%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET018-7 : TPTP v8.2.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 14:20:05 EDT 2024
% Result : Unsatisfiable 0.68s 0.69s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET018-7 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Jun 23 14:32:54 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.49/0.56 start to proof:theBenchmark
% 0.52/0.67 %-------------------------------------------
% 0.52/0.67 % File :CSE---1.7
% 0.52/0.67 % Problem :theBenchmark
% 0.52/0.67 % Transform :cnf
% 0.52/0.67 % Format :tptp:raw
% 0.52/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.52/0.67
% 0.52/0.67 % Result :Theorem 0.050000s
% 0.52/0.67 % Output :CNFRefutation 0.050000s
% 0.52/0.67 %-------------------------------------------
% 0.52/0.68 %--------------------------------------------------------------------------
% 0.52/0.68 % File : SET018-7 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.52/0.68 % Domain : Set Theory
% 0.52/0.68 % Problem : Second components of equal ordered pairs are equal
% 0.52/0.68 % Version : [Qua92] axioms : Augmented.
% 0.52/0.68 % English :
% 0.52/0.68
% 0.52/0.68 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.52/0.68 % Source : [Quaife]
% 0.52/0.68 % Names : OP5 [Qua92]
% 0.52/0.68 % : OP11 [Qua92]
% 0.52/0.68
% 0.52/0.68 % Status : Unsatisfiable
% 0.52/0.68 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.18 v7.3.0
% 0.52/0.68 % Syntax : Number of clauses : 170 ( 47 unt; 38 nHn; 105 RR)
% 0.52/0.68 % Number of literals : 343 ( 113 equ; 139 neg)
% 0.52/0.68 % Maximal clause size : 5 ( 2 avg)
% 0.52/0.68 % Maximal term depth : 6 ( 1 avg)
% 0.52/0.68 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.52/0.68 % Number of functors : 44 ( 44 usr; 12 con; 0-3 aty)
% 0.52/0.68 % Number of variables : 313 ( 53 sgn)
% 0.52/0.68 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.52/0.68
% 0.52/0.68 % Comments : Preceding lemmas are added.
% 0.52/0.68 % : OP5 uses an extra antecedent, not used in OP11. This is the
% 0.52/0.68 % OP11 version.
% 0.52/0.68 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.52/0.68 % : v7.3.0 - Changed first1 and second1 to first and second.
% 0.52/0.68 %--------------------------------------------------------------------------
% 0.52/0.68 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.52/0.68 include('Axioms/SET004-0.ax').
% 0.52/0.68 %--------------------------------------------------------------------------
% 0.52/0.68 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.52/0.68 cnf(corollary_1_to_unordered_pair,axiom,
% 0.52/0.68 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.52/0.68 | member(X,unordered_pair(X,Y)) ) ).
% 0.52/0.68
% 0.52/0.68 cnf(corollary_2_to_unordered_pair,axiom,
% 0.52/0.68 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.52/0.68 | member(Y,unordered_pair(X,Y)) ) ).
% 0.52/0.68
% 0.52/0.68 %----Corollaries to Cartesian product axiom.
% 0.52/0.68 cnf(corollary_1_to_cartesian_product,axiom,
% 0.52/0.68 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.52/0.68 | member(U,universal_class) ) ).
% 0.52/0.68
% 0.52/0.68 cnf(corollary_2_to_cartesian_product,axiom,
% 0.52/0.68 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.52/0.68 | member(V,universal_class) ) ).
% 0.52/0.68
% 0.52/0.68 %---- PARTIAL ORDER.
% 0.52/0.68 %----(PO1): reflexive.
% 0.52/0.68 cnf(subclass_is_reflexive,axiom,
% 0.52/0.68 subclass(X,X) ).
% 0.52/0.68
% 0.52/0.68 %----(PO2): antisymmetry is part of A-3.
% 0.52/0.68 %----(x < y), (y < x) --> (x = y).
% 0.52/0.68
% 0.52/0.68 %----(PO3): transitivity.
% 0.52/0.68 cnf(transitivity_of_subclass,axiom,
% 0.52/0.68 ( ~ subclass(X,Y)
% 0.52/0.68 | ~ subclass(Y,Z)
% 0.52/0.68 | subclass(X,Z) ) ).
% 0.52/0.68
% 0.52/0.68 %---- EQUALITY.
% 0.52/0.68 %----(EQ1): equality axiom.
% 0.52/0.68 %----a:x:(x = x).
% 0.52/0.68 %----This is always an axiom in the TPTP presentation.
% 0.52/0.68
% 0.52/0.68 %----(EQ2): expanded equality definition.
% 0.52/0.68 cnf(equality1,axiom,
% 0.52/0.68 ( X = Y
% 0.52/0.68 | member(not_subclass_element(X,Y),X)
% 0.52/0.68 | member(not_subclass_element(Y,X),Y) ) ).
% 0.52/0.68
% 0.52/0.68 cnf(equality2,axiom,
% 0.52/0.68 ( ~ member(not_subclass_element(X,Y),Y)
% 0.52/0.68 | X = Y
% 0.52/0.68 | member(not_subclass_element(Y,X),Y) ) ).
% 0.52/0.68
% 0.52/0.68 cnf(equality3,axiom,
% 0.52/0.68 ( ~ member(not_subclass_element(Y,X),X)
% 0.52/0.68 | X = Y
% 0.52/0.68 | member(not_subclass_element(X,Y),X) ) ).
% 0.52/0.68
% 0.52/0.68 cnf(equality4,axiom,
% 0.52/0.68 ( ~ member(not_subclass_element(X,Y),Y)
% 0.52/0.68 | ~ member(not_subclass_element(Y,X),X)
% 0.52/0.68 | X = Y ) ).
% 0.52/0.68
% 0.52/0.68 %---- SPECIAL CLASSES.
% 0.52/0.68 %----(SP1): lemma.
% 0.52/0.68 cnf(special_classes_lemma,axiom,
% 0.52/0.68 ~ member(Y,intersection(complement(X),X)) ).
% 0.52/0.68
% 0.52/0.68 %----(SP2): Existence of O (null class).
% 0.52/0.68 %----e:x:a:z:(-(z e x)).
% 0.52/0.68 cnf(existence_of_null_class,axiom,
% 0.52/0.68 ~ member(Z,null_class) ).
% 0.52/0.68
% 0.52/0.68 %----(SP3): O is a subclass of every class.
% 0.52/0.68 cnf(null_class_is_subclass,axiom,
% 0.52/0.68 subclass(null_class,X) ).
% 0.52/0.68
% 0.52/0.68 %----corollary.
% 0.52/0.68 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.52/0.68 ( ~ subclass(X,null_class)
% 0.52/0.68 | X = null_class ) ).
% 0.52/0.68
% 0.52/0.68 %----(SP4): uniqueness of null class.
% 0.52/0.68 cnf(null_class_is_unique,axiom,
% 0.52/0.68 ( Z = null_class
% 0.52/0.68 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.52/0.68
% 0.52/0.68 %----(SP5): O is a set (follows from axiom of infinity).
% 0.52/0.68 cnf(null_class_is_a_set,axiom,
% 0.52/0.68 member(null_class,universal_class) ).
% 0.52/0.68
% 0.52/0.68 %---- UNORDERED PAIRS.
% 0.52/0.68 %----(UP1): unordered pair is commutative.
% 0.52/0.68 cnf(commutativity_of_unordered_pair,axiom,
% 0.52/0.68 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.52/0.68
% 0.52/0.68 %----(UP2): if one argument is a proper class, pair contains only the
% 0.52/0.68 %----other. In a slightly different form to the paper
% 0.52/0.68 cnf(singleton_in_unordered_pair1,axiom,
% 0.52/0.68 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.52/0.68
% 0.52/0.68 cnf(singleton_in_unordered_pair2,axiom,
% 0.52/0.68 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.52/0.68
% 0.52/0.68 cnf(unordered_pair_equals_singleton1,axiom,
% 0.52/0.68 ( member(Y,universal_class)
% 0.52/0.68 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.52/0.68
% 0.52/0.68 cnf(unordered_pair_equals_singleton2,axiom,
% 0.52/0.68 ( member(X,universal_class)
% 0.52/0.68 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.52/0.68
% 0.52/0.68 %----(UP3): if both arguments are proper classes, pair is null.
% 0.52/0.68 cnf(null_unordered_pair,axiom,
% 0.52/0.68 ( unordered_pair(X,Y) = null_class
% 0.52/0.68 | member(X,universal_class)
% 0.52/0.68 | member(Y,universal_class) ) ).
% 0.52/0.68
% 0.52/0.68 %----(UP4): left cancellation for unordered pairs.
% 0.52/0.68 cnf(left_cancellation,axiom,
% 0.52/0.68 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.52/0.68 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.52/0.68 | Y = Z ) ).
% 0.52/0.68
% 0.52/0.68 %----(UP5): right cancellation for unordered pairs.
% 0.52/0.68 cnf(right_cancellation,axiom,
% 0.52/0.68 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.52/0.68 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.52/0.68 | X = Y ) ).
% 0.52/0.68
% 0.52/0.68 %----(UP6): corollary to (A-4).
% 0.52/0.68 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.52/0.68 ( ~ member(X,universal_class)
% 0.52/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.52/0.68
% 0.52/0.68 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.52/0.68 ( ~ member(Y,universal_class)
% 0.52/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.52/0.68
% 0.52/0.68 %----corollary to instantiate variables.
% 0.52/0.68 %----Not in the paper
% 0.52/0.68 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.52/0.68 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.52/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.52/0.68
% 0.52/0.68 %----(UP7): if both members of a pair belong to a set, the pair
% 0.52/0.68 %----is a subset.
% 0.52/0.68 cnf(unordered_pair_is_subset,axiom,
% 0.52/0.68 ( ~ member(X,Z)
% 0.52/0.68 | ~ member(Y,Z)
% 0.52/0.68 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.52/0.68
% 0.52/0.68 %---- SINGLETONS.
% 0.52/0.68 %----(SS1): every singleton is a set.
% 0.52/0.68 cnf(singletons_are_sets,axiom,
% 0.52/0.68 member(singleton(X),universal_class) ).
% 0.52/0.68
% 0.52/0.68 %----corollary, not in the paper.
% 0.52/0.68 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.52/0.68 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.52/0.68
% 0.52/0.68 %----(SS2): a set belongs to its singleton.
% 0.52/0.68 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.52/0.68 cnf(set_in_its_singleton,axiom,
% 0.52/0.68 ( ~ member(X,universal_class)
% 0.52/0.68 | member(X,singleton(X)) ) ).
% 0.52/0.68
% 0.52/0.68 %----corollary
% 0.52/0.68 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.52/0.68 ( ~ member(X,universal_class)
% 0.52/0.68 | singleton(X) != null_class ) ).
% 0.52/0.68
% 0.52/0.68 %----Not in the paper
% 0.52/0.68 cnf(null_class_in_its_singleton,axiom,
% 0.52/0.68 member(null_class,singleton(null_class)) ).
% 0.52/0.68
% 0.52/0.68 %----(SS3): only x can belong to {x}.
% 0.52/0.68 cnf(only_member_in_singleton,axiom,
% 0.52/0.68 ( ~ member(Y,singleton(X))
% 0.52/0.68 | Y = X ) ).
% 0.52/0.68
% 0.52/0.68 %----(SS4): if x is not a set, {x} = O.
% 0.52/0.68 cnf(singleton_is_null_class,axiom,
% 0.52/0.68 ( member(X,universal_class)
% 0.52/0.68 | singleton(X) = null_class ) ).
% 0.52/0.68
% 0.52/0.68 %----(SS5): a singleton set is determined by its element.
% 0.52/0.68 cnf(singleton_identified_by_element1,axiom,
% 0.52/0.69 ( singleton(X) != singleton(Y)
% 0.52/0.69 | ~ member(X,universal_class)
% 0.52/0.69 | X = Y ) ).
% 0.52/0.69
% 0.52/0.69 cnf(singleton_identified_by_element2,axiom,
% 0.52/0.69 ( singleton(X) != singleton(Y)
% 0.52/0.69 | ~ member(Y,universal_class)
% 0.52/0.69 | X = Y ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS5.5).
% 0.52/0.69 %----Not in the paper
% 0.52/0.69 cnf(singleton_in_unordered_pair3,axiom,
% 0.52/0.69 ( unordered_pair(Y,Z) != singleton(X)
% 0.52/0.69 | ~ member(X,universal_class)
% 0.52/0.69 | X = Y
% 0.52/0.69 | X = Z ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS6): existence of memb.
% 0.52/0.69 %----a:x:e:u:(((u e universal_class) & x = {u}) | (-e:y:((y
% 0.52/0.69 %----e universal_class) & x = {y}) & u = x)).
% 0.52/0.69 cnf(member_exists1,axiom,
% 0.52/0.69 ( ~ member(Y,universal_class)
% 0.52/0.69 | member(member_of(singleton(Y)),universal_class) ) ).
% 0.52/0.69
% 0.52/0.69 cnf(member_exists2,axiom,
% 0.52/0.69 ( ~ member(Y,universal_class)
% 0.52/0.69 | singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.52/0.69
% 0.52/0.69 cnf(member_exists3,axiom,
% 0.52/0.69 ( member(member_of(X),universal_class)
% 0.52/0.69 | member_of(X) = X ) ).
% 0.52/0.69
% 0.52/0.69 cnf(member_exists4,axiom,
% 0.52/0.69 ( singleton(member_of(X)) = X
% 0.52/0.69 | member_of(X) = X ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS7): uniqueness of memb of a singleton set.
% 0.52/0.69 %----a:x:a:u:(((u e universal_class) & x = {u}) ==> member_of(x) = u)
% 0.52/0.69 cnf(member_of_singleton_is_unique,axiom,
% 0.52/0.69 ( ~ member(U,universal_class)
% 0.52/0.69 | member_of(singleton(U)) = U ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS8): uniqueness of memb when x is not a singleton of a set.
% 0.52/0.69 %----a:x:a:u:((e:y:((y e universal_class) & x = {y})
% 0.52/0.69 %----& u = x) | member_of(x) = u)
% 0.52/0.69 cnf(member_of_non_singleton_unique1,axiom,
% 0.52/0.69 ( member(member_of1(X),universal_class)
% 0.52/0.69 | member_of(X) = X ) ).
% 0.52/0.69
% 0.52/0.69 cnf(member_of_non_singleton_unique2,axiom,
% 0.52/0.69 ( singleton(member_of1(X)) = X
% 0.52/0.69 | member_of(X) = X ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS9): corollary to (SS1).
% 0.52/0.69 cnf(corollary_2_to_singletons_are_sets,axiom,
% 0.52/0.69 ( singleton(member_of(X)) != X
% 0.52/0.69 | member(X,universal_class) ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS10).
% 0.52/0.69 cnf(property_of_singletons1,axiom,
% 0.52/0.69 ( singleton(member_of(X)) != X
% 0.52/0.69 | ~ member(Y,X)
% 0.52/0.69 | member_of(X) = Y ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS11).
% 0.52/0.69 cnf(property_of_singletons2,axiom,
% 0.52/0.69 ( ~ member(X,Y)
% 0.52/0.69 | subclass(singleton(X),Y) ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS12): there are at most two subsets of a singleton.
% 0.52/0.69 cnf(two_subsets_of_singleton,axiom,
% 0.52/0.69 ( ~ subclass(X,singleton(Y))
% 0.52/0.69 | X = null_class
% 0.52/0.69 | singleton(Y) = X ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS13): a class contains 0, 1, or at least 2 members.
% 0.52/0.69 cnf(number_of_elements_in_class,axiom,
% 0.52/0.69 ( 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))
% 0.52/0.69 | singleton(not_subclass_element(X,null_class)) = X
% 0.52/0.69 | X = null_class ) ).
% 0.52/0.69
% 0.52/0.69 %----corollaries.
% 0.52/0.69 cnf(corollary_2_to_number_of_elements_in_class,axiom,
% 0.52/0.69 ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),X)
% 0.52/0.69 | singleton(not_subclass_element(X,null_class)) = X
% 0.52/0.69 | X = null_class ) ).
% 0.52/0.69
% 0.52/0.69 cnf(corollary_1_to_number_of_elements_in_class,axiom,
% 0.52/0.69 ( not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class) != not_subclass_element(X,null_class)
% 0.52/0.69 | singleton(not_subclass_element(X,null_class)) = X
% 0.52/0.69 | X = null_class ) ).
% 0.52/0.69
% 0.52/0.69 %----(SS14): relation to ordered pair.
% 0.52/0.69 %----It looks like we could simplify Godel's axioms by taking singleton
% 0.52/0.69 %----as a primitive and using the next as a definition. Not in the paper.
% 0.52/0.69 cnf(unordered_pairs_and_singletons,axiom,
% 0.52/0.69 unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ).
% 0.52/0.69
% 0.52/0.69 %---- ORDERED PAIRS.
% 0.52/0.69 %----(OP1): an ordered pair is a set.
% 0.52/0.69 cnf(ordered_pair_is_set,axiom,
% 0.52/0.69 member(ordered_pair(X,Y),universal_class) ).
% 0.52/0.69
% 0.52/0.69 %----(OP2): members of ordered pair.
% 0.52/0.69 cnf(singleton_member_of_ordered_pair,axiom,
% 0.68/0.69 member(singleton(X),ordered_pair(X,Y)) ).
% 0.68/0.69
% 0.68/0.69 cnf(unordered_pair_member_of_ordered_pair,axiom,
% 0.68/0.69 member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)) ).
% 0.68/0.69
% 0.68/0.69 %----(OP3): special cases.
% 0.68/0.69 cnf(property_1_of_ordered_pair,axiom,
% 0.68/0.69 ( unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y)
% 0.68/0.69 | member(Y,universal_class) ) ).
% 0.68/0.69
% 0.68/0.69 cnf(property_2_of_ordered_pair,axiom,
% 0.68/0.69 ( ~ member(Y,universal_class)
% 0.68/0.69 | unordered_pair(null_class,singleton(singleton(Y))) = ordered_pair(X,Y)
% 0.68/0.69 | member(X,universal_class) ) ).
% 0.68/0.69
% 0.68/0.69 cnf(property_3_of_ordered_pair,axiom,
% 0.68/0.69 ( unordered_pair(null_class,singleton(null_class)) = ordered_pair(X,Y)
% 0.68/0.69 | member(X,universal_class)
% 0.68/0.69 | member(Y,universal_class) ) ).
% 0.68/0.69
% 0.68/0.69 %----(OP4)-(OP5): an ordered pair uniquely determines its components.
% 0.68/0.69 %----(OP4). This OP10 from the paper. OP4 is now omitted
% 0.68/0.69 cnf(ordered_pair_determines_components1,axiom,
% 0.68/0.69 ( ordered_pair(W,X) != ordered_pair(Y,Z)
% 0.68/0.69 | ~ member(W,universal_class)
% 0.68/0.69 | W = Y ) ).
% 0.68/0.69
% 0.68/0.69 %----(OP5). This OP11 from the paper. OP5 is now omitted
% 0.68/0.69 cnf(ordered_pair_determines_components2,axiom,
% 0.68/0.69 ( ordered_pair(W,X) != ordered_pair(Y,Z)
% 0.68/0.69 | ~ member(X,universal_class)
% 0.68/0.69 | X = Z ) ).
% 0.68/0.69
% 0.68/0.69 %----(OP6): existence of 1st and 2nd.
% 0.68/0.69 %----a:x:e:u:e:v:((([u,v] e cross_product(universal_class,
% 0.68/0.69 %----universal_class)) & x = [u,v]) | (-e:y:e:z:(([y,z] e cross_product(
% 0.68/0.69 %----universal_class,universal_class)) & x = [y,z]) & u = x & v = x)).
% 0.68/0.69 cnf(existence_of_1st_and_2nd_1,axiom,
% 0.68/0.69 ( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.68/0.69 | member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ) ).
% 0.68/0.69
% 0.68/0.69 %----next is subsumed by Axiom B5'-b ([y,z]
% 0.68/0.69 %----e cross_product(universal_class,universal_class)) -->
% 0.68/0.69 %----([first([y,z]),second([y,z])] = [y,z]).
% 0.68/0.69
% 0.68/0.69 cnf(existence_of_1st_and_2nd_2,axiom,
% 0.68/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.68/0.69 | first(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 cnf(existence_of_1st_and_2nd_3,axiom,
% 0.68/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.68/0.69 | second(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 cnf(existence_of_1st_and_2nd_4,axiom,
% 0.68/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.68/0.69 | first(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 cnf(existence_of_1st_and_2nd_5,axiom,
% 0.68/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.68/0.69 | second(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 %----(OP7): uniqueness of 1st and 2nd when x is an ordered pair of sets.
% 0.68/0.69 %----a:x:a:u:a:v:([u,v] e cross_product(universal_class,universal_class)
% 0.68/0.69 %---- & x = [u,v] ==> first(x) = u & second(x) = v)
% 0.68/0.69 cnf(unique_1st_and_2nd_in_pair_of_sets1,axiom,
% 0.68/0.69 ( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
% 0.68/0.69 | first(ordered_pair(U,V)) = U ) ).
% 0.68/0.69
% 0.68/0.69 cnf(unique_1st_and_2nd_in_pair_of_sets2,axiom,
% 0.68/0.69 ( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
% 0.68/0.69 | second(ordered_pair(U,V)) = V ) ).
% 0.68/0.69
% 0.68/0.69 %----(OP8): uniqueness of 1st and 2nd when x is not an ordered pair
% 0.68/0.69 %----of sets. a:x:a:u:a:v:((e:y:e:z:(([y,z]
% 0.68/0.69 %----e cross_product(universal_class, universal_class)) & x = [y,z])
% 0.68/0.69 %----& u = x & v = x) | first(x) = u & second(x) = v)
% 0.68/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets1,axiom,
% 0.68/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.68/0.69 | first(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets2,axiom,
% 0.68/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.68/0.69 | second(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets3,axiom,
% 0.68/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.68/0.69 | first(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets4,axiom,
% 0.68/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.68/0.69 | second(X) = X ) ).
% 0.68/0.69
% 0.68/0.69 %----(OP9): corollaries to (OP1).
% 0.68/0.69 cnf(corollary_1_to_ordered_pairs_are_sets,axiom,
% 0.68/0.69 ( ordered_pair(first(X),second(X)) != X
% 0.68/0.69 | member(X,universal_class) ) ).
% 0.68/0.69
% 0.68/0.69 cnf(corollary_12to_ordered_pairs_are_sets,axiom,
% 0.68/0.69 ( ~ member(X,cross_product(universal_class,universal_class))
% 0.68/0.69 | member(X,universal_class) ) ).
% 0.68/0.69
% 0.68/0.69 %----(OP10): same as (OP4).
% 0.68/0.69 %----([w,x] = [y,z]), (w e universal_class) --> (w = y).
% 0.68/0.69 %----corollaries.
% 0.68/0.69 cnf(corollary_1_to_ordered_pair_determines_components1,axiom,
% 0.68/0.69 ( member(X,universal_class)
% 0.68/0.69 | first(ordered_pair(X,Y)) = ordered_pair(X,Y) ) ).
% 0.68/0.69
% 0.68/0.69 cnf(corollary_2_to_ordered_pair_determines_components1,axiom,
% 0.68/0.69 ( member(X,universal_class)
% 0.68/0.69 | second(ordered_pair(X,Y)) = ordered_pair(X,Y) ) ).
% 0.68/0.69
% 0.68/0.69 cnf(prove_ordered_pair_determines_components2_1,negated_conjecture,
% 0.68/0.69 ordered_pair(w,x) = ordered_pair(y,z) ).
% 0.68/0.69
% 0.68/0.69 cnf(prove_ordered_pair_determines_components2_2,negated_conjecture,
% 0.68/0.69 member(x,universal_class) ).
% 0.68/0.69
% 0.68/0.69 %----This is the extra clause from [Qua92] for OP4
% 0.68/0.69 % input_clause(prove_ordered_pair_determines_components1_2a,negated_conjecture,
% 0.68/0.69 % [++member(z,universal_class)]).
% 0.68/0.69
% 0.68/0.69 cnf(prove_ordered_pair_determines_components2_3,negated_conjecture,
% 0.68/0.69 x != z ).
% 0.68/0.69
% 0.68/0.69 %--------------------------------------------------------------------------
% 0.68/0.69 %-------------------------------------------
% 0.68/0.69 % Proof found
% 0.68/0.69 % SZS status Theorem for theBenchmark
% 0.68/0.69 % SZS output start Proof
% 0.68/0.69 %ClaNum:199(EqnAxiom:44)
% 0.68/0.69 %VarNum:1168(SingletonVarNum:276)
% 0.68/0.69 %MaxLitNum:5
% 0.68/0.69 %MaxfuncDepth:24
% 0.68/0.69 %SharedTerms:48
% 0.68/0.69 %goalClause: 49 67 74
% 0.68/0.69 %singleGoalClaCount:3
% 0.68/0.69 [45]P1(a1)
% 0.68/0.69 [46]P2(a2)
% 0.68/0.69 [47]P5(a4,a19)
% 0.68/0.69 [48]P5(a1,a19)
% 0.68/0.69 [49]P5(a25,a19)
% 0.68/0.69 [74]~E(a29,a25)
% 0.68/0.69 [54]P6(a5,f6(a19,a19))
% 0.68/0.69 [55]P6(a20,f6(a19,a19))
% 0.68/0.69 [56]P5(a4,f26(a4,a4))
% 0.68/0.69 [67]E(f26(f26(a27,a27),f26(a27,f26(a25,a25))),f26(f26(a28,a28),f26(a28,f26(a29,a29))))
% 0.68/0.69 [65]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.68/0.69 [72]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.68/0.69 [50]P6(x501,a19)
% 0.68/0.69 [51]P6(a4,x511)
% 0.68/0.69 [52]P6(x521,x521)
% 0.68/0.69 [75]~P5(x751,a4)
% 0.68/0.69 [63]P6(f21(x631),f6(f6(a19,a19),a19))
% 0.68/0.69 [64]P6(f11(x641),f6(f6(a19,a19),a19))
% 0.68/0.69 [73]E(f10(f9(x731),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x731),a13)))),f3(x731))
% 0.68/0.69 [53]E(f26(x531,x532),f26(x532,x531))
% 0.68/0.69 [57]P5(f26(x571,x572),a19)
% 0.68/0.69 [59]P6(f7(x591,x592),f6(a19,a19))
% 0.68/0.69 [60]P6(f26(x601,x601),f26(x602,x601))
% 0.68/0.69 [61]P6(f26(x611,x611),f26(x611,x612))
% 0.68/0.69 [66]P5(f26(x661,x661),f26(x662,f26(x661,x661)))
% 0.68/0.69 [76]~P5(x761,f10(f8(x762),x762))
% 0.68/0.69 [69]P5(f26(x691,x691),f26(f26(x691,x691),f26(x691,f26(x692,x692))))
% 0.68/0.69 [71]P5(f26(x711,f26(x712,x712)),f26(f26(x711,x711),f26(x711,f26(x712,x712))))
% 0.68/0.69 [70]E(f8(f10(f8(f26(x701,x701)),f8(f26(x702,x702)))),f26(x701,x702))
% 0.68/0.69 [62]E(f10(f6(x621,x622),x623),f10(x623,f6(x621,x622)))
% 0.68/0.69 [77]~P7(x771)+P2(x771)
% 0.68/0.69 [78]~P8(x781)+P2(x781)
% 0.68/0.69 [81]~P1(x811)+P6(a1,x811)
% 0.68/0.69 [82]~P1(x821)+P5(a4,x821)
% 0.68/0.69 [83]~P6(x831,a4)+E(x831,a4)
% 0.68/0.69 [85]P5(f22(x851),x851)+E(x851,a4)
% 0.68/0.69 [86]E(f14(x861),x861)+P5(f14(x861),a19)
% 0.68/0.69 [87]E(f14(x871),x871)+P5(f15(x871),a19)
% 0.68/0.69 [88]P5(x881,a19)+E(f26(x881,x881),a4)
% 0.68/0.69 [91]E(x911,a4)+P5(f16(x911,a4),x911)
% 0.68/0.69 [95]~P2(x951)+P6(x951,f6(a19,a19))
% 0.68/0.69 [113]P5(x1131,a19)+~P5(x1131,f6(a19,a19))
% 0.68/0.69 [84]E(x841,a4)+E(f10(x841,f22(x841)),a4)
% 0.68/0.69 [89]E(f14(x891),x891)+E(f26(f14(x891),f14(x891)),x891)
% 0.68/0.69 [90]E(f14(x901),x901)+E(f26(f15(x901),f15(x901)),x901)
% 0.68/0.69 [100]~P5(x1001,a19)+E(f14(f26(x1001,x1001)),x1001)
% 0.68/0.69 [104]P5(x1041,a19)+~E(f26(f14(x1041),f14(x1041)),x1041)
% 0.68/0.69 [129]~P5(x1291,a19)+P5(f14(f26(x1291,x1291)),a19)
% 0.68/0.69 [110]~P8(x1101)+E(f6(f9(f9(x1101)),f9(f9(x1101))),f9(x1101))
% 0.68/0.69 [133]~P7(x1331)+P2(f9(f11(f6(x1331,a19))))
% 0.68/0.69 [137]~P5(x1371,a19)+E(f26(f14(f26(x1371,x1371)),f14(f26(x1371,x1371))),f26(x1371,x1371))
% 0.68/0.69 [140]~P5(x1401,a19)+P5(f9(f10(a5,f6(a19,x1401))),a19)
% 0.68/0.69 [144]E(f12(x1441),x1441)+E(f26(f26(f12(x1441),f12(x1441)),f26(f12(x1441),f26(f24(x1441),f24(x1441)))),x1441)
% 0.68/0.69 [146]E(f24(x1461),x1461)+E(f26(f26(f12(x1461),f12(x1461)),f26(f12(x1461),f26(f24(x1461),f24(x1461)))),x1461)
% 0.68/0.69 [147]~P9(x1471)+P6(f7(x1471,f9(f11(f6(x1471,a19)))),a13)
% 0.68/0.69 [148]~P2(x1481)+P6(f7(x1481,f9(f11(f6(x1481,a19)))),a13)
% 0.68/0.69 [149]~P8(x1491)+P6(f9(f9(f11(f6(x1491,a19)))),f9(f9(x1491)))
% 0.68/0.69 [153]P5(x1531,a19)+~E(f26(f26(f12(x1531),f12(x1531)),f26(f12(x1531),f26(f24(x1531),f24(x1531)))),x1531)
% 0.68/0.69 [160]P9(x1601)+~P6(f7(x1601,f9(f11(f6(x1601,a19)))),a13)
% 0.68/0.69 [164]E(f12(x1641),x1641)+P5(f26(f26(f12(x1641),f12(x1641)),f26(f12(x1641),f26(f24(x1641),f24(x1641)))),f6(a19,a19))
% 0.68/0.69 [166]E(f24(x1661),x1661)+P5(f26(f26(f12(x1661),f12(x1661)),f26(f12(x1661),f26(f24(x1661),f24(x1661)))),f6(a19,a19))
% 0.68/0.69 [184]~P1(x1841)+P6(f9(f9(f11(f6(f10(a20,f6(x1841,a19)),a19)))),x1841)
% 0.68/0.69 [189]~P5(x1891,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1891),a19)),a19))))),a19)
% 0.68/0.69 [79]~E(x792,x791)+P6(x791,x792)
% 0.68/0.69 [80]~E(x801,x802)+P6(x801,x802)
% 0.68/0.69 [93]P5(x932,a19)+E(f26(x931,x932),f26(x931,x931))
% 0.68/0.69 [94]P5(x941,a19)+E(f26(x941,x942),f26(x942,x942))
% 0.68/0.69 [96]~P5(x962,a19)+~E(f26(x961,x962),a4)
% 0.68/0.69 [97]~P5(x971,a19)+~E(f26(x971,x972),a4)
% 0.68/0.69 [101]P6(x1011,x1012)+P5(f16(x1011,x1012),x1011)
% 0.68/0.69 [102]~P5(x1021,x1022)+~P5(x1021,f8(x1022))
% 0.68/0.69 [107]~P5(x1071,a19)+P5(x1071,f26(x1072,x1071))
% 0.68/0.69 [108]~P5(x1081,a19)+P5(x1081,f26(x1081,x1082))
% 0.68/0.69 [111]~P5(x1111,x1112)+P6(f26(x1111,x1111),x1112)
% 0.68/0.69 [112]E(x1121,x1122)+~P5(x1121,f26(x1122,x1122))
% 0.68/0.69 [121]P6(x1211,x1212)+~P5(f16(x1211,x1212),x1212)
% 0.68/0.69 [138]~P5(x1382,f9(x1381))+~E(f10(x1381,f6(f26(x1382,x1382),a19)),a4)
% 0.68/0.69 [142]P5(x1422,a19)+E(f26(f26(x1421,x1421),f26(x1421,f26(x1422,x1422))),f26(f26(x1421,x1421),f26(x1421,a4)))
% 0.68/0.69 [159]P5(x1591,x1592)+~P5(f26(f26(x1591,x1591),f26(x1591,f26(x1592,x1592))),a5)
% 0.68/0.69 [155]P5(x1551,a19)+E(f12(f26(f26(x1551,x1551),f26(x1551,f26(x1552,x1552)))),f26(f26(x1551,x1551),f26(x1551,f26(x1552,x1552))))
% 0.68/0.69 [156]P5(x1561,a19)+E(f24(f26(f26(x1561,x1561),f26(x1561,f26(x1562,x1562)))),f26(f26(x1561,x1561),f26(x1561,f26(x1562,x1562))))
% 0.68/0.69 [177]~P5(f26(f26(x1771,x1771),f26(x1771,f26(x1772,x1772))),a20)+E(f8(f10(f8(x1771),f8(f26(x1771,x1771)))),x1772)
% 0.68/0.69 [178]~P5(f26(f26(x1781,x1781),f26(x1781,f26(x1782,x1782))),f6(a19,a19))+E(f12(f26(f26(x1781,x1781),f26(x1781,f26(x1782,x1782)))),x1781)
% 0.68/0.69 [179]~P5(f26(f26(x1791,x1791),f26(x1791,f26(x1792,x1792))),f6(a19,a19))+E(f24(f26(f26(x1791,x1791),f26(x1791,f26(x1792,x1792)))),x1792)
% 0.68/0.69 [194]~P5(f26(f26(x1941,x1941),f26(x1941,f26(x1942,x1942))),f6(a19,a19))+P5(f26(f26(f12(f26(f26(x1941,x1941),f26(x1941,f26(x1942,x1942)))),f12(f26(f26(x1941,x1941),f26(x1941,f26(x1942,x1942))))),f26(f12(f26(f26(x1941,x1941),f26(x1941,f26(x1942,x1942)))),f26(f24(f26(f26(x1941,x1941),f26(x1941,f26(x1942,x1942)))),f24(f26(f26(x1941,x1941),f26(x1941,f26(x1942,x1942))))))),f6(a19,a19))
% 0.68/0.69 [126]P2(x1261)+~P3(x1261,x1262,x1263)
% 0.68/0.69 [127]P8(x1271)+~P4(x1272,x1273,x1271)
% 0.68/0.69 [128]P8(x1281)+~P4(x1282,x1281,x1283)
% 0.68/0.69 [136]~P4(x1361,x1362,x1363)+P3(x1361,x1362,x1363)
% 0.68/0.69 [119]P5(x1191,x1192)+~P5(x1191,f10(x1193,x1192))
% 0.68/0.69 [120]P5(x1201,x1202)+~P5(x1201,f10(x1202,x1203))
% 0.68/0.69 [130]~P3(x1302,x1301,x1303)+E(f9(f9(x1301)),f9(x1302))
% 0.68/0.69 [150]~P5(x1501,f6(x1502,x1503))+E(f26(f26(f12(x1501),f12(x1501)),f26(f12(x1501),f26(f24(x1501),f24(x1501)))),x1501)
% 0.68/0.69 [154]~P3(x1541,x1543,x1542)+P6(f9(f9(f11(f6(x1541,a19)))),f9(f9(x1542)))
% 0.68/0.69 [161]P5(x1611,a19)+~P5(f26(f26(x1612,x1612),f26(x1612,f26(x1611,x1611))),f6(x1613,x1614))
% 0.68/0.69 [162]P5(x1621,a19)+~P5(f26(f26(x1621,x1621),f26(x1621,f26(x1622,x1622))),f6(x1623,x1624))
% 0.68/0.69 [167]P5(x1671,x1672)+~P5(f26(f26(x1673,x1673),f26(x1673,f26(x1671,x1671))),f6(x1674,x1672))
% 0.68/0.69 [168]P5(x1681,x1682)+~P5(f26(f26(x1681,x1681),f26(x1681,f26(x1683,x1683))),f6(x1682,x1684))
% 0.68/0.69 [169]~E(f26(x1691,x1692),a4)+~P5(f26(f26(x1691,x1691),f26(x1691,f26(x1692,x1692))),f6(x1693,x1694))
% 0.68/0.69 [173]P5(x1731,f26(x1732,x1731))+~P5(f26(f26(x1732,x1732),f26(x1732,f26(x1731,x1731))),f6(x1733,x1734))
% 0.68/0.69 [174]P5(x1741,f26(x1741,x1742))+~P5(f26(f26(x1741,x1741),f26(x1741,f26(x1742,x1742))),f6(x1743,x1744))
% 0.68/0.69 [190]~P5(f26(f26(f26(f26(x1903,x1903),f26(x1903,f26(x1901,x1901))),f26(f26(x1903,x1903),f26(x1903,f26(x1901,x1901)))),f26(f26(f26(x1903,x1903),f26(x1903,f26(x1901,x1901))),f26(x1902,x1902))),f21(x1904))+P5(f26(f26(f26(f26(x1901,x1901),f26(x1901,f26(x1902,x1902))),f26(f26(x1901,x1901),f26(x1901,f26(x1902,x1902)))),f26(f26(f26(x1901,x1901),f26(x1901,f26(x1902,x1902))),f26(x1903,x1903))),x1904)
% 0.68/0.69 [191]~P5(f26(f26(f26(f26(x1912,x1912),f26(x1912,f26(x1911,x1911))),f26(f26(x1912,x1912),f26(x1912,f26(x1911,x1911)))),f26(f26(f26(x1912,x1912),f26(x1912,f26(x1911,x1911))),f26(x1913,x1913))),f11(x1914))+P5(f26(f26(f26(f26(x1911,x1911),f26(x1911,f26(x1912,x1912))),f26(f26(x1911,x1911),f26(x1911,f26(x1912,x1912)))),f26(f26(f26(x1911,x1911),f26(x1911,f26(x1912,x1912))),f26(x1913,x1913))),x1914)
% 0.68/0.69 [196]~P5(f26(f26(x1964,x1964),f26(x1964,f26(x1961,x1961))),f7(x1962,x1963))+P5(x1961,f9(f9(f11(f6(f10(x1962,f6(f9(f9(f11(f6(f10(x1963,f6(f26(x1964,x1964),a19)),a19)))),a19)),a19)))))
% 0.68/0.69 [141]~P2(x1411)+P7(x1411)+~P2(f9(f11(f6(x1411,a19))))
% 0.68/0.69 [170]P2(x1701)+~P6(x1701,f6(a19,a19))+~P6(f7(x1701,f9(f11(f6(x1701,a19)))),a13)
% 0.68/0.69 [181]E(x1811,a4)+E(f26(f16(x1811,a4),f16(x1811,a4)),x1811)+~E(f16(f10(f8(f26(f16(x1811,a4),f16(x1811,a4))),x1811),a4),f16(x1811,a4))
% 0.68/0.69 [183]E(x1831,a4)+E(f26(f16(x1831,a4),f16(x1831,a4)),x1831)+P5(f16(f10(f8(f26(f16(x1831,a4),f16(x1831,a4))),x1831),a4),x1831)
% 0.68/0.69 [186]E(x1861,a4)+E(f26(f16(x1861,a4),f16(x1861,a4)),x1861)+P5(f16(f10(f8(f26(f16(x1861,a4),f16(x1861,a4))),x1861),a4),f10(f8(f26(f16(x1861,a4),f16(x1861,a4))),x1861))
% 0.68/0.69 [187]P1(x1871)+~P5(a4,x1871)+~P6(f9(f9(f11(f6(f10(a20,f6(x1871,a19)),a19)))),x1871)
% 0.68/0.69 [195]~P5(x1951,a19)+E(x1951,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f26(x1951,x1951),a19)),a19))))))),x1951)
% 0.68/0.69 [99]~P6(x992,x991)+~P6(x991,x992)+E(x991,x992)
% 0.68/0.69 [92]P5(x922,a19)+P5(x921,a19)+E(f26(x921,x922),a4)
% 0.68/0.69 [103]P5(x1031,x1032)+P5(x1031,f8(x1032))+~P5(x1031,a19)
% 0.68/0.69 [114]E(x1141,x1142)+~E(f26(x1141,x1141),f26(x1142,x1142))+~P5(x1142,a19)
% 0.68/0.69 [115]E(x1151,x1152)+~E(f26(x1151,x1151),f26(x1152,x1152))+~P5(x1151,a19)
% 0.68/0.69 [122]E(f26(x1222,x1222),x1221)+~P6(x1221,f26(x1222,x1222))+E(x1221,a4)
% 0.68/0.69 [123]E(x1231,x1232)+P5(f16(x1232,x1231),x1232)+P5(f16(x1231,x1232),x1231)
% 0.68/0.69 [132]E(x1321,x1322)+P5(f16(x1322,x1321),x1322)+~P5(f16(x1321,x1322),x1322)
% 0.68/0.69 [134]E(x1341,x1342)+~P5(f16(x1342,x1341),x1341)+~P5(f16(x1341,x1342),x1342)
% 0.68/0.69 [118]~P5(x1182,x1181)+E(f14(x1181),x1182)+~E(f26(f14(x1181),f14(x1181)),x1181)
% 0.68/0.69 [135]P5(x1352,f9(x1351))+~P5(x1352,a19)+E(f10(x1351,f6(f26(x1352,x1352),a19)),a4)
% 0.68/0.70 [139]P5(x1392,a19)+P5(x1391,a19)+E(f26(f26(x1391,x1391),f26(x1391,f26(x1392,x1392))),f26(a4,f26(a4,a4)))
% 0.68/0.70 [151]P5(x1512,a19)+~P5(x1511,a19)+E(f26(a4,f26(f26(x1511,x1511),f26(x1511,x1511))),f26(f26(x1512,x1512),f26(x1512,f26(x1511,x1511))))
% 0.68/0.70 [180]~P5(x1801,x1802)+~P5(f26(f26(x1801,x1801),f26(x1801,f26(x1802,x1802))),f6(a19,a19))+P5(f26(f26(x1801,x1801),f26(x1801,f26(x1802,x1802))),a5)
% 0.68/0.70 [182]~P5(f26(f26(x1821,x1821),f26(x1821,f26(x1822,x1822))),f6(a19,a19))+~E(f8(f10(f8(x1821),f8(f26(x1821,x1821)))),x1822)+P5(f26(f26(x1821,x1821),f26(x1821,f26(x1822,x1822))),a20)
% 0.68/0.70 [185]~P2(x1851)+~P5(x1852,a19)+P5(f9(f9(f11(f6(f10(x1851,f6(x1852,a19)),a19)))),a19)
% 0.68/0.70 [105]~P6(x1051,x1053)+P6(x1051,x1052)+~P6(x1053,x1052)
% 0.68/0.70 [106]~P5(x1061,x1063)+P5(x1061,x1062)+~P6(x1063,x1062)
% 0.68/0.70 [116]E(x1161,x1162)+E(x1161,x1163)+~P5(x1161,f26(x1163,x1162))
% 0.68/0.70 [124]~P5(x1241,x1243)+~P5(x1241,x1242)+P5(x1241,f10(x1242,x1243))
% 0.68/0.70 [125]~P5(x1252,x1253)+~P5(x1251,x1253)+P6(f26(x1251,x1252),x1253)
% 0.68/0.70 [171]E(x1711,x1712)+~E(f26(x1713,x1711),f26(x1713,x1712))+~P5(f26(f26(x1711,x1711),f26(x1711,f26(x1712,x1712))),f6(a19,a19))
% 0.68/0.70 [172]E(x1721,x1722)+~E(f26(x1721,x1723),f26(x1722,x1723))+~P5(f26(f26(x1721,x1721),f26(x1721,f26(x1722,x1722))),f6(a19,a19))
% 0.68/0.70 [152]~P5(x1522,x1524)+~P5(x1521,x1523)+P5(f26(f26(x1521,x1521),f26(x1521,f26(x1522,x1522))),f6(x1523,x1524))
% 0.68/0.70 [157]E(x1571,x1572)+~P5(x1571,a19)+~E(f26(f26(x1573,x1573),f26(x1573,f26(x1571,x1571))),f26(f26(x1574,x1574),f26(x1574,f26(x1572,x1572))))
% 0.68/0.70 [158]E(x1581,x1582)+~P5(x1581,a19)+~E(f26(f26(x1581,x1581),f26(x1581,f26(x1583,x1583))),f26(f26(x1582,x1582),f26(x1582,f26(x1584,x1584))))
% 0.68/0.70 [192]~P5(f26(f26(f26(f26(x1922,x1922),f26(x1922,f26(x1923,x1923))),f26(f26(x1922,x1922),f26(x1922,f26(x1923,x1923)))),f26(f26(f26(x1922,x1922),f26(x1922,f26(x1923,x1923))),f26(x1921,x1921))),x1924)+P5(f26(f26(f26(f26(x1921,x1921),f26(x1921,f26(x1922,x1922))),f26(f26(x1921,x1921),f26(x1921,f26(x1922,x1922)))),f26(f26(f26(x1921,x1921),f26(x1921,f26(x1922,x1922))),f26(x1923,x1923))),f21(x1924))+~P5(f26(f26(f26(f26(x1921,x1921),f26(x1921,f26(x1922,x1922))),f26(f26(x1921,x1921),f26(x1921,f26(x1922,x1922)))),f26(f26(f26(x1921,x1921),f26(x1921,f26(x1922,x1922))),f26(x1923,x1923))),f6(f6(a19,a19),a19))
% 0.68/0.70 [193]~P5(f26(f26(f26(f26(x1932,x1932),f26(x1932,f26(x1931,x1931))),f26(f26(x1932,x1932),f26(x1932,f26(x1931,x1931)))),f26(f26(f26(x1932,x1932),f26(x1932,f26(x1931,x1931))),f26(x1933,x1933))),x1934)+P5(f26(f26(f26(f26(x1931,x1931),f26(x1931,f26(x1932,x1932))),f26(f26(x1931,x1931),f26(x1931,f26(x1932,x1932)))),f26(f26(f26(x1931,x1931),f26(x1931,f26(x1932,x1932))),f26(x1933,x1933))),f11(x1934))+~P5(f26(f26(f26(f26(x1931,x1931),f26(x1931,f26(x1932,x1932))),f26(f26(x1931,x1931),f26(x1931,f26(x1932,x1932)))),f26(f26(f26(x1931,x1931),f26(x1931,f26(x1932,x1932))),f26(x1933,x1933))),f6(f6(a19,a19),a19))
% 0.68/0.70 [197]~P5(f26(f26(x1971,x1971),f26(x1971,f26(x1972,x1972))),f6(a19,a19))+P5(f26(f26(x1971,x1971),f26(x1971,f26(x1972,x1972))),f7(x1973,x1974))+~P5(x1972,f9(f9(f11(f6(f10(x1973,f6(f9(f9(f11(f6(f10(x1974,f6(f26(x1971,x1971),a19)),a19)))),a19)),a19)))))
% 0.68/0.70 [198]~P4(x1982,x1985,x1981)+~P5(f26(f26(x1983,x1983),f26(x1983,f26(x1984,x1984))),f9(x1985))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1981,f6(f26(f26(f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1983,x1983),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1983,x1983),a19)),a19)))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1983,x1983),a19)),a19))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1984,x1984),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1984,x1984),a19)),a19)))))))))),f26(f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1983,x1983),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1983,x1983),a19)),a19)))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1983,x1983),a19)),a19))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1984,x1984),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(x1984,x1984),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1982,f6(f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1985,f6(f26(f26(f26(x1983,x1983),f26(x1983,f26(x1984,x1984))),f26(f26(x1983,x1983),f26(x1983,f26(x1984,x1984)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1985,f6(f26(f26(f26(x1983,x1983),f26(x1983,f26(x1984,x1984))),f26(f26(x1983,x1983),f26(x1983,f26(x1984,x1984)))),a19)),a19)))))))),a19)),a19))))))))
% 0.68/0.70 [176]~P2(x1761)+P8(x1761)+~E(f6(f9(f9(x1761)),f9(f9(x1761))),f9(x1761))+~P6(f9(f9(f11(f6(x1761,a19)))),f9(f9(x1761)))
% 0.68/0.70 [117]E(x1171,x1172)+E(x1173,x1172)+~E(f26(x1173,x1171),f26(x1172,x1172))+~P5(x1172,a19)
% 0.68/0.70 [175]~P2(x1751)+P3(x1751,x1752,x1753)+~E(f9(f9(x1752)),f9(x1751))+~P6(f9(f9(f11(f6(x1751,a19)))),f9(f9(x1753)))
% 0.68/0.70 [188]~P8(x1883)+~P8(x1882)+~P3(x1881,x1882,x1883)+P4(x1881,x1882,x1883)+P5(f26(f26(f17(x1881,x1882,x1883),f17(x1881,x1882,x1883)),f26(f17(x1881,x1882,x1883),f26(f18(x1881,x1882,x1883),f18(x1881,x1882,x1883)))),f9(x1882))
% 0.68/0.70 [199]~P8(x1993)+~P8(x1992)+~P3(x1991,x1992,x1993)+P4(x1991,x1992,x1993)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1993,f6(f26(f26(f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),a19)),a19)))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),a19)),a19))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993)),a19)),a19)))))))))),f26(f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),a19)),a19)))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),a19)),a19))))))),f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1991,f6(f26(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1992,f6(f26(f26(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),f26(f17(x1991,x1992,x1993),f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993)))),f26(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),f26(f17(x1991,x1992,x1993),f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1992,f6(f26(f26(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),f26(f17(x1991,x1992,x1993),f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993)))),f26(f26(f17(x1991,x1992,x1993),f17(x1991,x1992,x1993)),f26(f17(x1991,x1992,x1993),f26(f18(x1991,x1992,x1993),f18(x1991,x1992,x1993))))),a19)),a19)))))))),a19)),a19))))))))
% 0.68/0.70 %EqnAxiom
% 0.68/0.70 [1]E(x11,x11)
% 0.68/0.70 [2]E(x22,x21)+~E(x21,x22)
% 0.68/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.68/0.70 [4]~E(x41,x42)+E(f26(x41,x43),f26(x42,x43))
% 0.68/0.70 [5]~E(x51,x52)+E(f26(x53,x51),f26(x53,x52))
% 0.68/0.70 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.68/0.70 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.68/0.70 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.68/0.70 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.68/0.70 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.68/0.70 [11]~E(x111,x112)+E(f12(x111),f12(x112))
% 0.68/0.70 [12]~E(x121,x122)+E(f16(x121,x123),f16(x122,x123))
% 0.68/0.70 [13]~E(x131,x132)+E(f16(x133,x131),f16(x133,x132))
% 0.68/0.70 [14]~E(x141,x142)+E(f21(x141),f21(x142))
% 0.68/0.70 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 0.68/0.70 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 0.68/0.70 [17]~E(x171,x172)+E(f11(x171),f11(x172))
% 0.68/0.70 [18]~E(x181,x182)+E(f24(x181),f24(x182))
% 0.68/0.70 [19]~E(x191,x192)+E(f18(x191,x193,x194),f18(x192,x193,x194))
% 0.68/0.70 [20]~E(x201,x202)+E(f18(x203,x201,x204),f18(x203,x202,x204))
% 0.68/0.70 [21]~E(x211,x212)+E(f18(x213,x214,x211),f18(x213,x214,x212))
% 0.68/0.70 [22]~E(x221,x222)+E(f8(x221),f8(x222))
% 0.68/0.70 [23]~E(x231,x232)+E(f17(x231,x233,x234),f17(x232,x233,x234))
% 0.68/0.70 [24]~E(x241,x242)+E(f17(x243,x241,x244),f17(x243,x242,x244))
% 0.68/0.70 [25]~E(x251,x252)+E(f17(x253,x254,x251),f17(x253,x254,x252))
% 0.68/0.70 [26]~E(x261,x262)+E(f22(x261),f22(x262))
% 0.68/0.70 [27]~E(x271,x272)+E(f14(x271),f14(x272))
% 0.68/0.70 [28]~E(x281,x282)+E(f15(x281),f15(x282))
% 0.68/0.70 [29]~E(x291,x292)+E(f3(x291),f3(x292))
% 0.68/0.70 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.68/0.70 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.68/0.70 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.68/0.70 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.68/0.70 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.68/0.70 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.68/0.70 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.68/0.70 [37]~P8(x371)+P8(x372)+~E(x371,x372)
% 0.68/0.70 [38]P6(x382,x383)+~E(x381,x382)+~P6(x381,x383)
% 0.68/0.70 [39]P6(x393,x392)+~E(x391,x392)+~P6(x393,x391)
% 0.68/0.70 [40]~P7(x401)+P7(x402)+~E(x401,x402)
% 0.68/0.70 [41]P4(x412,x413,x414)+~E(x411,x412)+~P4(x411,x413,x414)
% 0.68/0.70 [42]P4(x423,x422,x424)+~E(x421,x422)+~P4(x423,x421,x424)
% 0.68/0.70 [43]P4(x433,x434,x432)+~E(x431,x432)+~P4(x433,x434,x431)
% 0.68/0.70 [44]~P9(x441)+P9(x442)+~E(x441,x442)
% 0.68/0.70
% 0.68/0.70 %-------------------------------------------
% 0.68/0.70 cnf(211,plain,
% 0.68/0.70 (E(f26(f26(a28,a28),f26(a28,f26(a29,a29))),f26(f26(a27,a27),f26(a27,f26(a25,a25))))),
% 0.68/0.70 inference(scs_inference,[],[67,2])).
% 0.68/0.70 cnf(213,plain,
% 0.68/0.70 (~P5(x2131,a4)),
% 0.68/0.70 inference(rename_variables,[],[75])).
% 0.68/0.70 cnf(216,plain,
% 0.68/0.70 (~P5(x2161,f10(f8(x2162),x2162))),
% 0.68/0.70 inference(rename_variables,[],[76])).
% 0.68/0.70 cnf(219,plain,
% 0.68/0.70 (~P5(x2191,f10(f8(x2192),x2192))),
% 0.68/0.70 inference(rename_variables,[],[76])).
% 0.68/0.70 cnf(221,plain,
% 0.68/0.70 (~P5(x2211,f9(f8(f6(f26(x2211,x2211),a19))))),
% 0.68/0.70 inference(scs_inference,[],[67,75,76,216,2,82,91,101,138])).
% 0.68/0.70 cnf(223,plain,
% 0.68/0.70 (~P5(f26(f26(f26(f26(x2231,x2231),f26(x2231,f26(x2232,x2232))),f26(f26(x2231,x2231),f26(x2231,f26(x2232,x2232)))),f26(f26(f26(x2231,x2231),f26(x2231,f26(x2232,x2232))),f26(x2233,x2233))),f21(a4))),
% 0.68/0.70 inference(scs_inference,[],[67,75,213,76,216,2,82,91,101,138,190])).
% 0.68/0.70 cnf(224,plain,
% 0.68/0.70 (~P5(x2241,a4)),
% 0.68/0.70 inference(rename_variables,[],[75])).
% 0.68/0.70 cnf(227,plain,
% 0.68/0.70 (~P5(x2271,a4)),
% 0.68/0.70 inference(rename_variables,[],[75])).
% 0.68/0.70 cnf(229,plain,
% 0.68/0.70 (P5(f26(x2291,x2291),f26(f26(x2291,x2291),x2292))),
% 0.68/0.70 inference(scs_inference,[],[67,75,213,224,61,66,76,216,2,82,91,101,138,190,191,106])).
% 0.68/0.70 cnf(234,plain,
% 0.68/0.70 (~P5(x2341,f10(f8(x2342),x2342))),
% 0.68/0.70 inference(rename_variables,[],[76])).
% 0.68/0.70 cnf(238,plain,
% 0.68/0.70 (E(f26(f26(a27,f26(a25,a25)),f26(a27,a27)),f26(f26(a28,a28),f26(a28,f26(a29,a29))))),
% 0.68/0.70 inference(scs_inference,[],[49,67,75,213,224,53,61,66,76,216,219,2,82,91,101,138,190,191,106,124,157,3])).
% 0.68/0.70 cnf(241,plain,
% 0.68/0.70 (P5(a29,a19)),
% 0.68/0.70 inference(scs_inference,[],[49,67,75,213,224,53,61,66,76,216,219,2,82,91,101,138,190,191,106,124,157,3,30,32])).
% 0.68/0.70 cnf(243,plain,
% 0.68/0.70 (~P5(x2431,a4)),
% 0.68/0.70 inference(rename_variables,[],[75])).
% 0.68/0.70 cnf(251,plain,
% 0.68/0.70 (P6(f26(f26(a28,a28),f26(a28,f26(a29,a29))),f26(f26(a27,a27),f26(a27,f26(a25,a25))))),
% 0.68/0.70 inference(scs_inference,[],[49,67,52,50,75,213,224,227,243,53,61,47,66,76,216,219,234,2,82,91,101,138,190,191,106,124,157,3,30,32,33,123,187,38])).
% 0.68/0.70 cnf(283,plain,
% 0.68/0.70 ($false),
% 0.68/0.70 inference(scs_inference,[],[74,229,211,238,241,221,251,223,191,190,2,82,106,157]),
% 0.68/0.70 ['proof']).
% 0.68/0.70 % SZS output end Proof
% 0.68/0.70 % Total time :0.050000s
%------------------------------------------------------------------------------