TSTP Solution File: SET025-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET025-7 : 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 : n010.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 14:28:00 EDT 2023
% Result : Unsatisfiable 0.17s 0.62s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET025-7 : 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
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Aug 26 10:26:20 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.17/0.55 start to proof:theBenchmark
% 0.17/0.61 %-------------------------------------------
% 0.17/0.61 % File :CSE---1.6
% 0.17/0.61 % Problem :theBenchmark
% 0.17/0.61 % Transform :cnf
% 0.17/0.61 % Format :tptp:raw
% 0.17/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.17/0.61
% 0.17/0.61 % Result :Theorem 0.000000s
% 0.17/0.61 % Output :CNFRefutation 0.000000s
% 0.17/0.61 %-------------------------------------------
% 0.17/0.61 %--------------------------------------------------------------------------
% 0.17/0.61 % File : SET025-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.17/0.61 % Domain : Set Theory
% 0.17/0.61 % Problem : Ordered pairs are little sets
% 0.17/0.61 % Version : [Qua92] axioms : Augmented.
% 0.17/0.61 % English :
% 0.17/0.61
% 0.17/0.61 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.17/0.61 % Source : [Quaife]
% 0.17/0.61 % Names : OP1 [Qua92]
% 0.17/0.61
% 0.17/0.61 % Status : Unsatisfiable
% 0.17/0.61 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.27 v6.3.0, 0.18 v6.2.0, 0.10 v6.1.0, 0.29 v6.0.0, 0.00 v5.5.0, 0.15 v5.4.0, 0.10 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.36 v4.1.0, 0.23 v4.0.1, 0.18 v4.0.0, 0.27 v3.7.0, 0.20 v3.5.0, 0.18 v3.4.0, 0.17 v3.3.0, 0.14 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
% 0.17/0.61 % Syntax : Number of clauses : 145 ( 42 unt; 25 nHn; 96 RR)
% 0.17/0.61 % Number of literals : 294 ( 87 equ; 129 neg)
% 0.17/0.61 % Maximal clause size : 5 ( 2 avg)
% 0.17/0.61 % Maximal term depth : 6 ( 1 avg)
% 0.17/0.61 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.17/0.61 % Number of functors : 42 ( 42 usr; 10 con; 0-3 aty)
% 0.17/0.61 % Number of variables : 273 ( 46 sgn)
% 0.17/0.61 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.17/0.61
% 0.17/0.61 % Comments : Preceding lemmas are added.
% 0.17/0.61 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.17/0.61 %--------------------------------------------------------------------------
% 0.17/0.61 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.17/0.61 include('Axioms/SET004-0.ax').
% 0.17/0.61 %--------------------------------------------------------------------------
% 0.17/0.61 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.17/0.61 cnf(corollary_1_to_unordered_pair,axiom,
% 0.17/0.61 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.17/0.61 | member(X,unordered_pair(X,Y)) ) ).
% 0.17/0.61
% 0.17/0.61 cnf(corollary_2_to_unordered_pair,axiom,
% 0.17/0.61 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.17/0.61 | member(Y,unordered_pair(X,Y)) ) ).
% 0.17/0.61
% 0.17/0.61 %----Corollaries to Cartesian product axiom.
% 0.17/0.61 cnf(corollary_1_to_cartesian_product,axiom,
% 0.17/0.61 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.17/0.61 | member(U,universal_class) ) ).
% 0.17/0.61
% 0.17/0.61 cnf(corollary_2_to_cartesian_product,axiom,
% 0.17/0.61 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.17/0.61 | member(V,universal_class) ) ).
% 0.17/0.61
% 0.17/0.61 %---- PARTIAL ORDER.
% 0.17/0.61 %----(PO1): reflexive.
% 0.17/0.61 cnf(subclass_is_reflexive,axiom,
% 0.17/0.61 subclass(X,X) ).
% 0.17/0.61
% 0.17/0.61 %----(PO2): antisymmetry is part of A-3.
% 0.17/0.61 %----(x < y), (y < x) --> (x = y).
% 0.17/0.61
% 0.17/0.61 %----(PO3): transitivity.
% 0.17/0.61 cnf(transitivity_of_subclass,axiom,
% 0.17/0.61 ( ~ subclass(X,Y)
% 0.17/0.61 | ~ subclass(Y,Z)
% 0.17/0.61 | subclass(X,Z) ) ).
% 0.17/0.61
% 0.17/0.61 %---- EQUALITY.
% 0.17/0.61 %----(EQ1): equality axiom.
% 0.17/0.61 %----a:x:(x = x).
% 0.17/0.61 %----This is always an axiom in the TPTP presentation.
% 0.17/0.61
% 0.17/0.61 %----(EQ2): expanded equality definition.
% 0.17/0.61 cnf(equality1,axiom,
% 0.17/0.61 ( X = Y
% 0.17/0.61 | member(not_subclass_element(X,Y),X)
% 0.17/0.61 | member(not_subclass_element(Y,X),Y) ) ).
% 0.17/0.61
% 0.17/0.61 cnf(equality2,axiom,
% 0.17/0.61 ( ~ member(not_subclass_element(X,Y),Y)
% 0.17/0.61 | X = Y
% 0.17/0.61 | member(not_subclass_element(Y,X),Y) ) ).
% 0.17/0.61
% 0.17/0.61 cnf(equality3,axiom,
% 0.17/0.61 ( ~ member(not_subclass_element(Y,X),X)
% 0.17/0.61 | X = Y
% 0.17/0.61 | member(not_subclass_element(X,Y),X) ) ).
% 0.17/0.61
% 0.17/0.61 cnf(equality4,axiom,
% 0.17/0.61 ( ~ member(not_subclass_element(X,Y),Y)
% 0.17/0.61 | ~ member(not_subclass_element(Y,X),X)
% 0.17/0.61 | X = Y ) ).
% 0.17/0.61
% 0.17/0.61 %---- SPECIAL CLASSES.
% 0.17/0.61 %----(SP1): lemma.
% 0.17/0.61 cnf(special_classes_lemma,axiom,
% 0.17/0.61 ~ member(Y,intersection(complement(X),X)) ).
% 0.17/0.61
% 0.17/0.61 %----(SP2): Existence of O (null class).
% 0.17/0.61 %----e:x:a:z:(-(z e x)).
% 0.17/0.61 cnf(existence_of_null_class,axiom,
% 0.17/0.61 ~ member(Z,null_class) ).
% 0.17/0.61
% 0.17/0.61 %----(SP3): O is a subclass of every class.
% 0.17/0.61 cnf(null_class_is_subclass,axiom,
% 0.17/0.61 subclass(null_class,X) ).
% 0.17/0.61
% 0.17/0.61 %----corollary.
% 0.17/0.61 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.17/0.61 ( ~ subclass(X,null_class)
% 0.17/0.61 | X = null_class ) ).
% 0.17/0.61
% 0.17/0.61 %----(SP4): uniqueness of null class.
% 0.17/0.61 cnf(null_class_is_unique,axiom,
% 0.17/0.61 ( Z = null_class
% 0.17/0.61 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.17/0.61
% 0.17/0.61 %----(SP5): O is a set (follows from axiom of infinity).
% 0.17/0.61 cnf(null_class_is_a_set,axiom,
% 0.17/0.61 member(null_class,universal_class) ).
% 0.17/0.62
% 0.17/0.62 %---- UNORDERED PAIRS.
% 0.17/0.62 %----(UP1): unordered pair is commutative.
% 0.17/0.62 cnf(commutativity_of_unordered_pair,axiom,
% 0.17/0.62 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.17/0.62
% 0.17/0.62 %----(UP2): if one argument is a proper class, pair contains only the
% 0.17/0.62 %----other. In a slightly different form to the paper
% 0.17/0.62 cnf(singleton_in_unordered_pair1,axiom,
% 0.17/0.62 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.17/0.62
% 0.17/0.62 cnf(singleton_in_unordered_pair2,axiom,
% 0.17/0.62 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.17/0.62
% 0.17/0.62 cnf(unordered_pair_equals_singleton1,axiom,
% 0.17/0.62 ( member(Y,universal_class)
% 0.17/0.62 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.17/0.62
% 0.17/0.62 cnf(unordered_pair_equals_singleton2,axiom,
% 0.17/0.62 ( member(X,universal_class)
% 0.17/0.62 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.17/0.62
% 0.17/0.62 %----(UP3): if both arguments are proper classes, pair is null.
% 0.17/0.62 cnf(null_unordered_pair,axiom,
% 0.17/0.62 ( unordered_pair(X,Y) = null_class
% 0.17/0.62 | member(X,universal_class)
% 0.17/0.62 | member(Y,universal_class) ) ).
% 0.17/0.62
% 0.17/0.62 %----(UP4): left cancellation for unordered pairs.
% 0.17/0.62 cnf(left_cancellation,axiom,
% 0.17/0.62 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.17/0.62 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.17/0.62 | Y = Z ) ).
% 0.17/0.62
% 0.17/0.62 %----(UP5): right cancellation for unordered pairs.
% 0.17/0.62 cnf(right_cancellation,axiom,
% 0.17/0.62 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.17/0.62 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.17/0.62 | X = Y ) ).
% 0.17/0.62
% 0.17/0.62 %----(UP6): corollary to (A-4).
% 0.17/0.62 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.17/0.62 ( ~ member(X,universal_class)
% 0.17/0.62 | unordered_pair(X,Y) != null_class ) ).
% 0.17/0.62
% 0.17/0.62 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.17/0.62 ( ~ member(Y,universal_class)
% 0.17/0.62 | unordered_pair(X,Y) != null_class ) ).
% 0.17/0.62
% 0.17/0.62 %----corollary to instantiate variables.
% 0.17/0.62 %----Not in the paper
% 0.17/0.62 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.17/0.62 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.17/0.62 | unordered_pair(X,Y) != null_class ) ).
% 0.17/0.62
% 0.17/0.62 %----(UP7): if both members of a pair belong to a set, the pair
% 0.17/0.62 %----is a subset.
% 0.17/0.62 cnf(unordered_pair_is_subset,axiom,
% 0.17/0.62 ( ~ member(X,Z)
% 0.17/0.62 | ~ member(Y,Z)
% 0.17/0.62 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.17/0.62
% 0.17/0.62 %---- SINGLETONS.
% 0.17/0.62 %----(SS1): every singleton is a set.
% 0.17/0.62 cnf(singletons_are_sets,axiom,
% 0.17/0.62 member(singleton(X),universal_class) ).
% 0.17/0.62
% 0.17/0.62 %----corollary, not in the paper.
% 0.17/0.62 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.17/0.62 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.17/0.62
% 0.17/0.62 %----(SS2): a set belongs to its singleton.
% 0.17/0.62 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.17/0.62 cnf(set_in_its_singleton,axiom,
% 0.17/0.62 ( ~ member(X,universal_class)
% 0.17/0.62 | member(X,singleton(X)) ) ).
% 0.17/0.62
% 0.17/0.62 %----corollary
% 0.17/0.62 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.17/0.62 ( ~ member(X,universal_class)
% 0.17/0.62 | singleton(X) != null_class ) ).
% 0.17/0.62
% 0.17/0.62 %----Not in the paper
% 0.17/0.62 cnf(null_class_in_its_singleton,axiom,
% 0.17/0.62 member(null_class,singleton(null_class)) ).
% 0.17/0.62
% 0.17/0.62 %----(SS3): only x can belong to {x}.
% 0.17/0.62 cnf(only_member_in_singleton,axiom,
% 0.17/0.62 ( ~ member(Y,singleton(X))
% 0.17/0.62 | Y = X ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS4): if x is not a set, {x} = O.
% 0.17/0.62 cnf(singleton_is_null_class,axiom,
% 0.17/0.62 ( member(X,universal_class)
% 0.17/0.62 | singleton(X) = null_class ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS5): a singleton set is determined by its element.
% 0.17/0.62 cnf(singleton_identified_by_element1,axiom,
% 0.17/0.62 ( singleton(X) != singleton(Y)
% 0.17/0.62 | ~ member(X,universal_class)
% 0.17/0.62 | X = Y ) ).
% 0.17/0.62
% 0.17/0.62 cnf(singleton_identified_by_element2,axiom,
% 0.17/0.62 ( singleton(X) != singleton(Y)
% 0.17/0.62 | ~ member(Y,universal_class)
% 0.17/0.62 | X = Y ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS5.5).
% 0.17/0.62 %----Not in the paper
% 0.17/0.62 cnf(singleton_in_unordered_pair3,axiom,
% 0.17/0.62 ( unordered_pair(Y,Z) != singleton(X)
% 0.17/0.62 | ~ member(X,universal_class)
% 0.17/0.62 | X = Y
% 0.17/0.62 | X = Z ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS6): existence of memb.
% 0.17/0.62 %----a:x:e:u:(((u e universal_class) & x = {u}) | (-e:y:((y
% 0.17/0.62 %----e universal_class) & x = {y}) & u = x)).
% 0.17/0.62 cnf(member_exists1,axiom,
% 0.17/0.62 ( ~ member(Y,universal_class)
% 0.17/0.62 | member(member_of(singleton(Y)),universal_class) ) ).
% 0.17/0.62
% 0.17/0.62 cnf(member_exists2,axiom,
% 0.17/0.62 ( ~ member(Y,universal_class)
% 0.17/0.62 | singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.17/0.62
% 0.17/0.62 cnf(member_exists3,axiom,
% 0.17/0.62 ( member(member_of(X),universal_class)
% 0.17/0.62 | member_of(X) = X ) ).
% 0.17/0.62
% 0.17/0.62 cnf(member_exists4,axiom,
% 0.17/0.62 ( singleton(member_of(X)) = X
% 0.17/0.62 | member_of(X) = X ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS7): uniqueness of memb of a singleton set.
% 0.17/0.62 %----a:x:a:u:(((u e universal_class) & x = {u}) ==> member_of(x) = u)
% 0.17/0.62 cnf(member_of_singleton_is_unique,axiom,
% 0.17/0.62 ( ~ member(U,universal_class)
% 0.17/0.62 | member_of(singleton(U)) = U ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS8): uniqueness of memb when x is not a singleton of a set.
% 0.17/0.62 %----a:x:a:u:((e:y:((y e universal_class) & x = {y})
% 0.17/0.62 %----& u = x) | member_of(x) = u)
% 0.17/0.62 cnf(member_of_non_singleton_unique1,axiom,
% 0.17/0.62 ( member(member_of1(X),universal_class)
% 0.17/0.62 | member_of(X) = X ) ).
% 0.17/0.62
% 0.17/0.62 cnf(member_of_non_singleton_unique2,axiom,
% 0.17/0.62 ( singleton(member_of1(X)) = X
% 0.17/0.62 | member_of(X) = X ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS9): corollary to (SS1).
% 0.17/0.62 cnf(corollary_2_to_singletons_are_sets,axiom,
% 0.17/0.62 ( singleton(member_of(X)) != X
% 0.17/0.62 | member(X,universal_class) ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS10).
% 0.17/0.62 cnf(property_of_singletons1,axiom,
% 0.17/0.62 ( singleton(member_of(X)) != X
% 0.17/0.62 | ~ member(Y,X)
% 0.17/0.62 | member_of(X) = Y ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS11).
% 0.17/0.62 cnf(property_of_singletons2,axiom,
% 0.17/0.62 ( ~ member(X,Y)
% 0.17/0.62 | subclass(singleton(X),Y) ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS12): there are at most two subsets of a singleton.
% 0.17/0.62 cnf(two_subsets_of_singleton,axiom,
% 0.17/0.62 ( ~ subclass(X,singleton(Y))
% 0.17/0.62 | X = null_class
% 0.17/0.62 | singleton(Y) = X ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS13): a class contains 0, 1, or at least 2 members.
% 0.17/0.62 cnf(number_of_elements_in_class,axiom,
% 0.17/0.62 ( 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))
% 0.17/0.62 | singleton(not_subclass_element(X,null_class)) = X
% 0.17/0.62 | X = null_class ) ).
% 0.17/0.62
% 0.17/0.62 %----corollaries.
% 0.17/0.62 cnf(corollary_2_to_number_of_elements_in_class,axiom,
% 0.17/0.62 ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),X)
% 0.17/0.62 | singleton(not_subclass_element(X,null_class)) = X
% 0.17/0.62 | X = null_class ) ).
% 0.17/0.62
% 0.17/0.62 cnf(corollary_1_to_number_of_elements_in_class,axiom,
% 0.17/0.62 ( not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class) != not_subclass_element(X,null_class)
% 0.17/0.62 | singleton(not_subclass_element(X,null_class)) = X
% 0.17/0.62 | X = null_class ) ).
% 0.17/0.62
% 0.17/0.62 %----(SS14): relation to ordered pair.
% 0.17/0.62 %----It looks like we could simplify Godel's axioms by taking singleton
% 0.17/0.62 %----as a primitive and using the next as a definition. Not in the paper
% 0.17/0.62 cnf(unordered_pairs_and_singletons,axiom,
% 0.17/0.62 unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ).
% 0.17/0.62
% 0.17/0.62 cnf(prove_ordered_pair_is_set_1,negated_conjecture,
% 0.17/0.62 ~ member(ordered_pair(x,y),universal_class) ).
% 0.17/0.62
% 0.17/0.62 %--------------------------------------------------------------------------
% 0.17/0.62 %-------------------------------------------
% 0.17/0.62 % Proof found
% 0.17/0.62 % SZS status Theorem for theBenchmark
% 0.17/0.62 % SZS output start Proof
% 0.17/0.62 %ClaNum:174(EqnAxiom:44)
% 0.17/0.62 %VarNum:987(SingletonVarNum:242)
% 0.17/0.62 %MaxLitNum:5
% 0.17/0.62 %MaxfuncDepth:24
% 0.17/0.62 %SharedTerms:39
% 0.17/0.62 %goalClause: 71
% 0.17/0.62 %singleGoalClaCount:1
% 0.17/0.62 [45]P1(a1)
% 0.17/0.62 [46]P2(a2)
% 0.17/0.62 [47]P5(a4,a19)
% 0.17/0.62 [48]P5(a1,a19)
% 0.17/0.62 [53]P6(a5,f6(a19,a19))
% 0.17/0.62 [54]P6(a20,f6(a19,a19))
% 0.17/0.62 [55]P5(a4,f25(a4,a4))
% 0.17/0.62 [71]~P5(f25(f25(a26,a26),f25(a26,f25(a27,a27))),a19)
% 0.17/0.62 [64]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.17/0.62 [67]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.17/0.62 [49]P6(x491,a19)
% 0.17/0.62 [50]P6(a4,x501)
% 0.17/0.62 [51]P6(x511,x511)
% 0.17/0.62 [69]~P5(x691,a4)
% 0.17/0.62 [62]P6(f21(x621),f6(f6(a19,a19),a19))
% 0.17/0.62 [63]P6(f11(x631),f6(f6(a19,a19),a19))
% 0.17/0.62 [68]E(f10(f9(x681),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x681),a13)))),f3(x681))
% 0.17/0.62 [52]E(f25(x521,x522),f25(x522,x521))
% 0.17/0.62 [56]P5(f25(x561,x562),a19)
% 0.17/0.62 [58]P6(f7(x581,x582),f6(a19,a19))
% 0.17/0.62 [59]P6(f25(x591,x591),f25(x592,x591))
% 0.17/0.62 [60]P6(f25(x601,x601),f25(x601,x602))
% 0.17/0.62 [65]P5(f25(x651,x651),f25(x652,f25(x651,x651)))
% 0.17/0.62 [70]~P5(x701,f10(f8(x702),x702))
% 0.17/0.62 [66]E(f8(f10(f8(f25(x661,x661)),f8(f25(x662,x662)))),f25(x661,x662))
% 0.17/0.62 [61]E(f10(f6(x611,x612),x613),f10(x613,f6(x611,x612)))
% 0.17/0.62 [72]~P7(x721)+P2(x721)
% 0.17/0.62 [73]~P8(x731)+P2(x731)
% 0.17/0.62 [76]~P1(x761)+P6(a1,x761)
% 0.17/0.62 [77]~P1(x771)+P5(a4,x771)
% 0.17/0.62 [78]~P6(x781,a4)+E(x781,a4)
% 0.17/0.62 [80]P5(f22(x801),x801)+E(x801,a4)
% 0.17/0.62 [81]E(f14(x811),x811)+P5(f14(x811),a19)
% 0.17/0.62 [82]E(f14(x821),x821)+P5(f15(x821),a19)
% 0.17/0.62 [83]P5(x831,a19)+E(f25(x831,x831),a4)
% 0.17/0.62 [86]E(x861,a4)+P5(f16(x861,a4),x861)
% 0.17/0.62 [90]~P2(x901)+P6(x901,f6(a19,a19))
% 0.17/0.62 [79]E(x791,a4)+E(f10(x791,f22(x791)),a4)
% 0.17/0.62 [84]E(f14(x841),x841)+E(f25(f14(x841),f14(x841)),x841)
% 0.17/0.62 [85]E(f14(x851),x851)+E(f25(f15(x851),f15(x851)),x851)
% 0.17/0.62 [95]~P5(x951,a19)+E(f14(f25(x951,x951)),x951)
% 0.17/0.62 [99]P5(x991,a19)+~E(f25(f14(x991),f14(x991)),x991)
% 0.17/0.62 [123]~P5(x1231,a19)+P5(f14(f25(x1231,x1231)),a19)
% 0.17/0.62 [105]~P8(x1051)+E(f6(f9(f9(x1051)),f9(f9(x1051))),f9(x1051))
% 0.17/0.62 [127]~P7(x1271)+P2(f9(f11(f6(x1271,a19))))
% 0.17/0.62 [131]~P5(x1311,a19)+E(f25(f14(f25(x1311,x1311)),f14(f25(x1311,x1311))),f25(x1311,x1311))
% 0.17/0.62 [133]~P5(x1331,a19)+P5(f9(f10(a5,f6(a19,x1331))),a19)
% 0.17/0.62 [135]~P9(x1351)+P6(f7(x1351,f9(f11(f6(x1351,a19)))),a13)
% 0.17/0.62 [136]~P2(x1361)+P6(f7(x1361,f9(f11(f6(x1361,a19)))),a13)
% 0.17/0.62 [137]~P8(x1371)+P6(f9(f9(f11(f6(x1371,a19)))),f9(f9(x1371)))
% 0.17/0.62 [142]P9(x1421)+~P6(f7(x1421,f9(f11(f6(x1421,a19)))),a13)
% 0.17/0.62 [160]~P1(x1601)+P6(f9(f9(f11(f6(f10(a20,f6(x1601,a19)),a19)))),x1601)
% 0.17/0.62 [165]~P5(x1651,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1651),a19)),a19))))),a19)
% 0.17/0.62 [74]~E(x742,x741)+P6(x741,x742)
% 0.17/0.62 [75]~E(x751,x752)+P6(x751,x752)
% 0.17/0.62 [88]P5(x882,a19)+E(f25(x881,x882),f25(x881,x881))
% 0.17/0.62 [89]P5(x891,a19)+E(f25(x891,x892),f25(x892,x892))
% 0.17/0.62 [91]~P5(x912,a19)+~E(f25(x911,x912),a4)
% 0.17/0.62 [92]~P5(x921,a19)+~E(f25(x921,x922),a4)
% 0.17/0.62 [96]P6(x961,x962)+P5(f16(x961,x962),x961)
% 0.17/0.62 [97]~P5(x971,x972)+~P5(x971,f8(x972))
% 0.17/0.62 [102]~P5(x1021,a19)+P5(x1021,f25(x1022,x1021))
% 0.17/0.62 [103]~P5(x1031,a19)+P5(x1031,f25(x1031,x1032))
% 0.17/0.62 [106]~P5(x1061,x1062)+P6(f25(x1061,x1061),x1062)
% 0.17/0.62 [107]E(x1071,x1072)+~P5(x1071,f25(x1072,x1072))
% 0.17/0.62 [115]P6(x1151,x1152)+~P5(f16(x1151,x1152),x1152)
% 0.17/0.62 [132]~P5(x1322,f9(x1321))+~E(f10(x1321,f6(f25(x1322,x1322),a19)),a4)
% 0.17/0.62 [141]P5(x1411,x1412)+~P5(f25(f25(x1411,x1411),f25(x1411,f25(x1412,x1412))),a5)
% 0.17/0.62 [155]~P5(f25(f25(x1551,x1551),f25(x1551,f25(x1552,x1552))),a20)+E(f8(f10(f8(x1551),f8(f25(x1551,x1551)))),x1552)
% 0.17/0.62 [120]P2(x1201)+~P3(x1201,x1202,x1203)
% 0.17/0.62 [121]P8(x1211)+~P4(x1212,x1213,x1211)
% 0.17/0.62 [122]P8(x1221)+~P4(x1222,x1221,x1223)
% 0.17/0.62 [130]~P4(x1301,x1302,x1303)+P3(x1301,x1302,x1303)
% 0.17/0.62 [113]P5(x1131,x1132)+~P5(x1131,f10(x1133,x1132))
% 0.17/0.62 [114]P5(x1141,x1142)+~P5(x1141,f10(x1142,x1143))
% 0.17/0.62 [124]~P3(x1242,x1241,x1243)+E(f9(f9(x1241)),f9(x1242))
% 0.17/0.62 [138]~P5(x1381,f6(x1382,x1383))+E(f25(f25(f12(x1381),f12(x1381)),f25(f12(x1381),f25(f24(x1381),f24(x1381)))),x1381)
% 0.17/0.62 [140]~P3(x1401,x1403,x1402)+P6(f9(f9(f11(f6(x1401,a19)))),f9(f9(x1402)))
% 0.17/0.62 [143]P5(x1431,a19)+~P5(f25(f25(x1432,x1432),f25(x1432,f25(x1431,x1431))),f6(x1433,x1434))
% 0.17/0.62 [144]P5(x1441,a19)+~P5(f25(f25(x1441,x1441),f25(x1441,f25(x1442,x1442))),f6(x1443,x1444))
% 0.17/0.62 [145]P5(x1451,x1452)+~P5(f25(f25(x1453,x1453),f25(x1453,f25(x1451,x1451))),f6(x1454,x1452))
% 0.17/0.62 [146]P5(x1461,x1462)+~P5(f25(f25(x1461,x1461),f25(x1461,f25(x1463,x1463))),f6(x1462,x1464))
% 0.17/0.62 [147]~E(f25(x1471,x1472),a4)+~P5(f25(f25(x1471,x1471),f25(x1471,f25(x1472,x1472))),f6(x1473,x1474))
% 0.17/0.62 [151]P5(x1511,f25(x1512,x1511))+~P5(f25(f25(x1512,x1512),f25(x1512,f25(x1511,x1511))),f6(x1513,x1514))
% 0.17/0.62 [152]P5(x1521,f25(x1521,x1522))+~P5(f25(f25(x1521,x1521),f25(x1521,f25(x1522,x1522))),f6(x1523,x1524))
% 0.17/0.62 [166]~P5(f25(f25(f25(f25(x1663,x1663),f25(x1663,f25(x1661,x1661))),f25(f25(x1663,x1663),f25(x1663,f25(x1661,x1661)))),f25(f25(f25(x1663,x1663),f25(x1663,f25(x1661,x1661))),f25(x1662,x1662))),f21(x1664))+P5(f25(f25(f25(f25(x1661,x1661),f25(x1661,f25(x1662,x1662))),f25(f25(x1661,x1661),f25(x1661,f25(x1662,x1662)))),f25(f25(f25(x1661,x1661),f25(x1661,f25(x1662,x1662))),f25(x1663,x1663))),x1664)
% 0.17/0.62 [167]~P5(f25(f25(f25(f25(x1672,x1672),f25(x1672,f25(x1671,x1671))),f25(f25(x1672,x1672),f25(x1672,f25(x1671,x1671)))),f25(f25(f25(x1672,x1672),f25(x1672,f25(x1671,x1671))),f25(x1673,x1673))),f11(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)
% 0.17/0.62 [171]~P5(f25(f25(x1714,x1714),f25(x1714,f25(x1711,x1711))),f7(x1712,x1713))+P5(x1711,f9(f9(f11(f6(f10(x1712,f6(f9(f9(f11(f6(f10(x1713,f6(f25(x1714,x1714),a19)),a19)))),a19)),a19)))))
% 0.17/0.62 [134]~P2(x1341)+P7(x1341)+~P2(f9(f11(f6(x1341,a19))))
% 0.17/0.62 [148]P2(x1481)+~P6(x1481,f6(a19,a19))+~P6(f7(x1481,f9(f11(f6(x1481,a19)))),a13)
% 0.17/0.62 [157]E(x1571,a4)+E(f25(f16(x1571,a4),f16(x1571,a4)),x1571)+~E(f16(f10(f8(f25(f16(x1571,a4),f16(x1571,a4))),x1571),a4),f16(x1571,a4))
% 0.17/0.62 [159]E(x1591,a4)+E(f25(f16(x1591,a4),f16(x1591,a4)),x1591)+P5(f16(f10(f8(f25(f16(x1591,a4),f16(x1591,a4))),x1591),a4),x1591)
% 0.17/0.62 [162]E(x1621,a4)+E(f25(f16(x1621,a4),f16(x1621,a4)),x1621)+P5(f16(f10(f8(f25(f16(x1621,a4),f16(x1621,a4))),x1621),a4),f10(f8(f25(f16(x1621,a4),f16(x1621,a4))),x1621))
% 0.17/0.62 [163]P1(x1631)+~P5(a4,x1631)+~P6(f9(f9(f11(f6(f10(a20,f6(x1631,a19)),a19)))),x1631)
% 0.17/0.62 [170]~P5(x1701,a19)+E(x1701,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f25(x1701,x1701),a19)),a19))))))),x1701)
% 0.17/0.62 [94]~P6(x942,x941)+~P6(x941,x942)+E(x941,x942)
% 0.17/0.63 [87]P5(x872,a19)+P5(x871,a19)+E(f25(x871,x872),a4)
% 0.17/0.63 [98]P5(x981,x982)+P5(x981,f8(x982))+~P5(x981,a19)
% 0.17/0.63 [108]E(x1081,x1082)+~E(f25(x1081,x1081),f25(x1082,x1082))+~P5(x1082,a19)
% 0.17/0.63 [109]E(x1091,x1092)+~E(f25(x1091,x1091),f25(x1092,x1092))+~P5(x1091,a19)
% 0.17/0.63 [116]E(f25(x1162,x1162),x1161)+~P6(x1161,f25(x1162,x1162))+E(x1161,a4)
% 0.17/0.63 [117]E(x1171,x1172)+P5(f16(x1172,x1171),x1172)+P5(f16(x1171,x1172),x1171)
% 0.17/0.63 [126]E(x1261,x1262)+P5(f16(x1262,x1261),x1262)+~P5(f16(x1261,x1262),x1262)
% 0.17/0.63 [128]E(x1281,x1282)+~P5(f16(x1282,x1281),x1281)+~P5(f16(x1281,x1282),x1282)
% 0.17/0.63 [112]~P5(x1122,x1121)+E(f14(x1121),x1122)+~E(f25(f14(x1121),f14(x1121)),x1121)
% 0.17/0.63 [129]P5(x1292,f9(x1291))+~P5(x1292,a19)+E(f10(x1291,f6(f25(x1292,x1292),a19)),a4)
% 0.17/0.63 [156]~P5(x1561,x1562)+~P5(f25(f25(x1561,x1561),f25(x1561,f25(x1562,x1562))),f6(a19,a19))+P5(f25(f25(x1561,x1561),f25(x1561,f25(x1562,x1562))),a5)
% 0.17/0.63 [158]~P5(f25(f25(x1581,x1581),f25(x1581,f25(x1582,x1582))),f6(a19,a19))+~E(f8(f10(f8(x1581),f8(f25(x1581,x1581)))),x1582)+P5(f25(f25(x1581,x1581),f25(x1581,f25(x1582,x1582))),a20)
% 0.17/0.63 [161]~P2(x1611)+~P5(x1612,a19)+P5(f9(f9(f11(f6(f10(x1611,f6(x1612,a19)),a19)))),a19)
% 0.17/0.63 [100]~P6(x1001,x1003)+P6(x1001,x1002)+~P6(x1003,x1002)
% 0.17/0.63 [101]~P5(x1011,x1013)+P5(x1011,x1012)+~P6(x1013,x1012)
% 0.17/0.63 [110]E(x1101,x1102)+E(x1101,x1103)+~P5(x1101,f25(x1103,x1102))
% 0.17/0.63 [118]~P5(x1181,x1183)+~P5(x1181,x1182)+P5(x1181,f10(x1182,x1183))
% 0.17/0.63 [119]~P5(x1192,x1193)+~P5(x1191,x1193)+P6(f25(x1191,x1192),x1193)
% 0.17/0.63 [149]E(x1491,x1492)+~E(f25(x1493,x1491),f25(x1493,x1492))+~P5(f25(f25(x1491,x1491),f25(x1491,f25(x1492,x1492))),f6(a19,a19))
% 0.17/0.63 [150]E(x1501,x1502)+~E(f25(x1501,x1503),f25(x1502,x1503))+~P5(f25(f25(x1501,x1501),f25(x1501,f25(x1502,x1502))),f6(a19,a19))
% 0.17/0.63 [139]~P5(x1392,x1394)+~P5(x1391,x1393)+P5(f25(f25(x1391,x1391),f25(x1391,f25(x1392,x1392))),f6(x1393,x1394))
% 0.17/0.63 [168]~P5(f25(f25(f25(f25(x1682,x1682),f25(x1682,f25(x1683,x1683))),f25(f25(x1682,x1682),f25(x1682,f25(x1683,x1683)))),f25(f25(f25(x1682,x1682),f25(x1682,f25(x1683,x1683))),f25(x1681,x1681))),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))),f21(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))),f6(f6(a19,a19),a19))
% 0.17/0.63 [169]~P5(f25(f25(f25(f25(x1692,x1692),f25(x1692,f25(x1691,x1691))),f25(f25(x1692,x1692),f25(x1692,f25(x1691,x1691)))),f25(f25(f25(x1692,x1692),f25(x1692,f25(x1691,x1691))),f25(x1693,x1693))),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))),f11(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))
% 0.17/0.63 [172]P5(f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722))),f7(x1723,x1724))+~P5(f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722))),f6(a19,a19))+~P5(x1722,f9(f9(f11(f6(f10(x1723,f6(f9(f9(f11(f6(f10(x1724,f6(f25(x1721,x1721),a19)),a19)))),a19)),a19)))))
% 0.17/0.63 [173]~P4(x1732,x1735,x1731)+~P5(f25(f25(x1733,x1733),f25(x1733,f25(x1734,x1734))),f9(x1735))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1731,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1733,x1733),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1733,x1733),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1733,x1733),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1734,x1734),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1734,x1734),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1733,x1733),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1733,x1733),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1733,x1733),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1734,x1734),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(x1734,x1734),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1732,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1735,f6(f25(f25(f25(x1733,x1733),f25(x1733,f25(x1734,x1734))),f25(f25(x1733,x1733),f25(x1733,f25(x1734,x1734)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1735,f6(f25(f25(f25(x1733,x1733),f25(x1733,f25(x1734,x1734))),f25(f25(x1733,x1733),f25(x1733,f25(x1734,x1734)))),a19)),a19)))))))),a19)),a19))))))))
% 0.17/0.63 [154]~P2(x1541)+P8(x1541)+~E(f6(f9(f9(x1541)),f9(f9(x1541))),f9(x1541))+~P6(f9(f9(f11(f6(x1541,a19)))),f9(f9(x1541)))
% 0.17/0.63 [111]E(x1111,x1112)+E(x1113,x1112)+~E(f25(x1113,x1111),f25(x1112,x1112))+~P5(x1112,a19)
% 0.17/0.63 [153]~P2(x1531)+P3(x1531,x1532,x1533)+~E(f9(f9(x1532)),f9(x1531))+~P6(f9(f9(f11(f6(x1531,a19)))),f9(f9(x1533)))
% 0.17/0.63 [164]~P8(x1643)+~P8(x1642)+~P3(x1641,x1642,x1643)+P4(x1641,x1642,x1643)+P5(f25(f25(f17(x1641,x1642,x1643),f17(x1641,x1642,x1643)),f25(f17(x1641,x1642,x1643),f25(f18(x1641,x1642,x1643),f18(x1641,x1642,x1643)))),f9(x1642))
% 0.17/0.63 [174]~P8(x1743)+~P8(x1742)+~P3(x1741,x1742,x1743)+P4(x1741,x1742,x1743)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1743,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743)),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1741,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(f25(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),f25(f17(x1741,x1742,x1743),f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743)))),f25(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),f25(f17(x1741,x1742,x1743),f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1742,f6(f25(f25(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),f25(f17(x1741,x1742,x1743),f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743)))),f25(f25(f17(x1741,x1742,x1743),f17(x1741,x1742,x1743)),f25(f17(x1741,x1742,x1743),f25(f18(x1741,x1742,x1743),f18(x1741,x1742,x1743))))),a19)),a19)))))))),a19)),a19))))))))
% 0.17/0.63 %EqnAxiom
% 0.17/0.63 [1]E(x11,x11)
% 0.17/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.17/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.17/0.63 [4]~E(x41,x42)+E(f25(x41,x43),f25(x42,x43))
% 0.17/0.63 [5]~E(x51,x52)+E(f25(x53,x51),f25(x53,x52))
% 0.17/0.63 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.17/0.63 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.17/0.63 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.17/0.63 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.17/0.63 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.17/0.63 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.17/0.63 [12]~E(x121,x122)+E(f16(x121,x123),f16(x122,x123))
% 0.17/0.63 [13]~E(x131,x132)+E(f16(x133,x131),f16(x133,x132))
% 0.17/0.63 [14]~E(x141,x142)+E(f7(x141,x143),f7(x142,x143))
% 0.17/0.63 [15]~E(x151,x152)+E(f7(x153,x151),f7(x153,x152))
% 0.17/0.63 [16]~E(x161,x162)+E(f18(x161,x163,x164),f18(x162,x163,x164))
% 0.17/0.63 [17]~E(x171,x172)+E(f18(x173,x171,x174),f18(x173,x172,x174))
% 0.17/0.63 [18]~E(x181,x182)+E(f18(x183,x184,x181),f18(x183,x184,x182))
% 0.17/0.63 [19]~E(x191,x192)+E(f17(x191,x193,x194),f17(x192,x193,x194))
% 0.17/0.63 [20]~E(x201,x202)+E(f17(x203,x201,x204),f17(x203,x202,x204))
% 0.17/0.63 [21]~E(x211,x212)+E(f17(x213,x214,x211),f17(x213,x214,x212))
% 0.17/0.63 [22]~E(x221,x222)+E(f14(x221),f14(x222))
% 0.17/0.63 [23]~E(x231,x232)+E(f15(x231),f15(x232))
% 0.17/0.63 [24]~E(x241,x242)+E(f24(x241),f24(x242))
% 0.17/0.63 [25]~E(x251,x252)+E(f8(x251),f8(x252))
% 0.17/0.63 [26]~E(x261,x262)+E(f22(x261),f22(x262))
% 0.17/0.63 [27]~E(x271,x272)+E(f12(x271),f12(x272))
% 0.17/0.63 [28]~E(x281,x282)+E(f3(x281),f3(x282))
% 0.17/0.63 [29]~E(x291,x292)+E(f21(x291),f21(x292))
% 0.17/0.63 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.17/0.63 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.17/0.63 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.17/0.63 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.17/0.63 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.17/0.63 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.17/0.63 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.17/0.63 [37]P6(x372,x373)+~E(x371,x372)+~P6(x371,x373)
% 0.17/0.63 [38]P6(x383,x382)+~E(x381,x382)+~P6(x383,x381)
% 0.17/0.63 [39]~P8(x391)+P8(x392)+~E(x391,x392)
% 0.17/0.63 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.17/0.63 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.17/0.63 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.17/0.63 [43]~P9(x431)+P9(x432)+~E(x431,x432)
% 0.17/0.63 [44]~P7(x441)+P7(x442)+~E(x441,x442)
% 0.17/0.63
% 0.17/0.63 %-------------------------------------------
% 0.17/0.63 cnf(175,plain,
% 0.17/0.63 ($false),
% 0.17/0.63 inference(scs_inference,[],[71,56]),
% 0.17/0.63 ['proof']).
% 0.17/0.63 % SZS output end Proof
% 0.17/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------