%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL059-1 : 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 : n018.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 07:50:42 AM UTC 2026
% Result : Unsatisfiable 163.97s 42.89s
% Output : Refutation 166.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 5
% Syntax : Number of formulae : 945 ( 341 unt; 0 typ; 0 def)
% Number of atoms : 2938 ( 906 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 14482 (1575 ~; 977 |; 0 &;11930 @)
% ( 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 : 3141 ( 0 ^;3141 !; 0 ?;3141 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $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(624,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(625,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)],[624]) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[625:[bind(A,$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(644,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[626]) ).
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(1047,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)],[644,53]) ).
thf(1048,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)],[1047]) ).
thf(1049,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ ( G @ implies ) )),bind(E,$thf( G ))]]) ).
thf(1065,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1049]) ).
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(58,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(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 )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$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)],[60]) ).
thf(1,negated_conjecture,
~ ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_49) ).
thf(6,plain,
~ ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[82,7]) ).
thf(1969,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[1968]) ).
thf(1970,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[1969:[bind(A,$thf( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) )),bind(B,$thf( B ))]]) ).
thf(2071,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[1970]) ).
thf(2188,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)],[50,2071]) ).
thf(2189,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)],[2188]) ).
thf(2306,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)],[2189]) ).
thf(5613,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)],[1065,2306]) ).
thf(5614,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)],[5613]) ).
thf(5615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5614:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(5686,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[5615]) ).
thf(1021,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(1022,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)],[1021]) ).
thf(1023,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1022:[bind(A,$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(1066,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1023]) ).
thf(1451,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)],[1066,51]) ).
thf(1452,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)],[1451]) ).
thf(1453,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1452:[bind(A,$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(1469,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1453]) ).
thf(64,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(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 ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[66]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,7]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[67]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[68]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( A
!= ( a @ ( b @ implies ) ) )
| ( ( B @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[78]) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[85]) ).
thf(130,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,99]) ).
thf(131,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,78]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[91]) ).
thf(2300,plain,
! [A: $i] :
( ~ $true
| ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[2071]) ).
thf(2304,plain,
! [A: $i] :
( ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2300]) ).
thf(2716,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2304]) ).
thf(2717,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) ) ),
inference(simp,[status(thm)],[2716]) ).
thf(2718,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2717:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2778,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2718]) ).
thf(2185,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)],[50,2071]) ).
thf(2186,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)],[2185]) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2186:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2330,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2187]) ).
thf(3270,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)],[2330]) ).
thf(3288,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)],[3270]) ).
thf(4669,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)],[1065,3288]) ).
thf(4670,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)],[4669]) ).
thf(4671,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4670:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(4729,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)],[4671]) ).
thf(2285,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)],[1065,2071]) ).
thf(2286,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2285]) ).
thf(2287,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2286:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2350,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2287]) ).
thf(2397,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,2350]) ).
thf(2398,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2397]) ).
thf(2412,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2398]) ).
thf(1067,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)],[1065,50]) ).
thf(1068,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)],[1067]) ).
thf(1069,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1068:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1121,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1069]) ).
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(1313,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)],[1121,54]) ).
thf(1314,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)],[1313]) ).
thf(1315,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1314:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( H @ ( H @ implies ) @ not )),bind(E,$thf( E ))]]) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1315]) ).
thf(1748,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)],[1391,51]) ).
thf(1749,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)],[1748]) ).
thf(1750,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1749:[bind(A,$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(1770,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1750]) ).
thf(1802,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)],[1770,54]) ).
thf(1803,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)],[1802]) ).
thf(1804,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1803:[bind(A,$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(1838,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)],[1804]) ).
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(18676,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)],[1838,49]) ).
thf(18677,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)],[18676]) ).
thf(18678,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18677:[bind(A,$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(18906,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)],[18678]) ).
thf(72,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(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 ) ),
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$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)],[74]) ).
thf(209,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(210,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)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[211]) ).
thf(659,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)],[644,51]) ).
thf(660,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)],[659]) ).
thf(661,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$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(702,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[661]) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[702,7]) ).
thf(737,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[736]) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[737]) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( C
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[750]) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( b @ not @ ( a @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[938]) ).
thf(940,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( B @ ( b @ not @ ( a @ not @ implies ) @ not @ implies ) @ not )
!= b ) ),
inference(simp,[status(thm)],[939]) ).
thf(941,plain,
! [A: $i] :
( ( A @ ( b @ not @ ( a @ not @ implies ) @ not @ implies ) @ not )
!= b ),
inference(simp,[status(thm)],[940]) ).
thf(2190,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)],[1469,2071]) ).
thf(2191,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)],[2190]) ).
thf(2192,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2191:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(2331,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2192]) ).
thf(2240,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)],[1121,2071]) ).
thf(2241,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)],[2240]) ).
thf(2242,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2241:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2341,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2242]) ).
thf(2626,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)],[50,2304]) ).
thf(2627,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)],[2626]) ).
thf(2628,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ not @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2627:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2787,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)],[2628]) ).
thf(2305,plain,
! [A: $i] :
( ( ( A @ not )
!= A )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2300]) ).
thf(2578,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,2305]) ).
thf(2579,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B ) ),
inference(simp,[status(thm)],[2578]) ).
thf(2580,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2595,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(simp,[status(thm)],[2580]) ).
thf(8005,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)],[4729]) ).
thf(112,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,99]) ).
thf(113,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$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(115,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(3150,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 @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,2330]) ).
thf(3151,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 @ is_a_theorem ) ),
inference(simp,[status(thm)],[3150]) ).
thf(3152,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3151:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(3317,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)],[3152]) ).
thf(2569,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)],[11,2305]) ).
thf(2570,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)],[2569]) ).
thf(2571,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2570:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2590,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2571]) ).
thf(674,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)],[644,49]) ).
thf(675,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)],[674]) ).
thf(676,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[675:[bind(A,$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(693,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[676]) ).
thf(1033,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)],[693,53]) ).
thf(1034,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)],[1033]) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1034:[bind(A,$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(1063,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)],[1035]) ).
thf(10238,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)],[1063,51]) ).
thf(10239,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)],[10238]) ).
thf(10240,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10239:[bind(A,$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(10296,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)],[10240]) ).
thf(10625,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)],[10296,2071]) ).
thf(10626,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)],[10625]) ).
thf(10627,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10626:[bind(A,$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(10711,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)],[10627]) ).
thf(1292,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)],[702,54]) ).
thf(1293,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)],[1292]) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1293:[bind(A,$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(1380,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)],[1294]) ).
thf(11346,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)],[1380,51]) ).
thf(11347,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)],[11346]) ).
thf(11348,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11347:[bind(A,$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(11440,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)],[11348]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ 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 )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( A
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( b @ not @ ( a @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(55,plain,
! [A: $i] :
( ( A != a )
| ( ( b @ not @ ( a @ not @ implies ) @ not )
!= b ) ),
inference(simp,[status(thm)],[27]) ).
thf(56,plain,
( ( b @ not @ ( a @ not @ implies ) @ not )
!= b ),
inference(simp,[status(thm)],[55]) ).
thf(774,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[693,99]) ).
thf(775,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[774]) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[776]) ).
thf(653,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)],[644,50]) ).
thf(654,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)],[653]) ).
thf(655,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[654:[bind(A,$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(698,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)],[655]) ).
thf(1702,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)],[1391,50]) ).
thf(1703,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)],[1702]) ).
thf(1704,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1703:[bind(A,$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(1761,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)],[1704]) ).
thf(1660,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,7]) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1660]) ).
thf(1684,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1661]) ).
thf(22343,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( B @ ( B @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1684]) ).
thf(22346,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( B @ not )
!= b )
| ( B
!= ( b @ not ) )
| ( ( B @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22343]) ).
thf(22365,plain,
( ( ( b @ not @ not )
!= b )
| ( ( b @ not @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22346]) ).
thf(13027,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)],[234,2305]) ).
thf(13028,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)],[13027]) ).
thf(13029,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= A )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[13028:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2731,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)],[1065,2304]) ).
thf(2732,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)],[2731]) ).
thf(2733,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2732:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2781,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2733]) ).
thf(3663,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)],[1065,2781]) ).
thf(3688,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) )
| ~ ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3663]) ).
thf(10425,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)],[1065,3688]) ).
thf(10426,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)],[10425]) ).
thf(10427,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10426:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2275,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)],[11,2071]) ).
thf(2276,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)],[2275]) ).
thf(2277,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2276:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2348,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2277]) ).
thf(1076,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,101]) ).
thf(1077,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1078,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1077:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1078]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ 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 )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ 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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(1131,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)],[1121,50]) ).
thf(1132,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)],[1131]) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1133]) ).
thf(1199,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)],[1185,50]) ).
thf(1200,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)],[1199]) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1200:[bind(A,$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(1254,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)],[1201]) ).
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(215,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(216,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)],[215]) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(238,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)],[217]) ).
thf(2175,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)],[238,2071]) ).
thf(2176,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)],[2175]) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2176:[bind(A,$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(2328,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)],[2177]) ).
thf(2245,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)],[12,2071]) ).
thf(2246,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)],[2245]) ).
thf(2247,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2246:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(2342,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2247]) ).
thf(3013,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)],[11,2342]) ).
thf(3014,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)],[3013]) ).
thf(3029,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[3014]) ).
thf(1731,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)],[1391,49]) ).
thf(1732,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)],[1731]) ).
thf(1733,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1732:[bind(A,$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(1760,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)],[1733]) ).
thf(15104,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)],[234,13029]) ).
thf(15105,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)],[15104]) ).
thf(15106,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[15105:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(15231,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[15106]) ).
thf(2230,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)],[693,2071]) ).
thf(2231,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)],[2230]) ).
thf(2232,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2231:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(2339,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)],[2232]) ).
thf(343,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)],[238,50]) ).
thf(344,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)],[343]) ).
thf(345,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[344:[bind(A,$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(372,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)],[345]) ).
thf(2288,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)],[1065,2071]) ).
thf(2289,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2288]) ).
thf(2319,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2289]) ).
thf(3393,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)],[79,2319]) ).
thf(3394,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)],[3393]) ).
thf(3395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3394:[bind(A,$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(3410,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)],[3395]) ).
thf(1408,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)],[1066,50]) ).
thf(1409,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)],[1408]) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1409:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(1462,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)],[1410]) ).
thf(2999,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)],[1121,2342]) ).
thf(3000,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)],[2999]) ).
thf(3043,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)],[3000]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ 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 )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(19,plain,
! [A: $i] :
( ( A
!= ( a @ ( b @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(20,plain,
( ( a @ ( b @ implies ) @ ( a @ ( b @ implies ) @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(1266,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)],[1185,54]) ).
thf(1267,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)],[1266]) ).
thf(1268,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1267:[bind(A,$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(1398,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)],[1268]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,99]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[108]) ).
thf(145,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,117]) ).
thf(146,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[147]) ).
thf(244,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,158]) ).
thf(245,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ not @ implies ) ))]]) ).
thf(261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[246]) ).
thf(3638,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[2781]) ).
thf(12823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[234,3638]) ).
thf(12824,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(simp,[status(thm)],[12823]) ).
thf(12825,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12824:[bind(A,$thf( F @ ( F @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(13134,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)],[12825]) ).
thf(2379,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)],[1121,2350]) ).
thf(2380,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)],[2379]) ).
thf(2403,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2380]) ).
thf(12886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[234,2304]) ).
thf(12887,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)],[12886]) ).
thf(12888,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12887:[bind(A,$thf( D @ not )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(13148,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[12888]) ).
thf(13873,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)],[54,13148]) ).
thf(13874,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)],[13873]) ).
thf(13875,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[13874:[bind(A,$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(14024,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)],[13875]) ).
thf(10380,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)],[1121,3688]) ).
thf(10381,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)],[10380]) ).
thf(10382,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10381:[bind(A,$thf( J @ ( J @ implies ) @ not )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( J @ implies ) @ not ))]]) ).
thf(10454,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[10382]) ).
thf(25890,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[2778]) ).
thf(2210,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)],[1254,2071]) ).
thf(2211,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)],[2210]) ).
thf(2212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2211:[bind(A,$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(2335,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)],[2212]) ).
thf(12198,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)],[1398,51]) ).
thf(12199,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)],[12198]) ).
thf(12200,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12199:[bind(A,$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(12276,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)],[12200]) ).
thf(61,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(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 )
| ~ ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(84,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)],[63]) ).
thf(3289,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= B )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3270]) ).
thf(4006,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)],[1065,3289]) ).
thf(4007,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)],[4006]) ).
thf(4008,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[4007:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(4033,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[4008]) ).
thf(1655,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)],[1469,54]) ).
thf(1656,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)],[1655]) ).
thf(1657,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1656:[bind(A,$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(1700,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)],[1657]) ).
thf(16683,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)],[1700,51]) ).
thf(16684,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)],[16683]) ).
thf(16685,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16684:[bind(A,$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(16776,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)],[16685]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,99]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(22380,plain,
( ( ( b @ not @ not )
!= b )
| ( ( b @ not )
!= a ) ),
inference(simp,[status(thm)],[22365]) ).
thf(8004,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)],[4729]) ).
thf(8976,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)],[1065,8004]) ).
thf(8977,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)],[8976]) ).
thf(8978,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[8977:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(9124,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)],[1065,8978]) ).
thf(9125,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)],[9124]) ).
thf(9140,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[9125]) ).
thf(3019,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)],[1065,2342]) ).
thf(3020,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)],[3019]) ).
thf(3036,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[3020]) ).
thf(1668,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1469,99]) ).
thf(1669,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1668]) ).
thf(1670,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1669:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(1691,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[1670]) ).
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(177,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(178,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)],[177]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(201,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)],[179]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,78]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(206,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,117]) ).
thf(207,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(2395,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)],[79,2350]) ).
thf(2396,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)],[2395]) ).
thf(2409,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)],[2396]) ).
thf(8347,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)],[8005,2304]) ).
thf(8348,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)],[8347]) ).
thf(8349,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[8348:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(8484,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8349]) ).
thf(13055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ~ $true
| ( D @ ( D @ implies ) @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[234,8484]) ).
thf(13056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( D @ ( D @ implies ) @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[13055]) ).
thf(13057,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[13056:[bind(A,$thf( F @ ( I @ ( I @ implies ) @ not @ implies ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( I ))]]) ).
thf(13126,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)],[13057]) ).
thf(2515,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)],[50,2305]) ).
thf(2516,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)],[2515]) ).
thf(2517,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2516:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2596,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2517]) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,99]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(1072,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1071:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(1123,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[1072]) ).
thf(151,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 ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,117]) ).
thf(152,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 ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$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(160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[153]) ).
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 ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,50]) ).
thf(128,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)],[127]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$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(137,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)],[129]) ).
thf(274,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)],[137,50]) ).
thf(275,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)],[274]) ).
thf(276,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$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(297,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)],[276]) ).
thf(3639,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[2781]) ).
thf(4146,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)],[3639]) ).
thf(4160,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4146]) ).
thf(4117,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)],[3639,50]) ).
thf(4118,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)],[4117]) ).
thf(4119,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4118:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(4167,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)],[4119]) ).
thf(4854,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)],[4167,47]) ).
thf(4855,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)],[4854]) ).
thf(4856,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( A @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4855:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ ( H @ implies ) @ not @ not )),bind(D,$thf( A ))]]) ).
thf(4901,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)],[4856]) ).
thf(12603,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ 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)],[4901,51]) ).
thf(12604,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ 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)],[12603]) ).
thf(12605,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12604:[bind(A,$thf( G @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ implies ) )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( K )),bind(E,$thf( L ))]]) ).
thf(12700,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)],[12605]) ).
thf(283,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[137,78]) ).
thf(284,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(285,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$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(302,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(21,plain,
( ( ( a @ ( b @ implies ) )
!= ( b @ not ) )
| ( ( a @ ( b @ implies ) @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[20]) ).
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(306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,48]) ).
thf(307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[308]) ).
thf(13021,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)],[234,2071]) ).
thf(13022,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)],[13021]) ).
thf(13023,plain,
! [B: $i,A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[13022:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(14296,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)],[234,13023]) ).
thf(14297,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)],[14296]) ).
thf(14298,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14297:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(14556,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14298]) ).
thf(2548,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)],[1121,2305]) ).
thf(2549,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)],[2548]) ).
thf(2550,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2549:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2609,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[2550]) ).
thf(16273,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)],[54,13134]) ).
thf(16274,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)],[16273]) ).
thf(16275,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[16274:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G @ ( B @ implies ) ))]]) ).
thf(16423,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)],[16275]) ).
thf(2255,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)],[81,2071]) ).
thf(2256,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)],[2255]) ).
thf(2257,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2256:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2344,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2257]) ).
thf(2195,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)],[10,2071]) ).
thf(2196,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)],[2195]) ).
thf(2197,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2196:[bind(A,$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(2332,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)],[2197]) ).
thf(2357,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)],[50,2350]) ).
thf(2358,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)],[2357]) ).
thf(2413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2358]) ).
thf(6400,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)],[12,2413]) ).
thf(6401,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)],[6400]) ).
thf(6402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6401:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ not @ implies ) @ ( J @ implies ) )),bind(E,$thf( E ))]]) ).
thf(6445,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)],[6402]) ).
thf(22348,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( A @ ( B @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ( ( B @ ( B @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[22343]) ).
thf(22358,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( A
!= ( b @ not ) )
| ( ( B @ not )
!= ( a @ not ) )
| ( B
!= ( b @ not ) )
| ( ( B @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22348]) ).
thf(22374,plain,
( ( ( b @ not @ ( b @ not @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( b @ not @ not )
!= ( a @ not ) )
| ( ( b @ not @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22358]) ).
thf(23212,plain,
( ( ( b @ not @ ( b @ not @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( b @ not @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22374]) ).
thf(1630,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)],[1469,50]) ).
thf(1631,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)],[1630]) ).
thf(1632,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1631:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1687,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)],[1632]) ).
thf(715,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[702,99]) ).
thf(716,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[716:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[717]) ).
thf(2260,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)],[1066,2071]) ).
thf(2261,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)],[2260]) ).
thf(2262,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2261:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(2345,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2262]) ).
thf(13355,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)],[12276,2071]) ).
thf(13356,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)],[13355]) ).
thf(13357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[13356:[bind(A,$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(13463,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)],[13357]) ).
thf(1807,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1770,7]) ).
thf(1808,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1807]) ).
thf(1830,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1808]) ).
thf(24458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( A @ ( A @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1830]) ).
thf(2920,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)],[12,2341]) ).
thf(2921,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)],[2920]) ).
thf(2946,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)],[2921]) ).
thf(122,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)],[79,9]) ).
thf(123,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)],[122]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$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(141,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)],[124]) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,117]) ).
thf(1088,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1087]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1088:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[1089]) ).
thf(11757,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)],[11440,2071]) ).
thf(11758,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)],[11757]) ).
thf(11759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11758:[bind(A,$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(11877,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)],[11759]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,48]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[321]) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) )),bind(D,$thf( D ))]]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[323]) ).
thf(2681,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 )
!= ( C @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1121,2304]) ).
thf(2682,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 )
!= ( C @ is_a_theorem ) ) ),
inference(simp,[status(thm)],[2681]) ).
thf(2683,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2682:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2798,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2683]) ).
thf(12883,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)],[234,2304]) ).
thf(12884,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)],[12883]) ).
thf(12885,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12884:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2280,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)],[79,2071]) ).
thf(2281,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)],[2280]) ).
thf(2282,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2281:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(2349,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2282]) ).
thf(3001,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)],[12,2342]) ).
thf(3002,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)],[3001]) ).
thf(3032,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)],[3002]) ).
thf(3082,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)],[12,2348]) ).
thf(3083,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)],[3082]) ).
thf(3126,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3083]) ).
thf(22345,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( B @ not )
!= b )
| ( ( B @ ( B @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[22343]) ).
thf(22364,plain,
! [A: $i] :
( ( ( A @ not )
!= b )
| ( ( A @ ( A @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[22345]) ).
thf(3100,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)],[1065,2348]) ).
thf(3101,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)],[3100]) ).
thf(3115,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3101]) ).
thf(69,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(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 )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(80,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)],[71]) ).
thf(1481,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)],[1185,80]) ).
thf(1482,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)],[1481]) ).
thf(1483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1482:[bind(A,$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(1599,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)],[1483]) ).
thf(13009,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[234,99]) ).
thf(13010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[13009]) ).
thf(13011,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[13010:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(14973,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[234,13011]) ).
thf(14974,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14973]) ).
thf(14975,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14974:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(15101,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14975]) ).
thf(3230,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 @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1770,2330]) ).
thf(3231,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 @ is_a_theorem ) ),
inference(simp,[status(thm)],[3230]) ).
thf(3232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3231:[bind(A,$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(3306,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)],[3232]) ).
thf(2391,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)],[1770,2350]) ).
thf(2392,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)],[2391]) ).
thf(2408,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)],[2392]) ).
thf(9116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,8978]) ).
thf(9117,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9116]) ).
thf(9137,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[9117]) ).
thf(2381,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)],[12,2350]) ).
thf(2382,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)],[2381]) ).
thf(2423,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2382]) ).
thf(12826,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)],[234,3638]) ).
thf(12827,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)],[12826]) ).
thf(12828,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12827:[bind(A,$thf( E @ ( E @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(13135,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)],[12828]) ).
thf(253,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,158]) ).
thf(254,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$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(264,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(6421,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)],[11,2413]) ).
thf(6422,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)],[6421]) ).
thf(6423,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6422:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ ( F @ not @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(6454,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[6423]) ).
thf(154,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,117]) ).
thf(155,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$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(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= a )
| ( ( C @ ( B @ implies ) )
!= b )
| ( B
!= ( b @ not ) )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(601,plain,
! [A: $i] :
( ( ( A @ ( a @ not @ implies ) )
!= a )
| ( ( A @ ( b @ not @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[583]) ).
thf(8388,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)],[8005,50]) ).
thf(8389,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)],[8388]) ).
thf(8390,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[8389:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) @ not ))]]) ).
thf(8495,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)],[8390]) ).
thf(22,plain,
( ( ( a @ ( b @ implies ) )
!= ( b @ not ) )
| ( ( a @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[21]) ).
thf(11262,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)],[1380,49]) ).
thf(11263,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)],[11262]) ).
thf(11264,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11263:[bind(A,$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(11411,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)],[11264]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,99]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(118,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(18774,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)],[1838,51]) ).
thf(18775,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)],[18774]) ).
thf(18776,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18775:[bind(A,$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(18882,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)],[18776]) ).
thf(19115,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)],[18882,2071]) ).
thf(19116,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)],[19115]) ).
thf(19117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[19116:[bind(A,$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(19264,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)],[19117]) ).
thf(2932,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)],[11,2341]) ).
thf(2933,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)],[2932]) ).
thf(2959,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[2933]) ).
thf(256,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,158]) ).
thf(257,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$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(259,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(4125,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)],[3639,2071]) ).
thf(4126,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)],[4125]) ).
thf(4127,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4126:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) @ not ))]]) ).
thf(4171,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4127]) ).
thf(212,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(213,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)],[212]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(236,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)],[214]) ).
thf(3220,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 ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1066,2330]) ).
thf(3221,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 ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3220]) ).
thf(3222,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3221:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(3304,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[3222]) ).
thf(1411,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1066,99]) ).
thf(1412,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1411]) ).
thf(1413,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1412:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(1464,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[1413]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,117]) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(2265,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)],[80,2071]) ).
thf(2266,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)],[2265]) ).
thf(2267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2266:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( F @ ( I @ ( J @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2346,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)],[2267]) ).
thf(712,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)],[702,50]) ).
thf(713,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)],[712]) ).
thf(714,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[713:[bind(A,$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(755,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)],[714]) ).
thf(837,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)],[755,50]) ).
thf(838,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)],[837]) ).
thf(839,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[838:[bind(A,$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(880,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)],[839]) ).
thf(95,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,78]) ).
thf(96,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$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(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(2551,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)],[12,2305]) ).
thf(2552,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)],[2551]) ).
thf(2553,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2552:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(2610,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[2553]) ).
thf(2248,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)],[12,2071]) ).
thf(2249,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)],[2248]) ).
thf(2314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2249]) ).
thf(777,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)],[693,51]) ).
thf(778,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)],[777]) ).
thf(779,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[778:[bind(A,$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(816,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)],[779]) ).
thf(656,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[644,99]) ).
thf(657,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[656]) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[657:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(700,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[658]) ).
thf(16586,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)],[1700,49]) ).
thf(16587,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)],[16586]) ).
thf(16588,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16587:[bind(A,$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(16802,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)],[16588]) ).
thf(324,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 ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[81,48]) ).
thf(325,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 ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[326]) ).
thf(2180,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)],[1185,2071]) ).
thf(2181,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)],[2180]) ).
thf(2182,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2181:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( F @ ( I @ ( L @ ( L @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2329,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2182]) ).
thf(1662,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)],[1469,80]) ).
thf(1663,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)],[1662]) ).
thf(1664,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1663:[bind(A,$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(1688,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)],[1664]) ).
thf(221,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,78]) ).
thf(222,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(2393,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)],[11,2350]) ).
thf(2394,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)],[2393]) ).
thf(2418,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2394]) ).
thf(1102,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,7]) ).
thf(1103,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1102]) ).
thf(1116,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1103]) ).
thf(1196,plain,
! [A: $i] :
( ( A
!= ( a @ ( b @ implies ) ) )
| ( A
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1116]) ).
thf(1197,plain,
( ( b @ not @ ( a @ not @ implies ) )
!= ( a @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1198,plain,
( ( ( b @ not )
!= a )
| ( ( a @ not )
!= b ) ),
inference(simp,[status(thm)],[1197]) ).
thf(5228,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)],[2346]) ).
thf(5254,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)],[5228]) ).
thf(3354,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)],[702,2319]) ).
thf(3355,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)],[3354]) ).
thf(3356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3355:[bind(A,$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(3423,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)],[3356]) ).
thf(3190,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 ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[693,2330]) ).
thf(3191,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 ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3190]) ).
thf(3192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3191:[bind(A,$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(3325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[3192]) ).
thf(771,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)],[693,50]) ).
thf(772,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)],[771]) ).
thf(773,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[772:[bind(A,$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(812,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)],[773]) ).
thf(2200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[698,2071]) ).
thf(2201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2200]) ).
thf(2202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2201:[bind(A,$thf( G )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( G @ ( Q @ ( P @ implies ) @ ( Q @ ( N @ ( P @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2202]) ).
thf(23213,plain,
( ( ( b @ not @ ( b @ not @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( b @ not )
!= a ) ),
inference(simp,[status(thm)],[23212]) ).
thf(271,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)],[137,9]) ).
thf(272,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)],[271]) ).
thf(273,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$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(295,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)],[273]) ).
thf(318,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 @ ( E @ implies ) )
!= E )
| ~ $true
| ( F @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[137,48]) ).
thf(319,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 @ ( E @ implies ) )
!= E )
| ( F @ is_a_theorem ) ),
inference(simp,[status(thm)],[318]) ).
thf(320,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[319:[bind(A,$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(327,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[320]) ).
thf(22361,plain,
! [B: $i,A: $i] :
( ( B != a )
| ( ( B @ not )
!= b )
| ( A
!= ( b @ not ) )
| ( ( B @ not )
!= ( a @ not ) )
| ( ( B @ ( B @ not @ implies ) )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[22348]) ).
thf(22377,plain,
( ( ( a @ not )
!= b )
| ( ( a @ not )
!= ( a @ not ) )
| ( ( b @ not @ ( a @ not @ implies ) )
!= ( a @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[22361]) ).
thf(22793,plain,
( ( ( a @ not )
!= b )
| ( ( b @ not @ ( a @ not @ implies ) )
!= ( a @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[22377]) ).
thf(250,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,158]) ).
thf(251,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(252,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( H )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( M @ ( N @ not @ implies ) @ ( N @ implies ) @ not @ implies ) ))]]) ).
thf(263,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[252]) ).
thf(24459,plain,
! [C: $i,B: $i,A: $i] :
( ( B != a )
| ( ( C @ not )
!= b )
| ( ( A @ ( A @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[24458]) ).
thf(24460,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= b )
| ( ( A @ ( A @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[24459]) ).
thf(6388,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)],[1121,2413]) ).
thf(6389,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)],[6388]) ).
thf(6390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6389:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(6472,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)],[6390]) ).
thf(171,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(172,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)],[171]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(199,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)],[173]) ).
thf(3225,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)],[80,2330]) ).
thf(3226,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)],[3225]) ).
thf(3227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3226:[bind(A,$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(3305,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)],[3227]) ).
thf(3080,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)],[1121,2348]) ).
thf(3081,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)],[3080]) ).
thf(3114,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3081]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= B )
| ~ $true
| ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,48]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= B )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[309]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[311]) ).
thf(19774,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)],[234,12885]) ).
thf(19775,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)],[19774]) ).
thf(19776,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[19775:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(20115,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)],[19776]) ).
thf(2220,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)],[702,2071]) ).
thf(2221,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)],[2220]) ).
thf(2222,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2221:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(2337,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2222]) ).
thf(4111,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)],[3639,80]) ).
thf(4112,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)],[4111]) ).
thf(4113,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4112:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( G @ implies ) @ not ))]]) ).
thf(4164,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)],[4113]) ).
thf(1434,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)],[1066,53]) ).
thf(1435,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)],[1434]) ).
thf(1436,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1435:[bind(A,$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(1476,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1436]) ).
thf(2471,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)],[1476,2071]) ).
thf(2472,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)],[2471]) ).
thf(2473,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2472:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(2500,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2473]) ).
thf(1742,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1391,99]) ).
thf(1743,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1742]) ).
thf(1744,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1743:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(1766,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[1744]) ).
thf(3336,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)],[1469,2319]) ).
thf(3337,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)],[3336]) ).
thf(3338,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3337:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(3415,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3338]) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( B
!= ( b @ not ) )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(600,plain,
! [A: $i] :
( ( A @ ( a @ not @ implies ) @ ( A @ ( b @ not @ implies ) @ implies ) )
!= ( a @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[581]) ).
thf(2243,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)],[1121,2071]) ).
thf(2244,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)],[2243]) ).
thf(2320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2244]) ).
thf(3253,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)],[1065,2330]) ).
thf(3254,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)],[3253]) ).
thf(3284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3254]) ).
thf(3384,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)],[1770,2319]) ).
thf(3385,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)],[3384]) ).
thf(3386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3385:[bind(A,$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(3433,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)],[3386]) ).
thf(1776,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)],[1770,50]) ).
thf(1777,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)],[1776]) ).
thf(1778,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1777:[bind(A,$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(1839,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)],[1778]) ).
thf(2295,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)],[755,2071]) ).
thf(2296,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)],[2295]) ).
thf(2297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2296:[bind(A,$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(2352,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)],[2297]) ).
thf(10412,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)],[50,3688]) ).
thf(10413,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)],[10412]) ).
thf(10414,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[10413:[bind(A,$thf( F @ not )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ not ))]]) ).
thf(10464,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[10414]) ).
thf(1815,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1770,99]) ).
thf(1816,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1815]) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1816:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(1844,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[1817]) ).
thf(2270,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)],[1770,2071]) ).
thf(2271,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)],[2270]) ).
thf(2272,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2271:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(2347,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2272]) ).
thf(2278,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)],[11,2071]) ).
thf(2279,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)],[2278]) ).
thf(2325,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2279]) ).
thf(1107,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,158]) ).
thf(1108,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1107]) ).
thf(1109,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1108:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[1109]) ).
thf(3165,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 ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1391,2330]) ).
thf(3166,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 ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3165]) ).
thf(3167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3166:[bind(A,$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(3320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[3167]) ).
thf(2355,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)],[1185,2350]) ).
thf(2356,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)],[2355]) ).
thf(2406,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)],[2356]) ).
thf(12554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ not @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[4901,3288]) ).
thf(12555,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ not @ 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)],[12554]) ).
thf(12556,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12555:[bind(A,$thf( G @ ( H @ not @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( H ))]]) ).
thf(12685,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)],[12556]) ).
thf(2918,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)],[1121,2341]) ).
thf(2919,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)],[2918]) ).
thf(2971,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)],[2919]) ).
thf(133,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,78]) ).
thf(134,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$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(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(2385,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)],[81,2350]) ).
thf(2386,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)],[2385]) ).
thf(2416,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2386]) ).
thf(22344,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( B
!= ( b @ not ) )
| ( ( B @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22343]) ).
thf(22363,plain,
! [A: $i] :
( ( ( A @ ( b @ not @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( b @ not @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22344]) ).
thf(22785,plain,
! [A: $i] :
( ( ( A @ ( b @ not @ not @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( b @ not )
!= a ) ),
inference(simp,[status(thm)],[22363]) ).
thf(226,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(227,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)],[226]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(235,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)],[228]) ).
thf(4315,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)],[3638]) ).
thf(4321,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4315]) ).
thf(3375,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)],[81,2319]) ).
thf(3376,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)],[3375]) ).
thf(3377,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3376:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(3430,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3377]) ).
thf(17017,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)],[16776,2071]) ).
thf(17018,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)],[17017]) ).
thf(17019,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[17018:[bind(A,$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(17153,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)],[17019]) ).
thf(9091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1121,8978]) ).
thf(9092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9091]) ).
thf(9162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( D @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[9092]) ).
thf(6433,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)],[1065,2413]) ).
thf(6434,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)],[6433]) ).
thf(6435,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6434:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(6462,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[6435]) ).
thf(2371,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)],[702,2350]) ).
thf(2372,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)],[2371]) ).
thf(2421,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)],[2372]) ).
thf(5255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= C )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[5228]) ).
thf(7649,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)],[1065,5255]) ).
thf(7650,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)],[7649]) ).
thf(7651,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(pattern_uni,[status(thm)],[7650:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(7680,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(simp,[status(thm)],[7651]) ).
thf(2938,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)],[1065,2341]) ).
thf(2939,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)],[2938]) ).
thf(2956,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[2939]) ).
thf(280,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 )
!= ( b @ not @ ( a @ not @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[137,158]) ).
thf(281,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(282,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$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(300,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 )
!= ( b @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(13041,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)],[234,2330]) ).
thf(13042,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)],[13041]) ).
thf(13043,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[13042:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(3094,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)],[11,2348]) ).
thf(3095,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)],[3094]) ).
thf(3132,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3095]) ).
thf(9100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,8978]) ).
thf(9101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9100]) ).
thf(9156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( D @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[9101]) ).
thf(6717,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1760,2071]) ).
thf(6718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[6717]) ).
thf(6719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[6718:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( P @ ( O @ implies ) @ ( P @ ( M @ implies ) @ implies ) @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(6782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[6719]) ).
thf(2205,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)],[1391,2071]) ).
thf(2206,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)],[2205]) ).
thf(2207,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2206:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(2334,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)],[2207]) ).
thf(2359,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)],[1469,2350]) ).
thf(2360,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)],[2359]) ).
thf(2404,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2360]) ).
thf(2235,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)],[137,2071]) ).
thf(2236,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)],[2235]) ).
thf(2237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2236:[bind(A,$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(2340,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)],[2237]) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1065,78]) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[1081]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1082:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(3330,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)],[1185,2319]) ).
thf(3331,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)],[3330]) ).
thf(3332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3331:[bind(A,$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(3411,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)],[3332]) ).
thf(10340,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)],[1469,3688]) ).
thf(10341,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)],[10340]) ).
thf(10342,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10341:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A @ ( A @ not @ implies ) ))]]) ).
thf(10460,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10342]) ).
thf(26691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ $true
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[25890,234]) ).
thf(26692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[26691]) ).
thf(26693,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[26692:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(75,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(76,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)],[75]) ).
thf(77,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$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(83,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)],[77]) ).
thf(2290,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)],[644,2071]) ).
thf(2291,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)],[2290]) ).
thf(2292,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2291:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2351,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)],[2292]) ).
thf(26759,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ $true
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[25890,13148]) ).
thf(26760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[26759]) ).
thf(26761,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[26760:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(27103,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[26761]) ).
thf(86,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,78]) ).
thf(87,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 ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( a @ ( b @ implies ) @ ( b @ not @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(54385,plain,
$false,
inference(e,[status(thm)],[5686,1469,138,101,2778,4729,2412,18906,234,941,2331,2306,2341,2787,2595,8005,115,3317,2590,10711,11440,10,56,814,698,1761,1063,22365,13029,10427,2348,1127,1391,3688,25,1254,52,2328,3029,1760,15231,2339,372,702,3410,1462,3043,20,1398,57,78,261,13134,2403,3638,14024,10454,25890,238,2335,12276,84,4033,16776,116,22380,9140,3036,117,1691,13148,201,102,233,6,2409,13126,2596,1123,160,297,693,4160,12700,302,21,137,329,14556,2609,16423,13023,2344,2332,6445,23212,1687,757,2345,13463,24458,2946,1121,9,53,141,1118,11877,328,2798,22343,4167,12885,2349,2781,1700,3032,3126,2304,22364,3115,1599,15101,3306,2408,9137,1185,2423,8004,3639,750,2413,13135,264,6454,161,3289,601,8495,22,11411,118,19264,2959,259,27,12,54,4171,49,236,3304,1464,2319,159,2346,81,7,880,10296,98,2610,2314,816,700,16802,330,2329,1688,240,1838,2418,1198,5254,2350,3423,1066,3325,80,4901,1684,812,939,2333,23213,48,1770,295,18,327,22793,263,24460,6472,50,199,3305,3114,331,20115,2337,1830,4164,2500,1766,3415,600,2320,11,3288,3284,3433,1839,2352,99,10464,1844,2347,2325,1126,2071,3320,2305,2342,1476,2406,158,12685,2971,139,2416,22785,8,235,4321,3430,2330,17153,9162,6462,22363,2421,7680,2956,1116,300,13043,51,1380,3132,9156,6782,2334,8484,79,1197,2404,1065,18882,2340,1129,3411,644,47,15,8978,10460,26693,83,13011,5255,755,2351,27103,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL059-1 : 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
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 21:49:20 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.15 % [INFO] Parsing done (169ms).
% 1.29/1.16 % [INFO] Running in sequential loop mode.
% 1.80/1.55 % [INFO] eprover registered as external prover.
% 1.80/1.56 % [INFO] Scanning for conjecture ...
% 2.01/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.01/1.67 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.01/1.68 % [INFO] Problem is propositional (TPTP CNF).
% 2.01/1.69 % [INFO] Type checking passed.
% 2.01/1.69 % [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 ...
% 163.97/42.88 % External prover 'e' found a proof!
% 163.97/42.88 % [INFO] Killing All external provers ...
% 163.97/42.89 % Time passed: 42334ms (effective reasoning time: 41718ms)
% 163.97/42.89 % Axioms used in derivation (4): cn_1, cn_3, condensed_detachment, cn_2
% 163.97/42.89 % No. of inferences in proof: 945
% 163.97/42.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 42334 ms resp. 41718 ms w/o parsing
% 166.25/43.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 166.25/43.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------