%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:50:40 AM UTC 2026
% Result : Unsatisfiable 201.19s 59.06s
% Output : Refutation 193.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 5
% Syntax : Number of formulae : 1331 ( 453 unt; 0 typ; 0 def)
% Number of atoms : 4221 (1248 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 21588 (2275 ~;1446 |; 0 &;17867 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 4702 ( 0 ^;4702 !; 0 ?;4702 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(not_decl,type,
not: $i > $i ).
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(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 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(36,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)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[37]) ).
thf(68,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)],[12,51]) ).
thf(69,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)],[68]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[70]) ).
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 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,51]) ).
thf(129,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)],[128]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[129:[bind(A,$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(138,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)],[130]) ).
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(1,negated_conjecture,
~ ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_21) ).
thf(6,plain,
~ ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,7]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[71]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[72]) ).
thf(87,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,79]) ).
thf(88,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$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(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(62,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)],[51,9]) ).
thf(63,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)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( E @ not )),bind(D,$thf( A ))]]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[64]) ).
thf(1617,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[80,7]) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[1617]) ).
thf(1619,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[1618:[bind(A,$thf( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) )),bind(B,$thf( B ))]]) ).
thf(1750,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[1619]) ).
thf(2004,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)],[82,1750]) ).
thf(2005,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)],[2004]) ).
thf(2006,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2005:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(2072,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2006]) ).
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 )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(39,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)],[38]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) )),bind(D,$thf( D ))]]) ).
thf(52,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)],[40]) ).
thf(617,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)],[10,52]) ).
thf(618,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)],[617]) ).
thf(619,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[618:[bind(A,$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(648,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[619]) ).
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(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 )
| ~ $true
| ~ ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(45,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)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[46]) ).
thf(1034,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)],[648,54]) ).
thf(1035,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)],[1034]) ).
thf(1036,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1035:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ ( G @ implies ) )),bind(E,$thf( G ))]]) ).
thf(1055,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1036]) ).
thf(1064,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)],[1055,51]) ).
thf(1065,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)],[1064]) ).
thf(1066,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1065:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1114,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1066]) ).
thf(2029,plain,
! [A: $i] :
( ~ $true
| ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[1750]) ).
thf(2032,plain,
! [A: $i] :
( ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2029]) ).
thf(2258,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)],[11,2032]) ).
thf(2259,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)],[2258]) ).
thf(2260,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2259:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2396,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)],[2260]) ).
thf(27668,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)],[2396]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,51]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(83,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[75]) ).
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 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,9]) ).
thf(211,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)],[210]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[212]) ).
thf(27974,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)],[27668,236]) ).
thf(27975,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)],[27974]) ).
thf(27976,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[27975:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(47,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(48,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)],[47]) ).
thf(28739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ( D @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[27976,48]) ).
thf(28740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ 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)],[28739]) ).
thf(28741,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ not @ implies ) @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[28740:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ not @ implies ) )),bind(D,$thf( F ))]]) ).
thf(29052,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ not @ implies ) @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[28741]) ).
thf(30928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem )
| ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[1114,29052]) ).
thf(30929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[30928]) ).
thf(30930,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[30929:[bind(A,$thf( H @ ( H @ implies ) )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ implies ) ))]]) ).
thf(31394,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[30930]) ).
thf(2009,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)],[51,1750]) ).
thf(2010,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)],[2009]) ).
thf(2011,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2010:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2011]) ).
thf(2900,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)],[2073]) ).
thf(2915,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)],[2900]) ).
thf(31795,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 ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31394,2915]) ).
thf(31796,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 ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31795]) ).
thf(31797,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[31796:[bind(A,$thf( G @ ( H @ not @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( H ))]]) ).
thf(32323,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31797]) ).
thf(4406,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)],[1055,2915]) ).
thf(4407,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)],[4406]) ).
thf(4408,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4407:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(4551,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)],[4408]) ).
thf(7149,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)],[4551]) ).
thf(34279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32323,7149]) ).
thf(34280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[34279]) ).
thf(34281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[34280:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(39991,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( E @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,34281]) ).
thf(39992,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( E @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[39991]) ).
thf(39993,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[39992:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( G @ ( H @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(40139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[39993]) ).
thf(2278,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)],[1055,2032]) ).
thf(2279,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)],[2278]) ).
thf(2280,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2279:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2400,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2280]) ).
thf(3274,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[2400]) ).
thf(31838,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31394,3274]) ).
thf(31839,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[31838]) ).
thf(31840,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[31839:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(7150,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)],[4551]) ).
thf(7348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[7150,1750]) ).
thf(7349,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)],[7348]) ).
thf(7350,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[7349:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(7545,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[7350]) ).
thf(34057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ~ $true
| ( D @ ( D @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32323,7545]) ).
thf(34058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( D @ ( D @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[34057]) ).
thf(34059,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[34058:[bind(A,$thf( J @ ( J @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( J @ ( J @ implies ) @ not )),bind(D,$thf( J ))]]) ).
thf(34580,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[34059]) ).
thf(47812,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[34580,7]) ).
thf(47813,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[47812]) ).
thf(48178,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[47813]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[79]) ).
thf(100,plain,
! [A: $i] :
( ( ( A @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[86]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,100]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[115]) ).
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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,117]) ).
thf(208,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(1919,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)],[1114,1750]) ).
thf(1920,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)],[1919]) ).
thf(1921,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1920:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2055,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[1921]) ).
thf(2580,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)],[1114,2055]) ).
thf(2581,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)],[2580]) ).
thf(2630,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)],[2581]) ).
thf(1016,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)],[10,54]) ).
thf(1017,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)],[1016]) ).
thf(1018,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1017:[bind(A,$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(1056,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1018]) ).
thf(1402,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1056,52]) ).
thf(1403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[1402]) ).
thf(1404,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1403:[bind(A,$thf( O @ ( P @ not @ implies ) )),bind(B,$thf( P )),bind(C,$thf( O @ ( P @ not @ implies ) @ ( P @ ( P @ not @ implies ) @ implies ) )),bind(D,$thf( O )),bind(E,$thf( P ))]]) ).
thf(1466,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1404]) ).
thf(76,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)],[51,51]) ).
thf(77,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)],[76]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(85,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)],[78]) ).
thf(4032,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)],[1466,85]) ).
thf(4033,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)],[4032]) ).
thf(4034,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[4033:[bind(A,$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(4188,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)],[4034]) ).
thf(280,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)],[138,51]) ).
thf(281,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)],[280]) ).
thf(282,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$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(301,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)],[282]) ).
thf(1914,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( F @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[301,1750]) ).
thf(1915,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( F @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[1914]) ).
thf(1916,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1915:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( S )),bind(E,$thf( T )),bind(F,$thf( H @ ( K @ ( N @ ( S @ ( T @ not @ implies ) @ ( T @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2077,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 @ is_a_theorem ),
inference(simp,[status(thm)],[1916]) ).
thf(650,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)],[648,52]) ).
thf(651,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)],[650]) ).
thf(652,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[651:[bind(A,$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(698,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[652]) ).
thf(750,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[698,100]) ).
thf(751,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[750]) ).
thf(752,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[751:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(762,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[752]) ).
thf(2885,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)],[1056,2073]) ).
thf(2886,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)],[2885]) ).
thf(2887,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2886:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(2940,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)],[2887]) ).
thf(1954,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)],[12,1750]) ).
thf(1955,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)],[1954]) ).
thf(1956,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1955:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(2062,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[1956]) ).
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 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(30,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)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$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(55,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)],[31]) ).
thf(1259,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)],[1114,55]) ).
thf(1260,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)],[1259]) ).
thf(1261,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1260:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( H @ ( H @ implies ) @ not )),bind(E,$thf( E ))]]) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1261]) ).
thf(1761,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)],[1384,52]) ).
thf(1762,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)],[1761]) ).
thf(1763,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1762:[bind(A,$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(1822,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1763]) ).
thf(1881,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)],[1822,55]) ).
thf(1882,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)],[1881]) ).
thf(1883,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1882:[bind(A,$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(1910,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)],[1883]) ).
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 )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(33,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)],[32]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$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(50,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)],[34]) ).
thf(18383,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)],[1910,50]) ).
thf(18384,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)],[18383]) ).
thf(18385,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18384:[bind(A,$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(18549,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)],[18385]) ).
thf(1517,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1466,100]) ).
thf(1518,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1517]) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1518:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(1533,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1519]) ).
thf(8867,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)],[1055,7149]) ).
thf(8868,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)],[8867]) ).
thf(8869,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[8868:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(9339,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)],[1114,8869]) ).
thf(9340,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)],[9339]) ).
thf(9400,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)],[9340]) ).
thf(2012,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)],[51,1750]) ).
thf(2013,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)],[2012]) ).
thf(2049,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)],[2013]) ).
thf(5717,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)],[1055,2049]) ).
thf(5718,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)],[5717]) ).
thf(5719,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5718:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(5898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[5719]) ).
thf(1283,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)],[698,55]) ).
thf(1284,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)],[1283]) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1284:[bind(A,$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(1366,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)],[1285]) ).
thf(11177,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)],[1366,50]) ).
thf(11178,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)],[11177]) ).
thf(11179,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11178:[bind(A,$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(11283,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)],[11179]) ).
thf(20108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11283,1750]) ).
thf(20109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[20108]) ).
thf(20110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[20109:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( M @ ( P @ ( Q @ not @ implies ) @ not @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( Q @ implies ) ))]]) ).
thf(20469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[20110]) ).
thf(32121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem )
| ( C @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31394,29052]) ).
thf(32122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ( C @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[32121]) ).
thf(32123,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[32122:[bind(A,$thf( F @ ( F @ not @ implies ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F ))]]) ).
thf(32428,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[32123]) ).
thf(44328,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ~ $true
| ( E @ ( E @ implies ) @ is_a_theorem )
| ( C @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32428,7545]) ).
thf(44329,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( E @ ( E @ implies ) @ is_a_theorem )
| ( C @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[44328]) ).
thf(44330,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[44329:[bind(A,$thf( K @ ( K @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( K @ ( K @ implies ) @ not )),bind(E,$thf( K ))]]) ).
thf(45501,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[44330]) ).
thf(14434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[236,1750]) ).
thf(14435,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)],[14434]) ).
thf(14436,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14435:[bind(A,$thf( D @ not )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(14856,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14436]) ).
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 )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[82,9]) ).
thf(124,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)],[123]) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$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(142,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)],[125]) ).
thf(1127,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)],[1114,51]) ).
thf(1128,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)],[1127]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1129]) ).
thf(1262,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)],[1176,55]) ).
thf(1263,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)],[1262]) ).
thf(1264,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1263:[bind(A,$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(1386,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)],[1264]) ).
thf(12828,plain,
! [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 @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1386,1750]) ).
thf(12829,plain,
! [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 @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[12828]) ).
thf(12830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12829:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( Q )),bind(E,$thf( K @ ( N @ ( Q @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(13095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[12830]) ).
thf(18220,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)],[1910,52]) ).
thf(18221,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)],[18220]) ).
thf(18222,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18221:[bind(A,$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(18522,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)],[18222]) ).
thf(18562,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)],[18522,1750]) ).
thf(18563,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)],[18562]) ).
thf(18564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18563:[bind(A,$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(18897,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)],[18564]) ).
thf(18197,plain,
! [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 @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1910,1750]) ).
thf(18198,plain,
! [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 @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[18197]) ).
thf(18199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18198:[bind(A,$thf( N )),bind(B,$thf( Q )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( N @ ( Q @ ( Q @ implies ) @ not @ implies ) @ ( N @ ( K @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(18517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[18199]) ).
thf(1949,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)],[1055,1750]) ).
thf(1950,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[1949]) ).
thf(1951,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1950:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2061,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[1951]) ).
thf(2094,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)],[12,2061]) ).
thf(2095,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)],[2094]) ).
thf(2146,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2095]) ).
thf(2082,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)],[1466,2061]) ).
thf(2083,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)],[2082]) ).
thf(2141,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2083]) ).
thf(286,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 ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ $true
| ( F @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[138,48]) ).
thf(287,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 ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( F @ is_a_theorem ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$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(296,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 ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[288]) ).
thf(22140,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 ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[296,138]) ).
thf(1190,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)],[1176,51]) ).
thf(1191,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)],[1190]) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1191:[bind(A,$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(1243,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)],[1192]) ).
thf(53572,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31840,100]) ).
thf(53573,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[53572]) ).
thf(53574,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[53573:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(9329,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)],[1055,8869]) ).
thf(9330,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)],[9329]) ).
thf(9396,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[9330]) ).
thf(2090,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)],[698,2061]) ).
thf(2091,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)],[2090]) ).
thf(2136,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)],[2091]) ).
thf(218,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)],[83,51]) ).
thf(219,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)],[218]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[219:[bind(A,$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 ) @ is_a_theorem ),
inference(simp,[status(thm)],[220]) ).
thf(347,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)],[240,51]) ).
thf(348,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)],[347]) ).
thf(349,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$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(374,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)],[349]) ).
thf(1979,plain,
! [E: $i,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 )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[374,1750]) ).
thf(1980,plain,
! [E: $i,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 )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[1979]) ).
thf(1981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1980:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( P )),bind(E,$thf( G @ ( J @ ( M @ ( P @ ( P @ ( P @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2067,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 @ is_a_theorem ),
inference(simp,[status(thm)],[1981]) ).
thf(2916,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= B )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2900]) ).
thf(3275,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[2400]) ).
thf(155,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,117]) ).
thf(156,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[155]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[157]) ).
thf(344,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,162]) ).
thf(345,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[344]) ).
thf(346,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( N @ ( N @ ( N @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(372,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(3282,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)],[1055,2400]) ).
thf(3318,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) )
| ~ ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3282]) ).
thf(10157,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)],[1114,3318]) ).
thf(10158,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)],[10157]) ).
thf(10159,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10158:[bind(A,$thf( J @ ( J @ implies ) @ not )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( J @ implies ) @ not ))]]) ).
thf(10251,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[10159]) ).
thf(2033,plain,
! [A: $i] :
( ( ( A @ not )
!= A )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2029]) ).
thf(14597,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)],[236,2033]) ).
thf(14598,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)],[14597]) ).
thf(14599,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= A )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14598:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(53308,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 @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31840,14599]) ).
thf(53309,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 @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[53308]) ).
thf(53310,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[53309:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(53664,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[53310]) ).
thf(3740,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)],[3275,51]) ).
thf(3741,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)],[3740]) ).
thf(3742,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3741:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(3776,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)],[3742]) ).
thf(2102,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)],[1176,2061]) ).
thf(2103,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)],[2102]) ).
thf(2126,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)],[2103]) ).
thf(190,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)],[51,48]) ).
thf(191,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)],[190]) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(196,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)],[192]) ).
thf(1492,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1466,7]) ).
thf(1493,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1492]) ).
thf(1521,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1493]) ).
thf(26221,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( B @ ( B @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1521]) ).
thf(26226,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( A @ ( B @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( B @ ( B @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[26221]) ).
thf(26229,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) )
| ( ( B @ not )
!= a )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[26226]) ).
thf(26247,plain,
( ( ( c @ ( b @ implies ) @ ( c @ ( b @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) @ not )
!= a )
| ( ( c @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[26229]) ).
thf(27192,plain,
( ( ( c @ ( b @ implies ) @ ( c @ ( b @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[26247]) ).
thf(1929,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)],[11,1750]) ).
thf(1930,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)],[1929]) ).
thf(1931,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1930:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2057,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[1931]) ).
thf(2651,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)],[11,2057]) ).
thf(2652,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)],[2651]) ).
thf(2708,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[2652]) ).
thf(1809,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)],[1384,51]) ).
thf(1810,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)],[1809]) ).
thf(1811,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1810:[bind(A,$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(1832,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)],[1811]) ).
thf(2116,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)],[51,2061]) ).
thf(2117,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)],[2116]) ).
thf(2138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2117]) ).
thf(6357,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)],[1114,2138]) ).
thf(6358,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)],[6357]) ).
thf(6359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6358:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(6434,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)],[6359]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ 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 )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(19,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(20,plain,
( ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( a @ implies ) @ ( b @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(2720,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)],[11,2062]) ).
thf(2721,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)],[2720]) ).
thf(2767,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2721]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ 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 )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( c @ ( b @ implies ) @ ( a @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(56,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) @ not )
!= b ) ),
inference(simp,[status(thm)],[28]) ).
thf(57,plain,
( ( c @ ( b @ implies ) @ ( a @ implies ) @ not )
!= b ),
inference(simp,[status(thm)],[56]) ).
thf(2338,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)],[51,2032]) ).
thf(2339,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)],[2338]) ).
thf(2340,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ not @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2339:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2388,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)],[2340]) ).
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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,162]) ).
thf(258,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$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(261,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(14790,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[236,100]) ).
thf(14791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14790]) ).
thf(14792,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14791:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(17943,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 @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[236,14792]) ).
thf(17944,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 @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17943]) ).
thf(17945,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17944:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(18043,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17945]) ).
thf(2880,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 @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,2073]) ).
thf(2881,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 @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2880]) ).
thf(2882,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2881:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(2939,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)],[2882]) ).
thf(5038,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)],[2939]) ).
thf(5052,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)],[5038]) ).
thf(659,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)],[648,50]) ).
thf(660,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)],[659]) ).
thf(661,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$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(704,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[661]) ).
thf(2830,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)],[704,2073]) ).
thf(2831,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)],[2830]) ).
thf(2832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2831:[bind(A,$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(2929,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)],[2832]) ).
thf(1419,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)],[1056,54]) ).
thf(1420,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)],[1419]) ).
thf(1421,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1420:[bind(A,$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(1460,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1421]) ).
thf(5113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ ( C @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1460,2073]) ).
thf(5114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ ( C @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[5113]) ).
thf(5115,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5114:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ ( E @ ( E @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(5264,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[5115]) ).
thf(3651,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)],[3275,1750]) ).
thf(3652,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)],[3651]) ).
thf(3653,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3652:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) @ not ))]]) ).
thf(3765,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3653]) ).
thf(14759,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ not @ is_a_theorem ) )
| ~ $true
| ( C @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[236,3765]) ).
thf(14760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ not @ is_a_theorem ) )
| ( C @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14759]) ).
thf(14761,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14760:[bind(A,$thf( G @ ( G @ implies ) @ not @ not )),bind(B,$thf( B )),bind(C,$thf( G ))]]) ).
thf(14881,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)],[14761]) ).
thf(3908,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)],[3274]) ).
thf(3934,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3908]) ).
thf(2169,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,2033]) ).
thf(2170,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B ) ),
inference(simp,[status(thm)],[2169]) ).
thf(2171,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2170:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2236,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(simp,[status(thm)],[2171]) ).
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 )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[83,9]) ).
thf(214,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)],[213]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(238,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)],[215]) ).
thf(1932,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)],[11,1750]) ).
thf(1933,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)],[1932]) ).
thf(2034,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[1933]) ).
thf(59,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)],[10,51]) ).
thf(60,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)],[59]) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$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(84,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)],[61]) ).
thf(5206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1460,51]) ).
thf(5207,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5206]) ).
thf(5208,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5207:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ ( E @ ( E @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(5259,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[5208]) ).
thf(774,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)],[704,52]) ).
thf(775,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)],[774]) ).
thf(776,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$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(821,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)],[776]) ).
thf(1025,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)],[704,54]) ).
thf(1026,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)],[1025]) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1026:[bind(A,$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(1054,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)],[1027]) ).
thf(9875,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)],[1054,52]) ).
thf(9876,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)],[9875]) ).
thf(9877,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9876:[bind(A,$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(10092,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)],[9877]) ).
thf(10344,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)],[10092,1750]) ).
thf(10345,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)],[10344]) ).
thf(10346,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10345:[bind(A,$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(10602,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)],[10346]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(584,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= b )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[58]) ).
thf(602,plain,
! [A: $i] :
( ( ( A @ ( a @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[584]) ).
thf(1934,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)],[138,1750]) ).
thf(1935,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)],[1934]) ).
thf(1936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1935:[bind(A,$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(2058,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)],[1936]) ).
thf(8380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[821,1750]) ).
thf(8381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8380]) ).
thf(8382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[8381:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( K @ ( P @ ( Q @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(8595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[8382]) ).
thf(34130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32323,3274]) ).
thf(34131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[34130]) ).
thf(34132,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[34131:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(422,plain,
! [H: $i,G: $i,F: $i,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 )
!= ( H @ is_a_theorem ) )
| ( ( F @ ( G @ ( H @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[301,162]) ).
thf(423,plain,
! [H: $i,G: $i,F: $i,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 )
!= ( H @ is_a_theorem ) )
| ( ( F @ ( G @ ( H @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[422]) ).
thf(424,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[423:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( U )),bind(E,$thf( V )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( J @ ( M @ ( P @ ( U @ ( V @ not @ implies ) @ ( V @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(453,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[424]) ).
thf(251,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,162]) ).
thf(252,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[251]) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ not @ implies ) ))]]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[253]) ).
thf(1073,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,265]) ).
thf(1074,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1073]) ).
thf(1075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ implies ) ))]]) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1075]) ).
thf(3749,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)],[3275]) ).
thf(3756,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3749]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,100]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(116,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(12848,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)],[1386,52]) ).
thf(12849,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)],[12848]) ).
thf(12850,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12849:[bind(A,$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(13105,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)],[12850]) ).
thf(13977,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)],[13105,1750]) ).
thf(13978,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)],[13977]) ).
thf(13979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[13978:[bind(A,$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(14253,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)],[13979]) ).
thf(26223,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( B @ ( B @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[26221]) ).
thf(26243,plain,
! [A: $i] :
( ( ( A @ not )
!= b )
| ( ( A @ ( A @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[26223]) ).
thf(10204,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)],[51,3318]) ).
thf(10205,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)],[10204]) ).
thf(10206,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[10205:[bind(A,$thf( F @ not )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ not ))]]) ).
thf(10243,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[10206]) ).
thf(14603,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)],[236,3274]) ).
thf(14604,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)],[14603]) ).
thf(14605,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14604:[bind(A,$thf( E @ ( E @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(14836,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)],[14605]) ).
thf(2592,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)],[1055,2055]) ).
thf(2593,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)],[2592]) ).
thf(2646,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[2593]) ).
thf(350,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,79]) ).
thf(351,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[350]) ).
thf(352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[351:[bind(A,$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(366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(90,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,79]) ).
thf(91,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(1952,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)],[1055,1750]) ).
thf(1953,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[1952]) ).
thf(2044,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[1953]) ).
thf(3000,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)],[1822,2044]) ).
thf(3001,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)],[3000]) ).
thf(3002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3001:[bind(A,$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(3037,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)],[3002]) ).
thf(417,plain,
! [G: $i,F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( G @ is_a_theorem )
| ~ $true
| ~ ( G @ ( F @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[301,9]) ).
thf(418,plain,
! [G: $i,F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( G @ is_a_theorem )
| ~ ( G @ ( F @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[417]) ).
thf(419,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[418:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( T )),bind(E,$thf( U )),bind(F,$thf( I @ ( L @ ( O @ ( T @ ( U @ not @ implies ) @ ( U @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )),bind(G,$thf( G ))]]) ).
thf(452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[419]) ).
thf(21444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[3275,14836]) ).
thf(21445,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21444]) ).
thf(21446,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[21445:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(24847,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[21446,3274]) ).
thf(24848,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[24847]) ).
thf(24849,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[24848:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(17290,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)],[236,14599]) ).
thf(17291,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)],[17290]) ).
thf(17292,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17291:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(17389,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17292]) ).
thf(2718,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)],[1114,2062]) ).
thf(2719,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)],[2718]) ).
thf(2773,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)],[2719]) ).
thf(1890,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1822,100]) ).
thf(1891,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1890]) ).
thf(1892,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1891:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(1900,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1892]) ).
thf(1093,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,7]) ).
thf(1094,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1093]) ).
thf(1108,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1094]) ).
thf(1187,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1108]) ).
thf(1188,plain,
( ( c @ ( a @ implies ) @ ( b @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1187]) ).
thf(1189,plain,
( ( ( c @ ( b @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( b != a ) ),
inference(simp,[status(thm)],[1188]) ).
thf(1254,plain,
( ( c != c )
| ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1189]) ).
thf(1255,plain,
b != a,
inference(simp,[status(thm)],[1254]) ).
thf(254,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,162]) ).
thf(255,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[254]) ).
thf(256,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$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(260,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[256]) ).
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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,117]) ).
thf(150,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(3012,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 @ ( D @ implies ) )
!= ( E @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1384,2044]) ).
thf(3013,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 @ ( D @ implies ) )
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[3012]) ).
thf(3014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3013:[bind(A,$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(3022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3014]) ).
thf(2870,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)],[1822,2073]) ).
thf(2871,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)],[2870]) ).
thf(2872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2871:[bind(A,$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(2937,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)],[2872]) ).
thf(10798,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 @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,5052]) ).
thf(10799,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 @ is_a_theorem )
!= ( D @ is_a_theorem ) ) ),
inference(simp,[status(thm)],[10798]) ).
thf(10800,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[10799:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(11003,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[10800]) ).
thf(21,plain,
( ( ( c @ ( a @ implies ) @ ( b @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[20]) ).
thf(11046,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)],[1366,52]) ).
thf(11047,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)],[11046]) ).
thf(11048,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11047:[bind(A,$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(11281,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)],[11048]) ).
thf(11497,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11281,51]) ).
thf(11498,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11497]) ).
thf(11499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11498:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( J @ ( M @ ( P @ ( Q @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( Q @ implies ) ))]]) ).
thf(11592,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[11499]) ).
thf(2106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[648,2061]) ).
thf(2107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2106]) ).
thf(2133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2107]) ).
thf(1984,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)],[648,1750]) ).
thf(1985,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)],[1984]) ).
thf(1986,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1985:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2068,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)],[1986]) ).
thf(789,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)],[704,51]) ).
thf(790,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)],[789]) ).
thf(791,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[790:[bind(A,$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(830,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)],[791]) ).
thf(1815,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1384,100]) ).
thf(1816,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1815]) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1816:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1817]) ).
thf(2157,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)],[11,2033]) ).
thf(2158,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)],[2157]) ).
thf(2159,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2158:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2228,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2159]) ).
thf(18809,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18522,100]) ).
thf(18810,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[18809]) ).
thf(18811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[18810:[bind(A,$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(18896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[18811]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(308,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 @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[10,49]) ).
thf(309,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 @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[308]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$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(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[310]) ).
thf(5053,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= C )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[5038]) ).
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 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(42,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)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( A @ not @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ not @ implies ) )),bind(C,$thf( E ))]]) ).
thf(53,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( A @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[43]) ).
thf(31761,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31394,53]) ).
thf(31762,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31761]) ).
thf(31763,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[31762:[bind(A,$thf( E @ ( E @ not @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(32316,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31763]) ).
thf(33263,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32316,3274]) ).
thf(33264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[33263]) ).
thf(33265,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[33264:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(34422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32323,100]) ).
thf(34423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[34422]) ).
thf(34424,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[34423:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(34547,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[34424]) ).
thf(37320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,34547]) ).
thf(37321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[37320]) ).
thf(37322,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[37321:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(37396,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[37322]) ).
thf(14164,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13105,51]) ).
thf(14165,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14164]) ).
thf(14166,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( E @ not @ implies ) @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[14165:[bind(A,$thf( K )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( P @ ( Q @ not @ implies ) @ ( K @ ( N @ ( N @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(14276,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( E @ not @ implies ) @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[14166]) ).
thf(1104,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,100]) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1104]) ).
thf(1106,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1105:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(1118,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1106]) ).
thf(323,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)],[83,49]) ).
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 )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(328,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)],[325]) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[698,7]) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[739]) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[740]) ).
thf(2961,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)],[698,2044]) ).
thf(2962,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)],[2961]) ).
thf(2963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[2962:[bind(A,$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(3032,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)],[2963]) ).
thf(1508,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)],[1466,55]) ).
thf(1509,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)],[1508]) ).
thf(1510,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1509:[bind(A,$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(1528,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)],[1510]) ).
thf(15714,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)],[1528,52]) ).
thf(15715,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)],[15714]) ).
thf(15716,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15715:[bind(A,$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(15993,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)],[15716]) ).
thf(16676,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15993,51]) ).
thf(16677,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16676]) ).
thf(16678,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16677:[bind(A,$thf( L )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( L @ ( O @ ( P @ not @ implies ) @ not @ implies ) @ ( P @ ( P @ not @ implies ) @ implies ) ))]]) ).
thf(16773,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[16678]) ).
thf(15860,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)],[1528,50]) ).
thf(15861,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)],[15860]) ).
thf(15862,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15861:[bind(A,$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(16023,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)],[15862]) ).
thf(2728,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)],[1055,2062]) ).
thf(2729,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)],[2728]) ).
thf(2781,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2729]) ).
thf(26222,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[26221]) ).
thf(26242,plain,
! [A: $i] :
( ( ( A @ ( c @ ( b @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[26222]) ).
thf(4111,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1822,85]) ).
thf(4112,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4111]) ).
thf(4113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( E @ not @ implies ) @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[4112:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( M @ ( N @ not @ implies ) @ ( K @ ( K @ implies ) @ not @ implies ) ))]]) ).
thf(4167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( E @ not @ implies ) @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[4113]) ).
thf(2845,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 ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1176,2073]) ).
thf(2846,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 ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2845]) ).
thf(2847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2846:[bind(A,$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(2932,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)],[2847]) ).
thf(1511,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)],[1466,51]) ).
thf(1512,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)],[1511]) ).
thf(1513,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1512:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1530,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)],[1513]) ).
thf(15201,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)],[55,14856]) ).
thf(15202,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)],[15201]) ).
thf(15203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[15202:[bind(A,$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(15339,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)],[15203]) ).
thf(3666,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ ( C @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[3275,2073]) ).
thf(3667,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( B @ ( C @ not @ implies ) @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3666]) ).
thf(3668,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3667:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(3770,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3668]) ).
thf(10527,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10092,100]) ).
thf(10528,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[10527]) ).
thf(10529,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[10528:[bind(A,$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(10588,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[10529]) ).
thf(2092,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,2061]) ).
thf(2093,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2092]) ).
thf(2140,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2093]) ).
thf(724,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)],[698,51]) ).
thf(725,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)],[724]) ).
thf(726,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$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(764,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)],[726]) ).
thf(888,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)],[764,51]) ).
thf(889,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)],[888]) ).
thf(890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$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(938,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)],[890]) ).
thf(2663,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)],[12,2057]) ).
thf(2664,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)],[2663]) ).
thf(2702,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[2664]) ).
thf(2024,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)],[83,1750]) ).
thf(2025,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)],[2024]) ).
thf(2026,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2025:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2076,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2026]) ).
thf(31489,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31394,1750]) ).
thf(31490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31489]) ).
thf(31491,plain,
! [B: $i,A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[31490:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(52264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( A @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31491,3274]) ).
thf(52265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ not @ is_a_theorem )
| ~ ( A @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52264]) ).
thf(52266,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ~ ( A @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[52265:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(12822,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( C
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[753]) ).
thf(12823,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c @ ( b @ implies ) @ ( a @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[12822]) ).
thf(14431,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)],[236,1750]) ).
thf(14432,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)],[14431]) ).
thf(14433,plain,
! [B: $i,A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14432:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2813,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)],[1055,2073]) ).
thf(2814,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)],[2813]) ).
thf(2909,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2814]) ).
thf(2096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[704,2061]) ).
thf(2097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2096]) ).
thf(2144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2097]) ).
thf(1843,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1822,117]) ).
thf(1844,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1843]) ).
thf(1845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1844:[bind(A,$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(1906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1845]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,79]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[98]) ).
thf(396,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,99]) ).
thf(397,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[396]) ).
thf(398,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( N @ ( N @ ( N @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(412,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[398]) ).
thf(2890,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)],[1384,2073]) ).
thf(2891,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)],[2890]) ).
thf(2892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2891:[bind(A,$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(2941,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)],[2892]) ).
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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,117]) ).
thf(153,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$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(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(6366,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)],[12,2138]) ).
thf(6367,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)],[6366]) ).
thf(6368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6367:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ not @ implies ) @ ( J @ implies ) )),bind(E,$thf( E ))]]) ).
thf(6437,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)],[6368]) ).
thf(582,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[58]) ).
thf(601,plain,
! [A: $i] :
( ( A @ ( a @ implies ) @ ( A @ ( c @ ( b @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[582]) ).
thf(2248,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)],[1114,2032]) ).
thf(2249,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)],[2248]) ).
thf(2250,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2249:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2394,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)],[2250]) ).
thf(27069,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[2394]) ).
thf(3726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( B @ implies ) )
!= ( C @ not ) )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[3275,2044]) ).
thf(3727,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( B @ implies ) )
!= ( C @ not ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3726]) ).
thf(3728,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ not ) )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3727:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(3768,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ not ) )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3728]) ).
thf(1957,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)],[12,1750]) ).
thf(1958,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)],[1957]) ).
thf(2048,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[1958]) ).
thf(11315,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)],[11281,1750]) ).
thf(11316,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)],[11315]) ).
thf(11317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11316:[bind(A,$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(11566,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)],[11317]) ).
thf(13971,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( B @ ( c @ ( b @ implies ) @ ( a @ implies ) @ not @ implies ) @ not )
!= b ) ),
inference(simp,[status(thm)],[12823]) ).
thf(13972,plain,
! [A: $i] :
( ( A @ ( c @ ( b @ implies ) @ ( a @ implies ) @ not @ implies ) @ not )
!= b ),
inference(simp,[status(thm)],[13971]) ).
thf(1800,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)],[1384,50]) ).
thf(1801,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)],[1800]) ).
thf(1802,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1801:[bind(A,$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(1827,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)],[1802]) ).
thf(7805,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)],[1827,1750]) ).
thf(7806,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)],[7805]) ).
thf(7807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[7806:[bind(A,$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(8027,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)],[7807]) ).
thf(11514,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11281,100]) ).
thf(11515,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[11514]) ).
thf(11516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[11515:[bind(A,$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(11598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[11516]) ).
thf(104,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,100]) ).
thf(105,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$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(118,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(2649,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)],[1114,2057]) ).
thf(2650,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)],[2649]) ).
thf(2695,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[2650]) ).
thf(2112,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)],[1822,2061]) ).
thf(2113,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)],[2112]) ).
thf(2134,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)],[2113]) ).
thf(381,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,99]) ).
thf(382,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(383,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[382:[bind(A,$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(413,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(9366,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)],[11,8869]) ).
thf(9367,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)],[9366]) ).
thf(9418,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[9367]) ).
thf(10510,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10092,51]) ).
thf(10511,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[10510]) ).
thf(10512,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10511:[bind(A,$thf( J )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( O @ ( P @ not @ implies ) @ ( J @ ( J @ ( J @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(10582,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[10512]) ).
thf(16471,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)],[15993,1750]) ).
thf(16472,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)],[16471]) ).
thf(16473,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16472:[bind(A,$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(16779,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)],[16473]) ).
thf(1399,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)],[1056,51]) ).
thf(1400,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)],[1399]) ).
thf(1401,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1400:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(1464,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)],[1401]) ).
thf(14600,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)],[236,3274]) ).
thf(14601,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)],[14600]) ).
thf(14602,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14601:[bind(A,$thf( F @ ( F @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(14835,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)],[14602]) ).
thf(14018,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13105,2073]) ).
thf(14019,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14018]) ).
thf(14020,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( D @ ( E @ not @ implies ) @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[14019:[bind(A,$thf( K )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( P @ ( Q @ not @ implies ) @ ( K @ ( N @ ( N @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(14268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( D @ ( E @ not @ implies ) @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[14020]) ).
thf(5008,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ~ ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1822,2939]) ).
thf(5009,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ~ ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[5008]) ).
thf(5010,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( D @ ( E @ not @ implies ) @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5009:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( M @ ( N @ not @ implies ) @ ( K @ ( K @ implies ) @ not @ implies ) ))]]) ).
thf(5071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( D @ ( E @ not @ implies ) @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[5010]) ).
thf(384,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,99]) ).
thf(385,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(386,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$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(406,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(2594,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)],[12,2055]) ).
thf(2595,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)],[2594]) ).
thf(2624,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)],[2595]) ).
thf(1860,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1822,7]) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1860]) ).
thf(1894,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1861]) ).
thf(2970,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)],[1466,2044]) ).
thf(2971,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)],[2970]) ).
thf(2972,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[2971:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(3038,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[2972]) ).
thf(65,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)],[51,9]) ).
thf(66,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)],[65]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(81,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)],[67]) ).
thf(3746,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[3275,100]) ).
thf(3747,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3746]) ).
thf(3748,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3747:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) @ not ))]]) ).
thf(3779,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3748]) ).
thf(11357,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11281,2073]) ).
thf(11358,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11357]) ).
thf(11359,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11358:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( J @ ( M @ ( P @ ( Q @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( Q @ implies ) ))]]) ).
thf(11586,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[11359]) ).
thf(1969,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)],[240,1750]) ).
thf(1970,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)],[1969]) ).
thf(1971,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1970:[bind(A,$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(2065,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)],[1971]) ).
thf(15691,plain,
! [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 @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1528,1750]) ).
thf(15692,plain,
! [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 @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[15691]) ).
thf(15693,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( A @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[15692:[bind(A,$thf( M )),bind(B,$thf( J )),bind(C,$thf( O )),bind(D,$thf( M @ ( O @ ( O @ not @ implies ) @ implies ) @ ( M @ ( J @ ( O @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(15988,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( A @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[15693]) ).
thf(19254,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)],[55,14835]) ).
thf(19255,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)],[19254]) ).
thf(19256,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[19255:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G @ ( B @ implies ) ))]]) ).
thf(19385,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)],[19256]) ).
thf(615,plain,
! [A: $i] :
( ( A != c )
| ( a != a )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[602]) ).
thf(616,plain,
( ( c @ ( c @ ( b @ implies ) @ implies ) )
!= b ),
inference(simp,[status(thm)],[615]) ).
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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,79]) ).
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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(285,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$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(303,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(2584,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)],[11,2055]) ).
thf(2585,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)],[2584]) ).
thf(2632,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[2585]) ).
thf(2985,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)],[1176,2044]) ).
thf(2986,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)],[2985]) ).
thf(2987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[2986:[bind(A,$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(3027,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)],[2987]) ).
thf(336,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,9]) ).
thf(337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[336]) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[337:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( H @ ( K @ ( K @ ( K @ not @ implies ) @ implies ) @ not @ implies ) @ not )),bind(E,$thf( A ))]]) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[338]) ).
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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,79]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(134,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,100]) ).
thf(135,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(6348,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)],[1055,2138]) ).
thf(6349,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)],[6348]) ).
thf(6350,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6349:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(6429,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[6350]) ).
thf(311,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)],[11,49]) ).
thf(312,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)],[311]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(330,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)],[313]) ).
thf(3116,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1243,51]) ).
thf(3117,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3116]) ).
thf(3118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3117:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( N @ ( Q @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(3150,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)],[3118]) ).
thf(1061,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,99]) ).
thf(1062,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[1061]) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1062:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1112,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1063]) ).
thf(10165,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)],[1466,3318]) ).
thf(10166,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)],[10165]) ).
thf(10167,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10166:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A @ ( A @ not @ implies ) ))]]) ).
thf(10253,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10167]) ).
thf(27805,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)],[27668,14856]) ).
thf(27806,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)],[27805]) ).
thf(27807,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[27806:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(28215,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[27807]) ).
thf(29189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ $true
| ~ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[28215,14856]) ).
thf(29190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[29189]) ).
thf(29191,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[29190:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( F @ not @ implies ) @ implies ) ))]]) ).
thf(29761,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[29191]) ).
thf(2019,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)],[1384,1750]) ).
thf(2020,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)],[2019]) ).
thf(2021,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2020:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(2075,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)],[2021]) ).
thf(16111,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)],[236,14433]) ).
thf(16112,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)],[16111]) ).
thf(16113,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[16112:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(16310,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[16113]) ).
thf(428,plain,
! [G: $i,F: $i,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 )
!= ( G @ is_a_theorem ) )
| ( F @ ( G @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[301,51]) ).
thf(429,plain,
! [G: $i,F: $i,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 )
!= ( G @ is_a_theorem ) )
| ( F @ ( G @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( T )),bind(E,$thf( U )),bind(F,$thf( F )),bind(G,$thf( I @ ( L @ ( O @ ( T @ ( U @ not @ implies ) @ ( U @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(455,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 ) @ is_a_theorem ),
inference(simp,[status(thm)],[430]) ).
thf(1964,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)],[764,1750]) ).
thf(1965,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)],[1964]) ).
thf(1966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1965:[bind(A,$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(2064,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)],[1966]) ).
thf(4953,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 ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1466,2939]) ).
thf(4954,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 ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4953]) ).
thf(4955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[4954:[bind(A,$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(5089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[4955]) ).
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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,79]) ).
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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(11028,plain,
! [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 @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1366,1750]) ).
thf(11029,plain,
! [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 @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11028]) ).
thf(11030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ implies ) @ ( D @ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11029:[bind(A,$thf( Q )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( Q @ ( P @ implies ) @ ( Q @ ( K @ ( N @ ( P @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(11272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ implies ) @ ( D @ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[11030]) ).
thf(33998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( C @ ( D @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32323,2073]) ).
thf(33999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( C @ ( D @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[33998]) ).
thf(34000,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[33999:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(34571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[34000]) ).
thf(40505,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,34571]) ).
thf(40506,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[40505]) ).
thf(40507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[40506:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G @ ( H @ not @ implies ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(40654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[40507]) ).
thf(1095,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,162]) ).
thf(1096,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1095]) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1096:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1097]) ).
thf(14193,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13105,100]) ).
thf(14194,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[14193]) ).
thf(14195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[14194:[bind(A,$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(14287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[14195]) ).
thf(665,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)],[648,51]) ).
thf(666,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)],[665]) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$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(707,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)],[667]) ).
thf(1989,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)],[707,1750]) ).
thf(1990,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)],[1989]) ).
thf(1991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1990:[bind(A,$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(2069,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)],[1991]) ).
thf(1922,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)],[1114,1750]) ).
thf(1923,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)],[1922]) ).
thf(2054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[1923]) ).
thf(2205,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)],[51,2033]) ).
thf(2206,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)],[2205]) ).
thf(2207,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2206:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2239,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2207]) ).
thf(18778,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18522,51]) ).
thf(18779,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[18778]) ).
thf(18780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18779:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( M @ ( P @ ( Q @ not @ implies ) @ not @ implies ) @ ( K @ ( K @ implies ) @ not @ implies ) ))]]) ).
thf(18891,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[18780]) ).
thf(2820,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)],[1466,2073]) ).
thf(2821,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)],[2820]) ).
thf(2822,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2821:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(2927,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)],[2822]) ).
thf(3986,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)],[3275,85]) ).
thf(3987,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)],[3986]) ).
thf(3988,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3987:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( G @ implies ) @ not ))]]) ).
thf(4168,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)],[3988]) ).
thf(2991,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 @ ( D @ implies ) )
!= ( E @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[648,2044]) ).
thf(2992,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 @ ( D @ implies ) )
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[2991]) ).
thf(2993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[2992:[bind(A,$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(3031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[2993]) ).
thf(53171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ $true
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31840,2033]) ).
thf(53172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= C )
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[53171]) ).
thf(53173,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= A )
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[53172:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(691,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[648,100]) ).
thf(692,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[691]) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[692:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(705,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[693]) ).
thf(2118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1056,2061]) ).
thf(2119,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2118]) ).
thf(2143,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2119]) ).
thf(305,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)],[138,49]) ).
thf(306,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)],[305]) ).
thf(307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$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)],[307]) ).
thf(10378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( D @ ( E @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10092,2073]) ).
thf(10379,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( D @ ( E @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10378]) ).
thf(10380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10379:[bind(A,$thf( J )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( O @ ( P @ not @ implies ) @ ( J @ ( J @ ( J @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(10581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[10380]) ).
thf(4646,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)],[3776,48]) ).
thf(4647,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)],[4646]) ).
thf(4648,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( A @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4647:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ ( H @ implies ) @ not @ not )),bind(D,$thf( A ))]]) ).
thf(4713,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)],[4648]) ).
thf(12315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( D @ ( D @ not @ implies ) @ 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)],[4713,54]) ).
thf(12316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( D @ ( D @ not @ implies ) @ 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)],[12315]) ).
thf(12317,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12316:[bind(A,$thf( F @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ implies ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( H ))]]) ).
thf(12519,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)],[12317]) ).
thf(390,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,99]) ).
thf(391,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[390]) ).
thf(392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ not @ implies ) ))]]) ).
thf(409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[392]) ).
thf(1944,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)],[698,1750]) ).
thf(1945,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)],[1944]) ).
thf(1946,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1945:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(2060,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[1946]) ).
thf(52501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( A @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31491,34547]) ).
thf(52502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( D @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52501]) ).
thf(52503,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[52502:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(52813,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52503]) ).
thf(5100,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)],[1460,1750]) ).
thf(5101,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)],[5100]) ).
thf(5102,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5101:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(5262,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[5102]) ).
thf(2151,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)],[1114,2033]) ).
thf(2152,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)],[2151]) ).
thf(2153,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2152:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2224,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[2153]) ).
thf(356,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[240,48]) ).
thf(357,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( G @ ( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[358]) ).
thf(10142,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)],[1055,3318]) ).
thf(10143,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)],[10142]) ).
thf(10144,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10143:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2084,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)],[11,2061]) ).
thf(2085,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)],[2084]) ).
thf(2128,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2085]) ).
thf(2976,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 @ ( D @ implies ) )
!= ( E @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[704,2044]) ).
thf(2977,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 @ ( D @ implies ) )
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[2976]) ).
thf(2978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[2977:[bind(A,$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(3019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2978]) ).
thf(314,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)],[51,49]) ).
thf(315,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)],[314]) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(331,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)],[316]) ).
thf(1924,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)],[1466,1750]) ).
thf(1925,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)],[1924]) ).
thf(1926,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1925:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(2056,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[1926]) ).
thf(31803,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 @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31394,14433]) ).
thf(31804,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 @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31803]) ).
thf(31805,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[31804:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(32325,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31805]) ).
thf(2080,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)],[1114,2061]) ).
thf(2081,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)],[2080]) ).
thf(2145,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2081]) ).
thf(39944,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( E @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[28215,34281]) ).
thf(39945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( E @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[39944]) ).
thf(39946,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[39945:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(40118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[39946]) ).
thf(9348,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)],[12,8869]) ).
thf(9349,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)],[9348]) ).
thf(9406,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)],[9349]) ).
thf(33895,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32323,1750]) ).
thf(33896,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[33895]) ).
thf(33897,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[33896:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(34540,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[33897]) ).
thf(8049,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)],[1055,5053]) ).
thf(8050,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)],[8049]) ).
thf(8051,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(pattern_uni,[status(thm)],[8050:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(8151,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(simp,[status(thm)],[8051]) ).
thf(14501,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)],[236,2073]) ).
thf(14502,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)],[14501]) ).
thf(14503,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14502:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(23217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( E @ ( C @ not @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[236,14503]) ).
thf(23218,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( E @ ( C @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[23217]) ).
thf(23219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[23218:[bind(A,$thf( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(23442,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[23219]) ).
thf(7488,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)],[7150,51]) ).
thf(7489,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)],[7488]) ).
thf(7490,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[7489:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) @ not ))]]) ).
thf(7552,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)],[7490]) ).
thf(14541,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)],[236,2032]) ).
thf(14542,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)],[14541]) ).
thf(14543,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[14542:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(9855,plain,
! [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 @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1054,1750]) ).
thf(9856,plain,
! [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 @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9855]) ).
thf(9857,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9856:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(10082,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[9857]) ).
thf(35544,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 @ implies ) @ not @ is_a_theorem )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[55,34132]) ).
thf(35545,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 @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[35544]) ).
thf(35546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[35545:[bind(A,$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(35763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[35546]) ).
thf(52973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( D @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31840,18043]) ).
thf(52974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( D @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52973]) ).
thf(52975,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[52974:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D ))]]) ).
thf(53732,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52975]) ).
thf(2659,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)],[1055,2057]) ).
thf(2660,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)],[2659]) ).
thf(2696,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[2660]) ).
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 ) )
| ~ $true
| ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,48]) ).
thf(179,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)],[178]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(203,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)],[180]) ).
thf(353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[240,49]) ).
thf(354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[353]) ).
thf(355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( G @ ( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[355]) ).
thf(1999,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)],[1822,1750]) ).
thf(2000,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)],[1999]) ).
thf(2001,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2000:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(2071,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2001]) ).
thf(6393,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)],[11,2138]) ).
thf(6394,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)],[6393]) ).
thf(6395,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[6394:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ ( F @ not @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(6447,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[6395]) ).
thf(1448,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1056,100]) ).
thf(1449,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1448]) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1449:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(1459,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1450]) ).
thf(3003,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)],[82,2044]) ).
thf(3004,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)],[3003]) ).
thf(3005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3004:[bind(A,$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(3039,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)],[3005]) ).
thf(21740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16023,1750]) ).
thf(21741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[21740]) ).
thf(21742,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[21741:[bind(A,$thf( L )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( O @ ( P @ not @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( P @ ( P @ not @ implies ) @ implies ) ))]]) ).
thf(22134,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[21742]) ).
thf(2122,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)],[83,2061]) ).
thf(2123,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)],[2122]) ).
thf(2135,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2123]) ).
thf(2120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1384,2061]) ).
thf(2121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2120]) ).
thf(2130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[2121]) ).
thf(22,plain,
( ( ( c @ ( a @ implies ) )
!= c )
| ( b != b )
| ( ( c @ ( a @ implies ) @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
( ( ( c @ ( a @ implies ) )
!= c )
| ( ( c @ ( a @ implies ) @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[22]) ).
thf(143,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,117]) ).
thf(144,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$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(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(131,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,79]) ).
thf(132,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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(2732,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)],[12,2062]) ).
thf(2733,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)],[2732]) ).
thf(2764,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)],[2733]) ).
thf(1974,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)],[1176,1750]) ).
thf(1975,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)],[1974]) ).
thf(1976,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1975:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( F @ ( I @ ( L @ ( L @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2066,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[1976]) ).
thf(16707,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15993,100]) ).
thf(16708,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[16707]) ).
thf(16709,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[16708:[bind(A,$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(16778,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[16709]) ).
thf(3566,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)],[1055,2916]) ).
thf(3567,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)],[3566]) ).
thf(3568,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[3567:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(3645,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[3568]) ).
thf(34194,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[32323,7]) ).
thf(34195,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[34194]) ).
thf(34458,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[34195]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,100]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(53283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31840,16310]) ).
thf(53284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[53283]) ).
thf(53285,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[53284:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D ))]]) ).
thf(53657,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[53285]) ).
thf(224,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)],[83,48]) ).
thf(225,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)],[224]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$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)],[226]) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,79]) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[1067]) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1068:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1069]) ).
thf(2835,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 ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[764,2073]) ).
thf(2836,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 ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2835]) ).
thf(2837,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2836:[bind(A,$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(2930,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 ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2837]) ).
thf(277,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ( ( E @ ( F @ ( G @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,162]) ).
thf(278,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ( ( E @ ( F @ ( G @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[277]) ).
thf(279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( Q )),bind(D,$thf( R )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( I @ ( L @ ( Q @ ( R @ not @ implies ) @ ( R @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(21123,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)],[236,14543]) ).
thf(21124,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)],[21123]) ).
thf(21125,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[21124:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(21408,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)],[21125]) ).
thf(242,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,162]) ).
thf(243,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$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(262,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(22703,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ not @ implies ) @ ( C @ ( 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)],[18549,1750]) ).
thf(22704,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22703]) ).
thf(22705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[22704:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( P @ ( Q @ not @ implies ) @ ( P @ ( M @ implies ) @ implies ) @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(23092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[22705]) ).
thf(12290,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)],[4713,2915]) ).
thf(12291,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)],[12290]) ).
thf(12292,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[12291:[bind(A,$thf( G @ ( H @ not @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( H ))]]) ).
thf(12515,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)],[12292]) ).
thf(1476,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1466,117]) ).
thf(1477,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1476]) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1477:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1478]) ).
thf(3041,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1243,2073]) ).
thf(3042,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[3041]) ).
thf(3043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3042:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( N @ ( Q @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(3145,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 ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[3043]) ).
thf(320,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 @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[82,49]) ).
thf(321,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 @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[320]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$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(326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[322]) ).
thf(733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[698,117]) ).
thf(734,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[733]) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[734:[bind(A,$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(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[735]) ).
thf(1959,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)],[704,1750]) ).
thf(1960,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)],[1959]) ).
thf(1961,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1960:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(2063,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)],[1961]) ).
thf(18612,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18522,2073]) ).
thf(18613,plain,
! [F: $i,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 )
!= ( F @ is_a_theorem ) )
| ~ ( E @ ( F @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[18612]) ).
thf(18614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[18613:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( M @ ( P @ ( Q @ not @ implies ) @ not @ implies ) @ ( K @ ( K @ implies ) @ not @ implies ) ))]]) ).
thf(18907,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[18614]) ).
thf(815,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[704,100]) ).
thf(816,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[815]) ).
thf(817,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[816:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[817]) ).
thf(2114,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)],[82,2061]) ).
thf(2115,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)],[2114]) ).
thf(2127,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)],[2115]) ).
thf(317,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)],[12,49]) ).
thf(318,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)],[317]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) )),bind(D,$thf( D ))]]) ).
thf(332,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)],[319]) ).
thf(3009,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 @ ( C @ implies ) )
!= ( D @ not ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1056,2044]) ).
thf(3010,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 @ ( C @ implies ) )
!= ( D @ not ) ) ),
inference(simp,[status(thm)],[3009]) ).
thf(3011,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3010:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(3020,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3011]) ).
thf(1076,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1055,117]) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1077:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1078]) ).
thf(3015,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)],[83,2044]) ).
thf(3016,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)],[3015]) ).
thf(3017,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[3016:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(3025,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3017]) ).
thf(31782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ( D @ ( D @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[31394,3770]) ).
thf(31783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ not @ not @ implies ) @ not @ is_a_theorem ) )
| ( D @ ( D @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31782]) ).
thf(31784,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[31783:[bind(A,$thf( G @ ( K @ ( K @ implies ) @ not @ not @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( K ))]]) ).
thf(32321,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31784]) ).
thf(339,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[240,9]) ).
thf(340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[339]) ).
thf(341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( G @ ( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[341]) ).
thf(26224,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( B @ not )
!= b )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[26221]) ).
thf(26244,plain,
( ( ( c @ ( b @ implies ) @ not )
!= b )
| ( ( c @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[26224]) ).
thf(2014,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)],[1056,1750]) ).
thf(2015,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)],[2014]) ).
thf(2016,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2015:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(2074,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2016]) ).
thf(16522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( D @ ( E @ not @ implies ) @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15993,2073]) ).
thf(16523,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( D @ ( E @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[16522]) ).
thf(16524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16523:[bind(A,$thf( L )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( L @ ( O @ ( P @ not @ implies ) @ not @ implies ) @ ( P @ ( P @ not @ implies ) @ implies ) ))]]) ).
thf(16792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[16524]) ).
thf(5214,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1460,100]) ).
thf(5215,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 )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[5214]) ).
thf(5216,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(pattern_uni,[status(thm)],[5215:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(5261,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[5216]) ).
thf(1939,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)],[10,1750]) ).
thf(1940,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)],[1939]) ).
thf(1941,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1940:[bind(A,$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(2059,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)],[1941]) ).
thf(2172,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)],[12,2033]) ).
thf(2173,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)],[2172]) ).
thf(2174,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[2173:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(2238,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[2174]) ).
thf(1884,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)],[1822,51]) ).
thf(1885,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)],[1884]) ).
thf(1886,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1885:[bind(A,$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(1912,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)],[1886]) ).
thf(425,plain,
! [H: $i,G: $i,F: $i,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 )
!= ( H @ is_a_theorem ) )
| ( ( F @ ( G @ ( H @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[301,99]) ).
thf(426,plain,
! [H: $i,G: $i,F: $i,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 )
!= ( H @ is_a_theorem ) )
| ( ( F @ ( G @ ( H @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[425]) ).
thf(427,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[426:[bind(A,$thf( J )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( U )),bind(E,$thf( V )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( J @ ( M @ ( P @ ( U @ ( V @ not @ implies ) @ ( V @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(454,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ not @ implies ) @ ( G @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(3997,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)],[85,2073]) ).
thf(3998,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)],[3997]) ).
thf(3999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3998:[bind(A,$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(4174,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)],[3999]) ).
thf(81277,plain,
$false,
inference(e,[status(thm)],[138,101,2072,40139,31840,48178,234,2630,4188,2077,762,2940,2062,18549,31394,1533,9400,1750,5898,10,20469,45501,14856,142,13095,18897,18517,698,2146,27668,2141,22140,1243,53574,1386,301,9396,1366,2136,2400,2067,2916,3275,372,10251,53664,3776,2126,196,52,1055,27192,2708,1832,6434,20,2049,2767,4551,57,2388,261,18043,5052,2929,5264,34580,14881,3934,2236,238,2034,84,5259,2073,821,10602,602,2058,8595,34132,453,1119,3756,116,265,1521,14253,26243,10243,34281,14836,2646,3318,366,102,3037,452,6,24849,117,17389,85,2061,2773,1900,1255,260,160,3022,2937,11003,21,2032,2396,11592,28,2133,2068,830,7545,1836,2228,1910,18896,329,5053,33265,37396,9,53,14276,1118,328,753,3032,16773,16023,2781,26242,4167,1114,2932,1530,15339,3770,10588,2140,7150,938,2702,2076,1466,2915,52266,12823,14433,13105,2909,2057,1054,2144,1906,412,2033,2941,161,3274,32323,6437,601,27069,3768,2048,11566,13972,14792,8027,11598,118,2695,2134,413,9418,10582,54,16779,49,2055,236,704,1464,14835,14268,12,764,5071,406,11283,2624,1894,3038,81,3779,7,11586,2065,15988,19385,616,303,2632,3027,367,103,140,240,6429,1460,15993,330,3150,1112,10253,29761,2075,16310,1528,455,2064,5089,241,11272,40654,1176,1113,14287,2069,14599,2054,2239,18891,162,374,648,2927,4168,18522,3031,53173,48,18,705,2143,327,10581,12519,409,2060,707,52813,32428,5262,2224,370,10144,7149,2128,28215,2044,3019,50,331,1188,2056,32325,2145,11,40118,9406,34540,2939,8151,23442,7552,14543,10082,35763,53732,2696,203,368,2071,6447,1459,99,1108,3039,22134,2135,26,55,2130,23,2394,158,14503,139,2764,1822,8,2066,16778,3645,34547,82,29052,34458,119,58,53657,235,1116,2930,300,21408,32316,262,51,23092,12515,1527,26221,3145,326,8869,767,1056,31491,2063,10092,79,18907,828,3765,2127,34571,332,3020,1120,3025,1827,1384,32321,15,4713,369,2138,27976,83,11281,26244,2074,16792,5261,2059,2238,21446,1912,100,454,4174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % 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
% 0.11/0.37 % Computer : n012.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 21:46:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.74/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.92/0.99 % [INFO] Parsing done (144ms).
% 0.92/1.00 % [INFO] Running in sequential loop mode.
% 1.55/1.33 % [INFO] eprover registered as external prover.
% 1.55/1.33 % [INFO] Scanning for conjecture ...
% 1.74/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.74/1.43 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.74/1.44 % [INFO] Problem is propositional (TPTP CNF).
% 1.74/1.44 % [INFO] Type checking passed.
% 1.74/1.45 % [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 ...
% 201.19/59.05 % External prover 'e' found a proof!
% 201.19/59.05 % [INFO] Killing All external provers ...
% 201.19/59.06 % Time passed: 58561ms (effective reasoning time: 58048ms)
% 201.19/59.06 % Axioms used in derivation (4): cn_3, condensed_detachment, cn_1, cn_2
% 201.19/59.06 % No. of inferences in proof: 1331
% 201.19/59.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 58561 ms resp. 58048 ms w/o parsing
% 193.78/59.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 193.78/59.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------