%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL384-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 07:51:39 AM UTC 2026
% Result : Unsatisfiable 192.77s 49.71s
% Output : Refutation 181.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 884 ( 270 unt; 0 typ; 0 def)
% Number of atoms : 2293 (2292 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 14770 (1896 ~;1409 |; 0 &;11465 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 1909 ( 0 ^;1909 !; 0 ?;1909 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $i ).
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(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[18]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[48]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[10]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[53,11]) ).
thf(91,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
!= ( E @ ( D @ ( C @ ( C @ ifeq ) ) ) ) )
| ( true = D ) ),
inference(paramod_ordered,[status(thm)],[84,11]) ).
thf(103,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true != E )
| ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= D )
| ( true != C )
| ( ( B @ is_a_theorem )
!= C )
| ( true = D ) ),
inference(simp,[status(thm)],[91]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( B @ is_a_theorem )
!= true )
| ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[103]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( C @ ( D @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,84]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[96]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[107,11]) ).
thf(41,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( B @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[11,13]) ).
thf(50,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( E @ is_a_theorem ) )
| ( A != true )
| ( A
!= ( D @ is_a_theorem ) )
| ( ( true @ ( B @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[41]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= true )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[50]) ).
thf(316,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( D @ is_a_theorem )
!= true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,55]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( J @ ( K @ not @ implies ) @ ( K @ implies ) @ not )),bind(E,$thf( A ))]]) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[317]) ).
thf(6977,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[369,11]) ).
thf(1,negated_conjecture,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_45) ).
thf(7,plain,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(lifteq,[status(thm)],[8]) ).
thf(7071,plain,
! [C: $i,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 != true )
| ( ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[6977,9]) ).
thf(7072,plain,
! [C: $i,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 @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7071]) ).
thf(7073,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[7072:[bind(A,$thf( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(7281,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not @ is_a_theorem )
!= true ),
inference(simp,[status(thm)],[7073]) ).
thf(7351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[111,7281]) ).
thf(7352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7351]) ).
thf(7375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7352]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[14]) ).
thf(64,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 != true ) ),
inference(paramod_ordered,[status(thm)],[15,9]) ).
thf(65,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)],[64]) ).
thf(80,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)],[65]) ).
thf(147,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)],[80]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(3946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[237]) ).
thf(4016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( C != B )
| ( A != A )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4073,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4016]) ).
thf(18601,plain,
! [A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4073]) ).
thf(18609,plain,
! [A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[18601]) ).
thf(21609,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ ( x @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ not )
!= y ) ),
inference(eqfactor_ordered,[status(thm)],[18609]) ).
thf(21611,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( x != A )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[21609]) ).
thf(21624,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[21611]) ).
thf(3948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[237]) ).
thf(3971,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( C != C )
| ( A != B )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3948]) ).
thf(4029,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3971]) ).
thf(4556,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4029]) ).
thf(4560,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4556]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[16]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( B @ ( C @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,84]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[102]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[110,11]) ).
thf(70,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 ) )
| ( ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( A @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$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(83,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( A @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[71]) ).
thf(1295,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( A @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[83,11]) ).
thf(1336,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 ) )
| ( ( true @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,1295]) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1336:[bind(A,$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(1387,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1337]) ).
thf(24195,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1387,11]) ).
thf(4555,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4029]) ).
thf(4565,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ not )
!= ( z @ not ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4555]) ).
thf(4576,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4565]) ).
thf(6953,plain,
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y ) ),
inference(eqfactor_ordered,[status(thm)],[4576]) ).
thf(6965,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[6953]) ).
thf(6976,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[6965]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) )),bind(D,$thf( D ))]]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[44]) ).
thf(890,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[61,11]) ).
thf(913,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,890]) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( Q )),bind(B,$thf( O @ ( Q @ not @ implies ) )),bind(C,$thf( R )),bind(D,$thf( R @ ( Q @ implies ) @ ( R @ ( O @ ( Q @ not @ implies ) @ implies ) @ implies ) )),bind(E,$thf( O )),bind(F,$thf( Q ))]]) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[914]) ).
thf(2887,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[963,11]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[35]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[56,11]) ).
thf(2940,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[2887,429]) ).
thf(2941,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2940:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ ( G @ implies ) )),bind(E,$thf( G ))]]) ).
thf(3035,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[2941]) ).
thf(3047,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[3035,11]) ).
thf(3173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( true != true )
| ( ( B @ ( C @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[3047,111]) ).
thf(3174,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(simp,[status(thm)],[3173]) ).
thf(3175,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[3174:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(3203,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[3175]) ).
thf(336,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 ) )
| ( ( D @ is_a_theorem )
!= true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,55]) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[336:[bind(A,$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(364,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[337]) ).
thf(6064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ is_a_theorem )
!= true )
| ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[364,11]) ).
thf(6235,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 ) )
| ( true != true )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[3203,6064]) ).
thf(6236,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(simp,[status(thm)],[6235]) ).
thf(6237,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[6236:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( H @ ( H @ implies ) @ not )),bind(E,$thf( E ))]]) ).
thf(6356,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[6237]) ).
thf(40,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
!= ( E @ ( D @ ( C @ ( C @ ifeq ) ) ) ) )
| ( true = D ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true != E )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
!= D )
| ( true != C )
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= C )
| ( true = D ) ),
inference(simp,[status(thm)],[40]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[51]) ).
thf(2923,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[2887,57]) ).
thf(2924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[2923]) ).
thf(2925,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ( true @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2924:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( L @ ( I @ ( K @ not @ implies ) @ implies ) )),bind(E,$thf( L @ ( K @ implies ) ))]]) ).
thf(3028,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ( true @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[2925]) ).
thf(20795,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 )
!= ( F @ ( D @ ( E @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( F @ ( E @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[6356,3028]) ).
thf(20796,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[20795:[bind(A,$thf( G @ not )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( I )),bind(E,$thf( G )),bind(F,$thf( I @ ( L @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(21065,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[20796]) ).
thf(21116,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[21065,11]) ).
thf(21493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( E @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[21116,111]) ).
thf(21494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[21493]) ).
thf(21495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[21494:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( I @ ( L @ ( L @ implies ) @ not @ implies ) @ ( F @ implies ) ))]]) ).
thf(21595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[21495]) ).
thf(6755,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 ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[6356,890]) ).
thf(6756,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6755:[bind(A,$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(6881,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[6756]) ).
thf(7444,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[6881,11]) ).
thf(7473,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7444,57]) ).
thf(7474,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[7473]) ).
thf(7475,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ not @ implies ) @ is_a_theorem @ ( true @ ( A @ ( A @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7474:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( H @ ( H @ implies ) @ not )),bind(E,$thf( J @ ( K @ not @ implies ) ))]]) ).
thf(7673,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ not @ implies ) @ is_a_theorem @ ( true @ ( A @ ( A @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7475]) ).
thf(3949,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[237]) ).
thf(4007,plain,
! [C: $i,B: $i,A: $i] :
( ( z != C )
| ( x != B )
| ( C != y )
| ( A
!= ( z @ not ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3949]) ).
thf(4064,plain,
( ( z != y )
| ( ( y @ ( z @ not @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4007]) ).
thf(6899,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( z @ not @ implies ) ) )
| ( z != y )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4064]) ).
thf(6909,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( y != x )
| ( ( z @ not )
!= ( z @ not ) )
| ( z != y )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6899]) ).
thf(6924,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( y != x )
| ( z != y )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6909]) ).
thf(19628,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( x @ ( z @ not @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( y != x )
| ( z != y ) ),
inference(eqfactor_ordered,[status(thm)],[6924]) ).
thf(19637,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( x != x )
| ( y != x )
| ( z != y ) ),
inference(simp,[status(thm)],[19628]) ).
thf(19649,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( y != x )
| ( z != y ) ),
inference(simp,[status(thm)],[19637]) ).
thf(3945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[237]) ).
thf(3986,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( C
!= ( z @ ( y @ implies ) ) )
| ( B != x )
| ( C != z )
| ( A != x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4043,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3986]) ).
thf(1865,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 ) )
| ( true != true )
| ( ( D @ ( E @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,111]) ).
thf(1866,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(simp,[status(thm)],[1865]) ).
thf(1867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[1866:[bind(A,$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(1924,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[1867]) ).
thf(238,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)],[147]) ).
thf(256,plain,
! [A: $i] :
( ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(273,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)],[256]) ).
thf(284,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)],[273]) ).
thf(300,plain,
( ( ( z @ not )
!= x )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(977,plain,
( ( ( z @ not )
!= x )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( x != x ) ),
inference(simp,[status(thm)],[300]) ).
thf(994,plain,
( ( ( z @ not )
!= x )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y ) ),
inference(simp,[status(thm)],[977]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[147]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(4297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( C @ ( A @ implies ) ) )
| ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[242]) ).
thf(4326,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( A != A )
| ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( C != z )
| ( A != y )
| ( ( C @ ( B @ implies ) )
!= x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4297]) ).
thf(4443,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( z @ implies ) )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) ) ),
inference(simp,[status(thm)],[4326]) ).
thf(19081,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( z @ implies ) )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( y != x ) ),
inference(simp,[status(thm)],[4443]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(39,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ not @ implies ) )),bind(C,$thf( E ))]]) ).
thf(60,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[39]) ).
thf(152,plain,
! [A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[60,11]) ).
thf(7467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7444,152]) ).
thf(7468,plain,
! [A: $i] :
( ( true @ ( A @ not @ ( A @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7467:[bind(A,$thf( H @ not )),bind(B,$thf( H @ not )),bind(C,$thf( H )),bind(D,$thf( H @ not @ ( H @ not @ implies ) ))]]) ).
thf(7670,plain,
! [A: $i] :
( ( true @ ( A @ not @ ( A @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7468]) ).
thf(7726,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[7670,11]) ).
thf(461,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 ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,429]) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[461:[bind(A,$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(482,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[462]) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[482,11]) ).
thf(1403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1396,890]) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1403:[bind(A,$thf( O @ ( P @ not @ implies ) )),bind(B,$thf( P )),bind(C,$thf( O @ ( P @ not @ implies ) @ ( P @ ( P @ not @ implies ) @ implies ) )),bind(D,$thf( O )),bind(E,$thf( P ))]]) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1404]) ).
thf(1544,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1499,11]) ).
thf(4567,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4555]) ).
thf(4578,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4567]) ).
thf(12787,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4578]) ).
thf(12789,plain,
( ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[12787]) ).
thf(6897,plain,
( ( z != y )
| ( y != y )
| ( ( z @ not )
!= x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4064]) ).
thf(6918,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6897]) ).
thf(3947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[237]) ).
thf(3965,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( z @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(pattern_uni,[status(thm)],[3947:[bind(A,$thf( x )),bind(B,$thf( z )),bind(C,$thf( z @ ( y @ implies ) ))]]) ).
thf(4500,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= z )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3965]) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,152]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( M @ ( N @ not @ implies ) @ ( N @ implies ) )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( M @ ( N @ not @ implies ) @ ( N @ implies ) ))]]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[219]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[231,11]) ).
thf(1363,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[374,1295]) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1363:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G @ ( H @ not @ implies ) )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1364]) ).
thf(23743,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1385,11]) ).
thf(3938,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(4084,plain,
! [A: $i] :
( ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3938]) ).
thf(5015,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( A @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4084]) ).
thf(5030,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= y )
| ( A != A )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5037,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y )
| ( z != y ) ),
inference(simp,[status(thm)],[5030]) ).
thf(26,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 != true ) ),
inference(paramod_ordered,[status(thm)],[19,9]) ).
thf(27,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)],[26]) ).
thf(29,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)],[27]) ).
thf(141,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)],[29]) ).
thf(142,plain,
! [A: $i] :
( ( A @ ( z @ ( y @ implies ) @ ( x @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(4503,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[3965]) ).
thf(4510,plain,
( ( ( z @ ( y @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( z != x )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4528,plain,
( ( z != x )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4510]) ).
thf(19636,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( y != x )
| ( z != y ) ),
inference(simp,[status(thm)],[19628]) ).
thf(4564,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4555]) ).
thf(5025,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( A != A )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5032,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5025]) ).
thf(7405,plain,
! [A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5032]) ).
thf(7409,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= y )
| ( x != A )
| ( ( z @ not )
!= y )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7405]) ).
thf(7422,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= y )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7409]) ).
thf(3968,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3948]) ).
thf(4026,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[3968]) ).
thf(505,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 ) )
| ( ( C @ is_a_theorem )
!= true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,55]) ).
thf(506,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[505:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(542,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[506]) ).
thf(10179,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[542,11]) ).
thf(10289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[10179,7281]) ).
thf(10290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10289]) ).
thf(10291,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[10290:[bind(A,$thf( I @ ( J @ not @ implies ) @ ( J @ implies ) @ not )),bind(B,$thf( B )),bind(C,$thf( I )),bind(D,$thf( J ))]]) ).
thf(10559,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not @ is_a_theorem )
!= true ),
inference(simp,[status(thm)],[10291]) ).
thf(10645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[111,10559]) ).
thf(10646,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10645]) ).
thf(10663,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10646]) ).
thf(17481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7726,10663]) ).
thf(17482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[17481]) ).
thf(17483,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ not @ ( C @ not @ implies ) @ not @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[17482:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ not @ ( H @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(17594,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ not @ ( C @ not @ implies ) @ not @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[17483]) ).
thf(3990,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( z @ not )
!= A )
| ( ( C @ ( B @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( C != z )
| ( A != x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4047,plain,
( ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3990]) ).
thf(3992,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( z @ not )
!= A )
| ( C
!= ( z @ ( y @ implies ) ) )
| ( B != x )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4049,plain,
( ( y != x )
| ( ( z @ ( y @ implies ) @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3992]) ).
thf(11231,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4049]) ).
thf(11240,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[11231]) ).
thf(11252,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[11240]) ).
thf(20641,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( x @ ( z @ not @ implies ) )
!= ( x @ ( z @ not @ implies ) ) )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(eqfactor_ordered,[status(thm)],[11252]) ).
thf(20651,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ not )
!= x )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20641]) ).
thf(20662,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20651]) ).
thf(3118,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 != true ) ),
inference(paramod_ordered,[status(thm)],[3047,9]) ).
thf(3119,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)],[3118]) ).
thf(3190,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[3119]) ).
thf(3248,plain,
! [A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( A
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3190]) ).
thf(3249,plain,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[3248]) ).
thf(3944,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[237]) ).
thf(3955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( C != B )
| ( B != A )
| ( C != z )
| ( A != x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3944]) ).
thf(4095,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3955]) ).
thf(9005,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4095]) ).
thf(9016,plain,
( ( y != x )
| ( ( z @ not )
!= x )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( x != x ) ),
inference(simp,[status(thm)],[9005]) ).
thf(9027,plain,
( ( y != x )
| ( ( z @ not )
!= x )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[9016]) ).
thf(269,plain,
! [A: $i] :
( ( ( A @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( A != y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(288,plain,
( ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(3994,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( z @ not )
!= A )
| ( C
!= ( z @ ( y @ implies ) ) )
| ( B != x )
| ( C != z )
| ( A != x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4051,plain,
( ( y != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3994]) ).
thf(4802,plain,
( ( y != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= x )
| ( x != x ) ),
inference(simp,[status(thm)],[4051]) ).
thf(4803,plain,
( ( y != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[4802]) ).
thf(3064,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3047,1295]) ).
thf(3065,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3064:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(3213,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[3065]) ).
thf(5050,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[3213,11]) ).
thf(7335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[5050,7281]) ).
thf(7336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[7335]) ).
thf(7364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[7336]) ).
thf(9013,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[9005]) ).
thf(11230,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( z @ not @ implies ) )
!= ( x @ ( z @ not @ implies ) ) )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4049]) ).
thf(11237,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= ( z @ not ) )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[11230]) ).
thf(11250,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= x )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[11237]) ).
thf(5027,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not @ ( A @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5034,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not @ ( A @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5027]) ).
thf(14291,plain,
! [A: $i] :
( ( ( y @ ( A @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5034]) ).
thf(14292,plain,
! [A: $i] :
( ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[14291]) ).
thf(11228,plain,
( ( y != x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4049]) ).
thf(4506,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4524,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4506]) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
!= ( D @ ( C @ ( B @ ( B @ ifeq ) ) ) ) )
| ( true = C ) ),
inference(paramod_ordered,[status(thm)],[152,11]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true != D )
| ( ( A @ is_a_theorem )
!= C )
| ( true != B )
| ( ( A @ ( A @ not @ implies ) @ is_a_theorem )
!= B )
| ( true = C ) ),
inference(simp,[status(thm)],[167]) ).
thf(184,plain,
! [A: $i] :
( ( ( A @ ( A @ not @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[179]) ).
thf(4013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4070,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[4013]) ).
thf(1428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1396,57]) ).
thf(1429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1428]) ).
thf(1430,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( A @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1429:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( H @ ( J @ implies ) )),bind(D,$thf( H @ ( J @ ( J @ not @ implies ) @ implies ) ))]]) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( A @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1430]) ).
thf(7757,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( B @ ( C @ ( C @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7726,1489]) ).
thf(7758,plain,
! [A: $i] :
( ( true @ ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7757:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(7963,plain,
! [A: $i] :
( ( true @ ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7758]) ).
thf(8740,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[7963,11]) ).
thf(8808,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[8740,7281]) ).
thf(8809,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8808]) ).
thf(8951,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[8809]) ).
thf(4507,plain,
( ( ( z @ ( y @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( z != x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4525,plain,
( ( z != x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4507]) ).
thf(5278,plain,
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4525]) ).
thf(5289,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5278]) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[374,57]) ).
thf(619,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[618:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) )),bind(D,$thf( D ))]]) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[619]) ).
thf(11416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[632,11]) ).
thf(3672,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3203,9]) ).
thf(3673,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ 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)],[3672]) ).
thf(3749,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)],[3673]) ).
thf(3087,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3047,57]) ).
thf(3088,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[3087]) ).
thf(3089,plain,
! [A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3088:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7726,1295]) ).
thf(7728,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( A @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7727:[bind(A,$thf( F )),bind(B,$thf( F @ not )),bind(C,$thf( F @ not )),bind(D,$thf( D ))]]) ).
thf(7951,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( A @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7728]) ).
thf(10932,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[7951,11]) ).
thf(11062,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[10932,890]) ).
thf(11063,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[11062:[bind(A,$thf( O @ ( Q @ not @ not @ implies ) )),bind(B,$thf( Q )),bind(C,$thf( O @ ( Q @ not @ not @ implies ) @ ( Q @ not @ implies ) )),bind(D,$thf( O )),bind(E,$thf( Q @ not ))]]) ).
thf(11202,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[11063]) ).
thf(11510,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[11202,11]) ).
thf(11234,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= ( z @ not ) )
| ( y != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[11230]) ).
thf(11247,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( y != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[11234]) ).
thf(8023,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4047]) ).
thf(8034,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( y != x )
| ( ( z @ ( y @ implies ) )
!= y )
| ( x != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= y )
| ( x != x ) ),
inference(simp,[status(thm)],[8023]) ).
thf(8037,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( y != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= y ) ),
inference(simp,[status(thm)],[8034]) ).
thf(22721,plain,
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4560]) ).
thf(22724,plain,
( ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[22721]) ).
thf(22735,plain,
( ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[22724]) ).
thf(8022,plain,
( ( ( z @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4047]) ).
thf(8024,plain,
( ( ( z @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[8022]) ).
thf(8556,plain,
( ( ( y @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x ) ),
inference(eqfactor_ordered,[status(thm)],[8024]) ).
thf(8558,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[8556]) ).
thf(18611,plain,
! [A: $i] :
( ( ( z @ not )
!= z )
| ( x != A )
| ( ( z @ not )
!= y )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[18601]) ).
thf(18624,plain,
( ( ( z @ not )
!= z )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[18611]) ).
thf(8561,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( y != x )
| ( z != y )
| ( y != x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[8556]) ).
thf(8571,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( z != y )
| ( y != x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[8561]) ).
thf(10624,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[8740,10559]) ).
thf(10625,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10624]) ).
thf(10665,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10625]) ).
thf(270,plain,
! [A: $i] :
( ( A != z )
| ( x != x )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(289,plain,
( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(7410,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= y )
| ( x != A )
| ( ( z @ not )
!= y )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[7405]) ).
thf(7423,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= y )
| ( z != y ) ),
inference(simp,[status(thm)],[7410]) ).
thf(7329,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 != true ) ),
inference(paramod_ordered,[status(thm)],[17,7281]) ).
thf(7330,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)],[7329]) ).
thf(7369,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[7330]) ).
thf(4024,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( C != B )
| ( A != A )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4081,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4024]) ).
thf(4819,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[4081]) ).
thf(4820,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[4819]) ).
thf(66,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 ) )
| ( ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$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(81,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[67]) ).
thf(1088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[81,11]) ).
thf(1144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,1088]) ).
thf(1164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1144]) ).
thf(20672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ implies ) ) )
| ( ( B @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1164,11]) ).
thf(6964,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[6953]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[37]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,84]) ).
thf(94,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( I @ not )),bind(B,$thf( G )),bind(C,$thf( G @ ( I @ not @ not @ implies ) )),bind(D,$thf( I ))]]) ).
thf(113,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[94]) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[59,113]) ).
thf(17031,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3047,7375]) ).
thf(17032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[17031]) ).
thf(17033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( D @ implies ) @ not @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[17032:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(17040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( D @ implies ) @ not @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[17033]) ).
thf(608,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 ) )
| ( true != true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,57]) ).
thf(609,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 ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[608]) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[609:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[610]) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,627]) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[688]) ).
thf(15105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[701,11]) ).
thf(4015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( C != B )
| ( A != A )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4072,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[4015]) ).
thf(20650,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20641]) ).
thf(20685,plain,
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(eqfactor_ordered,[status(thm)],[20650]) ).
thf(20687,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20685]) ).
thf(3993,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( z @ not )
!= A )
| ( C
!= ( z @ ( y @ implies ) ) )
| ( B != x )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4050,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3993]) ).
thf(5016,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4084]) ).
thf(5021,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= y )
| ( x != A )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5045,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y ) ),
inference(simp,[status(thm)],[5021]) ).
thf(10631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[374,10559]) ).
thf(10632,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10631]) ).
thf(10670,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10632]) ).
thf(7992,plain,
( ( ( x @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4043]) ).
thf(8001,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7992]) ).
thf(3998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3949]) ).
thf(4055,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[3998]) ).
thf(21167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[21116,57]) ).
thf(21168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[21167]) ).
thf(21169,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[21168:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( J )),bind(D,$thf( A )),bind(E,$thf( G @ ( J @ ( J @ implies ) @ not @ implies ) ))]]) ).
thf(21569,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[21169]) ).
thf(942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,890]) ).
thf(958,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ implies ) ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[942]) ).
thf(19084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ implies ) ) )
| ( ( B @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[958,11]) ).
thf(272,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)],[256]) ).
thf(276,plain,
! [A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( A != A )
| ( ( z @ ( y @ implies ) )
!= x )
| ( A != z )
| ( x != x ) ),
inference(simp,[status(thm)],[272]) ).
thf(293,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[276]) ).
thf(3983,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( C != z )
| ( A != x )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4040,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3983]) ).
thf(4290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) )
!= B )
| ( ( y @ ( z @ not @ implies ) )
!= A )
| ( C != z )
| ( A != y )
| ( ( C @ ( B @ implies ) )
!= x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(4414,plain,
( ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( z @ ( x @ implies ) @ implies ) )
!= x )
| ( ( z @ ( x @ implies ) @ ( y @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4290]) ).
thf(18654,plain,
( ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( z @ ( x @ implies ) @ implies ) )
!= x )
| ( ( z @ ( y @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( y != x ) ),
inference(simp,[status(thm)],[4414]) ).
thf(18655,plain,
( ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( z @ ( x @ implies ) @ implies ) )
!= x )
| ( z != z )
| ( y != x )
| ( y != x ) ),
inference(simp,[status(thm)],[18654]) ).
thf(18656,plain,
( ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( z @ ( x @ implies ) @ implies ) )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[18655]) ).
thf(1841,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 ) )
| ( true != true )
| ( ( C @ ( D @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,111]) ).
thf(1842,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(simp,[status(thm)],[1841]) ).
thf(1843,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[1842:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(1943,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[1843]) ).
thf(4502,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[3965]) ).
thf(4515,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( z != x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4502]) ).
thf(4519,plain,
( ( z != x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4515]) ).
thf(4558,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4556]) ).
thf(22627,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4558]) ).
thf(22629,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[22627]) ).
thf(22669,plain,
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x ) ),
inference(eqfactor_ordered,[status(thm)],[22629]) ).
thf(22672,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[22669]) ).
thf(22685,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[22672]) ).
thf(4025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( C != B )
| ( A != A )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4082,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[4025]) ).
thf(7796,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7726,9]) ).
thf(7797,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ 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)],[7796]) ).
thf(7942,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[7797]) ).
thf(10690,plain,
! [A: $i] :
( ( ( A @ not )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( A @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7942]) ).
thf(9014,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( x != x ) ),
inference(simp,[status(thm)],[9005]) ).
thf(9026,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[9014]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[191,9]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ 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)],[196]) ).
thf(224,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)],[197]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(10622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[5050,10559]) ).
thf(10623,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10622]) ).
thf(10652,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10623]) ).
thf(5018,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not )
!= z )
| ( A != x )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5042,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5018]) ).
thf(6038,plain,
( ( ( y @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5042]) ).
thf(6047,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6038]) ).
thf(4000,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( C != y )
| ( A
!= ( z @ not ) )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3949]) ).
thf(4057,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[4000]) ).
thf(12196,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ ( y @ implies ) @ implies ) ) )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x ) ),
inference(eqfactor_ordered,[status(thm)],[4057]) ).
thf(12205,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[12196]) ).
thf(4002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( C != y )
| ( A
!= ( z @ not ) )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3949]) ).
thf(4059,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[4002]) ).
thf(11241,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[11231]) ).
thf(11253,plain,
( ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( y != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[11241]) ).
thf(11244,plain,
( ( z != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[11231]) ).
thf(11255,plain,
( ( z != x )
| ( ( z @ not )
!= x )
| ( y != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[11244]) ).
thf(945,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 @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,890]) ).
thf(956,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[945]) ).
thf(18658,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[956,11]) ).
thf(4557,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4556]) ).
thf(7794,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7726,7281]) ).
thf(7795,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[7794]) ).
thf(7937,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( A @ not @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[7795]) ).
thf(12788,plain,
( ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[12787]) ).
thf(4499,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( z @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[3965]) ).
thf(4521,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( z @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4499]) ).
thf(3729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( C @ ( D @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[3203,111]) ).
thf(3730,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(simp,[status(thm)],[3729]) ).
thf(3731,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[3730:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(3761,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[3731]) ).
thf(4639,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3761,57]) ).
thf(4640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[4639]) ).
thf(4641,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[4640:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( H @ ( K @ ( K @ implies ) @ not @ implies ) @ not )),bind(E,$thf( A ))]]) ).
thf(4785,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( C @ ( C @ implies ) @ not @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[4641]) ).
thf(3987,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( C
!= ( z @ ( y @ implies ) ) )
| ( B != x )
| ( C != z )
| ( A != x )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4044,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[3987]) ).
thf(5020,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= y )
| ( x != A )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5044,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5020]) ).
thf(24,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 != true ) ),
inference(paramod_ordered,[status(thm)],[17,9]) ).
thf(25,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)],[24]) ).
thf(28,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)],[25]) ).
thf(7805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7726,13]) ).
thf(7806,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ not @ is_a_theorem @ ( true @ ( A @ not @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7805:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(7976,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ not @ is_a_theorem @ ( true @ ( A @ not @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7806]) ).
thf(8048,plain,
! [A: $i] :
( ( true @ ( A @ not @ is_a_theorem @ ( true @ ( A @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[7976,11]) ).
thf(8026,plain,
( ( z != y )
| ( y != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[8022]) ).
thf(4023,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( C != B )
| ( A != A )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4080,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[4023]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[46]) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[62,113]) ).
thf(8633,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4072]) ).
thf(8645,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[8633]) ).
thf(8651,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[8645]) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1544,57]) ).
thf(1575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1574]) ).
thf(1576,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ ( B @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1575:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( J @ ( J @ not @ implies ) )),bind(D,$thf( I @ ( J @ not @ implies ) ))]]) ).
thf(1643,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ ( B @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1576]) ).
thf(7563,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( E @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7444,1643]) ).
thf(7564,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7563:[bind(A,$thf( I @ not )),bind(B,$thf( I @ not )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( I @ not @ ( I @ not @ implies ) ))]]) ).
thf(7658,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7564]) ).
thf(8277,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[7658,11]) ).
thf(8355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[8277,7281]) ).
thf(8356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8355]) ).
thf(8503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[8356]) ).
thf(18597,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[4073]) ).
thf(18613,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[18597]) ).
thf(11607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[11510,13]) ).
thf(11608,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ not @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[11607:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( I @ not )),bind(D,$thf( G @ ( I @ not @ not @ implies ) ))]]) ).
thf(11820,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ not @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[11608]) ).
thf(12264,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[11820,11]) ).
thf(7408,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not )
!= y )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[7405]) ).
thf(7421,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( z != y ) ),
inference(simp,[status(thm)],[7408]) ).
thf(520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,429]) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[520]) ).
thf(9355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[532,11]) ).
thf(3991,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( z @ not )
!= A )
| ( ( C @ ( B @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( C != z )
| ( A != x )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4048,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3991]) ).
thf(8027,plain,
( ( z != y )
| ( y != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= y )
| ( x != x ) ),
inference(simp,[status(thm)],[8022]) ).
thf(8041,plain,
( ( z != y )
| ( y != x )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= y ) ),
inference(simp,[status(thm)],[8027]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( x @ implies ) )
!= B )
| ( ( y @ ( z @ not @ implies ) )
!= A )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= x )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[240]) ).
thf(262,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= x )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[247]) ).
thf(1516,plain,
! [A: $i] :
( ( x != x )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= x )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[262]) ).
thf(1519,plain,
! [A: $i] :
( ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( z != z )
| ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) ) ),
inference(simp,[status(thm)],[1516]) ).
thf(1534,plain,
! [A: $i] :
( ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) ) ),
inference(simp,[status(thm)],[1519]) ).
thf(2221,plain,
! [A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1534]) ).
thf(2236,plain,
! [A: $i] :
( ( z != y )
| ( ( z @ not )
!= y )
| ( A != A )
| ( ( z @ ( y @ implies ) )
!= x )
| ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x )
| ( A != z )
| ( y != x ) ),
inference(simp,[status(thm)],[2221]) ).
thf(2252,plain,
( ( z != y )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[2236]) ).
thf(2265,plain,
( ( x != x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= x )
| ( y != x ) ),
inference(eqfactor_ordered,[status(thm)],[2252]) ).
thf(2267,plain,
( ( z != y )
| ( ( z @ not )
!= y )
| ( z != y )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[2265]) ).
thf(2268,plain,
( ( z != y )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[2267]) ).
thf(198,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 ) )
| ( ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,13]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$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(227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[199]) ).
thf(3440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[227,11]) ).
thf(4513,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4502]) ).
thf(4518,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4513]) ).
thf(5024,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( A @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5031,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( z != y ) ),
inference(simp,[status(thm)],[5024]) ).
thf(22725,plain,
( ( ( z @ not )
!= y )
| ( ( z @ not )
!= ( z @ not ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[22721]) ).
thf(22736,plain,
( ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[22725]) ).
thf(4739,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 ) )
| ( true != true )
| ( ( D @ ( E @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[3761,111]) ).
thf(4740,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(simp,[status(thm)],[4739]) ).
thf(4741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[4740:[bind(A,$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(4772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[4741]) ).
thf(7989,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= x )
| ( x != x ) ),
inference(simp,[status(thm)],[4043]) ).
thf(8008,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( x @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[7989]) ).
thf(10635,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 != true ) ),
inference(paramod_ordered,[status(thm)],[3203,10559]) ).
thf(10636,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)],[10635]) ).
thf(10671,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ implies ) @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10636]) ).
thf(3426,plain,
( ( ( z @ ( y @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[3249]) ).
thf(3427,plain,
( ( z != z )
| ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[3426]) ).
thf(3428,plain,
( ( y != x )
| ( ( y @ ( z @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[3427]) ).
thf(4327,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( A != A )
| ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( C != z )
| ( A != y )
| ( ( C @ ( B @ implies ) )
!= x )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[4297]) ).
thf(4444,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( y != x )
| ( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[4327]) ).
thf(671,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 @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,627]) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[671]) ).
thf(14318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[700,11]) ).
thf(981,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)],[300]) ).
thf(984,plain,
( ( y != y )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[981]) ).
thf(997,plain,
( ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[984]) ).
thf(8632,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4072]) ).
thf(8638,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[8632]) ).
thf(8658,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[8638]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,152]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ not @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[171]) ).
thf(2465,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( C @ ( C @ not @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[182,11]) ).
thf(9001,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( x != x ) ),
inference(simp,[status(thm)],[4095]) ).
thf(9017,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[9001]) ).
thf(570,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,57]) ).
thf(571,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[570]) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( J @ ( K @ not @ implies ) @ ( K @ implies ) @ not )),bind(E,$thf( A ))]]) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[572]) ).
thf(795,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 )
!= ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,641]) ).
thf(802,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[795]) ).
thf(16473,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[802,11]) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,152]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ ( D @ not @ implies ) ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[174]) ).
thf(2272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ ( D @ not @ implies ) ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[178,11]) ).
thf(3940,plain,
! [C: $i,B: $i,A: $i] :
( ( C != z )
| ( A != x )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(4086,plain,
! [A: $i] :
( ( ( z @ ( A @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( A @ ( x @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3940]) ).
thf(10649,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3047,10559]) ).
thf(10650,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)],[10649]) ).
thf(10651,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10650]) ).
thf(7407,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7405]) ).
thf(8559,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( z != y )
| ( y != x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[8556]) ).
thf(277,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)],[272]) ).
thf(2439,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)],[277]) ).
thf(2440,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)],[2439]) ).
thf(1147,plain,
! [G: $i,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 @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,1088]) ).
thf(1162,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1147]) ).
thf(20614,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1162,11]) ).
thf(4559,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4556]) ).
thf(4572,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4559]) ).
thf(11531,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11510,10559]) ).
thf(11532,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11531]) ).
thf(11769,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[11532]) ).
thf(3979,plain,
! [C: $i,B: $i,A: $i] :
( ( z != y )
| ( ( z @ not )
!= x )
| ( C != C )
| ( A != B )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3948]) ).
thf(4036,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3979]) ).
thf(6050,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= z )
| ( z != y )
| ( x != x ) ),
inference(simp,[status(thm)],[6038]) ).
thf(6053,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= z )
| ( z != y ) ),
inference(simp,[status(thm)],[6050]) ).
thf(200,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 ) )
| ( ( true @ ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,13]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$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(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[201]) ).
thf(3792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[228,113]) ).
thf(280,plain,
! [A: $i] :
( ( z != y )
| ( ( z @ not )
!= x )
| ( A != A )
| ( ( z @ ( y @ implies ) )
!= x )
| ( A != z )
| ( x != x ) ),
inference(simp,[status(thm)],[272]) ).
thf(296,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[280]) ).
thf(6049,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= z )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6038]) ).
thf(6052,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= z )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6049]) ).
thf(7355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3047,7281]) ).
thf(7356,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)],[7355]) ).
thf(7372,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[7356]) ).
thf(5019,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not )
!= z )
| ( A != x )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5043,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( z != y ) ),
inference(simp,[status(thm)],[5019]) ).
thf(8025,plain,
( ( ( z @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= y )
| ( x != x ) ),
inference(simp,[status(thm)],[8022]) ).
thf(8040,plain,
( ( ( z @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= y ) ),
inference(simp,[status(thm)],[8025]) ).
thf(30,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)],[28]) ).
thf(31,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)],[30]) ).
thf(32,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)],[31]) ).
thf(772,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 )
!= ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,641]) ).
thf(801,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[772]) ).
thf(15998,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ not ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[801,11]) ).
thf(6913,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( x != x )
| ( y != x )
| ( ( z @ not )
!= ( z @ not ) )
| ( z != y )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6899]) ).
thf(6916,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( y != x )
| ( z != y )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[6913]) ).
thf(1812,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 ) )
| ( true != true )
| ( ( C @ ( D @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[1544,111]) ).
thf(1813,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(simp,[status(thm)],[1812]) ).
thf(1814,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[1813:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K @ ( L @ not @ implies ) @ ( L @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1929,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[1814]) ).
thf(1352,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 ) )
| ( ( true @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,1295]) ).
thf(1353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1352:[bind(A,$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(1384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1353]) ).
thf(23279,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 )
= true ),
inference(rewrite,[status(thm)],[1384,11]) ).
thf(274,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)],[272]) ).
thf(291,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(4508,plain,
( ( ( z @ ( y @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( z != x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4526,plain,
( ( z != x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4508]) ).
thf(5026,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( A != A )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5033,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( z != y ) ),
inference(simp,[status(thm)],[5026]) ).
thf(143,plain,
! [A: $i] :
( ( A
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) @ not ) ),
inference(simp,[status(thm)],[143]) ).
thf(4561,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4556]) ).
thf(4573,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4561]) ).
thf(3645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3203,57]) ).
thf(3646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[3645]) ).
thf(3647,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3646:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(3783,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[3647]) ).
thf(21612,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ ( x @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[21609]) ).
thf(21625,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( x @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[21612]) ).
thf(2890,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( F @ not @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[2887,890]) ).
thf(2891,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2890:[bind(A,$thf( V )),bind(B,$thf( W )),bind(C,$thf( S @ ( V @ ( W @ not @ implies ) @ not @ implies ) )),bind(D,$thf( S @ ( V @ ( W @ not @ implies ) @ not @ implies ) @ ( W @ implies ) )),bind(E,$thf( S )),bind(F,$thf( V @ ( W @ not @ implies ) ))]]) ).
thf(3015,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[2891]) ).
thf(5803,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[3015,11]) ).
thf(5963,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 ) )
| ( true != true )
| ( ( D @ ( E @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[5803,111]) ).
thf(5964,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(simp,[status(thm)],[5963]) ).
thf(5965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[5964:[bind(A,$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(6016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[5965]) ).
thf(20653,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( z != x )
| ( ( z @ not )
!= x )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20641]) ).
thf(20664,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( z != x )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20653]) ).
thf(983,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( z != y )
| ( x != x ) ),
inference(simp,[status(thm)],[981]) ).
thf(996,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( z != y ) ),
inference(simp,[status(thm)],[983]) ).
thf(1423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1396,152]) ).
thf(1475,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= ( C @ ( C @ not @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1423]) ).
thf(25138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= ( C @ ( C @ not @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1475,11]) ).
thf(7343,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 != true ) ),
inference(paramod_ordered,[status(thm)],[3203,7281]) ).
thf(7344,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)],[7343]) ).
thf(7360,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)],[7344]) ).
thf(9015,plain,
( ( y != x )
| ( ( z @ not )
!= x )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[9005]) ).
thf(5028,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not @ ( A @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5035,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( z != y ) ),
inference(simp,[status(thm)],[5028]) ).
thf(5831,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[5803,57]) ).
thf(5832,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[5831]) ).
thf(5833,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[5832:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K )),bind(E,$thf( G @ ( J @ ( K @ not @ implies ) @ not @ implies ) ))]]) ).
thf(6013,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[5833]) ).
thf(7859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[7726,6013]) ).
thf(7860,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ ( C @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7859:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ not @ ( H @ not @ implies ) ))]]) ).
thf(7953,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ ( C @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7860]) ).
thf(19185,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ ( C @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[7953,11]) ).
thf(11596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11510,7281]) ).
thf(11597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11596]) ).
thf(11767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[11597]) ).
thf(3122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3047,13]) ).
thf(3123,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3122:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(3211,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[3123]) ).
thf(12810,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[3211,113]) ).
thf(21610,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( x @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[21609]) ).
thf(604,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 )
!= true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,57]) ).
thf(605,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[604:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[605]) ).
thf(12680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[642,11]) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,627]) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[691]) ).
thf(13867,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) )
| ( ( B @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[699,11]) ).
thf(8366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[8277,13]) ).
thf(8367,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( B @ not @ ( B @ not @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[8366:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( I @ not @ ( I @ not @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(8517,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( B @ not @ ( B @ not @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[8367]) ).
thf(9366,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ not @ ( B @ not @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[8517,11]) ).
thf(16929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7726,7375]) ).
thf(16930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[16929]) ).
thf(16931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ not @ ( D @ not @ implies ) @ not @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[16930:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ not @ implies ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(17051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ not @ ( D @ not @ implies ) @ not @ implies ) )
!= ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not ) ),
inference(simp,[status(thm)],[16931]) ).
thf(8560,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( y != x )
| ( ( z @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[8556]) ).
thf(3935,plain,
! [B: $i,A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( B @ ( B @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3749]) ).
thf(3936,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[3935]) ).
thf(489,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[484,9]) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ 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)],[489]) ).
thf(531,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)],[490]) ).
thf(4569,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= y )
| ( ( z @ not )
!= ( z @ not ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4555]) ).
thf(4580,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4569]) ).
thf(236,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)],[147]) ).
thf(255,plain,
! [A: $i] :
( ( A @ ( x @ implies ) @ ( A @ ( z @ ( y @ implies ) @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(8020,plain,
( ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( y != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4047]) ).
thf(491,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 ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,13]) ).
thf(492,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[492]) ).
thf(9651,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[538,11]) ).
thf(4511,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4502]) ).
thf(4529,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4511]) ).
thf(3995,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( z @ not )
!= A )
| ( C
!= ( z @ ( y @ implies ) ) )
| ( B != x )
| ( C != z )
| ( A != x )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4052,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[3995]) ).
thf(6962,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[6953]) ).
thf(10602,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7726,10559]) ).
thf(10603,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ not @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10602]) ).
thf(10653,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( A @ not @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10603]) ).
thf(5023,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= y )
| ( x != A )
| ( ( z @ not )
!= z )
| ( A != x )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5047,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= z )
| ( z != y ) ),
inference(simp,[status(thm)],[5023]) ).
thf(8003,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[7992]) ).
thf(63,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ not )
!= x ) ),
inference(simp,[status(thm)],[32]) ).
thf(6048,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( z != y )
| ( x != x ) ),
inference(simp,[status(thm)],[6038]) ).
thf(6051,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= z )
| ( z != y ) ),
inference(simp,[status(thm)],[6048]) ).
thf(10639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[8277,10559]) ).
thf(10640,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10639]) ).
thf(10667,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ ( B @ not @ implies ) @ not @ implies ) )
!= ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10640]) ).
thf(442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,429]) ).
thf(472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[442]) ).
thf(8263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[472,11]) ).
thf(493,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 ) )
| ( ( true @ ( true @ ( true @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,13]) ).
thf(494,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(539,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[494]) ).
thf(9948,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[539,113]) ).
thf(4501,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= z )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[3965]) ).
thf(4522,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= z )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4501]) ).
thf(789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,641]) ).
thf(800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[789]) ).
thf(15556,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[800,11]) ).
thf(1371,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( ( true @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,1295]) ).
thf(1372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1371:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( N @ ( K @ implies ) @ implies ) )),bind(E,$thf( K @ ( M @ implies ) )),bind(F,$thf( F ))]]) ).
thf(1388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1372]) ).
thf(24661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1388,11]) ).
thf(9312,plain,
! [B: $i,A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[531]) ).
thf(9313,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[9312]) ).
thf(18612,plain,
! [A: $i] :
( ( ( z @ not )
!= z )
| ( x != A )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[18601]) ).
thf(18625,plain,
( ( ( z @ not )
!= z )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[18612]) ).
thf(12790,plain,
( ( ( z @ not )
!= z )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[12787]) ).
thf(410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( C @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[374,152]) ).
thf(416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( C @ ( C @ not @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[410]) ).
thf(7391,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( C @ ( C @ not @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[416,11]) ).
thf(452,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( D @ is_a_theorem @ ( true @ ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[11,429]) ).
thf(470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( D @ is_a_theorem ) )
| ( A != true )
| ( A
!= ( D @ ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( B = true ) ),
inference(simp,[status(thm)],[452]) ).
thf(478,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[470]) ).
thf(8687,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 ) )
| ( true != true )
| ( ( C @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[1396,478]) ).
thf(8688,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(simp,[status(thm)],[8687]) ).
thf(8689,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[8688:[bind(A,$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(8734,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ ( A @ ( A @ not @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[8689]) ).
thf(6963,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[6953]) ).
thf(6975,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[6963]) ).
thf(694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[374,627]) ).
thf(695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[694]) ).
thf(13021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[695,11]) ).
thf(4021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( C @ ( A @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4078,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[4021]) ).
thf(3963,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( C != B )
| ( B != A )
| ( C != z )
| ( A != x )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3944]) ).
thf(4102,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( x @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3963]) ).
thf(11556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ not @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( C @ ( D @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[11510,84]) ).
thf(11557,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ not @ implies ) @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[11556:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( I @ ( K @ not @ not @ implies ) @ ( K @ not @ implies ) ))]]) ).
thf(11807,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ not @ implies ) @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[11557]) ).
thf(20167,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ not @ implies ) @ ( C @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[11807,11]) ).
thf(4562,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4556]) ).
thf(4574,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= x )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4562]) ).
thf(14293,plain,
! [A: $i] :
( ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[14291]) ).
thf(14306,plain,
( ( ( z @ not @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( z != y ) ),
inference(simp,[status(thm)],[14293]) ).
thf(939,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 @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,890]) ).
thf(960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[939]) ).
thf(19097,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[960,11]) ).
thf(5009,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x )
| ( x != x ) ),
inference(simp,[status(thm)],[4102]) ).
thf(5010,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[5009]) ).
thf(20652,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20641]) ).
thf(20663,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( x @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[20652]) ).
thf(4509,plain,
( ( ( z @ ( y @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( z != x )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4527,plain,
( ( z != x )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[4509]) ).
thf(5118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[5050,13]) ).
thf(5119,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[5118:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ implies ) )),bind(D,$thf( H @ ( G @ implies ) ))]]) ).
thf(5243,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[5119]) ).
thf(14742,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[5243,11]) ).
thf(3985,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( z @ not @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( C
!= ( z @ ( y @ implies ) ) )
| ( B != x )
| ( ( C @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3945]) ).
thf(4042,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3985]) ).
thf(271,plain,
! [A: $i] :
( ( A != z )
| ( x != x )
| ( A != y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(290,plain,
( ( z != y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(17586,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 @ ( D @ not @ implies ) @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3047,10663]) ).
thf(17587,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 @ ( D @ not @ implies ) @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[17586]) ).
thf(17588,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[17587:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( D ))]]) ).
thf(17621,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ implies ) @ not @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[17588]) ).
thf(68,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 ) )
| ( ( true @ ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$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(82,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[69]) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[82,113]) ).
thf(4017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( C != B )
| ( A != A )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( B
!= ( z @ ( y @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4074,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[4017]) ).
thf(7621,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 ) )
| ( true != true )
| ( ( D @ ( E @ not @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[7444,111]) ).
thf(7622,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(simp,[status(thm)],[7621]) ).
thf(7623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[7622:[bind(A,$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(7680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ not @ implies ) @ ( B @ ( B @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[7623]) ).
thf(1131,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( D @ ( E @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[484,1088]) ).
thf(1163,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( D @ ( E @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1131]) ).
thf(20627,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( D @ ( E @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1163,11]) ).
thf(11227,plain,
( ( y != x )
| ( ( z @ ( y @ implies ) @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4049]) ).
thf(5287,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( z != x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5278]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,152]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ not @ implies ) ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[177]) ).
thf(2421,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ not @ implies ) ) )
| ( ( B @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[180,11]) ).
thf(12231,plain,
( ( ( z @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x ) ),
inference(eqfactor_ordered,[status(thm)],[12205]) ).
thf(12240,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[12231]) ).
thf(658,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,627]) ).
thf(696,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[658]) ).
thf(13453,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( E @ ( E @ ( E @ not @ implies ) @ implies ) @ not ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[696,11]) ).
thf(8019,plain,
( ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y )
| ( x != x ) ),
inference(simp,[status(thm)],[4047]) ).
thf(8038,plain,
( ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= y ) ),
inference(simp,[status(thm)],[8019]) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,641]) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[792]) ).
thf(17626,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) )
| ( ( B @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[805,11]) ).
thf(4504,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4523,plain,
( ( ( z @ ( y @ implies ) @ ( z @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4504]) ).
thf(5017,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( A @ implies ) ) )
| ( ( z @ not @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y )
| ( A != x ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5041,plain,
( ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( z != y ) ),
inference(simp,[status(thm)],[5017]) ).
thf(4568,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4555]) ).
thf(4579,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not @ ( z @ not @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4568]) ).
thf(18610,plain,
! [A: $i] :
( ( ( z @ ( x @ implies ) )
!= ( z @ not @ ( A @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[18601]) ).
thf(18623,plain,
( ( ( z @ not @ ( x @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ not )
!= y )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) ) ),
inference(simp,[status(thm)],[18610]) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,429]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[469]) ).
thf(8542,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( B @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[473,11]) ).
thf(98,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 ) )
| ( ( true @ ( D @ ( E @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,84]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$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(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[99]) ).
thf(1657,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 )
= true ),
inference(rewrite,[status(thm)],[108,11]) ).
thf(325,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( B @ is_a_theorem @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
!= ( E @ ( D @ ( C @ ( C @ ifeq ) ) ) ) )
| ( true = D )
| ( ( A @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[55,11]) ).
thf(354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true != E )
| ( ( B @ is_a_theorem )
!= D )
| ( true != C )
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= C )
| ( ( A @ is_a_theorem )
!= true )
| ( true = D ) ),
inference(simp,[status(thm)],[325]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
!= true )
| ( ( B @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[354]) ).
thf(12241,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[12231]) ).
thf(12253,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( z @ not @ implies ) ) )
| ( z != y )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[12241]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[374,9]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ 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)],[381]) ).
thf(415,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(278,plain,
! [A: $i] :
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( A @ ( z @ ( y @ implies ) @ implies ) )
!= ( A @ ( x @ implies ) ) )
| ( A != z )
| ( x != x ) ),
inference(simp,[status(thm)],[272]) ).
thf(294,plain,
( ( z != y )
| ( ( z @ not )
!= x )
| ( ( z @ ( z @ ( y @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(8819,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[8740,13]) ).
thf(8820,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ not @ is_a_theorem @ ( true @ ( A @ not @ ( A @ not @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[8819:[bind(A,$thf( I )),bind(B,$thf( I @ not @ ( I @ not @ not @ implies ) )),bind(C,$thf( I @ not ))]]) ).
thf(8986,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ not @ is_a_theorem @ ( true @ ( A @ not @ ( A @ not @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[8820]) ).
thf(10691,plain,
! [A: $i] :
( ( true @ ( A @ not @ is_a_theorem @ ( true @ ( A @ not @ ( A @ not @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[8986,11]) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[15,57]) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[585:[bind(A,$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(631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[586]) ).
thf(11281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[631,11]) ).
thf(11338,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( D @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[2887,11281]) ).
thf(11339,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[11338]) ).
thf(11340,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[11339:[bind(A,$thf( T )),bind(B,$thf( X )),bind(C,$thf( W @ ( X @ not @ implies ) @ ( W @ ( T @ implies ) @ implies ) )),bind(D,$thf( W @ ( X @ not @ implies ) @ ( W @ ( T @ implies ) @ implies ) @ ( X @ implies ) )),bind(E,$thf( T )),bind(F,$thf( X @ not )),bind(G,$thf( W ))]]) ).
thf(11362,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[11340]) ).
thf(5029,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= y )
| ( A != A )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5015]) ).
thf(5036,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= y )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5029]) ).
thf(982,plain,
( ( ( y @ ( z @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ not )
!= x )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[981]) ).
thf(566,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,57]) ).
thf(567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[566:[bind(A,$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(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[567]) ).
thf(12535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[639,11]) ).
thf(3942,plain,
! [C: $i,B: $i,A: $i] :
( ( C != z )
| ( A != x )
| ( C != y )
| ( B
!= ( z @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(4088,plain,
( ( z != y )
| ( ( z @ ( y @ implies ) @ ( x @ implies ) )
!= ( z @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[3942]) ).
thf(5022,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= y )
| ( x != A )
| ( ( z @ not )
!= z )
| ( A != x )
| ( ( y @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5016]) ).
thf(5046,plain,
( ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= z )
| ( ( z @ ( x @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[5022]) ).
thf(7339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[374,7281]) ).
thf(7340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[7339]) ).
thf(7367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not ) ),
inference(simp,[status(thm)],[7340]) ).
thf(4517,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( z != x )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( x != x ) ),
inference(simp,[status(thm)],[4502]) ).
thf(4520,plain,
( ( z != x )
| ( ( z @ ( y @ implies ) )
!= y )
| ( ( z @ not )
!= x )
| ( ( z @ ( y @ implies ) )
!= z ) ),
inference(simp,[status(thm)],[4517]) ).
thf(21613,plain,
! [A: $i] :
( ( ( z @ ( y @ implies ) )
!= z )
| ( x != x )
| ( ( z @ not )
!= z )
| ( x != A )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[21609]) ).
thf(21626,plain,
( ( ( z @ ( y @ implies ) )
!= z )
| ( ( z @ not )
!= z )
| ( ( z @ not )
!= y ) ),
inference(simp,[status(thm)],[21613]) ).
thf(10616,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 != true ) ),
inference(paramod_ordered,[status(thm)],[17,10559]) ).
thf(10617,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)],[10616]) ).
thf(10669,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not ) ),
inference(simp,[status(thm)],[10617]) ).
thf(4552,plain,
( ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( z @ ( y @ implies ) )
!= ( z @ not ) )
| ( ( z @ not )
!= x ) ),
inference(simp,[status(thm)],[4029]) ).
thf(3061,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[3047,55]) ).
thf(3062,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[3061]) ).
thf(3063,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[3062:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) )),bind(C,$thf( C ))]]) ).
thf(3212,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[3063]) ).
thf(29809,plain,
$false,
inference(e,[status(thm)],[7375,21624,4560,24195,6976,21595,7673,19649,1295,4043,1924,994,19081,7726,1544,12789,6918,4500,10,23743,5037,142,4528,19636,4564,7422,4026,17594,4047,20662,3249,9027,288,4803,7364,10559,9013,11250,14292,11228,14,4524,184,4070,8951,5289,11416,3749,3089,11510,11247,152,57,8037,22735,8558,29,18624,8571,10665,289,1489,7423,7369,4820,20672,6964,5032,84,821,17040,15105,4443,4578,4072,20687,4050,5045,147,10670,8001,4055,21569,19084,293,4040,18656,10932,1943,4519,22685,4082,10690,9026,233,10652,6047,5034,4576,12205,4059,11253,11255,6064,18658,4557,7937,18609,12788,4521,4785,429,6356,4044,5044,28,484,8048,8026,3028,4080,1012,224,8651,8503,18613,7281,12264,7421,9355,4048,9,4095,8041,4525,2268,3440,256,4049,4518,5031,22736,4772,8008,10671,3428,4444,14318,997,8658,2465,13,9017,16473,2272,4086,10651,237,7407,4081,8559,2440,3190,20614,4572,7444,11769,4036,6053,3792,296,17,6052,7372,5043,8040,32,22629,15998,21116,191,6916,1929,23279,291,5050,8740,641,4526,12,4558,5033,144,4573,3783,21625,6016,113,20664,996,7,25138,7360,9015,4073,890,5035,10179,4064,19185,11767,12810,21610,12680,13867,1396,1643,5042,9366,17051,80,8560,4084,3936,531,4580,255,8020,9651,20650,4529,374,4052,6962,10653,5047,8003,63,18,6051,10667,7942,8263,11252,9948,4522,15556,8024,31,24661,16,9313,18625,4057,12790,7391,11,10663,8734,6975,4414,6013,13021,4078,4102,20167,4574,14306,627,19097,55,5010,20663,4527,14742,4042,290,17621,1212,4074,3761,7680,20627,478,11227,5287,2421,6924,300,12240,13453,8038,17626,4523,3203,5041,4579,18623,8542,1657,358,12253,8277,415,4029,242,294,4051,10691,11362,3426,5036,5803,3965,982,12535,277,4088,5046,15,111,7367,4520,21626,1088,3047,10669,4552,11281,3212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL384-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 22:23:14 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.18/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.64/1.30 % [INFO] Parsing done (204ms).
% 1.64/1.31 % [INFO] Running in sequential loop mode.
% 2.35/1.73 % [INFO] eprover registered as external prover.
% 2.35/1.74 % [INFO] Scanning for conjecture ...
% 2.53/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.70/1.93 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.70/1.95 % [INFO] Problem is propositional (TPTP CNF).
% 2.70/1.96 % [INFO] Type checking passed.
% 2.70/1.97 % [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 ...
% 192.77/49.70 % External prover 'e' found a proof!
% 192.77/49.71 % [INFO] Killing All external provers ...
% 192.77/49.71 % Time passed: 49102ms (effective reasoning time: 48388ms)
% 192.77/49.71 % Axioms used in derivation (5): cn_2, ifeq_axiom, condensed_detachment, cn_1, cn_3
% 192.77/49.71 % No. of inferences in proof: 884
% 192.77/49.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 49102 ms resp. 48388 ms w/o parsing
% 181.12/50.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 181.12/50.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------