%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL049-1 : 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 : n014.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 07:50:40 AM UTC 2026
% Result : Unsatisfiable 224.18s 64.30s
% Output : Refutation 218.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 5
% Syntax : Number of formulae : 972 ( 351 unt; 0 typ; 0 def)
% Number of atoms : 3022 ( 931 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 14388 (1630 ~;1000 |; 0 &;11758 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 3291 ( 0 ^;3291 !; 0 ?;3291 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
thf(12,plain,
! [B: $i,A: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(cnf,[status(esa)],[8]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) )),bind(D,$thf( D ))]]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[39]) ).
thf(638,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,51]) ).
thf(639,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[638]) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( Q )),bind(B,$thf( O @ ( Q @ not @ implies ) )),bind(C,$thf( R )),bind(D,$thf( R @ ( Q @ implies ) @ ( R @ ( O @ ( Q @ not @ implies ) @ implies ) @ implies ) )),bind(E,$thf( O )),bind(F,$thf( Q ))]]) ).
thf(671,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[640]) ).
thf(4,axiom,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
thf(11,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true
| ~ ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[45]) ).
thf(976,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,53]) ).
thf(977,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[976]) ).
thf(978,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[977:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ ( G @ implies ) )),bind(E,$thf( G ))]]) ).
thf(1017,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[978]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[36]) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,50]) ).
thf(1051,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1050]) ).
thf(1052,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1051:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1080,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1052]) ).
thf(28,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(29,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[28]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( L )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( L @ implies ) )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) ))]]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30]) ).
thf(1275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,54]) ).
thf(1276,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1275]) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1276:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( H @ ( H @ implies ) @ not )),bind(E,$thf( E ))]]) ).
thf(1355,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1277]) ).
thf(1707,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1355,51]) ).
thf(1708,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1707]) ).
thf(1709,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1708:[bind(A,$thf( Q )),bind(B,$thf( P @ ( Q @ not @ implies ) )),bind(C,$thf( N )),bind(D,$thf( P @ ( Q @ not @ implies ) @ ( N @ ( N @ implies ) @ not @ implies ) )),bind(E,$thf( P )),bind(F,$thf( Q ))]]) ).
thf(1727,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1709]) ).
thf(1,negated_conjecture,
~ ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_20) ).
thf(6,plain,
~ ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(1933,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,7]) ).
thf(1934,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1933]) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1934]) ).
thf(2583,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( A @ ( A @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[1964]) ).
thf(9928,plain,
! [C: $i,B: $i,A: $i] :
( ( B != b )
| ( ( C @ not )
!= ( b @ ( a @ implies ) ) )
| ( ( A @ ( A @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[2583]) ).
thf(9929,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( b @ ( a @ implies ) ) )
| ( ( A @ ( A @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[9928]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,50]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(81,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[75]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,9]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[100]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,9]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( E @ not )),bind(D,$thf( A ))]]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[61]) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[82,7]) ).
thf(2238,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2237]) ).
thf(2239,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2238:[bind(A,$thf( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) )),bind(B,$thf( B ))]]) ).
thf(2392,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2239]) ).
thf(2724,plain,
! [A: $i] :
( ~ $true
| ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[2392]) ).
thf(2740,plain,
! [A: $i] :
( ( ( A @ not )
!= A )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2724]) ).
thf(4340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,2740]) ).
thf(4341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4340]) ).
thf(4342,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= A )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4341:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(11941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,4342]) ).
thf(11942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11941]) ).
thf(11943,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[11942:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(12057,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11943]) ).
thf(708,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,51]) ).
thf(709,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[708]) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[709:[bind(A,$thf( V )),bind(B,$thf( W )),bind(C,$thf( S @ ( V @ ( W @ not @ implies ) @ not @ implies ) )),bind(D,$thf( S @ ( V @ ( W @ not @ implies ) @ not @ implies ) @ ( W @ implies ) )),bind(E,$thf( S )),bind(F,$thf( V @ ( W @ not @ implies ) ))]]) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[710]) ).
thf(2664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,2392]) ).
thf(2665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2664]) ).
thf(2666,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2665:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(2778,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2666]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,50]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[104]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[106]) ).
thf(305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,9]) ).
thf(306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[305]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( H @ ( K @ ( K @ ( K @ not @ implies ) @ implies ) @ not @ implies ) @ not )),bind(E,$thf( A ))]]) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[307]) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,7]) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[750]) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[751]) ).
thf(961,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( C != a ) ),
inference(simp,[status(thm)],[776]) ).
thf(962,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( a @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[961]) ).
thf(1925,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,54]) ).
thf(1926,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1925]) ).
thf(1927,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1926:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) )),bind(E,$thf( I @ ( I @ implies ) @ not )),bind(F,$thf( F ))]]) ).
thf(1969,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1927]) ).
thf(19114,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1969,51]) ).
thf(19115,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[19114]) ).
thf(19116,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[19115:[bind(A,$thf( W @ ( Z @ ( ZA @ not @ implies ) @ not @ implies ) )),bind(B,$thf( U )),bind(C,$thf( Z )),bind(D,$thf( ZA )),bind(E,$thf( W @ ( Z @ ( ZA @ not @ implies ) @ not @ implies ) @ ( U @ ( U @ implies ) @ not @ implies ) )),bind(F,$thf( W )),bind(G,$thf( Z @ ( ZA @ not @ implies ) ))]]) ).
thf(19246,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[19116]) ).
thf(19318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19246,2392]) ).
thf(19319,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[19318]) ).
thf(19320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[19319:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( L @ ( O @ ( P @ not @ implies ) @ not @ implies ) @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(19611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[19320]) ).
thf(2739,plain,
! [A: $i] :
( ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2724]) ).
thf(3013,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2739]) ).
thf(3014,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) ) ),
inference(simp,[status(thm)],[3013]) ).
thf(3015,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3014:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(3168,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3015]) ).
thf(4271,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[3168]) ).
thf(5193,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4271,50]) ).
thf(5194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5193]) ).
thf(5195,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5194:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(5253,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5195]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[46]) ).
thf(5904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ( D @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[5253,47]) ).
thf(5905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ( D @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5904]) ).
thf(5906,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( A @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5905:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ ( H @ implies ) @ not @ not )),bind(D,$thf( A ))]]) ).
thf(5940,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( A @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5906]) ).
thf(4361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,2392]) ).
thf(4362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4361]) ).
thf(4363,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4362:[bind(A,$thf( D @ not )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(4529,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4363]) ).
thf(16656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[5940,4529]) ).
thf(16657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16656]) ).
thf(16658,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[16657:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D ))]]) ).
thf(16836,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16658]) ).
thf(2614,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2392]) ).
thf(2615,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2614]) ).
thf(2616,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2615:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2768,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2616]) ).
thf(2823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,2768]) ).
thf(2824,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2823]) ).
thf(2856,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2824]) ).
thf(7965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( D @ implies ) @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2856]) ).
thf(7966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[7965]) ).
thf(7967,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[7966:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ ( F @ not @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(8005,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[7967]) ).
thf(1278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,54]) ).
thf(1279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1278]) ).
thf(1280,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1279:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) )),bind(E,$thf( L )),bind(F,$thf( F ))]]) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1280]) ).
thf(31,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(32,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[33]) ).
thf(10015,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( H @ ( G @ implies ) @ ( H @ ( F @ implies ) @ implies ) @ ( F @ ( G @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1323,49]) ).
thf(10016,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( H @ ( G @ implies ) @ ( H @ ( F @ implies ) @ implies ) @ ( F @ ( G @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[10015]) ).
thf(10017,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10016:[bind(A,$thf( ZD @ ( ZG @ ( ZH @ not @ implies ) @ not @ implies ) @ ( ZD @ ( ZA @ implies ) @ implies ) )),bind(B,$thf( ZA )),bind(C,$thf( ZG )),bind(D,$thf( ZH )),bind(E,$thf( ZD @ ( ZG @ ( ZH @ not @ implies ) @ not @ implies ) @ ( ZD @ ( ZA @ implies ) @ implies ) @ ( ZH @ implies ) )),bind(F,$thf( ZA )),bind(G,$thf( ZG @ ( ZH @ not @ implies ) @ not )),bind(H,$thf( ZD ))]]) ).
thf(10149,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[10017]) ).
thf(1114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,50]) ).
thf(1115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1114]) ).
thf(1116,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1116]) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,50]) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[70]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[72]) ).
thf(1819,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1145,79]) ).
thf(1820,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1819]) ).
thf(1821,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1820:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( N @ ( N @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(1882,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1821]) ).
thf(969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,53]) ).
thf(970,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[969]) ).
thf(971,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[970:[bind(A,$thf( P @ ( P @ not @ implies ) )),bind(B,$thf( P )),bind(C,$thf( N )),bind(D,$thf( N @ ( P @ ( P @ not @ implies ) @ implies ) @ ( N @ ( P @ implies ) @ implies ) )),bind(E,$thf( P ))]]) ).
thf(1015,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[971]) ).
thf(1402,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,51]) ).
thf(1403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[1402]) ).
thf(1404,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1403:[bind(A,$thf( O @ ( P @ not @ implies ) )),bind(B,$thf( P )),bind(C,$thf( O @ ( P @ not @ implies ) @ ( P @ ( P @ not @ implies ) @ implies ) )),bind(D,$thf( O )),bind(E,$thf( P ))]]) ).
thf(1426,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1404]) ).
thf(1609,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,7]) ).
thf(1610,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1609]) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1610]) ).
thf(2062,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( B @ ( B @ not @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1637]) ).
thf(2654,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,2392]) ).
thf(2655,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2654]) ).
thf(2656,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2655:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(2776,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2656]) ).
thf(3083,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,2739]) ).
thf(3084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3083]) ).
thf(3085,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ not @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3084:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(3153,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ not @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3085]) ).
thf(2797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,2768]) ).
thf(2798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2797]) ).
thf(2854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2798]) ).
thf(2684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,2392]) ).
thf(2685,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2684]) ).
thf(2686,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2685:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2782,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2686]) ).
thf(3761,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[2782]) ).
thf(3788,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3761]) ).
thf(5607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,3788]) ).
thf(5608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) ) ),
inference(simp,[status(thm)],[5607]) ).
thf(5609,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5608:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(5785,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5609]) ).
thf(9023,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[5785]) ).
thf(15243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[1017,9023]) ).
thf(15244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[15243]) ).
thf(15245,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15244:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(15503,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,15245]) ).
thf(15504,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[15503]) ).
thf(15579,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[15504]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,50]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[67]) ).
thf(2617,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[1017,2392]) ).
thf(2618,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2617]) ).
thf(2733,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2618]) ).
thf(3948,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,2733]) ).
thf(3949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[3948]) ).
thf(3950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3949:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( L @ ( M @ not @ implies ) @ ( M @ implies ) @ not @ implies ) ))]]) ).
thf(4043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3950]) ).
thf(2624,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2392]) ).
thf(2625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2624]) ).
thf(2626,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2625:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(2770,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2626]) ).
thf(3464,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2770]) ).
thf(3465,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3464]) ).
thf(3534,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[3465]) ).
thf(19020,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( H @ ( G @ implies ) @ ( H @ ( F @ implies ) @ implies ) @ ( F @ ( G @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1969,49]) ).
thf(19021,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( H @ ( G @ implies ) @ ( H @ ( F @ implies ) @ implies ) @ ( F @ ( G @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[19020]) ).
thf(19022,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[19021:[bind(A,$thf( ZA @ ( ZB @ not @ implies ) @ ( ZA @ ( X @ implies ) @ implies ) )),bind(B,$thf( U )),bind(C,$thf( X )),bind(D,$thf( ZB )),bind(E,$thf( ZA @ ( ZB @ not @ implies ) @ ( ZA @ ( X @ implies ) @ implies ) @ ( U @ ( U @ implies ) @ not @ implies ) )),bind(F,$thf( X )),bind(G,$thf( ZB @ not )),bind(H,$thf( ZA ))]]) ).
thf(19230,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[19022]) ).
thf(5140,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4271,2392]) ).
thf(5141,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5140]) ).
thf(5142,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5141:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) @ not ))]]) ).
thf(5257,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5142]) ).
thf(3654,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[1017,2782]) ).
thf(3655,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3654]) ).
thf(3781,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3655]) ).
thf(1284,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1145,54]) ).
thf(1285,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1284]) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1285:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( A )),bind(E,$thf( I @ ( L @ ( L @ implies ) @ not @ implies ) @ not )),bind(F,$thf( F ))]]) ).
thf(1327,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1286]) ).
thf(7911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( D @ implies ) @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2856]) ).
thf(7912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[7911]) ).
thf(7913,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[7912:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(8012,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[7913]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,7]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[68]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( B @ not )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[76]) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ not )
!= a )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[113]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,133]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[147]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,158]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[195]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[197]) ).
thf(1044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,208]) ).
thf(1045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[1044]) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1078,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1046]) ).
thf(685,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,49]) ).
thf(686,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[685]) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[686:[bind(A,$thf( T )),bind(B,$thf( X )),bind(C,$thf( W @ ( X @ not @ implies ) @ ( W @ ( T @ implies ) @ implies ) )),bind(D,$thf( W @ ( X @ not @ implies ) @ ( W @ ( T @ implies ) @ implies ) @ ( X @ implies ) )),bind(E,$thf( T )),bind(F,$thf( X @ not )),bind(G,$thf( W ))]]) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[687]) ).
thf(1001,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[727,53]) ).
thf(1002,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1002:[bind(A,$thf( M )),bind(B,$thf( P )),bind(C,$thf( S @ ( S @ ( S @ not @ implies ) @ implies ) )),bind(D,$thf( P @ ( S @ ( S @ ( S @ not @ implies ) @ implies ) @ not @ implies ) @ ( P @ ( M @ implies ) @ implies ) )),bind(E,$thf( S ))]]) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1003]) ).
thf(8825,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1016,51]) ).
thf(8826,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[8825]) ).
thf(8827,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[8826:[bind(A,$thf( T )),bind(B,$thf( S @ ( T @ not @ implies ) )),bind(C,$thf( N )),bind(D,$thf( S @ ( T @ not @ implies ) @ ( N @ ( N @ ( N @ not @ implies ) @ implies ) @ not @ implies ) )),bind(E,$thf( S )),bind(F,$thf( T ))]]) ).
thf(8911,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[8827]) ).
thf(10078,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1323,51]) ).
thf(10079,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[10078]) ).
thf(10080,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10079:[bind(A,$thf( Z @ ( ZC @ ( ZF @ ( ZG @ not @ implies ) @ not @ implies ) @ not @ implies ) )),bind(B,$thf( ZC )),bind(C,$thf( ZF )),bind(D,$thf( ZG )),bind(E,$thf( Z @ ( ZC @ ( ZF @ ( ZG @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( ZG @ implies ) )),bind(F,$thf( Z )),bind(G,$thf( ZC @ ( ZF @ ( ZG @ not @ implies ) @ not @ implies ) ))]]) ).
thf(10163,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[10080]) ).
thf(10369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10163,133]) ).
thf(10370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a ) ),
inference(simp,[status(thm)],[10369]) ).
thf(10371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[10370:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( I @ ( L @ ( O @ ( P @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( P @ implies ) ))]]) ).
thf(10545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[10371]) ).
thf(1601,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,54]) ).
thf(1602,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1601]) ).
thf(1603,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1602:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) )),bind(D,$thf( K @ ( K @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(1641,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1603]) ).
thf(14293,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1641,51]) ).
thf(14294,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[14293]) ).
thf(14295,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[14294:[bind(A,$thf( V @ ( Y @ ( Z @ not @ implies ) @ not @ implies ) )),bind(B,$thf( Y )),bind(C,$thf( Z )),bind(D,$thf( V @ ( Y @ ( Z @ not @ implies ) @ not @ implies ) @ ( Z @ ( Z @ not @ implies ) @ implies ) )),bind(E,$thf( V )),bind(F,$thf( Y @ ( Z @ not @ implies ) ))]]) ).
thf(14396,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[14295]) ).
thf(3987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,2733]) ).
thf(3988,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[3987]) ).
thf(3989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3988:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( I @ ( L @ ( M @ not @ implies ) @ not @ implies ) @ ( M @ implies ) ))]]) ).
thf(4030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[3989]) ).
thf(1952,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,79]) ).
thf(1953,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1952]) ).
thf(1954,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( E @ not @ implies ) @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1953:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( M @ ( N @ not @ implies ) @ ( K @ ( K @ implies ) @ not @ implies ) ))]]) ).
thf(1967,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( E @ not @ implies ) @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1954]) ).
thf(4465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,158]) ).
thf(4466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4465]) ).
thf(4467,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ not )
!= a )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4466:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(2687,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,2392]) ).
thf(2688,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2687]) ).
thf(2748,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2688]) ).
thf(7411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ not ) )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2748]) ).
thf(7412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ not ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[7411]) ).
thf(7413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[7412:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(7628,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[7413]) ).
thf(3789,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= B )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3761]) ).
thf(4171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= C )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,3789]) ).
thf(4172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= C ) ),
inference(simp,[status(thm)],[4171]) ).
thf(4173,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[4172:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(4249,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[4173]) ).
thf(2886,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2740]) ).
thf(2887,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B ) ),
inference(simp,[status(thm)],[2886]) ).
thf(2888,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2887:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2957,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(simp,[status(thm)],[2888]) ).
thf(758,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,50]) ).
thf(759,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[758]) ).
thf(760,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[759:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( I @ ( L @ ( M @ not @ implies ) @ not @ implies ) @ ( M @ implies ) ))]]) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[760]) ).
thf(875,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[787,50]) ).
thf(876,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[875]) ).
thf(877,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[876:[bind(A,$thf( H )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( M @ ( P @ ( Q @ not @ implies ) @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) ))]]) ).
thf(898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[877]) ).
thf(91,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,50]) ).
thf(92,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( L @ ( M @ not @ implies ) @ ( M @ implies ) @ not @ implies ) ))]]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[93]) ).
thf(172,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,50]) ).
thf(173,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[172]) ).
thf(174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( P @ ( Q @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[174]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( A @ not @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ not @ implies ) )),bind(C,$thf( E ))]]) ).
thf(52,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( A @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[42]) ).
thf(23410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( E @ ( C @ not @ implies ) @ not )
!= a )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,4467]) ).
thf(23411,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( E @ ( C @ not @ implies ) @ not )
!= a )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[23410]) ).
thf(23412,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ not @ implies ) @ not )
!= a )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[23411:[bind(A,$thf( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(23555,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ not @ implies ) @ not )
!= a )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[23412]) ).
thf(169,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ $true
| ~ ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[97,9]) ).
thf(170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[169]) ).
thf(171,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( H @ ( K @ ( P @ ( Q @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) )),bind(F,$thf( F ))]]) ).
thf(184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[171]) ).
thf(2689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[727,2392]) ).
thf(2690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2689]) ).
thf(2691,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2690:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(2755,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2691]) ).
thf(4270,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[3168]) ).
thf(4930,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,4270]) ).
thf(4931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4930]) ).
thf(4932,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4931:[bind(A,$thf( E @ ( E @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(5106,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4932]) ).
thf(18780,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4271,5106]) ).
thf(18781,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[18780]) ).
thf(18782,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[18781:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(9137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8911,2392]) ).
thf(9138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9137]) ).
thf(9139,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9138:[bind(A,$thf( I )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( N @ ( O @ not @ implies ) @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(9315,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[9139]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,133]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[144]) ).
thf(5201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= a )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4271,158]) ).
thf(5202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= a )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5201]) ).
thf(5203,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ not )
!= a )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5202:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(5256,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ not )
!= a )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5203]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(19,plain,
! [A: $i] :
( ( A
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[15]) ).
thf(20,plain,
( ( b @ ( b @ ( a @ implies ) @ implies ) @ ( b @ ( b @ ( a @ implies ) @ implies ) @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[19]) ).
thf(2609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1355,2392]) ).
thf(2610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2609]) ).
thf(2611,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2610:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(2767,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2611]) ).
thf(2709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[79,2392]) ).
thf(2710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2709]) ).
thf(2711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2710:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( F @ ( I @ ( J @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2711]) ).
thf(25882,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ~ ( F @ is_a_theorem )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[333,2759]) ).
thf(25883,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ ( F @ is_a_theorem )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[25882]) ).
thf(25884,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[25883:[bind(A,$thf( I @ ( L @ ( M @ not @ implies ) @ not @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( L )),bind(F,$thf( M ))]]) ).
thf(26160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[25884]) ).
thf(5221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4271,79]) ).
thf(5222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5221]) ).
thf(5223,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5222:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( G @ implies ) @ not ))]]) ).
thf(5264,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5223]) ).
thf(3468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2770]) ).
thf(3469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3468]) ).
thf(3524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[3469]) ).
thf(186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,158]) ).
thf(187,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[188]) ).
thf(3960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,2733]) ).
thf(3961,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[3960]) ).
thf(3962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3961:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( L @ ( M @ not @ implies ) @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(4050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3962]) ).
thf(6024,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ $true
| ~ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[54,4529]) ).
thf(6025,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6024]) ).
thf(6026,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[6025:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(6157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6026]) ).
thf(28449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[18782,4270]) ).
thf(28450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[28449]) ).
thf(28451,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[28450:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2827,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2768]) ).
thf(2828,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2827]) ).
thf(2861,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2828]) ).
thf(126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,76]) ).
thf(127,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( L @ ( M @ not @ implies ) @ ( M @ implies ) @ not @ implies ) ))]]) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(2634,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[787,2392]) ).
thf(2635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2634]) ).
thf(2636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2635:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( G @ ( L @ ( O @ ( P @ not @ implies ) @ not @ implies ) @ ( P @ implies ) @ not @ implies ) ))]]) ).
thf(2772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2636]) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[727,7]) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[809]) ).
thf(835,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[810]) ).
thf(25141,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( C != a ) ),
inference(simp,[status(thm)],[835]) ).
thf(25142,plain,
! [B: $i,A: $i] :
( ( B @ ( a @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[25141]) ).
thf(25587,plain,
! [B: $i,A: $i] :
( ( ( B @ ( a @ not @ implies ) )
!= b )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[25142]) ).
thf(9024,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[5785]) ).
thf(10860,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1327,51]) ).
thf(10861,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[10860]) ).
thf(10862,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10861:[bind(A,$thf( U )),bind(B,$thf( T @ ( U @ not @ implies ) )),bind(C,$thf( O )),bind(D,$thf( R )),bind(E,$thf( T @ ( U @ not @ implies ) @ ( O @ ( R @ ( R @ implies ) @ not @ implies ) @ not @ implies ) )),bind(F,$thf( T )),bind(G,$thf( U ))]]) ).
thf(10951,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[10862]) ).
thf(11169,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10951,2392]) ).
thf(11170,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11169]) ).
thf(11171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11170:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( O @ ( P @ not @ implies ) @ ( J @ ( M @ ( M @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(11357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[11171]) ).
thf(2589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,2392]) ).
thf(2590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2589]) ).
thf(2591,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2590:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( N @ ( K @ implies ) @ implies ) @ ( K @ ( M @ implies ) @ implies ) ))]]) ).
thf(2762,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2591]) ).
thf(4278,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) )
| ~ ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[1017,3168]) ).
thf(4323,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) )
| ~ ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4278]) ).
thf(2639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,2392]) ).
thf(2640,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2639]) ).
thf(2641,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2640:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2773,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2641]) ).
thf(322,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,208]) ).
thf(323,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[322]) ).
thf(324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[323:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( N @ ( N @ ( N @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[324]) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,133]) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[153]) ).
thf(274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,208]) ).
thf(275,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[274]) ).
thf(276,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( O )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( P @ ( O @ implies ) @ ( P @ ( M @ implies ) @ implies ) @ ( M @ ( O @ implies ) @ implies ) ))]]) ).
thf(297,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[276]) ).
thf(7935,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( E @ ( E @ implies ) @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,2856]) ).
thf(7936,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( E @ ( E @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[7935]) ).
thf(7937,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[7936:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(7989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[7937]) ).
thf(761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,158]) ).
thf(762,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[761]) ).
thf(763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[762:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( I @ ( L @ ( M @ not @ implies ) @ not @ implies ) @ ( M @ implies ) ))]]) ).
thf(788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[763]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,76]) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[122]) ).
thf(2644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,2392]) ).
thf(2645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2644]) ).
thf(2646,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2645:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2774,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2646]) ).
thf(3552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2774]) ).
thf(3553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3552]) ).
thf(3618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3553]) ).
thf(3746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( D @ ( E @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[79,2782]) ).
thf(3747,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( D @ ( E @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3746]) ).
thf(3748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3747:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( G @ ( J @ ( K @ not @ implies ) @ not @ implies ) ))]]) ).
thf(3799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[3748]) ).
thf(2619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,2392]) ).
thf(2620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2619]) ).
thf(2621,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2620:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(2769,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2621]) ).
thf(14899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14396,2392]) ).
thf(14900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14899]) ).
thf(14901,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[14900:[bind(A,$thf( K )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( K @ ( N @ ( O @ not @ implies ) @ not @ implies ) @ ( O @ ( O @ not @ implies ) @ implies ) ))]]) ).
thf(15142,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[14901]) ).
thf(826,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[727,51]) ).
thf(827,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[826]) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[827:[bind(A,$thf( N )),bind(B,$thf( Q )),bind(C,$thf( V @ ( W @ not @ implies ) @ ( W @ implies ) )),bind(D,$thf( Q @ ( V @ ( W @ not @ implies ) @ ( W @ implies ) @ not @ implies ) @ ( Q @ ( N @ implies ) @ implies ) )),bind(E,$thf( V )),bind(F,$thf( W ))]]) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[828]) ).
thf(2704,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,2392]) ).
thf(2705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2704]) ).
thf(2706,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2705:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2758,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2706]) ).
thf(4458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,3168]) ).
thf(4459,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4458:[bind(A,$thf( F @ ( F @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(4544,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4459]) ).
thf(12986,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( E @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[54,4544]) ).
thf(12987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( E @ implies ) @ is_a_theorem ) )
| ~ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12986]) ).
thf(12988,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12987:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G @ ( B @ implies ) ))]]) ).
thf(13153,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12988]) ).
thf(817,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[727,50]) ).
thf(818,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[817]) ).
thf(819,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[818:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( M @ ( N @ not @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( N @ implies ) ))]]) ).
thf(842,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[819]) ).
thf(2807,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,2768]) ).
thf(2808,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2807]) ).
thf(2840,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2808]) ).
thf(2815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,2768]) ).
thf(2816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2815]) ).
thf(2858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2816]) ).
thf(7089,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[2759]) ).
thf(7116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[7089]) ).
thf(5997,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,4529]) ).
thf(5998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[5997]) ).
thf(6148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[5998]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,7]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(1053,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,158]) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[1053]) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1054:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1082,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1055]) ).
thf(25708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[333,133]) ).
thf(25709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[25708]) ).
thf(25710,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not )
!= a )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[25709:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(62,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,9]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[64]) ).
thf(14896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14396,133]) ).
thf(14897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[14896]) ).
thf(14898,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[14897:[bind(A,$thf( K )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( K @ ( N @ ( O @ not @ implies ) @ not @ implies ) @ ( O @ ( O @ not @ implies ) @ implies ) ))]]) ).
thf(15141,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[14898]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[25]) ).
thf(635,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= b )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[55]) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= b )
| ( C != b )
| ( B != a )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[635]) ).
thf(637,plain,
! [A: $i] :
( ( ( b @ ( A @ implies ) )
!= b )
| ( ( a @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[636]) ).
thf(6114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4271,4529]) ).
thf(6115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6114]) ).
thf(6116,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[6115:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(6181,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6116]) ).
thf(17673,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[6181,133]) ).
thf(17674,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17673]) ).
thf(17675,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ not )
!= a )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17674:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(18055,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ not )
!= a )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17675]) ).
thf(16425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[5940,52]) ).
thf(16426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16425]) ).
thf(16427,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[16426:[bind(A,$thf( E @ ( E @ not @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(16844,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16427]) ).
thf(1581,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,133]) ).
thf(1582,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a ) ),
inference(simp,[status(thm)],[1581]) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1582:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(1644,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1583]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,158]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[206]) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,50]) ).
thf(1618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1617]) ).
thf(1619,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1618:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1647,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1619]) ).
thf(2679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1647,2392]) ).
thf(2680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2679]) ).
thf(2681,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2680:[bind(A,$thf( F )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( F @ ( N @ ( O @ not @ implies ) @ ( O @ ( O @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2781,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2681]) ).
thf(86,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[78,9]) ).
thf(87,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( G @ ( L @ ( M @ not @ implies ) @ ( M @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[88]) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,133]) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1363,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1362:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1363]) ).
thf(1906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,133]) ).
thf(1907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[1906]) ).
thf(1908,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1907:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(1974,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1908]) ).
thf(2791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,2768]) ).
thf(2792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2791]) ).
thf(2862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2792]) ).
thf(2604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,2392]) ).
thf(2605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2604]) ).
thf(2606,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2605:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(2766,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2606]) ).
thf(2694,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2392]) ).
thf(2695,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2694]) ).
thf(2696,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2695:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2756,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2696]) ).
thf(1944,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,158]) ).
thf(1945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[1944]) ).
thf(1946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1945:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( L @ ( M @ not @ implies ) @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(1979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1946]) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[722,133]) ).
thf(739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[738]) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[739:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(779,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[740]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,76]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(3580,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2774]) ).
thf(3581,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3580]) ).
thf(3592,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3581]) ).
thf(2904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,2740]) ).
thf(2905,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C ) ),
inference(simp,[status(thm)],[2904]) ).
thf(2906,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2905:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2963,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[2906]) ).
thf(280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,208]) ).
thf(281,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[280]) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ not @ implies ) ))]]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[282]) ).
thf(1056,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,300]) ).
thf(1057,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[1056]) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1057:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ implies ) ))]]) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1058]) ).
thf(3476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,2770]) ).
thf(3477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3476]) ).
thf(3508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[3477]) ).
thf(1684,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1355,49]) ).
thf(1685,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1684]) ).
thf(1686,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1685:[bind(A,$thf( W @ ( Y @ implies ) )),bind(B,$thf( Z @ ( Y @ implies ) @ ( Z @ ( W @ implies ) @ implies ) )),bind(C,$thf( T )),bind(D,$thf( Z @ ( Y @ implies ) @ ( Z @ ( W @ implies ) @ implies ) @ ( T @ ( T @ implies ) @ not @ implies ) )),bind(E,$thf( W )),bind(F,$thf( Y )),bind(G,$thf( Z ))]]) ).
thf(1732,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1686]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ $true
| ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,47]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[241]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[243]) ).
thf(1941,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1727,50]) ).
thf(1942,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1941]) ).
thf(1943,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1942:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( L @ ( M @ not @ implies ) @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(1977,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1943]) ).
thf(2714,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1977,2392]) ).
thf(2715,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2714]) ).
thf(2716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2715:[bind(A,$thf( G )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( G @ ( O @ ( P @ not @ implies ) @ ( M @ ( M @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2716]) ).
thf(292,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,208]) ).
thf(293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[292]) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( J @ ( J @ ( J @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[294]) ).
thf(2697,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,2392]) ).
thf(2698,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2697]) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2698]) ).
thf(4468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,2739]) ).
thf(4469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4468]) ).
thf(4470,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4469:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,47]) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[235]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[237]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,133]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[156]) ).
thf(3496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2770]) ).
thf(3497,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3496]) ).
thf(3523,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[3497]) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,7]) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[691]) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[692]) ).
thf(965,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( ( C @ ( A @ ( B @ not @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[717]) ).
thf(7117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= C )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[7089]) ).
thf(12097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not )
!= D )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,7117]) ).
thf(12098,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not )
!= D ) ),
inference(simp,[status(thm)],[12097]) ).
thf(12099,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(pattern_uni,[status(thm)],[12098:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(12186,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(simp,[status(thm)],[12099]) ).
thf(4330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( C @ ( D @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,2782]) ).
thf(4331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( C @ ( D @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4330]) ).
thf(4332,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4331:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(23097,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( E @ ( C @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,4332]) ).
thf(23098,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( E @ ( C @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[23097]) ).
thf(23099,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[23098:[bind(A,$thf( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(23386,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[23099]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[18]) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( a @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(2892,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2740]) ).
thf(2893,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C ) ),
inference(simp,[status(thm)],[2892]) ).
thf(2894,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2893:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(2959,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[2894]) ).
thf(25588,plain,
! [B: $i,A: $i] :
( ( ( B @ ( a @ not @ implies ) )
!= b )
| ( B != b )
| ( A != a ) ),
inference(simp,[status(thm)],[25587]) ).
thf(25589,plain,
( ( b @ ( a @ not @ implies ) )
!= b ),
inference(simp,[status(thm)],[25588]) ).
thf(3993,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1145,2733]) ).
thf(3994,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) )
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[3993]) ).
thf(3995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3994:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( J @ ( M @ ( M @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(4032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3995]) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,53]) ).
thf(1374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[1373]) ).
thf(1375,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( I )),bind(B,$thf( I @ ( I @ not @ implies ) )),bind(C,$thf( I @ ( I @ ( I @ not @ implies ) @ ( I @ ( I @ not @ implies ) @ not @ implies ) @ implies ) )),bind(D,$thf( I ))]]) ).
thf(1427,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1375]) ).
thf(2065,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1427,133]) ).
thf(2066,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[2065]) ).
thf(2067,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[2066:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(2134,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[2067]) ).
thf(26,plain,
! [A: $i] :
( ( A != b )
| ( ( b @ ( a @ implies ) )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(27,plain,
( ( b @ ( a @ implies ) )
!= ( a @ not ) ),
inference(simp,[status(thm)],[26]) ).
thf(308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[112,9]) ).
thf(309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[308]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( G @ ( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[310]) ).
thf(175,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( E @ ( F @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,76]) ).
thf(176,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( E @ ( F @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( P @ ( Q @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,133]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(159,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[150]) ).
thf(3411,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2756]) ).
thf(3412,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3411]) ).
thf(3436,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3412]) ).
thf(4355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,133]) ).
thf(4356,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4355]) ).
thf(4357,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= a )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4356:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(8362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,4357]) ).
thf(8363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( C @ not )
!= a )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8362]) ).
thf(8364,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[8363:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(8461,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8364]) ).
thf(11166,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10951,133]) ).
thf(11167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a ) ),
inference(simp,[status(thm)],[11166]) ).
thf(11168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[11167:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( O @ ( P @ not @ implies ) @ ( J @ ( M @ ( M @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(11355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[11168]) ).
thf(2674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1145,2392]) ).
thf(2675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2674]) ).
thf(2676,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2675:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( F @ ( I @ ( L @ ( L @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2780,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2676]) ).
thf(189,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( E @ ( F @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,158]) ).
thf(190,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( E @ ( F @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[189]) ).
thf(191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( P @ ( Q @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[191]) ).
thf(2699,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1427,2392]) ).
thf(2700,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2699]) ).
thf(2701,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(2757,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2701]) ).
thf(9808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[9024,50]) ).
thf(9809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9808]) ).
thf(9810,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[9809:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) @ not ))]]) ).
thf(9905,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9810]) ).
thf(2934,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2740]) ).
thf(2935,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B ) ),
inference(simp,[status(thm)],[2934]) ).
thf(2936,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2935:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2974,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2936]) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[727,133]) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[797]) ).
thf(799,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[799]) ).
thf(1042,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,7]) ).
thf(1043,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1042]) ).
thf(1069,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1043]) ).
thf(1148,plain,
! [A: $i] :
( ( A
!= ( b @ ( b @ ( a @ implies ) @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[1069]) ).
thf(1149,plain,
( ( b @ ( b @ ( a @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[1148]) ).
thf(963,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( ( B @ ( a @ not @ implies ) @ not )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[962]) ).
thf(964,plain,
! [A: $i] :
( ( A @ ( a @ not @ implies ) @ not )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[963]) ).
thf(1180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1145,50]) ).
thf(1181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1180]) ).
thf(1182,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1181:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( J @ ( M @ ( M @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(1213,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1182]) ).
thf(3376,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2756]) ).
thf(3377,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3376]) ).
thf(3423,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3377]) ).
thf(114,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,76]) ).
thf(115,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(277,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ( ( E @ ( F @ ( G @ not @ implies ) @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,208]) ).
thf(278,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ( ( E @ ( F @ ( G @ not @ implies ) @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[277]) ).
thf(279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( Q )),bind(D,$thf( R )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( I @ ( L @ ( Q @ ( R @ not @ implies ) @ ( R @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(299,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[279]) ).
thf(56,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,50]) ).
thf(57,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[56]) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[58]) ).
thf(2647,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[1080,2392]) ).
thf(2648,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2647]) ).
thf(2752,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2648]) ).
thf(3388,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,2756]) ).
thf(3389,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3388]) ).
thf(3444,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3389]) ).
thf(1742,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,79]) ).
thf(1743,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1742]) ).
thf(1744,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1743:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( L @ ( M @ not @ implies ) @ ( M @ ( M @ not @ implies ) @ implies ) ))]]) ).
thf(1873,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1744]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,133]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( N @ ( K @ implies ) @ implies ) @ ( K @ ( M @ implies ) @ implies ) ))]]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[141]) ).
thf(1393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,50]) ).
thf(1394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1393]) ).
thf(1395,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1394:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(1420,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1395]) ).
thf(1021,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,133]) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[1021]) ).
thf(1023,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1022:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(1081,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1023]) ).
thf(7923,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( E @ ( E @ implies ) @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2856]) ).
thf(7924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( E @ ( E @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[7923]) ).
thf(7925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[7924:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ not @ implies ) @ ( J @ implies ) )),bind(E,$thf( E ))]]) ).
thf(8020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[7925]) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ( C != b )
| ( B
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( A @ ( B @ not @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[965]) ).
thf(968,plain,
! [A: $i] :
( ( b @ ( A @ ( b @ ( a @ implies ) @ not @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[967]) ).
thf(2787,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,2768]) ).
thf(2788,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2787]) ).
thf(2846,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2788]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[46]) ).
thf(2142,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( ( B @ not )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( B @ not @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2062]) ).
thf(2143,plain,
! [A: $i] :
( ( ( A @ not )
!= ( b @ ( a @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2142]) ).
thf(5054,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[4270]) ).
thf(5079,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5054]) ).
thf(2799,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2768]) ).
thf(2800,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2799]) ).
thf(2850,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2800]) ).
thf(4358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,2392]) ).
thf(4359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4358]) ).
thf(4360,plain,
! [B: $i,A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4359:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(18270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( C @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,4470]) ).
thf(18271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( C @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[18270]) ).
thf(18272,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[18271:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(18584,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[18272]) ).
thf(1024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,137]) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1024]) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1025:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1026]) ).
thf(163,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,133]) ).
thf(164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( G @ ( J @ ( O @ ( P @ not @ implies ) @ ( P @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[165]) ).
thf(13528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,4323]) ).
thf(13529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[13528]) ).
thf(13530,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[13529:[bind(A,$thf( J @ ( J @ implies ) @ not )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( J @ implies ) @ not ))]]) ).
thf(13602,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[13530]) ).
thf(325,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[112,47]) ).
thf(326,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[325]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( G @ ( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[327]) ).
thf(13470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,4323]) ).
thf(13471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[13470]) ).
thf(13472,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[13471:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A @ ( A @ not @ implies ) ))]]) ).
thf(13605,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[13472]) ).
thf(19315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19246,133]) ).
thf(19316,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= a ) ),
inference(simp,[status(thm)],[19315]) ).
thf(19317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[19316:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( L @ ( O @ ( P @ not @ implies ) @ not @ implies ) @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(19610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[19317]) ).
thf(2584,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,2392]) ).
thf(2585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2584]) ).
thf(2586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2585:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( G @ ( J @ ( O @ ( P @ not @ implies ) @ ( P @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2586]) ).
thf(1620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,158]) ).
thf(1621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[1620]) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1621:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1649,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1622]) ).
thf(9824,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[9024,2739]) ).
thf(9825,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9824]) ).
thf(9826,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[9825:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(9912,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9826]) ).
thf(13553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,4323]) ).
thf(13554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[13553]) ).
thf(13555,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[13554:[bind(A,$thf( F @ not )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ not ))]]) ).
thf(13615,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[13555]) ).
thf(2649,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1213,2392]) ).
thf(2650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2649]) ).
thf(2651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2650:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( P )),bind(E,$thf( G @ ( J @ ( M @ ( P @ ( P @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2651]) ).
thf(1660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1355,133]) ).
thf(1661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[1660]) ).
thf(1662,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[1661:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(1734,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[1662]) ).
thf(3548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2774]) ).
thf(3549,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3548]) ).
thf(3593,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3549]) ).
thf(1698,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1355,50]) ).
thf(1699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1698]) ).
thf(1700,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1699:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( K @ ( N @ ( N @ implies ) @ not @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1700]) ).
thf(2819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1145,2768]) ).
thf(2820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2819]) ).
thf(2853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2820]) ).
thf(2928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,2740]) ).
thf(2929,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2928]) ).
thf(2930,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2929:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2971,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2930]) ).
thf(2594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,2392]) ).
thf(2595,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2594]) ).
thf(2596,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2595:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(2764,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2596]) ).
thf(699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,50]) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[699]) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( N @ ( M @ implies ) @ ( N @ ( K @ ( M @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(731,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[701]) ).
thf(10372,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10163,2392]) ).
thf(10373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10372]) ).
thf(10374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10373:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( I @ ( L @ ( O @ ( P @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( P @ implies ) ))]]) ).
thf(10546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[10374]) ).
thf(13500,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ( ( B @ ( B @ implies ) )
!= ( C @ ( C @ implies ) @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,4323]) ).
thf(13501,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ( ( B @ ( B @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[13500]) ).
thf(13502,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[13501:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(14209,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1641,49]) ).
thf(14210,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[14209]) ).
thf(14211,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[14210:[bind(A,$thf( Z @ ( ZA @ not @ implies ) @ ( Z @ ( W @ implies ) @ implies ) )),bind(B,$thf( W )),bind(C,$thf( ZA )),bind(D,$thf( Z @ ( ZA @ not @ implies ) @ ( Z @ ( W @ implies ) @ implies ) @ ( ZA @ ( ZA @ not @ implies ) @ implies ) )),bind(E,$thf( W )),bind(F,$thf( ZA @ not )),bind(G,$thf( Z ))]]) ).
thf(14368,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[14211]) ).
thf(3380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2756]) ).
thf(3381,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3380]) ).
thf(3430,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3381]) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,76]) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1039]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1040:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1041]) ).
thf(3972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,2733]) ).
thf(3973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ not ) ) ),
inference(simp,[status(thm)],[3972]) ).
thf(3974,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3973:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(4025,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3974]) ).
thf(2669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,2392]) ).
thf(2670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2669]) ).
thf(2671,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2670:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( F @ ( I @ ( L @ ( L @ ( L @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2779,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2671]) ).
thf(2627,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,2392]) ).
thf(2628,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2627]) ).
thf(2736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2628]) ).
thf(3942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1426,2733]) ).
thf(3943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ not ) ) ),
inference(simp,[status(thm)],[3942]) ).
thf(3944,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3943:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(4039,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3944]) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[81,47]) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[255]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,7]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[89]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ implies ) @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(8474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[110,4360]) ).
thf(8475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8474]) ).
thf(8476,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[8475:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(8675,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8476]) ).
thf(2805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,2768]) ).
thf(2806,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2805]) ).
thf(2847,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2806]) ).
thf(3560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1080,2774]) ).
thf(3561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3560]) ).
thf(3605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3561]) ).
thf(679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,133]) ).
thf(680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[679]) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[680:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[681]) ).
thf(5229,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[4271]) ).
thf(5236,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5229]) ).
thf(2795,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1017,2768]) ).
thf(2796,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2795]) ).
thf(2864,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2796]) ).
thf(9134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8911,133]) ).
thf(9135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= a ) ),
inference(simp,[status(thm)],[9134]) ).
thf(9136,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(pattern_uni,[status(thm)],[9135:[bind(A,$thf( I )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( N @ ( O @ not @ implies ) @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(9314,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= a ),
inference(simp,[status(thm)],[9136]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[81,9]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[103]) ).
thf(311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,50]) ).
thf(312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[311]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(337,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[313]) ).
thf(5137,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4271,133]) ).
thf(5138,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= a )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5137]) ).
thf(5139,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not @ not )
!= a )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5138:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) @ not ))]]) ).
thf(5255,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not @ not )
!= a )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5139]) ).
thf(49104,plain,
$false,
inference(e,[status(thm)],[9929,12057,2778,333,962,19611,16836,8005,10149,1882,2062,2776,3153,2854,15579,4043,3534,10,19230,2740,5257,3781,1327,8012,1078,1426,8911,10545,14396,4030,1967,4467,25,7628,4249,2957,898,185,52,23555,184,2755,19246,110,1323,18782,9315,157,5256,20,2767,4270,1641,26160,78,3788,5264,3524,2782,211,4050,6157,28451,2861,132,2772,133,25587,2392,9024,11357,2762,6,4323,2773,334,1355,160,297,7989,2733,788,137,3618,97,3799,2769,15142,847,2758,13153,842,2840,1017,4544,9,53,2858,7116,6148,109,1082,1964,25710,77,15141,5253,637,18055,16844,1016,10163,1644,212,2781,96,1419,1974,2862,2766,2756,1979,779,134,3592,2748,2963,1071,10951,3508,1732,266,2761,298,2729,4470,264,161,3523,965,1727,12186,23386,22,5940,2959,25589,4032,2134,27,12,54,787,335,181,159,49,2759,3436,8461,11355,76,7,2856,208,1969,2774,81,1080,2780,213,2757,9905,2974,848,4332,1149,964,2770,1213,3423,1015,135,299,80,25142,2752,722,3444,1873,7117,162,5785,1420,4529,112,1081,8020,968,1145,2846,776,48,2143,1647,5079,2850,4360,18584,18,1070,50,1637,182,717,13602,5106,336,13605,19610,727,4342,11,1427,3168,2760,1649,9912,671,13615,2775,1734,3593,1721,3789,2853,158,55,2971,2764,731,10546,13502,14368,8,6181,3430,1077,2739,4025,2779,835,51,2736,2768,300,4039,273,4357,79,635,94,15245,8675,1977,2847,3605,9023,723,47,15,5236,2864,4271,9314,2583,111,337,5255,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL049-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.16/5.44 % Computer : n014.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 21:46:07 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 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
% 1.28/6.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/6.53 % [INFO] Parsing done (256ms).
% 1.83/6.55 % [INFO] Running in sequential loop mode.
% 2.63/7.15 % [INFO] eprover registered as external prover.
% 2.86/7.16 % [INFO] Scanning for conjecture ...
% 2.95/7.28 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.10/7.33 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.10/7.34 % [INFO] Problem is propositional (TPTP CNF).
% 3.10/7.34 % [INFO] Type checking passed.
% 3.10/7.35 % [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 ...
% 224.18/64.29 % External prover 'e' found a proof!
% 224.18/64.29 % [INFO] Killing All external provers ...
% 224.18/64.29 % Time passed: 58645ms (effective reasoning time: 57735ms)
% 224.18/64.29 % Axioms used in derivation (4): cn_1, cn_3, condensed_detachment, cn_2
% 224.18/64.29 % No. of inferences in proof: 972
% 224.18/64.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 58645 ms resp. 57735 ms w/o parsing
% 218.67/64.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 218.67/64.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------