TSTP Solution File: SEU200+2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU200+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n018.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 16:18:21 EDT 2023
% Result : Theorem 1.60s 1.75s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU200+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 01:42:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 1.60/1.72 %-------------------------------------------
% 1.60/1.72 % File :CSE---1.6
% 1.60/1.72 % Problem :theBenchmark
% 1.60/1.72 % Transform :cnf
% 1.60/1.72 % Format :tptp:raw
% 1.60/1.72 % Command :java -jar mcs_scs.jar %d %s
% 1.60/1.72
% 1.60/1.72 % Result :Theorem 0.990000s
% 1.60/1.72 % Output :CNFRefutation 0.990000s
% 1.60/1.72 %-------------------------------------------
% 1.60/1.72 %------------------------------------------------------------------------------
% 1.60/1.72 % File : SEU200+2 : TPTP v8.1.2. Released v3.3.0.
% 1.60/1.72 % Domain : Set theory
% 1.60/1.72 % Problem : MPTP chainy problem t118_relat_1
% 1.60/1.72 % Version : [Urb07] axioms : Especial.
% 1.60/1.72 % English :
% 1.60/1.72
% 1.60/1.72 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 1.60/1.72 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 1.60/1.72 % Source : [Urb07]
% 1.60/1.72 % Names : chainy-t118_relat_1 [Urb07]
% 1.60/1.72
% 1.60/1.72 % Status : Theorem
% 1.60/1.72 % Rating : 0.14 v7.5.0, 0.16 v7.4.0, 0.13 v7.3.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.21 v6.2.0, 0.24 v6.1.0, 0.30 v6.0.0, 0.26 v5.4.0, 0.36 v5.3.0, 0.41 v5.2.0, 0.25 v5.1.0, 0.29 v5.0.0, 0.33 v4.1.0, 0.39 v4.0.0, 0.42 v3.7.0, 0.40 v3.5.0, 0.37 v3.4.0, 0.42 v3.3.0
% 1.60/1.72 % Syntax : Number of formulae : 193 ( 49 unt; 0 def)
% 1.60/1.72 % Number of atoms : 490 ( 109 equ)
% 1.60/1.72 % Maximal formula atoms : 11 ( 2 avg)
% 1.60/1.72 % Number of connectives : 362 ( 65 ~; 7 |; 86 &)
% 1.60/1.72 % ( 64 <=>; 140 =>; 0 <=; 0 <~>)
% 1.60/1.72 % Maximal formula depth : 14 ( 5 avg)
% 1.60/1.73 % Maximal term depth : 3 ( 1 avg)
% 1.60/1.73 % Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% 1.60/1.73 % Number of functors : 25 ( 25 usr; 1 con; 0-3 aty)
% 1.60/1.73 % Number of variables : 413 ( 396 !; 17 ?)
% 1.60/1.73 % SPC : FOF_THM_RFO_SEQ
% 1.60/1.73
% 1.60/1.73 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 1.60/1.73 % library, www.mizar.org
% 1.60/1.73 %------------------------------------------------------------------------------
% 1.60/1.73 fof(antisymmetry_r2_hidden,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( in(A,B)
% 1.60/1.73 => ~ in(B,A) ) ).
% 1.60/1.73
% 1.60/1.73 fof(antisymmetry_r2_xboole_0,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( proper_subset(A,B)
% 1.60/1.73 => ~ proper_subset(B,A) ) ).
% 1.60/1.73
% 1.60/1.73 fof(cc1_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( empty(A)
% 1.60/1.73 => relation(A) ) ).
% 1.60/1.73
% 1.60/1.73 fof(commutativity_k2_tarski,axiom,
% 1.60/1.73 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 1.60/1.73
% 1.60/1.73 fof(commutativity_k2_xboole_0,axiom,
% 1.60/1.73 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 1.60/1.73
% 1.60/1.73 fof(commutativity_k3_xboole_0,axiom,
% 1.60/1.73 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 1.60/1.73
% 1.60/1.73 fof(d10_relat_1,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( relation(B)
% 1.60/1.73 => ( B = identity_relation(A)
% 1.60/1.73 <=> ! [C,D] :
% 1.60/1.73 ( in(ordered_pair(C,D),B)
% 1.60/1.73 <=> ( in(C,A)
% 1.60/1.73 & C = D ) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d10_xboole_0,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( A = B
% 1.60/1.73 <=> ( subset(A,B)
% 1.60/1.73 & subset(B,A) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d11_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( relation(A)
% 1.60/1.73 => ! [B,C] :
% 1.60/1.73 ( relation(C)
% 1.60/1.73 => ( C = relation_dom_restriction(A,B)
% 1.60/1.73 <=> ! [D,E] :
% 1.60/1.73 ( in(ordered_pair(D,E),C)
% 1.60/1.73 <=> ( in(D,B)
% 1.60/1.73 & in(ordered_pair(D,E),A) ) ) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d12_relat_1,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( relation(B)
% 1.60/1.73 => ! [C] :
% 1.60/1.73 ( relation(C)
% 1.60/1.73 => ( C = relation_rng_restriction(A,B)
% 1.60/1.73 <=> ! [D,E] :
% 1.60/1.73 ( in(ordered_pair(D,E),C)
% 1.60/1.73 <=> ( in(E,A)
% 1.60/1.73 & in(ordered_pair(D,E),B) ) ) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d1_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( relation(A)
% 1.60/1.73 <=> ! [B] :
% 1.60/1.73 ~ ( in(B,A)
% 1.60/1.73 & ! [C,D] : B != ordered_pair(C,D) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d1_setfam_1,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( ( A != empty_set
% 1.60/1.73 => ( B = set_meet(A)
% 1.60/1.73 <=> ! [C] :
% 1.60/1.73 ( in(C,B)
% 1.60/1.73 <=> ! [D] :
% 1.60/1.73 ( in(D,A)
% 1.60/1.73 => in(C,D) ) ) ) )
% 1.60/1.73 & ( A = empty_set
% 1.60/1.73 => ( B = set_meet(A)
% 1.60/1.73 <=> B = empty_set ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d1_tarski,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( B = singleton(A)
% 1.60/1.73 <=> ! [C] :
% 1.60/1.73 ( in(C,B)
% 1.60/1.73 <=> C = A ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d1_xboole_0,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( A = empty_set
% 1.60/1.73 <=> ! [B] : ~ in(B,A) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d1_zfmisc_1,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( B = powerset(A)
% 1.60/1.73 <=> ! [C] :
% 1.60/1.73 ( in(C,B)
% 1.60/1.73 <=> subset(C,A) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d2_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( relation(A)
% 1.60/1.73 => ! [B] :
% 1.60/1.73 ( relation(B)
% 1.60/1.73 => ( A = B
% 1.60/1.73 <=> ! [C,D] :
% 1.60/1.73 ( in(ordered_pair(C,D),A)
% 1.60/1.73 <=> in(ordered_pair(C,D),B) ) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d2_subset_1,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( ( ~ empty(A)
% 1.60/1.73 => ( element(B,A)
% 1.60/1.73 <=> in(B,A) ) )
% 1.60/1.73 & ( empty(A)
% 1.60/1.73 => ( element(B,A)
% 1.60/1.73 <=> empty(B) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d2_tarski,axiom,
% 1.60/1.73 ! [A,B,C] :
% 1.60/1.73 ( C = unordered_pair(A,B)
% 1.60/1.73 <=> ! [D] :
% 1.60/1.73 ( in(D,C)
% 1.60/1.73 <=> ( D = A
% 1.60/1.73 | D = B ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d2_xboole_0,axiom,
% 1.60/1.73 ! [A,B,C] :
% 1.60/1.73 ( C = set_union2(A,B)
% 1.60/1.73 <=> ! [D] :
% 1.60/1.73 ( in(D,C)
% 1.60/1.73 <=> ( in(D,A)
% 1.60/1.73 | in(D,B) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d2_zfmisc_1,axiom,
% 1.60/1.73 ! [A,B,C] :
% 1.60/1.73 ( C = cartesian_product2(A,B)
% 1.60/1.73 <=> ! [D] :
% 1.60/1.73 ( in(D,C)
% 1.60/1.73 <=> ? [E,F] :
% 1.60/1.73 ( in(E,A)
% 1.60/1.73 & in(F,B)
% 1.60/1.73 & D = ordered_pair(E,F) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d3_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( relation(A)
% 1.60/1.73 => ! [B] :
% 1.60/1.73 ( relation(B)
% 1.60/1.73 => ( subset(A,B)
% 1.60/1.73 <=> ! [C,D] :
% 1.60/1.73 ( in(ordered_pair(C,D),A)
% 1.60/1.73 => in(ordered_pair(C,D),B) ) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d3_tarski,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( subset(A,B)
% 1.60/1.73 <=> ! [C] :
% 1.60/1.73 ( in(C,A)
% 1.60/1.73 => in(C,B) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d3_xboole_0,axiom,
% 1.60/1.73 ! [A,B,C] :
% 1.60/1.73 ( C = set_intersection2(A,B)
% 1.60/1.73 <=> ! [D] :
% 1.60/1.73 ( in(D,C)
% 1.60/1.73 <=> ( in(D,A)
% 1.60/1.73 & in(D,B) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d4_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( relation(A)
% 1.60/1.73 => ! [B] :
% 1.60/1.73 ( B = relation_dom(A)
% 1.60/1.73 <=> ! [C] :
% 1.60/1.73 ( in(C,B)
% 1.60/1.73 <=> ? [D] : in(ordered_pair(C,D),A) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d4_subset_1,axiom,
% 1.60/1.73 ! [A] : cast_to_subset(A) = A ).
% 1.60/1.73
% 1.60/1.73 fof(d4_tarski,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( B = union(A)
% 1.60/1.73 <=> ! [C] :
% 1.60/1.73 ( in(C,B)
% 1.60/1.73 <=> ? [D] :
% 1.60/1.73 ( in(C,D)
% 1.60/1.73 & in(D,A) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d4_xboole_0,axiom,
% 1.60/1.73 ! [A,B,C] :
% 1.60/1.73 ( C = set_difference(A,B)
% 1.60/1.73 <=> ! [D] :
% 1.60/1.73 ( in(D,C)
% 1.60/1.73 <=> ( in(D,A)
% 1.60/1.73 & ~ in(D,B) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d5_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( relation(A)
% 1.60/1.73 => ! [B] :
% 1.60/1.73 ( B = relation_rng(A)
% 1.60/1.73 <=> ! [C] :
% 1.60/1.73 ( in(C,B)
% 1.60/1.73 <=> ? [D] : in(ordered_pair(D,C),A) ) ) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d5_subset_1,axiom,
% 1.60/1.73 ! [A,B] :
% 1.60/1.73 ( element(B,powerset(A))
% 1.60/1.73 => subset_complement(A,B) = set_difference(A,B) ) ).
% 1.60/1.73
% 1.60/1.73 fof(d5_tarski,axiom,
% 1.60/1.73 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ).
% 1.60/1.73
% 1.60/1.73 fof(d6_relat_1,axiom,
% 1.60/1.73 ! [A] :
% 1.60/1.73 ( relation(A)
% 1.60/1.73 => relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(d7_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( relation(A)
% 1.60/1.74 => ! [B] :
% 1.60/1.74 ( relation(B)
% 1.60/1.74 => ( B = relation_inverse(A)
% 1.60/1.74 <=> ! [C,D] :
% 1.60/1.74 ( in(ordered_pair(C,D),B)
% 1.60/1.74 <=> in(ordered_pair(D,C),A) ) ) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(d7_xboole_0,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( disjoint(A,B)
% 1.60/1.74 <=> set_intersection2(A,B) = empty_set ) ).
% 1.60/1.74
% 1.60/1.74 fof(d8_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( relation(A)
% 1.60/1.74 => ! [B] :
% 1.60/1.74 ( relation(B)
% 1.60/1.74 => ! [C] :
% 1.60/1.74 ( relation(C)
% 1.60/1.74 => ( C = relation_composition(A,B)
% 1.60/1.74 <=> ! [D,E] :
% 1.60/1.74 ( in(ordered_pair(D,E),C)
% 1.60/1.74 <=> ? [F] :
% 1.60/1.74 ( in(ordered_pair(D,F),A)
% 1.60/1.74 & in(ordered_pair(F,E),B) ) ) ) ) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(d8_setfam_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(powerset(A)))
% 1.60/1.74 => ! [C] :
% 1.60/1.74 ( element(C,powerset(powerset(A)))
% 1.60/1.74 => ( C = complements_of_subsets(A,B)
% 1.60/1.74 <=> ! [D] :
% 1.60/1.74 ( element(D,powerset(A))
% 1.60/1.74 => ( in(D,C)
% 1.60/1.74 <=> in(subset_complement(A,D),B) ) ) ) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(d8_xboole_0,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( proper_subset(A,B)
% 1.60/1.74 <=> ( subset(A,B)
% 1.60/1.74 & A != B ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k1_relat_1,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k1_setfam_1,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k1_tarski,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k1_xboole_0,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k1_zfmisc_1,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k2_relat_1,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k2_subset_1,axiom,
% 1.60/1.74 ! [A] : element(cast_to_subset(A),powerset(A)) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k2_tarski,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k2_xboole_0,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k2_zfmisc_1,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k3_relat_1,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k3_subset_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(A))
% 1.60/1.74 => element(subset_complement(A,B),powerset(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k3_tarski,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k3_xboole_0,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k4_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( relation(A)
% 1.60/1.74 => relation(relation_inverse(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k4_tarski,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k4_xboole_0,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k5_relat_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ( relation(A)
% 1.60/1.74 & relation(B) )
% 1.60/1.74 => relation(relation_composition(A,B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k5_setfam_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(powerset(A)))
% 1.60/1.74 => element(union_of_subsets(A,B),powerset(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k6_relat_1,axiom,
% 1.60/1.74 ! [A] : relation(identity_relation(A)) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k6_setfam_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(powerset(A)))
% 1.60/1.74 => element(meet_of_subsets(A,B),powerset(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k6_subset_1,axiom,
% 1.60/1.74 ! [A,B,C] :
% 1.60/1.74 ( ( element(B,powerset(A))
% 1.60/1.74 & element(C,powerset(A)) )
% 1.60/1.74 => element(subset_difference(A,B,C),powerset(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k7_relat_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( relation(A)
% 1.60/1.74 => relation(relation_dom_restriction(A,B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k7_setfam_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(powerset(A)))
% 1.60/1.74 => element(complements_of_subsets(A,B),powerset(powerset(A))) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_k8_relat_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( relation(B)
% 1.60/1.74 => relation(relation_rng_restriction(A,B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(dt_m1_subset_1,axiom,
% 1.60/1.74 $true ).
% 1.60/1.74
% 1.60/1.74 fof(existence_m1_subset_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ? [B] : element(B,A) ).
% 1.60/1.74
% 1.60/1.74 fof(fc10_relat_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ( empty(A)
% 1.60/1.74 & relation(B) )
% 1.60/1.74 => ( empty(relation_composition(B,A))
% 1.60/1.74 & relation(relation_composition(B,A)) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc1_relat_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ( relation(A)
% 1.60/1.74 & relation(B) )
% 1.60/1.74 => relation(set_intersection2(A,B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc1_subset_1,axiom,
% 1.60/1.74 ! [A] : ~ empty(powerset(A)) ).
% 1.60/1.74
% 1.60/1.74 fof(fc1_xboole_0,axiom,
% 1.60/1.74 empty(empty_set) ).
% 1.60/1.74
% 1.60/1.74 fof(fc1_zfmisc_1,axiom,
% 1.60/1.74 ! [A,B] : ~ empty(ordered_pair(A,B)) ).
% 1.60/1.74
% 1.60/1.74 fof(fc2_relat_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ( relation(A)
% 1.60/1.74 & relation(B) )
% 1.60/1.74 => relation(set_union2(A,B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc2_subset_1,axiom,
% 1.60/1.74 ! [A] : ~ empty(singleton(A)) ).
% 1.60/1.74
% 1.60/1.74 fof(fc2_xboole_0,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ~ empty(A)
% 1.60/1.74 => ~ empty(set_union2(A,B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc3_subset_1,axiom,
% 1.60/1.74 ! [A,B] : ~ empty(unordered_pair(A,B)) ).
% 1.60/1.74
% 1.60/1.74 fof(fc3_xboole_0,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ~ empty(A)
% 1.60/1.74 => ~ empty(set_union2(B,A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc4_relat_1,axiom,
% 1.60/1.74 ( empty(empty_set)
% 1.60/1.74 & relation(empty_set) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc4_subset_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ( ~ empty(A)
% 1.60/1.74 & ~ empty(B) )
% 1.60/1.74 => ~ empty(cartesian_product2(A,B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc5_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( ( ~ empty(A)
% 1.60/1.74 & relation(A) )
% 1.60/1.74 => ~ empty(relation_dom(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc6_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( ( ~ empty(A)
% 1.60/1.74 & relation(A) )
% 1.60/1.74 => ~ empty(relation_rng(A)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc7_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( empty(A)
% 1.60/1.74 => ( empty(relation_dom(A))
% 1.60/1.74 & relation(relation_dom(A)) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc8_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( empty(A)
% 1.60/1.74 => ( empty(relation_rng(A))
% 1.60/1.74 & relation(relation_rng(A)) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(fc9_relat_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ( empty(A)
% 1.60/1.74 & relation(B) )
% 1.60/1.74 => ( empty(relation_composition(A,B))
% 1.60/1.74 & relation(relation_composition(A,B)) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(idempotence_k2_xboole_0,axiom,
% 1.60/1.74 ! [A,B] : set_union2(A,A) = A ).
% 1.60/1.74
% 1.60/1.74 fof(idempotence_k3_xboole_0,axiom,
% 1.60/1.74 ! [A,B] : set_intersection2(A,A) = A ).
% 1.60/1.74
% 1.60/1.74 fof(involutiveness_k3_subset_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(A))
% 1.60/1.74 => subset_complement(A,subset_complement(A,B)) = B ) ).
% 1.60/1.74
% 1.60/1.74 fof(involutiveness_k4_relat_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( relation(A)
% 1.60/1.74 => relation_inverse(relation_inverse(A)) = A ) ).
% 1.60/1.74
% 1.60/1.74 fof(involutiveness_k7_setfam_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(powerset(A)))
% 1.60/1.74 => complements_of_subsets(A,complements_of_subsets(A,B)) = B ) ).
% 1.60/1.74
% 1.60/1.74 fof(irreflexivity_r2_xboole_0,axiom,
% 1.60/1.74 ! [A,B] : ~ proper_subset(A,A) ).
% 1.60/1.74
% 1.60/1.74 fof(l1_zfmisc_1,lemma,
% 1.60/1.74 ! [A] : singleton(A) != empty_set ).
% 1.60/1.74
% 1.60/1.74 fof(l23_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( in(A,B)
% 1.60/1.74 => set_union2(singleton(A),B) = B ) ).
% 1.60/1.74
% 1.60/1.74 fof(l25_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ~ ( disjoint(singleton(A),B)
% 1.60/1.74 & in(A,B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l28_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ~ in(A,B)
% 1.60/1.74 => disjoint(singleton(A),B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l2_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( subset(singleton(A),B)
% 1.60/1.74 <=> in(A,B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l32_xboole_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( set_difference(A,B) = empty_set
% 1.60/1.74 <=> subset(A,B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l3_subset_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(A))
% 1.60/1.74 => ! [C] :
% 1.60/1.74 ( in(C,B)
% 1.60/1.74 => in(C,A) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l3_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B,C] :
% 1.60/1.74 ( subset(A,B)
% 1.60/1.74 => ( in(C,A)
% 1.60/1.74 | subset(A,set_difference(B,singleton(C))) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l4_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( subset(A,singleton(B))
% 1.60/1.74 <=> ( A = empty_set
% 1.60/1.74 | A = singleton(B) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l50_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( in(A,B)
% 1.60/1.74 => subset(A,union(B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l55_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B,C,D] :
% 1.60/1.74 ( in(ordered_pair(A,B),cartesian_product2(C,D))
% 1.60/1.74 <=> ( in(A,C)
% 1.60/1.74 & in(B,D) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(l71_subset_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( ! [C] :
% 1.60/1.74 ( in(C,A)
% 1.60/1.74 => in(C,B) )
% 1.60/1.74 => element(A,powerset(B)) ) ).
% 1.60/1.74
% 1.60/1.74 fof(rc1_relat_1,axiom,
% 1.60/1.74 ? [A] :
% 1.60/1.74 ( empty(A)
% 1.60/1.74 & relation(A) ) ).
% 1.60/1.74
% 1.60/1.74 fof(rc1_subset_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ( ~ empty(A)
% 1.60/1.74 => ? [B] :
% 1.60/1.74 ( element(B,powerset(A))
% 1.60/1.74 & ~ empty(B) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(rc1_xboole_0,axiom,
% 1.60/1.74 ? [A] : empty(A) ).
% 1.60/1.74
% 1.60/1.74 fof(rc2_relat_1,axiom,
% 1.60/1.74 ? [A] :
% 1.60/1.74 ( ~ empty(A)
% 1.60/1.74 & relation(A) ) ).
% 1.60/1.74
% 1.60/1.74 fof(rc2_subset_1,axiom,
% 1.60/1.74 ! [A] :
% 1.60/1.74 ? [B] :
% 1.60/1.74 ( element(B,powerset(A))
% 1.60/1.74 & empty(B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(rc2_xboole_0,axiom,
% 1.60/1.74 ? [A] : ~ empty(A) ).
% 1.60/1.74
% 1.60/1.74 fof(redefinition_k5_setfam_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(powerset(A)))
% 1.60/1.74 => union_of_subsets(A,B) = union(B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(redefinition_k6_setfam_1,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( element(B,powerset(powerset(A)))
% 1.60/1.74 => meet_of_subsets(A,B) = set_meet(B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(redefinition_k6_subset_1,axiom,
% 1.60/1.74 ! [A,B,C] :
% 1.60/1.74 ( ( element(B,powerset(A))
% 1.60/1.74 & element(C,powerset(A)) )
% 1.60/1.74 => subset_difference(A,B,C) = set_difference(B,C) ) ).
% 1.60/1.74
% 1.60/1.74 fof(reflexivity_r1_tarski,axiom,
% 1.60/1.74 ! [A,B] : subset(A,A) ).
% 1.60/1.74
% 1.60/1.74 fof(symmetry_r1_xboole_0,axiom,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( disjoint(A,B)
% 1.60/1.74 => disjoint(B,A) ) ).
% 1.60/1.74
% 1.60/1.74 fof(t106_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B,C,D] :
% 1.60/1.74 ( in(ordered_pair(A,B),cartesian_product2(C,D))
% 1.60/1.74 <=> ( in(A,C)
% 1.60/1.74 & in(B,D) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(t10_zfmisc_1,lemma,
% 1.60/1.74 ! [A,B,C,D] :
% 1.60/1.74 ~ ( unordered_pair(A,B) = unordered_pair(C,D)
% 1.60/1.74 & A != C
% 1.60/1.74 & A != D ) ).
% 1.60/1.74
% 1.60/1.74 fof(t115_relat_1,lemma,
% 1.60/1.74 ! [A,B,C] :
% 1.60/1.74 ( relation(C)
% 1.60/1.74 => ( in(A,relation_rng(relation_rng_restriction(B,C)))
% 1.60/1.74 <=> ( in(A,B)
% 1.60/1.74 & in(A,relation_rng(C)) ) ) ) ).
% 1.60/1.74
% 1.60/1.74 fof(t116_relat_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( relation(B)
% 1.60/1.74 => subset(relation_rng(relation_rng_restriction(A,B)),A) ) ).
% 1.60/1.74
% 1.60/1.74 fof(t117_relat_1,lemma,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( relation(B)
% 1.60/1.74 => subset(relation_rng_restriction(A,B),B) ) ).
% 1.60/1.74
% 1.60/1.74 fof(t118_relat_1,conjecture,
% 1.60/1.74 ! [A,B] :
% 1.60/1.74 ( relation(B)
% 1.60/1.75 => subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t118_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( subset(A,B)
% 1.60/1.75 => ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
% 1.60/1.75 & subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t119_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B,C,D] :
% 1.60/1.75 ( ( subset(A,B)
% 1.60/1.75 & subset(C,D) )
% 1.60/1.75 => subset(cartesian_product2(A,C),cartesian_product2(B,D)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t12_xboole_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( subset(A,B)
% 1.60/1.75 => set_union2(A,B) = B ) ).
% 1.60/1.75
% 1.60/1.75 fof(t136_zfmisc_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ? [B] :
% 1.60/1.75 ( in(A,B)
% 1.60/1.75 & ! [C,D] :
% 1.60/1.75 ( ( in(C,B)
% 1.60/1.75 & subset(D,C) )
% 1.60/1.75 => in(D,B) )
% 1.60/1.75 & ! [C] :
% 1.60/1.75 ( in(C,B)
% 1.60/1.75 => in(powerset(C),B) )
% 1.60/1.75 & ! [C] :
% 1.60/1.75 ~ ( subset(C,B)
% 1.60/1.75 & ~ are_equipotent(C,B)
% 1.60/1.75 & ~ in(C,B) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t17_xboole_1,lemma,
% 1.60/1.75 ! [A,B] : subset(set_intersection2(A,B),A) ).
% 1.60/1.75
% 1.60/1.75 fof(t19_xboole_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( ( subset(A,B)
% 1.60/1.75 & subset(A,C) )
% 1.60/1.75 => subset(A,set_intersection2(B,C)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t1_boole,axiom,
% 1.60/1.75 ! [A] : set_union2(A,empty_set) = A ).
% 1.60/1.75
% 1.60/1.75 fof(t1_subset,axiom,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( in(A,B)
% 1.60/1.75 => element(A,B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t1_xboole_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( ( subset(A,B)
% 1.60/1.75 & subset(B,C) )
% 1.60/1.75 => subset(A,C) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t1_zfmisc_1,lemma,
% 1.60/1.75 powerset(empty_set) = singleton(empty_set) ).
% 1.60/1.75
% 1.60/1.75 fof(t20_relat_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( relation(C)
% 1.60/1.75 => ( in(ordered_pair(A,B),C)
% 1.60/1.75 => ( in(A,relation_dom(C))
% 1.60/1.75 & in(B,relation_rng(C)) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t21_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t25_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ! [B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => ( subset(A,B)
% 1.60/1.75 => ( subset(relation_dom(A),relation_dom(B))
% 1.60/1.75 & subset(relation_rng(A),relation_rng(B)) ) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t26_xboole_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( subset(A,B)
% 1.60/1.75 => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t28_xboole_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( subset(A,B)
% 1.60/1.75 => set_intersection2(A,B) = A ) ).
% 1.60/1.75
% 1.60/1.75 fof(t2_boole,axiom,
% 1.60/1.75 ! [A] : set_intersection2(A,empty_set) = empty_set ).
% 1.60/1.75
% 1.60/1.75 fof(t2_subset,axiom,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( element(A,B)
% 1.60/1.75 => ( empty(B)
% 1.60/1.75 | in(A,B) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t2_tarski,axiom,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( ! [C] :
% 1.60/1.75 ( in(C,A)
% 1.60/1.75 <=> in(C,B) )
% 1.60/1.75 => A = B ) ).
% 1.60/1.75
% 1.60/1.75 fof(t2_xboole_1,lemma,
% 1.60/1.75 ! [A] : subset(empty_set,A) ).
% 1.60/1.75
% 1.60/1.75 fof(t30_relat_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( relation(C)
% 1.60/1.75 => ( in(ordered_pair(A,B),C)
% 1.60/1.75 => ( in(A,relation_field(C))
% 1.60/1.75 & in(B,relation_field(C)) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t33_xboole_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( subset(A,B)
% 1.60/1.75 => subset(set_difference(A,C),set_difference(B,C)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t33_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B,C,D] :
% 1.60/1.75 ( ordered_pair(A,B) = ordered_pair(C,D)
% 1.60/1.75 => ( A = C
% 1.60/1.75 & B = D ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t36_xboole_1,lemma,
% 1.60/1.75 ! [A,B] : subset(set_difference(A,B),A) ).
% 1.60/1.75
% 1.60/1.75 fof(t37_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ( relation_rng(A) = relation_dom(relation_inverse(A))
% 1.60/1.75 & relation_dom(A) = relation_rng(relation_inverse(A)) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t37_xboole_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( set_difference(A,B) = empty_set
% 1.60/1.75 <=> subset(A,B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t37_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( subset(singleton(A),B)
% 1.60/1.75 <=> in(A,B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t38_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( subset(unordered_pair(A,B),C)
% 1.60/1.75 <=> ( in(A,C)
% 1.60/1.75 & in(B,C) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t39_xboole_1,lemma,
% 1.60/1.75 ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ).
% 1.60/1.75
% 1.60/1.75 fof(t39_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( subset(A,singleton(B))
% 1.60/1.75 <=> ( A = empty_set
% 1.60/1.75 | A = singleton(B) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t3_boole,axiom,
% 1.60/1.75 ! [A] : set_difference(A,empty_set) = A ).
% 1.60/1.75
% 1.60/1.75 fof(t3_subset,axiom,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( element(A,powerset(B))
% 1.60/1.75 <=> subset(A,B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t3_xboole_0,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( ~ ( ~ disjoint(A,B)
% 1.60/1.75 & ! [C] :
% 1.60/1.75 ~ ( in(C,A)
% 1.60/1.75 & in(C,B) ) )
% 1.60/1.75 & ~ ( ? [C] :
% 1.60/1.75 ( in(C,A)
% 1.60/1.75 & in(C,B) )
% 1.60/1.75 & disjoint(A,B) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t3_xboole_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( subset(A,empty_set)
% 1.60/1.75 => A = empty_set ) ).
% 1.60/1.75
% 1.60/1.75 fof(t40_xboole_1,lemma,
% 1.60/1.75 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ).
% 1.60/1.75
% 1.60/1.75 fof(t43_subset_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( element(B,powerset(A))
% 1.60/1.75 => ! [C] :
% 1.60/1.75 ( element(C,powerset(A))
% 1.60/1.75 => ( disjoint(B,C)
% 1.60/1.75 <=> subset(B,subset_complement(A,C)) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t44_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ! [B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t45_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ! [B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t45_xboole_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( subset(A,B)
% 1.60/1.75 => B = set_union2(A,set_difference(B,A)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t46_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ! [B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => ( subset(relation_rng(A),relation_dom(B))
% 1.60/1.75 => relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t46_setfam_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( element(B,powerset(powerset(A)))
% 1.60/1.75 => ~ ( B != empty_set
% 1.60/1.75 & complements_of_subsets(A,B) = empty_set ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t46_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( in(A,B)
% 1.60/1.75 => set_union2(singleton(A),B) = B ) ).
% 1.60/1.75
% 1.60/1.75 fof(t47_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ! [B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => ( subset(relation_dom(A),relation_rng(B))
% 1.60/1.75 => relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t47_setfam_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( element(B,powerset(powerset(A)))
% 1.60/1.75 => ( B != empty_set
% 1.60/1.75 => subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t48_setfam_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( element(B,powerset(powerset(A)))
% 1.60/1.75 => ( B != empty_set
% 1.60/1.75 => union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t48_xboole_1,lemma,
% 1.60/1.75 ! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ).
% 1.60/1.75
% 1.60/1.75 fof(t4_boole,axiom,
% 1.60/1.75 ! [A] : set_difference(empty_set,A) = empty_set ).
% 1.60/1.75
% 1.60/1.75 fof(t4_subset,axiom,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( ( in(A,B)
% 1.60/1.75 & element(B,powerset(C)) )
% 1.60/1.75 => element(A,C) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t4_xboole_0,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( ~ ( ~ disjoint(A,B)
% 1.60/1.75 & ! [C] : ~ in(C,set_intersection2(A,B)) )
% 1.60/1.75 & ~ ( ? [C] : in(C,set_intersection2(A,B))
% 1.60/1.75 & disjoint(A,B) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t50_subset_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( A != empty_set
% 1.60/1.75 => ! [B] :
% 1.60/1.75 ( element(B,powerset(A))
% 1.60/1.75 => ! [C] :
% 1.60/1.75 ( element(C,A)
% 1.60/1.75 => ( ~ in(C,B)
% 1.60/1.75 => in(C,subset_complement(A,B)) ) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t54_subset_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( element(C,powerset(A))
% 1.60/1.75 => ~ ( in(B,subset_complement(A,C))
% 1.60/1.75 & in(B,C) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t56_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ( ! [B,C] : ~ in(ordered_pair(B,C),A)
% 1.60/1.75 => A = empty_set ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t5_subset,axiom,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ~ ( in(A,B)
% 1.60/1.75 & element(B,powerset(C))
% 1.60/1.75 & empty(C) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t60_relat_1,lemma,
% 1.60/1.75 ( relation_dom(empty_set) = empty_set
% 1.60/1.75 & relation_rng(empty_set) = empty_set ) ).
% 1.60/1.75
% 1.60/1.75 fof(t60_xboole_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ~ ( subset(A,B)
% 1.60/1.75 & proper_subset(B,A) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t63_xboole_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( ( subset(A,B)
% 1.60/1.75 & disjoint(B,C) )
% 1.60/1.75 => disjoint(A,C) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t64_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ( ( relation_dom(A) = empty_set
% 1.60/1.75 | relation_rng(A) = empty_set )
% 1.60/1.75 => A = empty_set ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t65_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation(A)
% 1.60/1.75 => ( relation_dom(A) = empty_set
% 1.60/1.75 <=> relation_rng(A) = empty_set ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t65_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( set_difference(A,singleton(B)) = A
% 1.60/1.75 <=> ~ in(B,A) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t69_enumset1,lemma,
% 1.60/1.75 ! [A] : unordered_pair(A,A) = singleton(A) ).
% 1.60/1.75
% 1.60/1.75 fof(t6_boole,axiom,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( empty(A)
% 1.60/1.75 => A = empty_set ) ).
% 1.60/1.75
% 1.60/1.75 fof(t6_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( subset(singleton(A),singleton(B))
% 1.60/1.75 => A = B ) ).
% 1.60/1.75
% 1.60/1.75 fof(t71_relat_1,lemma,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ( relation_dom(identity_relation(A)) = A
% 1.60/1.75 & relation_rng(identity_relation(A)) = A ) ).
% 1.60/1.75
% 1.60/1.75 fof(t74_relat_1,lemma,
% 1.60/1.75 ! [A,B,C,D] :
% 1.60/1.75 ( relation(D)
% 1.60/1.75 => ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
% 1.60/1.75 <=> ( in(A,C)
% 1.60/1.75 & in(ordered_pair(A,B),D) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t7_boole,axiom,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ~ ( in(A,B)
% 1.60/1.75 & empty(B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t7_xboole_1,lemma,
% 1.60/1.75 ! [A,B] : subset(A,set_union2(A,B)) ).
% 1.60/1.75
% 1.60/1.75 fof(t83_xboole_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( disjoint(A,B)
% 1.60/1.75 <=> set_difference(A,B) = A ) ).
% 1.60/1.75
% 1.60/1.75 fof(t86_relat_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( relation(C)
% 1.60/1.75 => ( in(A,relation_dom(relation_dom_restriction(C,B)))
% 1.60/1.75 <=> ( in(A,B)
% 1.60/1.75 & in(A,relation_dom(C)) ) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t88_relat_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => subset(relation_dom_restriction(B,A),B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t8_boole,axiom,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ~ ( empty(A)
% 1.60/1.75 & A != B
% 1.60/1.75 & empty(B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t8_xboole_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( ( subset(A,B)
% 1.60/1.75 & subset(C,B) )
% 1.60/1.75 => subset(set_union2(A,C),B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t8_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( singleton(A) = unordered_pair(B,C)
% 1.60/1.75 => A = B ) ).
% 1.60/1.75
% 1.60/1.75 fof(t90_relat_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t92_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( in(A,B)
% 1.60/1.75 => subset(A,union(B)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t94_relat_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t99_relat_1,lemma,
% 1.60/1.75 ! [A,B] :
% 1.60/1.75 ( relation(B)
% 1.60/1.75 => subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t99_zfmisc_1,lemma,
% 1.60/1.75 ! [A] : union(powerset(A)) = A ).
% 1.60/1.75
% 1.60/1.75 fof(t9_tarski,axiom,
% 1.60/1.75 ! [A] :
% 1.60/1.75 ? [B] :
% 1.60/1.75 ( in(A,B)
% 1.60/1.75 & ! [C,D] :
% 1.60/1.75 ( ( in(C,B)
% 1.60/1.75 & subset(D,C) )
% 1.60/1.75 => in(D,B) )
% 1.60/1.75 & ! [C] :
% 1.60/1.75 ~ ( in(C,B)
% 1.60/1.75 & ! [D] :
% 1.60/1.75 ~ ( in(D,B)
% 1.60/1.75 & ! [E] :
% 1.60/1.75 ( subset(E,C)
% 1.60/1.75 => in(E,D) ) ) )
% 1.60/1.75 & ! [C] :
% 1.60/1.75 ~ ( subset(C,B)
% 1.60/1.75 & ~ are_equipotent(C,B)
% 1.60/1.75 & ~ in(C,B) ) ) ).
% 1.60/1.75
% 1.60/1.75 fof(t9_zfmisc_1,lemma,
% 1.60/1.75 ! [A,B,C] :
% 1.60/1.75 ( singleton(A) = unordered_pair(B,C)
% 1.60/1.75 => B = C ) ).
% 1.60/1.75
% 1.60/1.75 %------------------------------------------------------------------------------
% 1.60/1.75 %-------------------------------------------
% 1.60/1.75 % Proof found
% 1.60/1.75 % SZS status Theorem for theBenchmark
% 1.60/1.75 % SZS output start Proof
% 1.60/1.75 %ClaNum:505(EqnAxiom:181)
% 1.60/1.75 %VarNum:2311(SingletonVarNum:715)
% 1.60/1.75 %MaxLitNum:7
% 1.60/1.75 %MaxfuncDepth:3
% 1.60/1.75 %SharedTerms:27
% 1.60/1.75 %goalClause: 191 226
% 1.60/1.75 %singleGoalClaCount:2
% 1.60/1.75 [185]P1(a1)
% 1.60/1.75 [186]P1(a5)
% 1.60/1.75 [187]P1(a47)
% 1.60/1.75 [188]P5(a1)
% 1.60/1.75 [189]P5(a5)
% 1.60/1.75 [190]P5(a50)
% 1.60/1.75 [191]P5(a51)
% 1.60/1.75 [219]~P1(a50)
% 1.60/1.75 [220]~P1(a53)
% 1.60/1.75 [182]E(f4(a1),a1)
% 1.60/1.75 [183]E(f72(a1),a1)
% 1.60/1.75 [201]E(f83(a1,a1),f69(a1))
% 1.60/1.75 [226]~P8(f72(f78(a54,a51)),f72(a51))
% 1.60/1.75 [198]P8(a1,x1981)
% 1.60/1.75 [202]P8(x2021,x2021)
% 1.60/1.75 [223]~P7(x2231,x2231)
% 1.60/1.75 [192]P1(f52(x1921))
% 1.60/1.75 [193]P5(f55(x1931))
% 1.60/1.75 [197]E(f77(a1,x1971),a1)
% 1.60/1.75 [199]E(f79(x1991,a1),x1991)
% 1.60/1.75 [200]E(f77(x2001,a1),x2001)
% 1.60/1.75 [203]E(f79(x2031,x2031),x2031)
% 1.60/1.75 [204]P6(x2041,f56(x2041))
% 1.60/1.75 [205]P6(x2051,f57(x2051))
% 1.60/1.75 [206]P2(x2061,f69(x2061))
% 1.60/1.75 [207]P2(f6(x2071),x2071)
% 1.60/1.75 [208]P2(f52(x2081),f69(x2081))
% 1.60/1.75 [221]~P1(f69(x2211))
% 1.60/1.75 [222]~E(f83(x2221,x2221),a1)
% 1.60/1.75 [194]E(f4(f55(x1941)),x1941)
% 1.60/1.75 [195]E(f76(f69(x1951)),x1951)
% 1.60/1.75 [196]E(f72(f55(x1961)),x1961)
% 1.60/1.75 [211]E(f77(x2111,f77(x2111,a1)),a1)
% 1.60/1.75 [214]E(f77(x2141,f77(x2141,x2141)),x2141)
% 1.60/1.75 [209]E(f83(x2091,x2092),f83(x2092,x2091))
% 1.60/1.75 [210]E(f79(x2101,x2102),f79(x2102,x2101))
% 1.60/1.75 [212]P8(x2121,f79(x2121,x2122))
% 1.60/1.75 [213]P8(f77(x2131,x2132),x2131)
% 1.60/1.75 [224]~P1(f83(x2241,x2242))
% 1.60/1.75 [215]E(f79(x2151,f77(x2152,x2151)),f79(x2151,x2152))
% 1.60/1.75 [216]E(f77(f79(x2161,x2162),x2162),f77(x2161,x2162))
% 1.60/1.75 [217]E(f77(x2171,f77(x2171,x2172)),f77(x2172,f77(x2172,x2171)))
% 1.60/1.75 [228]~P1(x2281)+E(x2281,a1)
% 1.60/1.75 [230]~P1(x2301)+P5(x2301)
% 1.60/1.75 [248]~P8(x2481,a1)+E(x2481,a1)
% 1.60/1.75 [235]~P1(x2351)+P1(f4(x2351))
% 1.60/1.75 [236]~P1(x2361)+P1(f72(x2361))
% 1.60/1.75 [237]~P1(x2371)+P5(f4(x2371))
% 1.60/1.75 [238]~P1(x2381)+P5(f72(x2381))
% 1.60/1.75 [239]~P5(x2391)+P5(f73(x2391))
% 1.60/1.75 [245]P1(x2451)+~P1(f48(x2451))
% 1.60/1.75 [249]P6(f7(x2491),x2491)+E(x2491,a1)
% 1.60/1.75 [250]P5(x2501)+P6(f64(x2501),x2501)
% 1.60/1.75 [257]P1(x2571)+P2(f48(x2571),f69(x2571))
% 1.60/1.75 [242]~P5(x2421)+E(f73(f73(x2421)),x2421)
% 1.60/1.75 [246]~P5(x2461)+E(f72(f73(x2461)),f4(x2461))
% 1.60/1.75 [247]~P5(x2471)+E(f4(f73(x2471)),f72(x2471))
% 1.60/1.75 [268]~P5(x2681)+E(f79(f4(x2681),f72(x2681)),f75(x2681))
% 1.60/1.75 [343]~P5(x3431)+P8(x3431,f2(f4(x3431),f72(x3431)))
% 1.60/1.75 [241]~E(x2411,x2412)+P8(x2411,x2412)
% 1.60/1.75 [251]~P6(x2512,x2511)+~E(x2511,a1)
% 1.60/1.75 [252]~P7(x2521,x2522)+~E(x2521,x2522)
% 1.60/1.75 [256]~P1(x2561)+~P6(x2562,x2561)
% 1.60/1.75 [263]~P7(x2631,x2632)+P8(x2631,x2632)
% 1.60/1.75 [264]~P6(x2641,x2642)+P2(x2641,x2642)
% 1.60/1.75 [265]~P3(x2652,x2651)+P3(x2651,x2652)
% 1.60/1.75 [291]~P6(x2912,x2911)+~P6(x2911,x2912)
% 1.60/1.75 [292]~P7(x2922,x2921)+~P7(x2921,x2922)
% 1.60/1.75 [293]~P8(x2932,x2931)+~P7(x2931,x2932)
% 1.60/1.75 [260]~P8(x2601,x2602)+E(f77(x2601,x2602),a1)
% 1.60/1.75 [262]P8(x2621,x2622)+~E(f77(x2621,x2622),a1)
% 1.60/1.75 [266]~P5(x2661)+P5(f74(x2661,x2662))
% 1.60/1.75 [267]~P5(x2672)+P5(f78(x2671,x2672))
% 1.60/1.75 [269]~P8(x2691,x2692)+E(f79(x2691,x2692),x2692)
% 1.60/1.75 [270]~P3(x2701,x2702)+E(f77(x2701,x2702),x2701)
% 1.60/1.75 [271]P3(x2711,x2712)+~E(f77(x2711,x2712),x2711)
% 1.60/1.75 [281]~E(x2811,a1)+P8(x2811,f83(x2812,x2812))
% 1.60/1.75 [283]~P6(x2831,x2832)+P8(x2831,f76(x2832))
% 1.60/1.75 [284]~P8(x2841,x2842)+P2(x2841,f69(x2842))
% 1.60/1.75 [298]P8(x2981,x2982)+~P2(x2981,f69(x2982))
% 1.60/1.75 [299]~P5(x2991)+P8(f74(x2991,x2992),x2991)
% 1.60/1.75 [300]~P5(x3002)+P8(f78(x3001,x3002),x3002)
% 1.60/1.75 [305]P1(x3051)+~P1(f79(x3052,x3051))
% 1.60/1.75 [306]P1(x3061)+~P1(f79(x3061,x3062))
% 1.60/1.75 [307]P6(x3071,x3072)+P3(f83(x3071,x3071),x3072)
% 1.60/1.75 [308]P8(x3081,x3082)+P6(f12(x3081,x3082),x3081)
% 1.60/1.75 [309]P3(x3091,x3092)+P6(f58(x3091,x3092),x3092)
% 1.60/1.75 [310]P3(x3101,x3102)+P6(f58(x3101,x3102),x3101)
% 1.60/1.75 [313]P6(f69(x3131),f56(x3132))+~P6(x3131,f56(x3132))
% 1.60/1.75 [317]~P2(x3172,f69(x3171))+E(f81(x3171,x3172),f77(x3171,x3172))
% 1.60/1.75 [318]P6(f46(x3181,x3182),x3181)+P2(x3181,f69(x3182))
% 1.60/1.75 [325]~P6(x3251,x3252)+P8(f83(x3251,x3251),x3252)
% 1.60/1.75 [357]P8(x3571,x3572)+~P6(f12(x3571,x3572),x3572)
% 1.60/1.75 [358]~P6(x3582,f57(x3581))+P6(f65(x3581,x3582),f57(x3581))
% 1.60/1.75 [359]~P2(x3592,f69(x3591))+P2(f81(x3591,x3592),f69(x3591))
% 1.60/1.75 [364]~P6(f46(x3641,x3642),x3642)+P2(x3641,f69(x3642))
% 1.60/1.75 [370]~P6(x3701,x3702)+~P3(f83(x3701,x3701),x3702)
% 1.60/1.75 [388]E(x3881,x3882)+~P8(f83(x3881,x3881),f83(x3882,x3882))
% 1.60/1.75 [273]~P5(x2732)+E(f71(f55(x2731),x2732),f74(x2732,x2731))
% 1.60/1.75 [311]P6(x3112,x3111)+E(f77(x3111,f83(x3112,x3112)),x3111)
% 1.60/1.75 [323]~P3(x3231,x3232)+E(f77(x3231,f77(x3231,x3232)),a1)
% 1.60/1.75 [328]~P8(x3281,x3282)+E(f79(x3281,f77(x3282,x3281)),x3282)
% 1.60/1.75 [329]~P8(x3291,x3292)+E(f77(x3291,f77(x3291,x3292)),x3291)
% 1.60/1.75 [331]~P6(x3311,x3312)+E(f79(f83(x3311,x3311),x3312),x3312)
% 1.60/1.75 [339]E(f84(x3391,x3392),f76(x3392))+~P2(x3392,f69(f69(x3391)))
% 1.60/1.75 [340]E(f70(x3401,x3402),f80(x3402))+~P2(x3402,f69(f69(x3401)))
% 1.60/1.75 [344]~P2(x3442,f69(x3441))+E(f81(x3441,f81(x3441,x3442)),x3442)
% 1.60/1.75 [352]P3(x3521,x3522)+~E(f77(x3521,f77(x3521,x3522)),a1)
% 1.60/1.75 [360]~P5(x3602)+P8(f72(f78(x3601,x3602)),x3601)
% 1.60/1.75 [365]~P5(x3651)+P8(f72(f74(x3651,x3652)),f72(x3651))
% 1.60/1.75 [371]~P6(x3712,x3711)+~E(f77(x3711,f83(x3712,x3712)),x3711)
% 1.60/1.75 [377]~P2(x3772,f69(f69(x3771)))+E(f3(x3771,f3(x3771,x3772)),x3772)
% 1.60/1.75 [383]P2(f84(x3831,x3832),f69(x3831))+~P2(x3832,f69(f69(x3831)))
% 1.60/1.75 [384]P2(f70(x3841,x3842),f69(x3841))+~P2(x3842,f69(f69(x3841)))
% 1.60/1.75 [389]~P2(x3892,f69(f69(x3891)))+P2(f3(x3891,x3892),f69(f69(x3891)))
% 1.60/1.75 [402]P3(x4021,x4022)+P6(f60(x4021,x4022),f77(x4021,f77(x4021,x4022)))
% 1.60/1.75 [381]~P5(x3811)+E(f77(f4(x3811),f77(f4(x3811),x3812)),f4(f74(x3811,x3812)))
% 1.60/1.75 [296]E(x2961,x2962)+~E(f83(x2963,x2963),f83(x2961,x2962))
% 1.60/1.75 [297]E(x2971,x2972)+~E(f83(x2971,x2971),f83(x2972,x2973))
% 1.60/1.75 [353]P6(x3531,x3532)+~P8(f83(x3533,x3531),x3532)
% 1.60/1.75 [354]P6(x3541,x3542)+~P8(f83(x3541,x3543),x3542)
% 1.60/1.75 [372]~P8(x3721,x3723)+P8(f2(x3721,x3722),f2(x3723,x3722))
% 1.60/1.75 [373]~P8(x3732,x3733)+P8(f2(x3731,x3732),f2(x3731,x3733))
% 1.60/1.75 [374]~P8(x3741,x3743)+P8(f77(x3741,x3742),f77(x3743,x3742))
% 1.60/1.75 [395]P5(x3951)+~E(f64(x3951),f83(f83(x3952,x3953),f83(x3952,x3952)))
% 1.60/1.75 [416]~P3(x4161,x4162)+~P6(x4163,f77(x4161,f77(x4161,x4162)))
% 1.60/1.75 [423]~P8(x4231,x4233)+P8(f77(x4231,f77(x4231,x4232)),f77(x4233,f77(x4233,x4232)))
% 1.60/1.75 [424]E(x4241,x4242)+~E(f83(f83(x4243,x4241),f83(x4243,x4243)),f83(f83(x4244,x4242),f83(x4244,x4244)))
% 1.60/1.75 [425]E(x4251,x4252)+~E(f83(f83(x4251,x4253),f83(x4251,x4251)),f83(f83(x4252,x4254),f83(x4252,x4252)))
% 1.60/1.75 [448]P6(x4481,x4482)+~P6(f83(f83(x4483,x4481),f83(x4483,x4483)),f2(x4484,x4482))
% 1.60/1.75 [450]P6(x4501,x4502)+~P6(f83(f83(x4501,x4503),f83(x4501,x4501)),f2(x4502,x4504))
% 1.60/1.75 [232]~P5(x2321)+E(x2321,a1)+~E(f4(x2321),a1)
% 1.60/1.75 [233]~P5(x2331)+E(x2331,a1)+~E(f72(x2331),a1)
% 1.60/1.75 [243]~P5(x2431)+~E(f72(x2431),a1)+E(f4(x2431),a1)
% 1.60/1.75 [244]~P5(x2441)+~E(f4(x2441),a1)+E(f72(x2441),a1)
% 1.60/1.75 [253]~P5(x2531)+P1(x2531)+~P1(f4(x2531))
% 1.60/1.75 [254]~P5(x2541)+P1(x2541)+~P1(f72(x2541))
% 1.60/1.75 [434]~P5(x4341)+E(x4341,a1)+P6(f83(f83(f61(x4341),f63(x4341)),f83(f61(x4341),f61(x4341))),x4341)
% 1.60/1.75 [234]~P1(x2342)+~P1(x2341)+E(x2341,x2342)
% 1.60/1.75 [255]~P1(x2552)+~P1(x2551)+P2(x2551,x2552)
% 1.60/1.75 [258]~P2(x2581,x2582)+P1(x2581)+~P1(x2582)
% 1.60/1.75 [272]P7(x2721,x2722)+~P8(x2721,x2722)+E(x2721,x2722)
% 1.60/1.75 [275]~P2(x2752,x2751)+P1(x2751)+P6(x2752,x2751)
% 1.60/1.75 [301]~P8(x3012,x3011)+~P8(x3011,x3012)+E(x3011,x3012)
% 1.60/1.75 [229]~E(x2292,a1)+~E(x2291,a1)+E(x2291,f80(x2292))
% 1.60/1.75 [231]~E(x2311,f80(x2312))+E(x2311,a1)+~E(x2312,a1)
% 1.60/1.75 [285]~P1(x2852)+~P5(x2851)+P1(f71(x2851,x2852))
% 1.60/1.75 [286]~P1(x2861)+~P5(x2862)+P1(f71(x2861,x2862))
% 1.60/1.75 [287]~P5(x2872)+~P5(x2871)+P5(f79(x2871,x2872))
% 1.60/1.75 [288]~P1(x2882)+~P5(x2881)+P5(f71(x2881,x2882))
% 1.60/1.75 [289]~P1(x2891)+~P5(x2892)+P5(f71(x2891,x2892))
% 1.60/1.75 [290]~P5(x2902)+~P5(x2901)+P5(f71(x2901,x2902))
% 1.60/1.75 [312]P1(x3121)+P1(x3122)+~P1(f2(x3122,x3121))
% 1.60/1.75 [342]E(f8(x3422,x3421),x3422)+P6(f8(x3422,x3421),x3421)+E(x3421,f83(x3422,x3422))
% 1.60/1.75 [345]P6(x3451,f56(x3452))+P4(x3451,f56(x3452))+~P8(x3451,f56(x3452))
% 1.60/1.75 [346]P6(x3461,f57(x3462))+P4(x3461,f57(x3462))+~P8(x3461,f57(x3462))
% 1.60/1.75 [362]E(x3621,f83(x3622,x3622))+~P8(x3621,f83(x3622,x3622))+E(x3621,a1)
% 1.60/1.75 [363]E(x3631,x3632)+P6(f59(x3631,x3632),x3632)+P6(f59(x3631,x3632),x3631)
% 1.60/1.75 [368]P6(f13(x3682,x3681),x3681)+P8(f13(x3682,x3681),x3682)+E(x3681,f69(x3682))
% 1.60/1.75 [369]P6(f26(x3692,x3691),x3691)+P6(f33(x3692,x3691),x3692)+E(x3691,f76(x3692))
% 1.60/1.75 [387]~E(f8(x3872,x3871),x3872)+~P6(f8(x3872,x3871),x3871)+E(x3871,f83(x3872,x3872))
% 1.60/1.75 [394]P6(f26(x3942,x3941),x3941)+P6(f26(x3942,x3941),f33(x3942,x3941))+E(x3941,f76(x3942))
% 1.60/1.75 [399]E(x3991,x3992)+~P6(f59(x3991,x3992),x3992)+~P6(f59(x3991,x3992),x3991)
% 1.60/1.75 [401]~P6(f13(x4012,x4011),x4011)+~P8(f13(x4012,x4011),x4012)+E(x4011,f69(x4012))
% 1.60/1.75 [351]E(x3511,a1)+~P2(x3511,f69(f69(x3512)))+~E(f3(x3512,x3511),a1)
% 1.60/1.75 [378]~P5(x3782)+~P5(x3781)+P8(f4(f71(x3781,x3782)),f4(x3781))
% 1.60/1.75 [379]~P5(x3792)+~P5(x3791)+P8(f72(f71(x3791,x3792)),f72(x3792))
% 1.60/1.75 [382]~P5(x3822)+~P5(x3821)+P5(f77(x3821,f77(x3821,x3822)))
% 1.60/1.75 [417]E(x4171,a1)+~P2(x4171,f69(f69(x4172)))+E(f82(x4172,x4172,f70(x4172,x4171)),f84(x4172,f3(x4172,x4171)))
% 1.60/1.75 [418]E(x4181,a1)+~P2(x4181,f69(f69(x4182)))+E(f82(x4182,x4182,f84(x4182,x4181)),f70(x4182,f3(x4182,x4181)))
% 1.60/1.75 [455]~P5(x4551)+~P6(x4552,x4551)+E(f83(f83(f66(x4551,x4552),f68(x4551,x4552)),f83(f66(x4551,x4552),f66(x4551,x4552))),x4552)
% 1.60/1.75 [314]~P8(x3143,x3142)+P6(x3141,x3142)+~P6(x3141,x3143)
% 1.60/1.75 [315]~P8(x3151,x3153)+P8(x3151,x3152)+~P8(x3153,x3152)
% 1.60/1.75 [316]~P3(x3163,x3162)+P3(x3161,x3162)+~P8(x3161,x3163)
% 1.60/1.75 [334]~P3(x3343,x3342)+~P6(x3341,x3342)+~P6(x3341,x3343)
% 1.60/1.75 [294]~P8(x2941,x2943)+P6(x2941,x2942)+~E(x2942,f69(x2943))
% 1.60/1.75 [295]~P6(x2951,x2953)+P8(x2951,x2952)+~E(x2953,f69(x2952))
% 1.60/1.76 [303]~P6(x3031,x3033)+E(x3031,x3032)+~E(x3033,f83(x3032,x3032))
% 1.60/1.76 [322]~P1(x3221)+~P6(x3222,x3223)+~P2(x3223,f69(x3221))
% 1.60/1.76 [337]P6(x3371,x3372)+~P6(x3371,x3373)+~P2(x3373,f69(x3372))
% 1.60/1.76 [338]P2(x3381,x3382)+~P6(x3381,x3383)+~P2(x3383,f69(x3382))
% 1.60/1.76 [347]~P8(x3471,x3473)+P6(x3471,f56(x3472))+~P6(x3473,f56(x3472))
% 1.60/1.76 [348]~P8(x3481,x3483)+P6(x3481,f57(x3482))+~P6(x3483,f57(x3482))
% 1.60/1.76 [366]~P6(x3662,x3663)+~P6(x3661,x3663)+P8(f83(x3661,x3662),x3663)
% 1.60/1.76 [367]~P8(x3672,x3673)+~P8(x3671,x3673)+P8(f79(x3671,x3672),x3673)
% 1.60/1.76 [380]~P8(x3801,x3803)+~P6(x3803,f57(x3802))+P6(x3801,f65(x3802,x3803))
% 1.60/1.76 [396]~P6(x3961,x3962)+~P6(x3961,f81(x3963,x3962))+~P2(x3962,f69(x3963))
% 1.60/1.76 [403]~P2(x4033,f69(x4031))+~P2(x4032,f69(x4031))+E(f82(x4031,x4032,x4033),f77(x4032,x4033))
% 1.60/1.76 [413]~P6(x4131,x4133)+~E(x4133,f76(x4132))+P6(x4131,f27(x4132,x4133,x4131))
% 1.60/1.76 [414]~P6(x4143,x4142)+~E(x4142,f76(x4141))+P6(f27(x4141,x4142,x4143),x4141)
% 1.60/1.76 [422]~P2(x4223,f69(x4221))+~P2(x4222,f69(x4221))+P2(f82(x4221,x4222,x4223),f69(x4221))
% 1.60/1.76 [442]P6(f17(x4422,x4423,x4421),x4421)+P6(f22(x4422,x4423,x4421),x4422)+E(x4421,f2(x4422,x4423))
% 1.60/1.76 [443]P6(f17(x4432,x4433,x4431),x4431)+P6(f23(x4432,x4433,x4431),x4433)+E(x4431,f2(x4432,x4433))
% 1.60/1.76 [444]P6(f35(x4442,x4443,x4441),x4441)+P6(f35(x4442,x4443,x4441),x4442)+E(x4441,f77(x4442,x4443))
% 1.60/1.76 [453]~E(f14(x4532,x4533,x4531),x4533)+~P6(f14(x4532,x4533,x4531),x4531)+E(x4531,f83(x4532,x4533))
% 1.60/1.76 [454]~E(f14(x4542,x4543,x4541),x4542)+~P6(f14(x4542,x4543,x4541),x4541)+E(x4541,f83(x4542,x4543))
% 1.60/1.76 [457]P6(f35(x4572,x4573,x4571),x4571)+~P6(f35(x4572,x4573,x4571),x4573)+E(x4571,f77(x4572,x4573))
% 1.60/1.76 [461]~P6(f18(x4612,x4613,x4611),x4611)+~P6(f18(x4612,x4613,x4611),x4613)+E(x4611,f79(x4612,x4613))
% 1.60/1.76 [462]~P6(f18(x4622,x4623,x4621),x4621)+~P6(f18(x4622,x4623,x4621),x4622)+E(x4621,f79(x4622,x4623))
% 1.60/1.76 [400]~P8(x4002,x4003)+P6(x4001,x4002)+P8(x4002,f77(x4003,f83(x4001,x4001)))
% 1.60/1.76 [406]P6(x4061,x4062)+~P5(x4063)+~P6(x4061,f4(f74(x4063,x4062)))
% 1.60/1.76 [407]P6(x4071,x4072)+~P5(x4073)+~P6(x4071,f72(f78(x4072,x4073)))
% 1.60/1.76 [408]~P8(x4081,x4083)+~P8(x4081,x4082)+P8(x4081,f77(x4082,f77(x4082,x4083)))
% 1.60/1.76 [409]~P5(x4092)+P6(x4091,f4(x4092))+~P6(x4091,f4(f74(x4092,x4093)))
% 1.60/1.76 [410]~P5(x4102)+P6(x4101,f72(x4102))+~P6(x4101,f72(f78(x4103,x4102)))
% 1.60/1.76 [435]~P5(x4352)+P6(x4351,f4(x4352))+~P6(f83(f83(x4351,x4353),f83(x4351,x4351)),x4352)
% 1.60/1.76 [436]~P5(x4362)+P6(x4361,f72(x4362))+~P6(f83(f83(x4363,x4361),f83(x4363,x4363)),x4362)
% 1.60/1.76 [437]~P5(x4372)+P6(x4371,f75(x4372))+~P6(f83(f83(x4373,x4371),f83(x4373,x4373)),x4372)
% 1.60/1.76 [438]~P5(x4382)+P6(x4381,f75(x4382))+~P6(f83(f83(x4381,x4383),f83(x4381,x4381)),x4382)
% 1.60/1.76 [451]P6(f28(x4512,x4513,x4511),x4511)+P6(f28(x4512,x4513,x4511),x4513)+E(x4511,f77(x4512,f77(x4512,x4513)))
% 1.60/1.76 [452]P6(f28(x4522,x4523,x4521),x4521)+P6(f28(x4522,x4523,x4521),x4522)+E(x4521,f77(x4522,f77(x4522,x4523)))
% 1.60/1.76 [488]P6(f17(x4882,x4883,x4881),x4881)+E(x4881,f2(x4882,x4883))+E(f83(f83(f22(x4882,x4883,x4881),f23(x4882,x4883,x4881)),f83(f22(x4882,x4883,x4881),f22(x4882,x4883,x4881))),f17(x4882,x4883,x4881))
% 1.60/1.76 [277]P6(x2771,x2772)+~E(x2771,x2773)+~E(x2772,f83(x2774,x2773))
% 1.60/1.76 [278]P6(x2781,x2782)+~E(x2781,x2783)+~E(x2782,f83(x2783,x2784))
% 1.60/1.76 [302]E(x3021,x3022)+E(x3021,x3023)+~E(f83(x3021,x3024),f83(x3023,x3022))
% 1.60/1.76 [319]~P6(x3191,x3194)+P6(x3191,x3192)+~E(x3192,f79(x3193,x3194))
% 1.60/1.76 [320]~P6(x3201,x3203)+P6(x3201,x3202)+~E(x3202,f79(x3203,x3204))
% 1.60/1.76 [321]~P6(x3211,x3213)+P6(x3211,x3212)+~E(x3213,f77(x3212,x3214))
% 1.60/1.76 [336]~P6(x3364,x3363)+~P6(x3364,x3361)+~E(x3361,f77(x3362,x3363))
% 1.60/1.76 [393]~P8(x3932,x3934)+~P8(x3931,x3933)+P8(f2(x3931,x3932),f2(x3933,x3934))
% 1.60/1.76 [474]~P6(x4744,x4743)+~E(x4743,f2(x4741,x4742))+P6(f19(x4741,x4742,x4743,x4744),x4741)
% 1.60/1.76 [475]~P6(x4754,x4753)+~E(x4753,f2(x4751,x4752))+P6(f21(x4751,x4752,x4753,x4754),x4752)
% 1.60/1.76 [385]~P6(x3851,x3853)+P6(x3851,x3852)+~E(x3853,f77(x3854,f77(x3854,x3852)))
% 1.60/1.76 [428]~P6(x4282,x4284)+~P6(x4281,x4283)+P6(f83(f83(x4281,x4282),f83(x4281,x4281)),f2(x4283,x4284))
% 1.60/1.76 [456]P6(x4561,x4562)+~P5(x4563)+~P6(f83(f83(x4561,x4564),f83(x4561,x4561)),f71(f55(x4562),x4563))
% 1.60/1.76 [468]~P5(x4683)+P6(f83(f83(x4681,x4682),f83(x4681,x4681)),x4683)+~P6(f83(f83(x4681,x4682),f83(x4681,x4681)),f71(f55(x4684),x4683))
% 1.60/1.76 [500]~P6(x5004,x5003)+~E(x5003,f2(x5001,x5002))+E(f83(f83(f19(x5001,x5002,x5003,x5004),f21(x5001,x5002,x5003,x5004)),f83(f19(x5001,x5002,x5003,x5004),f19(x5001,x5002,x5003,x5004))),x5004)
% 1.60/1.76 [326]~P5(x3262)+~P5(x3261)+~P8(x3261,x3262)+P8(f4(x3261),f4(x3262))
% 1.60/1.76 [327]~P5(x3272)+~P5(x3271)+~P8(x3271,x3272)+P8(f72(x3271),f72(x3272))
% 1.60/1.76 [391]P6(f11(x3911,x3912),x3911)+~P6(f9(x3911,x3912),x3912)+E(x3911,a1)+E(x3912,f80(x3911))
% 1.60/1.76 [419]~P6(f9(x4191,x4192),x4192)+~P6(f9(x4191,x4192),f11(x4191,x4192))+E(x4191,a1)+E(x4192,f80(x4191))
% 1.60/1.76 [375]~P5(x3752)+~P5(x3751)+~P8(f72(x3751),f4(x3752))+E(f4(f71(x3751,x3752)),f4(x3751))
% 1.60/1.76 [376]~P5(x3761)+~P5(x3762)+~P8(f4(x3762),f72(x3761))+E(f72(f71(x3761,x3762)),f72(x3762))
% 1.60/1.76 [476]~P5(x4762)+~P5(x4761)+P8(x4761,x4762)+P6(f83(f83(f24(x4761,x4762),f25(x4761,x4762)),f83(f24(x4761,x4762),f24(x4761,x4762))),x4761)
% 1.60/1.76 [477]~P5(x4771)+E(f20(x4772,x4771),f29(x4772,x4771))+E(x4771,f55(x4772))+P6(f83(f83(f20(x4772,x4771),f29(x4772,x4771)),f83(f20(x4772,x4771),f20(x4772,x4771))),x4771)
% 1.60/1.76 [479]~P5(x4791)+P6(f20(x4792,x4791),x4792)+E(x4791,f55(x4792))+P6(f83(f83(f20(x4792,x4791),f29(x4792,x4791)),f83(f20(x4792,x4791),f20(x4792,x4791))),x4791)
% 1.60/1.76 [480]~P5(x4802)+P6(f31(x4802,x4801),x4801)+E(x4801,f4(x4802))+P6(f83(f83(f31(x4802,x4801),f32(x4802,x4801)),f83(f31(x4802,x4801),f31(x4802,x4801))),x4802)
% 1.60/1.76 [481]~P5(x4812)+P6(f36(x4812,x4811),x4811)+E(x4811,f72(x4812))+P6(f83(f83(f38(x4812,x4811),f36(x4812,x4811)),f83(f38(x4812,x4811),f38(x4812,x4811))),x4812)
% 1.75/1.76 [486]~P5(x4862)+~P5(x4861)+P8(x4861,x4862)+~P6(f83(f83(f24(x4861,x4862),f25(x4861,x4862)),f83(f24(x4861,x4862),f24(x4861,x4862))),x4862)
% 1.75/1.76 [398]~P3(x3981,x3983)+~P2(x3983,f69(x3982))+~P2(x3981,f69(x3982))+P8(x3981,f81(x3982,x3983))
% 1.75/1.76 [411]P3(x4111,x4112)+~P8(x4111,f81(x4113,x4112))+~P2(x4112,f69(x4113))+~P2(x4111,f69(x4113))
% 1.75/1.76 [412]P6(x4122,x4123)+P6(f10(x4121,x4123,x4122),x4121)+~E(x4123,f80(x4121))+E(x4121,a1)
% 1.75/1.76 [415]~P6(x4153,x4152)+~P6(f26(x4152,x4151),x4153)+~P6(f26(x4152,x4151),x4151)+E(x4151,f76(x4152))
% 1.75/1.76 [426]P6(x4262,x4263)+~E(x4263,f80(x4261))+~P6(x4262,f10(x4261,x4263,x4262))+E(x4261,a1)
% 1.75/1.76 [433]E(f14(x4332,x4333,x4331),x4333)+E(f14(x4332,x4333,x4331),x4332)+P6(f14(x4332,x4333,x4331),x4331)+E(x4331,f83(x4332,x4333))
% 1.75/1.76 [458]P6(f18(x4582,x4583,x4581),x4581)+P6(f18(x4582,x4583,x4581),x4583)+P6(f18(x4582,x4583,x4581),x4582)+E(x4581,f79(x4582,x4583))
% 1.75/1.76 [473]P6(f35(x4732,x4733,x4731),x4733)+~P6(f35(x4732,x4733,x4731),x4731)+~P6(f35(x4732,x4733,x4731),x4732)+E(x4731,f77(x4732,x4733))
% 1.75/1.76 [404]~P5(x4042)+~P6(x4041,x4043)+~P6(x4041,f4(x4042))+P6(x4041,f4(f74(x4042,x4043)))
% 1.75/1.76 [405]~P5(x4053)+~P6(x4051,x4052)+~P6(x4051,f72(x4053))+P6(x4051,f72(f78(x4052,x4053)))
% 1.75/1.76 [432]P2(f34(x4322,x4323,x4321),f69(x4322))+E(x4321,f3(x4322,x4323))+~P2(x4321,f69(f69(x4322)))+~P2(x4323,f69(f69(x4322)))
% 1.75/1.76 [471]~P5(x4712)+~P6(f36(x4712,x4711),x4711)+E(x4711,f72(x4712))+~P6(f83(f83(x4713,f36(x4712,x4711)),f83(x4713,x4713)),x4712)
% 1.75/1.76 [478]~P5(x4782)+~P6(x4781,x4783)+~E(x4783,f4(x4782))+P6(f83(f83(x4781,f30(x4782,x4783,x4781)),f83(x4781,x4781)),x4782)
% 1.75/1.76 [482]~P6(f28(x4822,x4823,x4821),x4821)+~P6(f28(x4822,x4823,x4821),x4823)+~P6(f28(x4822,x4823,x4821),x4822)+E(x4821,f77(x4822,f77(x4822,x4823)))
% 1.75/1.76 [485]~P5(x4852)+~P6(f31(x4852,x4851),x4851)+E(x4851,f4(x4852))+~P6(f83(f83(f31(x4852,x4851),x4853),f83(f31(x4852,x4851),f31(x4852,x4851))),x4852)
% 1.75/1.76 [491]~P5(x4911)+~P6(x4913,x4912)+~E(x4912,f72(x4911))+P6(f83(f83(f37(x4911,x4912,x4913),x4913),f83(f37(x4911,x4912,x4913),f37(x4911,x4912,x4913))),x4911)
% 1.75/1.76 [304]~P6(x3041,x3044)+E(x3041,x3042)+E(x3041,x3043)+~E(x3044,f83(x3043,x3042))
% 1.75/1.76 [335]~P6(x3351,x3354)+P6(x3351,x3352)+~P6(x3354,x3353)+~E(x3352,f76(x3353))
% 1.75/1.76 [349]~P6(x3491,x3494)+P6(x3491,x3492)+P6(x3491,x3493)+~E(x3492,f77(x3494,x3493))
% 1.75/1.76 [350]~P6(x3501,x3504)+P6(x3501,x3502)+P6(x3501,x3503)+~E(x3504,f79(x3503,x3502))
% 1.75/1.76 [397]~P6(x3971,x3974)+~P6(x3971,x3973)+P6(x3971,x3972)+~E(x3972,f77(x3973,f77(x3973,x3974)))
% 1.75/1.76 [431]~P5(x4313)+E(x4311,x4312)+~E(x4313,f55(x4314))+~P6(f83(f83(x4311,x4312),f83(x4311,x4311)),x4313)
% 1.75/1.76 [439]~P5(x4393)+P6(x4391,x4392)+~E(x4392,f72(x4393))+~P6(f83(f83(x4394,x4391),f83(x4394,x4394)),x4393)
% 1.75/1.76 [440]~P5(x4403)+P6(x4401,x4402)+~E(x4402,f4(x4403))+~P6(f83(f83(x4401,x4404),f83(x4401,x4401)),x4403)
% 1.75/1.76 [441]~P5(x4413)+P6(x4411,x4412)+~E(x4413,f55(x4412))+~P6(f83(f83(x4411,x4414),f83(x4411,x4411)),x4413)
% 1.75/1.76 [469]~P5(x4694)+~P6(x4691,x4693)+~P6(f83(f83(x4691,x4692),f83(x4691,x4691)),x4694)+P6(f83(f83(x4691,x4692),f83(x4691,x4691)),f71(f55(x4693),x4694))
% 1.75/1.76 [487]~P5(x4871)+~E(f20(x4872,x4871),f29(x4872,x4871))+~P6(f20(x4872,x4871),x4872)+E(x4871,f55(x4872))+~P6(f83(f83(f20(x4872,x4871),f29(x4872,x4871)),f83(f20(x4872,x4871),f20(x4872,x4871))),x4871)
% 1.75/1.76 [489]~P5(x4892)+~P5(x4891)+E(x4891,x4892)+P6(f83(f83(f15(x4891,x4892),f16(x4891,x4892)),f83(f15(x4891,x4892),f15(x4891,x4892))),x4892)+P6(f83(f83(f15(x4891,x4892),f16(x4891,x4892)),f83(f15(x4891,x4892),f15(x4891,x4892))),x4891)
% 1.75/1.76 [490]~P5(x4901)+~P5(x4902)+E(x4901,f73(x4902))+P6(f83(f83(f39(x4902,x4901),f40(x4902,x4901)),f83(f39(x4902,x4901),f39(x4902,x4901))),x4901)+P6(f83(f83(f40(x4902,x4901),f39(x4902,x4901)),f83(f40(x4902,x4901),f40(x4902,x4901))),x4902)
% 1.75/1.76 [492]~P5(x4922)+~P5(x4921)+E(x4921,x4922)+~P6(f83(f83(f15(x4921,x4922),f16(x4921,x4922)),f83(f15(x4921,x4922),f15(x4921,x4922))),x4922)+~P6(f83(f83(f15(x4921,x4922),f16(x4921,x4922)),f83(f15(x4921,x4922),f15(x4921,x4922))),x4921)
% 1.75/1.76 [493]~P5(x4931)+~P5(x4932)+E(x4931,f73(x4932))+~P6(f83(f83(f39(x4932,x4931),f40(x4932,x4931)),f83(f39(x4932,x4931),f39(x4932,x4931))),x4931)+~P6(f83(f83(f40(x4932,x4931),f39(x4932,x4931)),f83(f40(x4932,x4931),f40(x4932,x4931))),x4932)
% 1.75/1.76 [390]~P6(x3903,x3901)+P6(f9(x3901,x3902),x3902)+E(x3901,a1)+E(x3902,f80(x3901))+P6(f9(x3901,x3902),x3903)
% 1.75/1.76 [392]~P2(x3922,x3921)+P6(x3922,x3923)+P6(x3922,f81(x3921,x3923))+~P2(x3923,f69(x3921))+E(x3921,a1)
% 1.75/1.76 [472]P6(f34(x4722,x4723,x4721),x4721)+E(x4721,f3(x4722,x4723))+P6(f81(x4722,f34(x4722,x4723,x4721)),x4723)+~P2(x4721,f69(f69(x4722)))+~P2(x4723,f69(f69(x4722)))
% 1.75/1.76 [484]~P6(f34(x4842,x4843,x4841),x4841)+E(x4841,f3(x4842,x4843))+~P2(x4841,f69(f69(x4842)))+~P2(x4843,f69(f69(x4842)))+~P6(f81(x4842,f34(x4842,x4843,x4841)),x4843)
% 1.75/1.76 [494]~P5(x4941)+~P5(x4942)+P6(f41(x4942,x4943,x4941),x4943)+E(x4941,f74(x4942,x4943))+P6(f83(f83(f41(x4942,x4943,x4941),f49(x4942,x4943,x4941)),f83(f41(x4942,x4943,x4941),f41(x4942,x4943,x4941))),x4941)
% 1.75/1.76 [495]~P5(x4951)+~P5(x4953)+P6(f67(x4952,x4953,x4951),x4952)+E(x4951,f78(x4952,x4953))+P6(f83(f83(f62(x4952,x4953,x4951),f67(x4952,x4953,x4951)),f83(f62(x4952,x4953,x4951),f62(x4952,x4953,x4951))),x4951)
% 1.75/1.76 [496]~P5(x4961)+~P5(x4962)+E(x4961,f74(x4962,x4963))+P6(f83(f83(f41(x4962,x4963,x4961),f49(x4962,x4963,x4961)),f83(f41(x4962,x4963,x4961),f41(x4962,x4963,x4961))),x4961)+P6(f83(f83(f41(x4962,x4963,x4961),f49(x4962,x4963,x4961)),f83(f41(x4962,x4963,x4961),f41(x4962,x4963,x4961))),x4962)
% 1.75/1.76 [497]~P5(x4971)+~P5(x4973)+E(x4971,f78(x4972,x4973))+P6(f83(f83(f62(x4972,x4973,x4971),f67(x4972,x4973,x4971)),f83(f62(x4972,x4973,x4971),f62(x4972,x4973,x4971))),x4971)+P6(f83(f83(f62(x4972,x4973,x4971),f67(x4972,x4973,x4971)),f83(f62(x4972,x4973,x4971),f62(x4972,x4973,x4971))),x4973)
% 1.75/1.76 [341]~P6(x3413,x3411)+~P6(x3412,x3414)+P6(x3412,x3413)+E(x3411,a1)+~E(x3414,f80(x3411))
% 1.75/1.76 [420]~E(x4201,x4202)+~P5(x4203)+~P6(x4201,x4204)+~E(x4203,f55(x4204))+P6(f83(f83(x4201,x4202),f83(x4201,x4201)),x4203)
% 1.75/1.76 [459]~P5(x4593)+~P5(x4594)+~E(x4593,f73(x4594))+~P6(f83(f83(x4592,x4591),f83(x4592,x4592)),x4594)+P6(f83(f83(x4591,x4592),f83(x4591,x4591)),x4593)
% 1.75/1.76 [460]~P5(x4603)+~P5(x4604)+~E(x4604,f73(x4603))+~P6(f83(f83(x4602,x4601),f83(x4602,x4602)),x4604)+P6(f83(f83(x4601,x4602),f83(x4601,x4601)),x4603)
% 1.75/1.76 [445]~P5(x4454)+~P5(x4453)+P6(x4451,x4452)+~E(x4453,f74(x4454,x4452))+~P6(f83(f83(x4451,x4455),f83(x4451,x4451)),x4453)
% 1.75/1.76 [446]~P5(x4464)+~P5(x4463)+P6(x4461,x4462)+~E(x4463,f78(x4462,x4464))+~P6(f83(f83(x4465,x4461),f83(x4465,x4465)),x4463)
% 1.75/1.76 [464]~P5(x4644)+~P5(x4643)+~E(x4644,f74(x4643,x4645))+~P6(f83(f83(x4641,x4642),f83(x4641,x4641)),x4644)+P6(f83(f83(x4641,x4642),f83(x4641,x4641)),x4643)
% 1.75/1.76 [465]~P5(x4654)+~P5(x4653)+~E(x4654,f78(x4655,x4653))+~P6(f83(f83(x4651,x4652),f83(x4651,x4651)),x4654)+P6(f83(f83(x4651,x4652),f83(x4651,x4651)),x4653)
% 1.75/1.76 [470]~P6(x4705,x4703)+~P6(x4704,x4702)+~P6(f17(x4702,x4703,x4701),x4701)+E(x4701,f2(x4702,x4703))+~E(f17(x4702,x4703,x4701),f83(f83(x4704,x4705),f83(x4704,x4704)))
% 1.75/1.76 [421]~P6(x4216,x4214)+~P6(x4215,x4213)+P6(x4211,x4212)+~E(x4212,f2(x4213,x4214))+~E(x4211,f83(f83(x4215,x4216),f83(x4215,x4215)))
% 1.75/1.76 [498]~P5(x4981)+~P5(x4983)+~P5(x4982)+E(x4981,f71(x4982,x4983))+P6(f83(f83(f42(x4982,x4983,x4981),f44(x4982,x4983,x4981)),f83(f42(x4982,x4983,x4981),f42(x4982,x4983,x4981))),x4981)+P6(f83(f83(f42(x4982,x4983,x4981),f45(x4982,x4983,x4981)),f83(f42(x4982,x4983,x4981),f42(x4982,x4983,x4981))),x4982)
% 1.75/1.76 [499]~P5(x4991)+~P5(x4993)+~P5(x4992)+E(x4991,f71(x4992,x4993))+P6(f83(f83(f42(x4992,x4993,x4991),f44(x4992,x4993,x4991)),f83(f42(x4992,x4993,x4991),f42(x4992,x4993,x4991))),x4991)+P6(f83(f83(f45(x4992,x4993,x4991),f44(x4992,x4993,x4991)),f83(f45(x4992,x4993,x4991),f45(x4992,x4993,x4991))),x4993)
% 1.75/1.76 [501]~P5(x5011)+~P5(x5012)+~P6(f41(x5012,x5013,x5011),x5013)+E(x5011,f74(x5012,x5013))+~P6(f83(f83(f41(x5012,x5013,x5011),f49(x5012,x5013,x5011)),f83(f41(x5012,x5013,x5011),f41(x5012,x5013,x5011))),x5011)+~P6(f83(f83(f41(x5012,x5013,x5011),f49(x5012,x5013,x5011)),f83(f41(x5012,x5013,x5011),f41(x5012,x5013,x5011))),x5012)
% 1.75/1.76 [502]~P5(x5021)+~P5(x5023)+~P6(f67(x5022,x5023,x5021),x5022)+E(x5021,f78(x5022,x5023))+~P6(f83(f83(f62(x5022,x5023,x5021),f67(x5022,x5023,x5021)),f83(f62(x5022,x5023,x5021),f62(x5022,x5023,x5021))),x5021)+~P6(f83(f83(f62(x5022,x5023,x5021),f67(x5022,x5023,x5021)),f83(f62(x5022,x5023,x5021),f62(x5022,x5023,x5021))),x5023)
% 1.75/1.76 [429]~P6(x4292,x4294)+~P2(x4292,f69(x4291))+P6(f81(x4291,x4292),x4293)+~E(x4294,f3(x4291,x4293))+~P2(x4293,f69(f69(x4291)))+~P2(x4294,f69(f69(x4291)))
% 1.75/1.76 [430]P6(x4301,x4302)+~P2(x4301,f69(x4303))+~P6(f81(x4303,x4301),x4304)+~E(x4302,f3(x4303,x4304))+~P2(x4302,f69(f69(x4303)))+~P2(x4304,f69(f69(x4303)))
% 1.75/1.76 [466]~P5(x4663)+~P5(x4665)+~P6(x4662,x4664)+~E(x4663,f78(x4664,x4665))+~P6(f83(f83(x4661,x4662),f83(x4661,x4661)),x4665)+P6(f83(f83(x4661,x4662),f83(x4661,x4661)),x4663)
% 1.75/1.76 [467]~P5(x4673)+~P5(x4674)+~P6(x4671,x4675)+~E(x4673,f74(x4674,x4675))+~P6(f83(f83(x4671,x4672),f83(x4671,x4671)),x4674)+P6(f83(f83(x4671,x4672),f83(x4671,x4671)),x4673)
% 1.75/1.76 [504]~P5(x5044)+~P5(x5043)+~P5(x5042)+~E(x5044,f71(x5042,x5043))+~P6(f83(f83(x5041,x5045),f83(x5041,x5041)),x5044)+P6(f83(f83(x5041,f43(x5042,x5043,x5044,x5041,x5045)),f83(x5041,x5041)),x5042)
% 1.75/1.76 [505]~P5(x5053)+~P5(x5052)+~P5(x5051)+~E(x5053,f71(x5051,x5052))+~P6(f83(f83(x5054,x5055),f83(x5054,x5054)),x5053)+P6(f83(f83(f43(x5051,x5052,x5053,x5054,x5055),x5055),f83(f43(x5051,x5052,x5053,x5054,x5055),f43(x5051,x5052,x5053,x5054,x5055))),x5052)
% 1.75/1.76 [503]~P5(x5031)+~P5(x5033)+~P5(x5032)+E(x5031,f71(x5032,x5033))+~P6(f83(f83(x5034,f44(x5032,x5033,x5031)),f83(x5034,x5034)),x5033)+~P6(f83(f83(f42(x5032,x5033,x5031),x5034),f83(f42(x5032,x5033,x5031),f42(x5032,x5033,x5031))),x5032)+~P6(f83(f83(f42(x5032,x5033,x5031),f44(x5032,x5033,x5031)),f83(f42(x5032,x5033,x5031),f42(x5032,x5033,x5031))),x5031)
% 1.75/1.76 [483]~P5(x4833)+~P5(x4835)+~P5(x4834)+~E(x4833,f71(x4834,x4835))+~P6(f83(f83(x4831,x4836),f83(x4831,x4831)),x4834)+P6(f83(f83(x4831,x4832),f83(x4831,x4831)),x4833)+~P6(f83(f83(x4836,x4832),f83(x4836,x4836)),x4835)
% 1.75/1.76 %EqnAxiom
% 1.75/1.76 [1]E(x11,x11)
% 1.75/1.76 [2]E(x22,x21)+~E(x21,x22)
% 1.75/1.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.75/1.76 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 1.75/1.76 [5]~E(x51,x52)+E(f72(x51),f72(x52))
% 1.75/1.76 [6]~E(x61,x62)+E(f52(x61),f52(x62))
% 1.75/1.76 [7]~E(x71,x72)+E(f55(x71),f55(x72))
% 1.75/1.76 [8]~E(x81,x82)+E(f74(x81,x83),f74(x82,x83))
% 1.75/1.76 [9]~E(x91,x92)+E(f74(x93,x91),f74(x93,x92))
% 1.75/1.76 [10]~E(x101,x102)+E(f83(x101,x103),f83(x102,x103))
% 1.75/1.76 [11]~E(x111,x112)+E(f83(x113,x111),f83(x113,x112))
% 1.75/1.76 [12]~E(x121,x122)+E(f69(x121),f69(x122))
% 1.75/1.76 [13]~E(x131,x132)+E(f76(x131),f76(x132))
% 1.75/1.76 [14]~E(x141,x142)+E(f2(x141,x143),f2(x142,x143))
% 1.75/1.76 [15]~E(x151,x152)+E(f2(x153,x151),f2(x153,x152))
% 1.75/1.76 [16]~E(x161,x162)+E(f42(x161,x163,x164),f42(x162,x163,x164))
% 1.75/1.76 [17]~E(x171,x172)+E(f42(x173,x171,x174),f42(x173,x172,x174))
% 1.75/1.76 [18]~E(x181,x182)+E(f42(x183,x184,x181),f42(x183,x184,x182))
% 1.75/1.76 [19]~E(x191,x192)+E(f77(x191,x193),f77(x192,x193))
% 1.75/1.76 [20]~E(x201,x202)+E(f77(x203,x201),f77(x203,x202))
% 1.75/1.76 [21]~E(x211,x212)+E(f79(x211,x213),f79(x212,x213))
% 1.75/1.76 [22]~E(x221,x222)+E(f79(x223,x221),f79(x223,x222))
% 1.75/1.76 [23]~E(x231,x232)+E(f23(x231,x233,x234),f23(x232,x233,x234))
% 1.75/1.76 [24]~E(x241,x242)+E(f23(x243,x241,x244),f23(x243,x242,x244))
% 1.75/1.76 [25]~E(x251,x252)+E(f23(x253,x254,x251),f23(x253,x254,x252))
% 1.75/1.76 [26]~E(x261,x262)+E(f36(x261,x263),f36(x262,x263))
% 1.75/1.76 [27]~E(x271,x272)+E(f36(x273,x271),f36(x273,x272))
% 1.75/1.76 [28]~E(x281,x282)+E(f3(x281,x283),f3(x282,x283))
% 1.75/1.76 [29]~E(x291,x292)+E(f3(x293,x291),f3(x293,x292))
% 1.75/1.76 [30]~E(x301,x302)+E(f82(x301,x303,x304),f82(x302,x303,x304))
% 1.75/1.76 [31]~E(x311,x312)+E(f82(x313,x311,x314),f82(x313,x312,x314))
% 1.75/1.76 [32]~E(x321,x322)+E(f82(x323,x324,x321),f82(x323,x324,x322))
% 1.75/1.76 [33]~E(x331,x332)+E(f56(x331),f56(x332))
% 1.75/1.76 [34]~E(x341,x342)+E(f57(x341),f57(x342))
% 1.75/1.76 [35]~E(x351,x352)+E(f18(x351,x353,x354),f18(x352,x353,x354))
% 1.75/1.76 [36]~E(x361,x362)+E(f18(x363,x361,x364),f18(x363,x362,x364))
% 1.75/1.76 [37]~E(x371,x372)+E(f18(x373,x374,x371),f18(x373,x374,x372))
% 1.75/1.76 [38]~E(x381,x382)+E(f6(x381),f6(x382))
% 1.75/1.76 [39]~E(x391,x392)+E(f41(x391,x393,x394),f41(x392,x393,x394))
% 1.75/1.76 [40]~E(x401,x402)+E(f41(x403,x401,x404),f41(x403,x402,x404))
% 1.75/1.76 [41]~E(x411,x412)+E(f41(x413,x414,x411),f41(x413,x414,x412))
% 1.75/1.76 [42]~E(x421,x422)+E(f73(x421),f73(x422))
% 1.75/1.76 [43]~E(x431,x432)+E(f45(x431,x433,x434),f45(x432,x433,x434))
% 1.75/1.76 [44]~E(x441,x442)+E(f45(x443,x441,x444),f45(x443,x442,x444))
% 1.75/1.76 [45]~E(x451,x452)+E(f45(x453,x454,x451),f45(x453,x454,x452))
% 1.75/1.76 [46]~E(x461,x462)+E(f38(x461,x463),f38(x462,x463))
% 1.75/1.76 [47]~E(x471,x472)+E(f38(x473,x471),f38(x473,x472))
% 1.75/1.76 [48]~E(x481,x482)+E(f84(x481,x483),f84(x482,x483))
% 1.75/1.76 [49]~E(x491,x492)+E(f84(x493,x491),f84(x493,x492))
% 1.75/1.76 [50]~E(x501,x502)+E(f34(x501,x503,x504),f34(x502,x503,x504))
% 1.75/1.76 [51]~E(x511,x512)+E(f34(x513,x511,x514),f34(x513,x512,x514))
% 1.75/1.76 [52]~E(x521,x522)+E(f34(x523,x524,x521),f34(x523,x524,x522))
% 1.75/1.76 [53]~E(x531,x532)+E(f35(x531,x533,x534),f35(x532,x533,x534))
% 1.75/1.76 [54]~E(x541,x542)+E(f35(x543,x541,x544),f35(x543,x542,x544))
% 1.75/1.76 [55]~E(x551,x552)+E(f35(x553,x554,x551),f35(x553,x554,x552))
% 1.75/1.76 [56]~E(x561,x562)+E(f22(x561,x563,x564),f22(x562,x563,x564))
% 1.75/1.76 [57]~E(x571,x572)+E(f22(x573,x571,x574),f22(x573,x572,x574))
% 1.75/1.76 [58]~E(x581,x582)+E(f22(x583,x584,x581),f22(x583,x584,x582))
% 1.75/1.76 [59]~E(x591,x592)+E(f24(x591,x593),f24(x592,x593))
% 1.75/1.76 [60]~E(x601,x602)+E(f24(x603,x601),f24(x603,x602))
% 1.75/1.76 [61]~E(x611,x612)+E(f28(x611,x613,x614),f28(x612,x613,x614))
% 1.75/1.76 [62]~E(x621,x622)+E(f28(x623,x621,x624),f28(x623,x622,x624))
% 1.75/1.76 [63]~E(x631,x632)+E(f28(x633,x634,x631),f28(x633,x634,x632))
% 1.75/1.76 [64]~E(x641,x642)+E(f59(x641,x643),f59(x642,x643))
% 1.75/1.76 [65]~E(x651,x652)+E(f59(x653,x651),f59(x653,x652))
% 1.75/1.76 [66]~E(x661,x662)+E(f19(x661,x663,x664,x665),f19(x662,x663,x664,x665))
% 1.75/1.76 [67]~E(x671,x672)+E(f19(x673,x671,x674,x675),f19(x673,x672,x674,x675))
% 1.75/1.76 [68]~E(x681,x682)+E(f19(x683,x684,x681,x685),f19(x683,x684,x682,x685))
% 1.75/1.76 [69]~E(x691,x692)+E(f19(x693,x694,x695,x691),f19(x693,x694,x695,x692))
% 1.75/1.76 [70]~E(x701,x702)+E(f66(x701,x703),f66(x702,x703))
% 1.75/1.76 [71]~E(x711,x712)+E(f66(x713,x711),f66(x713,x712))
% 1.75/1.76 [72]~E(x721,x722)+E(f16(x721,x723),f16(x722,x723))
% 1.75/1.76 [73]~E(x731,x732)+E(f16(x733,x731),f16(x733,x732))
% 1.75/1.76 [74]~E(x741,x742)+E(f17(x741,x743,x744),f17(x742,x743,x744))
% 1.75/1.76 [75]~E(x751,x752)+E(f17(x753,x751,x754),f17(x753,x752,x754))
% 1.75/1.76 [76]~E(x761,x762)+E(f17(x763,x764,x761),f17(x763,x764,x762))
% 1.75/1.76 [77]~E(x771,x772)+E(f15(x771,x773),f15(x772,x773))
% 1.75/1.76 [78]~E(x781,x782)+E(f15(x783,x781),f15(x783,x782))
% 1.75/1.76 [79]~E(x791,x792)+E(f70(x791,x793),f70(x792,x793))
% 1.75/1.76 [80]~E(x801,x802)+E(f70(x803,x801),f70(x803,x802))
% 1.75/1.76 [81]~E(x811,x812)+E(f31(x811,x813),f31(x812,x813))
% 1.75/1.76 [82]~E(x821,x822)+E(f31(x823,x821),f31(x823,x822))
% 1.75/1.76 [83]~E(x831,x832)+E(f14(x831,x833,x834),f14(x832,x833,x834))
% 1.75/1.76 [84]~E(x841,x842)+E(f14(x843,x841,x844),f14(x843,x842,x844))
% 1.75/1.76 [85]~E(x851,x852)+E(f14(x853,x854,x851),f14(x853,x854,x852))
% 1.75/1.76 [86]~E(x861,x862)+E(f81(x861,x863),f81(x862,x863))
% 1.75/1.76 [87]~E(x871,x872)+E(f81(x873,x871),f81(x873,x872))
% 1.75/1.76 [88]~E(x881,x882)+E(f25(x881,x883),f25(x882,x883))
% 1.75/1.76 [89]~E(x891,x892)+E(f25(x893,x891),f25(x893,x892))
% 1.75/1.76 [90]~E(x901,x902)+E(f75(x901),f75(x902))
% 1.75/1.76 [91]~E(x911,x912)+E(f71(x911,x913),f71(x912,x913))
% 1.75/1.76 [92]~E(x921,x922)+E(f71(x923,x921),f71(x923,x922))
% 1.75/1.76 [93]~E(x931,x932)+E(f78(x931,x933),f78(x932,x933))
% 1.75/1.76 [94]~E(x941,x942)+E(f78(x943,x941),f78(x943,x942))
% 1.75/1.76 [95]~E(x951,x952)+E(f43(x951,x953,x954,x955,x956),f43(x952,x953,x954,x955,x956))
% 1.75/1.76 [96]~E(x961,x962)+E(f43(x963,x961,x964,x965,x966),f43(x963,x962,x964,x965,x966))
% 1.75/1.76 [97]~E(x971,x972)+E(f43(x973,x974,x971,x975,x976),f43(x973,x974,x972,x975,x976))
% 1.75/1.76 [98]~E(x981,x982)+E(f43(x983,x984,x985,x981,x986),f43(x983,x984,x985,x982,x986))
% 1.75/1.76 [99]~E(x991,x992)+E(f43(x993,x994,x995,x996,x991),f43(x993,x994,x995,x996,x992))
% 1.75/1.76 [100]~E(x1001,x1002)+E(f61(x1001),f61(x1002))
% 1.75/1.76 [101]~E(x1011,x1012)+E(f29(x1011,x1013),f29(x1012,x1013))
% 1.75/1.76 [102]~E(x1021,x1022)+E(f29(x1023,x1021),f29(x1023,x1022))
% 1.75/1.76 [103]~E(x1031,x1032)+E(f44(x1031,x1033,x1034),f44(x1032,x1033,x1034))
% 1.75/1.76 [104]~E(x1041,x1042)+E(f44(x1043,x1041,x1044),f44(x1043,x1042,x1044))
% 1.75/1.76 [105]~E(x1051,x1052)+E(f44(x1053,x1054,x1051),f44(x1053,x1054,x1052))
% 1.75/1.76 [106]~E(x1061,x1062)+E(f65(x1061,x1063),f65(x1062,x1063))
% 1.75/1.76 [107]~E(x1071,x1072)+E(f65(x1073,x1071),f65(x1073,x1072))
% 1.75/1.76 [108]~E(x1081,x1082)+E(f8(x1081,x1083),f8(x1082,x1083))
% 1.75/1.76 [109]~E(x1091,x1092)+E(f8(x1093,x1091),f8(x1093,x1092))
% 1.75/1.76 [110]~E(x1101,x1102)+E(f20(x1101,x1103),f20(x1102,x1103))
% 1.75/1.76 [111]~E(x1111,x1112)+E(f20(x1113,x1111),f20(x1113,x1112))
% 1.75/1.76 [112]~E(x1121,x1122)+E(f37(x1121,x1123,x1124),f37(x1122,x1123,x1124))
% 1.75/1.76 [113]~E(x1131,x1132)+E(f37(x1133,x1131,x1134),f37(x1133,x1132,x1134))
% 1.75/1.76 [114]~E(x1141,x1142)+E(f37(x1143,x1144,x1141),f37(x1143,x1144,x1142))
% 1.75/1.76 [115]~E(x1151,x1152)+E(f62(x1151,x1153,x1154),f62(x1152,x1153,x1154))
% 1.75/1.76 [116]~E(x1161,x1162)+E(f62(x1163,x1161,x1164),f62(x1163,x1162,x1164))
% 1.75/1.76 [117]~E(x1171,x1172)+E(f62(x1173,x1174,x1171),f62(x1173,x1174,x1172))
% 1.75/1.76 [118]~E(x1181,x1182)+E(f27(x1181,x1183,x1184),f27(x1182,x1183,x1184))
% 1.75/1.76 [119]~E(x1191,x1192)+E(f27(x1193,x1191,x1194),f27(x1193,x1192,x1194))
% 1.75/1.76 [120]~E(x1201,x1202)+E(f27(x1203,x1204,x1201),f27(x1203,x1204,x1202))
% 1.75/1.76 [121]~E(x1211,x1212)+E(f80(x1211),f80(x1212))
% 1.75/1.76 [122]~E(x1221,x1222)+E(f12(x1221,x1223),f12(x1222,x1223))
% 1.75/1.76 [123]~E(x1231,x1232)+E(f12(x1233,x1231),f12(x1233,x1232))
% 1.75/1.76 [124]~E(x1241,x1242)+E(f67(x1241,x1243,x1244),f67(x1242,x1243,x1244))
% 1.75/1.76 [125]~E(x1251,x1252)+E(f67(x1253,x1251,x1254),f67(x1253,x1252,x1254))
% 1.75/1.76 [126]~E(x1261,x1262)+E(f67(x1263,x1264,x1261),f67(x1263,x1264,x1262))
% 1.75/1.76 [127]~E(x1271,x1272)+E(f26(x1271,x1273),f26(x1272,x1273))
% 1.75/1.76 [128]~E(x1281,x1282)+E(f26(x1283,x1281),f26(x1283,x1282))
% 1.75/1.76 [129]~E(x1291,x1292)+E(f40(x1291,x1293),f40(x1292,x1293))
% 1.75/1.76 [130]~E(x1301,x1302)+E(f40(x1303,x1301),f40(x1303,x1302))
% 1.75/1.76 [131]~E(x1311,x1312)+E(f46(x1311,x1313),f46(x1312,x1313))
% 1.75/1.76 [132]~E(x1321,x1322)+E(f46(x1323,x1321),f46(x1323,x1322))
% 1.75/1.76 [133]~E(x1331,x1332)+E(f39(x1331,x1333),f39(x1332,x1333))
% 1.75/1.76 [134]~E(x1341,x1342)+E(f39(x1343,x1341),f39(x1343,x1342))
% 1.75/1.76 [135]~E(x1351,x1352)+E(f64(x1351),f64(x1352))
% 1.75/1.76 [136]~E(x1361,x1362)+E(f9(x1361,x1363),f9(x1362,x1363))
% 1.75/1.76 [137]~E(x1371,x1372)+E(f9(x1373,x1371),f9(x1373,x1372))
% 1.75/1.76 [138]~E(x1381,x1382)+E(f30(x1381,x1383,x1384),f30(x1382,x1383,x1384))
% 1.75/1.76 [139]~E(x1391,x1392)+E(f30(x1393,x1391,x1394),f30(x1393,x1392,x1394))
% 1.75/1.76 [140]~E(x1401,x1402)+E(f30(x1403,x1404,x1401),f30(x1403,x1404,x1402))
% 1.75/1.76 [141]~E(x1411,x1412)+E(f33(x1411,x1413),f33(x1412,x1413))
% 1.75/1.76 [142]~E(x1421,x1422)+E(f33(x1423,x1421),f33(x1423,x1422))
% 1.75/1.76 [143]~E(x1431,x1432)+E(f13(x1431,x1433),f13(x1432,x1433))
% 1.75/1.76 [144]~E(x1441,x1442)+E(f13(x1443,x1441),f13(x1443,x1442))
% 1.75/1.76 [145]~E(x1451,x1452)+E(f58(x1451,x1453),f58(x1452,x1453))
% 1.75/1.76 [146]~E(x1461,x1462)+E(f58(x1463,x1461),f58(x1463,x1462))
% 1.75/1.76 [147]~E(x1471,x1472)+E(f49(x1471,x1473,x1474),f49(x1472,x1473,x1474))
% 1.75/1.76 [148]~E(x1481,x1482)+E(f49(x1483,x1481,x1484),f49(x1483,x1482,x1484))
% 1.75/1.76 [149]~E(x1491,x1492)+E(f49(x1493,x1494,x1491),f49(x1493,x1494,x1492))
% 1.75/1.76 [150]~E(x1501,x1502)+E(f11(x1501,x1503),f11(x1502,x1503))
% 1.75/1.76 [151]~E(x1511,x1512)+E(f11(x1513,x1511),f11(x1513,x1512))
% 1.75/1.76 [152]~E(x1521,x1522)+E(f48(x1521),f48(x1522))
% 1.75/1.76 [153]~E(x1531,x1532)+E(f68(x1531,x1533),f68(x1532,x1533))
% 1.75/1.76 [154]~E(x1541,x1542)+E(f68(x1543,x1541),f68(x1543,x1542))
% 1.75/1.76 [155]~E(x1551,x1552)+E(f10(x1551,x1553,x1554),f10(x1552,x1553,x1554))
% 1.75/1.76 [156]~E(x1561,x1562)+E(f10(x1563,x1561,x1564),f10(x1563,x1562,x1564))
% 1.75/1.76 [157]~E(x1571,x1572)+E(f10(x1573,x1574,x1571),f10(x1573,x1574,x1572))
% 1.75/1.76 [158]~E(x1581,x1582)+E(f63(x1581),f63(x1582))
% 1.75/1.76 [159]~E(x1591,x1592)+E(f21(x1591,x1593,x1594,x1595),f21(x1592,x1593,x1594,x1595))
% 1.75/1.76 [160]~E(x1601,x1602)+E(f21(x1603,x1601,x1604,x1605),f21(x1603,x1602,x1604,x1605))
% 1.75/1.76 [161]~E(x1611,x1612)+E(f21(x1613,x1614,x1611,x1615),f21(x1613,x1614,x1612,x1615))
% 1.75/1.76 [162]~E(x1621,x1622)+E(f21(x1623,x1624,x1625,x1621),f21(x1623,x1624,x1625,x1622))
% 1.75/1.76 [163]~E(x1631,x1632)+E(f32(x1631,x1633),f32(x1632,x1633))
% 1.75/1.76 [164]~E(x1641,x1642)+E(f32(x1643,x1641),f32(x1643,x1642))
% 1.75/1.76 [165]~E(x1651,x1652)+E(f60(x1651,x1653),f60(x1652,x1653))
% 1.75/1.76 [166]~E(x1661,x1662)+E(f60(x1663,x1661),f60(x1663,x1662))
% 1.75/1.76 [167]~E(x1671,x1672)+E(f7(x1671),f7(x1672))
% 1.75/1.76 [168]~P1(x1681)+P1(x1682)+~E(x1681,x1682)
% 1.75/1.76 [169]P6(x1692,x1693)+~E(x1691,x1692)+~P6(x1691,x1693)
% 1.75/1.76 [170]P6(x1703,x1702)+~E(x1701,x1702)+~P6(x1703,x1701)
% 1.75/1.76 [171]~P5(x1711)+P5(x1712)+~E(x1711,x1712)
% 1.75/1.76 [172]P8(x1722,x1723)+~E(x1721,x1722)+~P8(x1721,x1723)
% 1.75/1.76 [173]P8(x1733,x1732)+~E(x1731,x1732)+~P8(x1733,x1731)
% 1.75/1.76 [174]P2(x1742,x1743)+~E(x1741,x1742)+~P2(x1741,x1743)
% 1.75/1.76 [175]P2(x1753,x1752)+~E(x1751,x1752)+~P2(x1753,x1751)
% 1.75/1.76 [176]P3(x1762,x1763)+~E(x1761,x1762)+~P3(x1761,x1763)
% 1.75/1.76 [177]P3(x1773,x1772)+~E(x1771,x1772)+~P3(x1773,x1771)
% 1.75/1.76 [178]P7(x1782,x1783)+~E(x1781,x1782)+~P7(x1781,x1783)
% 1.75/1.76 [179]P7(x1793,x1792)+~E(x1791,x1792)+~P7(x1793,x1791)
% 1.75/1.76 [180]P4(x1802,x1803)+~E(x1801,x1802)+~P4(x1801,x1803)
% 1.75/1.76 [181]P4(x1813,x1812)+~E(x1811,x1812)+~P4(x1813,x1811)
% 1.75/1.76
% 1.75/1.76 %-------------------------------------------
% 1.75/1.77 cnf(507,plain,
% 1.75/1.77 (~P6(f56(x5071),x5071)),
% 1.75/1.77 inference(scs_inference,[],[182,204,2,291])).
% 1.75/1.77 cnf(511,plain,
% 1.75/1.77 (~P6(x5111,a1)),
% 1.75/1.77 inference(scs_inference,[],[185,182,226,204,2,291,263,256])).
% 1.75/1.77 cnf(522,plain,
% 1.75/1.77 (P8(x5221,x5221)),
% 1.75/1.77 inference(rename_variables,[],[202])).
% 1.75/1.77 cnf(525,plain,
% 1.75/1.77 (P8(x5251,x5251)),
% 1.75/1.77 inference(rename_variables,[],[202])).
% 1.75/1.77 cnf(528,plain,
% 1.75/1.77 (P2(f6(x5281),x5281)),
% 1.75/1.77 inference(rename_variables,[],[207])).
% 1.75/1.77 cnf(542,plain,
% 1.75/1.77 (P2(x5421,f69(x5421))),
% 1.75/1.77 inference(rename_variables,[],[206])).
% 1.75/1.77 cnf(545,plain,
% 1.75/1.77 (P2(x5451,f69(x5451))),
% 1.75/1.77 inference(rename_variables,[],[206])).
% 1.75/1.77 cnf(548,plain,
% 1.75/1.77 (P2(x5481,f69(x5481))),
% 1.75/1.77 inference(rename_variables,[],[206])).
% 1.75/1.77 cnf(551,plain,
% 1.75/1.77 (P2(x5511,f69(x5511))),
% 1.75/1.77 inference(rename_variables,[],[206])).
% 1.75/1.77 cnf(556,plain,
% 1.75/1.77 (P2(f6(x5561),x5561)),
% 1.75/1.77 inference(rename_variables,[],[207])).
% 1.75/1.77 cnf(558,plain,
% 1.75/1.77 (P2(x5581,f69(x5581))),
% 1.75/1.77 inference(rename_variables,[],[206])).
% 1.75/1.77 cnf(560,plain,
% 1.75/1.77 (P8(x5601,f79(x5601,x5602))),
% 1.75/1.77 inference(rename_variables,[],[212])).
% 1.75/1.77 cnf(562,plain,
% 1.75/1.77 (P8(x5621,x5621)),
% 1.75/1.77 inference(rename_variables,[],[202])).
% 1.75/1.77 cnf(564,plain,
% 1.75/1.77 (P6(x5641,f56(x5641))),
% 1.75/1.77 inference(rename_variables,[],[204])).
% 1.75/1.77 cnf(566,plain,
% 1.75/1.77 (P6(x5661,f56(x5661))),
% 1.75/1.77 inference(rename_variables,[],[204])).
% 1.75/1.77 cnf(568,plain,
% 1.75/1.77 (E(f79(x5681,x5681),x5681)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(574,plain,
% 1.75/1.77 (P8(a1,x5741)),
% 1.75/1.77 inference(rename_variables,[],[198])).
% 1.75/1.77 cnf(583,plain,
% 1.75/1.77 (E(f77(x5831,f77(x5831,x5832)),f77(x5832,f77(x5832,x5831)))),
% 1.75/1.77 inference(rename_variables,[],[217])).
% 1.75/1.77 cnf(586,plain,
% 1.75/1.77 (P2(f52(x5861),f69(x5861))),
% 1.75/1.77 inference(rename_variables,[],[208])).
% 1.75/1.77 cnf(589,plain,
% 1.75/1.77 (P2(f52(x5891),f69(x5891))),
% 1.75/1.77 inference(rename_variables,[],[208])).
% 1.75/1.77 cnf(592,plain,
% 1.75/1.77 (E(f79(x5921,x5921),x5921)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(594,plain,
% 1.75/1.77 (~P6(x5941,f52(a1))),
% 1.75/1.77 inference(scs_inference,[],[202,522,525,198,185,219,182,226,203,568,204,564,566,206,542,545,548,551,207,528,556,212,213,200,222,208,586,589,211,217,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322])).
% 1.75/1.77 cnf(595,plain,
% 1.75/1.77 (P2(f52(x5951),f69(x5951))),
% 1.75/1.77 inference(rename_variables,[],[208])).
% 1.75/1.77 cnf(598,plain,
% 1.75/1.77 (E(f79(x5981,x5981),x5981)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(601,plain,
% 1.75/1.77 (E(f79(x6011,x6011),x6011)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(604,plain,
% 1.75/1.77 (E(f79(x6041,x6041),x6041)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(607,plain,
% 1.75/1.77 (E(f79(x6071,x6071),x6071)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(610,plain,
% 1.75/1.77 (E(f79(x6101,x6101),x6101)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(613,plain,
% 1.75/1.77 (E(f79(x6131,x6131),x6131)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(616,plain,
% 1.75/1.77 (E(f79(x6161,x6161),x6161)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(621,plain,
% 1.75/1.77 (E(f79(x6211,a1),x6211)),
% 1.75/1.77 inference(rename_variables,[],[199])).
% 1.75/1.77 cnf(627,plain,
% 1.75/1.77 (~P6(x6271,f81(f56(x6271),f56(x6271)))),
% 1.75/1.77 inference(scs_inference,[],[202,522,525,562,198,185,219,182,226,203,568,592,598,601,604,607,610,613,204,564,566,206,542,545,548,551,558,207,528,556,212,213,199,200,222,193,208,586,589,196,211,217,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396])).
% 1.75/1.77 cnf(629,plain,
% 1.75/1.77 (~P6(x6291,f79(f76(f52(a1)),f76(f52(a1))))),
% 1.75/1.77 inference(scs_inference,[],[202,522,525,562,198,185,219,182,226,203,568,592,598,601,604,607,610,613,616,204,564,566,206,542,545,548,551,558,207,528,556,212,213,199,200,222,193,208,586,589,196,211,217,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414])).
% 1.75/1.77 cnf(630,plain,
% 1.75/1.77 (E(f79(x6301,x6301),x6301)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(636,plain,
% 1.75/1.77 (E(f77(x6361,f77(x6361,x6362)),f77(x6362,f77(x6362,x6361)))),
% 1.75/1.77 inference(rename_variables,[],[217])).
% 1.75/1.77 cnf(637,plain,
% 1.75/1.77 (P6(x6371,f56(x6371))),
% 1.75/1.77 inference(rename_variables,[],[204])).
% 1.75/1.77 cnf(642,plain,
% 1.75/1.77 (P6(x6421,f77(f56(x6421),f77(f56(x6421),f56(x6421))))),
% 1.75/1.77 inference(scs_inference,[],[202,522,525,562,198,185,219,182,226,203,568,592,598,601,604,607,610,613,616,204,564,566,637,206,542,545,548,551,558,207,528,556,212,213,199,621,200,222,193,208,586,589,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397])).
% 1.75/1.77 cnf(647,plain,
% 1.75/1.77 (E(f79(x6471,x6471),x6471)),
% 1.75/1.77 inference(rename_variables,[],[203])).
% 1.75/1.77 cnf(651,plain,
% 1.75/1.77 (P3(x6511,f77(a1,x6512))),
% 1.75/1.77 inference(scs_inference,[],[202,522,525,562,198,574,185,219,182,226,203,568,592,598,601,604,607,610,613,616,630,204,564,566,637,206,542,545,548,551,558,207,528,556,212,213,199,621,200,222,193,208,586,589,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265])).
% 1.75/1.77 cnf(661,plain,
% 1.75/1.77 (P8(f72(f78(x6611,a51)),x6611)),
% 1.75/1.77 inference(scs_inference,[],[191,202,522,525,562,198,574,185,186,187,219,182,226,203,568,592,598,601,604,607,610,613,616,630,204,564,566,637,206,542,545,548,551,558,207,528,556,212,213,199,621,200,222,193,208,586,589,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265,264,230,228,281,360])).
% 1.75/1.77 cnf(671,plain,
% 1.75/1.77 (P2(a1,f69(x6711))),
% 1.75/1.77 inference(scs_inference,[],[191,202,522,525,562,198,574,185,186,187,219,182,226,203,568,592,598,601,604,607,610,613,616,630,204,564,566,637,206,542,545,548,551,558,207,528,556,212,213,199,621,200,222,193,208,586,589,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265,264,230,228,281,360,306,305,300,299,284])).
% 1.75/1.77 cnf(870,plain,
% 1.75/1.77 (~P6(f12(f72(f78(a54,a51)),f72(a51)),f72(a51))),
% 1.75/1.77 inference(scs_inference,[],[191,202,522,525,562,198,574,185,186,187,219,182,226,203,568,592,598,601,604,607,610,613,616,630,204,564,566,637,206,542,545,548,551,558,207,528,556,212,213,199,621,200,222,193,208,586,589,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265,264,230,228,281,360,306,305,300,299,284,283,267,266,245,242,239,238,237,236,235,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,4,448,424,374,373,372,370,365,357])).
% 1.75/1.77 cnf(878,plain,
% 1.75/1.77 (P6(f12(f72(f78(a54,a51)),f72(a51)),f72(f78(a54,a51)))),
% 1.75/1.77 inference(scs_inference,[],[191,202,522,525,562,198,574,185,186,187,219,182,226,203,568,592,598,601,604,607,610,613,616,630,204,564,566,637,206,542,545,548,551,558,207,528,556,212,213,199,621,200,222,193,208,586,589,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265,264,230,228,281,360,306,305,300,299,284,283,267,266,245,242,239,238,237,236,235,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,4,448,424,374,373,372,370,365,357,343,325,309,308])).
% 1.75/1.77 cnf(904,plain,
% 1.75/1.77 (~E(f77(f83(x9041,x9041),f77(f83(x9041,x9041),f56(x9041))),a1)),
% 1.75/1.77 inference(scs_inference,[],[191,202,522,525,562,198,574,185,186,187,219,182,226,203,568,592,598,601,604,607,610,613,616,630,204,564,566,637,206,542,545,548,551,558,207,528,556,212,213,199,621,200,222,193,208,586,589,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265,264,230,228,281,360,306,305,300,299,284,283,267,266,245,242,239,238,237,236,235,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,4,448,424,374,373,372,370,365,357,343,325,309,308,307,273,270,269,260,257,247,246,296,416,381,371,352])).
% 1.75/1.77 cnf(914,plain,
% 1.75/1.77 (P2(f79(f76(f52(a1)),f76(f52(a1))),f69(x9141))),
% 1.75/1.77 inference(scs_inference,[],[191,202,522,525,562,198,574,185,186,187,219,182,226,203,568,592,598,601,604,607,610,613,616,630,204,564,566,637,206,542,545,548,551,558,207,528,556,212,560,213,199,621,200,222,193,208,586,589,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265,264,230,228,281,360,306,305,300,299,284,283,267,266,245,242,239,238,237,236,235,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,4,448,424,374,373,372,370,365,357,343,325,309,308,307,273,270,269,260,257,247,246,296,416,381,371,352,331,329,328,323,318])).
% 1.75/1.77 cnf(955,plain,
% 1.75/1.77 (P7(f78(a54,a51),a51)),
% 1.75/1.77 inference(scs_inference,[],[191,202,522,525,562,223,198,574,185,186,187,219,182,226,203,568,592,598,601,604,607,610,613,616,630,647,204,564,566,637,205,206,542,545,548,551,558,207,528,556,212,560,213,199,621,200,222,193,208,586,589,595,209,196,211,217,583,636,2,291,263,256,252,251,248,241,354,353,298,250,249,5,310,271,262,384,383,340,339,177,176,175,174,173,172,170,169,168,3,316,301,275,258,234,385,338,337,336,322,321,320,319,295,294,278,277,231,303,233,396,414,350,349,304,397,421,293,265,264,230,228,281,360,306,305,300,299,284,283,267,266,245,242,239,238,237,236,235,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,4,448,424,374,373,372,370,365,357,343,325,309,308,307,273,270,269,260,257,247,246,296,416,381,371,352,331,329,328,323,318,313,311,297,268,450,423,389,388,377,359,358,344,402,317,425,179,178,171,334,315,314,272])).
% 1.75/1.77 cnf(1061,plain,
% 1.75/1.77 (~P6(x10611,a1)),
% 1.75/1.77 inference(rename_variables,[],[511])).
% 1.75/1.77 cnf(1064,plain,
% 1.75/1.77 (~P6(x10641,a1)),
% 1.75/1.77 inference(rename_variables,[],[511])).
% 1.75/1.77 cnf(1067,plain,
% 1.75/1.77 (~P6(x10671,a1)),
% 1.75/1.77 inference(rename_variables,[],[511])).
% 1.75/1.77 cnf(1068,plain,
% 1.75/1.77 (~P6(x10681,f79(f76(f52(a1)),f76(f52(a1))))),
% 1.75/1.77 inference(rename_variables,[],[629])).
% 1.75/1.77 cnf(1071,plain,
% 1.75/1.77 (~P6(x10711,a1)),
% 1.75/1.77 inference(rename_variables,[],[511])).
% 1.75/1.77 cnf(1072,plain,
% 1.75/1.77 (~P6(x10721,f79(f76(f52(a1)),f76(f52(a1))))),
% 1.75/1.77 inference(rename_variables,[],[629])).
% 1.75/1.77 cnf(1080,plain,
% 1.75/1.77 (~P6(x10801,a1)),
% 1.75/1.77 inference(rename_variables,[],[511])).
% 1.75/1.77 cnf(1089,plain,
% 1.75/1.77 (~P6(x10891,f81(f56(x10891),f56(x10891)))),
% 1.75/1.77 inference(rename_variables,[],[627])).
% 1.75/1.77 cnf(1090,plain,
% 1.75/1.77 (P6(x10901,f56(x10901))),
% 1.75/1.77 inference(rename_variables,[],[204])).
% 1.75/1.77 cnf(1107,plain,
% 1.75/1.77 (~P6(x11071,f81(f56(x11071),f56(x11071)))),
% 1.75/1.77 inference(rename_variables,[],[627])).
% 1.75/1.77 cnf(1110,plain,
% 1.75/1.77 (~P6(f56(x11101),x11101)),
% 1.75/1.77 inference(rename_variables,[],[507])).
% 1.75/1.77 cnf(1113,plain,
% 1.75/1.77 (P6(x11131,f56(x11131))),
% 1.75/1.77 inference(rename_variables,[],[204])).
% 1.75/1.77 cnf(1124,plain,
% 1.75/1.77 (~P6(f56(x11241),x11241)),
% 1.75/1.77 inference(rename_variables,[],[507])).
% 1.75/1.77 cnf(1145,plain,
% 1.75/1.77 ($false),
% 1.75/1.77 inference(scs_inference,[],[191,189,220,183,192,202,188,206,207,204,1090,1113,205,222,642,627,1089,1107,507,1110,1124,914,661,629,1068,1072,651,878,594,870,904,511,1061,1064,1067,1071,1080,671,955,363,468,452,451,398,478,472,335,292,248,353,309,260,416,314,275,321,320,278,407,348,312,290,289,288,287,436,408,382,379,410]),
% 1.75/1.77 ['proof']).
% 1.75/1.77 % SZS output end Proof
% 1.75/1.77 % Total time :0.990000s
%------------------------------------------------------------------------------