%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:21:05 AM UTC 2026
% Result : Unsatisfiable 150.17s 52.96s
% Output : Refutation 151.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 21
% Syntax : Number of formulae : 1131 ( 400 unt; 0 typ; 0 def)
% Number of atoms : 3280 ( 849 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 29041 (1164 ~;1057 |; 0 &;26820 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 14 con; 0-8 aty)
% Number of variables : 4834 ( 0 ^;4834 !; 0 ?;4834 :)
% Comments :
%------------------------------------------------------------------------------
thf(achievable_decl,type,
achievable: $i > $i > $o ).
thf(row_decl,type,
row: $i > $i ).
thf(n8_decl,type,
n8: $i ).
thf(squares_decl,type,
squares: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(covered_decl,type,
covered: $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(n2_decl,type,
n2: $i ).
thf(n3_decl,type,
n3: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n4_decl,type,
n4: $i ).
thf(n5_decl,type,
n5: $i ).
thf(n6_decl,type,
n6: $i ).
thf(n7_decl,type,
n7: $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(removed_decl,type,
removed: $i ).
thf(not_covered_decl,type,
not_covered: $i ).
thf(n9_decl,type,
n9: $i ).
thf(18,axiom,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_row_initially) ).
thf(56,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',place_vertical_pieces) ).
thf(48,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(49,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(230,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,49]) ).
thf(231,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(7,axiom,
( ( removed @ complement )
= not_covered ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_removed_is_not_covered) ).
thf(34,plain,
( ( removed @ complement )
= not_covered ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,plain,
( ( removed @ complement )
= not_covered ),
inference(lifteq,[status(thm)],[34]) ).
thf(10,axiom,
( ( not_covered @ complement )
= covered ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_not_covered_is_covered) ).
thf(40,plain,
( ( not_covered @ complement )
= covered ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,plain,
( ( not_covered @ complement )
= covered ),
inference(lifteq,[status(thm)],[40]) ).
thf(3,axiom,
( ( n1 @ successor )
= n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_1_is_2) ).
thf(26,plain,
( ( n1 @ successor )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
( ( n1 @ successor )
= n2 ),
inference(lifteq,[status(thm)],[26]) ).
thf(342,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[232,35,41,27]) ).
thf(348,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[342,49]) ).
thf(349,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(350,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[349:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(2,axiom,
( ( n2 @ successor )
= n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_2_is_3) ).
thf(24,plain,
( ( n2 @ successor )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
( ( n2 @ successor )
= n3 ),
inference(lifteq,[status(thm)],[24]) ).
thf(20,axiom,
( ( covered @ complement )
= not_covered ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_covered_is_not_covered) ).
thf(59,plain,
( ( covered @ complement )
= not_covered ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,plain,
( ( covered @ complement )
= not_covered ),
inference(lifteq,[status(thm)],[59]) ).
thf(558,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(rewrite,[status(thm)],[350,25,41,60]) ).
thf(569,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,49]) ).
thf(570,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[569]) ).
thf(571,plain,
not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(8,axiom,
( ( n3 @ successor )
= n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_3_is_4) ).
thf(36,plain,
( ( n3 @ successor )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,plain,
( ( n3 @ successor )
= n4 ),
inference(lifteq,[status(thm)],[36]) ).
thf(2158,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[571,37,41,60]) ).
thf(2161,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2158,49]) ).
thf(2162,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2161]) ).
thf(2163,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2162:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4,axiom,
( ( n4 @ successor )
= n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_4_is_5) ).
thf(28,plain,
( ( n4 @ successor )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
( ( n4 @ successor )
= n5 ),
inference(lifteq,[status(thm)],[28]) ).
thf(5171,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[2163,41,60,29]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_5_and_6) ).
thf(38,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(5184,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5171,39]) ).
thf(5185,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5184]) ).
thf(5186,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5185:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(21,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_7_and_8) ).
thf(61,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(62,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(5267,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5186,62]) ).
thf(5268,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5267]) ).
thf(5269,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5268:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(243,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ complement )
!= ( I @ complement ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[60,49]) ).
thf(244,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( covered ))]]) ).
thf(7820,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5269,244]) ).
thf(7821,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7820]) ).
thf(7822,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7821:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(6,axiom,
( ( n5 @ successor )
= n6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_5_is_6) ).
thf(32,plain,
( ( n5 @ successor )
= n6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
( ( n5 @ successor )
= n6 ),
inference(lifteq,[status(thm)],[32]) ).
thf(13227,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7822,33,41,60]) ).
thf(13264,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13227,62]) ).
thf(13265,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[13264]) ).
thf(13266,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[13265:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(13,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_2_and_3) ).
thf(46,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(47,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(345,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[342,47]) ).
thf(346,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(347,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(359,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[347,49]) ).
thf(360,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(361,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(794,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(rewrite,[status(thm)],[361,25,60]) ).
thf(807,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[794,39]) ).
thf(808,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[807]) ).
thf(809,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[808:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(17,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_3_and_4) ).
thf(54,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(55,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(853,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[809,55]) ).
thf(854,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[853]) ).
thf(855,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(19,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_1_and_2) ).
thf(57,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(58,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(1016,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[855,58]) ).
thf(1017,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1016]) ).
thf(1018,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1017:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1367,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1018,62]) ).
thf(1368,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1367]) ).
thf(1369,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1368:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(2174,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2158,47]) ).
thf(2175,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2174]) ).
thf(2176,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2175:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(2196,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2176,49]) ).
thf(2197,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2196]) ).
thf(2198,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2197:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(5492,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[2198,60,29]) ).
thf(5505,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,39]) ).
thf(5506,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5505]) ).
thf(5507,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5506:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5591,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5507,62]) ).
thf(5592,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5591]) ).
thf(5593,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5592:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(15,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_6_and_7) ).
thf(50,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(51,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(506,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,51]) ).
thf(507,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(508,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(16,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_4_and_5) ).
thf(52,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(53,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(623,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[508,53]) ).
thf(624,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[623]) ).
thf(625,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[624:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(679,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[625,49]) ).
thf(680,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(681,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[680:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(2441,plain,
covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[681,35,41,27,60]) ).
thf(2461,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2441,47]) ).
thf(2462,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2461]) ).
thf(2463,plain,
covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2462:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(7747,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5593,244]) ).
thf(7748,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7747]) ).
thf(7749,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7748:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(8444,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7749,33,41,60]) ).
thf(8461,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8444,51]) ).
thf(8462,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8461]) ).
thf(8463,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8462:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(261,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ complement )
!= ( I @ complement ) )
| ( covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[41,49]) ).
thf(262,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( not_covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( not_covered ))]]) ).
thf(8603,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8463,262]) ).
thf(8604,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8603]) ).
thf(8605,plain,
covered @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n6 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8604:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(5,axiom,
( ( n6 @ successor )
= n7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_6_is_7) ).
thf(30,plain,
( ( n6 @ successor )
= n7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
( ( n6 @ successor )
= n7 ),
inference(lifteq,[status(thm)],[30]) ).
thf(40705,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(rewrite,[status(thm)],[8605,41,60,31]) ).
thf(40768,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40705,55]) ).
thf(40769,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[40768]) ).
thf(40770,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[40769:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(618,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,53]) ).
thf(619,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[618]) ).
thf(620,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[619:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1,negated_conjecture,
~ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_row_8_can_be_covered) ).
thf(22,plain,
~ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
~ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(649,plain,
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[620,23]) ).
thf(650,plain,
( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[649]) ).
thf(666,plain,
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[650]) ).
thf(5580,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5507,55]) ).
thf(5581,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5580]) ).
thf(5582,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5581:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1108,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[794,62]) ).
thf(1109,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1108]) ).
thf(1110,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1109:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1096,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,62]) ).
thf(1097,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1096]) ).
thf(1098,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1097:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1525,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,49]) ).
thf(1526,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1525]) ).
thf(1527,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1526:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4004,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[1527,35,41,27,60]) ).
thf(4020,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4004,47]) ).
thf(4021,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4020]) ).
thf(4022,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4021:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(303,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( B @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(304,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( removed @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[303:[bind(A,$thf( A )),bind(B,$thf( removed ))]]) ).
thf(333,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( removed @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(626,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,53]) ).
thf(627,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[626]) ).
thf(628,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[627:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(12,axiom,
( ( n8 @ successor )
= n9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_8_is_9) ).
thf(44,plain,
( ( n8 @ successor )
= n9 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,plain,
( ( n8 @ successor )
= n9 ),
inference(lifteq,[status(thm)],[44]) ).
thf(156,plain,
( ( ( n1 @ successor )
!= ( n8 @ successor ) )
| ( n9 = n2 ) ),
inference(paramod_ordered,[status(thm)],[27,45]) ).
thf(170,plain,
( ( n1 != n8 )
| ( n9 = n2 ) ),
inference(simp,[status(thm)],[156]) ).
thf(801,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[794,53]) ).
thf(802,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[801]) ).
thf(803,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[802:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(833,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[803,51]) ).
thf(834,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[833]) ).
thf(835,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(989,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[835,58]) ).
thf(990,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[989]) ).
thf(991,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[990:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1324,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[991,49]) ).
thf(1325,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1324]) ).
thf(1326,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1325:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(3417,plain,
covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1326,37,41,60]) ).
thf(5172,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5171,53]) ).
thf(5173,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5172]) ).
thf(5174,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5173:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5232,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5174,62]) ).
thf(5233,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5232]) ).
thf(5234,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5233:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(7964,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5234,244]) ).
thf(7965,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7964]) ).
thf(7966,plain,
not_covered @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7965:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered ))]]) ).
thf(18917,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7966,33,41,60]) ).
thf(18970,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18917,62]) ).
thf(18971,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[18970]) ).
thf(18972,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[18971:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(80,plain,
( ( ( n6 @ successor )
!= ( n4 @ successor ) )
| ( n7 = n5 ) ),
inference(paramod_ordered,[status(thm)],[29,31]) ).
thf(84,plain,
( ( n6 != n4 )
| ( n7 = n5 ) ),
inference(simp,[status(thm)],[80]) ).
thf(11,axiom,
( ( n7 @ successor )
= n8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_7_is_8) ).
thf(42,plain,
( ( n7 @ successor )
= n8 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,plain,
( ( n7 @ successor )
= n8 ),
inference(lifteq,[status(thm)],[42]) ).
thf(129,plain,
( ( ( n7 @ successor )
!= ( n5 @ successor ) )
| ( n6 = n8 ) ),
inference(paramod_ordered,[status(thm)],[43,33]) ).
thf(141,plain,
( ( n7 != n5 )
| ( n6 = n8 ) ),
inference(simp,[status(thm)],[129]) ).
thf(8452,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8444,39]) ).
thf(8453,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8452]) ).
thf(8454,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8453:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(8497,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8454,62]) ).
thf(8498,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8497]) ).
thf(8499,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8498:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(9310,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8499,23]) ).
thf(9311,plain,
( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[9310]) ).
thf(9332,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n6 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[9311]) ).
thf(9334,plain,
( ( n6 @ row )
!= ( n8 @ row ) ),
inference(simp,[status(thm)],[9332]) ).
thf(9335,plain,
n6 != n8,
inference(simp,[status(thm)],[9334]) ).
thf(9336,plain,
n7 != n5,
inference(simplifyReflect,[status(thm)],[141,9335]) ).
thf(9337,plain,
n6 != n4,
inference(simplifyReflect,[status(thm)],[84,9336]) ).
thf(549,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[508,49]) ).
thf(550,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(551,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[550:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(2095,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[551,35,41,27,60]) ).
thf(2112,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2095,47]) ).
thf(2113,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2112]) ).
thf(2114,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2113:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(200,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,47]) ).
thf(201,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( A @ row ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(2448,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2441,39]) ).
thf(2449,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2448]) ).
thf(2450,plain,
covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2449:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(2479,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2450,55]) ).
thf(2480,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2479]) ).
thf(2481,plain,
covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2480:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(2564,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2481,49]) ).
thf(2565,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2564]) ).
thf(2566,plain,
covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2565:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( covered ))]]) ).
thf(6729,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(rewrite,[status(thm)],[2566,25,41,60]) ).
thf(6730,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6729,53]) ).
thf(6731,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6730]) ).
thf(6732,plain,
not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6731:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(5583,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5507,58]) ).
thf(5584,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5583]) ).
thf(5585,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5584:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5933,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5585,62]) ).
thf(5934,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5933]) ).
thf(5935,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5934:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(7803,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5935,244]) ).
thf(7804,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7803]) ).
thf(7805,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7804:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(12306,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7805,33,41,60]) ).
thf(12332,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12306,51]) ).
thf(12333,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[12332]) ).
thf(12334,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[12333:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(815,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[794,51]) ).
thf(816,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[815]) ).
thf(817,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[816:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(962,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[817,58]) ).
thf(963,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[962]) ).
thf(964,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[963:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1286,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[964,49]) ).
thf(1287,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1286]) ).
thf(1288,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1287:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(3317,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1288,37,41,60]) ).
thf(5513,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,58]) ).
thf(5514,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5513]) ).
thf(5515,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5514:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5667,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5515,51]) ).
thf(5668,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5667]) ).
thf(5669,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5668:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(8466,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8444,62]) ).
thf(8467,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8466]) ).
thf(8468,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8467:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(8546,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8468,244]) ).
thf(8547,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8546]) ).
thf(8548,plain,
not_covered @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n6 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8547:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered ))]]) ).
thf(35312,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(rewrite,[status(thm)],[8548,41,60,31]) ).
thf(35371,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35312,55]) ).
thf(35372,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35371]) ).
thf(35373,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35372:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(35487,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35373,58]) ).
thf(35488,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35487]) ).
thf(35489,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35488:[bind(A,$thf( n7 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(36991,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35489,62]) ).
thf(36992,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[36991]) ).
thf(36993,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[36992:[bind(A,$thf( n7 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(38533,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36993,23]) ).
thf(38534,plain,
( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[38533]) ).
thf(38582,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n7 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[38534]) ).
thf(38588,plain,
( ( n7 @ row )
!= ( n8 @ row ) ),
inference(simp,[status(thm)],[38582]) ).
thf(38590,plain,
n7 != n8,
inference(simp,[status(thm)],[38588]) ).
thf(810,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[794,55]) ).
thf(811,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[810]) ).
thf(812,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[811:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(888,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[812,51]) ).
thf(889,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1051,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[890,58]) ).
thf(1052,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1051]) ).
thf(1053,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1052:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1391,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1053,49]) ).
thf(1392,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1393,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1392:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(3624,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1393,37,41,60]) ).
thf(3647,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3624,47]) ).
thf(3648,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3647]) ).
thf(3649,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3648:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(136,plain,
( ( ( n7 @ successor )
!= ( n3 @ successor ) )
| ( n4 = n8 ) ),
inference(paramod_ordered,[status(thm)],[37,43]) ).
thf(143,plain,
( ( n7 != n3 )
| ( n4 = n8 ) ),
inference(simp,[status(thm)],[136]) ).
thf(2203,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2176,23]) ).
thf(2204,plain,
( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2203]) ).
thf(2218,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n4 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[2204]) ).
thf(2224,plain,
( ( n4 @ row )
!= ( n8 @ row ) ),
inference(simp,[status(thm)],[2218]) ).
thf(2225,plain,
n4 != n8,
inference(simp,[status(thm)],[2224]) ).
thf(4870,plain,
n7 != n3,
inference(simplifyReflect,[status(thm)],[143,2225]) ).
thf(1979,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1369,49]) ).
thf(1980,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1979]) ).
thf(1981,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1980:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4781,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1981,37,60]) ).
thf(4784,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4781,53]) ).
thf(4785,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4784]) ).
thf(4786,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4785:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(4854,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4786,51]) ).
thf(4855,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4854]) ).
thf(4856,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4855:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(572,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,39]) ).
thf(573,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(574,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1085,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[574,62]) ).
thf(1086,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1085]) ).
thf(1087,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1086:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(1434,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1087,49]) ).
thf(1435,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1434]) ).
thf(1436,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1435:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(3693,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1436,37,41,60]) ).
thf(5672,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5515,62]) ).
thf(5673,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5672]) ).
thf(5674,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5673:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1127,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[855,62]) ).
thf(1128,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1127]) ).
thf(1129,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(1699,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1129,49]) ).
thf(1700,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1699]) ).
thf(1701,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1700:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4242,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1701,37,41,60]) ).
thf(4245,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4242,53]) ).
thf(4246,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4245]) ).
thf(4247,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4246:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(3715,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3693,47]) ).
thf(3716,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3715]) ).
thf(3717,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3716:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(670,plain,
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[625,23]) ).
thf(671,plain,
( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[670]) ).
thf(690,plain,
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(1078,plain,
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[690]) ).
thf(5510,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,55]) ).
thf(5511,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5510]) ).
thf(5512,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5511:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5627,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5512,58]) ).
thf(5628,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5627]) ).
thf(5629,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5628:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(6027,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5629,62]) ).
thf(6028,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6027]) ).
thf(6029,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6028:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(8110,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6029,244]) ).
thf(8111,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8110]) ).
thf(8112,plain,
not_covered @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8111:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered ))]]) ).
thf(26135,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[8112,33,41,60]) ).
thf(1093,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,62]) ).
thf(1094,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1093]) ).
thf(1095,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1094:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1354,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1018,49]) ).
thf(1355,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1354]) ).
thf(1356,plain,
not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1355:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(3486,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1356,37,41,60]) ).
thf(3489,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3486,53]) ).
thf(3490,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3489]) ).
thf(3491,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3490:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(3541,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3491,47]) ).
thf(3542,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3541]) ).
thf(3543,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3542:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(3593,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3543,49]) ).
thf(3594,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3593]) ).
thf(3595,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3594:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(7614,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[3595,41,60,29]) ).
thf(7635,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7614,62]) ).
thf(7636,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7635]) ).
thf(7637,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7636:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(5516,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,51]) ).
thf(5517,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5516]) ).
thf(5518,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5517:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(127,plain,
( ( ( n7 @ successor )
!= ( n4 @ successor ) )
| ( n5 = n8 ) ),
inference(paramod_ordered,[status(thm)],[43,29]) ).
thf(142,plain,
( ( n7 != n4 )
| ( n5 = n8 ) ),
inference(simp,[status(thm)],[127]) ).
thf(5890,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5582,58]) ).
thf(5891,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5890]) ).
thf(5892,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5891:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(6350,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5892,62]) ).
thf(6351,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6350]) ).
thf(6352,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6351:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(6558,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6352,23]) ).
thf(6559,plain,
( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6558]) ).
thf(6572,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n5 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[6559]) ).
thf(6579,plain,
( ( n5 @ row )
!= ( n8 @ row ) ),
inference(simp,[status(thm)],[6572]) ).
thf(6580,plain,
n5 != n8,
inference(simp,[status(thm)],[6579]) ).
thf(6583,plain,
n7 != n4,
inference(simplifyReflect,[status(thm)],[142,6580]) ).
thf(35391,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35312,47]) ).
thf(35392,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35391]) ).
thf(35393,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35392:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(35728,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35393,62]) ).
thf(35729,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35728]) ).
thf(35730,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35729:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(8190,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6352,244]) ).
thf(8191,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8190]) ).
thf(8192,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8191:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(29653,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[8192,33,60]) ).
thf(909,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[809,58]) ).
thf(910,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(911,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[910:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1158,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[911,49]) ).
thf(1159,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1158]) ).
thf(1160,plain,
not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1159:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(3130,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1160,37,41,60]) ).
thf(3138,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3130,39]) ).
thf(3139,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3138]) ).
thf(3140,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3139:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(277,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( n3 @ successor )
!= ( A @ successor ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[37,49]) ).
thf(278,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( n3 ))]]) ).
thf(320,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(5193,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5171,51]) ).
thf(5194,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5193]) ).
thf(5195,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5194:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(561,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,51]) ).
thf(562,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[561]) ).
thf(563,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[562:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(633,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,53]) ).
thf(634,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[633]) ).
thf(635,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(721,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[635,49]) ).
thf(722,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[721]) ).
thf(723,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[722:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(2770,plain,
covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[723,37,41,60]) ).
thf(2777,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2770,39]) ).
thf(2778,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2777]) ).
thf(2779,plain,
covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2778:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(2817,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2779,47]) ).
thf(2818,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2817]) ).
thf(2819,plain,
covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2818:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(944,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[803,58]) ).
thf(945,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[944]) ).
thf(946,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[945:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1262,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[946,62]) ).
thf(1263,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1264,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1263:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(123,plain,
( ( ( not_covered @ complement )
!= ( removed @ complement ) )
| ( not_covered = covered ) ),
inference(paramod_ordered,[status(thm)],[41,35]) ).
thf(125,plain,
( ( not_covered != removed )
| ( not_covered = covered ) ),
inference(simp,[status(thm)],[123]) ).
thf(3701,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3693,39]) ).
thf(3702,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3701]) ).
thf(3703,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3702:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(3747,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3703,47]) ).
thf(3748,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3747]) ).
thf(3749,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3748:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(7790,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5674,244]) ).
thf(7791,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7790]) ).
thf(7792,plain,
not_covered @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7791:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered ))]]) ).
thf(11069,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7792,33,41,60]) ).
thf(11098,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11069,62]) ).
thf(11099,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[11098]) ).
thf(11100,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[11099:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(293,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( H @ complement ) )
| ( I @ complement @ ( not_covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(294,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( not_covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( removed @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( removed ))]]) ).
thf(325,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( not_covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( removed @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(4263,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4242,51]) ).
thf(4264,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4263]) ).
thf(4265,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4264:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(265,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ complement )
!= ( B @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[41,49]) ).
thf(266,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( A )),bind(B,$thf( not_covered ))]]) ).
thf(316,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(29710,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29653,58]) ).
thf(29711,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[29710]) ).
thf(29712,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[29711:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(35394,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35312,62]) ).
thf(35395,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35394]) ).
thf(35396,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35395:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(922,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[794,58]) ).
thf(923,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[922]) ).
thf(924,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(279,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( n2 @ successor )
!= ( A @ successor ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[25,49]) ).
thf(280,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( n2 ))]]) ).
thf(321,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(189,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,39]) ).
thf(190,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(191,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(207,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,47]) ).
thf(208,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(211,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( A @ row ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(76,plain,
( ( ( n6 @ successor )
!= ( n2 @ successor ) )
| ( n7 = n3 ) ),
inference(paramod_ordered,[status(thm)],[25,31]) ).
thf(83,plain,
( ( n6 != n2 )
| ( n7 = n3 ) ),
inference(simp,[status(thm)],[76]) ).
thf(4871,plain,
n6 != n2,
inference(simplifyReflect,[status(thm)],[83,4870]) ).
thf(1023,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[855,49]) ).
thf(1024,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1023]) ).
thf(1025,plain,
not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1024:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(3032,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1025,37,41,60]) ).
thf(3035,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3032,53]) ).
thf(3036,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3035]) ).
thf(3037,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3036:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(3069,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3037,49]) ).
thf(3070,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3069]) ).
thf(3071,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3070:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(7251,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[3071,41,60,29]) ).
thf(7271,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7251,62]) ).
thf(7272,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7271]) ).
thf(7273,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7272:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(1111,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,62]) ).
thf(1112,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1111]) ).
thf(1113,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1112:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(1638,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1113,49]) ).
thf(1639,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1638]) ).
thf(1640,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1639:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4067,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[1640,35,41,27,60]) ).
thf(4082,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4067,51]) ).
thf(4083,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4082]) ).
thf(4084,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4083:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(4113,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,47]) ).
thf(4114,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4113]) ).
thf(4115,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4114:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(112,plain,
( ( ( n3 @ successor )
!= ( n2 @ successor ) )
| ( n4 = n3 ) ),
inference(paramod_ordered,[status(thm)],[25,37]) ).
thf(117,plain,
( ( n3 != n2 )
| ( n4 = n3 ) ),
inference(simp,[status(thm)],[112]) ).
thf(67,plain,
( ( ( n4 @ successor )
!= ( n2 @ successor ) )
| ( n5 = n3 ) ),
inference(paramod_ordered,[status(thm)],[29,25]) ).
thf(71,plain,
( ( n4 != n2 )
| ( n5 = n3 ) ),
inference(simp,[status(thm)],[67]) ).
thf(106,plain,
( ( ( n5 @ successor )
!= ( n3 @ successor ) )
| ( n6 = n4 ) ),
inference(paramod_ordered,[status(thm)],[33,37]) ).
thf(114,plain,
( ( n5 != n3 )
| ( n6 = n4 ) ),
inference(simp,[status(thm)],[106]) ).
thf(4872,plain,
( ( n7 != n7 )
| ( n5 != n3 )
| ( n6 != n4 ) ),
inference(paramod_ordered,[status(thm)],[84,4870]) ).
thf(4873,plain,
( ( n5 != n3 )
| ( n6 != n4 ) ),
inference(pattern_uni,[status(thm)],[4872:[]]) ).
thf(6134,plain,
( ( n6 != n6 )
| ( n5 != n3 )
| ( n4 != n4 )
| ( n5 != n3 ) ),
inference(paramod_ordered,[status(thm)],[114,4873]) ).
thf(6135,plain,
( ( n6 != n6 )
| ( n5 != n3 ) ),
inference(simp,[status(thm)],[6134]) ).
thf(6136,plain,
n5 != n3,
inference(pattern_uni,[status(thm)],[6135:[]]) ).
thf(6148,plain,
n4 != n2,
inference(simplifyReflect,[status(thm)],[71,6136]) ).
thf(6155,plain,
( ( n4 != n4 )
| ( n3 != n2 )
| ( n3 != n2 ) ),
inference(paramod_ordered,[status(thm)],[117,6148]) ).
thf(6156,plain,
( ( n4 != n4 )
| ( n3 != n2 ) ),
inference(simp,[status(thm)],[6155]) ).
thf(6157,plain,
n3 != n2,
inference(pattern_uni,[status(thm)],[6156:[]]) ).
thf(88,plain,
( ( ( n5 @ successor )
!= ( n2 @ successor ) )
| ( n6 = n3 ) ),
inference(paramod_ordered,[status(thm)],[25,33]) ).
thf(95,plain,
( ( n5 != n2 )
| ( n6 = n3 ) ),
inference(simp,[status(thm)],[88]) ).
thf(110,plain,
( ( ( n6 @ successor )
!= ( n3 @ successor ) )
| ( n7 = n4 ) ),
inference(paramod_ordered,[status(thm)],[31,37]) ).
thf(113,plain,
( ( n6 != n3 )
| ( n7 = n4 ) ),
inference(simp,[status(thm)],[110]) ).
thf(6586,plain,
n6 != n3,
inference(simplifyReflect,[status(thm)],[113,6583]) ).
thf(6591,plain,
n5 != n2,
inference(simplifyReflect,[status(thm)],[95,6586]) ).
thf(4085,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4067,47]) ).
thf(4086,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4085]) ).
thf(4087,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4086:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5493,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,53]) ).
thf(5494,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5493]) ).
thf(5495,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5494:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5546,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5495,58]) ).
thf(5547,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5546]) ).
thf(5548,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5547:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(5777,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5548,62]) ).
thf(5778,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5777]) ).
thf(5779,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5778:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(7911,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5779,244]) ).
thf(7912,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7911]) ).
thf(7913,plain,
not_covered @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7912:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered ))]]) ).
thf(16957,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7913,33,41,60]) ).
thf(7623,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7614,55]) ).
thf(7624,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7623]) ).
thf(7625,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7624:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(7665,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7625,62]) ).
thf(7666,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7665]) ).
thf(7667,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7666:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(8184,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7667,244]) ).
thf(8185,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8184]) ).
thf(8186,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8185:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(28376,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[8186,33,41,60]) ).
thf(28434,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28376,51]) ).
thf(28435,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[28434]) ).
thf(28436,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[28435:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(933,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[812,58]) ).
thf(934,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[933]) ).
thf(935,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[934:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1233,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[935,62]) ).
thf(1234,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1235,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1234:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1889,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1235,49]) ).
thf(1890,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1889]) ).
thf(1891,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1890:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4677,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1891,37,41,60]) ).
thf(4699,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4677,47]) ).
thf(4700,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4699]) ).
thf(4701,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4700:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(255,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ complement )
!= ( H @ complement ) )
| ( I @ complement @ ( covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[41,49]) ).
thf(256,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( not_covered ))]]) ).
thf(312,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(93,plain,
( ( ( n6 @ successor )
!= ( n5 @ successor ) )
| ( n7 = n6 ) ),
inference(paramod_ordered,[status(thm)],[33,31]) ).
thf(96,plain,
( ( n6 != n5 )
| ( n7 = n6 ) ),
inference(simp,[status(thm)],[93]) ).
thf(9338,plain,
( ( n7 != n7 )
| ( n6 != n5 )
| ( n6 != n5 ) ),
inference(paramod_ordered,[status(thm)],[96,9336]) ).
thf(9339,plain,
( ( n7 != n7 )
| ( n6 != n5 ) ),
inference(simp,[status(thm)],[9338]) ).
thf(9340,plain,
n6 != n5,
inference(pattern_uni,[status(thm)],[9339:[]]) ).
thf(700,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,49]) ).
thf(701,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[700]) ).
thf(702,plain,
not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[701:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(2649,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[702,37,41,60]) ).
thf(2658,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2649,55]) ).
thf(2659,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2658]) ).
thf(2660,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2659:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(2923,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2819,49]) ).
thf(2924,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2923]) ).
thf(2925,plain,
covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2924:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( covered ))]]) ).
thf(7114,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[2925,41,60,29]) ).
thf(7127,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7114,58]) ).
thf(7128,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7127]) ).
thf(7129,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7128:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1058,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[890,49]) ).
thf(1059,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1060,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1059:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(3097,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1060,37,41,60]) ).
thf(26185,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26135,58]) ).
thf(26186,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[26185]) ).
thf(26187,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[26186:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(241,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ complement )
!= ( F @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( not_covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[60,49]) ).
thf(242,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( not_covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( covered ))]]) ).
thf(334,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( not_covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(4803,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4781,51]) ).
thf(4804,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4803]) ).
thf(4805,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4804:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(4913,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4805,47]) ).
thf(4914,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4913]) ).
thf(4915,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4914:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(35376,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35312,58]) ).
thf(35377,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35376]) ).
thf(35378,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35377:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(35616,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35378,62]) ).
thf(35617,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35616]) ).
thf(35618,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35617:[bind(A,$thf( n7 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(7800,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7637,244]) ).
thf(7801,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7800]) ).
thf(7802,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7801:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(12164,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7802,33,41,60]) ).
thf(12188,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12164,51]) ).
thf(12189,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[12188]) ).
thf(12190,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[12189:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(2474,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2450,49]) ).
thf(2475,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2474]) ).
thf(2476,plain,
covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2475:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( covered ))]]) ).
thf(6696,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(rewrite,[status(thm)],[2476,25,41,60]) ).
thf(658,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[620,49]) ).
thf(659,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[658]) ).
thf(660,plain,
not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[659:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(2350,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[660,35,41,27,60]) ).
thf(2359,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2350,55]) ).
thf(2360,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2359]) ).
thf(2361,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2360:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(2383,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2361,49]) ).
thf(2384,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2383]) ).
thf(2385,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2384:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(6603,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(rewrite,[status(thm)],[2385,25,41,60]) ).
thf(6618,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6603,51]) ).
thf(6619,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6618]) ).
thf(6620,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6619:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(92,plain,
( ( ( n5 @ successor )
!= ( n1 @ successor ) )
| ( n6 = n2 ) ),
inference(paramod_ordered,[status(thm)],[27,33]) ).
thf(98,plain,
( ( n5 != n1 )
| ( n6 = n2 ) ),
inference(simp,[status(thm)],[92]) ).
thf(4878,plain,
n5 != n1,
inference(simplifyReflect,[status(thm)],[98,4871]) ).
thf(1172,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[911,62]) ).
thf(1173,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1174,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1173:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(235,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ complement )
!= ( G @ complement ) )
| ( I @ complement @ ( H @ complement @ ( not_covered @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[60,49]) ).
thf(236,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( not_covered @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( covered ))]]) ).
thf(329,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( not_covered @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(1132,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[620,62]) ).
thf(1133,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1132]) ).
thf(1134,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1133:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1735,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1134,49]) ).
thf(1736,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1735]) ).
thf(1737,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1736:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4417,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[1737,35,41,27,60]) ).
thf(2682,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2660,49]) ).
thf(2683,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2682]) ).
thf(2684,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2683:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(6852,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[2684,41,60,29]) ).
thf(5549,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5495,51]) ).
thf(5550,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5549]) ).
thf(5551,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5550:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1940,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1264,49]) ).
thf(1941,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1940]) ).
thf(1942,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1941:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4746,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1942,37,41,60]) ).
thf(291,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( G @ complement ) )
| ( I @ complement @ ( H @ complement @ ( not_covered @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(292,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( not_covered @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( removed @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( removed ))]]) ).
thf(324,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( not_covered @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( removed @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[292]) ).
thf(267,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ complement )
!= ( C @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( covered @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[41,49]) ).
thf(268,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( covered @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( not_covered ))]]) ).
thf(317,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( covered @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(1803,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1174,49]) ).
thf(1804,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1803]) ).
thf(1805,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1804:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4544,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1805,37,41,60]) ).
thf(1494,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1095,49]) ).
thf(1495,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1494]) ).
thf(1496,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1495:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(3901,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1496,37,41,60]) ).
thf(3914,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3901,55]) ).
thf(3915,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3914]) ).
thf(3916,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3915:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(4806,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4781,47]) ).
thf(4807,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4806]) ).
thf(4808,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4807:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(586,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,49]) ).
thf(587,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[586]) ).
thf(588,plain,
not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[587:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( not_covered ))]]) ).
thf(2226,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[588,37,41,60]) ).
thf(2243,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2226,47]) ).
thf(2244,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2243]) ).
thf(2245,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2244:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(104,plain,
( ( ( n4 @ successor )
!= ( n3 @ successor ) )
| ( n5 = n4 ) ),
inference(paramod_ordered,[status(thm)],[29,37]) ).
thf(118,plain,
( ( n4 != n3 )
| ( n5 = n4 ) ),
inference(simp,[status(thm)],[104]) ).
thf(6151,plain,
( ( n5 != n5 )
| ( n4 != n3 )
| ( n4 != n3 ) ),
inference(paramod_ordered,[status(thm)],[118,6136]) ).
thf(6152,plain,
( ( n5 != n5 )
| ( n4 != n3 ) ),
inference(simp,[status(thm)],[6151]) ).
thf(6153,plain,
n4 != n3,
inference(pattern_uni,[status(thm)],[6152:[]]) ).
thf(297,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( F @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( not_covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(298,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( not_covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( removed @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( removed ))]]) ).
thf(328,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( not_covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( removed @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(40776,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40705,58]) ).
thf(40777,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[40776]) ).
thf(40778,plain,
covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[40777:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(1218,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[935,49]) ).
thf(1219,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1218]) ).
thf(1220,plain,
not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1219:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(3219,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1220,37,41,60]) ).
thf(3239,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3219,47]) ).
thf(3240,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3239]) ).
thf(3241,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3240:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(3256,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3241,49]) ).
thf(3257,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3256]) ).
thf(3258,plain,
covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3257:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(7453,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[3258,41,60,29]) ).
thf(540,plain,
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[508,23]) ).
thf(541,plain,
( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[540]) ).
thf(554,plain,
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(3712,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3693,51]) ).
thf(3713,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3712]) ).
thf(3714,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3713:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(7459,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7453,39]) ).
thf(7460,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7459]) ).
thf(7461,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7460:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(7502,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7461,62]) ).
thf(7503,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7502]) ).
thf(7504,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7503:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(8079,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7504,244]) ).
thf(8080,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8079]) ).
thf(8081,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8080:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(22776,plain,
not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[8081,33,41,60]) ).
thf(22826,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22776,51]) ).
thf(22827,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[22826]) ).
thf(22828,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[22827:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1533,plain,
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,23]) ).
thf(1534,plain,
( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1533]) ).
thf(1547,plain,
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[1534]) ).
thf(2053,plain,
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[1547]) ).
thf(3426,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3417,39]) ).
thf(3427,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3426]) ).
thf(3428,plain,
covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3427:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(1205,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[924,62]) ).
thf(1206,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1205]) ).
thf(1207,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1206:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(2803,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2779,49]) ).
thf(2804,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2803]) ).
thf(2805,plain,
covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2804:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( covered ))]]) ).
thf(6946,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[2805,41,60,29]) ).
thf(6623,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6603,62]) ).
thf(6624,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6623]) ).
thf(6625,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6624:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(2488,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2450,47]) ).
thf(2489,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2488]) ).
thf(2490,plain,
covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2489:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(2619,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2490,49]) ).
thf(2620,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2619]) ).
thf(2621,plain,
covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2620:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( covered ))]]) ).
thf(6790,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(rewrite,[status(thm)],[2621,25,41,60]) ).
thf(6803,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6790,58]) ).
thf(6804,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6803]) ).
thf(6805,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6804:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(1986,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1369,23]) ).
thf(1987,plain,
( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1986]) ).
thf(2001,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n3 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[1987]) ).
thf(2005,plain,
( ( n3 @ row )
!= ( n8 @ row ) ),
inference(simp,[status(thm)],[2001]) ).
thf(2006,plain,
n3 != n8,
inference(simp,[status(thm)],[2005]) ).
thf(2368,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2350,47]) ).
thf(2369,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2368]) ).
thf(2370,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2369:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(5555,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5495,62]) ).
thf(5556,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5555]) ).
thf(5557,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5556:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(289,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( P @ ( O @ ( not_covered @ ( not_covered @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) )
| ( P @ ( O @ ( covered @ ( covered @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) )
| ~ $true
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[49,39]) ).
thf(290,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( P @ ( O @ ( not_covered @ ( not_covered @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) )
| ( P @ ( O @ ( covered @ ( covered @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(311,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) )
!= ( P @ ( O @ ( not_covered @ ( not_covered @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) ) )
| ( ( A @ successor @ row )
!= ( J @ row ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ( P @ ( O @ ( covered @ ( covered @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) ),
inference(simp,[status(thm)],[290]) ).
thf(7474,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7453,62]) ).
thf(7475,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7474]) ).
thf(7476,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7475:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1742,plain,
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1134,23]) ).
thf(1743,plain,
( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1742]) ).
thf(1757,plain,
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[1743]) ).
thf(2189,plain,
( ( ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[1757]) ).
thf(6867,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6852,51]) ).
thf(6868,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6867]) ).
thf(6869,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6868:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(5522,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,62]) ).
thf(5523,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5522]) ).
thf(5524,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5523:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(7849,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7273,244]) ).
thf(7850,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7849]) ).
thf(7851,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7850:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(15106,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[7851,33,41,60]) ).
thf(15145,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15106,62]) ).
thf(15146,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[15145]) ).
thf(15147,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[15146:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(29813,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29712,51]) ).
thf(29814,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[29813]) ).
thf(29815,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[29814:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(733,plain,
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[554]) ).
thf(3923,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3901,47]) ).
thf(3924,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3923]) ).
thf(3925,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3924:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1122,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[812,62]) ).
thf(1123,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1124,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1123:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(26201,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26135,62]) ).
thf(26202,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[26201]) ).
thf(26203,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[26202:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(257,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ complement )
!= ( E @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[41,49]) ).
thf(258,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( not_covered ))]]) ).
thf(313,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(605,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[574,49]) ).
thf(606,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[605]) ).
thf(607,plain,
not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[606:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(2289,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[607,37,41,60]) ).
thf(2306,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2289,47]) ).
thf(2307,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2306]) ).
thf(2308,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2307:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(1105,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,62]) ).
thf(1106,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1105]) ).
thf(1107,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(3781,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3714,47]) ).
thf(3782,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3781]) ).
thf(3783,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3782:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(305,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( C @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( not_covered @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(306,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( not_covered @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( removed @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( removed ))]]) ).
thf(335,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( not_covered @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( removed @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(1088,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[809,62]) ).
thf(1089,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1088]) ).
thf(1090,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1089:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(269,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( n8 @ successor )
!= ( A @ successor ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( n9 @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[45,49]) ).
thf(270,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n9 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( n8 ))]]) ).
thf(318,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n9 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(107,plain,
( ( ( n1 @ successor )
!= ( n3 @ successor ) )
| ( n4 = n2 ) ),
inference(paramod_ordered,[status(thm)],[37,27]) ).
thf(119,plain,
( ( n1 != n3 )
| ( n4 = n2 ) ),
inference(simp,[status(thm)],[107]) ).
thf(6154,plain,
n1 != n3,
inference(simplifyReflect,[status(thm)],[119,6148]) ).
thf(7468,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7453,51]) ).
thf(7469,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7468]) ).
thf(7470,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7469:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(2810,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2779,55]) ).
thf(2811,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2810]) ).
thf(2812,plain,
covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2811:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(2893,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2812,49]) ).
thf(2894,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2893]) ).
thf(2895,plain,
covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n4 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2894:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( covered ))]]) ).
thf(7053,plain,
not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(rewrite,[status(thm)],[2895,41,60,29]) ).
thf(29823,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29712,62]) ).
thf(29824,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[29823]) ).
thf(29825,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[29824:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(6022,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5629,51]) ).
thf(6023,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6022]) ).
thf(6024,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6023:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(2667,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2649,47]) ).
thf(2668,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2667]) ).
thf(2669,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2668:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(4428,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4417,55]) ).
thf(4429,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4428]) ).
thf(4430,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4429:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(355,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[347,23]) ).
thf(356,plain,
( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(364,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n2 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[356]) ).
thf(367,plain,
( ( n2 @ row )
!= ( n8 @ row ) ),
inference(simp,[status(thm)],[364]) ).
thf(286,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) )
| ( R @ complement @ ( Q @ complement @ ( P @ complement @ ( O @ complement @ ( N @ complement @ ( M @ complement @ ( L @ complement @ ( K @ complement @ squares ) ) ) ) ) ) ) @ ( J @ successor @ row @ achievable ) )
| ~ $true
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[49,49]) ).
thf(287,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) )
| ( R @ complement @ ( Q @ complement @ ( P @ complement @ ( O @ complement @ ( N @ complement @ ( M @ complement @ ( L @ complement @ ( K @ complement @ squares ) ) ) ) ) ) ) @ ( J @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ complement @ complement @ ( H @ complement @ complement @ ( G @ complement @ complement @ ( F @ complement @ complement @ ( E @ complement @ complement @ ( D @ complement @ complement @ ( C @ complement @ complement @ ( B @ complement @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( S )),bind(B,$thf( T )),bind(C,$thf( U )),bind(D,$thf( V )),bind(E,$thf( W )),bind(F,$thf( X )),bind(G,$thf( Y )),bind(H,$thf( Z )),bind(I,$thf( ZA )),bind(J,$thf( S @ successor )),bind(K,$thf( T @ complement )),bind(L,$thf( U @ complement )),bind(M,$thf( V @ complement )),bind(N,$thf( W @ complement )),bind(O,$thf( X @ complement )),bind(P,$thf( Y @ complement )),bind(Q,$thf( Z @ complement )),bind(R,$thf( ZA @ complement ))]]) ).
thf(323,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ complement @ complement @ ( H @ complement @ complement @ ( G @ complement @ complement @ ( F @ complement @ complement @ ( E @ complement @ complement @ ( D @ complement @ complement @ ( C @ complement @ complement @ ( B @ complement @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(7264,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7251,58]) ).
thf(7265,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7264]) ).
thf(7266,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7265:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(7300,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7266,62]) ).
thf(7301,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7300]) ).
thf(7302,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7301:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(16990,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16957,58]) ).
thf(16991,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[16990]) ).
thf(16992,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[16991:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(17064,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16992,62]) ).
thf(17065,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[17064]) ).
thf(17066,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[17065:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(4294,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4247,51]) ).
thf(4295,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4294]) ).
thf(4296,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4295:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(5005,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4856,47]) ).
thf(5006,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5005]) ).
thf(5007,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5006:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(192,plain,
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,23]) ).
thf(193,plain,
( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(194,plain,
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(196,plain,
( ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( removed != covered )
| ( removed != covered )
| ( not_covered != covered )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(198,plain,
( ( removed != covered )
| ( not_covered != covered )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(237,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ complement )
!= ( H @ complement ) )
| ( I @ complement @ ( not_covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[60,49]) ).
thf(238,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( not_covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( covered ))]]) ).
thf(330,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( not_covered @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(4552,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4544,39]) ).
thf(4553,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4552]) ).
thf(4554,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4553:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(89,plain,
( ( ( n5 @ successor )
!= ( n4 @ successor ) )
| ( n6 = n5 ) ),
inference(paramod_ordered,[status(thm)],[33,29]) ).
thf(97,plain,
( ( n5 != n4 )
| ( n6 = n5 ) ),
inference(simp,[status(thm)],[89]) ).
thf(6587,plain,
( ( n7 != n7 )
| ( n5 != n4 )
| ( n6 != n4 ) ),
inference(paramod_ordered,[status(thm)],[84,6583]) ).
thf(6588,plain,
( ( n5 != n4 )
| ( n6 != n4 ) ),
inference(pattern_uni,[status(thm)],[6587:[]]) ).
thf(7645,plain,
( ( n6 != n6 )
| ( n5 != n4 )
| ( n5 != n4 )
| ( n5 != n4 ) ),
inference(paramod_ordered,[status(thm)],[97,6588]) ).
thf(7646,plain,
( ( n6 != n6 )
| ( n5 != n4 ) ),
inference(simp,[status(thm)],[7645]) ).
thf(7647,plain,
n5 != n4,
inference(pattern_uni,[status(thm)],[7646:[]]) ).
thf(205,plain,
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,23]) ).
thf(206,plain,
( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(210,plain,
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(223,plain,
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[210]) ).
thf(1044,plain,
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[666]) ).
thf(3510,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3486,47]) ).
thf(3511,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[3510]) ).
thf(3512,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[3511:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(17004,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16957,62]) ).
thf(17005,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[17004]) ).
thf(17006,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[17005:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(1645,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1113,23]) ).
thf(1646,plain,
( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1645]) ).
thf(1662,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( n8 @ row ) ) ),
inference(simp,[status(thm)],[1646]) ).
thf(2782,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2770,55]) ).
thf(2783,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2782]) ).
thf(2784,plain,
covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2783:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(1669,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1124,49]) ).
thf(1670,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1669]) ).
thf(1671,plain,
covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1670:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered )),bind(I,$thf( covered ))]]) ).
thf(4207,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1671,37,41,60]) ).
thf(203,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,39]) ).
thf(204,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(209,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) ) )
| ( ( n1 @ row )
!= ( A @ row ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(281,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,49]) ).
thf(282,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( removed @ complement @ ( removed @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n1 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(482,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(rewrite,[status(thm)],[283,35,41,27,60]) ).
thf(485,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[482,47]) ).
thf(486,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(487,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(4564,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4544,51]) ).
thf(4565,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4564]) ).
thf(4566,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4565:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(4857,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4786,47]) ).
thf(4858,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4857]) ).
thf(4859,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4858:[bind(A,$thf( n4 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(233,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( n4 @ successor )
!= ( A @ successor ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[29,49]) ).
thf(234,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[233:[bind(A,$thf( n4 ))]]) ).
thf(327,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(18950,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18917,55]) ).
thf(18951,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[18950]) ).
thf(18952,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[18951:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(19033,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18952,62]) ).
thf(19034,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[19033]) ).
thf(19035,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[19034:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(8087,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7302,244]) ).
thf(8088,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8087]) ).
thf(8089,plain,
not_covered @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8088:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered )),bind(H,$thf( covered ))]]) ).
thf(24008,plain,
not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[8089,33,41,60]) ).
thf(24060,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24008,51]) ).
thf(24061,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[24060]) ).
thf(24062,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[24061:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(5227,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5174,51]) ).
thf(5228,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5227]) ).
thf(5229,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5228:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(275,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( P @ ( O @ ( N @ ( M @ ( L @ ( not_covered @ ( not_covered @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) )
| ( P @ ( O @ ( N @ ( M @ ( L @ ( covered @ ( covered @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) )
| ~ $true
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[49,47]) ).
thf(276,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( P @ ( O @ ( N @ ( M @ ( L @ ( not_covered @ ( not_covered @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) )
| ( P @ ( O @ ( N @ ( M @ ( L @ ( covered @ ( covered @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(310,plain,
! [P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) )
!= ( P @ ( O @ ( N @ ( M @ ( L @ ( not_covered @ ( not_covered @ ( K @ squares ) ) ) ) ) ) ) ) )
| ( ( A @ successor @ row )
!= ( J @ row ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ( P @ ( O @ ( N @ ( M @ ( L @ ( covered @ ( covered @ ( K @ squares ) ) ) ) ) ) ) @ ( J @ row @ achievable ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(197,plain,
( ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( removed != covered )
| ( removed != covered )
| ( not_covered != covered )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[194]) ).
thf(199,plain,
( ( removed != covered )
| ( not_covered != covered )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[197]) ).
thf(78,plain,
( ( ( n6 @ successor )
!= ( n1 @ successor ) )
| ( n7 = n2 ) ),
inference(paramod_ordered,[status(thm)],[27,31]) ).
thf(81,plain,
( ( n6 != n1 )
| ( n7 = n2 ) ),
inference(simp,[status(thm)],[78]) ).
thf(138,plain,
( ( ( n7 @ successor )
!= ( n2 @ successor ) )
| ( n3 = n8 ) ),
inference(paramod_ordered,[status(thm)],[25,43]) ).
thf(139,plain,
( ( n7 != n2 )
| ( n3 = n8 ) ),
inference(simp,[status(thm)],[138]) ).
thf(4189,plain,
n7 != n2,
inference(simplifyReflect,[status(thm)],[139,2006]) ).
thf(4190,plain,
n6 != n1,
inference(simplifyReflect,[status(thm)],[81,4189]) ).
thf(301,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( D @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( not_covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(302,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( not_covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( removed @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( removed ))]]) ).
thf(331,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( not_covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( removed @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[302]) ).
thf(4435,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4417,47]) ).
thf(4436,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[4435]) ).
thf(4437,plain,
not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[4436:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(28444,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28376,62]) ).
thf(28445,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[28444]) ).
thf(28446,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[28445:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(63,plain,
( ( ( n1 @ successor )
!= ( n2 @ successor ) )
| ( n3 = n2 ) ),
inference(paramod_ordered,[status(thm)],[27,25]) ).
thf(65,plain,
( ( n1 != n2 )
| ( n3 = n2 ) ),
inference(simp,[status(thm)],[63]) ).
thf(6159,plain,
n1 != n2,
inference(simplifyReflect,[status(thm)],[65,6157]) ).
thf(22834,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22776,62]) ).
thf(22835,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[22834]) ).
thf(22836,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[22835:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(307,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( n6 @ successor )
!= ( A @ successor ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[31,49]) ).
thf(308,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( n6 ))]]) ).
thf(336,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[308]) ).
thf(1139,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[803,62]) ).
thf(1140,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1139]) ).
thf(1141,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1140:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(24069,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24008,62]) ).
thf(24070,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[24069]) ).
thf(24071,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[24070:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(13241,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13227,39]) ).
thf(13242,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( F @ ( not_covered @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( covered @ ( covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[13241]) ).
thf(13243,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[13242:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(259,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ complement )
!= ( F @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[41,49]) ).
thf(260,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( not_covered ))]]) ).
thf(314,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( covered @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( not_covered @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(2088,plain,
( ( ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[1662]) ).
thf(29718,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29653,51]) ).
thf(29719,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[29718]) ).
thf(29720,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[29719:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(2790,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2770,47]) ).
thf(2791,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( C @ ( not_covered @ ( not_covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( C @ ( covered @ ( covered @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2790]) ).
thf(2792,plain,
covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2791:[bind(A,$thf( n4 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(1248,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[946,49]) ).
thf(1249,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[1248]) ).
thf(1250,plain,
not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[1249:[bind(A,$thf( n3 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(3284,plain,
covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[1250,37,41,60]) ).
thf(8006,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7476,244]) ).
thf(8007,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( covered @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[8006]) ).
thf(8008,plain,
not_covered @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ squares ) ) ) ) ) ) ) @ ( n5 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[8007:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( covered ))]]) ).
thf(20888,plain,
not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(rewrite,[status(thm)],[8008,33,41,60]) ).
thf(368,plain,
n2 != n8,
inference(simp,[status(thm)],[367]) ).
thf(5630,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5512,51]) ).
thf(5631,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5630]) ).
thf(5632,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5631:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(20940,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20888,62]) ).
thf(20941,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[20940]) ).
thf(20942,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[20941:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(5897,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5582,62]) ).
thf(5898,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5897]) ).
thf(5899,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5898:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(271,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( n7 @ successor )
!= ( A @ successor ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[43,49]) ).
thf(272,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( n7 ))]]) ).
thf(319,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(133,plain,
( ( ( n7 @ successor )
!= ( n6 @ successor ) )
| ( n7 = n8 ) ),
inference(paramod_ordered,[status(thm)],[43,31]) ).
thf(146,plain,
( ( n7 != n6 )
| ( n7 = n8 ) ),
inference(simp,[status(thm)],[133]) ).
thf(38591,plain,
n7 != n6,
inference(simplifyReflect,[status(thm)],[146,38590]) ).
thf(878,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[812,49]) ).
thf(879,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n3 @ row @ achievable ) )
!= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(880,plain,
not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ ( covered @ complement @ ( covered @ complement @ ( not_covered @ complement @ ( not_covered @ complement @ squares ) ) ) ) ) ) ) @ ( n3 @ successor @ row @ achievable ),
inference(pattern_uni,[status(thm)],[879:[bind(A,$thf( n3 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(2956,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n4 @ row @ achievable ),
inference(rewrite,[status(thm)],[880,37,41,60]) ).
thf(26286,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26187,62]) ).
thf(26287,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[26286]) ).
thf(26288,plain,
covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[26287:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(15137,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15106,51]) ).
thf(15138,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[15137]) ).
thf(15139,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[15138:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(299,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( I @ complement ) )
| ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(300,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( not_covered @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( removed @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( removed ))]]) ).
thf(263,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ complement )
!= ( D @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[41,49]) ).
thf(264,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not_covered ))]]) ).
thf(315,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(13255,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13227,51]) ).
thf(13256,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[13255]) ).
thf(13257,plain,
not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[13256:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(13312,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13243,62]) ).
thf(13313,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[13312]) ).
thf(13314,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[13313:[bind(A,$thf( n6 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(295,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( removed @ complement )
!= ( E @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( not_covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[35,49]) ).
thf(296,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( not_covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( removed @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( removed ))]]) ).
thf(326,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( not_covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( removed @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(12340,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12306,62]) ).
thf(12341,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[12340]) ).
thf(12342,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[12341:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(35503,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35373,62]) ).
thf(35504,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[35503]) ).
thf(35505,plain,
covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n7 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[35504:[bind(A,$thf( n7 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(195,plain,
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( removed @ ( removed @ ( not_covered @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( n1 != n8 ) ),
inference(simp,[status(thm)],[194]) ).
thf(131,plain,
( ( ( n7 @ successor )
!= ( n1 @ successor ) )
| ( n2 = n8 ) ),
inference(paramod_ordered,[status(thm)],[43,27]) ).
thf(144,plain,
( ( n7 != n1 )
| ( n2 = n8 ) ),
inference(simp,[status(thm)],[131]) ).
thf(5019,plain,
n7 != n1,
inference(simplifyReflect,[status(thm)],[144,368]) ).
thf(12196,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12164,62]) ).
thf(12197,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[12196]) ).
thf(12198,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[12197:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(5198,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5171,62]) ).
thf(5199,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5198]) ).
thf(5200,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5199:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(6872,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6852,62]) ).
thf(6873,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[6872]) ).
thf(6874,plain,
covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[6873:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(5635,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5512,62]) ).
thf(5636,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5635]) ).
thf(5637,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5636:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(239,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ complement )
!= ( E @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( not_covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[60,49]) ).
thf(240,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( not_covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( covered ))]]) ).
thf(332,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( not_covered @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(69,plain,
( ( ( n4 @ successor )
!= ( n1 @ successor ) )
| ( n5 = n2 ) ),
inference(paramod_ordered,[status(thm)],[29,27]) ).
thf(73,plain,
( ( n4 != n1 )
| ( n5 = n2 ) ),
inference(simp,[status(thm)],[69]) ).
thf(6595,plain,
n4 != n1,
inference(simplifyReflect,[status(thm)],[73,6591]) ).
thf(5772,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5548,51]) ).
thf(5773,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( not_covered @ ( not_covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( covered @ ( covered @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[5772]) ).
thf(5774,plain,
not_covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[5773:[bind(A,$thf( n5 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(245,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ complement )
!= ( D @ complement ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( not_covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[60,49]) ).
thf(246,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( not_covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( covered ))]]) ).
thf(337,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( not_covered @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(7054,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7053,53]) ).
thf(7055,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( not_covered @ ( not_covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( covered @ ( covered @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[7054]) ).
thf(7056,plain,
not_covered @ ( covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n5 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[7055:[bind(A,$thf( n5 )),bind(B,$thf( not_covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( not_covered ))]]) ).
thf(273,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ $true
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[49,23]) ).
thf(274,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( A @ successor @ row @ achievable ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n8 @ row @ achievable ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(309,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) )
!= ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ ( covered @ squares ) ) ) ) ) ) ) ) )
| ( ( A @ successor @ row )
!= ( n8 @ row ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(29729,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29653,62]) ).
thf(29730,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ) )
!= ( not_covered @ ( not_covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( covered @ ( covered @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[29729]) ).
thf(29731,plain,
covered @ ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ squares ) ) ) ) ) ) ) @ ( n6 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[29730:[bind(A,$thf( n6 )),bind(B,$thf( not_covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(284,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( n1 @ successor )
!= ( A @ successor ) )
| ( I @ complement @ ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(paramod_ordered,[status(thm)],[27,49]) ).
thf(285,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( n1 ))]]) ).
thf(322,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ complement @ ( G @ complement @ ( F @ complement @ ( E @ complement @ ( D @ complement @ ( C @ complement @ ( B @ complement @ ( A @ complement @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ squares ) ) ) ) ) ) ) @ ( n1 @ row @ achievable ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(2451,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2441,55]) ).
thf(2452,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ) )
!= ( G @ ( F @ ( E @ ( D @ ( not_covered @ ( not_covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) )
| ( G @ ( F @ ( E @ ( D @ ( covered @ ( covered @ ( C @ ( B @ squares ) ) ) ) ) ) ) @ ( A @ row @ achievable ) ) ),
inference(simp,[status(thm)],[2451]) ).
thf(2453,plain,
covered @ ( not_covered @ ( not_covered @ ( not_covered @ ( covered @ ( covered @ ( not_covered @ ( covered @ squares ) ) ) ) ) ) ) @ ( n2 @ row @ achievable ),
inference(pattern_uni,[status(thm)],[2452:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( not_covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( covered ))]]) ).
thf(73112,plain,
$false,
inference(e,[status(thm)],[13266,809,1369,5593,2463,40770,666,5582,1110,347,4022,333,628,170,3417,18972,8463,9337,2114,13227,202,6732,12334,3317,5669,38590,56,3649,4870,4856,3693,5674,4247,3717,1078,26135,1095,7637,42,5935,5518,6583,35730,29653,3140,320,37,25,24,5195,2819,5269,52,5585,1264,125,3749,817,1087,11100,325,2158,4265,316,35489,29,6579,8468,46,29712,35396,57,924,9336,321,211,574,4871,7273,5892,4115,6157,6591,4087,16957,28436,4701,5629,12306,312,8454,61,60,9340,11069,2660,7129,3037,5174,3097,26187,2441,334,4915,35618,12190,5507,6696,33,6620,4878,5512,1174,28,38,625,329,7625,5779,4417,5492,6852,5551,4746,324,5515,317,6603,4544,53,3916,6148,4808,2245,6153,36993,328,40778,7453,554,3714,22828,18917,2053,3428,1207,6946,6625,2649,3032,8499,3703,6805,12164,5234,911,2006,7614,41,2370,2450,3486,5557,244,3624,508,311,558,7476,2189,6869,794,4004,3130,5524,2176,15147,15106,45,29815,733,3491,32,34,4786,191,3925,2225,22,44,4677,59,1124,27,26203,54,313,2308,1107,49,3783,335,1090,318,6154,7470,7053,29825,2361,6024,4805,2669,39,22776,890,3219,7504,4430,2812,367,35312,323,7302,17066,964,4296,2289,5007,198,330,4554,2770,2350,7647,223,6029,35,4084,1044,2481,3241,1113,563,3512,17006,5495,4067,2005,1662,9334,2784,812,342,1018,194,5548,4207,1134,209,487,4566,4859,1547,855,690,327,5171,38588,19035,24062,48,5229,1098,310,199,2224,4190,331,28376,7667,1235,6352,5186,50,1053,18952,4437,28446,4781,6159,22836,31,336,1141,7461,7251,24071,13243,314,43,991,2088,482,29720,2490,2792,3284,20888,368,2226,5632,20942,40,26,946,5899,6790,55,7114,23,319,38591,2956,24008,26288,58,7266,15139,6586,2095,40705,2779,300,620,315,35393,36,30,13257,51,13314,35378,1757,6580,835,262,210,326,12342,35505,195,5019,6729,35373,12198,635,5200,6874,6136,3543,8444,4242,5637,47,62,9335,332,1129,6595,5774,3901,803,337,935,7056,309,4189,29731,322,2453,16992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/11.01 % Computer : n012.cluster.edu
% 0.13/11.01 % Model : x86_64 x86_64
% 0.13/11.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/11.01 % Memory : 8046.5625MB
% 0.13/11.01 % OS : Linux 6.8.0-71-generic
% 0.13/11.01 % CPULimit : 300
% 0.13/11.01 % WCLimit : 300
% 0.13/11.01 % DateTime : Sat Sep 26 05:04:02 UTC 2026
% 0.13/11.02 % CPUTime :
% 0.13/11.02 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/11.44 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/11.59 % [INFO] Parsing done (145ms).
% 0.16/11.60 % [INFO] Running in sequential loop mode.
% 0.16/11.90 % [INFO] eprover registered as external prover.
% 0.16/11.91 % [INFO] Scanning for conjecture ...
% 0.16/11.99 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 1.93/12.04 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 1.93/12.07 % [INFO] Problem is propositional (TPTP CNF).
% 1.93/12.07 % [INFO] Type checking passed.
% 1.93/12.08 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 150.17/52.95 % External prover 'e' found a proof!
% 150.17/52.95 % [INFO] Killing All external provers ...
% 150.17/52.95 % Time passed: 41827ms (effective reasoning time: 41352ms)
% 150.17/52.96 % Axioms used in derivation (20): successor_of_2_is_3, successor_of_7_is_8, cover_columns_1_and_2, cover_columns_5_and_6, complement_of_covered_is_not_covered, successor_of_3_is_4, cover_columns_2_and_3, successor_of_6_is_7, complement_of_removed_is_not_covered, cover_columns_7_and_8, successor_of_1_is_2, cover_columns_4_and_5, first_row_initially, successor_of_8_is_9, complement_of_not_covered_is_covered, cover_columns_3_and_4, place_vertical_pieces, successor_of_4_is_5, successor_of_5_is_6, cover_columns_6_and_7
% 150.17/52.96 % No. of inferences in proof: 1131
% 150.17/52.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 41827 ms resp. 41352 ms w/o parsing
% 151.25/53.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 151.25/53.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------