f10(x1301,f6(f25(x1302,x1302),a19)),a4)
% 0.20/0.65 [157]~P5(x1571,x1572)+~P5(f25(f25(x1571,x1571),f25(x1571,f25(x1572,x1572))),f6(a19,a19))+P5(f25(f25(x1571,x1571),f25(x1571,f25(x1572,x1572))),a5)
% 0.20/0.65 [159]~P5(f25(f25(x1591,x1591),f25(x1591,f25(x1592,x1592))),f6(a19,a19))+~E(f8(f10(f8(x1591),f8(f25(x1591,x1591)))),x1592)+P5(f25(f25(x1591,x1591),f25(x1591,f25(x1592,x1592))),a20)
% 0.20/0.65 [162]~P2(x1621)+~P5(x1622,a19)+P5(f9(f9(f11(f6(f10(x1621,f6(x1622,a19)),a19)))),a19)
% 0.20/0.65 [101]~P6(x1011,x1013)+P6(x1011,x1012)+~P6(x1013,x1012)
% 0.20/0.65 [102]~P5(x1021,x1023)+P5(x1021,x1022)+~P6(x1023,x1022)
% 0.20/0.65 [111]E(x1111,x1112)+E(x1111,x1113)+~P5(x1111,f25(x1113,x1112))
% 0.20/0.65 [119]~P5(x1191,x1193)+~P5(x1191,x1192)+P5(x1191,f10(x1192,x1193))
% 0.20/0.65 [120]~P5(x1202,x1203)+~P5(x1201,x1203)+P6(f25(x1201,x1202),x1203)
% 0.20/0.65 [150]E(x1501,x1502)+~E(f25(x1503,x1501),f25(x1503,x1502))+~P5(f25(f25(x1501,x1501),f25(x1501,f25(x1502,x1502))),f6(a19,a19))
% 0.20/0.65 [151]E(x1511,x1512)+~E(f25(x1511,x1513),f25(x1512,x1513))+~P5(f25(f25(x1511,x1511),f25(x1511,f25(x1512,x1512))),f6(a19,a19))
% 0.20/0.65 [140]~P5(x1402,x1404)+~P5(x1401,x1403)+P5(f25(f25(x1401,x1401),f25(x1401,f25(x1402,x1402))),f6(x1403,x1404))
% 0.20/0.65 [169]~P5(f25(f25(f25(f25(x1692,x1692),f25(x1692,f25(x1693,x1693))),f25(f25(x1692,x1692),f25(x1692,f25(x1693,x1693)))),f25(f25(f25(x1692,x1692),f25(x1692,f25(x1693,x1693))),f25(x1691,x1691))),x1694)+P5(f25(f25(f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692))),f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692)))),f25(f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692))),f25(x1693,x1693))),f21(x1694))+~P5(f25(f25(f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692))),f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692)))),f25(f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692))),f25(x1693,x1693))),f6(f6(a19,a19),a19))
% 0.20/0.65 [170]~P5(f25(f25(f25(f25(x1702,x1702),f25(x1702,f25(x1701,x1701))),f25(f25(x1702,x1702),f25(x1702,f25(x1701,x1701)))),f25(f25(f25(x1702,x1702),f25(x1702,f25(x1701,x1701))),f25(x1703,x1703))),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))),f11(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))),f6(f6(a19,a19),a19))
% 0.20/0.65 [173]P5(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f7(x1733,x1734))+~P5(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f6(a19,a19))+~P5(x1732,f9(f9(f11(f6(f10(x1733,f6(f9(f9(f11(f6(f10(x1734,f6(f25(x1731,x1731),a19)),a19)))),a19)),a19)))))
% 0.20/0.65 [174]~P4(x1742,x1745,x1741)+~P5(f25(f25(x1743,x1743),f25(x1743,f25(x1744,x1744))),f9(x1745))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1743,x1743),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1743,x1743),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1743,x1743),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1744,x1744),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1744,x1744),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1743,x1743),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1743,x1743),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1743,x1743),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1744,x1744),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(x1744,x1744),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1745,f6(f25(f25(f25(x1743,x1743),f25(x1743,f25(x1744,x1744))),f25(f25(x1743,x1743),f25(x1743,f25(x1744,x1744)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1745,f6(f25(f25(f25(x1743,x1743),f25(x1743,f25(x1744,x1744))),f25(f25(x1743,x1743),f25(x1743,f25(x1744,x1744)))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.65 [155]~P2(x1551)+P8(x1551)+~E(f6(f9(f9(x1551)),f9(f9(x1551))),f9(x1551))+~P6(f9(f9(f11(f6(x1551,a19)))),f9(f9(x1551)))
% 0.20/0.65 [112]E(x1121,x1122)+E(x1123,x1122)+~E(f25(x1123,x1121),f25(x1122,x1122))+~P5(x1122,a19)
% 0.20/0.65 [154]~P2(x1541)+P3(x1541,x1542,x1543)+~E(f9(f9(x1542)),f9(x1541))+~P6(f9(f9(f11(f6(x1541,a19)))),f9(f9(x1543)))
% 0.20/0.65 [165]~P8(x1653)+~P8(x1652)+~P3(x1651,x1652,x1653)+P4(x1651,x1652,x1653)+P5(f25(f25(f17(x1651,x1652,x1653),f17(x1651,x1652,x1653)),f25(f17(x1651,x1652,x1653),f25(f18(x1651,x1652,x1653),f18(x1651,x1652,x1653)))),f9(x1652))
% 0.20/0.65 [175]~P8(x1753)+~P8(x1752)+~P3(x1751,x1752,x1753)+P4(x1751,x1752,x1753)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1753,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753)),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1751,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1752,f6(f25(f25(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),f25(f17(x1751,x1752,x1753),f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753)))),f25(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),f25(f17(x1751,x1752,x1753),f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1752,f6(f25(f25(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),f25(f17(x1751,x1752,x1753),f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753)))),f25(f25(f17(x1751,x1752,x1753),f17(x1751,x1752,x1753)),f25(f17(x1751,x1752,x1753),f25(f18(x1751,x1752,x1753),f18(x1751,x1752,x1753))))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.65 %EqnAxiom
% 0.20/0.65 [1]E(x11,x11)
% 0.20/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.65 [4]~E(x41,x42)+E(f25(x41,x43),f25(x42,x43))
% 0.20/0.65 [5]~E(x51,x52)+E(f25(x53,x51),f25(x53,x52))
% 0.20/0.65 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.20/0.65 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.20/0.65 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.20/0.65 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.20/0.65 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.20/0.65 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.20/0.65 [12]~E(x121,x122)+E(f16(x121,x123),f16(x122,x123))
% 0.20/0.65 [13]~E(x131,x132)+E(f16(x133,x131),f16(x133,x132))
% 0.20/0.65 [14]~E(x141,x142)+E(f24(x141),f24(x142))
% 0.20/0.65 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 0.20/0.65 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 0.20/0.65 [17]~E(x171,x172)+E(f17(x171,x173,x174),f17(x172,x173,x174))
% 0.20/0.65 [18]~E(x181,x182)+E(f17(x183,x181,x184),f17(x183,x182,x184))
% 0.20/0.65 [19]~E(x191,x192)+E(f17(x193,x194,x191),f17(x193,x194,x192))
% 0.20/0.65 [20]~E(x201,x202)+E(f12(x201),f12(x202))
% 0.20/0.65 [21]~E(x211,x212)+E(f18(x211,x213,x214),f18(x212,x213,x214))
% 0.20/0.65 [22]~E(x221,x222)+E(f18(x223,x221,x224),f18(x223,x222,x224))
% 0.20/0.65 [23]~E(x231,x232)+E(f18(x233,x234,x231),f18(x233,x234,x232))
% 0.20/0.65 [24]~E(x241,x242)+E(f21(x241),f21(x242))
% 0.20/0.65 [25]~E(x251,x252)+E(f15(x251),f15(x252))
% 0.20/0.65 [26]~E(x261,x262)+E(f14(x261),f14(x262))
% 0.20/0.65 [27]~E(x271,x272)+E(f8(x271),f8(x272))
% 0.20/0.65 [28]~E(x281,x282)+E(f22(x281),f22(x282))
% 0.20/0.65 [29]~E(x291,x292)+E(f3(x291),f3(x292))
% 0.20/0.65 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.20/0.65 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.20/0.65 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.20/0.65 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.20/0.65 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.20/0.65 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.20/0.65 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.20/0.65 [37]P6(x372,x373)+~E(x371,x372)+~P6(x371,x373)
% 0.20/0.65 [38]P6(x383,x382)+~E(x381,x382)+~P6(x383,x381)
% 0.20/0.65 [39]~P8(x391)+P8(x392)+~E(x391,x392)
% 0.20/0.65 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.20/0.65 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.20/0.65 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.20/0.65 [43]~P9(x431)+P9(x432)+~E(x431,x432)
% 0.20/0.65 [44]~P7(x441)+P7(x442)+~E(x441,x442)
% 0.20/0.65
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 cnf(180,plain,
% 0.20/0.65 ($false),
% 0.20/0.65 inference(scs_inference,[],[72,70,64,56,2,78,104]),
% 0.20/0.65 ['proof']).
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time :0.000000s
%------------------------------------------------------------------------------