%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL113-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:50:52 AM UTC 2026
% Result : Unsatisfiable 124.27s 44.56s
% Output : Refutation 125.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 7
% Syntax : Number of formulae : 2109 ( 991 unt; 0 typ; 0 def)
% Number of atoms : 3623 (3622 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 29427 (3155 ~;1514 |; 0 &;24758 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 5746 ( 0 ^;5746 !; 0 ?;5746 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
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(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[11]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mv_1) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[15]) ).
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(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(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,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)],[13]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ 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)],[16,14]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[52]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[59,12]) ).
thf(102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( E @ is_a_theorem @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[12,90]) ).
thf(112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( A != true )
| ( A
!= ( E @ is_a_theorem ) )
| ( B = true ) ),
inference(simp,[status(thm)],[102]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( B @ is_a_theorem )
!= true )
| ( ( B @ ( A @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[112]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mv_5) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[21]) ).
thf(46,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)],[12,14]) ).
thf(54,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)],[46]) ).
thf(61,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)],[54]) ).
thf(611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ 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)],[22,61]) ).
thf(612,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( I @ not @ ( J @ not @ implies ) )),bind(D,$thf( J @ ( I @ implies ) ))]]) ).
thf(623,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[612]) ).
thf(7817,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true )
| ( ( B @ ( A @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[623,12]) ).
thf(1,negated_conjecture,
( ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_33) ).
thf(8,plain,
( ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,plain,
( ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(lifteq,[status(thm)],[9]) ).
thf(1764,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,10]) ).
thf(1765,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1764]) ).
thf(1766,plain,
( ( a @ ( b @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[1765:[bind(A,$thf( b @ ( a @ not @ implies ) )),bind(B,$thf( a @ ( b @ not @ implies ) ))]]) ).
thf(1933,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,1766]) ).
thf(1934,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1933]) ).
thf(1935,plain,
( ( a @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[1934:[bind(A,$thf( b @ not )),bind(B,$thf( a ))]]) ).
thf(7839,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,1935]) ).
thf(7840,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7839]) ).
thf(8123,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7840]) ).
thf(9809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,8123]) ).
thf(9810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9809]) ).
thf(9811,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( ( A @ not @ not @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[9810:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(9864,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( ( A @ not @ not @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9811]) ).
thf(13891,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ not @ ( D @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,9864]) ).
thf(13892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ not @ ( D @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[13891]) ).
thf(13893,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ not @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[13892:[bind(A,$thf( F @ not @ not )),bind(B,$thf( H @ not @ not )),bind(C,$thf( H )),bind(D,$thf( F ))]]) ).
thf(13950,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ not @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[13893]) ).
thf(5,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',mv_2) ).
thf(17,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)],[5]) ).
thf(18,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)],[17]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ 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)],[16,14]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ implies ) @ ( H @ implies ) )),bind(D,$thf( D ))]]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[48]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[57,12]) ).
thf(253,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[18,234]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( O )),bind(B,$thf( O @ ( M @ implies ) )),bind(C,$thf( P )),bind(D,$thf( P @ ( O @ implies ) @ ( P @ ( O @ ( M @ implies ) @ implies ) @ implies ) )),bind(E,$thf( M )),bind(F,$thf( O ))]]) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[254]) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[277,12]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ 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)],[22,14]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( L )),bind(B,$thf( K )),bind(C,$thf( L @ ( K @ implies ) @ ( K @ not @ ( L @ not @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[39]) ).
thf(644,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[62,12]) ).
thf(1163,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( E @ not @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1104,644]) ).
thf(1164,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1163:[bind(A,$thf( O @ not )),bind(B,$thf( N @ not )),bind(C,$thf( O @ ( N @ implies ) )),bind(D,$thf( O @ ( N @ implies ) @ ( N @ not @ implies ) )),bind(E,$thf( N )),bind(F,$thf( O ))]]) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1164]) ).
thf(1194,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1178,12]) ).
thf(74,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)],[18,14]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( A @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$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(89,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)],[75]) ).
thf(1581,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)],[89,12]) ).
thf(1637,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1194,1581]) ).
thf(1638,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1637:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ implies ) )),bind(D,$thf( G @ not )),bind(E,$thf( E ))]]) ).
thf(1680,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1638]) ).
thf(46092,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1680,12]) ).
thf(45,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(55,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) ) )
| ( A != true )
| ( A
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( B = true ) ),
inference(simp,[status(thm)],[45]) ).
thf(63,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)],[55]) ).
thf(1154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ 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)],[1104,63]) ).
thf(1155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ 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)],[1154]) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ( true @ ( C @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1155:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ ( H @ implies ) @ implies ) )),bind(E,$thf( K @ ( J @ implies ) ))]]) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ( true @ ( C @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1156]) ).
thf(46474,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( F @ ( E @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[46092,1175]) ).
thf(46475,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[46474:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( H )),bind(D,$thf( H @ ( K @ implies ) )),bind(E,$thf( J )),bind(F,$thf( J @ ( K @ not @ implies ) ))]]) ).
thf(46854,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[46475]) ).
thf(47534,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[46854,12]) ).
thf(7836,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,10]) ).
thf(7837,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7836]) ).
thf(7838,plain,
( ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[7837:[bind(A,$thf( b @ ( a @ not @ implies ) )),bind(B,$thf( a @ ( b @ not @ implies ) ))]]) ).
thf(8319,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,7838]) ).
thf(8320,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8319]) ).
thf(8321,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8320:[bind(A,$thf( a @ ( b @ not @ implies ) @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not ))]]) ).
thf(8464,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,8321]) ).
thf(8465,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8464]) ).
thf(8466,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8465:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not ))]]) ).
thf(8697,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,8466]) ).
thf(8698,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8697]) ).
thf(8699,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8698:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not ))]]) ).
thf(9031,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,8699]) ).
thf(9032,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9031]) ).
thf(9033,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[9032:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not ))]]) ).
thf(10632,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,9033]) ).
thf(10633,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10632]) ).
thf(10634,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[10633:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ))]]) ).
thf(47726,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,10634]) ).
thf(47727,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[47726]) ).
thf(48199,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[47727]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mv_3) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[19]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ 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)],[20,14]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( L @ ( L @ ( M @ implies ) @ implies ) @ ( M @ ( M @ ( L @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[189]) ).
thf(4347,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[213,12]) ).
thf(4389,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( F @ implies ) @ implies ) @ ( F @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1104,4347]) ).
thf(4390,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[4389:[bind(A,$thf( Q @ ( P @ implies ) )),bind(B,$thf( Q )),bind(C,$thf( P @ ( P @ ( Q @ implies ) @ implies ) )),bind(D,$thf( P @ ( P @ ( Q @ implies ) @ implies ) @ ( Q @ implies ) )),bind(E,$thf( P )),bind(F,$thf( Q ))]]) ).
thf(4499,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[4390]) ).
thf(4518,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[4499,12]) ).
thf(252,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( D @ is_a_theorem @ ( true @ ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[12,234]) ).
thf(266,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( D @ is_a_theorem ) )
| ( A != true )
| ( A
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( B = true ) ),
inference(simp,[status(thm)],[252]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[266]) ).
thf(5373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( C @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[4518,275]) ).
thf(5374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[5373]) ).
thf(5375,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[5374:[bind(A,$thf( K )),bind(B,$thf( Q @ ( P @ implies ) @ ( Q @ implies ) )),bind(C,$thf( K @ ( K @ ( Q @ ( P @ implies ) @ ( Q @ implies ) @ implies ) @ implies ) )),bind(D,$thf( P )),bind(E,$thf( Q ))]]) ).
thf(5426,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[5375]) ).
thf(6277,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( F @ ( E @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[5426,1175]) ).
thf(6278,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6277:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ implies ) )),bind(E,$thf( A )),bind(F,$thf( A ))]]) ).
thf(6338,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[6278,12]) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1194,61]) ).
thf(1230,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ is_a_theorem )
!= true )
| ( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[1229:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ not )),bind(D,$thf( G @ ( F @ implies ) ))]]) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ is_a_theorem )
!= true )
| ( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1230]) ).
thf(29427,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ is_a_theorem )
!= true )
| ( ( B @ ( A @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1277,12]) ).
thf(8036,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,1766]) ).
thf(8037,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8036]) ).
thf(8038,plain,
( ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8037:[bind(A,$thf( b @ not )),bind(B,$thf( a ))]]) ).
thf(30073,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8038]) ).
thf(30074,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30073]) ).
thf(30075,plain,
( ( a @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[30074:[bind(A,$thf( a @ not )),bind(B,$thf( b @ not @ not ))]]) ).
thf(30284,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,30075]) ).
thf(30285,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30284]) ).
thf(30426,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30285]) ).
thf(31485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30426]) ).
thf(31486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[31485]) ).
thf(31642,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[31486]) ).
thf(34615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not )
!= ( a @ not @ not ) )
| ( ( A @ ( A @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ not @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[31642]) ).
thf(34616,plain,
( ( a @ not @ ( a @ not @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[34615:[bind(A,$thf( a @ not )),bind(B,$thf( a @ not )),bind(C,$thf( a @ not ))]]) ).
thf(6445,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( true != true )
| ( ( C @ ( B @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[6338,113]) ).
thf(6446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[6445]) ).
thf(6447,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[6446:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(6554,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[6447]) ).
thf(6935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[6554,113]) ).
thf(6936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[6935]) ).
thf(6937,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[6936:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ implies ) @ ( E @ implies ) ))]]) ).
thf(7033,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[6937]) ).
thf(30330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,30075]) ).
thf(30331,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30330]) ).
thf(30427,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30331]) ).
thf(1851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[1194,113]) ).
thf(1852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[1851]) ).
thf(1853,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[1852:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( H @ implies ) @ ( H @ not @ implies ) ))]]) ).
thf(1920,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[1853]) ).
thf(2421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( true != true )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[1920,113]) ).
thf(2422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[2421]) ).
thf(2423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[2422:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( L @ ( K @ implies ) @ ( K @ not @ implies ) @ ( F @ implies ) ))]]) ).
thf(2489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[2423]) ).
thf(8192,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8038]) ).
thf(8193,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8192]) ).
thf(8194,plain,
( ( b @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8193:[bind(A,$thf( a @ not )),bind(B,$thf( b @ not @ not ))]]) ).
thf(8254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2489,8194]) ).
thf(8255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8254]) ).
thf(8288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8255]) ).
thf(664,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 @ ( F @ ( E @ implies ) @ ( E @ not @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[18,644]) ).
thf(665,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ not @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[664:[bind(A,$thf( X @ not @ ( W @ not @ implies ) )),bind(B,$thf( W @ ( X @ implies ) )),bind(C,$thf( T )),bind(D,$thf( T @ ( X @ not @ ( W @ not @ implies ) @ implies ) @ ( T @ ( W @ ( X @ implies ) @ implies ) @ implies ) )),bind(E,$thf( X )),bind(F,$thf( W ))]]) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ not @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[665]) ).
thf(12596,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ not @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[706,12]) ).
thf(659,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( D @ is_a_theorem @ ( true @ ( D @ ( F @ ( E @ implies ) @ ( E @ not @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[12,644]) ).
thf(695,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( D @ is_a_theorem ) )
| ( A != true )
| ( A
!= ( D @ ( F @ ( E @ implies ) @ ( E @ not @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( B = true ) ),
inference(simp,[status(thm)],[659]) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[695]) ).
thf(12759,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ not @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( E @ not @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( D @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[12596,704]) ).
thf(12760,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ not @ ( B @ not @ implies ) @ implies ) @ ( A @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( E @ not @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[12759]) ).
thf(12761,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[12760:[bind(A,$thf( T @ ( S @ implies ) )),bind(B,$thf( S @ not )),bind(C,$thf( T @ not )),bind(D,$thf( T @ ( S @ implies ) @ ( T @ not @ not @ ( S @ not @ not @ implies ) @ implies ) )),bind(E,$thf( S )),bind(F,$thf( T ))]]) ).
thf(12978,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[12761]) ).
thf(13641,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[12978,1175]) ).
thf(13642,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[13641:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ not @ not )),bind(D,$thf( K @ not @ not )),bind(E,$thf( K @ ( J @ implies ) ))]]) ).
thf(13841,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[13642]) ).
thf(14158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[13841,12]) ).
thf(8330,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,7838]) ).
thf(8331,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8330]) ).
thf(8332,plain,
( ( b @ ( a @ not @ implies ) @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8331:[bind(A,$thf( a @ ( b @ not @ implies ) @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not ))]]) ).
thf(8398,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8332]) ).
thf(8399,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8398]) ).
thf(8430,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8399]) ).
thf(14184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,8430]) ).
thf(14185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[14184]) ).
thf(14186,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[14185:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ not @ not @ implies ) ))]]) ).
thf(14574,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[14186]) ).
thf(616,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)],[61,12]) ).
thf(618,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)],[616]) ).
thf(628,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)],[618]) ).
thf(592,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)],[18,61]) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[592:[bind(A,$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(632,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)],[593]) ).
thf(9866,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)],[632,12]) ).
thf(10204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ 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)],[6554,9866]) ).
thf(10205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ 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)],[10204]) ).
thf(10206,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[10205:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ implies ) )),bind(D,$thf( A )),bind(E,$thf( E ))]]) ).
thf(10307,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[10206]) ).
thf(17898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[10307,1935]) ).
thf(17899,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[17898]) ).
thf(18272,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[17899]) ).
thf(10623,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,9033]) ).
thf(10624,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10623]) ).
thf(10625,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[10624:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ))]]) ).
thf(12146,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,10625]) ).
thf(12147,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[12146]) ).
thf(12148,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[12147:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ))]]) ).
thf(571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ 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)],[20,61]) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( K @ ( K @ ( J @ implies ) @ implies ) )),bind(D,$thf( J @ ( J @ ( K @ implies ) @ implies ) ))]]) ).
thf(636,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[572]) ).
thf(10754,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[636,12]) ).
thf(11092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( C @ ( C @ ( D @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[6554,10754]) ).
thf(11093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ ( D @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[11092]) ).
thf(11094,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[11093:[bind(A,$thf( H @ ( H @ implies ) @ ( E @ implies ) )),bind(B,$thf( H )),bind(C,$thf( E )),bind(D,$thf( H @ ( H @ implies ) ))]]) ).
thf(11172,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[11094]) ).
thf(11453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( C @ ( C @ ( D @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[11172,10754]) ).
thf(11454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ ( D @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[11453]) ).
thf(11455,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[11454:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( F @ ( F @ implies ) )),bind(D,$thf( A ))]]) ).
thf(11556,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[11455]) ).
thf(20890,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11556,1935]) ).
thf(20891,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[20890]) ).
thf(21299,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[20891]) ).
thf(11232,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,1935]) ).
thf(11233,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[11232]) ).
thf(11527,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[11233]) ).
thf(6377,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)],[6338,61]) ).
thf(6378,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)],[6377]) ).
thf(6379,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6378:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ implies ) )),bind(C,$thf( C ))]]) ).
thf(6571,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)],[6379]) ).
thf(47680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[47534,6571]) ).
thf(47681,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[47680:[bind(A,$thf( K @ ( K @ implies ) )),bind(B,$thf( I )),bind(C,$thf( K @ ( K @ implies ) @ ( I @ not @ implies ) )),bind(D,$thf( K ))]]) ).
thf(48263,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[47681]) ).
thf(51610,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[48263,12]) ).
thf(51650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8430]) ).
thf(51651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[51650]) ).
thf(51652,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[51651:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( I @ implies ) @ ( G @ not @ implies ) ))]]) ).
thf(52384,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[51652]) ).
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 )
!= ( 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)],[18,14]) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$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(87,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)],[71]) ).
thf(1286,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)],[87,12]) ).
thf(1337,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1194,1286]) ).
thf(1371,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1337]) ).
thf(32695,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( D @ ( E @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1371,12]) ).
thf(3906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2489,1766]) ).
thf(3907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3906]) ).
thf(3944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[3907]) ).
thf(1352,plain,
! [G: $i,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 @ ( 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)],[18,1286]) ).
thf(1353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( A @ ( C @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1352:[bind(A,$thf( ZC @ ( ZB @ implies ) )),bind(B,$thf( Y @ ( ZB @ implies ) @ ( Y @ ( ZC @ implies ) @ implies ) )),bind(C,$thf( ZA )),bind(D,$thf( ZA @ ( ZC @ ( ZB @ implies ) @ implies ) @ ( ZA @ ( Y @ ( ZB @ implies ) @ ( Y @ ( ZC @ implies ) @ implies ) @ implies ) @ implies ) )),bind(E,$thf( ZC )),bind(F,$thf( ZB )),bind(G,$thf( Y ))]]) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( A @ ( C @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1353]) ).
thf(33746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( A @ ( C @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1373,12]) ).
thf(34083,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( A @ ( C @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( G @ ( F @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( G @ ( F @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[33746,1175]) ).
thf(34084,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[34083:[bind(A,$thf( M )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( M @ ( P @ implies ) @ ( M @ ( Q @ implies ) @ implies ) )),bind(F,$thf( O )),bind(G,$thf( O @ ( Q @ ( P @ implies ) @ implies ) ))]]) ).
thf(34373,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[34084]) ).
thf(35137,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[34373,12]) ).
thf(35282,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[35137,6571]) ).
thf(35283,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[35282:[bind(A,$thf( M @ ( M @ implies ) )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( M @ ( M @ implies ) @ ( K @ ( J @ implies ) @ implies ) )),bind(E,$thf( M ))]]) ).
thf(35834,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[35283]) ).
thf(36037,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[35834,12]) ).
thf(36534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,1766]) ).
thf(36535,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[36534]) ).
thf(36683,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[36535]) ).
thf(36789,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[36683]) ).
thf(6369,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)],[6338,1581]) ).
thf(6370,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6369:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(6568,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[6370]) ).
thf(11734,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[6568,12]) ).
thf(8708,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8466]) ).
thf(8709,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8708]) ).
thf(8710,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8709:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not ))]]) ).
thf(12027,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,8710]) ).
thf(12028,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[12027]) ).
thf(12055,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[12028]) ).
thf(1957,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,1935]) ).
thf(1958,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1957]) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1958]) ).
thf(1983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[22,1968]) ).
thf(1984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1983]) ).
thf(1985,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1984:[bind(A,$thf( L )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( L @ ( K @ implies ) @ ( K @ not @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(1995,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1985]) ).
thf(6339,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,10]) ).
thf(6340,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6339]) ).
thf(6544,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[6340]) ).
thf(8475,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8321]) ).
thf(8476,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8475]) ).
thf(8477,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[8476:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not ))]]) ).
thf(11415,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,8477]) ).
thf(11416,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11415]) ).
thf(11517,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[11416]) ).
thf(1150,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ 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)],[1104,63]) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[1150:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(1190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1151]) ).
thf(25613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1190,12]) ).
thf(46500,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( D @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[46092,25613]) ).
thf(46501,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( D @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[46500]) ).
thf(46502,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[46501:[bind(A,$thf( R @ ( Q @ implies ) )),bind(B,$thf( Q @ ( O @ implies ) )),bind(C,$thf( R )),bind(D,$thf( R @ ( Q @ implies ) @ ( Q @ ( O @ implies ) @ not @ implies ) )),bind(E,$thf( O )),bind(F,$thf( Q )),bind(G,$thf( R ))]]) ).
thf(46861,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[46502]) ).
thf(57116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[46861,30075]) ).
thf(57117,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[57116]) ).
thf(57481,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[57117]) ).
thf(2446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1920,1766]) ).
thf(2447,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2446]) ).
thf(2463,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[2447]) ).
thf(8496,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,8321]) ).
thf(8497,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8496]) ).
thf(8507,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[8497]) ).
thf(35597,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,1766]) ).
thf(35598,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[35597]) ).
thf(35735,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[35598]) ).
thf(1130,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1104,234]) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1130:[bind(A,$thf( Q )),bind(B,$thf( R )),bind(C,$thf( R @ ( Q @ implies ) @ ( O @ implies ) )),bind(D,$thf( R @ ( Q @ implies ) @ ( O @ implies ) @ ( R @ implies ) )),bind(E,$thf( O )),bind(F,$thf( R @ ( Q @ implies ) ))]]) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1131]) ).
thf(2584,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1177,12]) ).
thf(8410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,8332]) ).
thf(8411,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8410]) ).
thf(8434,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8411]) ).
thf(8473,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,8321]) ).
thf(8474,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8473]) ).
thf(8509,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[8474]) ).
thf(47517,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( ( A @ not )
!= ( b @ ( a @ not @ implies ) @ not @ not ) ) ),
inference(simp,[status(thm)],[8509]) ).
thf(8543,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8477]) ).
thf(8544,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8543]) ).
thf(8572,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8544]) ).
thf(10437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8572]) ).
thf(10438,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10437]) ).
thf(10439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[10438:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(10478,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10439]) ).
thf(8328,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,7838]) ).
thf(8329,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8328]) ).
thf(8368,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[8329]) ).
thf(25228,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not )
!= ( a @ ( b @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[8368]) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[16,90]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[108]) ).
thf(278,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[118,12]) ).
thf(279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[278,234]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( J @ ( I @ implies ) @ ( J @ implies ) )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( N @ implies ) )),bind(E,$thf( I )),bind(F,$thf( J ))]]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[280]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[323,12]) ).
thf(8760,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,8710]) ).
thf(8761,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8760]) ).
thf(8811,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8761]) ).
thf(21112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[11556,1175]) ).
thf(21113,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[21112:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( I @ ( I @ implies ) )),bind(E,$thf( I @ ( I @ implies ) ))]]) ).
thf(21331,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[21113]) ).
thf(21393,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[21331,12]) ).
thf(21647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[21393,1175]) ).
thf(21648,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[21647:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(21866,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[21648]) ).
thf(21912,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[21866,12]) ).
thf(22314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[21912,90]) ).
thf(22315,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[22314:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) @ ( G @ implies ) ))]]) ).
thf(22372,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[22315]) ).
thf(23462,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[22372,12]) ).
thf(30342,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[23462,30075]) ).
thf(30343,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30342]) ).
thf(30392,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30343]) ).
thf(29765,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8332]) ).
thf(29766,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29765]) ).
thf(30145,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29766]) ).
thf(4613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[4518,113]) ).
thf(4614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[4613]) ).
thf(4615,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[4614:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ ( I @ implies ) @ implies ) @ ( I @ implies ) ))]]) ).
thf(4683,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[4615]) ).
thf(5203,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4683,1766]) ).
thf(5204,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5203]) ).
thf(5237,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[5204]) ).
thf(22300,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8038]) ).
thf(22301,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22300]) ).
thf(22338,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[22301]) ).
thf(22469,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[22338]) ).
thf(22470,plain,
( ( a @ not @ ( a @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[22469]) ).
thf(47892,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,30075]) ).
thf(47893,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[47892]) ).
thf(48214,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[47893]) ).
thf(13048,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,12148]) ).
thf(13049,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[13048]) ).
thf(13050,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[13049:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ))]]) ).
thf(16539,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,13050]) ).
thf(16540,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[16539]) ).
thf(16541,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[16540:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ))]]) ).
thf(25845,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,16541]) ).
thf(25846,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[25845]) ).
thf(25847,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[25846:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not ))]]) ).
thf(26010,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,25847]) ).
thf(26011,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[26010]) ).
thf(26044,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[26011]) ).
thf(21536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,1968]) ).
thf(21537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[21536]) ).
thf(21538,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[21537:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ ( I @ implies ) @ ( I @ ( I @ implies ) @ implies ) ))]]) ).
thf(21849,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[21538]) ).
thf(16550,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,13050]) ).
thf(16551,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[16550]) ).
thf(16552,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[16551:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ))]]) ).
thf(16650,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,16552]) ).
thf(16651,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[16650]) ).
thf(16698,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[16651]) ).
thf(2374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ 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)],[1920,14]) ).
thf(2375,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2374:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( A )),bind(E,$thf( J @ ( I @ implies ) @ ( I @ not @ implies ) ))]]) ).
thf(2473,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[2375]) ).
thf(5878,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[2473,12]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,10]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[285]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( A
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( B
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[1071]) ).
thf(1073,plain,
! [A: $i] :
( ( b @ not @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1072]) ).
thf(14341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[14158,113]) ).
thf(14342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[14341]) ).
thf(14343,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[14342:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ not @ not @ implies ) ))]]) ).
thf(14538,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[14343]) ).
thf(1195,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,10]) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1195]) ).
thf(1269,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1196]) ).
thf(47735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,1968]) ).
thf(47736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[47735]) ).
thf(47737,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[47736:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(48275,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[47737]) ).
thf(1592,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ 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)],[329,1581]) ).
thf(1593,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1592:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ implies ) )),bind(D,$thf( G ))]]) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1593]) ).
thf(50764,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1690,12]) ).
thf(51147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[50764,30075]) ).
thf(51148,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[51147]) ).
thf(51476,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[51148]) ).
thf(7607,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( true != true )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[7033,113]) ).
thf(7608,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[7607]) ).
thf(7609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[7608:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( K @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(7730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[7609]) ).
thf(16083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7730,1766]) ).
thf(16084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16083]) ).
thf(16196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[16084]) ).
thf(21946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8430]) ).
thf(21947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[21946]) ).
thf(21948,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[21947:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) @ ( G @ implies ) ))]]) ).
thf(22402,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[21948]) ).
thf(1197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1194,14]) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ implies ) @ ( H @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1198]) ).
thf(29004,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1276,12]) ).
thf(1989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,1968]) ).
thf(1990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1989]) ).
thf(1991,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[1990:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(1998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1991]) ).
thf(30012,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,1998]) ).
thf(30013,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30012]) ).
thf(30014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( C @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[30013:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(30209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( C @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30014]) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ 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)],[22,63]) ).
thf(866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ 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)],[865]) ).
thf(867,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( A @ not @ ( B @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( I @ not @ ( J @ not @ implies ) )),bind(D,$thf( J @ ( I @ implies ) ))]]) ).
thf(897,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( A @ not @ ( B @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[867]) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[329,897]) ).
thf(981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[931]) ).
thf(17285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[981,12]) ).
thf(17589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[17285,8194]) ).
thf(17590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[17589]) ).
thf(17734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( C @ not ) )
| ( B
!= ( D @ not ) ) ),
inference(simp,[status(thm)],[17590]) ).
thf(17791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(simp,[status(thm)],[17734]) ).
thf(29503,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,1935]) ).
thf(29504,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29503]) ).
thf(30171,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29504]) ).
thf(30634,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,30171]) ).
thf(30635,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30634]) ).
thf(30707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( B @ not ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30635]) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1194,63]) ).
thf(1247,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[1246:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ implies ) @ ( H @ not @ implies ) )),bind(D,$thf( D ))]]) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1247]) ).
thf(32165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1285,12]) ).
thf(10708,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,10634]) ).
thf(10709,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10708]) ).
thf(10737,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[10709]) ).
thf(8244,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,8194]) ).
thf(8245,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8244]) ).
thf(8303,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8245]) ).
thf(30358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4683,30075]) ).
thf(30359,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30358]) ).
thf(30375,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30359]) ).
thf(46153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[46092,1935]) ).
thf(46154,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[46153]) ).
thf(46748,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[46154]) ).
thf(1259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1194,644]) ).
thf(1266,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1259]) ).
thf(26257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1266,12]) ).
thf(21435,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,1935]) ).
thf(21436,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[21435]) ).
thf(21839,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[21436]) ).
thf(5481,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[5426,1968]) ).
thf(5482,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[5481]) ).
thf(5483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[5482:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( M @ ( L @ implies ) @ ( M @ implies ) @ implies ) @ implies ) ))]]) ).
thf(5636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[5483]) ).
thf(8250,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,8194]) ).
thf(8251,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8250]) ).
thf(8293,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8251]) ).
thf(12446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8293]) ).
thf(12447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[12446]) ).
thf(12448,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[12447:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(12503,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[12448]) ).
thf(12511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,12503]) ).
thf(12512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[12511]) ).
thf(12585,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[12512]) ).
thf(8260,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8194]) ).
thf(8261,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8260]) ).
thf(8285,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8261]) ).
thf(48069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8285]) ).
thf(48070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[48069]) ).
thf(48071,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[48070:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(48297,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[48071]) ).
thf(30272,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11556,30075]) ).
thf(30273,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30272]) ).
thf(30385,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30273]) ).
thf(36613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,8038]) ).
thf(36614,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[36613]) ).
thf(36700,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[36614]) ).
thf(14475,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,8710]) ).
thf(14476,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14475]) ).
thf(14521,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[14476]) ).
thf(2640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,1968]) ).
thf(2641,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2640]) ).
thf(2642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2641:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) @ ( K @ implies ) ))]]) ).
thf(2723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2642]) ).
thf(1167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1104,90]) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1167:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1168]) ).
thf(24047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1181,12]) ).
thf(4641,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,1766]) ).
thf(4642,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4641]) ).
thf(4679,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[4642]) ).
thf(1947,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,1935]) ).
thf(1948,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1947]) ).
thf(1967,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= a ),
inference(simp,[status(thm)],[1948]) ).
thf(8197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,8038]) ).
thf(8198,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8197]) ).
thf(8224,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8198]) ).
thf(2585,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,10]) ).
thf(2586,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2585]) ).
thf(2711,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2586]) ).
thf(5339,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( C
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[2711]) ).
thf(5340,plain,
! [B: $i,A: $i] :
( ( b @ ( a @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[5339]) ).
thf(5341,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ not @ implies ) @ ( B @ implies ) )
!= a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[5340]) ).
thf(5342,plain,
! [A: $i] :
( ( b @ ( a @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[5341]) ).
thf(6981,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,1766]) ).
thf(6982,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6981]) ).
thf(7028,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[6982]) ).
thf(30356,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[5426,30075]) ).
thf(30357,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30356]) ).
thf(30397,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30357]) ).
thf(6810,plain,
! [A: $i] :
( ( A
!= ( a @ ( b @ not @ implies ) ) )
| ( A
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[6544]) ).
thf(6811,plain,
( ( a @ ( b @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[6810]) ).
thf(6812,plain,
( ( b != a )
| ( ( b @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[6811]) ).
thf(7078,plain,
( ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[6812]) ).
thf(7079,plain,
b != a,
inference(simp,[status(thm)],[7078]) ).
thf(48121,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8710]) ).
thf(48122,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[48121]) ).
thf(48223,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[48122]) ).
thf(8752,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8710]) ).
thf(8753,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8752]) ).
thf(8816,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8753]) ).
thf(8547,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,8477]) ).
thf(8548,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8547]) ).
thf(8578,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8548]) ).
thf(30310,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,30075]) ).
thf(30311,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30310]) ).
thf(30409,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ not @ not ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30311]) ).
thf(34641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,30409]) ).
thf(34642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[34641]) ).
thf(34643,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ not @ not ) )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[34642:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(34783,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ not @ not ) )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[34643]) ).
thf(34960,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,34783]) ).
thf(34961,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[34960]) ).
thf(35083,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ not ) )
| ( ( B @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[34961]) ).
thf(44453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ not )
!= ( a @ not @ not ) )
| ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ implies ) ) )
| ( ( B @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[35083]) ).
thf(44454,plain,
( ( a @ ( a @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[44453:[bind(A,$thf( a )),bind(B,$thf( a )),bind(C,$thf( a ))]]) ).
thf(36803,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[36700]) ).
thf(30350,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,30075]) ).
thf(30351,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30350]) ).
thf(30410,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30351]) ).
thf(35669,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,8038]) ).
thf(35670,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[35669]) ).
thf(35730,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[35670]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ 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)],[16,14]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[50]) ).
thf(391,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[58,278]) ).
thf(425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
!= ( D @ ( C @ ( B @ ( B @ ifeq ) ) ) ) )
| ( true = C ) ),
inference(paramod_ordered,[status(thm)],[391,12]) ).
thf(426,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[425:[bind(A,$thf( I )),bind(B,$thf( true )),bind(C,$thf( true @ ( true @ ( true @ ( I @ is_a_theorem @ ifeq ) ) ) )),bind(D,$thf( true ))]]) ).
thf(436,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[426]) ).
thf(21944,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,10]) ).
thf(21945,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21944]) ).
thf(22352,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21945]) ).
thf(11945,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,8477]) ).
thf(11946,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11945]) ).
thf(12062,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[11946]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[16,10]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(13059,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,12148]) ).
thf(13060,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[13059]) ).
thf(13061,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[13060:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ))]]) ).
thf(13146,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,13061]) ).
thf(13147,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[13146]) ).
thf(13191,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[13147]) ).
thf(1771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( 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 )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,14]) ).
thf(1772,plain,
! [B: $i,A: $i] :
( ( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[1771:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(52402,plain,
! [B: $i,A: $i] :
( ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(rewrite,[status(thm)],[1772,12]) ).
thf(22298,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8710]) ).
thf(22299,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22298]) ).
thf(22353,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[22299]) ).
thf(8174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1920,8038]) ).
thf(8175,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8174]) ).
thf(8225,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8175]) ).
thf(4631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ 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)],[4518,63]) ).
thf(4632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ 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)],[4631]) ).
thf(4633,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[4632:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( F @ ( F @ ( G @ implies ) @ implies ) ))]]) ).
thf(4692,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[4633]) ).
thf(8313,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,7838]) ).
thf(8314,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8313]) ).
thf(8357,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[8314]) ).
thf(8776,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8710]) ).
thf(8777,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8776]) ).
thf(8806,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8777]) ).
thf(2609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,1935]) ).
thf(2610,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[2609]) ).
thf(2708,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= a ),
inference(simp,[status(thm)],[2610]) ).
thf(29535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8293]) ).
thf(29536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29535]) ).
thf(29537,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[29536:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(30221,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29537]) ).
thf(11885,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,8332]) ).
thf(11886,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11885]) ).
thf(12065,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[11886]) ).
thf(936,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[278,897]) ).
thf(979,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[936]) ).
thf(16712,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[979,12]) ).
thf(51224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[50764,8194]) ).
thf(51225,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[51224]) ).
thf(51437,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[51225]) ).
thf(18367,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( B
!= ( a @ ( b @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[8357]) ).
thf(18368,plain,
! [A: $i] :
( ( a @ ( b @ not @ implies ) @ not @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[18367]) ).
thf(2692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,1766]) ).
thf(2693,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2692]) ).
thf(2709,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[2693]) ).
thf(2744,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( C
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[2709]) ).
thf(2745,plain,
! [B: $i,A: $i] :
( ( b @ not @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2744]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[22,10]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[67]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( ( b @ not )
!= ( A @ not ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(8458,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,8321]) ).
thf(8459,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8458]) ).
thf(8500,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[8459]) ).
thf(30344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[10307,30075]) ).
thf(30345,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30344]) ).
thf(30429,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30345]) ).
thf(21710,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,1766]) ).
thf(21711,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21710]) ).
thf(21822,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[21711]) ).
thf(21903,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) )
!= a )
| ( ( A @ ( A @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[21822]) ).
thf(8418,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,8332]) ).
thf(8419,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8418]) ).
thf(8426,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8419]) ).
thf(17324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true )
| ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[17285,1935]) ).
thf(17325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[17324]) ).
thf(17720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( ( B @ ( A @ implies ) )
!= ( C @ not ) )
| ( B
!= ( D @ not ) ) ),
inference(simp,[status(thm)],[17325]) ).
thf(17779,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(simp,[status(thm)],[17720]) ).
thf(2355,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1920,1998]) ).
thf(2356,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2355]) ).
thf(2357,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( D @ not @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2356:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( M @ ( L @ implies ) @ ( L @ not @ implies ) @ ( G @ implies ) ))]]) ).
thf(2488,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( D @ not @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2357]) ).
thf(35621,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,8285]) ).
thf(35622,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[35621]) ).
thf(35623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[35622:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( I @ ( K @ ( J @ implies ) @ implies ) @ ( I @ implies ) ))]]) ).
thf(35774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[35623]) ).
thf(30322,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,30075]) ).
thf(30323,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30322]) ).
thf(30382,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30323]) ).
thf(10977,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( D @ ( E @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[7033,10754]) ).
thf(10978,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( D @ ( D @ ( E @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[10977]) ).
thf(10979,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[10978:[bind(A,$thf( K @ ( K @ implies ) @ ( H @ implies ) @ ( F @ implies ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( F )),bind(E,$thf( K @ ( K @ implies ) @ ( H @ implies ) ))]]) ).
thf(11201,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[10979]) ).
thf(30320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11201,30075]) ).
thf(30321,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30320]) ).
thf(30395,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30321]) ).
thf(31659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30221]) ).
thf(31660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[31659]) ).
thf(31785,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ not ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[31660]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(2514,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( ( b @ not )
!= ( A @ not ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[154]) ).
thf(2552,plain,
! [A: $i] :
( ( ( A @ not )
!= a )
| ( ( b @ not )
!= ( a @ not ) )
| ( ( a @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( A @ not )
!= b ) ),
inference(simp,[status(thm)],[2514]) ).
thf(12155,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,10625]) ).
thf(12156,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[12155]) ).
thf(12157,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[12156:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ))]]) ).
thf(48086,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,12157]) ).
thf(48087,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[48086]) ).
thf(48192,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[48087]) ).
thf(22065,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8572]) ).
thf(22066,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ) ),
inference(simp,[status(thm)],[22065]) ).
thf(22067,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(pattern_uni,[status(thm)],[22066:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) @ ( G @ implies ) ))]]) ).
thf(22374,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[22067]) ).
thf(1955,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,1935]) ).
thf(1956,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1955]) ).
thf(1963,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[1956]) ).
thf(21969,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,16552]) ).
thf(21970,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[21969]) ).
thf(22348,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[21970]) ).
thf(20633,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11201,1766]) ).
thf(20634,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[20633]) ).
thf(20755,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[20634]) ).
thf(22063,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,7838]) ).
thf(22064,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22063]) ).
thf(22343,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[22064]) ).
thf(24044,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( A
!= ( a @ ( b @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[22343]) ).
thf(24045,plain,
( ( a @ ( b @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[24044]) ).
thf(13116,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,13061]) ).
thf(13117,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[13116]) ).
thf(13183,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[13117]) ).
thf(1803,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( true != true )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[278,113]) ).
thf(1804,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[1803]) ).
thf(1805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[1804:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(1898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[1805]) ).
thf(30348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1898,30075]) ).
thf(30349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30348]) ).
thf(30424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30349]) ).
thf(6490,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,1766]) ).
thf(6491,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6490]) ).
thf(6536,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[6491]) ).
thf(6578,plain,
! [A: $i] :
( ( A != a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[6536]) ).
thf(6579,plain,
( ( b @ not )
!= a ),
inference(simp,[status(thm)],[6578]) ).
thf(29690,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,16541]) ).
thf(29691,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29690]) ).
thf(29692,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[29691:[bind(A,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not )),bind(B,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not ))]]) ).
thf(30438,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,29692]) ).
thf(30439,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30438]) ).
thf(30575,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[30439]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[67]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(3030,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= ( A @ ( B @ implies ) ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[161]) ).
thf(3048,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= ( A @ ( B @ implies ) ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( A
!= ( B @ not ) )
| ( B
!= ( A @ not ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[3030]) ).
thf(3084,plain,
( ( ( b @ ( a @ not @ implies ) )
!= ( a @ ( a @ not @ implies ) ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( a @ not @ not @ ( a @ not @ implies ) ) )
| ( ( a @ not @ not )
!= a )
| ( ( a @ not @ not )
!= b ) ),
inference(simp,[status(thm)],[3048]) ).
thf(8351,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,7838]) ).
thf(8352,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8351]) ).
thf(8367,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[8352]) ).
thf(14410,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,1766]) ).
thf(14411,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14410]) ).
thf(14533,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[14411]) ).
thf(13124,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,13061]) ).
thf(13125,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[13124]) ).
thf(13195,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[13125]) ).
thf(48160,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,13061]) ).
thf(48161,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[48160]) ).
thf(48195,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[48161]) ).
thf(21987,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8321]) ).
thf(21988,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21987]) ).
thf(22357,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[21988]) ).
thf(7893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,1968]) ).
thf(7894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7893]) ).
thf(7895,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( B @ not @ ( C @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[7894:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(8158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( B @ not @ ( C @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[7895]) ).
thf(30276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[17285,30075]) ).
thf(30277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[30276]) ).
thf(30388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( C @ not ) )
| ( B
!= ( D @ not ) ) ),
inference(simp,[status(thm)],[30277]) ).
thf(30435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( a @ not @ not ) )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(simp,[status(thm)],[30388]) ).
thf(37508,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ not @ not )
!= ( B @ not ) )
| ( ( C @ ( B @ implies ) )
!= ( C @ not @ ( A @ implies ) ) )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[30435]) ).
thf(37511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ not )
!= B )
| ( ( C @ not )
!= C )
| ( B != A )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(simp,[status(thm)],[37508]) ).
thf(37514,plain,
! [A: $i] :
( ( ( A @ not )
!= A )
| ( ( A @ not @ ( a @ not @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[37511]) ).
thf(38312,plain,
! [A: $i] :
( ( ( a @ not @ not )
!= ( A @ not ) )
| ( ( A @ not @ ( a @ not @ implies ) )
!= A )
| ( ( A @ not )
!= A ) ),
inference(eqfactor_ordered,[status(thm)],[37514]) ).
thf(38313,plain,
! [A: $i] :
( ( ( a @ not )
!= A )
| ( ( A @ not @ ( a @ not @ implies ) )
!= A )
| ( ( A @ not )
!= A ) ),
inference(simp,[status(thm)],[38312]) ).
thf(38314,plain,
( ( ( a @ not @ not @ ( a @ not @ implies ) )
!= ( a @ not ) )
| ( ( a @ not @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[38313]) ).
thf(36462,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,8194]) ).
thf(36463,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[36462]) ).
thf(36647,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[36463]) ).
thf(12212,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,12157]) ).
thf(12213,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[12212]) ).
thf(12276,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[12213]) ).
thf(17998,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[10307,1968]) ).
thf(17999,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[17998]) ).
thf(18000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[17999:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(18324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[18000]) ).
thf(21680,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,8477]) ).
thf(21681,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[21680]) ).
thf(21829,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[21681]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[22,90]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( L )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( L @ ( K @ implies ) @ ( K @ not @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[98]) ).
thf(2004,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[114,12]) ).
thf(2060,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ 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)],[2004,1286]) ).
thf(2061,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2060:[bind(A,$thf( Q @ ( P @ implies ) @ ( Q @ ( N @ implies ) @ implies ) @ ( N @ ( P @ implies ) @ implies ) )),bind(B,$thf( X )),bind(C,$thf( Y )),bind(D,$thf( Y @ ( X @ implies ) @ ( X @ not @ ( Y @ not @ implies ) @ implies ) )),bind(E,$thf( N )),bind(F,$thf( P )),bind(G,$thf( Q ))]]) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[2061]) ).
thf(3595,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[2124,12]) ).
thf(8178,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3595,8038]) ).
thf(8179,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8178]) ).
thf(8229,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8179]) ).
thf(47586,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,10]) ).
thf(47587,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[47586]) ).
thf(48175,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[47587]) ).
thf(3263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1898,1766]) ).
thf(3264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3263]) ).
thf(3295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[3264]) ).
thf(14392,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,8194]) ).
thf(14393,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14392]) ).
thf(14532,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[14393]) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ 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)],[20,14]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( C )),bind(D,$thf( L @ ( L @ ( M @ implies ) @ implies ) @ ( M @ ( M @ ( L @ implies ) @ implies ) @ implies ) ))]]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[191]) ).
thf(4724,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[215,436]) ).
thf(2321,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,1998]) ).
thf(2322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2321]) ).
thf(2323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2322:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( J @ ( I @ implies ) @ ( I @ not @ implies ) ))]]) ).
thf(2335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2323]) ).
thf(21975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ 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)],[21912,14]) ).
thf(21976,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ ( A @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[21975:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(22411,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ ( A @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[21976]) ).
thf(23069,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[22411,12]) ).
thf(8563,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,8477]) ).
thf(8564,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8563]) ).
thf(8586,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8564]) ).
thf(8527,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,8477]) ).
thf(8528,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8527]) ).
thf(8575,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8528]) ).
thf(9040,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8699]) ).
thf(9041,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9040]) ).
thf(9042,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem )
!= true ),
inference(pattern_uni,[status(thm)],[9041:[bind(A,$thf( b @ ( a @ not @ implies ) @ not @ not @ not @ not )),bind(B,$thf( a @ ( b @ not @ implies ) @ not @ not @ not @ not ))]]) ).
thf(9086,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,9042]) ).
thf(9087,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9086]) ).
thf(9140,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[9087]) ).
thf(52213,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8038]) ).
thf(52214,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[52213]) ).
thf(52302,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[52214]) ).
thf(1925,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,1766]) ).
thf(1926,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1925]) ).
thf(1943,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[1926]) ).
thf(11435,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,1766]) ).
thf(11436,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11435]) ).
thf(11514,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[11436]) ).
thf(11595,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( A @ ( B @ ( B @ implies ) @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[11514]) ).
thf(11596,plain,
! [A: $i] :
( ( a @ ( A @ ( A @ implies ) @ implies ) )
!= ( b @ not ) ),
inference(simp,[status(thm)],[11595]) ).
thf(20842,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ not @ not )
!= ( B @ not ) )
| ( ( C @ ( B @ implies ) )
!= ( C @ not @ ( A @ implies ) ) )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[17791]) ).
thf(20845,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ not )
!= B )
| ( ( C @ not )
!= C )
| ( B != A )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(simp,[status(thm)],[20842]) ).
thf(20848,plain,
! [A: $i] :
( ( ( A @ not )
!= A )
| ( ( A @ not @ ( b @ not @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[20845]) ).
thf(21368,plain,
! [A: $i] :
( ( ( b @ not @ not )
!= ( A @ not ) )
| ( ( A @ not @ ( b @ not @ implies ) )
!= A )
| ( ( A @ not )
!= A ) ),
inference(eqfactor_ordered,[status(thm)],[20848]) ).
thf(21369,plain,
! [A: $i] :
( ( ( b @ not )
!= A )
| ( ( A @ not @ ( b @ not @ implies ) )
!= A )
| ( ( A @ not )
!= A ) ),
inference(simp,[status(thm)],[21368]) ).
thf(21370,plain,
( ( ( b @ not @ not @ ( b @ not @ implies ) )
!= ( b @ not ) )
| ( ( b @ not @ not )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[21369]) ).
thf(21371,plain,
( ( ( b @ not @ not @ ( b @ not @ implies ) )
!= ( b @ not ) )
| ( ( b @ not )
!= b ) ),
inference(simp,[status(thm)],[21370]) ).
thf(21953,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,1935]) ).
thf(21954,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[21953]) ).
thf(22342,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[21954]) ).
thf(1927,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1104,1766]) ).
thf(1928,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1927]) ).
thf(1940,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[1928]) ).
thf(5328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= a )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[1940]) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[20,391]) ).
thf(410,plain,
( ( true @ ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[409:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( K @ ( K @ ( L @ implies ) @ implies ) @ ( L @ ( L @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(527,plain,
( ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[410,12]) ).
thf(29443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ not @ ( D @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,9864]) ).
thf(29444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ not @ ( D @ not @ not @ implies ) @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29443]) ).
thf(29445,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( A @ not @ not @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[29444:[bind(A,$thf( F @ not @ not )),bind(B,$thf( H @ not @ not )),bind(C,$thf( H )),bind(D,$thf( F ))]]) ).
thf(30191,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( A @ not @ not @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29445]) ).
thf(31317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30191]) ).
thf(31318,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[31317]) ).
thf(31423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ not @ not ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[31318]) ).
thf(8258,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,8194]) ).
thf(8259,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8258]) ).
thf(8289,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8259]) ).
thf(47761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8572]) ).
thf(47762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ) ),
inference(simp,[status(thm)],[47761]) ).
thf(47763,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(pattern_uni,[status(thm)],[47762:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(48279,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[47763]) ).
thf(9818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8123]) ).
thf(9819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9818]) ).
thf(9820,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[9819:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(9865,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9820]) ).
thf(8176,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,8038]) ).
thf(8177,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8176]) ).
thf(8221,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8177]) ).
thf(8822,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( B
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[8221]) ).
thf(8823,plain,
! [A: $i] :
( ( a @ not @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8822]) ).
thf(955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[22,897]) ).
thf(984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[955]) ).
thf(18930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[984,12]) ).
thf(25950,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,25847]) ).
thf(25951,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[25950]) ).
thf(26049,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[25951]) ).
thf(20607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11201,8194]) ).
thf(20608,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[20607]) ).
thf(20729,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[20608]) ).
thf(14398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ 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)],[14158,63]) ).
thf(14399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ 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)],[14398]) ).
thf(14400,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ not @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[14399:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ not @ not )),bind(D,$thf( H @ ( G @ implies ) ))]]) ).
thf(14558,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( B @ not @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[14400]) ).
thf(30332,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,30075]) ).
thf(30333,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30332]) ).
thf(30371,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30333]) ).
thf(6480,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)],[6338,63]) ).
thf(6481,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)],[6480]) ).
thf(6482,plain,
! [A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6481:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(8276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[5426,8194]) ).
thf(8277,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8276]) ).
thf(8302,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8277]) ).
thf(57213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[46861,8194]) ).
thf(57214,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[57213]) ).
thf(57465,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[57214]) ).
thf(34686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,30409]) ).
thf(34687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[34686]) ).
thf(34688,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[34687:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(34777,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[34688]) ).
thf(11291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,1968]) ).
thf(11292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[11291]) ).
thf(11293,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[11292:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(11545,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[11293]) ).
thf(22271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,1998]) ).
thf(22272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[22271]) ).
thf(22273,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[22272:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ implies ) @ ( H @ implies ) ))]]) ).
thf(22361,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[22273]) ).
thf(25926,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,25847]) ).
thf(25927,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[25926]) ).
thf(26060,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[25927]) ).
thf(23848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( C @ ( C @ ( D @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[23462,10754]) ).
thf(23849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( C @ ( C @ ( D @ implies ) @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[23848]) ).
thf(23850,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[23849:[bind(A,$thf( J @ ( J @ implies ) @ ( J @ implies ) @ ( E @ implies ) )),bind(B,$thf( J )),bind(C,$thf( E )),bind(D,$thf( J @ ( J @ implies ) @ ( J @ implies ) ))]]) ).
thf(23972,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[23850]) ).
thf(43732,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[23972,1935]) ).
thf(43733,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[43732]) ).
thf(44341,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[43733]) ).
thf(651,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[20,644]) ).
thf(693,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[651]) ).
thf(11597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[693,12]) ).
thf(874,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)],[18,63]) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[874:[bind(A,$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(900,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)],[875]) ).
thf(14595,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)],[900,12]) ).
thf(20565,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ 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)],[11201,14595]) ).
thf(20566,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ 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)],[20565]) ).
thf(20567,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[20566:[bind(A,$thf( Y @ ( X @ implies ) @ ( Y @ ( W @ ( W @ implies ) @ implies ) @ implies ) )),bind(B,$thf( X )),bind(C,$thf( W )),bind(D,$thf( Y @ ( X @ implies ) @ ( Y @ ( W @ ( W @ implies ) @ implies ) @ implies ) )),bind(E,$thf( W @ ( W @ implies ) )),bind(F,$thf( X )),bind(G,$thf( Y ))]]) ).
thf(20780,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[20567]) ).
thf(30306,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[20780,30075]) ).
thf(30307,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30306]) ).
thf(30411,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30307]) ).
thf(8180,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,8038]) ).
thf(8181,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8180]) ).
thf(8219,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8181]) ).
thf(11729,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) )
!= ( b @ not @ not ) )
| ( B
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[8219]) ).
thf(11730,plain,
! [A: $i] :
( ( A @ ( A @ ( a @ not @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[11729]) ).
thf(22122,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8332]) ).
thf(22123,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22122]) ).
thf(22351,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[22123]) ).
thf(928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[20,897]) ).
thf(985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[928]) ).
thf(19744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[985,12]) ).
thf(35661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,8710]) ).
thf(35662,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[35661]) ).
thf(35734,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[35662]) ).
thf(3612,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3595,1935]) ).
thf(3613,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[3612]) ).
thf(3742,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[3613]) ).
thf(52238,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,13061]) ).
thf(52239,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52238]) ).
thf(52314,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[52239]) ).
thf(3029,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( A @ ( B @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[161]) ).
thf(3041,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= b )
| ( ( a @ not )
!= ( A @ not ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( A @ ( B @ implies ) ) )
| ( A
!= ( B @ not ) )
| ( B
!= ( A @ not ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[3029]) ).
thf(3077,plain,
( ( ( a @ not @ not )
!= b )
| ( ( a @ ( b @ not @ implies ) )
!= ( a @ ( a @ not @ implies ) ) )
| ( ( a @ not @ not )
!= a )
| ( ( a @ not @ not )
!= b ) ),
inference(simp,[status(thm)],[3041]) ).
thf(9158,plain,
( ( ( a @ ( b @ not @ implies ) )
!= ( a @ ( a @ not @ implies ) ) )
| ( ( a @ not @ not )
!= a )
| ( ( a @ not @ not )
!= b ) ),
inference(simp,[status(thm)],[3077]) ).
thf(36603,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,8710]) ).
thf(36604,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[36603]) ).
thf(36676,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[36604]) ).
thf(14187,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,1935]) ).
thf(14188,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[14187]) ).
thf(14501,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[14188]) ).
thf(1492,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( A @ not )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1269]) ).
thf(1579,plain,
! [B: $i,A: $i] :
( ( B != a )
| ( A
!= ( b @ not ) )
| ( ( A @ not )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[1492]) ).
thf(1580,plain,
( ( b @ ( a @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[1579]) ).
thf(30063,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8710]) ).
thf(30064,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30063]) ).
thf(30167,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30064]) ).
thf(31026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,30382]) ).
thf(31027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[31026]) ).
thf(31028,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[31027:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(31115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[31028]) ).
thf(30698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,30171]) ).
thf(30699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30698]) ).
thf(30727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30699]) ).
thf(1931,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,1766]) ).
thf(1932,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1931]) ).
thf(1942,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[1932]) ).
thf(2147,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( A @ not )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[1942]) ).
thf(8529,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3595,8477]) ).
thf(8530,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8529]) ).
thf(8582,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8530]) ).
thf(50829,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[50764,1935]) ).
thf(50830,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[50829]) ).
thf(51475,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[50830]) ).
thf(18173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[10307,1766]) ).
thf(18174,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[18173]) ).
thf(18300,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[18174]) ).
thf(2149,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( A != b ) ),
inference(simp,[status(thm)],[2147]) ).
thf(2150,plain,
! [A: $i] :
( ( A @ ( b @ implies ) )
!= a ),
inference(simp,[status(thm)],[2149]) ).
thf(22005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,9865]) ).
thf(22006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[22005]) ).
thf(22346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[22006]) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1194,63]) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ 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)],[1250]) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( A @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1251:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F @ not )),bind(D,$thf( G @ ( F @ implies ) ))]]) ).
thf(1272,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ( true @ ( A @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1252]) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1194,1272]) ).
thf(1474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ not ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1436]) ).
thf(41099,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ not ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1474,12]) ).
thf(8683,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8466]) ).
thf(8684,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8683]) ).
thf(8736,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[8684]) ).
thf(16616,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,16552]) ).
thf(16617,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[16616]) ).
thf(16704,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[16617]) ).
thf(21736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,8285]) ).
thf(21737,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[21736]) ).
thf(21738,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[21737:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ ( I @ implies ) @ ( I @ ( I @ implies ) @ implies ) ))]]) ).
thf(21890,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[21738]) ).
thf(47970,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8194]) ).
thf(47971,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[47970]) ).
thf(48204,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[47971]) ).
thf(27721,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( B
!= ( b @ ( a @ not @ implies ) @ not @ not ) ) ),
inference(simp,[status(thm)],[8500]) ).
thf(27722,plain,
! [A: $i] :
( ( b @ ( a @ not @ implies ) @ not @ not @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[27721]) ).
thf(8625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8285]) ).
thf(8626,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8625]) ).
thf(8627,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[8626:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(8672,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8627]) ).
thf(5567,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[5426,1766]) ).
thf(5568,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[5567]) ).
thf(5610,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[5568]) ).
thf(5654,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[5610]) ).
thf(5655,plain,
! [B: $i,A: $i] :
( ( a @ ( B @ ( A @ implies ) @ ( B @ implies ) @ implies ) )
!= ( b @ not ) ),
inference(simp,[status(thm)],[5654]) ).
thf(20454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11201,1968]) ).
thf(20455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[20454]) ).
thf(20456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[20455:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( M @ ( M @ implies ) @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(20819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[20456]) ).
thf(12220,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,12157]) ).
thf(12221,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[12220]) ).
thf(12279,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[12221]) ).
thf(8450,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8321]) ).
thf(8451,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8450]) ).
thf(8503,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[8451]) ).
thf(8205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,8038]) ).
thf(8206,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8205]) ).
thf(8226,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8206]) ).
thf(8388,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[7817,8332]) ).
thf(8389,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8388]) ).
thf(8423,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not @ ( B @ not @ implies ) @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[8389]) ).
thf(46907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8423]) ).
thf(46908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[46907]) ).
thf(46909,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[46908:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(47087,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[46909]) ).
thf(8264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,8194]) ).
thf(8265,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8264]) ).
thf(8287,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8265]) ).
thf(10609,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,9033]) ).
thf(10610,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[10609]) ).
thf(10676,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[10610]) ).
thf(27735,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) )
| ( A
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not ) ) ),
inference(simp,[status(thm)],[10676]) ).
thf(27736,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[27735]) ).
thf(8541,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,8477]) ).
thf(8542,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8541]) ).
thf(8577,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8542]) ).
thf(1332,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ 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)],[22,1286]) ).
thf(1368,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ 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)],[1332]) ).
thf(32523,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( D @ ( E @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1368,12]) ).
thf(31056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[23462,30382]) ).
thf(31057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[31056]) ).
thf(31058,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[31057:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( J @ implies ) @ ( J @ implies ) @ ( E @ implies ) ))]]) ).
thf(31125,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[31058]) ).
thf(8236,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8194]) ).
thf(8237,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8236]) ).
thf(8297,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8237]) ).
thf(2102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2004,1766]) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2102]) ).
thf(2115,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[2103]) ).
thf(44037,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[23972,30075]) ).
thf(44038,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[44037]) ).
thf(44358,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[44038]) ).
thf(30340,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,30075]) ).
thf(30341,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30340]) ).
thf(30430,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30341]) ).
thf(8374,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8332]) ).
thf(8375,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8374]) ).
thf(8435,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8375]) ).
thf(8764,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,8710]) ).
thf(8765,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8764]) ).
thf(8800,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8765]) ).
thf(8168,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8038]) ).
thf(8169,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8168]) ).
thf(8216,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8169]) ).
thf(8445,plain,
! [A: $i] :
( ( A
!= ( b @ not @ not ) )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[8216]) ).
thf(8446,plain,
( ( b @ not @ not )
!= ( a @ not ) ),
inference(simp,[status(thm)],[8445]) ).
thf(30364,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,30075]) ).
thf(30365,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30364]) ).
thf(30391,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30365]) ).
thf(9112,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,9042]) ).
thf(9113,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9112]) ).
thf(9145,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[9113]) ).
thf(14125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,13950]) ).
thf(14126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14125]) ).
thf(14152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( D @ not @ not ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14126]) ).
thf(51820,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,7838]) ).
thf(51821,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[51820]) ).
thf(52321,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[51821]) ).
thf(2750,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( b != A )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(2801,plain,
! [A: $i] :
( ( ( A @ not )
!= a )
| ( ( b @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( A @ not )
!= b )
| ( ( b @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[2750]) ).
thf(16751,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true )
| ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[16712,1935]) ).
thf(16752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[16751]) ).
thf(17149,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) )
!= a )
| ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= ( D @ not ) )
| ( A
!= ( E @ not ) ) ),
inference(simp,[status(thm)],[16752]) ).
thf(17274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not ) ) ),
inference(simp,[status(thm)],[17149]) ).
thf(8190,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,8038]) ).
thf(8191,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8190]) ).
thf(8222,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8191]) ).
thf(9016,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[8222]) ).
thf(47855,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8332]) ).
thf(47856,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[47855]) ).
thf(48194,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[47856]) ).
thf(8270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1898,8194]) ).
thf(8271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8270]) ).
thf(8282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8271]) ).
thf(22053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8672]) ).
thf(22054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[22053]) ).
thf(22055,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[22054:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ implies ) @ ( H @ implies ) ))]]) ).
thf(22368,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[22055]) ).
thf(21604,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,8332]) ).
thf(21605,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[21604]) ).
thf(21797,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[21605]) ).
thf(2324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,1998]) ).
thf(2325,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[2324]) ).
thf(2326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( D @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[2325:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(2337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( D @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[2326]) ).
thf(2995,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,2337]) ).
thf(2996,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[2995]) ).
thf(2997,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( E @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[2996:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( G @ implies ) ))]]) ).
thf(3018,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( E @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[2997]) ).
thf(52044,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8194]) ).
thf(52045,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52044]) ).
thf(52293,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[52045]) ).
thf(52142,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,1998]) ).
thf(52143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[52142]) ).
thf(52144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[52143:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( J @ ( J @ implies ) @ ( H @ not @ implies ) ))]]) ).
thf(52378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[52144]) ).
thf(30296,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,30075]) ).
thf(30297,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30296]) ).
thf(30403,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30297]) ).
thf(21148,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11556,8194]) ).
thf(21149,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[21148]) ).
thf(21267,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[21149]) ).
thf(16628,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,16552]) ).
thf(16629,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[16628]) ).
thf(16700,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[16629]) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ 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)],[20,63]) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[818:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( L @ ( L @ ( M @ implies ) @ implies ) @ ( M @ ( M @ ( L @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[819]) ).
thf(15047,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[903,12]) ).
thf(51689,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,16552]) ).
thf(51690,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[51689]) ).
thf(52286,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[51690]) ).
thf(18149,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[10307,8194]) ).
thf(18150,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[18149]) ).
thf(18289,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[18150]) ).
thf(30015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8285]) ).
thf(30016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30015]) ).
thf(30017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[30016:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(30210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30017]) ).
thf(10682,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,10634]) ).
thf(10683,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10682]) ).
thf(10752,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[10683]) ).
thf(47748,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,7838]) ).
thf(47749,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[47748]) ).
thf(48208,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[47749]) ).
thf(1588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ 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)],[20,1581]) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1588:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( K @ ( K @ ( L @ implies ) @ implies ) )),bind(D,$thf( L @ ( L @ ( K @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(1686,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1589]) ).
thf(49945,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1686,12]) ).
thf(51807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,1968]) ).
thf(51808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[51807]) ).
thf(51809,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[51808:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( I @ implies ) @ ( G @ not @ implies ) ))]]) ).
thf(52360,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[51809]) ).
thf(1854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,113]) ).
thf(1855,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1854]) ).
thf(1856,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[1855:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(1891,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[1856]) ).
thf(55732,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[1891,1766]) ).
thf(55733,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[55732]) ).
thf(55956,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[55733]) ).
thf(1451,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 @ not @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[18,1272]) ).
thf(1469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ not ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1451]) ).
thf(38317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ not ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1469,12]) ).
thf(1949,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,1935]) ).
thf(1950,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1949]) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1950]) ).
thf(30334,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[12978,30075]) ).
thf(30335,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30334]) ).
thf(30379,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30335]) ).
thf(1431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[22,1272]) ).
thf(1475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ not ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1431]) ).
thf(41927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ not ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1475,12]) ).
thf(41985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ not ) ) ),
inference(paramod_ordered,[status(thm)],[41927,10]) ).
thf(41986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ not ) ) ),
inference(simp,[status(thm)],[41985]) ).
thf(41987,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[41986:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( b @ ( a @ not @ implies ) )),bind(D,$thf( a @ ( b @ not @ implies ) ))]]) ).
thf(52120,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,1766]) ).
thf(52121,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[52120]) ).
thf(52264,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[52121]) ).
thf(52401,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) )
!= a )
| ( ( A @ not )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[52264]) ).
thf(6815,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,10]) ).
thf(6816,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6815]) ).
thf(7027,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[6816]) ).
thf(8519,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8477]) ).
thf(8520,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8519]) ).
thf(8576,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8520]) ).
thf(11609,plain,
! [A: $i] :
( ( A
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( A
!= ( b @ ( a @ not @ implies ) @ not @ not ) ) ),
inference(simp,[status(thm)],[8503]) ).
thf(11610,plain,
( ( a @ ( b @ not @ implies ) @ not @ not )
!= ( b @ ( a @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[11609]) ).
thf(8782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,8710]) ).
thf(8783,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8782]) ).
thf(8803,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8783]) ).
thf(690,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[22,644]) ).
thf(694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[690]) ).
thf(11606,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( D @ not @ ( E @ not @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[694,12]) ).
thf(22235,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,1766]) ).
thf(22236,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22235]) ).
thf(22330,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[22236]) ).
thf(22431,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) )
!= a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[22330]) ).
thf(22432,plain,
( ( b @ not @ ( b @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[22431]) ).
thf(30104,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,13061]) ).
thf(30105,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30104]) ).
thf(30150,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30105]) ).
thf(35461,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,30075]) ).
thf(35462,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[35461]) ).
thf(35756,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[35462]) ).
thf(36466,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,8477]) ).
thf(36467,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[36466]) ).
thf(36682,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[36467]) ).
thf(16646,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,16552]) ).
thf(16647,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[16646]) ).
thf(16690,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[16647]) ).
thf(23899,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[23462,8038]) ).
thf(23900,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23899]) ).
thf(23942,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[23900]) ).
thf(8274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4683,8194]) ).
thf(8275,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8274]) ).
thf(8294,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8275]) ).
thf(14322,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,8332]) ).
thf(14323,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14322]) ).
thf(14509,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[14323]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( B
!= ( b @ not ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(173,plain,
( ( b @ not @ not @ ( a @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(1420,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1104,1272]) ).
thf(1472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( D @ not ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1420]) ).
thf(39119,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( D @ not ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1472,12]) ).
thf(8380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1920,8332]) ).
thf(8381,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8380]) ).
thf(8439,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8381]) ).
thf(9017,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,8699]) ).
thf(9018,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9017]) ).
thf(9081,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ implies ) ) ),
inference(simp,[status(thm)],[9018]) ).
thf(10540,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8672]) ).
thf(10541,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10540]) ).
thf(10542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( D @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[10541:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(10597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( D @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10542]) ).
thf(6969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ 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)],[6554,63]) ).
thf(6970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ 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)],[6969]) ).
thf(6971,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[6970:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(7052,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[6971]) ).
thf(1107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ 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)],[1104,14]) ).
thf(1108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1107:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(1185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1108]) ).
thf(24822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1185,12]) ).
thf(8384,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3595,8332]) ).
thf(8385,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8384]) ).
thf(8422,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8385]) ).
thf(1395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[20,1272]) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ not ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1395]) ).
thf(40289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ not ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1473,12]) ).
thf(22205,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8477]) ).
thf(22206,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22205]) ).
thf(22358,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[22206]) ).
thf(51597,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( A
!= ( a @ ( b @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[48208]) ).
thf(51598,plain,
! [A: $i] :
( ( a @ ( b @ not @ implies ) @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[51597]) ).
thf(22274,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,12157]) ).
thf(22275,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22274]) ).
thf(22332,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[22275]) ).
thf(9108,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,9042]) ).
thf(9109,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9108]) ).
thf(9137,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9109]) ).
thf(1986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,1968]) ).
thf(1987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1986]) ).
thf(1988,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1987:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( H @ implies ) @ ( H @ not @ implies ) ))]]) ).
thf(1996,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1988]) ).
thf(37490,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( A
!= ( b @ ( a @ not @ implies ) @ not @ not ) ) ),
inference(simp,[status(thm)],[22357]) ).
thf(37491,plain,
( ( b @ ( a @ not @ implies ) @ not @ not @ ( b @ ( a @ not @ implies ) @ not @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[37490]) ).
thf(14268,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,7838]) ).
thf(14269,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14268]) ).
thf(14536,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[14269]) ).
thf(28351,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ not @ not )
!= ( a @ ( b @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[14536]) ).
thf(28352,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ not )
!= ( a @ ( b @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[28351]) ).
thf(28354,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ not @ implies ) @ not )
!= ( B @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not )
!= ( a @ ( b @ not @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[28352]) ).
thf(28355,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ not @ implies ) @ not )
!= ( B @ not ) )
| ( B != a )
| ( A
!= ( b @ not ) )
| ( ( B @ not )
!= ( a @ ( b @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[28354]) ).
thf(28358,plain,
( ( ( b @ ( a @ not @ implies ) @ not )
!= ( a @ not ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[28355]) ).
thf(29900,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8194]) ).
thf(29901,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29900]) ).
thf(30114,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29901]) ).
thf(30606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30171]) ).
thf(30607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30606]) ).
thf(30765,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30607]) ).
thf(970,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ not @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[18,897]) ).
thf(983,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[970]) ).
thf(18371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[983,12]) ).
thf(29484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8430]) ).
thf(29485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29484]) ).
thf(29486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[29485:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(30207,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29486]) ).
thf(51699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,30382]) ).
thf(51700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[51699]) ).
thf(51701,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[51700:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( I @ implies ) @ ( G @ not @ implies ) ))]]) ).
thf(52396,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[51701]) ).
thf(22056,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,1968]) ).
thf(22057,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[22056]) ).
thf(22058,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[22057:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) @ ( G @ implies ) ))]]) ).
thf(22371,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[22058]) ).
thf(1977,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1104,1968]) ).
thf(1978,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1977]) ).
thf(1979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1978:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1979]) ).
thf(48042,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,1766]) ).
thf(48043,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[48042]) ).
thf(48213,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[48043]) ).
thf(35416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,8332]) ).
thf(35417,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[35416]) ).
thf(35760,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[35417]) ).
thf(14592,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ not @ not )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[14533]) ).
thf(14593,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ not )
!= b ) ),
inference(simp,[status(thm)],[14592]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(8199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,8038]) ).
thf(8200,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8199]) ).
thf(8215,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8200]) ).
thf(2664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( true != true )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[2584,113]) ).
thf(2665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[2664]) ).
thf(2666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[2665:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) @ ( K @ implies ) ))]]) ).
thf(2729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[2666]) ).
thf(43644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ not )
!= ( b @ not @ not ) )
| ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ implies ) ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[31785]) ).
thf(43645,plain,
( ( b @ ( b @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[43644:[bind(A,$thf( b )),bind(B,$thf( b )),bind(C,$thf( b ))]]) ).
thf(14182,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,10]) ).
thf(14183,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14182]) ).
thf(14518,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14183]) ).
thf(21378,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not @ not )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[14518]) ).
thf(21379,plain,
! [B: $i,A: $i] :
( ( B != a )
| ( A
!= ( b @ not ) )
| ( ( B @ not @ not )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[21378]) ).
thf(21380,plain,
( ( b @ ( a @ not @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[21379]) ).
thf(8248,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,8194]) ).
thf(8249,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8248]) ).
thf(8290,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8249]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( A
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(34,plain,
! [A: $i] :
( ( b @ ( a @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(23067,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( A
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[22352]) ).
thf(23068,plain,
( ( b @ ( a @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[23067]) ).
thf(29600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8123]) ).
thf(29601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29600]) ).
thf(29602,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[29601:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(30249,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( ( A @ not @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29602]) ).
thf(1650,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)],[18,1581]) ).
thf(1651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1650:[bind(A,$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(1684,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)],[1651]) ).
thf(48321,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)],[1684,12]) ).
thf(29659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,1968]) ).
thf(29660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29659]) ).
thf(29661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[29660:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(30261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29661]) ).
thf(31997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30261]) ).
thf(31998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[31997]) ).
thf(32120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[31998]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( A != b )
| ( B
!= ( a @ not ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(176,plain,
( ( ( a @ not @ not @ ( b @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( a @ not @ not )
!= b )
| ( ( b @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(1599,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ 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)],[278,1581]) ).
thf(1600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1599:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(1676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1600]) ).
thf(44496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1676,12]) ).
thf(52197,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8710]) ).
thf(52198,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52197]) ).
thf(52326,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[52198]) ).
thf(47528,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( A
!= ( b @ ( a @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[47517]) ).
thf(47529,plain,
! [A: $i] :
( ( A @ ( b @ ( a @ not @ implies ) @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[47528]) ).
thf(8525,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1920,8477]) ).
thf(8526,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8525]) ).
thf(8580,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8526]) ).
thf(9156,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( A != a ) ),
inference(simp,[status(thm)],[9016]) ).
thf(9157,plain,
! [A: $i] :
( ( A @ ( a @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[9156]) ).
thf(8788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,8710]) ).
thf(8789,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8788]) ).
thf(8809,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8789]) ).
thf(25240,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( A
!= ( a @ ( b @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[25228]) ).
thf(25241,plain,
! [A: $i] :
( ( A @ ( a @ ( b @ not @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[25240]) ).
thf(35529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,8194]) ).
thf(35530,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[35529]) ).
thf(35747,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[35530]) ).
thf(22261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8285]) ).
thf(22262,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[22261]) ).
thf(22263,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[22262:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) @ ( G @ implies ) ))]]) ).
thf(22419,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[22263]) ).
thf(7645,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ 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)],[7033,63]) ).
thf(7646,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ 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)],[7645]) ).
thf(7647,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[7646:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( I )),bind(D,$thf( A )),bind(E,$thf( I @ ( I @ implies ) @ ( F @ implies ) ))]]) ).
thf(7751,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[7647]) ).
thf(53734,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[52302]) ).
thf(18926,plain,
! [A: $i] :
( ( A
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) )
| ( A
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not ) ) ),
inference(simp,[status(thm)],[9081]) ).
thf(18927,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not @ not )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[18926]) ).
thf(22207,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8194]) ).
thf(22208,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22207]) ).
thf(22340,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[22208]) ).
thf(8531,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,8477]) ).
thf(8532,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8531]) ).
thf(8581,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8532]) ).
thf(1945,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[20,1935]) ).
thf(1946,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1945]) ).
thf(1965,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[1946]) ).
thf(834,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ 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)],[278,63]) ).
thf(835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[835]) ).
thf(13953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[896,12]) ).
thf(28728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[20780,8194]) ).
thf(28729,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[28728]) ).
thf(28924,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[28729]) ).
thf(52164,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,12157]) ).
thf(52165,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52164]) ).
thf(52333,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[52165]) ).
thf(50760,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( A
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[48175]) ).
thf(50761,plain,
! [A: $i] :
( ( b @ ( a @ not @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[50760]) ).
thf(3703,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3595,1766]) ).
thf(3704,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3703]) ).
thf(3737,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[3704]) ).
thf(3783,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( A @ not @ ( B @ not @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[3737]) ).
thf(47919,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,9042]) ).
thf(47920,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[47919]) ).
thf(48180,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[47920]) ).
thf(47596,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,1935]) ).
thf(47597,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[47596]) ).
thf(48193,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[47597]) ).
thf(8240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1104,8194]) ).
thf(8241,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8240]) ).
thf(8301,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8241]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[18,10]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[68]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(30969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,30382]) ).
thf(30970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30969]) ).
thf(30971,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[30970:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(31146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30971]) ).
thf(36247,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,1968]) ).
thf(36248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[36247]) ).
thf(36249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[36248:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( K @ implies ) @ ( I @ ( H @ implies ) @ implies ) ))]]) ).
thf(36751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[36249]) ).
thf(4836,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) )
!= a )
| ( B
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[4679]) ).
thf(4837,plain,
! [A: $i] :
( ( A @ ( A @ ( b @ not @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[4836]) ).
thf(8404,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,8332]) ).
thf(8405,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8404]) ).
thf(8432,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8405]) ).
thf(10332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,9865]) ).
thf(10333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10332]) ).
thf(10393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( D @ not ) )
| ( ( C @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10333]) ).
thf(8242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1920,8194]) ).
thf(8243,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8242]) ).
thf(8286,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8243]) ).
thf(14447,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,12157]) ).
thf(14448,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14447]) ).
thf(14517,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[14448]) ).
thf(2683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ 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)],[2584,63]) ).
thf(2684,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ 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)],[2683]) ).
thf(2685,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2684:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( I )),bind(E,$thf( I @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(2738,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[2685]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[20,90]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( C )),bind(D,$thf( L @ ( L @ ( M @ implies ) @ implies ) @ ( M @ ( M @ ( L @ implies ) @ implies ) @ implies ) ))]]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[203]) ).
thf(4149,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[212,12]) ).
thf(30776,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30249]) ).
thf(30777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30776]) ).
thf(30921,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not @ not ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30777]) ).
thf(1971,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,1968]) ).
thf(1972,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1971]) ).
thf(1973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1972:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(1997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1973]) ).
thf(8266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,8194]) ).
thf(8267,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8266]) ).
thf(8300,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8267]) ).
thf(8796,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,8710]) ).
thf(8797,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8796]) ).
thf(8799,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8797]) ).
thf(29654,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,10634]) ).
thf(29655,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29654]) ).
thf(30147,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29655]) ).
thf(9094,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,9042]) ).
thf(9095,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9094]) ).
thf(9146,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[9095]) ).
thf(30298,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,30075]) ).
thf(30299,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30298]) ).
thf(30423,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30299]) ).
thf(8396,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,8332]) ).
thf(8397,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8396]) ).
thf(8436,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8397]) ).
thf(6505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,1998]) ).
thf(6506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[6505]) ).
thf(6507,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[6506:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(6572,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[6507]) ).
thf(48135,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8038]) ).
thf(48136,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[48135]) ).
thf(48220,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[48136]) ).
thf(56452,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[20755]) ).
thf(56453,plain,
! [B: $i,A: $i] :
( ( a @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) )
!= ( b @ not ) ),
inference(simp,[status(thm)],[56452]) ).
thf(103,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 @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[18,90]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$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(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[104]) ).
thf(2151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[116,12]) ).
thf(46968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8423]) ).
thf(46969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[46968]) ).
thf(46970,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[46969:[bind(A,$thf( E @ not )),bind(B,$thf( F @ not )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(47096,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[46970]) ).
thf(10324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,9865]) ).
thf(10325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10324]) ).
thf(10385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10325]) ).
thf(291,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ 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)],[278,14]) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ implies ) @ ( C @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( A )),bind(E,$thf( I @ ( H @ implies ) @ ( I @ implies ) ))]]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ implies ) @ ( C @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[292]) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ implies ) @ ( C @ implies ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[320,12]) ).
thf(4527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,1998]) ).
thf(4528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[4527]) ).
thf(4529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ implies ) @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[4528:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ ( I @ ( J @ implies ) @ implies ) @ ( J @ implies ) ))]]) ).
thf(4699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ implies ) @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[4529]) ).
thf(21777,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,8038]) ).
thf(21778,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21777]) ).
thf(21837,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[21778]) ).
thf(23453,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ ( A @ implies ) )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[21837]) ).
thf(30302,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,30075]) ).
thf(30303,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30302]) ).
thf(30412,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30303]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[149]) ).
thf(230,plain,
! [A: $i] :
( ( ( a @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( A @ not )
!= b ) ),
inference(simp,[status(thm)],[227]) ).
thf(11496,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,8038]) ).
thf(11497,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11496]) ).
thf(11529,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[11497]) ).
thf(13203,plain,
! [B: $i,A: $i] :
( ( A
!= ( b @ not @ not ) )
| ( ( A @ ( B @ ( B @ implies ) @ implies ) )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[11529]) ).
thf(13204,plain,
! [A: $i] :
( ( b @ not @ not @ ( A @ ( A @ implies ) @ implies ) )
!= ( a @ not ) ),
inference(simp,[status(thm)],[13203]) ).
thf(16380,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) )
| ( A
!= ( a @ ( b @ not @ implies ) @ not @ not @ not ) ) ),
inference(simp,[status(thm)],[8736]) ).
thf(16381,plain,
( ( a @ ( b @ not @ implies ) @ not @ not @ not )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[16380]) ).
thf(51829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8572]) ).
thf(51830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ) ),
inference(simp,[status(thm)],[51829]) ).
thf(51831,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(pattern_uni,[status(thm)],[51830:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( I @ implies ) @ ( G @ not @ implies ) ))]]) ).
thf(52362,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[51831]) ).
thf(4519,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,10]) ).
thf(4520,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[4519]) ).
thf(4678,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[4520]) ).
thf(5656,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( B
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[4678]) ).
thf(5657,plain,
! [A: $i] :
( ( A @ ( A @ ( b @ ( a @ not @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[5656]) ).
thf(35225,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,30382]) ).
thf(35226,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[35225]) ).
thf(35227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[35226:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( I @ ( K @ ( J @ implies ) @ implies ) @ ( I @ implies ) ))]]) ).
thf(35817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[35227]) ).
thf(11965,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,1766]) ).
thf(11966,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[11965]) ).
thf(12049,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[11966]) ).
thf(36030,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) )
!= ( b @ not @ not ) )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[35730]) ).
thf(36031,plain,
! [B: $i,A: $i] :
( ( a @ not @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[36030]) ).
thf(11494,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,8710]) ).
thf(11495,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11494]) ).
thf(11519,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[11495]) ).
thf(30270,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30075]) ).
thf(30271,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30270]) ).
thf(30380,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30271]) ).
thf(21962,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,8806]) ).
thf(21963,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ) ),
inference(simp,[status(thm)],[21962]) ).
thf(21964,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(pattern_uni,[status(thm)],[21963:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) @ ( G @ implies ) ))]]) ).
thf(22407,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[21964]) ).
thf(12240,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,12157]) ).
thf(12241,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[12240]) ).
thf(12274,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[12241]) ).
thf(16676,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,16552]) ).
thf(16677,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[16676]) ).
thf(16703,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[16677]) ).
thf(15704,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8158]) ).
thf(15705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[15704]) ).
thf(15706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ implies ) @ ( A @ implies ) )
!= a )
| ( ( C @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[15705:[bind(A,$thf( F @ not )),bind(B,$thf( G @ not )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(15768,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ implies ) @ ( A @ implies ) )
!= a )
| ( ( C @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[15706]) ).
thf(16277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,15768]) ).
thf(16278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[16277]) ).
thf(16366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( D @ not ) )
| ( ( C @ ( D @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[16278]) ).
thf(47624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,30382]) ).
thf(47625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[47624]) ).
thf(47626,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[47625:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(48240,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[47626]) ).
thf(10350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,9865]) ).
thf(10351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10350]) ).
thf(10375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( D @ not ) )
| ( ( C @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10351]) ).
thf(51657,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,10]) ).
thf(51658,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[51657]) ).
thf(52267,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[51658]) ).
thf(53758,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( A @ not )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[52267]) ).
thf(14071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,13950]) ).
thf(14072,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14071]) ).
thf(14137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( C @ not @ not ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14072]) ).
thf(11459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,8285]) ).
thf(11460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[11459]) ).
thf(11461,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[11460:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(11558,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[11461]) ).
thf(8555,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,8477]) ).
thf(8556,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8555]) ).
thf(8573,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8556]) ).
thf(14477,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,8038]) ).
thf(14478,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[14477]) ).
thf(14499,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[14478]) ).
thf(14984,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ not @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[14499]) ).
thf(14985,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[14984]) ).
thf(20344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11201,1935]) ).
thf(20345,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[20344]) ).
thf(20731,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[20345]) ).
thf(8631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,8285]) ).
thf(8632,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[8631]) ).
thf(8633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[8632:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( K @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(8676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8633]) ).
thf(30018,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,12157]) ).
thf(30019,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30018]) ).
thf(30159,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[30019]) ).
thf(8280,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,8194]) ).
thf(8281,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8280]) ).
thf(8291,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8281]) ).
thf(21682,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,8194]) ).
thf(21683,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[21682]) ).
thf(21814,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[21683]) ).
thf(1631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ 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)],[22,1581]) ).
thf(1632,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1631:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( K @ ( J @ implies ) )),bind(D,$thf( J @ not @ ( K @ not @ implies ) )),bind(E,$thf( E ))]]) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1632]) ).
thf(45304,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1677,12]) ).
thf(245,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[20,234]) ).
thf(267,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[245]) ).
thf(5057,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[267,12]) ).
thf(35527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,8477]) ).
thf(35528,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[35527]) ).
thf(35721,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[35528]) ).
thf(8386,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,8332]) ).
thf(8387,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8386]) ).
thf(8440,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8387]) ).
thf(6393,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,1968]) ).
thf(6394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[6393]) ).
thf(6395,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[6394:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(6574,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[6395]) ).
thf(12308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( C
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[8226]) ).
thf(12309,plain,
! [B: $i,A: $i] :
( ( a @ not @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[12308]) ).
thf(30996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,30382]) ).
thf(30997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[30996]) ).
thf(30998,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[30997:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ ( I @ implies ) @ implies ) ))]]) ).
thf(31105,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30998]) ).
thf(30290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7730,30075]) ).
thf(30291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30290]) ).
thf(30419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30291]) ).
thf(287,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ 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)],[278,14]) ).
thf(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[288]) ).
thf(5661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[318,12]) ).
thf(1879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,1272]) ).
thf(1890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ is_a_theorem )
!= true )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1879]) ).
thf(53775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ is_a_theorem )
!= true )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1890,12]) ).
thf(14491,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,13061]) ).
thf(14492,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14491]) ).
thf(14493,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[14492]) ).
thf(55878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[1891,8038]) ).
thf(55879,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[55878]) ).
thf(55940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[55879]) ).
thf(10704,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,10634]) ).
thf(10705,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10704]) ).
thf(10749,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10705]) ).
thf(6348,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,1935]) ).
thf(6349,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[6348]) ).
thf(6542,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[6349]) ).
thf(8774,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,8710]) ).
thf(8775,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8774]) ).
thf(8804,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8775]) ).
thf(10346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,9865]) ).
thf(10347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10346]) ).
thf(10384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( D @ not ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[10347]) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ 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)],[20,14]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( B @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( K @ ( K @ ( J @ implies ) @ implies ) )),bind(D,$thf( J @ ( J @ ( K @ implies ) @ implies ) ))]]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( B @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[193]) ).
thf(3975,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( B @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[211,12]) ).
thf(14601,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ 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)],[1104,14595]) ).
thf(14602,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ 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)],[14601]) ).
thf(14603,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[14602:[bind(A,$thf( T )),bind(B,$thf( R )),bind(C,$thf( U @ ( T @ implies ) @ ( U @ ( R @ implies ) @ implies ) )),bind(D,$thf( U @ ( T @ implies ) @ ( U @ ( R @ implies ) @ implies ) @ ( R @ implies ) )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( U ))]]) ).
thf(14691,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[14603]) ).
thf(30368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14691,30075]) ).
thf(30369,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30368]) ).
thf(30384,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30369]) ).
thf(36349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,8332]) ).
thf(36350,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[36349]) ).
thf(36691,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[36350]) ).
thf(17722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( C @ not ) )
| ( B
!= ( D @ not ) ) ),
inference(simp,[status(thm)],[17325]) ).
thf(17781,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= a )
| ( ( C @ not @ ( A @ implies ) )
!= ( B @ not ) ) ),
inference(simp,[status(thm)],[17722]) ).
thf(52048,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8477]) ).
thf(52049,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[52048]) ).
thf(52248,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[52049]) ).
thf(35842,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) )
!= a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[35735]) ).
thf(35843,plain,
! [B: $i,A: $i] :
( ( b @ not @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[35842]) ).
thf(30314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2729,30075]) ).
thf(30315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30314]) ).
thf(30393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30315]) ).
thf(248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[22,234]) ).
thf(265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[248]) ).
thf(5047,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[265,12]) ).
thf(1953,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[22,1935]) ).
thf(1954,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1953]) ).
thf(1961,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[1954]) ).
thf(11469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,1998]) ).
thf(11470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[11469]) ).
thf(11471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( D @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[11470:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(11562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( D @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[11471]) ).
thf(1398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[329,1272]) ).
thf(1468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1398]) ).
thf(37515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( C @ not ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1468,12]) ).
thf(10370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,9865]) ).
thf(10371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( C @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10370]) ).
thf(10392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( D @ not ) )
| ( ( C @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[10371]) ).
thf(36133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,30382]) ).
thf(36134,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[36133]) ).
thf(36135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[36134:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( K @ implies ) @ ( I @ ( H @ implies ) @ implies ) ))]]) ).
thf(36719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[36135]) ).
thf(11368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[11172,113]) ).
thf(11369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(simp,[status(thm)],[11368]) ).
thf(11370,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(pattern_uni,[status(thm)],[11369:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(11573,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(simp,[status(thm)],[11370]) ).
thf(29898,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8477]) ).
thf(29899,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29898]) ).
thf(30156,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29899]) ).
thf(4534,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,1935]) ).
thf(4535,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[4534]) ).
thf(4673,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= a ),
inference(simp,[status(thm)],[4535]) ).
thf(52060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ 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)],[51610,63]) ).
thf(52061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ 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)],[52060]) ).
thf(52062,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ is_a_theorem @ ( true @ ( A @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[52061:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( E @ not )),bind(D,$thf( G @ ( G @ implies ) ))]]) ).
thf(52359,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ implies ) @ is_a_theorem @ ( true @ ( A @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[52062]) ).
thf(12029,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,8038]) ).
thf(12030,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[12029]) ).
thf(12042,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[12030]) ).
thf(13435,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[12042]) ).
thf(8246,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3595,8194]) ).
thf(8247,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8246]) ).
thf(8295,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8247]) ).
thf(54961,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( A @ not )
!= ( a @ ( b @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[52321]) ).
thf(44102,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[23972,8194]) ).
thf(44103,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[44102]) ).
thf(44328,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ ( B @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[44103]) ).
thf(51798,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,10634]) ).
thf(51799,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[51798]) ).
thf(52312,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[51799]) ).
thf(36472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ 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)],[36037,63]) ).
thf(36473,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ 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)],[36472]) ).
thf(36474,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ implies ) @ is_a_theorem @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[36473:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( G @ ( F @ implies ) )),bind(E,$thf( I @ ( I @ implies ) ))]]) ).
thf(36747,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ implies ) @ is_a_theorem @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[36474]) ).
thf(47578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8430]) ).
thf(47579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[47578]) ).
thf(47580,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(pattern_uni,[status(thm)],[47579:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(48305,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[47580]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,10]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[338]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[339]) ).
thf(12594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ not )
!= ( b @ not @ not ) )
| ( ( A @ ( A @ implies ) )
!= ( B @ ( C @ implies ) ) )
| ( ( B @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[12585]) ).
thf(12595,plain,
( ( b @ not @ ( b @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[12594:[bind(A,$thf( b @ not )),bind(B,$thf( b @ not )),bind(C,$thf( b @ not ))]]) ).
thf(31035,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,30382]) ).
thf(31036,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[31035]) ).
thf(31037,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(pattern_uni,[status(thm)],[31036:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ ( I @ implies ) @ ( I @ ( I @ implies ) @ implies ) ))]]) ).
thf(31118,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[31037]) ).
thf(30328,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,30075]) ).
thf(30329,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30328]) ).
thf(30402,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30329]) ).
thf(1101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(22435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( B != b )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[1101]) ).
thf(22454,plain,
! [A: $i] :
( ( A @ ( a @ not @ implies ) @ ( A @ ( b @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[22435]) ).
thf(21174,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11556,1766]) ).
thf(21175,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21174]) ).
thf(21266,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ ( B @ implies ) @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[21175]) ).
thf(14365,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,9042]) ).
thf(14366,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14365]) ).
thf(14512,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[14366]) ).
thf(13469,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[12978,1935]) ).
thf(13470,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[13469]) ).
thf(13801,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[13470]) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ not @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1194,897]) ).
thf(1267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( true @ ( D @ ( C @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1221]) ).
thf(26444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ not @ ( D @ not @ implies ) ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1267,12]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( ( b @ not )
!= ( A @ not ) )
| ( A != b )
| ( B
!= ( a @ not ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(177,plain,
( ( ( a @ not @ not )
!= a )
| ( ( a @ not @ not @ ( b @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(28422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[20780,1935]) ).
thf(28423,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[28422]) ).
thf(28887,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[28423]) ).
thf(51929,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8332]) ).
thf(51930,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[51929]) ).
thf(52329,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[51930]) ).
thf(51997,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,9042]) ).
thf(51998,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[51997]) ).
thf(52334,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[51998]) ).
thf(31148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,30114]) ).
thf(31149,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ not @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[31148]) ).
thf(31311,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( B @ not ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[31149]) ).
thf(9453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,8430]) ).
thf(9454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9453]) ).
thf(9455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[9454:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(9500,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( ( C @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[9455]) ).
thf(5438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[5426,1935]) ).
thf(5439,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[5438]) ).
thf(5613,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[5439]) ).
thf(29839,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,9042]) ).
thf(29840,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29839]) ).
thf(30184,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29840]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( A != b )
| ( B
!= ( a @ not ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(175,plain,
( ( ( a @ not @ not @ ( b @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( a @ not @ not @ ( b @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(47974,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,8477]) ).
thf(47975,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[47974]) ).
thf(48200,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[47975]) ).
thf(2596,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,1998]) ).
thf(2597,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2596]) ).
thf(2598,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2597:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( I @ implies ) @ ( L @ implies ) ))]]) ).
thf(2728,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2598]) ).
thf(8252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2729,8194]) ).
thf(8253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8252]) ).
thf(8299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8253]) ).
thf(30300,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[3595,30075]) ).
thf(30301,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30300]) ).
thf(30389,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30301]) ).
thf(21775,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21393,8710]) ).
thf(21776,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[21775]) ).
thf(21821,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[21776]) ).
thf(14261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,1968]) ).
thf(14262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14261]) ).
thf(14263,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[14262:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ not @ not @ implies ) ))]]) ).
thf(14554,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[14263]) ).
thf(49127,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( b @ not @ not ) )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[48220]) ).
thf(49128,plain,
! [A: $i] :
( ( a @ not @ ( A @ not @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[49127]) ).
thf(35329,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,1968]) ).
thf(35330,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[35329]) ).
thf(35331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[35330:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( I @ ( K @ ( J @ implies ) @ implies ) @ ( I @ implies ) ))]]) ).
thf(35763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[35331]) ).
thf(1959,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[18,1935]) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1959]) ).
thf(1966,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[1960]) ).
thf(11417,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,8194]) ).
thf(11418,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11417]) ).
thf(11530,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[11418]) ).
thf(5659,plain,
! [A: $i] :
( ( A != a )
| ( ( A @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[5657]) ).
thf(5660,plain,
( ( a @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ not ) ),
inference(simp,[status(thm)],[5659]) ).
thf(9130,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,9042]) ).
thf(9131,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[9130]) ).
thf(9141,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[9131]) ).
thf(1222,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1194,234]) ).
thf(1268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1222]) ).
thf(27724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1268,12]) ).
thf(8780,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,8710]) ).
thf(8781,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8780]) ).
thf(8812,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not ) ),
inference(simp,[status(thm)],[8781]) ).
thf(25952,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,25847]) ).
thf(25953,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[25952]) ).
thf(26033,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[25953]) ).
thf(36563,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,8285]) ).
thf(36564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[36563]) ).
thf(36565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[36564:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( K @ implies ) @ ( I @ ( H @ implies ) @ implies ) ))]]) ).
thf(36772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[36565]) ).
thf(30338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11573,30075]) ).
thf(30339,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30338]) ).
thf(30405,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30339]) ).
thf(1293,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ 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)],[20,1286]) ).
thf(1372,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ 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)],[1293]) ).
thf(33235,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( D @ ( E @ implies ) @ implies ) @ implies ) ) )
| ( ( C @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1372,12]) ).
thf(22051,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,10634]) ).
thf(22052,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22051]) ).
thf(22334,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[22052]) ).
thf(14434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,8285]) ).
thf(14435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[14434]) ).
thf(14436,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[14435:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ not @ not @ implies ) ))]]) ).
thf(14571,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[14436]) ).
thf(29546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[29427,8158]) ).
thf(29547,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( ( A @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29546]) ).
thf(29548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ implies ) @ ( A @ implies ) )
!= a )
| ( ( B @ not @ not @ is_a_theorem )
!= true ) ),
inference(pattern_uni,[status(thm)],[29547:[bind(A,$thf( F @ not )),bind(B,$thf( G @ not )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(30225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ implies ) @ ( A @ implies ) )
!= a )
| ( ( B @ not @ not @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[29548]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( ( b @ not )
!= ( A @ not ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(28082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14691,8194]) ).
thf(28083,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[28082]) ).
thf(28245,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[28083]) ).
thf(11947,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,8194]) ).
thf(11948,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11947]) ).
thf(12050,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[11948]) ).
thf(52147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,8285]) ).
thf(52148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[52147]) ).
thf(52149,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[52148:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( I @ implies ) @ ( G @ not @ implies ) ))]]) ).
thf(52380,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[52149]) ).
thf(8305,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,7838]) ).
thf(8306,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8305]) ).
thf(8356,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ ( a @ ( b @ not @ implies ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[8306]) ).
thf(35197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[35137,1935]) ).
thf(35198,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[35197]) ).
thf(35705,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[35198]) ).
thf(9013,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ not @ implies ) @ not ) )
| ( A
!= ( a @ ( b @ not @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[8356]) ).
thf(9014,plain,
( ( a @ ( b @ not @ implies ) @ not )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[9013]) ).
thf(15460,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14538,1766]) ).
thf(15461,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15460]) ).
thf(15576,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[15461]) ).
thf(6487,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,2337]) ).
thf(6488,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[6487]) ).
thf(6489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[6488:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ implies ) ))]]) ).
thf(6567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[6489]) ).
thf(23827,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[23462,1766]) ).
thf(23828,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23827]) ).
thf(23940,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[23828]) ).
thf(48064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,1998]) ).
thf(48065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[48064]) ).
thf(48066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[48065:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ ( J @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(48296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[48066]) ).
thf(13142,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,13061]) ).
thf(13143,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[13142]) ).
thf(13188,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[13143]) ).
thf(34788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( a @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,34777]) ).
thf(34789,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ not @ is_a_theorem ) )
| ( ( B @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[34788]) ).
thf(34933,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ ( C @ implies ) )
!= ( a @ not @ not ) ) ),
inference(simp,[status(thm)],[34789]) ).
thf(1401,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ not @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[278,1272]) ).
thf(1476,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( D @ not ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1401]) ).
thf(42793,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( D @ not ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1476,12]) ).
thf(14079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ not @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,13950]) ).
thf(14080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ not @ not @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14079]) ).
thf(14138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( D @ not @ not ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14080]) ).
thf(8272,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2584,8194]) ).
thf(8273,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8272]) ).
thf(8304,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[8273]) ).
thf(14444,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,1998]) ).
thf(14445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[14444]) ).
thf(14446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ not @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[14445:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ not @ not @ implies ) ))]]) ).
thf(14575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ not @ not @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[14446]) ).
thf(38315,plain,
( ( ( a @ not @ not @ ( a @ not @ implies ) )
!= ( a @ not ) )
| ( ( a @ not )
!= a ) ),
inference(simp,[status(thm)],[38314]) ).
thf(27801,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14691,1935]) ).
thf(27802,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[27801]) ).
thf(28252,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[27802]) ).
thf(36102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,1935]) ).
thf(36103,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[36102]) ).
thf(36694,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[36103]) ).
thf(46090,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ not @ not ) )
| ( ( A @ not @ ( B @ not @ implies ) )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[8229]) ).
thf(30326,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1194,30075]) ).
thf(30327,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30326]) ).
thf(30381,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30327]) ).
thf(36394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[36037,30075]) ).
thf(36395,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[36394]) ).
thf(36655,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[36395]) ).
thf(11836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,1968]) ).
thf(11837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[11836]) ).
thf(11838,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[11837:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ ( I @ implies ) @ implies ) ))]]) ).
thf(12093,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[11838]) ).
thf(30304,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,30075]) ).
thf(30305,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30304]) ).
thf(30428,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30305]) ).
thf(2051,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2004,1968]) ).
thf(2052,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2051]) ).
thf(2053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ ( D @ not @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2052:[bind(A,$thf( F )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( N @ not @ ( O @ not @ implies ) @ implies ) @ ( F @ implies ) ))]]) ).
thf(2123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ not @ ( D @ not @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2053]) ).
thf(12293,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[12049]) ).
thf(11998,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,1998]) ).
thf(11999,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[11998]) ).
thf(12000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[11999:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ ( J @ implies ) @ implies ) ))]]) ).
thf(12108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[12000]) ).
thf(51669,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,1935]) ).
thf(51670,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[51669]) ).
thf(52323,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[51670]) ).
thf(13168,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,13061]) ).
thf(13169,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[13168]) ).
thf(13192,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[13169]) ).
thf(7657,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,1766]) ).
thf(7658,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[7657]) ).
thf(7712,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[7658]) ).
thf(12262,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,12157]) ).
thf(12263,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[12262]) ).
thf(12292,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[12263]) ).
thf(47521,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( C @ ( C @ implies ) @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[18300]) ).
thf(1129,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ not @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1104,897]) ).
thf(1171,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) )
| ( ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1129]) ).
thf(22472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( D @ not @ ( E @ not @ implies ) ) )
| ( ( E @ ( D @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1171,12]) ).
thf(14390,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,8477]) ).
thf(14391,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14390]) ).
thf(14504,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[14391]) ).
thf(30294,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1920,30075]) ).
thf(30295,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30294]) ).
thf(30418,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30295]) ).
thf(1138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ 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)],[1104,61]) ).
thf(1139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(pattern_uni,[status(thm)],[1138:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ ( H @ implies ) @ implies ) )),bind(E,$thf( K @ ( J @ implies ) ))]]) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1139]) ).
thf(24641,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= true )
| ( ( C @ ( B @ implies ) @ is_a_theorem )
= true ) ),
inference(rewrite,[status(thm)],[1184,12]) ).
thf(22437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= a )
| ( ( C @ ( B @ implies ) )
!= ( b @ not ) )
| ( B != b )
| ( A
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[1101]) ).
thf(22455,plain,
! [A: $i] :
( ( ( A @ ( a @ not @ implies ) )
!= a )
| ( ( A @ ( b @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[22437]) ).
thf(35,plain,
! [A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
( ( b @ ( a @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[35]) ).
thf(12236,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[113,12157]) ).
thf(12237,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[12236]) ).
thf(12267,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not ) )
| ( ( B @ is_a_theorem )
!= true ) ),
inference(simp,[status(thm)],[12237]) ).
thf(10728,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,10634]) ).
thf(10729,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10728]) ).
thf(10733,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[10729]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( ( b @ not )
!= ( A @ not ) )
| ( A != b )
| ( B
!= ( a @ not ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(168,plain,
( ( ( a @ not @ not )
!= a )
| ( ( a @ not @ not )
!= b )
| ( ( b @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(30288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1104,30075]) ).
thf(30289,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30288]) ).
thf(30396,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30289]) ).
thf(3486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[2729,1766]) ).
thf(3487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3486]) ).
thf(3521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[3487]) ).
thf(47614,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[47534,16552]) ).
thf(47615,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[47614]) ).
thf(48221,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[47615]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[20,10]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[186]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(2749,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( b != A )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(2800,plain,
! [A: $i] :
( ( ( A @ not )
!= a )
| ( ( b @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( A @ not @ ( b @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[2749]) ).
thf(30274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14538,30075]) ).
thf(30275,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30274]) ).
thf(30377,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ not @ not @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30275]) ).
thf(25433,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( E @ not ) )
| ( ( D @ ( E @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6338,10384]) ).
thf(25434,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= ( E @ not ) )
| ( ( D @ ( E @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[25433]) ).
thf(25435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[25434:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( G @ implies ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(25586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( A @ implies ) )
!= ( C @ not ) )
| ( ( B @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[25435]) ).
thf(2303,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,1998]) ).
thf(2304,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2303]) ).
thf(2305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2304:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( L @ implies ) @ ( G @ implies ) ))]]) ).
thf(2334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2305]) ).
thf(22318,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,13061]) ).
thf(22319,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22318]) ).
thf(22337,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[22319]) ).
thf(8402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[7033,8332]) ).
thf(8403,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8402]) ).
thf(8424,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8403]) ).
thf(11353,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11172,8332]) ).
thf(11354,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[11353]) ).
thf(11509,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ implies ) @ implies ) @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[11354]) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1104,10]) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1105]) ).
thf(1172,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1106]) ).
thf(51972,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[51610,30075]) ).
thf(51973,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[51972]) ).
thf(52288,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ not @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[51973]) ).
thf(11986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,8285]) ).
thf(11987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( b @ not @ not ) ) ),
inference(simp,[status(thm)],[11986]) ).
thf(11988,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(pattern_uni,[status(thm)],[11987:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ ( I @ implies ) @ implies ) ))]]) ).
thf(12102,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[11988]) ).
thf(2510,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[154]) ).
thf(2549,plain,
! [A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( A @ not @ ( a @ not @ implies ) ) )
| ( ( a @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( A @ not )
!= b ) ),
inference(simp,[status(thm)],[2510]) ).
thf(8382,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,8332]) ).
thf(8383,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8382]) ).
thf(8437,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not ) ),
inference(simp,[status(thm)],[8383]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( B
!= ( b @ not ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(174,plain,
( ( ( b @ not @ not )
!= b )
| ( ( a @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(178,plain,
( ( b @ not @ not )
!= b ),
inference(simp,[status(thm)],[174]) ).
thf(1619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ 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)],[1104,1581]) ).
thf(1620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1619:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( L @ ( K @ implies ) )),bind(E,$thf( L @ ( K @ ( I @ implies ) @ implies ) )),bind(F,$thf( F ))]]) ).
thf(1685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1620]) ).
thf(49129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[1685,12]) ).
thf(30362,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,30075]) ).
thf(30363,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[30362]) ).
thf(30394,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ not @ not ) ),
inference(simp,[status(thm)],[30363]) ).
thf(4567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[4518,1968]) ).
thf(4568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[4567]) ).
thf(4569,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[4568:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ ( I @ implies ) @ implies ) @ ( I @ implies ) ))]]) ).
thf(4691,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ implies ) @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[4569]) ).
thf(13668,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[12978,8194]) ).
thf(13669,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[13668]) ).
thf(13802,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ ( A @ not @ not @ implies ) @ implies ) )
!= ( b @ not @ not ) ),
inference(simp,[status(thm)],[13669]) ).
thf(8549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[278,8477]) ).
thf(8550,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[8549]) ).
thf(8570,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not ) ),
inference(simp,[status(thm)],[8550]) ).
thf(48319,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[48213]) ).
thf(48320,plain,
! [A: $i] :
( ( b @ not @ ( A @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[48319]) ).
thf(56742,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) )
!= a )
| ( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[21266]) ).
thf(1951,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1104,1935]) ).
thf(1952,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1951]) ).
thf(1962,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[1952]) ).
thf(2517,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( A @ ( B @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[154]) ).
thf(2527,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( A @ ( B @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[2517]) ).
thf(2563,plain,
! [A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( a @ ( A @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( A @ not )
!= b ) ),
inference(simp,[status(thm)],[2527]) ).
thf(22172,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[21912,9042]) ).
thf(22173,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[22172]) ).
thf(22341,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[22173]) ).
thf(1929,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[22,1766]) ).
thf(1930,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1929]) ).
thf(1944,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[1930]) ).
thf(3096,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[1944]) ).
thf(6978,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,2337]) ).
thf(6979,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[6978]) ).
thf(6980,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[6979:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( J @ ( J @ implies ) @ ( G @ implies ) ))]]) ).
thf(7056,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[6980]) ).
thf(10690,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[329,10634]) ).
thf(10691,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[10690]) ).
thf(10745,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[10691]) ).
thf(11759,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[11734,1935]) ).
thf(11760,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[11759]) ).
thf(12047,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[11760]) ).
thf(14256,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[14158,10634]) ).
thf(14257,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not @ is_a_theorem ) ),
inference(simp,[status(thm)],[14256]) ).
thf(14531,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ not @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) @ not @ not @ not @ not @ not ) ),
inference(simp,[status(thm)],[14257]) ).
thf(56808,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[46861,1935]) ).
thf(56809,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[56808]) ).
thf(57494,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[56809]) ).
thf(8213,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[6554,8038]) ).
thf(8214,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ not @ not @ ( a @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[8213]) ).
thf(8232,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( b @ not @ not @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[8214]) ).
thf(62096,plain,
$false,
inference(e,[status(thm)],[13950,48199,34616,30427,8288,14574,628,18272,12148,234,9864,21299,11527,52384,32695,3944,36789,12055,1995,6544,11517,57481,2463,8507,35735,8434,47517,10478,25228,8811,30392,6338,30145,11556,5237,22470,48214,26044,21849,16698,5878,1073,14538,31642,1269,48275,51476,16196,22402,29004,8430,30209,17791,30707,32165,10737,8303,30375,46748,10,26257,21839,5636,12585,48297,30385,36700,17285,14521,2723,24047,4679,1935,8699,1967,8224,5342,7028,30397,7079,48223,8816,8578,44454,36803,30410,35730,436,22352,12062,25,13191,52402,22353,8225,4692,8357,8806,2708,30221,12065,16712,51437,18368,2745,157,16552,14,8500,30429,21903,8426,17779,2488,35774,30382,30395,31785,2552,48192,22374,1963,22338,22348,20755,8293,24045,20,13183,30424,6579,30575,3084,8367,14533,13195,48195,22357,8158,38314,36647,12276,18324,21829,8229,48175,3295,14532,29427,8321,4724,1581,2335,23069,8586,61,8575,9140,52302,1943,11596,21371,22342,5328,527,31423,8289,48279,9865,8823,18930,26049,20729,35083,14558,30371,6482,8302,57465,34777,6571,11545,8123,22361,26060,44341,11597,30411,7730,20848,11730,22351,19744,35734,3742,52314,9158,36676,14501,1580,30167,31115,30727,2147,8582,51475,18300,275,21,2150,22346,41099,1920,329,8736,16704,21912,21890,48204,27722,10634,8672,5655,46092,20819,1968,12279,8503,8226,47087,8287,27736,8577,32523,3595,31125,8297,11734,2115,44358,30430,8435,7838,35137,8800,10676,8446,30391,9145,14152,317,52321,2801,17274,9016,48194,8282,2709,22368,8572,21797,3018,52293,52378,22343,30403,21267,16700,15047,16541,52286,21370,18289,30210,10752,48208,49945,4518,52360,55956,38317,1964,1942,30379,41987,52401,7027,8576,11610,8803,8219,11606,22432,30150,35756,36682,16690,23942,8294,14509,173,39119,13,8439,30435,4347,9081,10597,7052,24822,20780,8422,40289,1286,22358,51598,22332,9137,1996,37491,28358,30114,30765,18371,1071,30207,52396,7817,22371,2001,48213,35760,14593,17,10625,149,8215,2729,43645,21380,8290,32,34,23068,30249,48321,32120,176,44496,52326,21822,47529,8580,9157,8809,46861,25241,8332,35747,22419,2489,7751,53734,8222,18927,22340,8581,1965,47534,12,13953,11201,28924,52333,50761,3783,48180,704,48193,8301,86,31146,36751,52264,4837,8432,10393,8286,14517,2738,4149,30921,1997,8300,8799,30075,30147,5610,9146,30423,1194,8436,6572,48220,113,56453,2151,47096,10385,736,4699,23453,1492,30412,230,14595,13204,1175,16381,9042,52362,5657,35817,12049,21393,36031,11519,30380,22407,12274,16703,16366,13050,48240,21837,10375,53758,7033,14137,8423,11558,8573,14985,20731,51610,25847,8676,30159,8291,21814,45304,5340,5057,35721,8440,6574,25613,6811,278,12309,9033,31105,30419,5661,53775,14493,55940,10749,6542,8804,10384,3975,30384,8194,36691,30191,17781,52248,12978,35843,8477,30393,5047,3737,1961,11562,37515,36683,10392,63,36719,18,11573,30156,8466,4673,52359,13435,8295,14158,54961,44328,28351,52312,23462,36747,67,48305,370,12595,8216,8509,30171,31118,30402,22454,21266,14512,10307,13801,26444,177,28887,52329,2337,52334,1898,31311,9500,5613,154,2711,11,30184,175,48200,2728,14518,2584,8299,30389,1766,21821,1272,14554,10754,49128,35763,1966,11530,5660,15768,30261,9141,9866,27724,1998,8812,26033,1940,36772,52267,30405,28352,33235,34783,22334,8285,4678,14571,8221,30225,11514,158,5426,28245,41927,12050,52380,29692,8356,35705,12157,9014,15576,23972,6567,23940,4683,1101,48296,13188,2004,34933,42793,8,14138,6554,8304,14592,11172,6536,14575,8710,36037,38315,30409,28252,36694,46090,30381,36655,12093,30426,30428,2123,21378,12293,12108,52323,13192,14536,7712,12292,19,47521,22472,8368,14504,8038,30418,24641,14499,22455,36,12267,10733,168,30396,14984,3521,48221,37514,210,2800,30377,25586,2334,22337,8424,12503,11509,1172,897,52288,1891,12102,2549,12042,644,8437,178,49129,15,30394,4691,13802,8570,48320,56742,1962,2563,22341,3096,7056,10745,14691,12047,13061,90,50764,14531,1944,57494,22330,11529,8232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL113-10 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.12/11.23 % Computer : n012.cluster.edu
% 0.12/11.23 % Model : x86_64 x86_64
% 0.12/11.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/11.23 % Memory : 8046.5625MB
% 0.12/11.23 % OS : Linux 6.8.0-71-generic
% 0.12/11.23 % CPULimit : 300
% 0.12/11.23 % WCLimit : 300
% 0.12/11.23 % DateTime : Fri Sep 25 21:52:32 UTC 2026
% 0.12/11.23 % CPUTime :
% 0.12/11.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/11.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/11.86 % [INFO] Parsing done (147ms).
% 0.16/11.88 % [INFO] Running in sequential loop mode.
% 1.64/12.21 % [INFO] eprover registered as external prover.
% 1.64/12.22 % [INFO] Scanning for conjecture ...
% 1.64/12.29 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.80/12.32 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.80/12.33 % [INFO] Problem is propositional (TPTP CNF).
% 1.80/12.34 % [INFO] Type checking passed.
% 1.80/12.34 % [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 ...
% 124.27/44.55 % External prover 'e' found a proof!
% 124.27/44.55 % [INFO] Killing All external provers ...
% 124.27/44.56 % Time passed: 33203ms (effective reasoning time: 32675ms)
% 124.27/44.56 % Axioms used in derivation (6): mv_5, condensed_detachment, mv_2, mv_3, ifeq_axiom, mv_1
% 124.27/44.56 % No. of inferences in proof: 2109
% 124.27/44.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 33203 ms resp. 32675 ms w/o parsing
% 125.38/44.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 125.38/44.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------