%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL384+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 07:51:40 AM UTC 2026
% Result : Theorem 158.08s 42.81s
% Output : Refutation 160.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 5
% Syntax : Number of formulae : 978 ( 363 unt; 0 typ; 0 def)
% Number of atoms : 3018 ( 942 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 15334 (1624 ~;1010 |; 2 &;12696 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 3230 ( 0 ^;3230 !; 0 ?;3230 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(z_decl,type,
z: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
thf(14,plain,
! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,plain,
! [B: $i,A: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(cnf,[status(esa)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
thf(10,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(cnf,[status(esa)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ is_a_theorem )
& ( B @ ( A @ implies ) @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(8,plain,
! [A: $i,B: $i] :
( ( ( A @ is_a_theorem )
& ( B @ ( A @ implies ) @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(34,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)],[11,9]) ).
thf(35,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)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$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(50,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)],[36]) ).
thf(766,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ 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)],[15,50]) ).
thf(767,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[766]) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[767:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(770,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[768]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
thf(12,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(cnf,[status(esa)],[12]) ).
thf(31,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)],[13,9]) ).
thf(32,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)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[33]) ).
thf(802,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ 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)],[770,49]) ).
thf(803,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ 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)],[802]) ).
thf(804,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[803:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ ( G @ implies ) )),bind(E,$thf( G ))]]) ).
thf(840,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[804]) ).
thf(1,conjecture,
z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_45) ).
thf(2,negated_conjecture,
~ ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(881,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,7]) ).
thf(882,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[881]) ).
thf(892,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[882]) ).
thf(467,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)],[11,49]) ).
thf(468,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)],[467]) ).
thf(469,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[468:[bind(A,$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(484,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[469]) ).
thf(43,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)],[15,9]) ).
thf(44,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)],[43]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) )),bind(D,$thf( D ))]]) ).
thf(53,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)],[45]) ).
thf(1271,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)],[484,53]) ).
thf(1272,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)],[1271]) ).
thf(1273,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1272:[bind(A,$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(1322,plain,
! [B: $i,A: $i] : ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1273]) ).
thf(40,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)],[15,9]) ).
thf(41,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)],[40]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[42]) ).
thf(854,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)],[840,52]) ).
thf(855,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)],[854]) ).
thf(856,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[855:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(900,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[856]) ).
thf(935,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)],[900,50]) ).
thf(936,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)],[935]) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[936:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( H @ ( H @ implies ) @ not )),bind(E,$thf( E ))]]) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[937]) ).
thf(1274,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)],[948,53]) ).
thf(1275,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)],[1274]) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1275:[bind(A,$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(1323,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1276]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,7]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[73]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[74]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[81]) ).
thf(103,plain,
! [A: $i] :
( ( ( A @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[88]) ).
thf(1453,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1323,103]) ).
thf(1454,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1453]) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1454:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(1501,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[1455]) ).
thf(70,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)],[13,52]) ).
thf(71,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)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(85,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[72]) ).
thf(215,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)],[85,9]) ).
thf(216,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)],[215]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[217]) ).
thf(64,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)],[52,9]) ).
thf(65,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)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( E @ not )),bind(D,$thf( A ))]]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[66]) ).
thf(2113,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[83,7]) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2113]) ).
thf(2115,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2114:[bind(A,$thf( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) )),bind(B,$thf( B ))]]) ).
thf(2240,plain,
! [A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2115]) ).
thf(2643,plain,
! [A: $i] :
( ~ $true
| ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[2240]) ).
thf(2672,plain,
! [A: $i] :
( ( ( A @ not )
!= A )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2643]) ).
thf(17537,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)],[240,2672]) ).
thf(17538,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)],[17537]) ).
thf(17539,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= A )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17538:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(95,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,81]) ).
thf(96,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(1262,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ 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)],[770,53]) ).
thf(1263,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ 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)],[1262]) ).
thf(1264,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1263:[bind(A,$thf( S @ ( V @ ( W @ not @ implies ) @ not @ implies ) )),bind(B,$thf( V )),bind(C,$thf( W )),bind(D,$thf( S @ ( V @ ( W @ not @ implies ) @ not @ implies ) @ ( W @ implies ) )),bind(E,$thf( S )),bind(F,$thf( V @ ( W @ not @ implies ) ))]]) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1264]) ).
thf(2593,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)],[840,2240]) ).
thf(2594,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2593]) ).
thf(2595,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2594:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(2685,plain,
! [A: $i] :
~ ( A @ ( A @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2595]) ).
thf(2714,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)],[1320,2685]) ).
thf(2715,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)],[2714]) ).
thf(2778,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)],[2715]) ).
thf(2722,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)],[52,2685]) ).
thf(2723,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)],[2722]) ).
thf(2787,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2723]) ).
thf(2513,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)],[52,2240]) ).
thf(2514,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)],[2513]) ).
thf(2515,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2514:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(2701,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2515]) ).
thf(4599,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)],[2701]) ).
thf(4616,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)],[4599]) ).
thf(6632,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)],[840,4616]) ).
thf(6633,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)],[6632]) ).
thf(6634,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[6633:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(6778,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)],[6634]) ).
thf(7762,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)],[6778]) ).
thf(16795,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)],[840,7762]) ).
thf(16796,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)],[16795]) ).
thf(16797,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[16796:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(722,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ 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)],[85,50]) ).
thf(723,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ 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)],[722]) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not )),bind(E,$thf( E ))]]) ).
thf(777,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)],[724]) ).
thf(2671,plain,
! [A: $i] :
( ( ( A @ not @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[2643]) ).
thf(3587,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)],[52,2671]) ).
thf(3588,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)],[3587]) ).
thf(3589,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ not @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3588:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(3762,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)],[3589]) ).
thf(1423,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)],[1322,50]) ).
thf(1424,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)],[1423]) ).
thf(1425,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( C @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1424:[bind(A,$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(1442,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)],[1425]) ).
thf(10393,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)],[1442,53]) ).
thf(10394,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)],[10393]) ).
thf(10395,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10394:[bind(A,$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(10542,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)],[10395]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,103]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[108]) ).
thf(2596,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)],[840,2240]) ).
thf(2597,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2596]) ).
thf(2669,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2597]) ).
thf(4316,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)],[85,2669]) ).
thf(4317,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)],[4316]) ).
thf(4318,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[4317:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(4408,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[4318]) ).
thf(3672,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)],[840,2671]) ).
thf(3673,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)],[3672]) ).
thf(3674,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3673:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(3781,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3674]) ).
thf(3897,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
| ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[3781]) ).
thf(4189,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)],[3897,52]) ).
thf(4190,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)],[4189]) ).
thf(4191,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4190:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) @ not ))]]) ).
thf(4276,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)],[4191]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[46]) ).
thf(5264,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)],[4276,47]) ).
thf(5265,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)],[5264]) ).
thf(5266,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( A @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5265:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ ( H @ implies ) @ not @ not )),bind(D,$thf( A ))]]) ).
thf(5300,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)],[5266]) ).
thf(4448,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)],[52,2701]) ).
thf(4449,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)],[4448]) ).
thf(4450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4449:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(4661,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)],[4450]) ).
thf(16127,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ~ ( E @ is_a_theorem )
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[5300,4661]) ).
thf(16128,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ ( E @ is_a_theorem )
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16127]) ).
thf(16129,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[16128:[bind(A,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( H )),bind(D,$thf( K )),bind(E,$thf( L ))]]) ).
thf(16449,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)],[16129]) ).
thf(3647,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)],[13,2671]) ).
thf(3648,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)],[3647]) ).
thf(3649,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3648:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(3776,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)],[3649]) ).
thf(24729,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)],[3776]) ).
thf(25540,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)],[24729,240]) ).
thf(25541,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)],[25540]) ).
thf(25542,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[25541:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(218,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)],[85,9]) ).
thf(219,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)],[218]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[219:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(242,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)],[220]) ).
thf(26330,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true
| ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[25542,242]) ).
thf(26331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[26330]) ).
thf(26332,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[26331:[bind(A,$thf( Q @ ( Q @ ( Q @ not @ implies ) @ implies ) )),bind(B,$thf( B )),bind(C,$thf( Q @ ( Q @ ( Q @ not @ implies ) @ implies ) )),bind(D,$thf( Q @ ( Q @ ( Q @ not @ implies ) @ implies ) )),bind(E,$thf( Q ))]]) ).
thf(26510,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[26332]) ).
thf(907,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)],[900,52]) ).
thf(908,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)],[907]) ).
thf(909,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[908:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[909]) ).
thf(2598,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)],[951,2240]) ).
thf(2599,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)],[2598]) ).
thf(2600,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2599:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( F @ ( I @ ( L @ ( L @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2686,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2600]) ).
thf(10022,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)],[840,2787]) ).
thf(10023,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)],[10022]) ).
thf(10024,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10023:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(10093,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[10024]) ).
thf(78,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)],[15,52]) ).
thf(79,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)],[78]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$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)],[80]) ).
thf(134,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,81]) ).
thf(135,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$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(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(4488,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)],[948,2701]) ).
thf(4489,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)],[4488]) ).
thf(4490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[4489:[bind(A,$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(4638,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)],[4490]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(1790,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[60]) ).
thf(1820,plain,
! [A: $i] :
( ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1790]) ).
thf(1892,plain,
! [A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1820]) ).
thf(1903,plain,
! [A: $i] :
( ( y != A )
| ( ( z @ not )
!= x )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1892]) ).
thf(1919,plain,
( ( ( z @ not )
!= x )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1903]) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,120]) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[851]) ).
thf(853,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[852:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[853]) ).
thf(16154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[5300,53]) ).
thf(16155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ ( B @ implies ) @ not @ not @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16154]) ).
thf(16156,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[16155:[bind(A,$thf( G @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ implies ) )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( K )),bind(E,$thf( L ))]]) ).
thf(16456,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)],[16156]) ).
thf(1391,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)],[1322,52]) ).
thf(1392,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)],[1391]) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1392:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1441,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)],[1393]) ).
thf(10404,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)],[1442,2240]) ).
thf(10405,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)],[10404]) ).
thf(10406,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( A @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10405:[bind(A,$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(10545,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)],[10406]) ).
thf(1363,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)],[1320,50]) ).
thf(1364,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)],[1363]) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1364:[bind(A,$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(1382,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)],[1365]) ).
thf(9768,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)],[1382,53]) ).
thf(9769,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)],[9768]) ).
thf(9770,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9769:[bind(A,$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(9922,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)],[9770]) ).
thf(10175,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)],[9922,2240]) ).
thf(10176,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)],[10175]) ).
thf(10177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10176:[bind(A,$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(10326,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)],[10177]) ).
thf(3921,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)],[840,3781]) ).
thf(3938,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) )
| ~ ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3921]) ).
thf(17441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true
| ~ ( D @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[240,2701]) ).
thf(17442,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 @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17441]) ).
thf(17443,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17442:[bind(A,$thf( G @ ( H @ not @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( H ))]]) ).
thf(17610,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17443]) ).
thf(2568,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)],[13,2240]) ).
thf(2569,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)],[2568]) ).
thf(2570,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2569:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(2680,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2570]) ).
thf(3079,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)],[13,2680]) ).
thf(3080,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)],[3079]) ).
thf(3116,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3080]) ).
thf(2548,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)],[484,2240]) ).
thf(2549,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)],[2548]) ).
thf(2550,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2549:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(2708,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2550]) ).
thf(1888,plain,
! [A: $i] :
( ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( A != y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1907,plain,
( ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[1888]) ).
thf(2578,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)],[900,2240]) ).
thf(2579,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)],[2578]) ).
thf(2580,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(2682,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2580]) ).
thf(3493,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,2672]) ).
thf(3494,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= B ) ),
inference(simp,[status(thm)],[3493]) ).
thf(3495,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(pattern_uni,[status(thm)],[3494:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(3542,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) ),
inference(simp,[status(thm)],[3495]) ).
thf(37,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)],[11,9]) ).
thf(38,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)],[37]) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$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(51,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)],[39]) ).
thf(971,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ 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)],[770,51]) ).
thf(972,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ 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)],[971]) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[972:[bind(A,$thf( W @ ( X @ not @ implies ) @ ( W @ ( T @ implies ) @ implies ) )),bind(B,$thf( T )),bind(C,$thf( X )),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(1016,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[973]) ).
thf(1144,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1016,103]) ).
thf(1145,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1144]) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(1191,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[1146]) ).
thf(9855,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)],[1382,51]) ).
thf(9856,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)],[9855]) ).
thf(9857,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9856:[bind(A,$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(9911,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)],[9857]) ).
thf(12860,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)],[9911,2240]) ).
thf(12861,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)],[12860]) ).
thf(12862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[12861:[bind(A,$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(13025,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)],[12862]) ).
thf(7729,plain,
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1919]) ).
thf(7731,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( z != y )
| ( x != x ) ),
inference(simp,[status(thm)],[7729]) ).
thf(7743,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( z != y ) ),
inference(simp,[status(thm)],[7731]) ).
thf(799,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[770,52]) ).
thf(800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( N )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( N @ ( M @ implies ) @ ( N @ ( K @ ( M @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(838,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)],[801]) ).
thf(2523,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)],[838,2240]) ).
thf(2524,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)],[2523]) ).
thf(2525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2524:[bind(A,$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(2703,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)],[2525]) ).
thf(2633,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)],[15,2240]) ).
thf(2634,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)],[2633]) ).
thf(2635,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2634:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(2698,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2635]) ).
thf(3105,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)],[15,2680]) ).
thf(3106,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)],[3105]) ).
thf(3131,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3106]) ).
thf(492,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)],[484,49]) ).
thf(493,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)],[492]) ).
thf(494,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$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(531,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[494]) ).
thf(2488,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)],[531,2240]) ).
thf(2489,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)],[2488]) ).
thf(2490,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2489:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(2691,plain,
! [A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2490]) ).
thf(1022,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)],[951,52]) ).
thf(1023,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)],[1022]) ).
thf(1024,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$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(1064,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)],[1024]) ).
thf(1199,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)],[1064,52]) ).
thf(1200,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)],[1199]) ).
thf(1201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1200:[bind(A,$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(1247,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)],[1201]) ).
thf(9992,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)],[13,2787]) ).
thf(9993,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)],[9992]) ).
thf(9994,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[9993:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ ( F @ not @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(10074,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[9994]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,7]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[18]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( A
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(57,plain,
! [A: $i] :
( ( A @ ( z @ ( y @ implies ) @ ( x @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(4289,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)],[1322,2669]) ).
thf(4290,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)],[4289]) ).
thf(4291,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[4290:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(4390,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[4291]) ).
thf(1461,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)],[1323,52]) ).
thf(1462,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)],[1461]) ).
thf(1463,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1462:[bind(A,$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(1505,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)],[1463]) ).
thf(1733,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1505,52]) ).
thf(1734,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1733]) ).
thf(1735,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( E @ not @ implies ) @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1734:[bind(A,$thf( H )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( P @ ( Q @ not @ implies ) @ ( N @ ( N @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(1778,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)],[1735]) ).
thf(4617,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= B )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[4599]) ).
thf(16,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(20,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(4385,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)],[1320,2669]) ).
thf(4386,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)],[4385]) ).
thf(4387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[4386:[bind(A,$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(4411,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)],[4387]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,103]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(121,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(1334,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1320,103]) ).
thf(1335,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1334]) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1335:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[1336]) ).
thf(67,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)],[52,9]) ).
thf(68,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)],[67]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(2756,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)],[951,2685]) ).
thf(2757,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)],[2756]) ).
thf(2777,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)],[2757]) ).
thf(157,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,120]) ).
thf(158,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$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(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(4298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ not ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,2669]) ).
thf(4299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( C @ implies ) )
!= ( D @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[4298]) ).
thf(4300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4299:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(4396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[4300]) ).
thf(10010,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)],[900,2787]) ).
thf(10011,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)],[10010]) ).
thf(10012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10011:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(10085,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)],[10012]) ).
thf(212,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)],[85,52]) ).
thf(213,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)],[212]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[214]) ).
thf(15350,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)],[1322,3938]) ).
thf(15351,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)],[15350]) ).
thf(15352,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[15351:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A @ ( A @ not @ implies ) ))]]) ).
thf(15536,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[15352]) ).
thf(25390,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)],[24729,17610]) ).
thf(25391,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)],[25390]) ).
thf(25392,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[25391:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(25720,plain,
! [B: $i,A: $i] :
( ~ ( B @ is_a_theorem )
| ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[25392]) ).
thf(26624,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)],[25720,17610]) ).
thf(26625,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)],[26624]) ).
thf(26626,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[26625:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( F @ not @ implies ) @ implies ) ))]]) ).
thf(27119,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[26626]) ).
thf(61,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)],[52,52]) ).
thf(62,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)],[61]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(87,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)],[63]) ).
thf(4843,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)],[3897,87]) ).
thf(4844,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)],[4843]) ).
thf(4845,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ not @ implies ) @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4844:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( G @ implies ) @ not ))]]) ).
thf(4924,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)],[4845]) ).
thf(2724,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)],[1323,2685]) ).
thf(2725,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)],[2724]) ).
thf(2804,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)],[2725]) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,120]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[147]) ).
thf(247,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,160]) ).
thf(248,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$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(265,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(3175,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)],[13,2682]) ).
thf(3176,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)],[3175]) ).
thf(3211,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3176]) ).
thf(486,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[484,120]) ).
thf(487,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[486]) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[487:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[488]) ).
thf(1891,plain,
! [A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1820]) ).
thf(1896,plain,
! [A: $i] :
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1891]) ).
thf(1052,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)],[951,50]) ).
thf(1053,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)],[1052]) ).
thf(1054,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1053:[bind(A,$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(1075,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)],[1054]) ).
thf(3367,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)],[1075,2240]) ).
thf(3368,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)],[3367]) ).
thf(3369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3368:[bind(A,$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(3421,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)],[3369]) ).
thf(17199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( C @ implies ) @ not @ is_a_theorem ) )
| ~ ( C @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[240,3781]) ).
thf(17200,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17199:[bind(A,$thf( F @ ( F @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(17614,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)],[17200]) ).
thf(20811,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)],[50,17614]) ).
thf(20812,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)],[20811]) ).
thf(20813,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[20812:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G @ ( B @ implies ) ))]]) ).
thf(20998,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)],[20813]) ).
thf(3275,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)],[900,2698]) ).
thf(3276,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)],[3275]) ).
thf(3301,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)],[3276]) ).
thf(489,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)],[484,52]) ).
thf(490,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)],[489]) ).
thf(491,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[490:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( J @ ( L @ ( L @ not @ implies ) @ implies ) @ ( J @ ( L @ implies ) @ implies ) ))]]) ).
thf(529,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)],[491]) ).
thf(17072,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)],[840,16797]) ).
thf(17073,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)],[17072]) ).
thf(17157,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[17073]) ).
thf(1899,plain,
! [A: $i] :
( ( z != y )
| ( ( z @ not )
!= x )
| ( A != A )
| ( ( z @ ( y @ implies ) )
!= x )
| ( A != z )
| ( x != x ) ),
inference(simp,[status(thm)],[1891]) ).
thf(1915,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[1899]) ).
thf(98,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,81]) ).
thf(99,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(2754,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,2685]) ).
thf(2755,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2754]) ).
thf(2790,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2755]) ).
thf(4012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,2686]) ).
thf(4013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4012]) ).
thf(4059,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)],[4013]) ).
thf(168,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)],[52,47]) ).
thf(169,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)],[168]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(201,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)],[170]) ).
thf(2533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,2240]) ).
thf(2534,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)],[2533]) ).
thf(2535,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2534:[bind(A,$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(2705,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)],[2535]) ).
thf(866,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,160]) ).
thf(867,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[866]) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[867:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(894,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[868]) ).
thf(19457,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)],[240,17539]) ).
thf(19458,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)],[19457]) ).
thf(19459,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[19458:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(19571,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= B )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[19459]) ).
thf(122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,52]) ).
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 )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$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(143,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)],[124]) ).
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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[143,160]) ).
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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[277]) ).
thf(279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$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(302,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(3201,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)],[15,2682]) ).
thf(3202,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)],[3201]) ).
thf(3233,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)],[3202]) ).
thf(3657,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)],[900,2671]) ).
thf(3658,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)],[3657]) ).
thf(3659,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3658:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(3778,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)],[3659]) ).
thf(2516,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)],[52,2240]) ).
thf(2517,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)],[2516]) ).
thf(2673,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)],[2517]) ).
thf(7730,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7729]) ).
thf(2613,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)],[82,2240]) ).
thf(2614,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)],[2613]) ).
thf(2615,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2614:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(2690,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2615]) ).
thf(4114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,2690]) ).
thf(4115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[4114]) ).
thf(4140,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)],[4115]) ).
thf(2581,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)],[900,2240]) ).
thf(2582,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)],[2581]) ).
thf(2670,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2582]) ).
thf(7763,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)],[6778]) ).
thf(8221,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)],[7763,52]) ).
thf(8222,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)],[8221]) ).
thf(8223,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem )
| ( C @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[8222:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) @ not ))]]) ).
thf(8386,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)],[8223]) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[60]) ).
thf(1819,plain,
! [A: $i] :
( ( A @ ( x @ implies ) @ ( A @ ( z @ ( y @ implies ) @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1788]) ).
thf(959,plain,
! [A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( A
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[892]) ).
thf(960,plain,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[959]) ).
thf(961,plain,
( ( ( z @ ( y @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[960]) ).
thf(1194,plain,
( ( z != z )
| ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[961]) ).
thf(1195,plain,
( ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[1194]) ).
thf(26850,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[25720,103]) ).
thf(26851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[26850]) ).
thf(26852,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[26851:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(27213,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[26852]) ).
thf(28107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,27213]) ).
thf(28108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[28107]) ).
thf(28109,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[28108:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ ( G @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(28318,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[28109]) ).
thf(1893,plain,
! [A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( A != z )
| ( x != x ) ),
inference(simp,[status(thm)],[1891]) ).
thf(1910,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1893]) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[770,103]) ).
thf(806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[805]) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[806:[bind(A,$thf( M )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(842,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[807]) ).
thf(3089,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)],[840,2680]) ).
thf(3090,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)],[3089]) ).
thf(3122,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3090]) ).
thf(2553,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)],[948,2240]) ).
thf(2554,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)],[2553]) ).
thf(2555,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2554:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(2709,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)],[2555]) ).
thf(1941,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)],[777,53]) ).
thf(1942,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)],[1941]) ).
thf(1943,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1942:[bind(A,$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(1986,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)],[1943]) ).
thf(2623,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)],[1986,2240]) ).
thf(2624,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)],[2623]) ).
thf(2625,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2624:[bind(A,$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(2694,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)],[2625]) ).
thf(131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,103]) ).
thf(132,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(1483,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)],[1323,50]) ).
thf(1484,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)],[1483]) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ ( A @ ( C @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1484:[bind(A,$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(1500,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)],[1485]) ).
thf(10860,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)],[1500,2240]) ).
thf(10861,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)],[10860]) ).
thf(10862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10861:[bind(A,$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(11019,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)],[10862]) ).
thf(2716,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)],[1322,2685]) ).
thf(2717,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)],[2716]) ).
thf(2801,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2717]) ).
thf(1328,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)],[1320,52]) ).
thf(1329,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)],[1328]) ).
thf(1330,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1329:[bind(A,$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(1380,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)],[1330]) ).
thf(2618,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)],[1380,2240]) ).
thf(2619,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)],[2618]) ).
thf(2620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2619:[bind(A,$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(2692,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)],[2620]) ).
thf(2748,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)],[900,2685]) ).
thf(2749,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)],[2748]) ).
thf(2798,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2749]) ).
thf(3271,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)],[13,2698]) ).
thf(3272,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)],[3271]) ).
thf(3326,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[3272]) ).
thf(15361,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)],[52,3938]) ).
thf(15362,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)],[15361]) ).
thf(15363,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[15362:[bind(A,$thf( F @ not )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ not ))]]) ).
thf(15510,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ ( B @ not @ implies ) @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[15363]) ).
thf(5746,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)],[840,4617]) ).
thf(5747,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)],[5746]) ).
thf(5748,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[5747:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(5818,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( B @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[5748]) ).
thf(9269,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)],[840,2673]) ).
thf(9270,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)],[9269]) ).
thf(9271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[9270:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(9392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[9271]) ).
thf(2571,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)],[13,2240]) ).
thf(2572,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)],[2571]) ).
thf(2649,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ not ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2572]) ).
thf(2503,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)],[777,2240]) ).
thf(2504,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)],[2503]) ).
thf(2505,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2504:[bind(A,$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(2697,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)],[2505]) ).
thf(10058,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)],[15,2787]) ).
thf(10059,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)],[10058]) ).
thf(10060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[10059:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ not @ implies ) @ ( J @ implies ) )),bind(E,$thf( E ))]]) ).
thf(10075,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)],[10060]) ).
thf(338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,52]) ).
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 )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[338]) ).
thf(340,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$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(371,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)],[340]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,81]) ).
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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(2518,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)],[1323,2240]) ).
thf(2519,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)],[2518]) ).
thf(2520,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2519:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(2702,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2520]) ).
thf(3297,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)],[15,2698]) ).
thf(3298,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)],[3297]) ).
thf(3306,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)],[3298]) ).
thf(1138,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)],[1016,52]) ).
thf(1139,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)],[1138]) ).
thf(1140,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1139:[bind(A,$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(1187,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)],[1140]) ).
thf(9779,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)],[1382,2240]) ).
thf(9780,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)],[9779]) ).
thf(9781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ implies ) @ ( D @ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[9780:[bind(A,$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(9925,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)],[9781]) ).
thf(540,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)],[531,52]) ).
thf(541,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)],[540]) ).
thf(542,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[541:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ ( E @ ( E @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(586,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)],[542]) ).
thf(26352,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)],[25542,47]) ).
thf(26353,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)],[26352]) ).
thf(26354,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ not @ implies ) @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[26353:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ not @ implies ) )),bind(D,$thf( F ))]]) ).
thf(26518,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ not @ implies ) @ is_a_theorem )
| ( B @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[26354]) ).
thf(209,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,120]) ).
thf(210,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(2762,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)],[82,2685]) ).
thf(2763,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)],[2762]) ).
thf(2788,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)],[2763]) ).
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 )
!= ( F @ is_a_theorem ) )
| ( ( E @ ( F @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[143,81]) ).
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 )
!= ( F @ is_a_theorem ) )
| ( ( E @ ( F @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( P @ ( Q @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(298,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(17836,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)],[50,17610]) ).
thf(17837,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)],[17836]) ).
thf(17838,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17837:[bind(A,$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(18048,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)],[17838]) ).
thf(17395,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[240,103]) ).
thf(17396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[17395]) ).
thf(17397,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17396:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(19826,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[240,17397]) ).
thf(19827,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[19826]) ).
thf(19828,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[19827:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(19941,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[19828]) ).
thf(244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,160]) ).
thf(245,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ not @ implies ) ))]]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[246]) ).
thf(10849,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)],[1500,53]) ).
thf(10850,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)],[10849]) ).
thf(10851,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10850:[bind(A,$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(11016,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)],[10851]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,120]) ).
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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(3083,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)],[900,2680]) ).
thf(3084,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)],[3083]) ).
thf(3111,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[3084]) ).
thf(3478,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)],[13,2672]) ).
thf(3479,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)],[3478]) ).
thf(3480,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[3479:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(3536,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( A @ ( A @ ( A @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[3480]) ).
thf(2744,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)],[13,2685]) ).
thf(2745,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)],[2744]) ).
thf(2791,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ implies ) @ not ) ),
inference(simp,[status(thm)],[2745]) ).
thf(2734,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)],[85,2685]) ).
thf(2735,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)],[2734]) ).
thf(2789,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2735]) ).
thf(17064,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)],[900,16797]) ).
thf(17065,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)],[17064]) ).
thf(17141,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)],[17065]) ).
thf(12117,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)],[4661]) ).
thf(12160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= C )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[12117]) ).
thf(14649,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)],[840,12160]) ).
thf(14650,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)],[14649]) ).
thf(14651,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(pattern_uni,[status(thm)],[14650:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(14731,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( C @ ( C @ implies ) ) ),
inference(simp,[status(thm)],[14651]) ).
thf(2498,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)],[1322,2240]) ).
thf(2499,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)],[2498]) ).
thf(2500,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2499:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(2695,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2500]) ).
thf(25,plain,
! [A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(26,plain,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
( ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ not )
!= x ) ),
inference(simp,[status(thm)],[26]) ).
thf(58,plain,
! [A: $i] :
( ( A
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(59,plain,
( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) @ not ) ),
inference(simp,[status(thm)],[58]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,103]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( N @ ( K @ implies ) @ implies ) @ ( K @ ( M @ implies ) @ implies ) ))]]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(28,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)],[13,9]) ).
thf(29,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)],[28]) ).
thf(30,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( A @ not @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ not @ implies ) )),bind(C,$thf( E ))]]) ).
thf(54,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( A @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30]) ).
thf(2538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[529,2240]) ).
thf(2539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2538]) ).
thf(2540,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2539:[bind(A,$thf( F )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( F @ ( M @ ( O @ ( O @ not @ implies ) @ implies ) @ ( M @ ( O @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2706,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)],[2540]) ).
thf(224,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,81]) ).
thf(225,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(3281,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)],[840,2698]) ).
thf(3282,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)],[3281]) ).
thf(3302,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[3282]) ).
thf(7725,plain,
( ( ( z @ not )
!= x )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( x != x ) ),
inference(simp,[status(thm)],[1919]) ).
thf(7741,plain,
( ( ( z @ not )
!= x )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y ) ),
inference(simp,[status(thm)],[7725]) ).
thf(75,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,52]) ).
thf(76,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[75]) ).
thf(77,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[77]) ).
thf(10936,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)],[1500,51]) ).
thf(10937,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)],[10936]) ).
thf(10938,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10937:[bind(A,$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(11005,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)],[10938]) ).
thf(13691,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)],[11005,2240]) ).
thf(13692,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)],[13691]) ).
thf(13693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[13692:[bind(A,$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(13876,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)],[13693]) ).
thf(3442,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)],[52,2672]) ).
thf(3443,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)],[3442]) ).
thf(3444,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3443:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(3551,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3444]) ).
thf(1091,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)],[948,51]) ).
thf(1092,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)],[1091]) ).
thf(1093,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1092:[bind(A,$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(1122,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)],[1093]) ).
thf(2563,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)],[1016,2240]) ).
thf(2564,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)],[2563]) ).
thf(2565,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2564:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( L @ ( M @ not @ implies ) @ ( L @ ( I @ implies ) @ implies ) @ ( M @ implies ) ))]]) ).
thf(2679,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)],[2565]) ).
thf(3364,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)],[1075,53]) ).
thf(3365,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)],[3364]) ).
thf(3366,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3365:[bind(A,$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(3420,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)],[3366]) ).
thf(5577,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)],[3420,2240]) ).
thf(5578,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)],[5577]) ).
thf(5579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( D @ not @ implies ) @ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5578:[bind(A,$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(5657,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)],[5579]) ).
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 )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[82,9]) ).
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 )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[128]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[129:[bind(A,$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(140,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)],[130]) ).
thf(1890,plain,
! [A: $i] :
( ( A != z )
| ( x != x )
| ( A != y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1909,plain,
( ( z != y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[1890]) ).
thf(291,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)],[143,47]) ).
thf(292,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)],[291]) ).
thf(293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$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(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 ) @ 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)],[293]) ).
thf(24520,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)],[301,143]) ).
thf(271,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[143,52]) ).
thf(272,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[271]) ).
thf(273,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$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(299,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)],[273]) ).
thf(253,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,160]) ).
thf(254,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( D @ ( E @ ( F @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( O )),bind(B,$thf( M )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( P @ ( O @ implies ) @ ( P @ ( M @ implies ) @ implies ) @ ( M @ ( O @ implies ) @ implies ) ))]]) ).
thf(267,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(2493,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)],[1320,2240]) ).
thf(2494,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)],[2493]) ).
thf(2495,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2494:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( H @ ( K @ ( L @ not @ implies ) @ not @ implies ) @ ( L @ implies ) ))]]) ).
thf(2693,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2495]) ).
thf(3179,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)],[900,2682]) ).
thf(3180,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)],[3179]) ).
thf(3206,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)],[3180]) ).
thf(14529,plain,
! [A: $i] :
( ( ( A @ ( x @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1896]) ).
thf(14530,plain,
! [A: $i] :
( ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[14529]) ).
thf(151,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,120]) ).
thf(152,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$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(162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(2636,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)],[15,2240]) ).
thf(2637,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)],[2636]) ).
thf(2665,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2637]) ).
thf(4253,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)],[3897]) ).
thf(4255,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4253]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[46]) ).
thf(1603,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)],[1380,52]) ).
thf(1604,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)],[1603]) ).
thf(1605,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1604:[bind(A,$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(1647,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)],[1605]) ).
thf(17317,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)],[240,2240]) ).
thf(17318,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)],[17317]) ).
thf(17319,plain,
! [B: $i,A: $i] :
( ~ ( A @ not @ is_a_theorem )
| ~ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[17318:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2558,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1064,2240]) ).
thf(2559,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2558]) ).
thf(2560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2559:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( P )),bind(E,$thf( G @ ( J @ ( M @ ( P @ ( P @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2678,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)],[2560]) ).
thf(4503,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)],[1016,2701]) ).
thf(4504,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)],[4503]) ).
thf(4505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[4504:[bind(A,$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(4641,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)],[4505]) ).
thf(3185,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)],[840,2682]) ).
thf(3186,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)],[3185]) ).
thf(3209,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[3186]) ).
thf(4301,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)],[1323,2669]) ).
thf(4302,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)],[4301]) ).
thf(4303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[4302:[bind(A,$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(4398,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)],[4303]) ).
thf(2608,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)],[143,2240]) ).
thf(2609,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)],[2608]) ).
thf(2610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2609:[bind(A,$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(2688,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)],[2610]) ).
thf(2638,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1505,2240]) ).
thf(2639,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2638]) ).
thf(2640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2639:[bind(A,$thf( G )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( G @ ( O @ ( P @ not @ implies ) @ ( M @ ( M @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(2700,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)],[2640]) ).
thf(1667,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ 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)],[1441,52]) ).
thf(1668,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1667]) ).
thf(1669,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1668:[bind(A,$thf( G )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( D )),bind(E,$thf( G @ ( O @ ( P @ not @ implies ) @ ( P @ ( P @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(1711,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)],[1669]) ).
thf(545,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[531,103]) ).
thf(546,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[545]) ).
thf(547,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ ( D @ ( D @ not @ implies ) @ not @ implies ) @ implies ) ))]]) ).
thf(576,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(2271,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)],[1986,52]) ).
thf(2272,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)],[2271]) ).
thf(2273,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2272:[bind(A,$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(2322,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)],[2273]) ).
thf(10633,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)],[10542,2240]) ).
thf(10634,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)],[10633]) ).
thf(10635,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10634:[bind(A,$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(10767,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)],[10635]) ).
thf(1897,plain,
! [A: $i] :
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( A != z )
| ( x != x ) ),
inference(simp,[status(thm)],[1891]) ).
thf(1913,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1897]) ).
thf(860,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,103]) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[860]) ).
thf(862,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[861:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ implies ) ))]]) ).
thf(903,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[862]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,81]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[91]) ).
thf(3896,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ ( A @ implies ) @ not @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[3781]) ).
thf(6004,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)],[3896]) ).
thf(6041,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ not )
!= ( A @ ( A @ implies ) ) )
| ~ ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6004]) ).
thf(757,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 )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,50]) ).
thf(758,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 )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[757]) ).
thf(759,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( A )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( A )),bind(E,$thf( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not )),bind(F,$thf( F ))]]) ).
thf(790,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)],[759]) ).
thf(2628,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)],[790,2240]) ).
thf(2629,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)],[2628]) ).
thf(2630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2629:[bind(A,$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(2696,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)],[2630]) ).
thf(174,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)],[13,47]) ).
thf(175,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)],[174]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$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)],[176]) ).
thf(15424,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)],[900,3938]) ).
thf(15425,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)],[15424]) ).
thf(15426,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[15425:[bind(A,$thf( J @ ( J @ implies ) @ not )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( J @ implies ) @ not ))]]) ).
thf(15525,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ implies ) @ not @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[15426]) ).
thf(2543,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)],[85,2240]) ).
thf(2544,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)],[2543]) ).
thf(2545,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2544:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2707,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(simp,[status(thm)],[2545]) ).
thf(17114,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)],[15,16797]) ).
thf(17115,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)],[17114]) ).
thf(17152,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)],[17115]) ).
thf(11570,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)],[11016,2240]) ).
thf(11571,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)],[11570]) ).
thf(11572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[11571:[bind(A,$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(11717,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)],[11572]) ).
thf(55,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ not )
!= x ) ),
inference(simp,[status(thm)],[27]) ).
thf(15435,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)],[840,3938]) ).
thf(15436,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)],[15435]) ).
thf(15437,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) )
!= ( A @ ( A @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[15436:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2770,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)],[15,2685]) ).
thf(2771,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)],[2770]) ).
thf(2786,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[2771]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,103]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(10481,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)],[1442,51]) ).
thf(10482,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)],[10481]) ).
thf(10483,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[10482:[bind(A,$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(10563,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)],[10483]) ).
thf(1396,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1322,103]) ).
thf(1397,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1396]) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1397:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ not @ implies ) @ ( K @ ( K @ not @ implies ) @ implies ) ))]]) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[1398]) ).
thf(1085,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[948,103]) ).
thf(1086,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[1085]) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[1086:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( M @ ( M @ implies ) @ not @ implies ) @ ( J @ ( G @ implies ) @ implies ) ))]]) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[1087]) ).
thf(2583,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)],[1122,2240]) ).
thf(2584,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)],[2583]) ).
thf(2585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2584:[bind(A,$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(2683,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)],[2585]) ).
thf(256,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,160]) ).
thf(257,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(258,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$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(262,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(7732,plain,
( ( y != y )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7729]) ).
thf(7744,plain,
( ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7732]) ).
thf(1889,plain,
! [A: $i] :
( ( A != z )
| ( x != x )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1908,plain,
( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ),
inference(simp,[status(thm)],[1889]) ).
thf(4215,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)],[3897,2240]) ).
thf(4216,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)],[4215]) ).
thf(4217,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4216:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) @ not ))]]) ).
thf(4281,plain,
! [A: $i] :
( ~ ( A @ ( A @ implies ) @ not @ not @ is_a_theorem )
| ( A @ ( A @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4217]) ).
thf(3517,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)],[15,2672]) ).
thf(3518,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)],[3517]) ).
thf(3519,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(pattern_uni,[status(thm)],[3518:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(3558,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( A @ ( B @ not @ implies ) @ ( B @ implies ) ) ),
inference(simp,[status(thm)],[3519]) ).
thf(2528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ 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)],[770,2240]) ).
thf(2529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2528]) ).
thf(2530,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2529:[bind(A,$thf( M )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( J @ ( L @ not @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2704,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)],[2530]) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[840,81]) ).
thf(879,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(880,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[879:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(897,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[880]) ).
thf(495,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[484,103]) ).
thf(496,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( I @ ( K @ ( K @ not @ implies ) @ implies ) @ ( I @ ( K @ implies ) @ implies ) ))]]) ).
thf(532,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[497]) ).
thf(229,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)],[85,47]) ).
thf(230,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)],[229]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(239,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)],[231]) ).
thf(1079,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)],[948,52]) ).
thf(1080,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)],[1079]) ).
thf(1081,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1080:[bind(A,$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(1129,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)],[1081]) ).
thf(30259,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)],[900,26518]) ).
thf(30260,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)],[30259]) ).
thf(30261,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[30260:[bind(A,$thf( H @ ( H @ implies ) )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ implies ) ))]]) ).
thf(30527,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ is_a_theorem )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[30261]) ).
thf(2603,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)],[11,2240]) ).
thf(2604,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)],[2603]) ).
thf(2605,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2604:[bind(A,$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(2687,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)],[2605]) ).
thf(2508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1441,2240]) ).
thf(2509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[2508]) ).
thf(2510,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2509:[bind(A,$thf( F )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( F @ ( N @ ( O @ not @ implies ) @ ( O @ ( O @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(2699,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)],[2510]) ).
thf(18495,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)],[240,17319]) ).
thf(18496,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)],[18495]) ).
thf(18497,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[18496:[bind(A,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(18719,plain,
! [B: $i,A: $i] :
( ~ ( B @ not @ is_a_theorem )
| ~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[18497]) ).
thf(3484,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)],[900,2672]) ).
thf(3485,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)],[3484]) ).
thf(3486,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[3485:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(3538,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not )
!= ( A @ ( B @ ( B @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[3486]) ).
thf(13236,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)],[10563,2240]) ).
thf(13237,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)],[13236]) ).
thf(13238,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[13237:[bind(A,$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(13400,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)],[13238]) ).
thf(8210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[7763,2671]) ).
thf(8211,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)],[8210]) ).
thf(8212,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[8211:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ implies ) @ not @ implies ) ))]]) ).
thf(8380,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
| ( B @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8212]) ).
thf(1895,plain,
! [A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( A != A )
| ( ( z @ ( y @ implies ) )
!= x )
| ( A != z )
| ( x != x ) ),
inference(simp,[status(thm)],[1891]) ).
thf(1912,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[1895]) ).
thf(17047,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)],[13,16797]) ).
thf(17048,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)],[17047]) ).
thf(17123,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( B @ ( B @ implies ) @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[17048]) ).
thf(52877,plain,
$false,
inference(e,[status(thm)],[892,1322,1501,17539,101,2778,2787,16797,777,3762,10542,2671,120,4408,16449,10,26510,2686,10093,142,4638,3781,1919,898,16456,1441,10545,24,52,10326,14,3938,17610,3116,2708,1907,3776,2682,3542,1191,13025,7743,2703,2698,3131,1323,838,2691,1247,10074,770,57,4390,1778,4617,20,4411,121,1383,84,2777,164,4396,10085,238,15536,27119,4924,2804,265,3211,527,1896,3421,20998,60,3301,529,17157,1915,102,2790,4059,85,201,2705,894,19571,302,160,3233,21,4661,3778,2673,7730,4140,2670,8386,7762,1819,1195,484,28318,1910,842,3122,2685,1064,2709,2694,53,141,11019,948,2801,2692,9,2798,3326,1075,2240,1016,15510,5818,4276,9392,2649,1382,27213,13,2697,10075,371,25720,17614,105,2702,3306,1187,9925,586,26518,237,2788,298,18048,19941,264,11016,161,3111,3536,2791,2789,17141,14731,7763,2695,27,59,118,12,54,49,2706,236,25542,3302,7741,86,13876,3551,81,4616,1122,900,2679,7,2669,5657,103,140,1909,240,24520,1820,299,267,2693,3206,14530,162,531,2665,4255,48,1647,17319,2678,4641,3209,4398,2688,2700,840,12160,9911,1711,50,576,2322,2701,951,11,11005,143,10767,1913,903,104,6041,2696,87,203,15525,2707,961,17152,26,11717,55,24729,15437,2786,119,3896,2680,82,3420,10563,8,1444,1442,1133,2683,9922,262,7744,51,1380,1986,790,1908,17397,3897,5300,4281,3558,2704,897,960,532,239,242,1129,30527,1500,2687,6778,2699,1505,47,18719,15,3538,2672,1320,13400,8380,1912,2690,17123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL384+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n001.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 22:28:57 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.82/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.15 % [INFO] Parsing done (169ms).
% 1.18/1.17 % [INFO] Running in sequential loop mode.
% 1.69/1.57 % [INFO] eprover registered as external prover.
% 1.69/1.57 % [INFO] Scanning for conjecture ...
% 1.88/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.02/1.70 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.02/1.72 % [INFO] Problem is first-order (TPTP FOF).
% 2.02/1.72 % [INFO] Type checking passed.
% 2.02/1.73 % [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 ...
% 158.08/42.80 % External prover 'e' found a proof!
% 158.08/42.80 % [INFO] Killing All external provers ...
% 158.08/42.81 % Time passed: 42264ms (effective reasoning time: 41632ms)
% 158.08/42.81 % Solved by 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)>
% 158.08/42.81 % Axioms used in derivation (4): cn_3, cn_1, condensed_detachment, cn_2
% 158.08/42.81 % No. of inferences in proof: 978
% 158.08/42.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 42264 ms resp. 41632 ms w/o parsing
% 160.69/43.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 160.69/43.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------