TSTP Solution File: SET118-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET118-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n017.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 14:28:50 EDT 2023
% Result : Unsatisfiable 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET118-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:09:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 % File :CSE---1.6
% 0.20/0.67 % Problem :theBenchmark
% 0.20/0.67 % Transform :cnf
% 0.20/0.67 % Format :tptp:raw
% 0.20/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.67
% 0.20/0.67 % Result :Theorem 0.020000s
% 0.20/0.67 % Output :CNFRefutation 0.020000s
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 %--------------------------------------------------------------------------
% 0.20/0.67 % File : SET118-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.20/0.67 % Domain : Set Theory
% 0.20/0.67 % Problem : Corollary 2 to every ordered pair being a set
% 0.20/0.67 % Version : [Qua92] axioms : Augmented.
% 0.20/0.67 % English :
% 0.20/0.67
% 0.20/0.67 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.20/0.67 % Source : [Quaife]
% 0.20/0.67 % Names : OP9.2 [Quaife]
% 0.20/0.67
% 0.20/0.67 % Status : Unsatisfiable
% 0.20/0.67 % Rating : 0.10 v8.1.0, 0.05 v7.4.0, 0.06 v7.3.0
% 0.20/0.67 % Syntax : Number of clauses : 165 ( 46 unt; 36 nHn; 102 RR)
% 0.20/0.67 % Number of literals : 334 ( 108 equ; 137 neg)
% 0.20/0.67 % Maximal clause size : 5 ( 2 avg)
% 0.20/0.67 % Maximal term depth : 6 ( 1 avg)
% 0.20/0.67 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.20/0.67 % Number of functors : 41 ( 41 usr; 9 con; 0-3 aty)
% 0.20/0.67 % Number of variables : 307 ( 53 sgn)
% 0.20/0.67 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.20/0.67
% 0.20/0.67 % Comments : Preceding lemmas are added.
% 0.20/0.67 % : Not in [Qua92].
% 0.20/0.67 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.20/0.67 % : v7.3.0 - Changed first1 and second1 to first and second.
% 0.20/0.67 %--------------------------------------------------------------------------
% 0.20/0.67 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.20/0.67 include('Axioms/SET004-0.ax').
% 0.20/0.67 %--------------------------------------------------------------------------
% 0.20/0.67 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.20/0.67 cnf(corollary_1_to_unordered_pair,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.68 | member(X,unordered_pair(X,Y)) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(corollary_2_to_unordered_pair,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.68 | member(Y,unordered_pair(X,Y)) ) ).
% 0.20/0.68
% 0.20/0.68 %----Corollaries to Cartesian product axiom.
% 0.20/0.68 cnf(corollary_1_to_cartesian_product,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.68 | member(U,universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(corollary_2_to_cartesian_product,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.68 | member(V,universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 %---- PARTIAL ORDER.
% 0.20/0.68 %----(PO1): reflexive.
% 0.20/0.68 cnf(subclass_is_reflexive,axiom,
% 0.20/0.68 subclass(X,X) ).
% 0.20/0.68
% 0.20/0.68 %----(PO2): antisymmetry is part of A-3.
% 0.20/0.68 %----(x < y), (y < x) --> (x = y).
% 0.20/0.68
% 0.20/0.68 %----(PO3): transitivity.
% 0.20/0.68 cnf(transitivity_of_subclass,axiom,
% 0.20/0.68 ( ~ subclass(X,Y)
% 0.20/0.68 | ~ subclass(Y,Z)
% 0.20/0.68 | subclass(X,Z) ) ).
% 0.20/0.68
% 0.20/0.68 %---- EQUALITY.
% 0.20/0.68 %----(EQ1): equality axiom.
% 0.20/0.68 %----a:x:(x = x).
% 0.20/0.68 %----This is always an axiom in the TPTP presentation.
% 0.20/0.68
% 0.20/0.68 %----(EQ2): expanded equality definition.
% 0.20/0.68 cnf(equality1,axiom,
% 0.20/0.68 ( X = Y
% 0.20/0.68 | member(not_subclass_element(X,Y),X)
% 0.20/0.68 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(equality2,axiom,
% 0.20/0.68 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.68 | X = Y
% 0.20/0.68 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(equality3,axiom,
% 0.20/0.68 ( ~ member(not_subclass_element(Y,X),X)
% 0.20/0.68 | X = Y
% 0.20/0.68 | member(not_subclass_element(X,Y),X) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(equality4,axiom,
% 0.20/0.68 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.68 | ~ member(not_subclass_element(Y,X),X)
% 0.20/0.68 | X = Y ) ).
% 0.20/0.68
% 0.20/0.68 %---- SPECIAL CLASSES.
% 0.20/0.68 %----(SP1): lemma.
% 0.20/0.68 cnf(special_classes_lemma,axiom,
% 0.20/0.68 ~ member(Y,intersection(complement(X),X)) ).
% 0.20/0.68
% 0.20/0.68 %----(SP2): Existence of O (null class).
% 0.20/0.68 %----e:x:a:z:(-(z e x)).
% 0.20/0.68 cnf(existence_of_null_class,axiom,
% 0.20/0.68 ~ member(Z,null_class) ).
% 0.20/0.68
% 0.20/0.68 %----(SP3): O is a subclass of every class.
% 0.20/0.68 cnf(null_class_is_subclass,axiom,
% 0.20/0.68 subclass(null_class,X) ).
% 0.20/0.68
% 0.20/0.68 %----corollary.
% 0.20/0.68 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.20/0.68 ( ~ subclass(X,null_class)
% 0.20/0.68 | X = null_class ) ).
% 0.20/0.68
% 0.20/0.68 %----(SP4): uniqueness of null class.
% 0.20/0.68 cnf(null_class_is_unique,axiom,
% 0.20/0.68 ( Z = null_class
% 0.20/0.68 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.20/0.68
% 0.20/0.68 %----(SP5): O is a set (follows from axiom of infinity).
% 0.20/0.68 cnf(null_class_is_a_set,axiom,
% 0.20/0.68 member(null_class,universal_class) ).
% 0.20/0.68
% 0.20/0.68 %---- UNORDERED PAIRS.
% 0.20/0.68 %----(UP1): unordered pair is commutative.
% 0.20/0.68 cnf(commutativity_of_unordered_pair,axiom,
% 0.20/0.68 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.20/0.68
% 0.20/0.68 %----(UP2): if one argument is a proper class, pair contains only the
% 0.20/0.68 %----other. In a slightly different form to the paper
% 0.20/0.68 cnf(singleton_in_unordered_pair1,axiom,
% 0.20/0.68 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.20/0.68
% 0.20/0.68 cnf(singleton_in_unordered_pair2,axiom,
% 0.20/0.68 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.20/0.68
% 0.20/0.68 cnf(unordered_pair_equals_singleton1,axiom,
% 0.20/0.68 ( member(Y,universal_class)
% 0.20/0.68 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(unordered_pair_equals_singleton2,axiom,
% 0.20/0.68 ( member(X,universal_class)
% 0.20/0.68 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.20/0.68
% 0.20/0.68 %----(UP3): if both arguments are proper classes, pair is null.
% 0.20/0.68 cnf(null_unordered_pair,axiom,
% 0.20/0.68 ( unordered_pair(X,Y) = null_class
% 0.20/0.68 | member(X,universal_class)
% 0.20/0.68 | member(Y,universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 %----(UP4): left cancellation for unordered pairs.
% 0.20/0.68 cnf(left_cancellation,axiom,
% 0.20/0.68 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.20/0.68 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.20/0.68 | Y = Z ) ).
% 0.20/0.68
% 0.20/0.68 %----(UP5): right cancellation for unordered pairs.
% 0.20/0.68 cnf(right_cancellation,axiom,
% 0.20/0.68 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.20/0.68 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.20/0.68 | X = Y ) ).
% 0.20/0.68
% 0.20/0.68 %----(UP6): corollary to (A-4).
% 0.20/0.68 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.20/0.68 ( ~ member(X,universal_class)
% 0.20/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.68
% 0.20/0.68 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.20/0.68 ( ~ member(Y,universal_class)
% 0.20/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.68
% 0.20/0.68 %----corollary to instantiate variables.
% 0.20/0.68 %----Not in the paper
% 0.20/0.68 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.68
% 0.20/0.68 %----(UP7): if both members of a pair belong to a set, the pair
% 0.20/0.68 %----is a subset.
% 0.20/0.68 cnf(unordered_pair_is_subset,axiom,
% 0.20/0.68 ( ~ member(X,Z)
% 0.20/0.68 | ~ member(Y,Z)
% 0.20/0.68 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.20/0.68
% 0.20/0.68 %---- SINGLETONS.
% 0.20/0.68 %----(SS1): every singleton is a set.
% 0.20/0.68 cnf(singletons_are_sets,axiom,
% 0.20/0.68 member(singleton(X),universal_class) ).
% 0.20/0.68
% 0.20/0.68 %----corollary, not in the paper.
% 0.20/0.68 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.20/0.68 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.20/0.68
% 0.20/0.68 %----(SS2): a set belongs to its singleton.
% 0.20/0.68 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.20/0.68 cnf(set_in_its_singleton,axiom,
% 0.20/0.68 ( ~ member(X,universal_class)
% 0.20/0.68 | member(X,singleton(X)) ) ).
% 0.20/0.68
% 0.20/0.68 %----corollary
% 0.20/0.68 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.20/0.68 ( ~ member(X,universal_class)
% 0.20/0.68 | singleton(X) != null_class ) ).
% 0.20/0.68
% 0.20/0.68 %----Not in the paper
% 0.20/0.68 cnf(null_class_in_its_singleton,axiom,
% 0.20/0.68 member(null_class,singleton(null_class)) ).
% 0.20/0.68
% 0.20/0.68 %----(SS3): only x can belong to {x}.
% 0.20/0.68 cnf(only_member_in_singleton,axiom,
% 0.20/0.68 ( ~ member(Y,singleton(X))
% 0.20/0.68 | Y = X ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS4): if x is not a set, {x} = O.
% 0.20/0.68 cnf(singleton_is_null_class,axiom,
% 0.20/0.68 ( member(X,universal_class)
% 0.20/0.68 | singleton(X) = null_class ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS5): a singleton set is determined by its element.
% 0.20/0.68 cnf(singleton_identified_by_element1,axiom,
% 0.20/0.68 ( singleton(X) != singleton(Y)
% 0.20/0.68 | ~ member(X,universal_class)
% 0.20/0.68 | X = Y ) ).
% 0.20/0.68
% 0.20/0.68 cnf(singleton_identified_by_element2,axiom,
% 0.20/0.68 ( singleton(X) != singleton(Y)
% 0.20/0.68 | ~ member(Y,universal_class)
% 0.20/0.68 | X = Y ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS5.5).
% 0.20/0.68 %----Not in the paper
% 0.20/0.68 cnf(singleton_in_unordered_pair3,axiom,
% 0.20/0.68 ( unordered_pair(Y,Z) != singleton(X)
% 0.20/0.68 | ~ member(X,universal_class)
% 0.20/0.68 | X = Y
% 0.20/0.68 | X = Z ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS6): existence of memb.
% 0.20/0.68 %----a:x:e:u:(((u e universal_class) & x = {u}) | (-e:y:((y
% 0.20/0.68 %----e universal_class) & x = {y}) & u = x)).
% 0.20/0.68 cnf(member_exists1,axiom,
% 0.20/0.68 ( ~ member(Y,universal_class)
% 0.20/0.68 | member(member_of(singleton(Y)),universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(member_exists2,axiom,
% 0.20/0.68 ( ~ member(Y,universal_class)
% 0.20/0.68 | singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(member_exists3,axiom,
% 0.20/0.68 ( member(member_of(X),universal_class)
% 0.20/0.68 | member_of(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 cnf(member_exists4,axiom,
% 0.20/0.68 ( singleton(member_of(X)) = X
% 0.20/0.68 | member_of(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS7): uniqueness of memb of a singleton set.
% 0.20/0.68 %----a:x:a:u:(((u e universal_class) & x = {u}) ==> member_of(x) = u)
% 0.20/0.68 cnf(member_of_singleton_is_unique,axiom,
% 0.20/0.68 ( ~ member(U,universal_class)
% 0.20/0.68 | member_of(singleton(U)) = U ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS8): uniqueness of memb when x is not a singleton of a set.
% 0.20/0.68 %----a:x:a:u:((e:y:((y e universal_class) & x = {y})
% 0.20/0.68 %----& u = x) | member_of(x) = u)
% 0.20/0.68 cnf(member_of_non_singleton_unique1,axiom,
% 0.20/0.68 ( member(member_of1(X),universal_class)
% 0.20/0.68 | member_of(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 cnf(member_of_non_singleton_unique2,axiom,
% 0.20/0.68 ( singleton(member_of1(X)) = X
% 0.20/0.69 | member_of(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 %----(SS9): corollary to (SS1).
% 0.20/0.69 cnf(corollary_2_to_singletons_are_sets,axiom,
% 0.20/0.69 ( singleton(member_of(X)) != X
% 0.20/0.69 | member(X,universal_class) ) ).
% 0.20/0.69
% 0.20/0.69 %----(SS10).
% 0.20/0.69 cnf(property_of_singletons1,axiom,
% 0.20/0.69 ( singleton(member_of(X)) != X
% 0.20/0.69 | ~ member(Y,X)
% 0.20/0.69 | member_of(X) = Y ) ).
% 0.20/0.69
% 0.20/0.69 %----(SS11).
% 0.20/0.69 cnf(property_of_singletons2,axiom,
% 0.20/0.69 ( ~ member(X,Y)
% 0.20/0.69 | subclass(singleton(X),Y) ) ).
% 0.20/0.69
% 0.20/0.69 %----(SS12): there are at most two subsets of a singleton.
% 0.20/0.69 cnf(two_subsets_of_singleton,axiom,
% 0.20/0.69 ( ~ subclass(X,singleton(Y))
% 0.20/0.69 | X = null_class
% 0.20/0.69 | singleton(Y) = X ) ).
% 0.20/0.69
% 0.20/0.69 %----(SS13): a class contains 0, 1, or at least 2 members.
% 0.20/0.69 cnf(number_of_elements_in_class,axiom,
% 0.20/0.69 ( 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))
% 0.20/0.69 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.69 | X = null_class ) ).
% 0.20/0.69
% 0.20/0.69 %----corollaries.
% 0.20/0.69 cnf(corollary_2_to_number_of_elements_in_class,axiom,
% 0.20/0.69 ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),X)
% 0.20/0.69 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.69 | X = null_class ) ).
% 0.20/0.69
% 0.20/0.69 cnf(corollary_1_to_number_of_elements_in_class,axiom,
% 0.20/0.69 ( not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class) != not_subclass_element(X,null_class)
% 0.20/0.69 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.69 | X = null_class ) ).
% 0.20/0.69
% 0.20/0.69 %----(SS14): relation to ordered pair.
% 0.20/0.69 %----It looks like we could simplify Godel's axioms by taking singleton
% 0.20/0.69 %----as a primitive and using the next as a definition. Not in the paper
% 0.20/0.69 cnf(unordered_pairs_and_singletons,axiom,
% 0.20/0.69 unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ).
% 0.20/0.69
% 0.20/0.69 %---- ORDERED PAIRS.
% 0.20/0.69 %----(OP1): an ordered pair is a set.
% 0.20/0.69 cnf(ordered_pair_is_set,axiom,
% 0.20/0.69 member(ordered_pair(X,Y),universal_class) ).
% 0.20/0.69
% 0.20/0.69 %----(OP2): members of ordered pair.
% 0.20/0.69 cnf(singleton_member_of_ordered_pair,axiom,
% 0.20/0.69 member(singleton(X),ordered_pair(X,Y)) ).
% 0.20/0.69
% 0.20/0.69 cnf(unordered_pair_member_of_ordered_pair,axiom,
% 0.20/0.69 member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)) ).
% 0.20/0.69
% 0.20/0.69 %----(OP3): special cases.
% 0.20/0.69 cnf(property_1_of_ordered_pair,axiom,
% 0.20/0.69 ( unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y)
% 0.20/0.69 | member(Y,universal_class) ) ).
% 0.20/0.69
% 0.20/0.69 cnf(property_2_of_ordered_pair,axiom,
% 0.20/0.69 ( ~ member(Y,universal_class)
% 0.20/0.69 | unordered_pair(null_class,singleton(singleton(Y))) = ordered_pair(X,Y)
% 0.20/0.69 | member(X,universal_class) ) ).
% 0.20/0.69
% 0.20/0.69 cnf(property_3_of_ordered_pair,axiom,
% 0.20/0.69 ( unordered_pair(null_class,singleton(null_class)) = ordered_pair(X,Y)
% 0.20/0.69 | member(X,universal_class)
% 0.20/0.69 | member(Y,universal_class) ) ).
% 0.20/0.69
% 0.20/0.69 %----(OP4)-(OP5): an ordered pair uniquely determines its components.
% 0.20/0.69 %----(OP4). This OP10 from the paper. OP4 is now omitted
% 0.20/0.69 cnf(ordered_pair_determines_components1,axiom,
% 0.20/0.69 ( ordered_pair(W,X) != ordered_pair(Y,Z)
% 0.20/0.69 | ~ member(W,universal_class)
% 0.20/0.69 | W = Y ) ).
% 0.20/0.69
% 0.20/0.69 %----(OP5). This OP11 from the paper. OP5 is now omitted
% 0.20/0.69 cnf(ordered_pair_determines_components2,axiom,
% 0.20/0.69 ( ordered_pair(W,X) != ordered_pair(Y,Z)
% 0.20/0.69 | ~ member(X,universal_class)
% 0.20/0.69 | X = Z ) ).
% 0.20/0.69
% 0.20/0.69 %----(OP6): existence of 1st and 2nd.
% 0.20/0.69 %----a:x:e:u:e:v:((([u,v] e cross_product(universal_class,
% 0.20/0.69 %----universal_class)) & x = [u,v]) | (-e:y:e:z:(([y,z] e cross_product(
% 0.20/0.69 %----universal_class,universal_class)) & x = [y,z]) & u = x & v = x)).
% 0.20/0.69 cnf(existence_of_1st_and_2nd_1,axiom,
% 0.20/0.69 ( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.20/0.69 | member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ) ).
% 0.20/0.69
% 0.20/0.69 %----next is subsumed by Axiom B5'-b ([y,z]
% 0.20/0.69 %----e cross_product(universal_class,universal_class)) -->
% 0.20/0.69 %----([first([y,z]),second([y,z])] = [y,z]).
% 0.20/0.69
% 0.20/0.69 cnf(existence_of_1st_and_2nd_2,axiom,
% 0.20/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.20/0.69 | first(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 cnf(existence_of_1st_and_2nd_3,axiom,
% 0.20/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.20/0.69 | second(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 cnf(existence_of_1st_and_2nd_4,axiom,
% 0.20/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.20/0.69 | first(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 cnf(existence_of_1st_and_2nd_5,axiom,
% 0.20/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.20/0.69 | second(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 %----(OP7): uniqueness of 1st and 2nd when x is an ordered pair of sets.
% 0.20/0.69 %----a:x:a:u:a:v:([u,v] e cross_product(universal_class,universal_class)
% 0.20/0.69 %---- & x = [u,v] ==> first(x) = u & second(x) = v)
% 0.20/0.69 cnf(unique_1st_and_2nd_in_pair_of_sets1,axiom,
% 0.20/0.69 ( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
% 0.20/0.69 | first(ordered_pair(U,V)) = U ) ).
% 0.20/0.69
% 0.20/0.69 cnf(unique_1st_and_2nd_in_pair_of_sets2,axiom,
% 0.20/0.69 ( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
% 0.20/0.69 | second(ordered_pair(U,V)) = V ) ).
% 0.20/0.69
% 0.20/0.69 %----(OP8): uniqueness of 1st and 2nd when x is not an ordered pair
% 0.20/0.69 %----of sets. a:x:a:u:a:v:((e:y:e:z:(([y,z]
% 0.20/0.69 %----e cross_product(universal_class, universal_class)) & x = [y,z])
% 0.20/0.69 %----& u = x & v = x) | first(x) = u & second(x) = v)
% 0.20/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets1,axiom,
% 0.20/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.20/0.69 | first(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets2,axiom,
% 0.20/0.69 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.20/0.69 | second(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets3,axiom,
% 0.20/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.20/0.69 | first(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 cnf(unique_1st_and_2nd_in_pair_of_non_sets4,axiom,
% 0.20/0.69 ( ordered_pair(first(X),second(X)) = X
% 0.20/0.69 | second(X) = X ) ).
% 0.20/0.69
% 0.20/0.69 cnf(prove_corollary_2_to_ordered_pairs_are_sets_1,negated_conjecture,
% 0.20/0.69 member(x,cross_product(universal_class,universal_class)) ).
% 0.20/0.69
% 0.20/0.69 cnf(prove_corollary_2_to_ordered_pairs_are_sets_2,negated_conjecture,
% 0.20/0.69 ~ member(x,universal_class) ).
% 0.20/0.69
% 0.20/0.69 %--------------------------------------------------------------------------
% 0.20/0.69 %-------------------------------------------
% 0.20/0.69 % Proof found
% 0.20/0.69 % SZS status Theorem for theBenchmark
% 0.20/0.69 % SZS output start Proof
% 0.20/0.69 %ClaNum:194(EqnAxiom:44)
% 0.20/0.69 %VarNum:1137(SingletonVarNum:270)
% 0.20/0.69 %MaxLitNum:5
% 0.20/0.69 %MaxfuncDepth:24
% 0.20/0.69 %SharedTerms:36
% 0.20/0.69 %goalClause: 56 73
% 0.20/0.69 %singleGoalClaCount:2
% 0.20/0.69 [45]P1(a1)
% 0.20/0.69 [46]P2(a2)
% 0.20/0.69 [47]P5(a4,a19)
% 0.20/0.69 [48]P5(a1,a19)
% 0.20/0.69 [73]~P5(a26,a19)
% 0.20/0.69 [53]P6(a5,f6(a19,a19))
% 0.20/0.69 [54]P6(a20,f6(a19,a19))
% 0.20/0.69 [55]P5(a4,f25(a4,a4))
% 0.20/0.69 [56]P5(a26,f6(a19,a19))
% 0.20/0.69 [65]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.20/0.69 [71]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.20/0.69 [49]P6(x491,a19)
% 0.20/0.69 [50]P6(a4,x501)
% 0.20/0.69 [51]P6(x511,x511)
% 0.20/0.69 [74]~P5(x741,a4)
% 0.20/0.69 [63]P6(f21(x631),f6(f6(a19,a19),a19))
% 0.20/0.69 [64]P6(f11(x641),f6(f6(a19,a19),a19))
% 0.20/0.69 [72]E(f10(f9(x721),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x721),a13)))),f3(x721))
% 0.20/0.69 [52]E(f25(x521,x522),f25(x522,x521))
% 0.20/0.69 [57]P5(f25(x571,x572),a19)
% 0.20/0.69 [59]P6(f7(x591,x592),f6(a19,a19))
% 0.20/0.69 [60]P6(f25(x601,x601),f25(x602,x601))
% 0.20/0.69 [61]P6(f25(x611,x611),f25(x611,x612))
% 0.20/0.69 [66]P5(f25(x661,x661),f25(x662,f25(x661,x661)))
% 0.20/0.69 [75]~P5(x751,f10(f8(x752),x752))
% 0.20/0.69 [68]P5(f25(x681,x681),f25(f25(x681,x681),f25(x681,f25(x682,x682))))
% 0.20/0.69 [70]P5(f25(x701,f25(x702,x702)),f25(f25(x701,x701),f25(x701,f25(x702,x702))))
% 0.20/0.69 [69]E(f8(f10(f8(f25(x691,x691)),f8(f25(x692,x692)))),f25(x691,x692))
% 0.20/0.69 [62]E(f10(f6(x621,x622),x623),f10(x623,f6(x621,x622)))
% 0.20/0.69 [76]~P7(x761)+P2(x761)
% 0.20/0.69 [77]~P8(x771)+P2(x771)
% 0.20/0.69 [80]~P1(x801)+P6(a1,x801)
% 0.20/0.69 [81]~P1(x811)+P5(a4,x811)
% 0.20/0.69 [82]~P6(x821,a4)+E(x821,a4)
% 0.20/0.69 [84]P5(f22(x841),x841)+E(x841,a4)
% 0.20/0.69 [85]E(f14(x851),x851)+P5(f14(x851),a19)
% 0.20/0.69 [86]E(f14(x861),x861)+P5(f15(x861),a19)
% 0.20/0.69 [87]P5(x871,a19)+E(f25(x871,x871),a4)
% 0.20/0.69 [90]E(x901,a4)+P5(f16(x901,a4),x901)
% 0.20/0.69 [94]~P2(x941)+P6(x941,f6(a19,a19))
% 0.20/0.69 [83]E(x831,a4)+E(f10(x831,f22(x831)),a4)
% 0.20/0.69 [88]E(f14(x881),x881)+E(f25(f14(x881),f14(x881)),x881)
% 0.20/0.69 [89]E(f14(x891),x891)+E(f25(f15(x891),f15(x891)),x891)
% 0.20/0.69 [99]~P5(x991,a19)+E(f14(f25(x991,x991)),x991)
% 0.20/0.69 [103]P5(x1031,a19)+~E(f25(f14(x1031),f14(x1031)),x1031)
% 0.20/0.69 [127]~P5(x1271,a19)+P5(f14(f25(x1271,x1271)),a19)
% 0.20/0.69 [109]~P8(x1091)+E(f6(f9(f9(x1091)),f9(f9(x1091))),f9(x1091))
% 0.20/0.69 [131]~P7(x1311)+P2(f9(f11(f6(x1311,a19))))
% 0.20/0.69 [135]~P5(x1351,a19)+E(f25(f14(f25(x1351,x1351)),f14(f25(x1351,x1351))),f25(x1351,x1351))
% 0.20/0.69 [138]~P5(x1381,a19)+P5(f9(f10(a5,f6(a19,x1381))),a19)
% 0.20/0.69 [142]E(f12(x1421),x1421)+E(f25(f25(f12(x1421),f12(x1421)),f25(f12(x1421),f25(f24(x1421),f24(x1421)))),x1421)
% 0.20/0.69 [144]E(f24(x1441),x1441)+E(f25(f25(f12(x1441),f12(x1441)),f25(f12(x1441),f25(f24(x1441),f24(x1441)))),x1441)
% 0.20/0.69 [145]~P9(x1451)+P6(f7(x1451,f9(f11(f6(x1451,a19)))),a13)
% 0.20/0.69 [146]~P2(x1461)+P6(f7(x1461,f9(f11(f6(x1461,a19)))),a13)
% 0.20/0.69 [147]~P8(x1471)+P6(f9(f9(f11(f6(x1471,a19)))),f9(f9(x1471)))
% 0.20/0.69 [155]P9(x1551)+~P6(f7(x1551,f9(f11(f6(x1551,a19)))),a13)
% 0.20/0.69 [159]E(f12(x1591),x1591)+P5(f25(f25(f12(x1591),f12(x1591)),f25(f12(x1591),f25(f24(x1591),f24(x1591)))),f6(a19,a19))
% 0.20/0.69 [161]E(f24(x1611),x1611)+P5(f25(f25(f12(x1611),f12(x1611)),f25(f12(x1611),f25(f24(x1611),f24(x1611)))),f6(a19,a19))
% 0.20/0.69 [179]~P1(x1791)+P6(f9(f9(f11(f6(f10(a20,f6(x1791,a19)),a19)))),x1791)
% 0.20/0.69 [184]~P5(x1841,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1841),a19)),a19))))),a19)
% 0.20/0.69 [78]~E(x782,x781)+P6(x781,x782)
% 0.20/0.69 [79]~E(x791,x792)+P6(x791,x792)
% 0.20/0.69 [92]P5(x922,a19)+E(f25(x921,x922),f25(x921,x921))
% 0.20/0.69 [93]P5(x931,a19)+E(f25(x931,x932),f25(x932,x932))
% 0.20/0.69 [95]~P5(x952,a19)+~E(f25(x951,x952),a4)
% 0.20/0.69 [96]~P5(x961,a19)+~E(f25(x961,x962),a4)
% 0.20/0.69 [100]P6(x1001,x1002)+P5(f16(x1001,x1002),x1001)
% 0.20/0.69 [101]~P5(x1011,x1012)+~P5(x1011,f8(x1012))
% 0.20/0.69 [106]~P5(x1061,a19)+P5(x1061,f25(x1062,x1061))
% 0.20/0.69 [107]~P5(x1071,a19)+P5(x1071,f25(x1071,x1072))
% 0.20/0.69 [110]~P5(x1101,x1102)+P6(f25(x1101,x1101),x1102)
% 0.20/0.69 [111]E(x1111,x1112)+~P5(x1111,f25(x1112,x1112))
% 0.20/0.69 [119]P6(x1191,x1192)+~P5(f16(x1191,x1192),x1192)
% 0.20/0.69 [136]~P5(x1362,f9(x1361))+~E(f10(x1361,f6(f25(x1362,x1362),a19)),a4)
% 0.20/0.69 [140]P5(x1402,a19)+E(f25(f25(x1401,x1401),f25(x1401,f25(x1402,x1402))),f25(f25(x1401,x1401),f25(x1401,a4)))
% 0.20/0.69 [154]P5(x1541,x1542)+~P5(f25(f25(x1541,x1541),f25(x1541,f25(x1542,x1542))),a5)
% 0.20/0.69 [172]~P5(f25(f25(x1721,x1721),f25(x1721,f25(x1722,x1722))),a20)+E(f8(f10(f8(x1721),f8(f25(x1721,x1721)))),x1722)
% 0.20/0.69 [173]~P5(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f6(a19,a19))+E(f12(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732)))),x1731)
% 0.20/0.69 [174]~P5(f25(f25(x1741,x1741),f25(x1741,f25(x1742,x1742))),f6(a19,a19))+E(f24(f25(f25(x1741,x1741),f25(x1741,f25(x1742,x1742)))),x1742)
% 0.20/0.69 [189]~P5(f25(f25(x1891,x1891),f25(x1891,f25(x1892,x1892))),f6(a19,a19))+P5(f25(f25(f12(f25(f25(x1891,x1891),f25(x1891,f25(x1892,x1892)))),f12(f25(f25(x1891,x1891),f25(x1891,f25(x1892,x1892))))),f25(f12(f25(f25(x1891,x1891),f25(x1891,f25(x1892,x1892)))),f25(f24(f25(f25(x1891,x1891),f25(x1891,f25(x1892,x1892)))),f24(f25(f25(x1891,x1891),f25(x1891,f25(x1892,x1892))))))),f6(a19,a19))
% 0.20/0.69 [124]P2(x1241)+~P3(x1241,x1242,x1243)
% 0.20/0.69 [125]P8(x1251)+~P4(x1252,x1253,x1251)
% 0.20/0.69 [126]P8(x1261)+~P4(x1262,x1261,x1263)
% 0.20/0.69 [134]~P4(x1341,x1342,x1343)+P3(x1341,x1342,x1343)
% 0.20/0.69 [117]P5(x1171,x1172)+~P5(x1171,f10(x1173,x1172))
% 0.20/0.69 [118]P5(x1181,x1182)+~P5(x1181,f10(x1182,x1183))
% 0.20/0.69 [128]~P3(x1282,x1281,x1283)+E(f9(f9(x1281)),f9(x1282))
% 0.20/0.69 [148]~P5(x1481,f6(x1482,x1483))+E(f25(f25(f12(x1481),f12(x1481)),f25(f12(x1481),f25(f24(x1481),f24(x1481)))),x1481)
% 0.20/0.69 [151]~P3(x1511,x1513,x1512)+P6(f9(f9(f11(f6(x1511,a19)))),f9(f9(x1512)))
% 0.20/0.69 [156]P5(x1561,a19)+~P5(f25(f25(x1562,x1562),f25(x1562,f25(x1561,x1561))),f6(x1563,x1564))
% 0.20/0.69 [157]P5(x1571,a19)+~P5(f25(f25(x1571,x1571),f25(x1571,f25(x1572,x1572))),f6(x1573,x1574))
% 0.20/0.69 [162]P5(x1621,x1622)+~P5(f25(f25(x1623,x1623),f25(x1623,f25(x1621,x1621))),f6(x1624,x1622))
% 0.20/0.69 [163]P5(x1631,x1632)+~P5(f25(f25(x1631,x1631),f25(x1631,f25(x1633,x1633))),f6(x1632,x1634))
% 0.20/0.69 [164]~E(f25(x1641,x1642),a4)+~P5(f25(f25(x1641,x1641),f25(x1641,f25(x1642,x1642))),f6(x1643,x1644))
% 0.20/0.69 [168]P5(x1681,f25(x1682,x1681))+~P5(f25(f25(x1682,x1682),f25(x1682,f25(x1681,x1681))),f6(x1683,x1684))
% 0.20/0.69 [169]P5(x1691,f25(x1691,x1692))+~P5(f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692))),f6(x1693,x1694))
% 0.20/0.69 [185]~P5(f25(f25(f25(f25(x1853,x1853),f25(x1853,f25(x1851,x1851))),f25(f25(x1853,x1853),f25(x1853,f25(x1851,x1851)))),f25(f25(f25(x1853,x1853),f25(x1853,f25(x1851,x1851))),f25(x1852,x1852))),f21(x1854))+P5(f25(f25(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852))),f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852)))),f25(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852))),f25(x1853,x1853))),x1854)
% 0.20/0.69 [186]~P5(f25(f25(f25(f25(x1862,x1862),f25(x1862,f25(x1861,x1861))),f25(f25(x1862,x1862),f25(x1862,f25(x1861,x1861)))),f25(f25(f25(x1862,x1862),f25(x1862,f25(x1861,x1861))),f25(x1863,x1863))),f11(x1864))+P5(f25(f25(f25(f25(x1861,x1861),f25(x1861,f25(x1862,x1862))),f25(f25(x1861,x1861),f25(x1861,f25(x1862,x1862)))),f25(f25(f25(x1861,x1861),f25(x1861,f25(x1862,x1862))),f25(x1863,x1863))),x1864)
% 0.20/0.69 [191]~P5(f25(f25(x1914,x1914),f25(x1914,f25(x1911,x1911))),f7(x1912,x1913))+P5(x1911,f9(f9(f11(f6(f10(x1912,f6(f9(f9(f11(f6(f10(x1913,f6(f25(x1914,x1914),a19)),a19)))),a19)),a19)))))
% 0.20/0.69 [139]~P2(x1391)+P7(x1391)+~P2(f9(f11(f6(x1391,a19))))
% 0.20/0.69 [165]P2(x1651)+~P6(x1651,f6(a19,a19))+~P6(f7(x1651,f9(f11(f6(x1651,a19)))),a13)
% 0.20/0.69 [176]E(x1761,a4)+E(f25(f16(x1761,a4),f16(x1761,a4)),x1761)+~E(f16(f10(f8(f25(f16(x1761,a4),f16(x1761,a4))),x1761),a4),f16(x1761,a4))
% 0.20/0.69 [178]E(x1781,a4)+E(f25(f16(x1781,a4),f16(x1781,a4)),x1781)+P5(f16(f10(f8(f25(f16(x1781,a4),f16(x1781,a4))),x1781),a4),x1781)
% 0.20/0.69 [181]E(x1811,a4)+E(f25(f16(x1811,a4),f16(x1811,a4)),x1811)+P5(f16(f10(f8(f25(f16(x1811,a4),f16(x1811,a4))),x1811),a4),f10(f8(f25(f16(x1811,a4),f16(x1811,a4))),x1811))
% 0.20/0.69 [182]P1(x1821)+~P5(a4,x1821)+~P6(f9(f9(f11(f6(f10(a20,f6(x1821,a19)),a19)))),x1821)
% 0.20/0.69 [190]~P5(x1901,a19)+E(x1901,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f25(x1901,x1901),a19)),a19))))))),x1901)
% 0.20/0.69 [98]~P6(x982,x981)+~P6(x981,x982)+E(x981,x982)
% 0.20/0.69 [91]P5(x912,a19)+P5(x911,a19)+E(f25(x911,x912),a4)
% 0.20/0.69 [102]P5(x1021,x1022)+P5(x1021,f8(x1022))+~P5(x1021,a19)
% 0.20/0.69 [112]E(x1121,x1122)+~E(f25(x1121,x1121),f25(x1122,x1122))+~P5(x1122,a19)
% 0.20/0.69 [113]E(x1131,x1132)+~E(f25(x1131,x1131),f25(x1132,x1132))+~P5(x1131,a19)
% 0.20/0.69 [120]E(f25(x1202,x1202),x1201)+~P6(x1201,f25(x1202,x1202))+E(x1201,a4)
% 0.20/0.69 [121]E(x1211,x1212)+P5(f16(x1212,x1211),x1212)+P5(f16(x1211,x1212),x1211)
% 0.20/0.69 [130]E(x1301,x1302)+P5(f16(x1302,x1301),x1302)+~P5(f16(x1301,x1302),x1302)
% 0.20/0.69 [132]E(x1321,x1322)+~P5(f16(x1322,x1321),x1321)+~P5(f16(x1321,x1322),x1322)
% 0.20/0.69 [116]~P5(x1162,x1161)+E(f14(x1161),x1162)+~E(f25(f14(x1161),f14(x1161)),x1161)
% 0.20/0.69 [133]P5(x1332,f9(x1331))+~P5(x1332,a19)+E(f10(x1331,f6(f25(x1332,x1332),a19)),a4)
% 0.20/0.69 [137]P5(x1372,a19)+P5(x1371,a19)+E(f25(f25(x1371,x1371),f25(x1371,f25(x1372,x1372))),f25(a4,f25(a4,a4)))
% 0.20/0.69 [149]P5(x1492,a19)+~P5(x1491,a19)+E(f25(a4,f25(f25(x1491,x1491),f25(x1491,x1491))),f25(f25(x1492,x1492),f25(x1492,f25(x1491,x1491))))
% 0.20/0.69 [175]~P5(x1751,x1752)+~P5(f25(f25(x1751,x1751),f25(x1751,f25(x1752,x1752))),f6(a19,a19))+P5(f25(f25(x1751,x1751),f25(x1751,f25(x1752,x1752))),a5)
% 0.20/0.69 [177]~P5(f25(f25(x1771,x1771),f25(x1771,f25(x1772,x1772))),f6(a19,a19))+~E(f8(f10(f8(x1771),f8(f25(x1771,x1771)))),x1772)+P5(f25(f25(x1771,x1771),f25(x1771,f25(x1772,x1772))),a20)
% 0.20/0.69 [180]~P2(x1801)+~P5(x1802,a19)+P5(f9(f9(f11(f6(f10(x1801,f6(x1802,a19)),a19)))),a19)
% 0.20/0.69 [104]~P6(x1041,x1043)+P6(x1041,x1042)+~P6(x1043,x1042)
% 0.20/0.69 [105]~P5(x1051,x1053)+P5(x1051,x1052)+~P6(x1053,x1052)
% 0.20/0.69 [114]E(x1141,x1142)+E(x1141,x1143)+~P5(x1141,f25(x1143,x1142))
% 0.20/0.69 [122]~P5(x1221,x1223)+~P5(x1221,x1222)+P5(x1221,f10(x1222,x1223))
% 0.20/0.69 [123]~P5(x1232,x1233)+~P5(x1231,x1233)+P6(f25(x1231,x1232),x1233)
% 0.20/0.69 [166]E(x1661,x1662)+~E(f25(x1663,x1661),f25(x1663,x1662))+~P5(f25(f25(x1661,x1661),f25(x1661,f25(x1662,x1662))),f6(a19,a19))
% 0.20/0.69 [167]E(x1671,x1672)+~E(f25(x1671,x1673),f25(x1672,x1673))+~P5(f25(f25(x1671,x1671),f25(x1671,f25(x1672,x1672))),f6(a19,a19))
% 0.20/0.69 [150]~P5(x1502,x1504)+~P5(x1501,x1503)+P5(f25(f25(x1501,x1501),f25(x1501,f25(x1502,x1502))),f6(x1503,x1504))
% 0.20/0.69 [152]E(x1521,x1522)+~P5(x1521,a19)+~E(f25(f25(x1523,x1523),f25(x1523,f25(x1521,x1521))),f25(f25(x1524,x1524),f25(x1524,f25(x1522,x1522))))
% 0.20/0.69 [153]E(x1531,x1532)+~P5(x1531,a19)+~E(f25(f25(x1531,x1531),f25(x1531,f25(x1533,x1533))),f25(f25(x1532,x1532),f25(x1532,f25(x1534,x1534))))
% 0.20/0.69 [187]~P5(f25(f25(f25(f25(x1872,x1872),f25(x1872,f25(x1873,x1873))),f25(f25(x1872,x1872),f25(x1872,f25(x1873,x1873)))),f25(f25(f25(x1872,x1872),f25(x1872,f25(x1873,x1873))),f25(x1871,x1871))),x1874)+P5(f25(f25(f25(f25(x1871,x1871),f25(x1871,f25(x1872,x1872))),f25(f25(x1871,x1871),f25(x1871,f25(x1872,x1872)))),f25(f25(f25(x1871,x1871),f25(x1871,f25(x1872,x1872))),f25(x1873,x1873))),f21(x1874))+~P5(f25(f25(f25(f25(x1871,x1871),f25(x1871,f25(x1872,x1872))),f25(f25(x1871,x1871),f25(x1871,f25(x1872,x1872)))),f25(f25(f25(x1871,x1871),f25(x1871,f25(x1872,x1872))),f25(x1873,x1873))),f6(f6(a19,a19),a19))
% 0.20/0.69 [188]~P5(f25(f25(f25(f25(x1882,x1882),f25(x1882,f25(x1881,x1881))),f25(f25(x1882,x1882),f25(x1882,f25(x1881,x1881)))),f25(f25(f25(x1882,x1882),f25(x1882,f25(x1881,x1881))),f25(x1883,x1883))),x1884)+P5(f25(f25(f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882))),f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882)))),f25(f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882))),f25(x1883,x1883))),f11(x1884))+~P5(f25(f25(f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882))),f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882)))),f25(f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882))),f25(x1883,x1883))),f6(f6(a19,a19),a19))
% 0.20/0.69 [192]~P5(f25(f25(x1921,x1921),f25(x1921,f25(x1922,x1922))),f6(a19,a19))+P5(f25(f25(x1921,x1921),f25(x1921,f25(x1922,x1922))),f7(x1923,x1924))+~P5(x1922,f9(f9(f11(f6(f10(x1923,f6(f9(f9(f11(f6(f10(x1924,f6(f25(x1921,x1921),a19)),a19)))),a19)),a19)))))
% 0.20/0.69 [193]~P4(x1932,x1935,x1931)+~P5(f25(f25(x1933,x1933),f25(x1933,f25(x1934,x1934))),f9(x1935))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1931,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1933,x1933),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1933,x1933),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1933,x1933),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1934,x1934),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1934,x1934),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1933,x1933),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1933,x1933),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1933,x1933),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1934,x1934),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(x1934,x1934),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1932,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1935,f6(f25(f25(f25(x1933,x1933),f25(x1933,f25(x1934,x1934))),f25(f25(x1933,x1933),f25(x1933,f25(x1934,x1934)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1935,f6(f25(f25(f25(x1933,x1933),f25(x1933,f25(x1934,x1934))),f25(f25(x1933,x1933),f25(x1933,f25(x1934,x1934)))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.69 [171]~P2(x1711)+P8(x1711)+~E(f6(f9(f9(x1711)),f9(f9(x1711))),f9(x1711))+~P6(f9(f9(f11(f6(x1711,a19)))),f9(f9(x1711)))
% 0.20/0.69 [115]E(x1151,x1152)+E(x1153,x1152)+~E(f25(x1153,x1151),f25(x1152,x1152))+~P5(x1152,a19)
% 0.20/0.69 [170]~P2(x1701)+P3(x1701,x1702,x1703)+~E(f9(f9(x1702)),f9(x1701))+~P6(f9(f9(f11(f6(x1701,a19)))),f9(f9(x1703)))
% 0.20/0.69 [183]~P8(x1833)+~P8(x1832)+~P3(x1831,x1832,x1833)+P4(x1831,x1832,x1833)+P5(f25(f25(f17(x1831,x1832,x1833),f17(x1831,x1832,x1833)),f25(f17(x1831,x1832,x1833),f25(f18(x1831,x1832,x1833),f18(x1831,x1832,x1833)))),f9(x1832))
% 0.20/0.69 [194]~P8(x1943)+~P8(x1942)+~P3(x1941,x1942,x1943)+P4(x1941,x1942,x1943)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1943,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943)),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1941,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1942,f6(f25(f25(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),f25(f17(x1941,x1942,x1943),f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943)))),f25(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),f25(f17(x1941,x1942,x1943),f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1942,f6(f25(f25(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),f25(f17(x1941,x1942,x1943),f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943)))),f25(f25(f17(x1941,x1942,x1943),f17(x1941,x1942,x1943)),f25(f17(x1941,x1942,x1943),f25(f18(x1941,x1942,x1943),f18(x1941,x1942,x1943))))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.69 %EqnAxiom
% 0.20/0.69 [1]E(x11,x11)
% 0.20/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.69 [4]~E(x41,x42)+E(f25(x41,x43),f25(x42,x43))
% 0.20/0.69 [5]~E(x51,x52)+E(f25(x53,x51),f25(x53,x52))
% 0.20/0.69 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.20/0.69 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.20/0.69 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.20/0.69 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.20/0.69 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.20/0.69 [11]~E(x111,x112)+E(f24(x111),f24(x112))
% 0.20/0.69 [12]~E(x121,x122)+E(f11(x121),f11(x122))
% 0.20/0.69 [13]~E(x131,x132)+E(f12(x131),f12(x132))
% 0.20/0.69 [14]~E(x141,x142)+E(f16(x141,x143),f16(x142,x143))
% 0.20/0.69 [15]~E(x151,x152)+E(f16(x153,x151),f16(x153,x152))
% 0.20/0.69 [16]~E(x161,x162)+E(f7(x161,x163),f7(x162,x163))
% 0.20/0.69 [17]~E(x171,x172)+E(f7(x173,x171),f7(x173,x172))
% 0.20/0.69 [18]~E(x181,x182)+E(f18(x181,x183,x184),f18(x182,x183,x184))
% 0.20/0.69 [19]~E(x191,x192)+E(f18(x193,x191,x194),f18(x193,x192,x194))
% 0.20/0.69 [20]~E(x201,x202)+E(f18(x203,x204,x201),f18(x203,x204,x202))
% 0.20/0.69 [21]~E(x211,x212)+E(f8(x211),f8(x212))
% 0.20/0.69 [22]~E(x221,x222)+E(f17(x221,x223,x224),f17(x222,x223,x224))
% 0.20/0.69 [23]~E(x231,x232)+E(f17(x233,x231,x234),f17(x233,x232,x234))
% 0.20/0.69 [24]~E(x241,x242)+E(f17(x243,x244,x241),f17(x243,x244,x242))
% 0.20/0.69 [25]~E(x251,x252)+E(f14(x251),f14(x252))
% 0.20/0.69 [26]~E(x261,x262)+E(f21(x261),f21(x262))
% 0.20/0.69 [27]~E(x271,x272)+E(f15(x271),f15(x272))
% 0.20/0.69 [28]~E(x281,x282)+E(f3(x281),f3(x282))
% 0.20/0.69 [29]~E(x291,x292)+E(f22(x291),f22(x292))
% 0.20/0.69 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.20/0.69 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.20/0.69 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.20/0.69 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.20/0.69 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.20/0.70 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.20/0.70 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.20/0.70 [37]P6(x372,x373)+~E(x371,x372)+~P6(x371,x373)
% 0.20/0.70 [38]P6(x383,x382)+~E(x381,x382)+~P6(x383,x381)
% 0.20/0.70 [39]~P8(x391)+P8(x392)+~E(x391,x392)
% 0.20/0.70 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.20/0.70 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.20/0.70 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.20/0.70 [43]~P7(x431)+P7(x432)+~E(x431,x432)
% 0.20/0.70 [44]~P9(x441)+P9(x442)+~E(x441,x442)
% 0.20/0.70
% 0.20/0.70 %-------------------------------------------
% 0.20/0.70 cnf(197,plain,
% 0.20/0.70 (~P5(x1971,a4)),
% 0.20/0.70 inference(rename_variables,[],[74])).
% 0.20/0.70 cnf(200,plain,
% 0.20/0.70 (~P5(x2001,f10(f8(x2002),x2002))),
% 0.20/0.70 inference(rename_variables,[],[75])).
% 0.20/0.70 cnf(208,plain,
% 0.20/0.70 (~P5(x2081,a4)),
% 0.20/0.70 inference(rename_variables,[],[74])).
% 0.20/0.70 cnf(211,plain,
% 0.20/0.70 (~P5(x2111,a4)),
% 0.20/0.70 inference(rename_variables,[],[74])).
% 0.20/0.70 cnf(214,plain,
% 0.20/0.70 (P6(x2141,x2141)),
% 0.20/0.70 inference(rename_variables,[],[51])).
% 0.20/0.70 cnf(222,plain,
% 0.20/0.70 ($false),
% 0.20/0.70 inference(scs_inference,[],[56,51,214,49,74,197,208,211,73,47,65,75,200,2,81,90,100,136,186,185,38,37,33,32,30,3,105]),
% 0.20/0.70 ['proof']).
% 0.20/0.70 % SZS output end Proof
% 0.20/0.70 % Total time :0.020000s
%------------------------------------------------------------------------------