%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET093-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 14:20:40 EDT 2024
% Result : Unsatisfiable 0.48s 0.68s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET093-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.03/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n027.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 16:43:54 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.47/0.55 start to proof:theBenchmark
% 0.48/0.67 %-------------------------------------------
% 0.48/0.67 % File :CSE---1.7
% 0.48/0.67 % Problem :theBenchmark
% 0.48/0.67 % Transform :cnf
% 0.48/0.67 % Format :tptp:raw
% 0.48/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.48/0.67
% 0.48/0.67 % Result :Theorem 0.070000s
% 0.48/0.67 % Output :CNFRefutation 0.070000s
% 0.48/0.67 %-------------------------------------------
% 0.48/0.67 %--------------------------------------------------------------------------
% 0.48/0.67 % File : SET093-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.48/0.67 % Domain : Set Theory
% 0.48/0.67 % Problem : Corollary to every singleton is a set
% 0.48/0.67 % Version : [Qua92] axioms : Augmented.
% 0.48/0.67 % English :
% 0.48/0.67
% 0.48/0.67 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.48/0.67 % Source : [Quaife]
% 0.48/0.67 % Names : SS9 [Qua92]
% 0.48/0.67
% 0.48/0.67 % Status : Unsatisfiable
% 0.48/0.67 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.14 v6.0.0, 0.00 v5.5.0, 0.10 v5.4.0, 0.15 v5.3.0, 0.17 v5.2.0, 0.12 v5.0.0, 0.14 v4.1.0, 0.08 v4.0.1, 0.09 v4.0.0, 0.18 v3.7.0, 0.20 v3.5.0, 0.18 v3.4.0, 0.08 v3.3.0, 0.07 v3.2.0, 0.08 v3.1.0, 0.09 v2.7.0, 0.08 v2.6.0, 0.00 v2.5.0, 0.09 v2.4.0, 0.00 v2.1.0
% 0.48/0.67 % Syntax : Number of clauses : 138 ( 42 unt; 21 nHn; 92 RR)
% 0.48/0.67 % Number of literals : 275 ( 75 equ; 123 neg)
% 0.48/0.67 % Maximal clause size : 5 ( 1 avg)
% 0.48/0.67 % Maximal term depth : 6 ( 1 avg)
% 0.48/0.67 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.48/0.67 % Number of functors : 41 ( 41 usr; 9 con; 0-3 aty)
% 0.48/0.67 % Number of variables : 261 ( 46 sgn)
% 0.48/0.67 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.48/0.67
% 0.48/0.67 % Comments : Preceding lemmas are added.
% 0.48/0.67 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.48/0.67 %--------------------------------------------------------------------------
% 0.48/0.67 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.48/0.67 include('Axioms/SET004-0.ax').
% 0.48/0.67 %--------------------------------------------------------------------------
% 0.48/0.67 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.48/0.67 cnf(corollary_1_to_unordered_pair,axiom,
% 0.48/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.48/0.67 | member(X,unordered_pair(X,Y)) ) ).
% 0.48/0.67
% 0.48/0.67 cnf(corollary_2_to_unordered_pair,axiom,
% 0.48/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.48/0.67 | member(Y,unordered_pair(X,Y)) ) ).
% 0.48/0.67
% 0.48/0.67 %----Corollaries to Cartesian product axiom.
% 0.48/0.67 cnf(corollary_1_to_cartesian_product,axiom,
% 0.48/0.67 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.48/0.67 | member(U,universal_class) ) ).
% 0.48/0.67
% 0.48/0.67 cnf(corollary_2_to_cartesian_product,axiom,
% 0.48/0.67 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.48/0.67 | member(V,universal_class) ) ).
% 0.48/0.67
% 0.48/0.67 %---- PARTIAL ORDER.
% 0.48/0.67 %----(PO1): reflexive.
% 0.48/0.67 cnf(subclass_is_reflexive,axiom,
% 0.48/0.67 subclass(X,X) ).
% 0.48/0.67
% 0.48/0.67 %----(PO2): antisymmetry is part of A-3.
% 0.48/0.67 %----(x < y), (y < x) --> (x = y).
% 0.48/0.67
% 0.48/0.67 %----(PO3): transitivity.
% 0.48/0.67 cnf(transitivity_of_subclass,axiom,
% 0.48/0.67 ( ~ subclass(X,Y)
% 0.48/0.67 | ~ subclass(Y,Z)
% 0.48/0.67 | subclass(X,Z) ) ).
% 0.48/0.67
% 0.48/0.67 %---- EQUALITY.
% 0.48/0.67 %----(EQ1): equality axiom.
% 0.48/0.67 %----a:x:(x = x).
% 0.48/0.67 %----This is always an axiom in the TPTP presentation.
% 0.48/0.67
% 0.48/0.67 %----(EQ2): expanded equality definition.
% 0.48/0.67 cnf(equality1,axiom,
% 0.48/0.67 ( X = Y
% 0.48/0.67 | member(not_subclass_element(X,Y),X)
% 0.48/0.67 | member(not_subclass_element(Y,X),Y) ) ).
% 0.48/0.67
% 0.48/0.67 cnf(equality2,axiom,
% 0.48/0.67 ( ~ member(not_subclass_element(X,Y),Y)
% 0.48/0.67 | X = Y
% 0.48/0.67 | member(not_subclass_element(Y,X),Y) ) ).
% 0.48/0.67
% 0.48/0.67 cnf(equality3,axiom,
% 0.48/0.67 ( ~ member(not_subclass_element(Y,X),X)
% 0.48/0.67 | X = Y
% 0.48/0.67 | member(not_subclass_element(X,Y),X) ) ).
% 0.48/0.67
% 0.48/0.67 cnf(equality4,axiom,
% 0.48/0.67 ( ~ member(not_subclass_element(X,Y),Y)
% 0.48/0.67 | ~ member(not_subclass_element(Y,X),X)
% 0.48/0.67 | X = Y ) ).
% 0.48/0.67
% 0.48/0.67 %---- SPECIAL CLASSES.
% 0.48/0.67 %----(SP1): lemma.
% 0.48/0.67 cnf(special_classes_lemma,axiom,
% 0.48/0.67 ~ member(Y,intersection(complement(X),X)) ).
% 0.48/0.67
% 0.48/0.67 %----(SP2): Existence of O (null class).
% 0.48/0.67 %----e:x:a:z:(-(z e x)).
% 0.48/0.67 cnf(existence_of_null_class,axiom,
% 0.48/0.67 ~ member(Z,null_class) ).
% 0.48/0.67
% 0.48/0.67 %----(SP3): O is a subclass of every class.
% 0.48/0.67 cnf(null_class_is_subclass,axiom,
% 0.48/0.67 subclass(null_class,X) ).
% 0.48/0.68
% 0.48/0.68 %----corollary.
% 0.48/0.68 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.48/0.68 ( ~ subclass(X,null_class)
% 0.48/0.68 | X = null_class ) ).
% 0.48/0.68
% 0.48/0.68 %----(SP4): uniqueness of null class.
% 0.48/0.68 cnf(null_class_is_unique,axiom,
% 0.48/0.68 ( Z = null_class
% 0.48/0.68 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.48/0.68
% 0.48/0.68 %----(SP5): O is a set (follows from axiom of infinity).
% 0.48/0.68 cnf(null_class_is_a_set,axiom,
% 0.48/0.68 member(null_class,universal_class) ).
% 0.48/0.68
% 0.48/0.68 %---- UNORDERED PAIRS.
% 0.48/0.68 %----(UP1): unordered pair is commutative.
% 0.48/0.68 cnf(commutativity_of_unordered_pair,axiom,
% 0.48/0.68 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.48/0.68
% 0.48/0.68 %----(UP2): if one argument is a proper class, pair contains only the
% 0.48/0.68 %----other. In a slightly different form to the paper
% 0.48/0.68 cnf(singleton_in_unordered_pair1,axiom,
% 0.48/0.68 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.48/0.68
% 0.48/0.68 cnf(singleton_in_unordered_pair2,axiom,
% 0.48/0.68 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.48/0.68
% 0.48/0.68 cnf(unordered_pair_equals_singleton1,axiom,
% 0.48/0.68 ( member(Y,universal_class)
% 0.48/0.68 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.48/0.68
% 0.48/0.68 cnf(unordered_pair_equals_singleton2,axiom,
% 0.48/0.68 ( member(X,universal_class)
% 0.48/0.68 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.48/0.68
% 0.48/0.68 %----(UP3): if both arguments are proper classes, pair is null.
% 0.48/0.68 cnf(null_unordered_pair,axiom,
% 0.48/0.68 ( unordered_pair(X,Y) = null_class
% 0.48/0.68 | member(X,universal_class)
% 0.48/0.68 | member(Y,universal_class) ) ).
% 0.48/0.68
% 0.48/0.68 %----(UP4): left cancellation for unordered pairs.
% 0.48/0.68 cnf(left_cancellation,axiom,
% 0.48/0.68 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.48/0.68 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.48/0.68 | Y = Z ) ).
% 0.48/0.68
% 0.48/0.68 %----(UP5): right cancellation for unordered pairs.
% 0.48/0.68 cnf(right_cancellation,axiom,
% 0.48/0.68 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.48/0.68 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.48/0.68 | X = Y ) ).
% 0.48/0.68
% 0.48/0.68 %----(UP6): corollary to (A-4).
% 0.48/0.68 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.48/0.68 ( ~ member(X,universal_class)
% 0.48/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.48/0.68
% 0.48/0.68 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.48/0.68 ( ~ member(Y,universal_class)
% 0.48/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.48/0.68
% 0.48/0.68 %----corollary to instantiate variables.
% 0.48/0.68 %----Not in the paper
% 0.48/0.68 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.48/0.68 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.48/0.68 | unordered_pair(X,Y) != null_class ) ).
% 0.48/0.68
% 0.48/0.68 %----(UP7): if both members of a pair belong to a set, the pair
% 0.48/0.68 %----is a subset.
% 0.48/0.68 cnf(unordered_pair_is_subset,axiom,
% 0.48/0.68 ( ~ member(X,Z)
% 0.48/0.68 | ~ member(Y,Z)
% 0.48/0.68 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.48/0.68
% 0.48/0.68 %---- SINGLETONS.
% 0.48/0.68 %----(SS1): every singleton is a set.
% 0.48/0.68 cnf(singletons_are_sets,axiom,
% 0.48/0.68 member(singleton(X),universal_class) ).
% 0.48/0.68
% 0.48/0.68 %----corollary, not in the paper.
% 0.48/0.68 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.48/0.68 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.48/0.68
% 0.48/0.68 %----(SS2): a set belongs to its singleton.
% 0.48/0.68 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.48/0.68 cnf(set_in_its_singleton,axiom,
% 0.48/0.68 ( ~ member(X,universal_class)
% 0.48/0.68 | member(X,singleton(X)) ) ).
% 0.48/0.68
% 0.48/0.68 %----corollary
% 0.48/0.68 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.48/0.68 ( ~ member(X,universal_class)
% 0.48/0.68 | singleton(X) != null_class ) ).
% 0.48/0.68
% 0.48/0.68 %----Not in the paper
% 0.48/0.68 cnf(null_class_in_its_singleton,axiom,
% 0.48/0.68 member(null_class,singleton(null_class)) ).
% 0.48/0.68
% 0.48/0.68 %----(SS3): only x can belong to {x}.
% 0.48/0.68 cnf(only_member_in_singleton,axiom,
% 0.48/0.68 ( ~ member(Y,singleton(X))
% 0.48/0.68 | Y = X ) ).
% 0.48/0.68
% 0.48/0.68 %----(SS4): if x is not a set, {x} = O.
% 0.48/0.68 cnf(singleton_is_null_class,axiom,
% 0.48/0.68 ( member(X,universal_class)
% 0.48/0.68 | singleton(X) = null_class ) ).
% 0.48/0.68
% 0.48/0.68 %----(SS5): a singleton set is determined by its element.
% 0.48/0.68 cnf(singleton_identified_by_element1,axiom,
% 0.48/0.68 ( singleton(X) != singleton(Y)
% 0.48/0.68 | ~ member(X,universal_class)
% 0.48/0.68 | X = Y ) ).
% 0.48/0.68
% 0.48/0.68 cnf(singleton_identified_by_element2,axiom,
% 0.48/0.68 ( singleton(X) != singleton(Y)
% 0.48/0.68 | ~ member(Y,universal_class)
% 0.48/0.68 | X = Y ) ).
% 0.48/0.68
% 0.48/0.68 %----(SS5.5).
% 0.48/0.68 %----Not in the paper
% 0.48/0.68 cnf(singleton_in_unordered_pair3,axiom,
% 0.48/0.68 ( unordered_pair(Y,Z) != singleton(X)
% 0.48/0.68 | ~ member(X,universal_class)
% 0.48/0.68 | X = Y
% 0.48/0.68 | X = Z ) ).
% 0.48/0.68
% 0.48/0.68 %----(SS6): existence of memb.
% 0.48/0.68 %----a:x:e:u:(((u e universal_class) & x = {u}) | (-e:y:((y
% 0.48/0.68 %----e universal_class) & x = {y}) & u = x)).
% 0.48/0.68 cnf(member_exists1,axiom,
% 0.48/0.68 ( ~ member(Y,universal_class)
% 0.48/0.68 | member(member_of(singleton(Y)),universal_class) ) ).
% 0.48/0.68
% 0.48/0.68 cnf(member_exists2,axiom,
% 0.48/0.68 ( ~ member(Y,universal_class)
% 0.48/0.68 | singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.48/0.68
% 0.48/0.68 cnf(member_exists3,axiom,
% 0.48/0.68 ( member(member_of(X),universal_class)
% 0.48/0.68 | member_of(X) = X ) ).
% 0.48/0.68
% 0.48/0.68 cnf(member_exists4,axiom,
% 0.48/0.68 ( singleton(member_of(X)) = X
% 0.48/0.68 | member_of(X) = X ) ).
% 0.48/0.68
% 0.48/0.68 %----(SS7): uniqueness of memb of a singleton set.
% 0.48/0.68 %----a:x:a:u:(((u e universal_class) & x = {u}) ==> member_of(x) = u)
% 0.48/0.68 cnf(member_of_singleton_is_unique,axiom,
% 0.48/0.68 ( ~ member(U,universal_class)
% 0.48/0.68 | member_of(singleton(U)) = U ) ).
% 0.48/0.68
% 0.48/0.68 %----(SS8): uniqueness of memb when x is not a singleton of a set.
% 0.48/0.68 %----a:x:a:u:((e:y:((y e universal_class) & x = {y})
% 0.48/0.68 %----& u = x) | member_of(x) = u)
% 0.48/0.68 cnf(member_of_non_singleton_unique1,axiom,
% 0.48/0.68 ( member(member_of1(X),universal_class)
% 0.48/0.68 | member_of(X) = X ) ).
% 0.48/0.68
% 0.48/0.68 cnf(member_of_non_singleton_unique2,axiom,
% 0.48/0.68 ( singleton(member_of1(X)) = X
% 0.48/0.68 | member_of(X) = X ) ).
% 0.48/0.68
% 0.48/0.68 cnf(prove_corollary_2_to_singletons_are_sets_1,negated_conjecture,
% 0.48/0.68 singleton(member_of(x)) = x ).
% 0.48/0.68
% 0.48/0.68 cnf(prove_corollary_2_to_singletons_are_sets_2,negated_conjecture,
% 0.48/0.68 ~ member(x,universal_class) ).
% 0.48/0.68
% 0.48/0.68 %--------------------------------------------------------------------------
% 0.48/0.68 %-------------------------------------------
% 0.48/0.68 % Proof found
% 0.48/0.68 % SZS status Theorem for theBenchmark
% 0.48/0.68 % SZS output start Proof
% 0.48/0.68 %ClaNum:167(EqnAxiom:44)
% 0.48/0.68 %VarNum:932(SingletonVarNum:230)
% 0.48/0.68 %MaxLitNum:5
% 0.48/0.68 %MaxfuncDepth:24
% 0.48/0.68 %SharedTerms:37
% 0.48/0.68 %goalClause: 52 69
% 0.48/0.68 %singleGoalClaCount:2
% 0.48/0.68 [45]P1(a1)
% 0.48/0.68 [46]P2(a2)
% 0.48/0.68 [47]P5(a4,a19)
% 0.48/0.68 [48]P5(a1,a19)
% 0.48/0.68 [69]~P5(a25,a19)
% 0.48/0.68 [54]P6(a6,f7(a19,a19))
% 0.48/0.68 [55]P6(a20,f7(a19,a19))
% 0.48/0.68 [56]P5(a4,f26(a4,a4))
% 0.48/0.68 [52]E(f26(f5(a25),f5(a25)),a25)
% 0.48/0.68 [65]E(f11(f10(f12(f7(a23,a19))),a23),a14)
% 0.48/0.68 [67]E(f11(f7(a19,a19),f11(f7(a19,a19),f9(f8(f9(a6),f10(f12(f7(a6,a19))))))),a23)
% 0.48/0.68 [49]P6(x491,a19)
% 0.48/0.68 [50]P6(a4,x501)
% 0.48/0.68 [51]P6(x511,x511)
% 0.48/0.68 [70]~P5(x701,a4)
% 0.48/0.68 [63]P6(f21(x631),f7(f7(a19,a19),a19))
% 0.48/0.68 [64]P6(f12(x641),f7(f7(a19,a19),a19))
% 0.48/0.68 [68]E(f11(f10(x681),f9(f10(f11(f8(f10(f12(f7(a6,a19))),x681),a14)))),f3(x681))
% 0.48/0.68 [53]E(f26(x531,x532),f26(x532,x531))
% 0.48/0.68 [57]P5(f26(x571,x572),a19)
% 0.48/0.68 [59]P6(f8(x591,x592),f7(a19,a19))
% 0.48/0.68 [60]P6(f26(x601,x601),f26(x602,x601))
% 0.48/0.68 [61]P6(f26(x611,x611),f26(x611,x612))
% 0.48/0.68 [66]P5(f26(x661,x661),f26(x662,f26(x661,x661)))
% 0.48/0.68 [71]~P5(x711,f11(f9(x712),x712))
% 0.48/0.68 [62]E(f11(f7(x621,x622),x623),f11(x623,f7(x621,x622)))
% 0.48/0.68 [72]~P7(x721)+P2(x721)
% 0.48/0.68 [73]~P8(x731)+P2(x731)
% 0.48/0.68 [76]~P1(x761)+P6(a1,x761)
% 0.48/0.68 [77]~P1(x771)+P5(a4,x771)
% 0.48/0.68 [78]~P6(x781,a4)+E(x781,a4)
% 0.48/0.68 [80]P5(f22(x801),x801)+E(x801,a4)
% 0.48/0.68 [81]E(f5(x811),x811)+P5(f5(x811),a19)
% 0.48/0.68 [82]E(f5(x821),x821)+P5(f15(x821),a19)
% 0.48/0.68 [83]P5(x831,a19)+E(f26(x831,x831),a4)
% 0.48/0.68 [86]E(x861,a4)+P5(f16(x861,a4),x861)
% 0.48/0.68 [90]~P2(x901)+P6(x901,f7(a19,a19))
% 0.48/0.68 [79]E(x791,a4)+E(f11(x791,f22(x791)),a4)
% 0.48/0.68 [84]E(f5(x841),x841)+E(f26(f5(x841),f5(x841)),x841)
% 0.48/0.68 [85]E(f5(x851),x851)+E(f26(f15(x851),f15(x851)),x851)
% 0.48/0.68 [95]~P5(x951,a19)+E(f5(f26(x951,x951)),x951)
% 0.48/0.68 [119]~P5(x1191,a19)+P5(f5(f26(x1191,x1191)),a19)
% 0.48/0.68 [104]~P8(x1041)+E(f7(f10(f10(x1041)),f10(f10(x1041))),f10(x1041))
% 0.48/0.68 [123]~P7(x1231)+P2(f10(f12(f7(x1231,a19))))
% 0.48/0.68 [127]~P5(x1271,a19)+E(f26(f5(f26(x1271,x1271)),f5(f26(x1271,x1271))),f26(x1271,x1271))
% 0.48/0.68 [129]~P5(x1291,a19)+P5(f10(f11(a6,f7(a19,x1291))),a19)
% 0.48/0.68 [131]~P9(x1311)+P6(f8(x1311,f10(f12(f7(x1311,a19)))),a14)
% 0.48/0.68 [132]~P2(x1321)+P6(f8(x1321,f10(f12(f7(x1321,a19)))),a14)
% 0.48/0.68 [133]~P8(x1331)+P6(f10(f10(f12(f7(x1331,a19)))),f10(f10(x1331)))
% 0.48/0.68 [138]P9(x1381)+~P6(f8(x1381,f10(f12(f7(x1381,a19)))),a14)
% 0.48/0.68 [154]~P1(x1541)+P6(f10(f10(f12(f7(f11(a20,f7(x1541,a19)),a19)))),x1541)
% 0.48/0.68 [158]~P5(x1581,a19)+P5(f9(f10(f10(f12(f7(f11(a6,f7(f9(x1581),a19)),a19))))),a19)
% 0.48/0.68 [74]~E(x742,x741)+P6(x741,x742)
% 0.48/0.68 [75]~E(x751,x752)+P6(x751,x752)
% 0.48/0.68 [88]P5(x882,a19)+E(f26(x881,x882),f26(x881,x881))
% 0.48/0.68 [89]P5(x891,a19)+E(f26(x891,x892),f26(x892,x892))
% 0.48/0.68 [91]~P5(x912,a19)+~E(f26(x911,x912),a4)
% 0.48/0.68 [92]~P5(x921,a19)+~E(f26(x921,x922),a4)
% 0.48/0.68 [96]P6(x961,x962)+P5(f16(x961,x962),x961)
% 0.48/0.68 [97]~P5(x971,x972)+~P5(x971,f9(x972))
% 0.48/0.68 [101]~P5(x1011,a19)+P5(x1011,f26(x1012,x1011))
% 0.48/0.68 [102]~P5(x1021,a19)+P5(x1021,f26(x1021,x1022))
% 0.48/0.69 [105]E(x1051,x1052)+~P5(x1051,f26(x1052,x1052))
% 0.48/0.69 [112]P6(x1121,x1122)+~P5(f16(x1121,x1122),x1122)
% 0.48/0.69 [128]~P5(x1282,f10(x1281))+~E(f11(x1281,f7(f26(x1282,x1282),a19)),a4)
% 0.48/0.69 [137]P5(x1371,x1372)+~P5(f26(f26(x1371,x1371),f26(x1371,f26(x1372,x1372))),a6)
% 0.48/0.69 [151]~P5(f26(f26(x1511,x1511),f26(x1511,f26(x1512,x1512))),a20)+E(f9(f11(f9(x1511),f9(f26(x1511,x1511)))),x1512)
% 0.48/0.69 [116]P2(x1161)+~P3(x1161,x1162,x1163)
% 0.48/0.69 [117]P8(x1171)+~P4(x1172,x1173,x1171)
% 0.48/0.69 [118]P8(x1181)+~P4(x1182,x1181,x1183)
% 0.48/0.69 [126]~P4(x1261,x1262,x1263)+P3(x1261,x1262,x1263)
% 0.48/0.69 [110]P5(x1101,x1102)+~P5(x1101,f11(x1103,x1102))
% 0.48/0.69 [111]P5(x1111,x1112)+~P5(x1111,f11(x1112,x1113))
% 0.48/0.69 [120]~P3(x1202,x1201,x1203)+E(f10(f10(x1201)),f10(x1202))
% 0.48/0.69 [134]~P5(x1341,f7(x1342,x1343))+E(f26(f26(f13(x1341),f13(x1341)),f26(f13(x1341),f26(f24(x1341),f24(x1341)))),x1341)
% 0.48/0.69 [136]~P3(x1361,x1363,x1362)+P6(f10(f10(f12(f7(x1361,a19)))),f10(f10(x1362)))
% 0.48/0.69 [139]P5(x1391,a19)+~P5(f26(f26(x1392,x1392),f26(x1392,f26(x1391,x1391))),f7(x1393,x1394))
% 0.48/0.69 [140]P5(x1401,a19)+~P5(f26(f26(x1401,x1401),f26(x1401,f26(x1402,x1402))),f7(x1403,x1404))
% 0.48/0.69 [141]P5(x1411,x1412)+~P5(f26(f26(x1413,x1413),f26(x1413,f26(x1411,x1411))),f7(x1414,x1412))
% 0.48/0.69 [142]P5(x1421,x1422)+~P5(f26(f26(x1421,x1421),f26(x1421,f26(x1423,x1423))),f7(x1422,x1424))
% 0.48/0.69 [143]~E(f26(x1431,x1432),a4)+~P5(f26(f26(x1431,x1431),f26(x1431,f26(x1432,x1432))),f7(x1433,x1434))
% 0.48/0.69 [147]P5(x1471,f26(x1472,x1471))+~P5(f26(f26(x1472,x1472),f26(x1472,f26(x1471,x1471))),f7(x1473,x1474))
% 0.48/0.69 [148]P5(x1481,f26(x1481,x1482))+~P5(f26(f26(x1481,x1481),f26(x1481,f26(x1482,x1482))),f7(x1483,x1484))
% 0.48/0.69 [159]~P5(f26(f26(f26(f26(x1593,x1593),f26(x1593,f26(x1591,x1591))),f26(f26(x1593,x1593),f26(x1593,f26(x1591,x1591)))),f26(f26(f26(x1593,x1593),f26(x1593,f26(x1591,x1591))),f26(x1592,x1592))),f21(x1594))+P5(f26(f26(f26(f26(x1591,x1591),f26(x1591,f26(x1592,x1592))),f26(f26(x1591,x1591),f26(x1591,f26(x1592,x1592)))),f26(f26(f26(x1591,x1591),f26(x1591,f26(x1592,x1592))),f26(x1593,x1593))),x1594)
% 0.48/0.69 [160]~P5(f26(f26(f26(f26(x1602,x1602),f26(x1602,f26(x1601,x1601))),f26(f26(x1602,x1602),f26(x1602,f26(x1601,x1601)))),f26(f26(f26(x1602,x1602),f26(x1602,f26(x1601,x1601))),f26(x1603,x1603))),f12(x1604))+P5(f26(f26(f26(f26(x1601,x1601),f26(x1601,f26(x1602,x1602))),f26(f26(x1601,x1601),f26(x1601,f26(x1602,x1602)))),f26(f26(f26(x1601,x1601),f26(x1601,f26(x1602,x1602))),f26(x1603,x1603))),x1604)
% 0.48/0.69 [164]~P5(f26(f26(x1644,x1644),f26(x1644,f26(x1641,x1641))),f8(x1642,x1643))+P5(x1641,f10(f10(f12(f7(f11(x1642,f7(f10(f10(f12(f7(f11(x1643,f7(f26(x1644,x1644),a19)),a19)))),a19)),a19)))))
% 0.48/0.69 [130]~P2(x1301)+P7(x1301)+~P2(f10(f12(f7(x1301,a19))))
% 0.48/0.69 [144]P2(x1441)+~P6(x1441,f7(a19,a19))+~P6(f8(x1441,f10(f12(f7(x1441,a19)))),a14)
% 0.48/0.69 [156]P1(x1561)+~P5(a4,x1561)+~P6(f10(f10(f12(f7(f11(a20,f7(x1561,a19)),a19)))),x1561)
% 0.48/0.69 [163]~P5(x1631,a19)+E(x1631,a4)+P5(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(a2,f7(f26(x1631,x1631),a19)),a19))))))),x1631)
% 0.48/0.69 [94]~P6(x942,x941)+~P6(x941,x942)+E(x941,x942)
% 0.48/0.69 [87]P5(x872,a19)+P5(x871,a19)+E(f26(x871,x872),a4)
% 0.48/0.69 [98]P5(x981,x982)+P5(x981,f9(x982))+~P5(x981,a19)
% 0.48/0.69 [106]E(x1061,x1062)+~E(f26(x1061,x1061),f26(x1062,x1062))+~P5(x1062,a19)
% 0.48/0.69 [107]E(x1071,x1072)+~E(f26(x1071,x1071),f26(x1072,x1072))+~P5(x1071,a19)
% 0.48/0.69 [113]E(x1131,x1132)+P5(f16(x1132,x1131),x1132)+P5(f16(x1131,x1132),x1131)
% 0.48/0.69 [122]E(x1221,x1222)+P5(f16(x1222,x1221),x1222)+~P5(f16(x1221,x1222),x1222)
% 0.48/0.69 [124]E(x1241,x1242)+~P5(f16(x1242,x1241),x1241)+~P5(f16(x1241,x1242),x1242)
% 0.48/0.69 [125]P5(x1252,f10(x1251))+~P5(x1252,a19)+E(f11(x1251,f7(f26(x1252,x1252),a19)),a4)
% 0.48/0.69 [152]~P5(x1521,x1522)+~P5(f26(f26(x1521,x1521),f26(x1521,f26(x1522,x1522))),f7(a19,a19))+P5(f26(f26(x1521,x1521),f26(x1521,f26(x1522,x1522))),a6)
% 0.48/0.69 [153]~P5(f26(f26(x1531,x1531),f26(x1531,f26(x1532,x1532))),f7(a19,a19))+~E(f9(f11(f9(x1531),f9(f26(x1531,x1531)))),x1532)+P5(f26(f26(x1531,x1531),f26(x1531,f26(x1532,x1532))),a20)
% 0.48/0.69 [155]~P2(x1551)+~P5(x1552,a19)+P5(f10(f10(f12(f7(f11(x1551,f7(x1552,a19)),a19)))),a19)
% 0.48/0.69 [99]~P6(x991,x993)+P6(x991,x992)+~P6(x993,x992)
% 0.48/0.69 [100]~P5(x1001,x1003)+P5(x1001,x1002)+~P6(x1003,x1002)
% 0.48/0.69 [108]E(x1081,x1082)+E(x1081,x1083)+~P5(x1081,f26(x1083,x1082))
% 0.48/0.69 [114]~P5(x1141,x1143)+~P5(x1141,x1142)+P5(x1141,f11(x1142,x1143))
% 0.48/0.69 [115]~P5(x1152,x1153)+~P5(x1151,x1153)+P6(f26(x1151,x1152),x1153)
% 0.48/0.69 [145]E(x1451,x1452)+~E(f26(x1453,x1451),f26(x1453,x1452))+~P5(f26(f26(x1451,x1451),f26(x1451,f26(x1452,x1452))),f7(a19,a19))
% 0.48/0.69 [146]E(x1461,x1462)+~E(f26(x1461,x1463),f26(x1462,x1463))+~P5(f26(f26(x1461,x1461),f26(x1461,f26(x1462,x1462))),f7(a19,a19))
% 0.48/0.69 [135]~P5(x1352,x1354)+~P5(x1351,x1353)+P5(f26(f26(x1351,x1351),f26(x1351,f26(x1352,x1352))),f7(x1353,x1354))
% 0.48/0.69 [161]~P5(f26(f26(f26(f26(x1612,x1612),f26(x1612,f26(x1613,x1613))),f26(f26(x1612,x1612),f26(x1612,f26(x1613,x1613)))),f26(f26(f26(x1612,x1612),f26(x1612,f26(x1613,x1613))),f26(x1611,x1611))),x1614)+P5(f26(f26(f26(f26(x1611,x1611),f26(x1611,f26(x1612,x1612))),f26(f26(x1611,x1611),f26(x1611,f26(x1612,x1612)))),f26(f26(f26(x1611,x1611),f26(x1611,f26(x1612,x1612))),f26(x1613,x1613))),f21(x1614))+~P5(f26(f26(f26(f26(x1611,x1611),f26(x1611,f26(x1612,x1612))),f26(f26(x1611,x1611),f26(x1611,f26(x1612,x1612)))),f26(f26(f26(x1611,x1611),f26(x1611,f26(x1612,x1612))),f26(x1613,x1613))),f7(f7(a19,a19),a19))
% 0.48/0.69 [162]~P5(f26(f26(f26(f26(x1622,x1622),f26(x1622,f26(x1621,x1621))),f26(f26(x1622,x1622),f26(x1622,f26(x1621,x1621)))),f26(f26(f26(x1622,x1622),f26(x1622,f26(x1621,x1621))),f26(x1623,x1623))),x1624)+P5(f26(f26(f26(f26(x1621,x1621),f26(x1621,f26(x1622,x1622))),f26(f26(x1621,x1621),f26(x1621,f26(x1622,x1622)))),f26(f26(f26(x1621,x1621),f26(x1621,f26(x1622,x1622))),f26(x1623,x1623))),f12(x1624))+~P5(f26(f26(f26(f26(x1621,x1621),f26(x1621,f26(x1622,x1622))),f26(f26(x1621,x1621),f26(x1621,f26(x1622,x1622)))),f26(f26(f26(x1621,x1621),f26(x1621,f26(x1622,x1622))),f26(x1623,x1623))),f7(f7(a19,a19),a19))
% 0.48/0.69 [165]P5(f26(f26(x1651,x1651),f26(x1651,f26(x1652,x1652))),f8(x1653,x1654))+~P5(f26(f26(x1651,x1651),f26(x1651,f26(x1652,x1652))),f7(a19,a19))+~P5(x1652,f10(f10(f12(f7(f11(x1653,f7(f10(f10(f12(f7(f11(x1654,f7(f26(x1651,x1651),a19)),a19)))),a19)),a19)))))
% 0.48/0.69 [166]~P4(x1662,x1665,x1661)+~P5(f26(f26(x1663,x1663),f26(x1663,f26(x1664,x1664))),f10(x1665))+E(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1661,f7(f26(f26(f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1663,x1663),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1663,x1663),a19)),a19)))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1663,x1663),a19)),a19))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1664,x1664),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1664,x1664),a19)),a19)))))))))),f26(f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1663,x1663),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1663,x1663),a19)),a19)))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1663,x1663),a19)),a19))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1664,x1664),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(x1664,x1664),a19)),a19))))))))))),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1662,f7(f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1665,f7(f26(f26(f26(x1663,x1663),f26(x1663,f26(x1664,x1664))),f26(f26(x1663,x1663),f26(x1663,f26(x1664,x1664)))),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1665,f7(f26(f26(f26(x1663,x1663),f26(x1663,f26(x1664,x1664))),f26(f26(x1663,x1663),f26(x1663,f26(x1664,x1664)))),a19)),a19)))))))),a19)),a19))))))))
% 0.48/0.69 [150]~P2(x1501)+P8(x1501)+~E(f7(f10(f10(x1501)),f10(f10(x1501))),f10(x1501))+~P6(f10(f10(f12(f7(x1501,a19)))),f10(f10(x1501)))
% 0.48/0.69 [109]E(x1091,x1092)+E(x1093,x1092)+~E(f26(x1093,x1091),f26(x1092,x1092))+~P5(x1092,a19)
% 0.48/0.69 [149]~P2(x1491)+P3(x1491,x1492,x1493)+~E(f10(f10(x1492)),f10(x1491))+~P6(f10(f10(f12(f7(x1491,a19)))),f10(f10(x1493)))
% 0.48/0.69 [157]~P8(x1573)+~P8(x1572)+~P3(x1571,x1572,x1573)+P4(x1571,x1572,x1573)+P5(f26(f26(f17(x1571,x1572,x1573),f17(x1571,x1572,x1573)),f26(f17(x1571,x1572,x1573),f26(f18(x1571,x1572,x1573),f18(x1571,x1572,x1573)))),f10(x1572))
% 0.48/0.69 [167]~P8(x1673)+~P8(x1672)+~P3(x1671,x1672,x1673)+P4(x1671,x1672,x1673)+~E(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1673,f7(f26(f26(f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),a19)),a19)))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),a19)),a19))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673)),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673)),a19)),a19)))))))))),f26(f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),a19)),a19)))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),a19)),a19))))))),f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673)),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673)),a19)),a19))))))))))),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1671,f7(f26(f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1672,f7(f26(f26(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),f26(f17(x1671,x1672,x1673),f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673)))),f26(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),f26(f17(x1671,x1672,x1673),f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673))))),a19)),a19))))))),f10(f11(a6,f7(a19,f10(f10(f12(f7(f11(x1672,f7(f26(f26(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),f26(f17(x1671,x1672,x1673),f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673)))),f26(f26(f17(x1671,x1672,x1673),f17(x1671,x1672,x1673)),f26(f17(x1671,x1672,x1673),f26(f18(x1671,x1672,x1673),f18(x1671,x1672,x1673))))),a19)),a19)))))))),a19)),a19))))))))
% 0.48/0.69 %EqnAxiom
% 0.48/0.69 [1]E(x11,x11)
% 0.48/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.48/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.48/0.69 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.48/0.69 [5]~E(x51,x52)+E(f10(x51),f10(x52))
% 0.48/0.69 [6]~E(x61,x62)+E(f26(x61,x63),f26(x62,x63))
% 0.48/0.69 [7]~E(x71,x72)+E(f26(x73,x71),f26(x73,x72))
% 0.48/0.69 [8]~E(x81,x82)+E(f11(x81,x83),f11(x82,x83))
% 0.48/0.69 [9]~E(x91,x92)+E(f11(x93,x91),f11(x93,x92))
% 0.48/0.69 [10]~E(x101,x102)+E(f7(x101,x103),f7(x102,x103))
% 0.48/0.69 [11]~E(x111,x112)+E(f7(x113,x111),f7(x113,x112))
% 0.48/0.69 [12]~E(x121,x122)+E(f12(x121),f12(x122))
% 0.48/0.69 [13]~E(x131,x132)+E(f17(x131,x133,x134),f17(x132,x133,x134))
% 0.48/0.69 [14]~E(x141,x142)+E(f17(x143,x141,x144),f17(x143,x142,x144))
% 0.48/0.69 [15]~E(x151,x152)+E(f17(x153,x154,x151),f17(x153,x154,x152))
% 0.48/0.69 [16]~E(x161,x162)+E(f18(x161,x163,x164),f18(x162,x163,x164))
% 0.48/0.69 [17]~E(x171,x172)+E(f18(x173,x171,x174),f18(x173,x172,x174))
% 0.48/0.69 [18]~E(x181,x182)+E(f18(x183,x184,x181),f18(x183,x184,x182))
% 0.48/0.69 [19]~E(x191,x192)+E(f16(x191,x193),f16(x192,x193))
% 0.48/0.69 [20]~E(x201,x202)+E(f16(x203,x201),f16(x203,x202))
% 0.48/0.69 [21]~E(x211,x212)+E(f9(x211),f9(x212))
% 0.48/0.69 [22]~E(x221,x222)+E(f8(x221,x223),f8(x222,x223))
% 0.48/0.69 [23]~E(x231,x232)+E(f8(x233,x231),f8(x233,x232))
% 0.48/0.69 [24]~E(x241,x242)+E(f13(x241),f13(x242))
% 0.48/0.69 [25]~E(x251,x252)+E(f3(x251),f3(x252))
% 0.48/0.69 [26]~E(x261,x262)+E(f22(x261),f22(x262))
% 0.48/0.69 [27]~E(x271,x272)+E(f15(x271),f15(x272))
% 0.48/0.69 [28]~E(x281,x282)+E(f24(x281),f24(x282))
% 0.48/0.69 [29]~E(x291,x292)+E(f21(x291),f21(x292))
% 0.48/0.69 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.48/0.69 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.48/0.69 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.48/0.69 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.48/0.69 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.48/0.69 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.48/0.69 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.48/0.69 [37]P6(x372,x373)+~E(x371,x372)+~P6(x371,x373)
% 0.48/0.69 [38]P6(x383,x382)+~E(x381,x382)+~P6(x383,x381)
% 0.48/0.69 [39]P4(x392,x393,x394)+~E(x391,x392)+~P4(x391,x393,x394)
% 0.48/0.69 [40]P4(x403,x402,x404)+~E(x401,x402)+~P4(x403,x401,x404)
% 0.48/0.69 [41]P4(x413,x414,x412)+~E(x411,x412)+~P4(x413,x414,x411)
% 0.48/0.69 [42]~P8(x421)+P8(x422)+~E(x421,x422)
% 0.48/0.69 [43]~P9(x431)+P9(x432)+~E(x431,x432)
% 0.48/0.69 [44]~P7(x441)+P7(x442)+~E(x441,x442)
% 0.48/0.69
% 0.48/0.69 %-------------------------------------------
% 0.48/0.69 cnf(178,plain,
% 0.48/0.69 (~P1(a4)),
% 0.48/0.69 inference(scs_inference,[],[52,70,2,77])).
% 0.48/0.69 cnf(179,plain,
% 0.48/0.69 (~P5(x1791,a4)),
% 0.48/0.69 inference(rename_variables,[],[70])).
% 0.48/0.69 cnf(182,plain,
% 0.48/0.69 (~P5(x1821,f11(f9(x1822),x1822))),
% 0.48/0.69 inference(rename_variables,[],[71])).
% 0.48/0.69 cnf(184,plain,
% 0.48/0.69 (P6(f11(f9(x1841),x1841),x1842)),
% 0.48/0.69 inference(scs_inference,[],[52,70,71,182,2,77,86,96])).
% 0.48/0.69 cnf(185,plain,
% 0.48/0.69 (~P5(x1851,f11(f9(x1852),x1852))),
% 0.48/0.69 inference(rename_variables,[],[71])).
% 0.48/0.69 cnf(187,plain,
% 0.48/0.69 (~P5(x1871,f10(f9(f7(f26(x1871,x1871),a19))))),
% 0.48/0.69 inference(scs_inference,[],[52,70,71,182,2,77,86,96,128])).
% 0.48/0.69 cnf(189,plain,
% 0.48/0.69 (~P5(f26(f26(f26(f26(x1891,x1891),f26(x1891,f26(x1892,x1892))),f26(f26(x1891,x1891),f26(x1891,f26(x1892,x1892)))),f26(f26(f26(x1891,x1891),f26(x1891,f26(x1892,x1892))),f26(x1893,x1893))),f21(a4))),
% 0.48/0.69 inference(scs_inference,[],[52,70,179,71,182,2,77,86,96,128,159])).
% 0.48/0.69 cnf(190,plain,
% 0.48/0.69 (~P5(x1901,a4)),
% 0.48/0.69 inference(rename_variables,[],[70])).
% 0.48/0.69 cnf(193,plain,
% 0.48/0.69 (~P5(x1931,a4)),
% 0.48/0.69 inference(rename_variables,[],[70])).
% 0.48/0.69 cnf(195,plain,
% 0.48/0.69 (E(f11(f7(f26(x1951,x1951),a19),f9(f7(f26(x1951,x1951),a19))),a4)),
% 0.48/0.69 inference(scs_inference,[],[52,70,179,190,62,71,182,2,77,86,96,128,159,160,3])).
% 0.48/0.69 cnf(198,plain,
% 0.48/0.69 (~E(a4,a25)),
% 0.48/0.69 inference(scs_inference,[],[52,69,70,179,190,47,62,71,182,2,77,86,96,128,159,160,3,30,32])).
% 0.48/0.69 cnf(200,plain,
% 0.48/0.69 (~P5(x2001,a4)),
% 0.48/0.69 inference(rename_variables,[],[70])).
% 0.48/0.69 cnf(201,plain,
% 0.48/0.69 (P6(a25,f26(f5(a25),f5(a25)))),
% 0.48/0.69 inference(scs_inference,[],[52,69,51,70,179,190,193,47,62,71,182,2,77,86,96,128,159,160,3,30,32,33,37])).
% 0.48/0.69 cnf(202,plain,
% 0.48/0.69 (P6(x2021,x2021)),
% 0.48/0.69 inference(rename_variables,[],[51])).
% 0.48/0.69 cnf(205,plain,
% 0.48/0.69 (~P6(a25,a4)),
% 0.48/0.69 inference(scs_inference,[],[52,69,51,202,50,70,179,190,193,47,62,71,182,2,77,86,96,128,159,160,3,30,32,33,37,38,94])).
% 0.48/0.69 cnf(208,plain,
% 0.48/0.69 (P5(f26(x2081,x2081),f26(f26(x2081,x2081),x2082))),
% 0.48/0.69 inference(scs_inference,[],[52,69,51,202,50,70,179,190,193,61,47,66,62,71,182,2,77,86,96,128,159,160,3,30,32,33,37,38,94,100])).
% 0.48/0.69 cnf(213,plain,
% 0.48/0.69 (~P5(x2131,f11(f9(x2132),x2132))),
% 0.48/0.69 inference(rename_variables,[],[71])).
% 0.48/0.69 cnf(216,plain,
% 0.48/0.69 (~P5(a4,f9(a19))),
% 0.48/0.69 inference(scs_inference,[],[52,69,51,202,50,70,179,190,193,200,61,47,66,62,71,182,185,213,2,77,86,96,128,159,160,3,30,32,33,37,38,94,100,113,114])).
% 0.48/0.69 cnf(222,plain,
% 0.48/0.69 (~E(a25,a4)),
% 0.48/0.69 inference(scs_inference,[],[52,69,51,202,49,50,70,179,190,193,200,61,47,66,62,71,182,185,213,2,77,86,96,128,159,160,3,30,32,33,37,38,94,100,113,114,156,75])).
% 0.48/0.69 cnf(247,plain,
% 0.48/0.69 (~P5(f26(f26(f26(f26(x2471,x2471),f26(x2471,f26(x2472,x2472))),f26(f26(x2471,x2471),f26(x2471,f26(x2472,x2472)))),f26(f26(f26(x2471,x2471),f26(x2471,f26(x2472,x2472))),f26(x2473,x2473))),f12(f21(a4)))),
% 0.48/0.69 inference(scs_inference,[],[189,160])).
% 0.48/0.69 cnf(253,plain,
% 0.48/0.69 (~P5(x2531,f10(f9(f7(f26(x2531,x2531),a19))))),
% 0.48/0.69 inference(rename_variables,[],[187])).
% 0.48/0.69 cnf(259,plain,
% 0.48/0.69 (~E(f26(f5(a25),f5(a25)),a4)),
% 0.48/0.69 inference(scs_inference,[],[195,201,222,187,189,205,160,80,2,77,159,100,38])).
% 0.48/0.69 cnf(267,plain,
% 0.48/0.69 (P5(a25,f26(f26(f5(a25),f5(a25)),x2671))),
% 0.48/0.69 inference(scs_inference,[],[52,198,195,201,222,208,184,187,189,178,205,71,160,80,2,77,159,100,38,114,37,30,3,32])).
% 0.48/0.69 cnf(268,plain,
% 0.48/0.69 (P5(f26(x2681,x2681),f26(f26(x2681,x2681),x2682))),
% 0.48/0.69 inference(rename_variables,[],[208])).
% 0.48/0.69 cnf(273,plain,
% 0.48/0.69 (E(f22(a25),f5(a25))),
% 0.48/0.69 inference(scs_inference,[],[52,198,195,201,222,208,268,184,187,253,189,178,205,71,160,80,2,77,159,100,38,114,37,30,3,32,33,83,105])).
% 0.48/0.69 cnf(303,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(scs_inference,[],[69,259,267,49,216,273,247,160,80,77,159,2,108,100]),
% 0.48/0.69 ['proof']).
% 0.48/0.69 % SZS output end Proof
% 0.48/0.69 % Total time :0.070000s
%------------------------------------------------------------------------------