TSTP Solution File: SET114-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET114-7 : 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 : n029.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 14:28:48 EDT 2023
% Result : Unsatisfiable 0.20s 0.68s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET114-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.17/0.35 % Computer : n029.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 10:39:54 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.59 start to proof:theBenchmark
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % File :CSE---1.6
% 0.20/0.66 % Problem :theBenchmark
% 0.20/0.66 % Transform :cnf
% 0.20/0.66 % Format :tptp:raw
% 0.20/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.66
% 0.20/0.66 % Result :Theorem 0.010000s
% 0.20/0.66 % Output :CNFRefutation 0.010000s
% 0.20/0.66 %-------------------------------------------
% 0.20/0.67 %--------------------------------------------------------------------------
% 0.20/0.67 % File : SET114-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.20/0.67 % Domain : Set Theory
% 0.20/0.67 % Problem : 2nd is unique if x is not an ordered pair of sets, part 1
% 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 : OP8.2 [Qua92]
% 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 : 161 ( 46 unt; 32 nHn; 102 RR)
% 0.20/0.67 % Number of literals : 326 ( 103 equ; 138 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 : 303 ( 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 % 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,
% 0.20/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.67 | member(X,unordered_pair(X,Y)) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(corollary_2_to_unordered_pair,axiom,
% 0.20/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.67 | member(Y,unordered_pair(X,Y)) ) ).
% 0.20/0.67
% 0.20/0.67 %----Corollaries to Cartesian product axiom.
% 0.20/0.67 cnf(corollary_1_to_cartesian_product,axiom,
% 0.20/0.67 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.67 | member(U,universal_class) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(corollary_2_to_cartesian_product,axiom,
% 0.20/0.67 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.67 | member(V,universal_class) ) ).
% 0.20/0.67
% 0.20/0.67 %---- PARTIAL ORDER.
% 0.20/0.67 %----(PO1): reflexive.
% 0.20/0.67 cnf(subclass_is_reflexive,axiom,
% 0.20/0.67 subclass(X,X) ).
% 0.20/0.67
% 0.20/0.67 %----(PO2): antisymmetry is part of A-3.
% 0.20/0.67 %----(x < y), (y < x) --> (x = y).
% 0.20/0.67
% 0.20/0.67 %----(PO3): transitivity.
% 0.20/0.67 cnf(transitivity_of_subclass,axiom,
% 0.20/0.67 ( ~ subclass(X,Y)
% 0.20/0.67 | ~ subclass(Y,Z)
% 0.20/0.67 | subclass(X,Z) ) ).
% 0.20/0.67
% 0.20/0.67 %---- EQUALITY.
% 0.20/0.67 %----(EQ1): equality axiom.
% 0.20/0.67 %----a:x:(x = x).
% 0.20/0.67 %----This is always an axiom in the TPTP presentation.
% 0.20/0.67
% 0.20/0.67 %----(EQ2): expanded equality definition.
% 0.20/0.67 cnf(equality1,axiom,
% 0.20/0.67 ( X = Y
% 0.20/0.67 | member(not_subclass_element(X,Y),X)
% 0.20/0.67 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(equality2,axiom,
% 0.20/0.67 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.67 | X = Y
% 0.20/0.67 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(equality3,axiom,
% 0.20/0.67 ( ~ member(not_subclass_element(Y,X),X)
% 0.20/0.67 | X = Y
% 0.20/0.67 | member(not_subclass_element(X,Y),X) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(equality4,axiom,
% 0.20/0.67 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.67 | ~ member(not_subclass_element(Y,X),X)
% 0.20/0.67 | X = Y ) ).
% 0.20/0.67
% 0.20/0.67 %---- SPECIAL CLASSES.
% 0.20/0.67 %----(SP1): lemma.
% 0.20/0.67 cnf(special_classes_lemma,axiom,
% 0.20/0.67 ~ member(Y,intersection(complement(X),X)) ).
% 0.20/0.67
% 0.20/0.67 %----(SP2): Existence of O (null class).
% 0.20/0.67 %----e:x:a:z:(-(z e x)).
% 0.20/0.67 cnf(existence_of_null_class,axiom,
% 0.20/0.67 ~ member(Z,null_class) ).
% 0.20/0.67
% 0.20/0.67 %----(SP3): O is a subclass of every class.
% 0.20/0.67 cnf(null_class_is_subclass,axiom,
% 0.20/0.67 subclass(null_class,X) ).
% 0.20/0.67
% 0.20/0.67 %----corollary.
% 0.20/0.67 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.20/0.67 ( ~ subclass(X,null_class)
% 0.20/0.67 | X = null_class ) ).
% 0.20/0.67
% 0.20/0.67 %----(SP4): uniqueness of null class.
% 0.20/0.67 cnf(null_class_is_unique,axiom,
% 0.20/0.67 ( Z = null_class
% 0.20/0.67 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.20/0.67
% 0.20/0.67 %----(SP5): O is a set (follows from axiom of infinity).
% 0.20/0.67 cnf(null_class_is_a_set,axiom,
% 0.20/0.67 member(null_class,universal_class) ).
% 0.20/0.67
% 0.20/0.67 %---- UNORDERED PAIRS.
% 0.20/0.67 %----(UP1): unordered pair is commutative.
% 0.20/0.67 cnf(commutativity_of_unordered_pair,axiom,
% 0.20/0.67 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.20/0.67
% 0.20/0.67 %----(UP2): if one argument is a proper class, pair contains only the
% 0.20/0.67 %----other. In a slightly different form to the paper
% 0.20/0.67 cnf(singleton_in_unordered_pair1,axiom,
% 0.20/0.67 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.20/0.67
% 0.20/0.67 cnf(singleton_in_unordered_pair2,axiom,
% 0.20/0.67 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.20/0.67
% 0.20/0.67 cnf(unordered_pair_equals_singleton1,axiom,
% 0.20/0.67 ( member(Y,universal_class)
% 0.20/0.67 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(unordered_pair_equals_singleton2,axiom,
% 0.20/0.67 ( member(X,universal_class)
% 0.20/0.67 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.20/0.67
% 0.20/0.67 %----(UP3): if both arguments are proper classes, pair is null.
% 0.20/0.67 cnf(null_unordered_pair,axiom,
% 0.20/0.67 ( unordered_pair(X,Y) = null_class
% 0.20/0.67 | member(X,universal_class)
% 0.20/0.67 | member(Y,universal_class) ) ).
% 0.20/0.67
% 0.20/0.67 %----(UP4): left cancellation for unordered pairs.
% 0.20/0.67 cnf(left_cancellation,axiom,
% 0.20/0.67 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.20/0.67 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.20/0.67 | Y = Z ) ).
% 0.20/0.67
% 0.20/0.67 %----(UP5): right cancellation for unordered pairs.
% 0.20/0.67 cnf(right_cancellation,axiom,
% 0.20/0.67 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.20/0.67 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.20/0.67 | X = Y ) ).
% 0.20/0.67
% 0.20/0.67 %----(UP6): corollary to (A-4).
% 0.20/0.67 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.20/0.67 ( ~ member(X,universal_class)
% 0.20/0.67 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.67
% 0.20/0.67 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.20/0.67 ( ~ member(Y,universal_class)
% 0.20/0.67 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.67
% 0.20/0.67 %----corollary to instantiate variables.
% 0.20/0.67 %----Not in the paper
% 0.20/0.67 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.20/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.67 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.67
% 0.20/0.67 %----(UP7): if both members of a pair belong to a set, the pair
% 0.20/0.67 %----is a subset.
% 0.20/0.67 cnf(unordered_pair_is_subset,axiom,
% 0.20/0.67 ( ~ member(X,Z)
% 0.20/0.67 | ~ member(Y,Z)
% 0.20/0.67 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.20/0.67
% 0.20/0.67 %---- SINGLETONS.
% 0.20/0.67 %----(SS1): every singleton is a set.
% 0.20/0.67 cnf(singletons_are_sets,axiom,
% 0.20/0.67 member(singleton(X),universal_class) ).
% 0.20/0.67
% 0.20/0.67 %----corollary, not in the paper.
% 0.20/0.67 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.20/0.67 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.20/0.67
% 0.20/0.67 %----(SS2): a set belongs to its singleton.
% 0.20/0.67 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.20/0.67 cnf(set_in_its_singleton,axiom,
% 0.20/0.67 ( ~ member(X,universal_class)
% 0.20/0.67 | member(X,singleton(X)) ) ).
% 0.20/0.67
% 0.20/0.67 %----corollary
% 0.20/0.67 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.20/0.67 ( ~ member(X,universal_class)
% 0.20/0.67 | singleton(X) != null_class ) ).
% 0.20/0.67
% 0.20/0.67 %----Not in the paper
% 0.20/0.67 cnf(null_class_in_its_singleton,axiom,
% 0.20/0.67 member(null_class,singleton(null_class)) ).
% 0.20/0.67
% 0.20/0.67 %----(SS3): only x can belong to {x}.
% 0.20/0.67 cnf(only_member_in_singleton,axiom,
% 0.20/0.67 ( ~ member(Y,singleton(X))
% 0.20/0.67 | Y = X ) ).
% 0.20/0.67
% 0.20/0.67 %----(SS4): if x is not a set, {x} = O.
% 0.20/0.67 cnf(singleton_is_null_class,axiom,
% 0.20/0.67 ( member(X,universal_class)
% 0.20/0.67 | singleton(X) = null_class ) ).
% 0.20/0.67
% 0.20/0.67 %----(SS5): a singleton set is determined by its element.
% 0.20/0.67 cnf(singleton_identified_by_element1,axiom,
% 0.20/0.67 ( singleton(X) != singleton(Y)
% 0.20/0.67 | ~ member(X,universal_class)
% 0.20/0.67 | X = Y ) ).
% 0.20/0.67
% 0.20/0.67 cnf(singleton_identified_by_element2,axiom,
% 0.20/0.67 ( singleton(X) != singleton(Y)
% 0.20/0.67 | ~ member(Y,universal_class)
% 0.20/0.67 | X = Y ) ).
% 0.20/0.67
% 0.20/0.67 %----(SS5.5).
% 0.20/0.67 %----Not in the paper
% 0.20/0.67 cnf(singleton_in_unordered_pair3,axiom,
% 0.20/0.67 ( unordered_pair(Y,Z) != singleton(X)
% 0.20/0.67 | ~ member(X,universal_class)
% 0.20/0.67 | X = Y
% 0.20/0.67 | X = Z ) ).
% 0.20/0.67
% 0.20/0.67 %----(SS6): existence of memb.
% 0.20/0.67 %----a:x:e:u:(((u e universal_class) & x = {u}) | (-e:y:((y
% 0.20/0.67 %----e universal_class) & x = {y}) & u = x)).
% 0.20/0.67 cnf(member_exists1,axiom,
% 0.20/0.67 ( ~ member(Y,universal_class)
% 0.20/0.67 | member(member_of(singleton(Y)),universal_class) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(member_exists2,axiom,
% 0.20/0.67 ( ~ member(Y,universal_class)
% 0.20/0.67 | singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.20/0.67
% 0.20/0.67 cnf(member_exists3,axiom,
% 0.20/0.67 ( member(member_of(X),universal_class)
% 0.20/0.67 | member_of(X) = X ) ).
% 0.20/0.67
% 0.20/0.67 cnf(member_exists4,axiom,
% 0.20/0.67 ( singleton(member_of(X)) = X
% 0.20/0.67 | member_of(X) = X ) ).
% 0.20/0.67
% 0.20/0.67 %----(SS7): uniqueness of memb of a singleton set.
% 0.20/0.67 %----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
% 0.20/0.68 | member_of(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS9): corollary to (SS1).
% 0.20/0.68 cnf(corollary_2_to_singletons_are_sets,axiom,
% 0.20/0.68 ( singleton(member_of(X)) != X
% 0.20/0.68 | member(X,universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS10).
% 0.20/0.68 cnf(property_of_singletons1,axiom,
% 0.20/0.68 ( singleton(member_of(X)) != X
% 0.20/0.68 | ~ member(Y,X)
% 0.20/0.68 | member_of(X) = Y ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS11).
% 0.20/0.68 cnf(property_of_singletons2,axiom,
% 0.20/0.68 ( ~ member(X,Y)
% 0.20/0.68 | subclass(singleton(X),Y) ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS12): there are at most two subsets of a singleton.
% 0.20/0.68 cnf(two_subsets_of_singleton,axiom,
% 0.20/0.68 ( ~ subclass(X,singleton(Y))
% 0.20/0.68 | X = null_class
% 0.20/0.68 | singleton(Y) = X ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS13): a class contains 0, 1, or at least 2 members.
% 0.20/0.68 cnf(number_of_elements_in_class,axiom,
% 0.20/0.68 ( 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))
% 0.20/0.68 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.68 | X = null_class ) ).
% 0.20/0.68
% 0.20/0.68 %----corollaries.
% 0.20/0.68 cnf(corollary_2_to_number_of_elements_in_class,axiom,
% 0.20/0.68 ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),X)
% 0.20/0.68 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.68 | X = null_class ) ).
% 0.20/0.68
% 0.20/0.68 cnf(corollary_1_to_number_of_elements_in_class,axiom,
% 0.20/0.68 ( not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class) != not_subclass_element(X,null_class)
% 0.20/0.68 | singleton(not_subclass_element(X,null_class)) = X
% 0.20/0.68 | X = null_class ) ).
% 0.20/0.68
% 0.20/0.68 %----(SS14): relation to ordered pair.
% 0.20/0.68 %----It looks like we could simplify Godel's axioms by taking singleton
% 0.20/0.68 %----as a primitive and using the next as a definition. Not in the paper
% 0.20/0.68 cnf(unordered_pairs_and_singletons,axiom,
% 0.20/0.68 unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ).
% 0.20/0.68
% 0.20/0.68 %---- ORDERED PAIRS.
% 0.20/0.68 %----(OP1): an ordered pair is a set.
% 0.20/0.68 cnf(ordered_pair_is_set,axiom,
% 0.20/0.68 member(ordered_pair(X,Y),universal_class) ).
% 0.20/0.68
% 0.20/0.68 %----(OP2): members of ordered pair.
% 0.20/0.68 cnf(singleton_member_of_ordered_pair,axiom,
% 0.20/0.68 member(singleton(X),ordered_pair(X,Y)) ).
% 0.20/0.68
% 0.20/0.68 cnf(unordered_pair_member_of_ordered_pair,axiom,
% 0.20/0.68 member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)) ).
% 0.20/0.68
% 0.20/0.68 %----(OP3): special cases.
% 0.20/0.68 cnf(property_1_of_ordered_pair,axiom,
% 0.20/0.68 ( unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y)
% 0.20/0.68 | member(Y,universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(property_2_of_ordered_pair,axiom,
% 0.20/0.68 ( ~ member(Y,universal_class)
% 0.20/0.68 | unordered_pair(null_class,singleton(singleton(Y))) = ordered_pair(X,Y)
% 0.20/0.68 | member(X,universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 cnf(property_3_of_ordered_pair,axiom,
% 0.20/0.68 ( unordered_pair(null_class,singleton(null_class)) = ordered_pair(X,Y)
% 0.20/0.68 | member(X,universal_class)
% 0.20/0.68 | member(Y,universal_class) ) ).
% 0.20/0.68
% 0.20/0.68 %----(OP4)-(OP5): an ordered pair uniquely determines its components.
% 0.20/0.68 %----(OP4). This OP10 from the paper. OP4 is now omitted
% 0.20/0.68 cnf(ordered_pair_determines_components1,axiom,
% 0.20/0.68 ( ordered_pair(W,X) != ordered_pair(Y,Z)
% 0.20/0.68 | ~ member(W,universal_class)
% 0.20/0.68 | W = Y ) ).
% 0.20/0.68
% 0.20/0.68 %----(OP5). This OP11 from the paper. OP5 is now omitted
% 0.20/0.68 cnf(ordered_pair_determines_components2,axiom,
% 0.20/0.68 ( ordered_pair(W,X) != ordered_pair(Y,Z)
% 0.20/0.68 | ~ member(X,universal_class)
% 0.20/0.68 | X = Z ) ).
% 0.20/0.68
% 0.20/0.68 %----(OP6): existence of 1st and 2nd.
% 0.20/0.68 %----a:x:e:u:e:v:((([u,v] e cross_product(universal_class,
% 0.20/0.68 %----universal_class)) & x = [u,v]) | (-e:y:e:z:(([y,z] e cross_product(
% 0.20/0.68 %----universal_class,universal_class)) & x = [y,z]) & u = x & v = x)).
% 0.20/0.68 cnf(existence_of_1st_and_2nd_1,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.20/0.68 | member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ) ).
% 0.20/0.68
% 0.20/0.68 %----next is subsumed by Axiom B5'-b ([y,z]
% 0.20/0.68 %----e cross_product(universal_class,universal_class)) -->
% 0.20/0.68 %----([first([y,z]),second([y,z])] = [y,z]).
% 0.20/0.68
% 0.20/0.68 cnf(existence_of_1st_and_2nd_2,axiom,
% 0.20/0.68 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.20/0.68 | first(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 cnf(existence_of_1st_and_2nd_3,axiom,
% 0.20/0.68 ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
% 0.20/0.68 | second(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 cnf(existence_of_1st_and_2nd_4,axiom,
% 0.20/0.68 ( ordered_pair(first(X),second(X)) = X
% 0.20/0.68 | first(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 cnf(existence_of_1st_and_2nd_5,axiom,
% 0.20/0.68 ( ordered_pair(first(X),second(X)) = X
% 0.20/0.68 | second(X) = X ) ).
% 0.20/0.68
% 0.20/0.68 %----(OP7): uniqueness of 1st and 2nd when x is an ordered pair of sets.
% 0.20/0.68 %----a:x:a:u:a:v:([u,v] e cross_product(universal_class,universal_class)
% 0.20/0.68 %---- & x = [u,v] ==> first(x) = u & second(x) = v)
% 0.20/0.68 cnf(unique_1st_and_2nd_in_pair_of_sets1,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
% 0.20/0.68 | first(ordered_pair(U,V)) = U ) ).
% 0.20/0.68
% 0.20/0.68 cnf(unique_1st_and_2nd_in_pair_of_sets2,axiom,
% 0.20/0.68 ( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
% 0.20/0.68 | second(ordered_pair(U,V)) = V ) ).
% 0.20/0.68
% 0.20/0.68 cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets2_1,negated_conjecture,
% 0.20/0.68 ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ).
% 0.20/0.68
% 0.20/0.68 cnf(prove_unique_2nd_in_pair_of_non_sets,negated_conjecture,
% 0.20/0.68 second(x) != x ).
% 0.20/0.68
% 0.20/0.68 %--------------------------------------------------------------------------
% 0.20/0.68 %-------------------------------------------
% 0.20/0.68 % Proof found
% 0.20/0.68 % SZS status Theorem for theBenchmark
% 0.20/0.68 % SZS output start Proof
% 0.20/0.68 %ClaNum:190(EqnAxiom:44)
% 0.20/0.68 %VarNum:1137(SingletonVarNum:270)
% 0.20/0.68 %MaxLitNum:5
% 0.20/0.68 %MaxfuncDepth:24
% 0.20/0.68 %SharedTerms:42
% 0.20/0.68 %goalClause: 72 75
% 0.20/0.68 %singleGoalClaCount:2
% 0.20/0.68 [45]P1(a1)
% 0.20/0.68 [46]P2(a2)
% 0.20/0.68 [47]P5(a4,a19)
% 0.20/0.68 [48]P5(a1,a19)
% 0.20/0.68 [53]P6(a5,f6(a19,a19))
% 0.20/0.68 [54]P6(a20,f6(a19,a19))
% 0.20/0.68 [55]P5(a4,f25(a4,a4))
% 0.20/0.68 [72]~E(f24(a26),a26)
% 0.20/0.68 [64]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.20/0.68 [75]~P5(f25(f25(f12(a26),f12(a26)),f25(f12(a26),f25(f24(a26),f24(a26)))),f6(a19,a19))
% 0.20/0.68 [70]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.20/0.68 [49]P6(x491,a19)
% 0.20/0.68 [50]P6(a4,x501)
% 0.20/0.68 [51]P6(x511,x511)
% 0.20/0.68 [73]~P5(x731,a4)
% 0.20/0.68 [62]P6(f21(x621),f6(f6(a19,a19),a19))
% 0.20/0.68 [63]P6(f11(x631),f6(f6(a19,a19),a19))
% 0.20/0.68 [71]E(f10(f9(x711),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x711),a13)))),f3(x711))
% 0.20/0.68 [52]E(f25(x521,x522),f25(x522,x521))
% 0.20/0.68 [56]P5(f25(x561,x562),a19)
% 0.20/0.68 [58]P6(f7(x581,x582),f6(a19,a19))
% 0.20/0.68 [59]P6(f25(x591,x591),f25(x592,x591))
% 0.20/0.68 [60]P6(f25(x601,x601),f25(x601,x602))
% 0.20/0.68 [65]P5(f25(x651,x651),f25(x652,f25(x651,x651)))
% 0.20/0.68 [74]~P5(x741,f10(f8(x742),x742))
% 0.20/0.68 [67]P5(f25(x671,x671),f25(f25(x671,x671),f25(x671,f25(x672,x672))))
% 0.20/0.68 [69]P5(f25(x691,f25(x692,x692)),f25(f25(x691,x691),f25(x691,f25(x692,x692))))
% 0.20/0.68 [68]E(f8(f10(f8(f25(x681,x681)),f8(f25(x682,x682)))),f25(x681,x682))
% 0.20/0.68 [61]E(f10(f6(x611,x612),x613),f10(x613,f6(x611,x612)))
% 0.20/0.68 [76]~P7(x761)+P2(x761)
% 0.20/0.68 [77]~P8(x771)+P2(x771)
% 0.20/0.68 [80]~P1(x801)+P6(a1,x801)
% 0.20/0.68 [81]~P1(x811)+P5(a4,x811)
% 0.20/0.68 [82]~P6(x821,a4)+E(x821,a4)
% 0.20/0.68 [84]P5(f22(x841),x841)+E(x841,a4)
% 0.20/0.68 [85]E(f14(x851),x851)+P5(f14(x851),a19)
% 0.20/0.68 [86]E(f14(x861),x861)+P5(f15(x861),a19)
% 0.20/0.68 [87]P5(x871,a19)+E(f25(x871,x871),a4)
% 0.20/0.68 [90]E(x901,a4)+P5(f16(x901,a4),x901)
% 0.20/0.68 [94]~P2(x941)+P6(x941,f6(a19,a19))
% 0.20/0.68 [83]E(x831,a4)+E(f10(x831,f22(x831)),a4)
% 0.20/0.68 [88]E(f14(x881),x881)+E(f25(f14(x881),f14(x881)),x881)
% 0.20/0.68 [89]E(f14(x891),x891)+E(f25(f15(x891),f15(x891)),x891)
% 0.20/0.68 [99]~P5(x991,a19)+E(f14(f25(x991,x991)),x991)
% 0.20/0.68 [103]P5(x1031,a19)+~E(f25(f14(x1031),f14(x1031)),x1031)
% 0.20/0.68 [127]~P5(x1271,a19)+P5(f14(f25(x1271,x1271)),a19)
% 0.20/0.68 [109]~P8(x1091)+E(f6(f9(f9(x1091)),f9(f9(x1091))),f9(x1091))
% 0.20/0.68 [131]~P7(x1311)+P2(f9(f11(f6(x1311,a19))))
% 0.20/0.68 [135]~P5(x1351,a19)+E(f25(f14(f25(x1351,x1351)),f14(f25(x1351,x1351))),f25(x1351,x1351))
% 0.20/0.68 [138]~P5(x1381,a19)+P5(f9(f10(a5,f6(a19,x1381))),a19)
% 0.20/0.68 [141]E(f12(x1411),x1411)+E(f25(f25(f12(x1411),f12(x1411)),f25(f12(x1411),f25(f24(x1411),f24(x1411)))),x1411)
% 0.20/0.68 [142]E(f24(x1421),x1421)+E(f25(f25(f12(x1421),f12(x1421)),f25(f12(x1421),f25(f24(x1421),f24(x1421)))),x1421)
% 0.20/0.68 [143]~P9(x1431)+P6(f7(x1431,f9(f11(f6(x1431,a19)))),a13)
% 0.20/0.68 [144]~P2(x1441)+P6(f7(x1441,f9(f11(f6(x1441,a19)))),a13)
% 0.20/0.68 [145]~P8(x1451)+P6(f9(f9(f11(f6(x1451,a19)))),f9(f9(x1451)))
% 0.20/0.68 [153]P9(x1531)+~P6(f7(x1531,f9(f11(f6(x1531,a19)))),a13)
% 0.20/0.68 [156]E(f12(x1561),x1561)+P5(f25(f25(f12(x1561),f12(x1561)),f25(f12(x1561),f25(f24(x1561),f24(x1561)))),f6(a19,a19))
% 0.20/0.68 [157]E(f24(x1571),x1571)+P5(f25(f25(f12(x1571),f12(x1571)),f25(f12(x1571),f25(f24(x1571),f24(x1571)))),f6(a19,a19))
% 0.20/0.68 [175]~P1(x1751)+P6(f9(f9(f11(f6(f10(a20,f6(x1751,a19)),a19)))),x1751)
% 0.20/0.68 [180]~P5(x1801,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1801),a19)),a19))))),a19)
% 0.20/0.68 [78]~E(x782,x781)+P6(x781,x782)
% 0.20/0.68 [79]~E(x791,x792)+P6(x791,x792)
% 0.20/0.68 [92]P5(x922,a19)+E(f25(x921,x922),f25(x921,x921))
% 0.20/0.68 [93]P5(x931,a19)+E(f25(x931,x932),f25(x932,x932))
% 0.20/0.68 [95]~P5(x952,a19)+~E(f25(x951,x952),a4)
% 0.20/0.68 [96]~P5(x961,a19)+~E(f25(x961,x962),a4)
% 0.20/0.68 [100]P6(x1001,x1002)+P5(f16(x1001,x1002),x1001)
% 0.20/0.68 [101]~P5(x1011,x1012)+~P5(x1011,f8(x1012))
% 0.20/0.68 [106]~P5(x1061,a19)+P5(x1061,f25(x1062,x1061))
% 0.20/0.68 [107]~P5(x1071,a19)+P5(x1071,f25(x1071,x1072))
% 0.20/0.68 [110]~P5(x1101,x1102)+P6(f25(x1101,x1101),x1102)
% 0.20/0.68 [111]E(x1111,x1112)+~P5(x1111,f25(x1112,x1112))
% 0.20/0.68 [119]P6(x1191,x1192)+~P5(f16(x1191,x1192),x1192)
% 0.20/0.68 [136]~P5(x1362,f9(x1361))+~E(f10(x1361,f6(f25(x1362,x1362),a19)),a4)
% 0.20/0.68 [140]P5(x1402,a19)+E(f25(f25(x1401,x1401),f25(x1401,f25(x1402,x1402))),f25(f25(x1401,x1401),f25(x1401,a4)))
% 0.20/0.68 [152]P5(x1521,x1522)+~P5(f25(f25(x1521,x1521),f25(x1521,f25(x1522,x1522))),a5)
% 0.20/0.68 [168]~P5(f25(f25(x1681,x1681),f25(x1681,f25(x1682,x1682))),a20)+E(f8(f10(f8(x1681),f8(f25(x1681,x1681)))),x1682)
% 0.20/0.68 [169]~P5(f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692))),f6(a19,a19))+E(f12(f25(f25(x1691,x1691),f25(x1691,f25(x1692,x1692)))),x1691)
% 0.20/0.68 [170]~P5(f25(f25(x1701,x1701),f25(x1701,f25(x1702,x1702))),f6(a19,a19))+E(f24(f25(f25(x1701,x1701),f25(x1701,f25(x1702,x1702)))),x1702)
% 0.20/0.68 [185]~P5(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852))),f6(a19,a19))+P5(f25(f25(f12(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852)))),f12(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852))))),f25(f12(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852)))),f25(f24(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852)))),f24(f25(f25(x1851,x1851),f25(x1851,f25(x1852,x1852))))))),f6(a19,a19))
% 0.20/0.68 [124]P2(x1241)+~P3(x1241,x1242,x1243)
% 0.20/0.68 [125]P8(x1251)+~P4(x1252,x1253,x1251)
% 0.20/0.68 [126]P8(x1261)+~P4(x1262,x1261,x1263)
% 0.20/0.68 [134]~P4(x1341,x1342,x1343)+P3(x1341,x1342,x1343)
% 0.20/0.68 [117]P5(x1171,x1172)+~P5(x1171,f10(x1173,x1172))
% 0.20/0.68 [118]P5(x1181,x1182)+~P5(x1181,f10(x1182,x1183))
% 0.20/0.68 [128]~P3(x1282,x1281,x1283)+E(f9(f9(x1281)),f9(x1282))
% 0.20/0.68 [146]~P5(x1461,f6(x1462,x1463))+E(f25(f25(f12(x1461),f12(x1461)),f25(f12(x1461),f25(f24(x1461),f24(x1461)))),x1461)
% 0.20/0.68 [149]~P3(x1491,x1493,x1492)+P6(f9(f9(f11(f6(x1491,a19)))),f9(f9(x1492)))
% 0.20/0.68 [154]P5(x1541,a19)+~P5(f25(f25(x1542,x1542),f25(x1542,f25(x1541,x1541))),f6(x1543,x1544))
% 0.20/0.68 [155]P5(x1551,a19)+~P5(f25(f25(x1551,x1551),f25(x1551,f25(x1552,x1552))),f6(x1553,x1554))
% 0.20/0.68 [158]P5(x1581,x1582)+~P5(f25(f25(x1583,x1583),f25(x1583,f25(x1581,x1581))),f6(x1584,x1582))
% 0.20/0.68 [159]P5(x1591,x1592)+~P5(f25(f25(x1591,x1591),f25(x1591,f25(x1593,x1593))),f6(x1592,x1594))
% 0.20/0.68 [160]~E(f25(x1601,x1602),a4)+~P5(f25(f25(x1601,x1601),f25(x1601,f25(x1602,x1602))),f6(x1603,x1604))
% 0.20/0.68 [164]P5(x1641,f25(x1642,x1641))+~P5(f25(f25(x1642,x1642),f25(x1642,f25(x1641,x1641))),f6(x1643,x1644))
% 0.20/0.68 [165]P5(x1651,f25(x1651,x1652))+~P5(f25(f25(x1651,x1651),f25(x1651,f25(x1652,x1652))),f6(x1653,x1654))
% 0.20/0.68 [181]~P5(f25(f25(f25(f25(x1813,x1813),f25(x1813,f25(x1811,x1811))),f25(f25(x1813,x1813),f25(x1813,f25(x1811,x1811)))),f25(f25(f25(x1813,x1813),f25(x1813,f25(x1811,x1811))),f25(x1812,x1812))),f21(x1814))+P5(f25(f25(f25(f25(x1811,x1811),f25(x1811,f25(x1812,x1812))),f25(f25(x1811,x1811),f25(x1811,f25(x1812,x1812)))),f25(f25(f25(x1811,x1811),f25(x1811,f25(x1812,x1812))),f25(x1813,x1813))),x1814)
% 0.20/0.68 [182]~P5(f25(f25(f25(f25(x1822,x1822),f25(x1822,f25(x1821,x1821))),f25(f25(x1822,x1822),f25(x1822,f25(x1821,x1821)))),f25(f25(f25(x1822,x1822),f25(x1822,f25(x1821,x1821))),f25(x1823,x1823))),f11(x1824))+P5(f25(f25(f25(f25(x1821,x1821),f25(x1821,f25(x1822,x1822))),f25(f25(x1821,x1821),f25(x1821,f25(x1822,x1822)))),f25(f25(f25(x1821,x1821),f25(x1821,f25(x1822,x1822))),f25(x1823,x1823))),x1824)
% 0.20/0.68 [187]~P5(f25(f25(x1874,x1874),f25(x1874,f25(x1871,x1871))),f7(x1872,x1873))+P5(x1871,f9(f9(f11(f6(f10(x1872,f6(f9(f9(f11(f6(f10(x1873,f6(f25(x1874,x1874),a19)),a19)))),a19)),a19)))))
% 0.20/0.68 [139]~P2(x1391)+P7(x1391)+~P2(f9(f11(f6(x1391,a19))))
% 0.20/0.68 [161]P2(x1611)+~P6(x1611,f6(a19,a19))+~P6(f7(x1611,f9(f11(f6(x1611,a19)))),a13)
% 0.20/0.68 [172]E(x1721,a4)+E(f25(f16(x1721,a4),f16(x1721,a4)),x1721)+~E(f16(f10(f8(f25(f16(x1721,a4),f16(x1721,a4))),x1721),a4),f16(x1721,a4))
% 0.20/0.68 [174]E(x1741,a4)+E(f25(f16(x1741,a4),f16(x1741,a4)),x1741)+P5(f16(f10(f8(f25(f16(x1741,a4),f16(x1741,a4))),x1741),a4),x1741)
% 0.20/0.68 [177]E(x1771,a4)+E(f25(f16(x1771,a4),f16(x1771,a4)),x1771)+P5(f16(f10(f8(f25(f16(x1771,a4),f16(x1771,a4))),x1771),a4),f10(f8(f25(f16(x1771,a4),f16(x1771,a4))),x1771))
% 0.20/0.68 [178]P1(x1781)+~P5(a4,x1781)+~P6(f9(f9(f11(f6(f10(a20,f6(x1781,a19)),a19)))),x1781)
% 0.20/0.68 [186]~P5(x1861,a19)+E(x1861,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f25(x1861,x1861),a19)),a19))))))),x1861)
% 0.20/0.68 [98]~P6(x982,x981)+~P6(x981,x982)+E(x981,x982)
% 0.20/0.68 [91]P5(x912,a19)+P5(x911,a19)+E(f25(x911,x912),a4)
% 0.20/0.68 [102]P5(x1021,x1022)+P5(x1021,f8(x1022))+~P5(x1021,a19)
% 0.20/0.68 [112]E(x1121,x1122)+~E(f25(x1121,x1121),f25(x1122,x1122))+~P5(x1122,a19)
% 0.20/0.68 [113]E(x1131,x1132)+~E(f25(x1131,x1131),f25(x1132,x1132))+~P5(x1131,a19)
% 0.20/0.68 [120]E(f25(x1202,x1202),x1201)+~P6(x1201,f25(x1202,x1202))+E(x1201,a4)
% 0.20/0.68 [121]E(x1211,x1212)+P5(f16(x1212,x1211),x1212)+P5(f16(x1211,x1212),x1211)
% 0.20/0.68 [130]E(x1301,x1302)+P5(f16(x1302,x1301),x1302)+~P5(f16(x1301,x1302),x1302)
% 0.20/0.68 [132]E(x1321,x1322)+~P5(f16(x1322,x1321),x1321)+~P5(f16(x1321,x1322),x1322)
% 0.20/0.68 [116]~P5(x1162,x1161)+E(f14(x1161),x1162)+~E(f25(f14(x1161),f14(x1161)),x1161)
% 0.20/0.68 [133]P5(x1332,f9(x1331))+~P5(x1332,a19)+E(f10(x1331,f6(f25(x1332,x1332),a19)),a4)
% 0.20/0.68 [137]P5(x1372,a19)+P5(x1371,a19)+E(f25(f25(x1371,x1371),f25(x1371,f25(x1372,x1372))),f25(a4,f25(a4,a4)))
% 0.20/0.68 [147]P5(x1472,a19)+~P5(x1471,a19)+E(f25(a4,f25(f25(x1471,x1471),f25(x1471,x1471))),f25(f25(x1472,x1472),f25(x1472,f25(x1471,x1471))))
% 0.20/0.68 [171]~P5(x1711,x1712)+~P5(f25(f25(x1711,x1711),f25(x1711,f25(x1712,x1712))),f6(a19,a19))+P5(f25(f25(x1711,x1711),f25(x1711,f25(x1712,x1712))),a5)
% 0.20/0.68 [173]~P5(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),f6(a19,a19))+~E(f8(f10(f8(x1731),f8(f25(x1731,x1731)))),x1732)+P5(f25(f25(x1731,x1731),f25(x1731,f25(x1732,x1732))),a20)
% 0.20/0.68 [176]~P2(x1761)+~P5(x1762,a19)+P5(f9(f9(f11(f6(f10(x1761,f6(x1762,a19)),a19)))),a19)
% 0.20/0.68 [104]~P6(x1041,x1043)+P6(x1041,x1042)+~P6(x1043,x1042)
% 0.20/0.68 [105]~P5(x1051,x1053)+P5(x1051,x1052)+~P6(x1053,x1052)
% 0.20/0.68 [114]E(x1141,x1142)+E(x1141,x1143)+~P5(x1141,f25(x1143,x1142))
% 0.20/0.68 [122]~P5(x1221,x1223)+~P5(x1221,x1222)+P5(x1221,f10(x1222,x1223))
% 0.20/0.68 [123]~P5(x1232,x1233)+~P5(x1231,x1233)+P6(f25(x1231,x1232),x1233)
% 0.20/0.68 [162]E(x1621,x1622)+~E(f25(x1623,x1621),f25(x1623,x1622))+~P5(f25(f25(x1621,x1621),f25(x1621,f25(x1622,x1622))),f6(a19,a19))
% 0.20/0.68 [163]E(x1631,x1632)+~E(f25(x1631,x1633),f25(x1632,x1633))+~P5(f25(f25(x1631,x1631),f25(x1631,f25(x1632,x1632))),f6(a19,a19))
% 0.20/0.68 [148]~P5(x1482,x1484)+~P5(x1481,x1483)+P5(f25(f25(x1481,x1481),f25(x1481,f25(x1482,x1482))),f6(x1483,x1484))
% 0.20/0.68 [150]E(x1501,x1502)+~P5(x1501,a19)+~E(f25(f25(x1503,x1503),f25(x1503,f25(x1501,x1501))),f25(f25(x1504,x1504),f25(x1504,f25(x1502,x1502))))
% 0.20/0.68 [151]E(x1511,x1512)+~P5(x1511,a19)+~E(f25(f25(x1511,x1511),f25(x1511,f25(x1513,x1513))),f25(f25(x1512,x1512),f25(x1512,f25(x1514,x1514))))
% 0.20/0.68 [183]~P5(f25(f25(f25(f25(x1832,x1832),f25(x1832,f25(x1833,x1833))),f25(f25(x1832,x1832),f25(x1832,f25(x1833,x1833)))),f25(f25(f25(x1832,x1832),f25(x1832,f25(x1833,x1833))),f25(x1831,x1831))),x1834)+P5(f25(f25(f25(f25(x1831,x1831),f25(x1831,f25(x1832,x1832))),f25(f25(x1831,x1831),f25(x1831,f25(x1832,x1832)))),f25(f25(f25(x1831,x1831),f25(x1831,f25(x1832,x1832))),f25(x1833,x1833))),f21(x1834))+~P5(f25(f25(f25(f25(x1831,x1831),f25(x1831,f25(x1832,x1832))),f25(f25(x1831,x1831),f25(x1831,f25(x1832,x1832)))),f25(f25(f25(x1831,x1831),f25(x1831,f25(x1832,x1832))),f25(x1833,x1833))),f6(f6(a19,a19),a19))
% 0.20/0.68 [184]~P5(f25(f25(f25(f25(x1842,x1842),f25(x1842,f25(x1841,x1841))),f25(f25(x1842,x1842),f25(x1842,f25(x1841,x1841)))),f25(f25(f25(x1842,x1842),f25(x1842,f25(x1841,x1841))),f25(x1843,x1843))),x1844)+P5(f25(f25(f25(f25(x1841,x1841),f25(x1841,f25(x1842,x1842))),f25(f25(x1841,x1841),f25(x1841,f25(x1842,x1842)))),f25(f25(f25(x1841,x1841),f25(x1841,f25(x1842,x1842))),f25(x1843,x1843))),f11(x1844))+~P5(f25(f25(f25(f25(x1841,x1841),f25(x1841,f25(x1842,x1842))),f25(f25(x1841,x1841),f25(x1841,f25(x1842,x1842)))),f25(f25(f25(x1841,x1841),f25(x1841,f25(x1842,x1842))),f25(x1843,x1843))),f6(f6(a19,a19),a19))
% 0.20/0.68 [188]~P5(f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882))),f6(a19,a19))+P5(f25(f25(x1881,x1881),f25(x1881,f25(x1882,x1882))),f7(x1883,x1884))+~P5(x1882,f9(f9(f11(f6(f10(x1883,f6(f9(f9(f11(f6(f10(x1884,f6(f25(x1881,x1881),a19)),a19)))),a19)),a19)))))
% 0.20/0.68 [189]~P4(x1892,x1895,x1891)+~P5(f25(f25(x1893,x1893),f25(x1893,f25(x1894,x1894))),f9(x1895))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1891,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1893,x1893),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1893,x1893),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1893,x1893),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1894,x1894),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1894,x1894),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1893,x1893),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1893,x1893),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1893,x1893),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1894,x1894),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(x1894,x1894),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1892,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1895,f6(f25(f25(f25(x1893,x1893),f25(x1893,f25(x1894,x1894))),f25(f25(x1893,x1893),f25(x1893,f25(x1894,x1894)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1895,f6(f25(f25(f25(x1893,x1893),f25(x1893,f25(x1894,x1894))),f25(f25(x1893,x1893),f25(x1893,f25(x1894,x1894)))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.68 [167]~P2(x1671)+P8(x1671)+~E(f6(f9(f9(x1671)),f9(f9(x1671))),f9(x1671))+~P6(f9(f9(f11(f6(x1671,a19)))),f9(f9(x1671)))
% 0.20/0.68 [115]E(x1151,x1152)+E(x1153,x1152)+~E(f25(x1153,x1151),f25(x1152,x1152))+~P5(x1152,a19)
% 0.20/0.68 [166]~P2(x1661)+P3(x1661,x1662,x1663)+~E(f9(f9(x1662)),f9(x1661))+~P6(f9(f9(f11(f6(x1661,a19)))),f9(f9(x1663)))
% 0.20/0.68 [179]~P8(x1793)+~P8(x1792)+~P3(x1791,x1792,x1793)+P4(x1791,x1792,x1793)+P5(f25(f25(f17(x1791,x1792,x1793),f17(x1791,x1792,x1793)),f25(f17(x1791,x1792,x1793),f25(f18(x1791,x1792,x1793),f18(x1791,x1792,x1793)))),f9(x1792))
% 0.20/0.68 [190]~P8(x1903)+~P8(x1902)+~P3(x1901,x1902,x1903)+P4(x1901,x1902,x1903)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1903,f6(f25(f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903)),a19)),a19)))))))))),f25(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),a19)),a19)))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),a19)),a19))))))),f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1901,f6(f25(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1902,f6(f25(f25(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),f25(f17(x1901,x1902,x1903),f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903)))),f25(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),f25(f17(x1901,x1902,x1903),f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1902,f6(f25(f25(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),f25(f17(x1901,x1902,x1903),f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903)))),f25(f25(f17(x1901,x1902,x1903),f17(x1901,x1902,x1903)),f25(f17(x1901,x1902,x1903),f25(f18(x1901,x1902,x1903),f18(x1901,x1902,x1903))))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.68 %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(f16(x91,x93),f16(x92,x93))
% 0.20/0.69 [10]~E(x101,x102)+E(f16(x103,x101),f16(x103,x102))
% 0.20/0.69 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113))
% 0.20/0.69 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122))
% 0.20/0.69 [13]~E(x131,x132)+E(f17(x131,x133,x134),f17(x132,x133,x134))
% 0.20/0.69 [14]~E(x141,x142)+E(f17(x143,x141,x144),f17(x143,x142,x144))
% 0.20/0.69 [15]~E(x151,x152)+E(f17(x153,x154,x151),f17(x153,x154,x152))
% 0.20/0.69 [16]~E(x161,x162)+E(f11(x161),f11(x162))
% 0.20/0.69 [17]~E(x171,x172)+E(f7(x171,x173),f7(x172,x173))
% 0.20/0.69 [18]~E(x181,x182)+E(f7(x183,x181),f7(x183,x182))
% 0.20/0.69 [19]~E(x191,x192)+E(f24(x191),f24(x192))
% 0.20/0.69 [20]~E(x201,x202)+E(f18(x201,x203,x204),f18(x202,x203,x204))
% 0.20/0.69 [21]~E(x211,x212)+E(f18(x213,x211,x214),f18(x213,x212,x214))
% 0.20/0.69 [22]~E(x221,x222)+E(f18(x223,x224,x221),f18(x223,x224,x222))
% 0.20/0.69 [23]~E(x231,x232)+E(f14(x231),f14(x232))
% 0.20/0.69 [24]~E(x241,x242)+E(f12(x241),f12(x242))
% 0.20/0.69 [25]~E(x251,x252)+E(f8(x251),f8(x252))
% 0.20/0.69 [26]~E(x261,x262)+E(f22(x261),f22(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(f21(x291),f21(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)
% 0.20/0.69 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.20/0.69 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.20/0.69 [37]P6(x372,x373)+~E(x371,x372)+~P6(x371,x373)
% 0.20/0.69 [38]P6(x383,x382)+~E(x381,x382)+~P6(x383,x381)
% 0.20/0.69 [39]~P8(x391)+P8(x392)+~E(x391,x392)
% 0.20/0.69 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.20/0.69 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.20/0.69 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.20/0.69 [43]~P7(x431)+P7(x432)+~E(x431,x432)
% 0.20/0.69 [44]~P9(x441)+P9(x442)+~E(x441,x442)
% 0.20/0.69
% 0.20/0.69 %-------------------------------------------
% 0.20/0.69 cnf(191,plain,
% 0.20/0.69 ($false),
% 0.20/0.69 inference(scs_inference,[],[72,75,157]),
% 0.20/0.69 ['proof']).
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69 % Total time :0.010000s
%------------------------------------------------------------------------------