TSTP Solution File: LCL250-10 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : LCL250-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 11:13:38 EDT 2024
% Result : Unsatisfiable 136.87s 38.16s
% Output : Refutation 137.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 11
% Syntax : Number of formulae : 1502 ( 944 unt; 0 typ; 0 def)
% Number of atoms : 2180 (2179 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 18627 (1528 ~; 678 |; 0 &;16421 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 3782 ( 0 ^3782 !; 0 ?;3782 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_type,type,
theorem: $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(q_type,type,
q: $i ).
thf(r_type,type,
r: $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(p_type,type,
p: $i ).
thf(true_type,type,
true: $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(axiom_type,type,
axiom: $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ A ) @ B )
= ( implies @ A @ B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
= true ),
inference(lifteq,[status(thm)],[21]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[15]) ).
thf(9,axiom,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(29,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(lifteq,[status(thm)],[29]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( ( ifeq @ A @ A @ B @ C )
!= ( ifeq @ ( axiom @ D ) @ true @ ( theorem @ D ) @ true ) ) ),
inference(paramod_ordered,[status(thm)],[16,30]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( A
!= ( axiom @ D ) )
| ( A != true )
| ( B
!= ( theorem @ D ) )
| ( C != true ) ),
inference(simp,[status(thm)],[65]) ).
thf(69,plain,
! [A: $i] :
( ( ( theorem @ A )
= true )
| ( ( axiom @ A )
!= true ) ),
inference(simp,[status(thm)],[67]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,69]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
= true ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( implies @ ( or @ I @ H ) @ ( or @ H @ I ) ))]]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
= true ),
inference(simp,[status(thm)],[84]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( implies @ A @ B ) @ ( or @ C @ D ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,99]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[369]) ).
thf(3,axiom,
! [A: $i] :
( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(17,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
inference(lifteq,[status(thm)],[17]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ A @ B ) @ C ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,18]) ).
thf(46,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(48,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(simp,[status(thm)],[46]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
= true )
| ( ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( axiom @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48,69]) ).
thf(76,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( H )),bind(B,$thf( implies @ ( implies @ H @ ( not @ H ) ) @ ( not @ H ) ))]]) ).
thf(81,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(simp,[status(thm)],[76]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
inference(lifteq,[status(thm)],[31]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ B @ C ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ C ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[81,32]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( I )),bind(B,$thf( implies @ ( implies @ I @ ( not @ I ) ) @ ( not @ I ) )),bind(C,$thf( C ))]]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[291]) ).
thf(3831,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[330,16]) ).
thf(3876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ ( implies @ D @ ( not @ D ) ) @ ( not @ D ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,3831]) ).
thf(3877,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ A ) @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[3876:[bind(A,$thf( not @ O )),bind(B,$thf( implies @ O @ ( not @ O ) )),bind(C,$thf( or @ ( not @ O ) @ ( not @ ( implies @ O @ ( not @ O ) ) ) )),bind(D,$thf( O ))]]) ).
thf(3984,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ A ) @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[3877]) ).
thf(4188,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ A ) @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[3984,16]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
inference(lifteq,[status(thm)],[23]) ).
thf(159,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( or @ D @ ( or @ C @ E ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( or @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,24]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ ( not @ A ) @ C ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( F )),bind(B,$thf( or @ G @ H )),bind(C,$thf( not @ F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ ( not @ A ) @ C ) ) ) )
= true ),
inference(simp,[status(thm)],[160]) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( implies @ A @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[175,28]) ).
thf(666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ D ) @ true )
= true )
| ( ( axiom @ ( implies @ ( implies @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( implies @ A @ C ) ) ) )
!= ( axiom @ D ) ) ),
inference(paramod_ordered,[status(thm)],[640,30]) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( implies @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( implies @ ( implies @ M @ ( or @ K @ N ) ) @ ( or @ K @ ( implies @ M @ N ) ) ))]]) ).
thf(673,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( implies @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[667]) ).
thf(12258,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( implies @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[673,16]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( or @ B @ A ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( or @ B @ A ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( or @ B @ A ) ) )
= true ),
inference(lifteq,[status(thm)],[19]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( axiom @ ( implies @ A @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,69]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
= true ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( implies @ G @ ( or @ F @ G ) ))]]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
= true ),
inference(simp,[status(thm)],[72]) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[79,32]) ).
thf(315,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ C @ ( or @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( implies @ H @ ( or @ G @ H ) )),bind(D,$thf( D ))]]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ C @ ( or @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[315]) ).
thf(5827,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ C @ ( or @ B @ C ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[343,16]) ).
thf(12351,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ D ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( implies @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( implies @ F @ ( or @ E @ F ) ) @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[12258,5827]) ).
thf(12352,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ B @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[12351:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( J )),bind(D,$thf( or @ G @ ( implies @ J @ J ) )),bind(E,$thf( G )),bind(F,$thf( J ))]]) ).
thf(12467,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ B @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[12352]) ).
thf(12485,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[12467,16]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
= true )
| ( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( axiom @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18,69]) ).
thf(78,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( D )),bind(B,$thf( implies @ ( or @ D @ D ) @ D ))]]) ).
thf(82,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
inference(simp,[status(thm)],[78]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ C ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ ( implies @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,32]) ).
thf(310,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ A @ A ) ) @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( E )),bind(B,$thf( or @ E @ E )),bind(C,$thf( E ))]]) ).
thf(342,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ A @ A ) ) @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[310]) ).
thf(785,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ ( or @ A @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[342,16]) ).
thf(12505,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[12485,785]) ).
thf(12506,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[12505:[bind(A,$thf( implies @ E @ E )),bind(B,$thf( E )),bind(C,$thf( implies @ E @ E ))]]) ).
thf(12700,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[12506]) ).
thf(12715,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ A ) )
= true ),
inference(rewrite,[status(thm)],[12700,16]) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,32]) ).
thf(458,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( implies @ B @ A ) ) @ true @ ( theorem @ ( or @ A @ ( not @ B ) ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[457:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( implies @ I @ G )),bind(D,$thf( or @ G @ ( not @ I ) ))]]) ).
thf(466,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( implies @ B @ A ) ) @ true @ ( theorem @ ( or @ A @ ( not @ B ) ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[458]) ).
thf(8198,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ B @ A ) ) @ true @ ( theorem @ ( or @ A @ ( not @ B ) ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[466,16]) ).
thf(12826,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ B @ ( not @ C ) ) ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ ( implies @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[12715,8198]) ).
thf(12827,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( not @ A ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[12826:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(13962,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ A ) ) )
= true ),
inference(rewrite,[status(thm)],[12827,16]) ).
thf(14018,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ A @ B ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,13962]) ).
thf(14019,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[14018:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(14188,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
= true ),
inference(simp,[status(thm)],[14019]) ).
thf(302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true = D )
| ( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true ) @ true )
!= ( ifeq @ C @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[32,16]) ).
thf(325,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true = D )
| ( ( theorem @ ( implies @ A @ B ) )
!= C )
| ( true != C )
| ( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true )
!= D )
| ( true != E ) ),
inference(simp,[status(thm)],[302]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ B ) )
!= true ) ),
inference(simp,[status(thm)],[325]) ).
thf(14265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ ( implies @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[14188,334]) ).
thf(14266,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( not @ ( not @ A ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[14265:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( not @ ( not @ E ) ))]]) ).
thf(14435,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( not @ ( not @ A ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[14266]) ).
thf(15207,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13962,14435]) ).
thf(15208,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[15207:[bind(A,$thf( E )),bind(B,$thf( or @ E @ ( not @ E ) ))]]) ).
thf(15298,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[15208]) ).
thf(17682,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[15298,16]) ).
thf(17848,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17682,14435]) ).
thf(17849,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[17848:[bind(A,$thf( G )),bind(B,$thf( not @ ( not @ ( or @ G @ ( not @ G ) ) ) ))]]) ).
thf(17918,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[17849]) ).
thf(25250,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[17918,16]) ).
thf(1,negated_conjecture,
( ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(12,plain,
( ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
( ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) )
!= true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) )
!= true ),
inference(lifteq,[status(thm)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( implies @ A @ ( not @ B ) ) ) ),
inference(rewrite,[status(thm)],[34,28]) ).
thf(261,plain,
( ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
!= true ),
inference(rewrite,[status(thm)],[14,260]) ).
thf(25307,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[25250,261]) ).
thf(25489,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[25307]) ).
thf(318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,32]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( or @ E @ F ))]]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[319]) ).
thf(981,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[345,16]) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ B @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[82,981]) ).
thf(991,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[990:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( implies @ ( or @ E @ E ) @ E ))]]) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[991]) ).
thf(2003,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[1054,16]) ).
thf(2055,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2003,30]) ).
thf(2056,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[2055:[bind(A,$thf( D )),bind(B,$thf( G )),bind(C,$thf( or @ D @ ( implies @ ( or @ G @ G ) @ G ) ))]]) ).
thf(2072,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[2056]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ C @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,20]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) )
= true ),
inference(simp,[status(thm)],[44]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[47,69]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
= true ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( implies @ G @ ( implies @ F @ G ) ))]]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
= true ),
inference(simp,[status(thm)],[74]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[80,32]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( implies @ A @ B ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( implies @ E @ F ))]]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( implies @ A @ B ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[301]) ).
thf(574,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( implies @ A @ B ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[339,16]) ).
thf(608,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( ( ifeq @ A @ A @ B @ C )
!= ( ifeq @ ( theorem @ E ) @ true @ ( theorem @ ( implies @ D @ E ) ) @ true ) ) ),
inference(paramod_ordered,[status(thm)],[16,574]) ).
thf(619,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( A
!= ( theorem @ E ) )
| ( A != true )
| ( B
!= ( theorem @ ( implies @ D @ E ) ) )
| ( C != true ) ),
inference(simp,[status(thm)],[608]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( ( theorem @ ( implies @ A @ B ) )
= true )
| ( ( theorem @ B )
!= true ) ),
inference(simp,[status(thm)],[619]) ).
thf(10860,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( theorem @ ( implies @ A @ B ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[629,261]) ).
thf(10861,plain,
( ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
!= true ),
inference(pattern_uni,[status(thm)],[10860:[bind(A,$thf( implies @ q @ r )),bind(B,$thf( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ))]]) ).
thf(17829,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[17682,10861]) ).
thf(17903,plain,
! [A: $i] :
( ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[17829]) ).
thf(2020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ C @ ( implies @ ( implies @ A @ B ) @ D ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,2003]) ).
thf(2021,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[2020:[bind(A,$thf( F )),bind(B,$thf( not @ F )),bind(C,$thf( C )),bind(D,$thf( not @ F ))]]) ).
thf(2070,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[2021]) ).
thf(11180,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( theorem @ ( implies @ A @ B ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[629,10861]) ).
thf(11181,plain,
( ( theorem @ r )
!= true ),
inference(pattern_uni,[status(thm)],[11180:[bind(A,$thf( not @ ( implies @ p @ ( not @ q ) ) )),bind(B,$thf( r ))]]) ).
thf(11281,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[2070,11181]) ).
thf(11318,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[11281]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,261]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(720,plain,
! [B: $i,A: $i] :
( ( ( or @ B @ A )
!= ( implies @ q @ r ) )
| ( ( or @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ D @ C )
!= ( implies @ q @ r ) )
| ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,720]) ).
thf(775,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ ( not @ B ) )
!= ( implies @ q @ r ) )
| ( ( implies @ B @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ ( not @ B ) )
!= ( implies @ q @ r ) )
| ( ( implies @ B @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[775]) ).
thf(1469,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ ( not @ B ) )
!= ( implies @ q @ r ) )
| ( B
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( A != r ) ),
inference(simp,[status(thm)],[781]) ).
thf(1472,plain,
( ( or @ r @ ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
!= ( implies @ q @ r ) ),
inference(simp,[status(thm)],[1469]) ).
thf(1544,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ q @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ r @ ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,1472]) ).
thf(1546,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= r )
| ( B
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ) ),
inference(simp,[status(thm)],[1544]) ).
thf(1549,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[1546]) ).
thf(11250,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( theorem @ ( implies @ A @ B ) )
!= ( theorem @ r ) ) ),
inference(paramod_ordered,[status(thm)],[629,11181]) ).
thf(11295,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( implies @ A @ B )
!= r ) ),
inference(simp,[status(thm)],[11250]) ).
thf(11329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ B ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[629,11295]) ).
thf(11330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( implies @ A @ ( implies @ B @ C ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[11329:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ F ))]]) ).
thf(11399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( implies @ A @ ( implies @ B @ C ) )
!= r ) ),
inference(simp,[status(thm)],[11330]) ).
thf(14228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[14188,11399]) ).
thf(14229,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[14228:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( implies @ H @ ( not @ ( not @ H ) ) ))]]) ).
thf(14419,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[14229]) ).
thf(17746,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ ( not @ ( implies @ A @ B ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,17682]) ).
thf(17747,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[17746:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(17926,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
= true ),
inference(simp,[status(thm)],[17747]) ).
thf(18112,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17926,30]) ).
thf(18113,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[18112:[bind(A,$thf( H )),bind(B,$thf( not @ ( not @ ( implies @ H @ ( not @ ( not @ H ) ) ) ) ))]]) ).
thf(18180,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[18113]) ).
thf(1016,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true = D )
| ( ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true )
!= ( ifeq @ C @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[981,16]) ).
thf(1033,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true = D )
| ( ( theorem @ B )
!= C )
| ( true != C )
| ( ( theorem @ ( or @ A @ B ) )
!= D )
| ( true != E ) ),
inference(simp,[status(thm)],[1016]) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ( ( theorem @ ( or @ A @ B ) )
= true )
| ( ( theorem @ B )
!= true ) ),
inference(simp,[status(thm)],[1033]) ).
thf(27744,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( theorem @ ( or @ A @ B ) )
!= ( theorem @ r ) ) ),
inference(paramod_ordered,[status(thm)],[1046,11181]) ).
thf(27844,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( or @ A @ B )
!= r ) ),
inference(simp,[status(thm)],[27744]) ).
thf(28399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17682,27844]) ).
thf(28400,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28399:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( or @ H @ ( not @ H ) ) ) ))]]) ).
thf(28526,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28400]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ D ) @ true )
= true )
| ( ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
!= ( axiom @ D ) ) ),
inference(paramod_ordered,[status(thm)],[24,30]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( implies @ ( or @ M @ ( or @ K @ N ) ) @ ( or @ K @ ( or @ M @ N ) ) ))]]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[166]) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[177,16]) ).
thf(874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ D @ E ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ E ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[855,32]) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[874:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( implies @ ( or @ N @ ( or @ L @ O ) ) @ ( or @ L @ ( or @ N @ O ) ) )),bind(E,$thf( E ))]]) ).
thf(904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[875]) ).
thf(20432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[904,16]) ).
thf(12536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ A @ B ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( implies @ D @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,12485]) ).
thf(12537,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
= true ),
inference(pattern_uni,[status(thm)],[12536:[bind(A,$thf( E )),bind(B,$thf( implies @ G @ G )),bind(C,$thf( not @ E )),bind(D,$thf( G ))]]) ).
thf(12710,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
= true ),
inference(simp,[status(thm)],[12537]) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,32]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ B @ A ) ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( or @ H @ G )),bind(D,$thf( or @ G @ H ))]]) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ B @ A ) ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[358]) ).
thf(3106,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( or @ B @ A ) ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[379,16]) ).
thf(12580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ ( or @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[12485,3106]) ).
thf(12581,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ B @ B ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[12580:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( implies @ F @ F )),bind(D,$thf( A ))]]) ).
thf(12690,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ B @ B ) @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[12581]) ).
thf(23685,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[12690,16]) ).
thf(23874,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[23685,11181]) ).
thf(23940,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ B ) @ A )
!= r ),
inference(simp,[status(thm)],[23874]) ).
thf(23994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ D @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,23940]) ).
thf(23995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ D @ D ) )
| ( B != C ) ),
inference(simp,[status(thm)],[23994]) ).
thf(23996,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ C @ C ) ) ),
inference(simp,[status(thm)],[23995]) ).
thf(5889,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ E @ ( or @ D @ E ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,5827]) ).
thf(5890,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[5889:[bind(A,$thf( or @ J @ L )),bind(B,$thf( L )),bind(C,$thf( or @ ( or @ J @ L ) @ ( not @ L ) )),bind(D,$thf( J )),bind(E,$thf( L ))]]) ).
thf(6001,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[5890]) ).
thf(6747,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[6001,16]) ).
thf(11267,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[6747,11181]) ).
thf(11311,plain,
! [B: $i,A: $i] :
( ( or @ ( or @ A @ B ) @ ( not @ B ) )
!= r ),
inference(simp,[status(thm)],[11267]) ).
thf(11442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ ( implies @ A @ B ) @ ( not @ D ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,11311]) ).
thf(11443,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ A ) @ ( not @ A ) )
!= r ),
inference(pattern_uni,[status(thm)],[11442:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(11445,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ A ) @ ( not @ A ) )
!= r ),
inference(simp,[status(thm)],[11443]) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[82,574]) ).
thf(584,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[583:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( implies @ ( or @ E @ E ) @ E ))]]) ).
thf(625,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[584]) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[625,16]) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1139,785]) ).
thf(1195,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( or @ C @ C ) ) ),
inference(simp,[status(thm)],[1142]) ).
thf(33707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( or @ C @ C ) ) ),
inference(rewrite,[status(thm)],[1195,16]) ).
thf(370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( or @ D @ C ) @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,99]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[370:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
= true ),
inference(simp,[status(thm)],[371]) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[377,981]) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1007:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( implies @ ( or @ K @ ( not @ J ) ) @ ( implies @ J @ K ) ))]]) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1008]) ).
thf(29830,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1050,16]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( or @ C @ D ) @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,22]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
= true ),
inference(simp,[status(thm)],[90]) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[79,574]) ).
thf(616,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[615:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ H @ ( or @ G @ H ) ))]]) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[616]) ).
thf(1325,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[626,16]) ).
thf(1341,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ C @ ( implies @ E @ ( implies @ A @ B ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,1325]) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1341:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
= true ),
inference(simp,[status(thm)],[1342]) ).
thf(1442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ D ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1391,30]) ).
thf(1443,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[1442:[bind(A,$thf( J )),bind(B,$thf( E )),bind(C,$thf( I )),bind(D,$thf( implies @ E @ ( implies @ J @ ( implies @ I @ J ) ) ))]]) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[1443]) ).
thf(14092,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13962,11295]) ).
thf(14093,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ B ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[14092:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( or @ F @ ( not @ F ) ))]]) ).
thf(14171,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[14093]) ).
thf(28401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6747,27844]) ).
thf(28402,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ ( or @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28401:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( or @ ( or @ G @ I ) @ ( not @ I ) ))]]) ).
thf(28527,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ ( or @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(simp,[status(thm)],[28402]) ).
thf(32460,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ ( or @ ( implies @ A @ B ) @ ( not @ E ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,28527]) ).
thf(32461,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( or @ ( implies @ C @ A ) @ ( not @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[32460:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(32465,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( or @ ( implies @ C @ A ) @ ( not @ A ) ) )
!= r ),
inference(simp,[status(thm)],[32461]) ).
thf(6759,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[6747,261]) ).
thf(6870,plain,
! [B: $i,A: $i] :
( ( or @ ( or @ A @ B ) @ ( not @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[6759]) ).
thf(6910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( or @ C @ D ) @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,6870]) ).
thf(6914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( not @ A )
!= ( or @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[6910]) ).
thf(6918,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ ( not @ C ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( not @ A )
!= ( or @ B @ C ) ) ),
inference(simp,[status(thm)],[6914]) ).
thf(14214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ B @ C ) )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14188,629]) ).
thf(14215,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[14214:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( implies @ G @ ( not @ ( not @ G ) ) ))]]) ).
thf(14414,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
= true ),
inference(simp,[status(thm)],[14215]) ).
thf(296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[80,32]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[296:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( implies @ H @ ( implies @ G @ H ) )),bind(D,$thf( D ))]]) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[297]) ).
thf(5249,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[337,16]) ).
thf(5303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ E @ ( implies @ D @ E ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,5249]) ).
thf(5304,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[5303:[bind(A,$thf( implies @ J @ L )),bind(B,$thf( L )),bind(C,$thf( or @ ( implies @ J @ L ) @ ( not @ L ) )),bind(D,$thf( J )),bind(E,$thf( L ))]]) ).
thf(5431,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[5304]) ).
thf(6054,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[5431,16]) ).
thf(28355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6054,27844]) ).
thf(28356,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ ( implies @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28355:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( or @ ( implies @ G @ I ) @ ( not @ I ) ))]]) ).
thf(28504,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ ( implies @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(simp,[status(thm)],[28356]) ).
thf(6851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6747,30]) ).
thf(6852,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[6851:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( or @ ( or @ F @ H ) @ ( not @ H ) ))]]) ).
thf(6883,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[6852]) ).
thf(23740,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[23685,261]) ).
thf(23938,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ B ) @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[23740]) ).
thf(24167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ D @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,23938]) ).
thf(24170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( B
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= ( implies @ D @ D ) )
| ( B != C ) ),
inference(simp,[status(thm)],[24167]) ).
thf(24173,plain,
! [A: $i] :
( ( not @ ( implies @ q @ r ) )
!= ( implies @ A @ A ) ),
inference(simp,[status(thm)],[24170]) ).
thf(353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[99,32]) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( implies @ ( or @ J @ I ) @ ( or @ I @ J ) )),bind(D,$thf( D ))]]) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[354]) ).
thf(6219,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[376,16]) ).
thf(603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[80,574]) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[603:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ H @ ( implies @ G @ H ) ))]]) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[604]) ).
thf(1552,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[638,16]) ).
thf(11345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ E )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1552,11295]) ).
thf(11346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ D @ ( implies @ C @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11345:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( implies @ F @ ( implies @ K @ ( implies @ J @ K ) ) ))]]) ).
thf(11409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ D @ ( implies @ C @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[11346]) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ B @ C ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ C ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[82,32]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ B @ B ) @ B ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( E )),bind(B,$thf( implies @ ( or @ E @ E ) @ E )),bind(C,$thf( C ))]]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ B @ B ) @ B ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[306]) ).
thf(5475,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ B @ B ) @ B ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[340,16]) ).
thf(5533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ ( or @ D @ D ) @ D ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,5475]) ).
thf(5534,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[5533:[bind(A,$thf( K )),bind(B,$thf( or @ K @ K )),bind(C,$thf( or @ K @ ( not @ ( or @ K @ K ) ) )),bind(D,$thf( K ))]]) ).
thf(5652,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[5534]) ).
thf(6578,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
= true ),
inference(rewrite,[status(thm)],[5652,16]) ).
thf(6651,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ B @ C ) ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ ( or @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6578,3106]) ).
thf(6652,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[6651:[bind(A,$thf( F )),bind(B,$thf( not @ ( or @ F @ F ) )),bind(C,$thf( F ))]]) ).
thf(6739,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[6652]) ).
thf(7322,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[6739,16]) ).
thf(14064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ B @ C ) ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ ( or @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[13962,3106]) ).
thf(14065,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ A ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[14064:[bind(A,$thf( D )),bind(B,$thf( not @ D )),bind(C,$thf( D ))]]) ).
thf(14196,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ A ) @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[14065]) ).
thf(14661,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ A ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[14196,16]) ).
thf(15047,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( or @ ( not @ A ) @ A ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14661,14435]) ).
thf(15048,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ ( not @ A ) @ A ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[15047:[bind(A,$thf( D )),bind(B,$thf( or @ ( not @ D ) @ D ))]]) ).
thf(15286,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ ( not @ A ) @ A ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[15048]) ).
thf(17424,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( or @ ( not @ A ) @ A ) ) ) )
= true ),
inference(rewrite,[status(thm)],[15286,16]) ).
thf(15054,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12715,14435]) ).
thf(15055,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[15054:[bind(A,$thf( D )),bind(B,$thf( implies @ D @ D ))]]) ).
thf(15289,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[15055]) ).
thf(16032,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
= true ),
inference(rewrite,[status(thm)],[15289,16]) ).
thf(16167,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[16032,11181]) ).
thf(16229,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ A ) ) )
!= r ),
inference(simp,[status(thm)],[16167]) ).
thf(14103,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[13962,11181]) ).
thf(14151,plain,
! [A: $i] :
( ( or @ A @ ( not @ A ) )
!= r ),
inference(simp,[status(thm)],[14103]) ).
thf(14198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,14151]) ).
thf(14199,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( not @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[14198:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(14200,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( not @ A ) ) )
!= r ),
inference(simp,[status(thm)],[14199]) ).
thf(14245,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[14188,261]) ).
thf(14399,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( not @ A ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[14245]) ).
thf(3177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( or @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[2003,3106]) ).
thf(3178,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[3177:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( implies @ ( or @ F @ F ) @ F )),bind(D,$thf( A ))]]) ).
thf(3230,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[3178]) ).
thf(3475,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[3230,16]) ).
thf(11204,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[3475,10861]) ).
thf(11246,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11204]) ).
thf(22415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ ( or @ D @ D ) @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,11246]) ).
thf(22420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( B != r )
| ( ( not @ A )
!= ( implies @ ( or @ D @ D ) @ D ) )
| ( B != C ) ),
inference(simp,[status(thm)],[22415]) ).
thf(22424,plain,
! [A: $i] :
( ( implies @ ( or @ A @ A ) @ A )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(simp,[status(thm)],[22420]) ).
thf(11193,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[6578,10861]) ).
thf(11224,plain,
! [A: $i] :
( ( or @ A @ ( not @ ( or @ A @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11193]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,14]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( or @ A @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ ( implies @ A @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,108]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(rewrite,[status(thm)],[136,260]) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1139,981]) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1152:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( implies @ ( or @ H @ H ) @ H ) ))]]) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1153]) ).
thf(34117,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1196,16]) ).
thf(451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( implies @ D @ C ) @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,375]) ).
thf(452,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[451:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[452]) ).
thf(11272,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[463,11181]) ).
thf(11308,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[11272]) ).
thf(28345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ B ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1046,27844]) ).
thf(28346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( or @ A @ ( or @ B @ C ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[28345:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( or @ E @ F ))]]) ).
thf(28499,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( or @ A @ ( or @ B @ C ) )
!= r ) ),
inference(simp,[status(thm)],[28346]) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( ( or @ B @ A )
!= ( implies @ q @ r ) )
| ( ( or @ A @ B )
!= ( or @ B @ A ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[720]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( ( or @ B @ A )
!= ( implies @ q @ r ) )
| ( A != B )
| ( B != A )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[776]) ).
thf(782,plain,
! [A: $i] :
( ( ( or @ A @ A )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[777]) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,782]) ).
thf(978,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(pattern_uni,[status(thm)],[977:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(980,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[978]) ).
thf(1058,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( not @ A ) ) )
| ( ( implies @ q @ r )
!= ( implies @ q @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[980]) ).
thf(1061,plain,
! [A: $i] :
( ( A != q )
| ( ( not @ A )
!= r )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( not @ A ) ) ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1073,plain,
( ( ( not @ q )
!= r )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[1061]) ).
thf(17686,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ B @ C ) )
= true )
| ( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17682,629]) ).
thf(17687,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[17686:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( or @ H @ ( not @ H ) ) ) ))]]) ).
thf(17907,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) )
= true ),
inference(simp,[status(thm)],[17687]) ).
thf(872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( or @ D @ ( or @ C @ E ) ) @ ( or @ C @ ( implies @ A @ B ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,855]) ).
thf(873,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ ( not @ C ) @ ( or @ B @ A ) ) @ ( or @ B @ ( implies @ C @ A ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[872:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ ( not @ C ) @ ( or @ B @ A ) ) @ ( or @ B @ ( implies @ C @ A ) ) ) )
= true ),
inference(simp,[status(thm)],[873]) ).
thf(20145,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ C @ ( or @ B @ A ) ) @ ( or @ B @ ( implies @ C @ A ) ) ) )
= true ),
inference(rewrite,[status(thm)],[903,28]) ).
thf(27829,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ B @ C ) )
= true )
| ( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13962,1046]) ).
thf(27830,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( or @ B @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[27829:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( or @ F @ ( not @ F ) ))]]) ).
thf(27953,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( or @ B @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[27830]) ).
thf(28189,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[27953,11181]) ).
thf(28266,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[28189]) ).
thf(12617,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[12485,11181]) ).
thf(12658,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ B ) )
!= r ),
inference(simp,[status(thm)],[12617]) ).
thf(12712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( implies @ D @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,12658]) ).
thf(12713,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ B ) )
!= r ),
inference(pattern_uni,[status(thm)],[12712:[bind(A,$thf( E )),bind(B,$thf( implies @ G @ G )),bind(C,$thf( not @ E )),bind(D,$thf( G ))]]) ).
thf(12714,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ B ) )
!= r ),
inference(simp,[status(thm)],[12713]) ).
thf(3917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ ( implies @ D @ ( not @ D ) ) @ ( not @ D ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,3831]) ).
thf(3918,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[3917:[bind(A,$thf( M )),bind(B,$thf( implies @ M @ ( not @ M ) )),bind(C,$thf( implies @ M @ ( not @ ( implies @ M @ ( not @ M ) ) ) )),bind(D,$thf( M ))]]) ).
thf(3973,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[3918]) ).
thf(4006,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[3973,16]) ).
thf(4076,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4006,30]) ).
thf(4077,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[4076:[bind(A,$thf( H )),bind(B,$thf( implies @ H @ ( not @ ( implies @ H @ ( not @ H ) ) ) ))]]) ).
thf(4097,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[4077]) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[99,981]) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( implies @ ( or @ J @ I ) @ ( or @ I @ J ) ))]]) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1024]) ).
thf(27045,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1042,16]) ).
thf(27254,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[27045,11181]) ).
thf(27331,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) )
!= r ),
inference(simp,[status(thm)],[27254]) ).
thf(27385,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ ( implies @ ( implies @ A @ B ) @ ( or @ D @ E ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,27331]) ).
thf(27386,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ ( implies @ C @ A ) @ ( or @ A @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[27385:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( not @ F ))]]) ).
thf(27391,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ ( implies @ C @ A ) @ ( or @ A @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[27386]) ).
thf(11279,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[79,11181]) ).
thf(11303,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( or @ A @ B ) )
!= r ),
inference(simp,[status(thm)],[11279]) ).
thf(1028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[79,981]) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1028:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ H @ ( or @ G @ H ) ))]]) ).
thf(1044,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1029]) ).
thf(1627,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1044,16]) ).
thf(3139,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ D @ E ) ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( or @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[1627,3106]) ).
thf(3140,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[3139:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( implies @ I @ ( or @ H @ I ) )),bind(E,$thf( A ))]]) ).
thf(3225,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[3140]) ).
thf(3238,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[3225,16]) ).
thf(11196,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[3238,10861]) ).
thf(11236,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11196]) ).
thf(21850,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ E @ ( or @ D @ E ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,11236]) ).
thf(21853,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( B != r )
| ( ( not @ A )
!= ( implies @ E @ ( or @ D @ E ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[21850]) ).
thf(21857,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= ( implies @ B @ ( or @ A @ B ) ) ),
inference(simp,[status(thm)],[21853]) ).
thf(14318,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ B @ ( not @ C ) ) ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ ( implies @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[14188,8198]) ).
thf(14319,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[14318:[bind(A,$thf( E )),bind(B,$thf( not @ ( not @ E ) )),bind(C,$thf( E ))]]) ).
thf(14449,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[14319]) ).
thf(17156,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(rewrite,[status(thm)],[14449,16]) ).
thf(17160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ B @ C ) )
= true )
| ( ( theorem @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17156,629]) ).
thf(17161,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( or @ ( not @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[17160:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( or @ ( not @ ( not @ H ) ) @ ( not @ H ) ))]]) ).
thf(17380,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( or @ ( not @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[17161]) ).
thf(22059,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) )
= true ),
inference(rewrite,[status(thm)],[17380,28]) ).
thf(22245,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[22059,10861]) ).
thf(22300,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[22245]) ).
thf(17327,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17156,30]) ).
thf(17328,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[17327:[bind(A,$thf( G )),bind(B,$thf( or @ ( not @ ( not @ G ) ) @ ( not @ G ) ))]]) ).
thf(17392,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[17328]) ).
thf(18482,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[17392,28]) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ C @ ( implies @ ( implies @ A @ B ) @ D ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,1139]) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1155:[bind(A,$thf( F )),bind(B,$thf( not @ F )),bind(C,$thf( C )),bind(D,$thf( not @ F ))]]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[1156]) ).
thf(11280,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[1197,11181]) ).
thf(11288,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[11280]) ).
thf(2090,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[2070,261]) ).
thf(2141,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[2090]) ).
thf(11265,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[3238,11181]) ).
thf(11296,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A )
!= r ),
inference(simp,[status(thm)],[11265]) ).
thf(11930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ ( implies @ E @ ( implies @ A @ B ) ) @ C )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11296]) ).
thf(11931,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B )
!= r ),
inference(pattern_uni,[status(thm)],[11930:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(11934,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B )
!= r ),
inference(simp,[status(thm)],[11931]) ).
thf(11960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ C @ ( implies @ E @ C ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,11934]) ).
thf(11961,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ C @ ( implies @ E @ C ) ) )
| ( B != D ) ),
inference(simp,[status(thm)],[11960]) ).
thf(11962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ C )
!= r )
| ( ( not @ A )
!= ( implies @ B @ ( implies @ D @ B ) ) ) ),
inference(simp,[status(thm)],[11961]) ).
thf(16185,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16032,14435]) ).
thf(16186,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[16185:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ ( implies @ F @ F ) ) ))]]) ).
thf(16254,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[16186]) ).
thf(23082,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[16254,16]) ).
thf(11207,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[4006,10861]) ).
thf(11215,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11207]) ).
thf(17125,plain,
! [A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( not @ ( implies @ A @ ( not @ A ) ) )
!= r ) ),
inference(simp,[status(thm)],[11215]) ).
thf(17126,plain,
( ( not @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[17125]) ).
thf(11192,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[375,10861]) ).
thf(11228,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11192]) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( axiom @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[101,30]) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[420:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( implies @ ( or @ J @ ( not @ I ) ) @ ( implies @ I @ J ) ))]]) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[421]) ).
thf(2614,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[437,16]) ).
thf(11369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2614,11295]) ).
thf(11370,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11369:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( implies @ ( or @ K @ ( not @ J ) ) @ ( implies @ J @ K ) ))]]) ).
thf(11421,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11370]) ).
thf(21515,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ ( implies @ A @ B ) @ ( implies @ D @ E ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,11421]) ).
thf(21516,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( implies @ B @ ( not @ C ) ) @ ( implies @ C @ ( not @ B ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[21515:[bind(A,$thf( F )),bind(B,$thf( not @ G )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( not @ F ))]]) ).
thf(21517,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( implies @ B @ ( not @ C ) ) @ ( implies @ C @ ( not @ B ) ) ) )
!= r ),
inference(simp,[status(thm)],[21516]) ).
thf(14102,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[13962,10861]) ).
thf(14168,plain,
! [A: $i] :
( ( or @ A @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[14102]) ).
thf(14201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,14168]) ).
thf(14202,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( not @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[14201:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(14203,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( not @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[14202]) ).
thf(817,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,785]) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) )
!= ( or @ C @ C ) ) ),
inference(simp,[status(thm)],[817]) ).
thf(15590,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) )
!= ( or @ C @ C ) ) ),
inference(rewrite,[status(thm)],[830,16]) ).
thf(552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,32]) ).
thf(553,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( implies @ B @ ( not @ A ) ) ) @ true @ ( theorem @ ( implies @ A @ ( not @ B ) ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( implies @ J @ ( not @ H ) )),bind(D,$thf( implies @ H @ ( not @ J ) ))]]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( implies @ B @ ( not @ A ) ) ) @ true @ ( theorem @ ( implies @ A @ ( not @ B ) ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[553]) ).
thf(9911,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ B @ ( not @ A ) ) ) @ true @ ( theorem @ ( implies @ A @ ( not @ B ) ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[568,16]) ).
thf(14345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ ( not @ C ) ) ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ ( implies @ C @ ( not @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14188,9911]) ).
thf(14346,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[14345:[bind(A,$thf( D )),bind(B,$thf( not @ D )),bind(C,$thf( D ))]]) ).
thf(14415,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[14346]) ).
thf(15623,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
= true ),
inference(rewrite,[status(thm)],[14415,16]) ).
thf(15784,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15623,14435]) ).
thf(15785,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[15784:[bind(A,$thf( F )),bind(B,$thf( implies @ ( not @ F ) @ ( not @ F ) ))]]) ).
thf(15850,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[15785]) ).
thf(22793,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[15850,16]) ).
thf(22842,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[22793,261]) ).
thf(23019,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[22842]) ).
thf(812,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[80,785]) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( implies @ B @ ( implies @ A @ B ) )
!= ( or @ C @ C ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(15870,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( implies @ B @ ( implies @ A @ B ) )
!= ( or @ C @ C ) ) ),
inference(rewrite,[status(thm)],[832,16]) ).
thf(12769,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ ( implies @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[12715,334]) ).
thf(12770,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[12769:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(18081,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17926,11295]) ).
thf(18082,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[18081:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ I @ ( not @ ( not @ I ) ) ) ) ))]]) ).
thf(18171,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[18082]) ).
thf(609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[463,574]) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[609:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( implies @ ( implies @ L @ ( not @ J ) ) @ ( implies @ J @ ( not @ L ) ) ))]]) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[610]) ).
thf(10153,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[621,16]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3249,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[3238,261]) ).
thf(3318,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[3249]) ).
thf(4500,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ E @ ( or @ D @ E ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,3318]) ).
thf(4503,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( B
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= ( implies @ E @ ( or @ D @ E ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4500]) ).
thf(4507,plain,
! [B: $i,A: $i] :
( ( not @ ( implies @ q @ r ) )
!= ( implies @ B @ ( or @ A @ B ) ) ),
inference(simp,[status(thm)],[4503]) ).
thf(4509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ ( implies @ A @ B ) )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,4507]) ).
thf(4510,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( not @ ( implies @ q @ r ) ) ),
inference(pattern_uni,[status(thm)],[4509:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(4511,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( not @ ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[4510]) ).
thf(15766,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[15623,10861]) ).
thf(15823,plain,
! [A: $i] :
( ( implies @ ( not @ A ) @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[15766]) ).
thf(28323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ B ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[629,27844]) ).
thf(28324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( or @ A @ ( implies @ B @ C ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[28323:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ F ))]]) ).
thf(28482,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( or @ A @ ( implies @ B @ C ) )
!= r ) ),
inference(simp,[status(thm)],[28324]) ).
thf(772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ q @ r ) )
| ( ( or @ C @ D )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,720]) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( implies @ q @ r ) )
| ( ( or @ A @ ( not @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[772:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( implies @ q @ r ) )
| ( ( or @ A @ ( not @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[773]) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ C )
!= ( implies @ q @ r ) )
| ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,780]) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ A @ ( not @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[1274:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ A @ ( not @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1275]) ).
thf(1966,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ A @ ( not @ B ) )
!= ( implies @ B @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[1277]) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ B ) )
!= ( implies @ B @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[1966]) ).
thf(1992,plain,
! [A: $i] :
( ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[1975]) ).
thf(4518,plain,
! [A: $i] :
( ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( not @ q ) ) )
| ( ( implies @ q @ ( not @ A ) )
!= ( implies @ q @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[1992]) ).
thf(4530,plain,
! [A: $i] :
( ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( not @ q ) ) )
| ( q != q )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[4518]) ).
thf(4547,plain,
! [A: $i] :
( ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[4530]) ).
thf(9378,plain,
! [A: $i] :
( ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ ( not @ A ) ) )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ A @ ( not @ q ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4547]) ).
thf(9379,plain,
! [A: $i] :
( ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ ( not @ A ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ ( not @ A ) ) ) ),
inference(simp,[status(thm)],[9378]) ).
thf(15711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ C ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ ( implies @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[15623,32]) ).
thf(15712,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( not @ A ) ) @ true @ ( theorem @ ( not @ A ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[15711:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(15866,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( not @ A ) ) @ true @ ( theorem @ ( not @ A ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[15712]) ).
thf(24192,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ ( not @ A ) ) @ true @ ( theorem @ ( not @ A ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[15866,16]) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[80,981]) ).
thf(1011,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1010:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ H @ ( implies @ G @ H ) ))]]) ).
thf(1051,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1011]) ).
thf(1890,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1051,16]) ).
thf(3117,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ D @ E ) ) @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ ( or @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[1890,3106]) ).
thf(3118,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[3117:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( implies @ I @ ( implies @ H @ I ) )),bind(E,$thf( A ))]]) ).
thf(3232,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[3118]) ).
thf(3725,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[3232,16]) ).
thf(11379,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ E )
!= r )
| ( ( theorem @ ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[3725,11295]) ).
thf(11380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ D @ ( implies @ C @ D ) ) @ B ) )
!= r ),
inference(pattern_uni,[status(thm)],[11379:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( or @ ( implies @ K @ ( implies @ J @ K ) ) @ G ))]]) ).
thf(11426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ D @ ( implies @ C @ D ) ) @ B ) )
!= r ),
inference(simp,[status(thm)],[11380]) ).
thf(22626,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[17907,10861]) ).
thf(22689,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[22626]) ).
thf(22749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( not @ ( not @ ( implies @ A @ B ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,22689]) ).
thf(22750,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[22749:[bind(A,$thf( G )),bind(B,$thf( not @ ( not @ G ) )),bind(C,$thf( C )),bind(D,$thf( not @ G ))]]) ).
thf(22752,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[22750]) ).
thf(1967,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ A @ ( not @ B ) )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ B @ ( not @ A ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1277]) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ B ) )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ B @ ( not @ A ) ) ) ),
inference(simp,[status(thm)],[1967]) ).
thf(1985,plain,
! [A: $i] :
( ( ( not @ A )
!= r )
| ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ ( not @ A ) ) ) ),
inference(simp,[status(thm)],[1968]) ).
thf(11389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1197,11295]) ).
thf(11390,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ ( implies @ C @ ( not @ C ) ) @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11389:[bind(A,$thf( E )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( implies @ ( implies @ L @ ( not @ L ) ) @ ( not @ L ) ) ))]]) ).
thf(11431,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ ( implies @ C @ ( not @ C ) ) @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[11390]) ).
thf(3495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ ( implies @ ( implies @ A @ B ) @ D ) @ C ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,3475]) ).
thf(3496,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) )
= true ),
inference(pattern_uni,[status(thm)],[3495:[bind(A,$thf( F )),bind(B,$thf( not @ F )),bind(C,$thf( C )),bind(D,$thf( not @ F ))]]) ).
thf(3569,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) )
= true ),
inference(simp,[status(thm)],[3496]) ).
thf(11255,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[3569,11181]) ).
thf(11299,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A )
!= r ),
inference(simp,[status(thm)],[11255]) ).
thf(11274,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[99,11181]) ).
thf(11302,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) )
!= r ),
inference(simp,[status(thm)],[11274]) ).
thf(11941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ ( or @ D @ C ) @ ( implies @ A @ B ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,11302]) ).
thf(11942,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= r ),
inference(pattern_uni,[status(thm)],[11941:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(11944,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= r ),
inference(simp,[status(thm)],[11942]) ).
thf(1254,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1197,30]) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[1254:[bind(A,$thf( D )),bind(B,$thf( K )),bind(C,$thf( implies @ D @ ( implies @ ( implies @ K @ ( not @ K ) ) @ ( not @ K ) ) ))]]) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[1255]) ).
thf(813,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true = C )
| ( ( ifeq @ ( theorem @ ( or @ A @ A ) ) @ true @ ( theorem @ A ) @ true )
!= ( ifeq @ B @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[785,16]) ).
thf(833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true = C )
| ( ( theorem @ ( or @ A @ A ) )
!= B )
| ( true != B )
| ( ( theorem @ A )
!= C )
| ( true != D ) ),
inference(simp,[status(thm)],[813]) ).
thf(838,plain,
! [A: $i] :
( ( ( theorem @ A )
= true )
| ( ( theorem @ ( or @ A @ A ) )
!= true ) ),
inference(simp,[status(thm)],[833]) ).
thf(15881,plain,
! [A: $i] :
( ( ( not @ A )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[15823]) ).
thf(1644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ C @ ( implies @ E @ ( implies @ A @ B ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,1627]) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1644:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(1694,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
= true ),
inference(simp,[status(thm)],[1645]) ).
thf(1773,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1694,261]) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1773]) ).
thf(28327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[14414,27844]) ).
thf(28328,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28327:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( implies @ J @ ( not @ ( not @ J ) ) ) ))]]) ).
thf(28486,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28328]) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[99,574]) ).
thf(580,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[579:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( implies @ ( or @ J @ I ) @ ( or @ I @ J ) ))]]) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[580]) ).
thf(10398,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[622,16]) ).
thf(11257,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[10398,11181]) ).
thf(11287,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( or @ C @ B ) @ ( or @ B @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11257]) ).
thf(16709,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ ( implies @ A @ B ) @ ( or @ D @ E ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,11287]) ).
thf(16710,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ ( implies @ C @ A ) @ ( or @ A @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[16709:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( not @ F ))]]) ).
thf(16712,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ ( implies @ C @ A ) @ ( or @ A @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[16710]) ).
thf(870,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( or @ D @ ( or @ C @ E ) ) @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( or @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,855]) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( or @ ( not @ A ) @ C ) ) @ ( implies @ A @ ( or @ B @ C ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[870:[bind(A,$thf( F )),bind(B,$thf( or @ G @ H )),bind(C,$thf( not @ F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( or @ ( not @ A ) @ C ) ) @ ( implies @ A @ ( or @ B @ C ) ) ) )
= true ),
inference(simp,[status(thm)],[871]) ).
thf(19851,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( implies @ A @ C ) ) @ ( implies @ A @ ( or @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[902,28]) ).
thf(1151,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1139,261]) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1151]) ).
thf(11359,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ E )
!= r )
| ( ( theorem @ ( or @ ( implies @ C @ ( or @ B @ C ) ) @ A ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[3238,11295]) ).
thf(11360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ D @ ( or @ C @ D ) ) @ B ) )
!= r ),
inference(pattern_uni,[status(thm)],[11359:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( or @ ( implies @ K @ ( or @ J @ K ) ) @ G ))]]) ).
thf(11416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ D @ ( or @ C @ D ) ) @ B ) )
!= r ),
inference(simp,[status(thm)],[11360]) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( A != r )
| ( ( or @ A @ ( not @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[780]) ).
thf(1276,plain,
( ( or @ r @ ( not @ q ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[1273]) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ r @ ( not @ q ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,1276]) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( B != r )
| ( ( not @ A )
!= r )
| ( B
!= ( not @ q ) ) ),
inference(simp,[status(thm)],[1278]) ).
thf(1283,plain,
( ( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= r )
| ( ( not @ q )
!= r ) ),
inference(simp,[status(thm)],[1281]) ).
thf(1461,plain,
( ( ( not @ q )
!= r )
| ( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= ( not @ q ) )
| ( r != r ) ),
inference(eqfactor_ordered,[status(thm)],[1283]) ).
thf(1462,plain,
( ( ( not @ q )
!= r )
| ( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= ( not @ q ) ) ),
inference(simp,[status(thm)],[1461]) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1325,261]) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1337]) ).
thf(2342,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( ( implies @ C @ ( or @ B @ C ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(2345,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( or @ A @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[2342]) ).
thf(2347,plain,
! [B: $i,A: $i] :
( ( B
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( or @ A @ B )
!= r ) ),
inference(simp,[status(thm)],[2345]) ).
thf(2350,plain,
! [A: $i] :
( ( or @ A @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= r ),
inference(simp,[status(thm)],[2347]) ).
thf(2354,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,2350]) ).
thf(2355,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[2354:[bind(A,$thf( D )),bind(B,$thf( not @ ( implies @ p @ ( not @ q ) ) )),bind(C,$thf( not @ D ))]]) ).
thf(2356,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= r ),
inference(simp,[status(thm)],[2355]) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[375,574]) ).
thf(592,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[591:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( implies @ ( implies @ K @ I ) @ ( or @ I @ ( not @ K ) ) ))]]) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[592]) ).
thf(11453,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[632,16]) ).
thf(599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[377,574]) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( implies @ ( or @ K @ ( not @ J ) ) @ ( implies @ J @ K ) ))]]) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[600]) ).
thf(11696,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[636,16]) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,785]) ).
thf(831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( implies @ B @ ( or @ A @ B ) )
!= ( or @ C @ C ) ) ),
inference(simp,[status(thm)],[827]) ).
thf(15601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( implies @ B @ ( or @ A @ B ) )
!= ( or @ C @ C ) ) ),
inference(rewrite,[status(thm)],[831,16]) ).
thf(11365,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ E )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1325,11295]) ).
thf(11366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ D @ ( or @ C @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11365:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( implies @ F @ ( implies @ K @ ( or @ J @ K ) ) ))]]) ).
thf(11419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ D @ ( or @ C @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[11366]) ).
thf(18622,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ ( implies @ F @ ( implies @ A @ B ) ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[28,11419]) ).
thf(18623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ C @ ( implies @ A @ ( implies @ D @ A ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[18622:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( not @ G )),bind(F,$thf( B ))]]) ).
thf(18624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ C @ ( implies @ A @ ( implies @ D @ A ) ) ) )
!= r ),
inference(simp,[status(thm)],[18623]) ).
thf(12053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( implies @ A @ B ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[629,11399]) ).
thf(12054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ D )
!= true )
| ( ( implies @ A @ ( implies @ B @ ( implies @ C @ D ) ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[12053:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( implies @ F @ G ))]]) ).
thf(12137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ D )
!= true )
| ( ( implies @ A @ ( implies @ B @ ( implies @ C @ D ) ) )
!= r ) ),
inference(simp,[status(thm)],[12054]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( B
!= ( implies @ q @ r ) )
| ( ( or @ A @ B )
!= ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(135,plain,
! [A: $i] :
( ( or @ A @ ( implies @ q @ r ) )
!= ( implies @ ( and @ p @ q ) @ r ) ),
inference(simp,[status(thm)],[132]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( and @ p @ q ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( implies @ q @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,135]) ).
thf(138,plain,
! [A: $i] :
( ( implies @ A @ ( implies @ q @ r ) )
!= ( implies @ ( and @ p @ q ) @ r ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( D )),bind(B,$thf( implies @ q @ r )),bind(C,$thf( not @ D ))]]) ).
thf(139,plain,
! [A: $i] :
( ( implies @ A @ ( implies @ q @ r ) )
!= ( implies @ ( and @ p @ q ) @ r ) ),
inference(simp,[status(thm)],[138]) ).
thf(151,plain,
! [A: $i] :
( ( A
!= ( and @ p @ q ) )
| ( ( implies @ q @ r )
!= r ) ),
inference(simp,[status(thm)],[139]) ).
thf(152,plain,
( ( implies @ q @ r )
!= r ),
inference(simp,[status(thm)],[151]) ).
thf(17830,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[17682,11181]) ).
thf(17884,plain,
! [A: $i] :
( ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) )
!= r ),
inference(simp,[status(thm)],[17830]) ).
thf(12866,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[12715,10861]) ).
thf(12920,plain,
! [A: $i] :
( ( implies @ A @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[12866]) ).
thf(11205,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[99,10861]) ).
thf(11238,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11205]) ).
thf(22042,plain,
! [B: $i,A: $i] :
( ( ( or @ B @ A )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( or @ A @ B )
!= r ) ),
inference(simp,[status(thm)],[11238]) ).
thf(22367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( or @ C @ D )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,22042]) ).
thf(22368,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( or @ A @ ( not @ B ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[22367:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(22371,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( or @ A @ ( not @ B ) )
!= r ) ),
inference(simp,[status(thm)],[22368]) ).
thf(22387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ C )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,22371]) ).
thf(22388,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ A @ ( not @ B ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[22387:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(22389,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ A @ ( not @ B ) )
!= r ) ),
inference(simp,[status(thm)],[22388]) ).
thf(795,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( theorem @ C ) @ true )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,785]) ).
thf(796,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( not @ A ) ) ) @ true @ ( theorem @ ( not @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[795:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(847,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( not @ A ) ) ) @ true @ ( theorem @ ( not @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[796]) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( implies @ D @ ( not @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[855,847]) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ D ) ) @ true )
= true )
| ( ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) )
!= ( implies @ D @ ( not @ D ) ) ) ),
inference(simp,[status(thm)],[938]) ).
thf(24609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ D ) )
= true )
| ( ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) )
!= ( implies @ D @ ( not @ D ) ) ) ),
inference(rewrite,[status(thm)],[967,16]) ).
thf(25331,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ B ) ) ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,25250]) ).
thf(25332,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[25331:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(25544,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) ) )
= true ),
inference(simp,[status(thm)],[25332]) ).
thf(25852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25544,11295]) ).
thf(25853,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[25852:[bind(A,$thf( K )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( not @ ( not @ ( implies @ K @ ( not @ ( not @ K ) ) ) ) ) ) ))]]) ).
thf(25980,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[25853]) ).
thf(11335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ E )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1890,11295]) ).
thf(11336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ D @ ( implies @ C @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11335:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( or @ F @ ( implies @ K @ ( implies @ J @ K ) ) ))]]) ).
thf(11404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ D @ ( implies @ C @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[11336]) ).
thf(11441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( or @ C @ D ) @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,11311]) ).
thf(11444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( or @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[11441]) ).
thf(11446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ ( not @ C ) )
!= r )
| ( ( not @ A )
!= ( or @ B @ C ) ) ),
inference(simp,[status(thm)],[11444]) ).
thf(25275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25250,11399]) ).
thf(25276,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( not @ ( not @ ( or @ C @ ( not @ C ) ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[25275:[bind(A,$thf( K )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ ( not @ ( not @ ( not @ ( or @ K @ ( not @ K ) ) ) ) ) ))]]) ).
thf(25526,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( not @ ( not @ ( or @ C @ ( not @ C ) ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[25276]) ).
thf(6156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6054,30]) ).
thf(6157,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[6156:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( or @ ( implies @ F @ H ) @ ( not @ H ) ))]]) ).
thf(6187,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[6157]) ).
thf(23873,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[23685,10861]) ).
thf(23933,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ B ) @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[23873]) ).
thf(23997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ D @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,23933]) ).
thf(24000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( B != r )
| ( ( not @ A )
!= ( implies @ D @ D ) )
| ( B != C ) ),
inference(simp,[status(thm)],[23997]) ).
thf(24001,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= ( implies @ A @ A ) ),
inference(simp,[status(thm)],[24000]) ).
thf(11391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2070,11295]) ).
thf(11392,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ ( implies @ C @ ( not @ C ) ) @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11391:[bind(A,$thf( E )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( implies @ ( implies @ L @ ( not @ L ) ) @ ( not @ L ) ) ))]]) ).
thf(11398,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ ( implies @ C @ ( not @ C ) ) @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[11392]) ).
thf(6590,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[6578,261]) ).
thf(6717,plain,
! [A: $i] :
( ( or @ A @ ( not @ ( or @ A @ A ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[6590]) ).
thf(11259,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[1627,11181]) ).
thf(11312,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11259]) ).
thf(22961,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[22793,11181]) ).
thf(23042,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) )
!= r ),
inference(simp,[status(thm)],[22961]) ).
thf(28188,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[27953,10861]) ).
thf(28253,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( not @ B ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[28188]) ).
thf(13612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12710,30]) ).
thf(13613,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ B @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[13612:[bind(A,$thf( D )),bind(B,$thf( G )),bind(C,$thf( implies @ D @ ( implies @ G @ G ) ))]]) ).
thf(13668,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ B @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[13613]) ).
thf(3601,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[3569,261]) ).
thf(3676,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[3601]) ).
thf(140,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,14]) ).
thf(149,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(411,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(rewrite,[status(thm)],[149,260]) ).
thf(17936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( implies @ A @ B ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,17884]) ).
thf(17937,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[17936:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(17938,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[17937]) ).
thf(950,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ C @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,847]) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( implies @ B @ ( or @ A @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[950]) ).
thf(23368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ C ) )
= true )
| ( ( implies @ B @ ( or @ A @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(rewrite,[status(thm)],[960,16]) ).
thf(118,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,14]) ).
thf(127,plain,
! [A: $i] :
( ( implies @ ( or @ A @ A ) @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(188,plain,
! [A: $i] :
( ( ( or @ A @ A )
!= ( implies @ q @ r ) )
| ( A
!= ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(191,plain,
( ( or @ ( implies @ ( and @ p @ q ) @ r ) @ ( implies @ ( and @ p @ q ) @ r ) )
!= ( implies @ q @ r ) ),
inference(simp,[status(thm)],[188]) ).
thf(265,plain,
( ( or @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
!= ( implies @ q @ r ) ),
inference(rewrite,[status(thm)],[191,260]) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( ( implies @ ( or @ B @ B ) @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1191]) ).
thf(1843,plain,
! [A: $i] :
( ( implies @ ( or @ A @ A ) @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[1839]) ).
thf(11353,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6578,11295]) ).
thf(11354,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ ( or @ B @ B ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11353:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( or @ H @ ( not @ ( or @ H @ H ) ) ))]]) ).
thf(11413,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ ( or @ B @ B ) ) ) )
!= r ),
inference(simp,[status(thm)],[11354]) ).
thf(27715,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ B @ C ) )
= true )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16032,1046]) ).
thf(27716,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[27715:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ G @ G ) ) ))]]) ).
thf(27897,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
= true ),
inference(simp,[status(thm)],[27716]) ).
thf(29328,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[27897,10861]) ).
thf(29398,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[29328]) ).
thf(13995,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[13962,261]) ).
thf(14162,plain,
! [A: $i] :
( ( or @ A @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[13995]) ).
thf(28435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4006,27844]) ).
thf(28436,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( not @ ( implies @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28435:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( implies @ I @ ( not @ ( implies @ I @ ( not @ I ) ) ) ))]]) ).
thf(28473,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( not @ ( implies @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28436]) ).
thf(6062,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[6054,261]) ).
thf(6183,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ A @ B ) @ ( not @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[6062]) ).
thf(11262,plain,
! [A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[6578,11181]) ).
thf(11307,plain,
! [A: $i] :
( ( or @ A @ ( not @ ( or @ A @ A ) ) )
!= r ),
inference(simp,[status(thm)],[11262]) ).
thf(17852,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17682,30]) ).
thf(17853,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[17852:[bind(A,$thf( G )),bind(B,$thf( not @ ( not @ ( or @ G @ ( not @ G ) ) ) ))]]) ).
thf(17919,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[17853]) ).
thf(6118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ ( or @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[6054,3106]) ).
thf(6119,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ B ) @ ( implies @ A @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[6118:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( not @ G )),bind(D,$thf( implies @ E @ G ))]]) ).
thf(6195,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ B ) @ ( implies @ A @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[6119]) ).
thf(7037,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ B ) @ ( implies @ A @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[6195,16]) ).
thf(27387,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ ( implies @ ( or @ E @ D ) @ ( implies @ A @ B ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,27331]) ).
thf(27388,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ ( or @ A @ ( not @ C ) ) @ ( implies @ C @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[27387:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(27392,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ ( or @ A @ ( not @ C ) ) @ ( implies @ C @ A ) ) )
!= r ),
inference(simp,[status(thm)],[27388]) ).
thf(12109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4006,11399]) ).
thf(12110,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( implies @ C @ ( not @ C ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12109:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( implies @ J @ ( not @ ( implies @ J @ ( not @ J ) ) ) ))]]) ).
thf(12132,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( implies @ C @ ( not @ C ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[12110]) ).
thf(11266,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[81,11181]) ).
thf(11292,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= r ),
inference(simp,[status(thm)],[11266]) ).
thf(1062,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( not @ ( implies @ p @ ( not @ q ) ) )
!= A )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1074,plain,
( ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
!= ( implies @ q @ r ) )
| ( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= r ) ),
inference(simp,[status(thm)],[1062]) ).
thf(11322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ ( implies @ A @ B ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,11303]) ).
thf(11323,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= r ),
inference(pattern_uni,[status(thm)],[11322:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(11324,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= r ),
inference(simp,[status(thm)],[11323]) ).
thf(11347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ E )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1627,11295]) ).
thf(11348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ D @ ( or @ C @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11347:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( or @ F @ ( implies @ K @ ( or @ J @ K ) ) ))]]) ).
thf(11410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ D @ ( or @ C @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[11348]) ).
thf(11375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3475,11295]) ).
thf(11376,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ ( or @ C @ C ) @ C ) @ B ) )
!= r ),
inference(pattern_uni,[status(thm)],[11375:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( or @ ( implies @ ( or @ H @ H ) @ H ) @ F ))]]) ).
thf(11424,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ ( or @ C @ C ) @ C ) @ B ) )
!= r ),
inference(simp,[status(thm)],[11376]) ).
thf(17946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ B @ C ) )
= true )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17926,629]) ).
thf(17947,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[17946:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ I @ ( not @ ( not @ I ) ) ) ) ))]]) ).
thf(18168,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) ) )
= true ),
inference(simp,[status(thm)],[17947]) ).
thf(11201,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[2614,10861]) ).
thf(11223,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11201]) ).
thf(13966,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ B @ C ) )
= true )
| ( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13962,629]) ).
thf(13967,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( or @ B @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[13966:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( or @ F @ ( not @ F ) ))]]) ).
thf(14172,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( or @ B @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[13967]) ).
thf(15360,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[14172,261]) ).
thf(15531,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ B ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[15360]) ).
thf(4014,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[4006,261]) ).
thf(4091,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[4014]) ).
thf(155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( or @ C @ ( or @ D @ E ) ) @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ ( or @ C @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,24]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ B @ ( or @ ( not @ A ) @ C ) ) @ ( implies @ A @ ( or @ B @ C ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( F )),bind(B,$thf( or @ G @ H )),bind(C,$thf( G )),bind(D,$thf( not @ F )),bind(E,$thf( H ))]]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ B @ ( or @ ( not @ A ) @ C ) ) @ ( implies @ A @ ( or @ B @ C ) ) ) )
= true ),
inference(simp,[status(thm)],[156]) ).
thf(1099,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ B @ ( implies @ A @ C ) ) @ ( implies @ A @ ( or @ B @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[179,28]) ).
thf(1118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ C @ ( or @ D @ E ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ ( implies @ C @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,1099]) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( implies @ B @ C ) ) @ ( implies @ B @ ( or @ ( not @ A ) @ C ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1118:[bind(A,$thf( F )),bind(B,$thf( implies @ G @ H )),bind(C,$thf( G )),bind(D,$thf( not @ F )),bind(E,$thf( H ))]]) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( implies @ B @ C ) ) @ ( implies @ B @ ( or @ ( not @ A ) @ C ) ) ) )
= true ),
inference(simp,[status(thm)],[1119]) ).
thf(32476,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( implies @ B @ C ) ) @ ( implies @ B @ ( implies @ A @ C ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1137,28]) ).
thf(22952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22793,11295]) ).
thf(22953,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[22952:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ ( not @ I ) @ ( not @ I ) ) ) ))]]) ).
thf(23053,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[22953]) ).
thf(28377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25544,27844]) ).
thf(28378,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28377:[bind(A,$thf( K )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( not @ ( not @ ( implies @ K @ ( not @ ( not @ K ) ) ) ) ) ) ))]]) ).
thf(28515,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28378]) ).
thf(1013,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ D @ E ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[855,981]) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1013:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( implies @ ( or @ N @ ( or @ L @ O ) ) @ ( or @ L @ ( or @ N @ O ) ) ))]]) ).
thf(1052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1014]) ).
thf(30199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1052,16]) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[377,32]) ).
thf(483,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ B @ ( not @ A ) ) ) @ true @ ( theorem @ ( implies @ A @ B ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( or @ I @ ( not @ H ) )),bind(D,$thf( implies @ H @ I ))]]) ).
thf(492,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ B @ ( not @ A ) ) ) @ true @ ( theorem @ ( implies @ A @ B ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[483]) ).
thf(8731,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( or @ B @ ( not @ A ) ) ) @ true @ ( theorem @ ( implies @ A @ B ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[492,16]) ).
thf(23847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
!= ( theorem @ ( or @ D @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[23685,8731]) ).
thf(23848,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ ( implies @ A @ A ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[23847:[bind(A,$thf( not @ G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( implies @ F @ F ))]]) ).
thf(23968,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ ( implies @ A @ A ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[23848]) ).
thf(33717,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ A ) ) )
= true ),
inference(rewrite,[status(thm)],[23968,16]) ).
thf(33964,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ A ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[33717,10861]) ).
thf(34048,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[33964]) ).
thf(11195,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[1139,10861]) ).
thf(11217,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11195]) ).
thf(3738,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[3725,261]) ).
thf(3816,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[3738]) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,785]) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) )
!= ( or @ C @ C ) ) ),
inference(simp,[status(thm)],[822]) ).
thf(15886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) )
!= ( or @ C @ C ) ) ),
inference(rewrite,[status(thm)],[834,16]) ).
thf(5459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ E @ ( implies @ D @ E ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,3816]) ).
thf(5462,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( B
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= ( implies @ E @ ( implies @ D @ E ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[5459]) ).
thf(5465,plain,
! [B: $i,A: $i] :
( ( not @ ( implies @ q @ r ) )
!= ( implies @ B @ ( implies @ A @ B ) ) ),
inference(simp,[status(thm)],[5462]) ).
thf(1881,plain,
! [A: $i] :
( ( ( or @ A @ A )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( A != r ) ),
inference(simp,[status(thm)],[1843]) ).
thf(1884,plain,
( ( or @ r @ r )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[1881]) ).
thf(1886,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ r @ r ) ) ),
inference(paramod_ordered,[status(thm)],[28,1884]) ).
thf(1887,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( not @ A )
!= r )
| ( B != r ) ),
inference(simp,[status(thm)],[1886]) ).
thf(1888,plain,
! [A: $i] :
( ( ( implies @ A @ r )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[1887]) ).
thf(16036,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ B @ C ) )
= true )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16032,629]) ).
thf(16037,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[16036:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ G @ G ) ) ))]]) ).
thf(16247,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
= true ),
inference(simp,[status(thm)],[16037]) ).
thf(25421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25250,11295]) ).
thf(25422,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[25421:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( not @ ( not @ ( or @ J @ ( not @ J ) ) ) ) ) ))]]) ).
thf(25534,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[25422]) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,261]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(16593,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[14414,10861]) ).
thf(16652,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[16593]) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ D ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1325,30]) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( E )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( implies @ E @ ( implies @ J @ ( or @ I @ J ) ) ))]]) ).
thf(1392,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[1374]) ).
thf(12065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[6054,11399]) ).
thf(12066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ ( implies @ C @ D ) @ ( not @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12065:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( or @ ( implies @ H @ J ) @ ( not @ J ) ))]]) ).
thf(12147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ ( implies @ C @ D ) @ ( not @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[12066]) ).
thf(13475,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[12710,261]) ).
thf(13639,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[13475]) ).
thf(11264,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[1139,11181]) ).
thf(11284,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= r ),
inference(simp,[status(thm)],[11264]) ).
thf(11185,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[6054,10861]) ).
thf(11234,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ A @ B ) @ ( not @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11185]) ).
thf(22426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ ( implies @ A @ B ) @ C )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,22424]) ).
thf(22427,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(pattern_uni,[status(thm)],[22426:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(22428,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(simp,[status(thm)],[22427]) ).
thf(23086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ B @ C ) )
= true )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23082,629]) ).
thf(23087,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[23086:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( not @ ( not @ ( implies @ I @ I ) ) ) ) ))]]) ).
thf(23341,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) ) ) )
= true ),
inference(simp,[status(thm)],[23087]) ).
thf(6915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( B
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= ( or @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[6910]) ).
thf(6919,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ B ) ) ),
inference(simp,[status(thm)],[6915]) ).
thf(29376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27897,27844]) ).
thf(29377,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[29376:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( not @ ( not @ ( implies @ J @ J ) ) ) ))]]) ).
thf(29440,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[29377]) ).
thf(11254,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[6054,11181]) ).
thf(11304,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ A @ B ) @ ( not @ B ) )
!= r ),
inference(simp,[status(thm)],[11254]) ).
thf(22818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[22793,11399]) ).
thf(22819,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ ( not @ C ) @ ( not @ C ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[22818:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ ( not @ ( implies @ ( not @ J ) @ ( not @ J ) ) ) ))]]) ).
thf(23049,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ ( not @ C ) @ ( not @ C ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[22819]) ).
thf(11184,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[1890,10861]) ).
thf(11221,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11184]) ).
thf(11273,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[3475,11181]) ).
thf(11294,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A )
!= r ),
inference(simp,[status(thm)],[11273]) ).
thf(11924,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ ( or @ D @ D ) @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,11294]) ).
thf(11927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ ( or @ D @ D ) @ D ) )
| ( B != C ) ),
inference(simp,[status(thm)],[11924]) ).
thf(11929,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ ( or @ C @ C ) @ C ) ) ),
inference(simp,[status(thm)],[11927]) ).
thf(15660,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[15623,261]) ).
thf(15814,plain,
! [A: $i] :
( ( implies @ ( not @ A ) @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[15660]) ).
thf(16031,plain,
! [A: $i] :
( ( ( not @ A )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[15814]) ).
thf(15598,plain,
! [A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( ( not @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[14399]) ).
thf(15599,plain,
( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ ( not @ ( implies @ q @ r ) ) ) ),
inference(simp,[status(thm)],[15598]) ).
thf(1634,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1627,261]) ).
thf(1683,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1634]) ).
thf(22112,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[22059,261]) ).
thf(22306,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[22112]) ).
thf(17940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( implies @ A @ B ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,17903]) ).
thf(17941,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[17940:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(17942,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[17941]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[79,30]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ B @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( implies @ G @ ( or @ F @ G ) ))]]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ B @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[107]) ).
thf(193,plain,
( ( ifeq @ true @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[110,20]) ).
thf(17702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[17682,11399]) ).
thf(17703,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( or @ C @ ( not @ C ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[17702:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ ( not @ ( or @ I @ ( not @ I ) ) ) ))]]) ).
thf(17912,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( or @ C @ ( not @ C ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[17703]) ).
thf(23865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23685,11295]) ).
thf(23866,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ C @ C ) @ B ) )
!= r ),
inference(pattern_uni,[status(thm)],[23865:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( or @ ( implies @ H @ H ) @ F ))]]) ).
thf(23974,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ C @ C ) @ B ) )
!= r ),
inference(simp,[status(thm)],[23866]) ).
thf(1882,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ ( implies @ A @ B ) @ C )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,1843]) ).
thf(1883,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[1882:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(1885,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[1883]) ).
thf(1889,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ A ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[1885]) ).
thf(11199,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[1325,10861]) ).
thf(11248,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11199]) ).
thf(13978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13962,11399]) ).
thf(13979,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[13978:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( or @ G @ ( not @ G ) ))]]) ).
thf(14174,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[13979]) ).
thf(7148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( not @ B ) @ ( implies @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7037,30]) ).
thf(7149,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ B ) @ ( implies @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[7148:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( or @ ( not @ H ) @ ( implies @ G @ H ) ))]]) ).
thf(7195,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ B ) @ ( implies @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[7149]) ).
thf(8599,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ B @ ( implies @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[7195,28]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[82,30]) ).
thf(124,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( D )),bind(B,$thf( implies @ ( or @ D @ D ) @ D ))]]) ).
thf(129,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[124]) ).
thf(16166,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[16032,10861]) ).
thf(16237,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[16166]) ).
thf(11269,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[80,11181]) ).
thf(11300,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ B ) )
!= r ),
inference(simp,[status(thm)],[11269]) ).
thf(17014,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[16247,10861]) ).
thf(17069,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[17014]) ).
thf(6815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ ( or @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[6747,3106]) ).
thf(6816,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[6815:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( not @ G )),bind(D,$thf( or @ E @ G ))]]) ).
thf(6891,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[6816]) ).
thf(8015,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[6891,16]) ).
thf(8127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8015,30]) ).
thf(8128,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[8127:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( or @ ( not @ H ) @ ( or @ G @ H ) ))]]) ).
thf(8162,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[8128]) ).
thf(8980,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ B @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[8162,28]) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ B ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ ( implies @ B @ ( not @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,847]) ).
thf(955,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ B ) ) @ true )
= true )
| ( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( implies @ B @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[932]) ).
thf(22432,plain,
! [B: $i,A: $i] :
( ( ( theorem @ ( not @ B ) )
= true )
| ( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( implies @ B @ ( not @ B ) ) ) ),
inference(rewrite,[status(thm)],[955,16]) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[375,981]) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1001:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( implies @ ( implies @ K @ I ) @ ( or @ I @ ( not @ K ) ) ))]]) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1002]) ).
thf(28748,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1047,16]) ).
thf(1060,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( not @ A ) ) ) ),
inference(simp,[status(thm)],[1058]) ).
thf(6205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ C @ D ) @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,6183]) ).
thf(6207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( not @ A )
!= ( implies @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[6205]) ).
thf(6211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ ( not @ C ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( not @ A )
!= ( implies @ B @ C ) ) ),
inference(simp,[status(thm)],[6207]) ).
thf(878,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ D ) @ true @ ( theorem @ E ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( implies @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[855,32]) ).
thf(879,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ B @ ( or @ A @ C ) ) ) @ true @ ( theorem @ ( or @ A @ ( or @ B @ C ) ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[878:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( or @ L @ ( or @ J @ M ) )),bind(E,$thf( or @ J @ ( or @ L @ M ) ))]]) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ ( or @ B @ ( or @ A @ C ) ) ) @ true @ ( theorem @ ( or @ A @ ( or @ B @ C ) ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[879]) ).
thf(21119,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( or @ B @ ( or @ A @ C ) ) ) @ true @ ( theorem @ ( or @ A @ ( or @ B @ C ) ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[906,16]) ).
thf(11258,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[1552,11181]) ).
thf(11315,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11258]) ).
thf(13435,plain,
! [A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( A != r ) ),
inference(simp,[status(thm)],[12920]) ).
thf(13436,plain,
( ( not @ ( implies @ p @ ( not @ q ) ) )
!= r ),
inference(simp,[status(thm)],[13435]) ).
thf(27470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ B @ C ) )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14188,1046]) ).
thf(27471,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[27470:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( implies @ G @ ( not @ ( not @ G ) ) ))]]) ).
thf(27903,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
= true ),
inference(simp,[status(thm)],[27471]) ).
thf(28369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ D )
!= true )
| ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,27844]) ).
thf(28370,plain,
! [B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( implies @ B @ A )
!= r ) ),
inference(pattern_uni,[status(thm)],[28369:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(28511,plain,
! [B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( implies @ B @ A )
!= r ) ),
inference(simp,[status(thm)],[28370]) ).
thf(29631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ C )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27903,28511]) ).
thf(29632,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[29631:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( or @ E @ ( implies @ J @ ( not @ ( not @ J ) ) ) )),bind(D,$thf( D ))]]) ).
thf(29798,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[29632]) ).
thf(28385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[22059,27844]) ).
thf(28386,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( implies @ ( not @ C ) @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28385:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( implies @ ( not @ J ) @ ( not @ J ) ) ))]]) ).
thf(28519,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( implies @ ( not @ C ) @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[28386]) ).
thf(28389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6578,27844]) ).
thf(28390,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( not @ ( or @ B @ B ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28389:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( or @ H @ ( not @ ( or @ H @ H ) ) ))]]) ).
thf(28521,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( not @ ( or @ B @ B ) ) ) )
!= r ),
inference(simp,[status(thm)],[28390]) ).
thf(12749,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[12715,261]) ).
thf(12913,plain,
! [A: $i] :
( ( implies @ A @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[12749]) ).
thf(4230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ B @ C ) ) @ true )
= true )
| ( ( theorem @ ( or @ ( not @ A ) @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ ( or @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4188,3106]) ).
thf(4231,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( implies @ A @ ( not @ A ) ) ) @ ( not @ A ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[4230:[bind(A,$thf( H )),bind(B,$thf( not @ ( implies @ H @ ( not @ H ) ) )),bind(C,$thf( not @ H ))]]) ).
thf(4282,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( implies @ A @ ( not @ A ) ) ) @ ( not @ A ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[4231]) ).
thf(4308,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ ( implies @ A @ ( not @ A ) ) ) @ ( not @ A ) ) )
= true ),
inference(rewrite,[status(thm)],[4282,16]) ).
thf(266,plain,
! [A: $i] :
( ( or @ A @ ( implies @ q @ r ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(rewrite,[status(thm)],[135,260]) ).
thf(3486,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[3475,261]) ).
thf(3563,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ ( or @ B @ B ) @ B ) @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[3486]) ).
thf(1018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ C @ D ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[463,981]) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1018:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( implies @ ( implies @ L @ ( not @ J ) ) @ ( implies @ J @ ( not @ L ) ) ))]]) ).
thf(1053,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[1019]) ).
thf(31179,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[1053,16]) ).
thf(12081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6578,11399]) ).
thf(12082,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ C @ ( not @ ( or @ C @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12081:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( or @ I @ ( not @ ( or @ I @ I ) ) ))]]) ).
thf(12155,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ C @ ( not @ ( or @ C @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[12082]) ).
thf(27743,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( theorem @ ( or @ A @ B ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1046,10861]) ).
thf(27867,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( or @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[27743]) ).
thf(32995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ D )
!= true )
| ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,27867]) ).
thf(32996,plain,
! [B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( implies @ B @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[32995:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(33169,plain,
! [B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( implies @ B @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[32996]) ).
thf(11381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4006,11295]) ).
thf(11382,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( implies @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11381:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( implies @ I @ ( not @ ( implies @ I @ ( not @ I ) ) ) ))]]) ).
thf(11427,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( implies @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[11382]) ).
thf(412,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[411]) ).
thf(25430,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[25250,11181]) ).
thf(25481,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[25430]) ).
thf(25549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ B ) ) ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,25481]) ).
thf(25550,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[25549:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ F ) )),bind(C,$thf( not @ F ))]]) ).
thf(25551,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[25550]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ q @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ ( and @ p @ q ) @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,191]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( A != q )
| ( B != r )
| ( ( not @ A )
!= ( implies @ ( and @ p @ q ) @ r ) )
| ( B
!= ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(206,plain,
( ( ( implies @ ( and @ p @ q ) @ r )
!= ( not @ q ) )
| ( ( implies @ ( and @ p @ q ) @ r )
!= r ) ),
inference(simp,[status(thm)],[203]) ).
thf(264,plain,
( ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ q ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= r ) ),
inference(rewrite,[status(thm)],[206,260]) ).
thf(8725,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( not @ E ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( implies @ A @ B )
!= ( not @ C ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,6918]) ).
thf(8726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( implies @ C @ A )
!= ( not @ B ) ) ),
inference(pattern_uni,[status(thm)],[8725:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(8728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( implies @ C @ A )
!= ( not @ B ) ) ),
inference(simp,[status(thm)],[8726]) ).
thf(29730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27903,27844]) ).
thf(29731,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[29730:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( implies @ J @ ( not @ ( not @ J ) ) ) ))]]) ).
thf(29785,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[29731]) ).
thf(6911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ ( implies @ A @ B ) @ ( not @ D ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,6870]) ).
thf(6912,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ A ) @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[6911:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(6916,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ A ) @ ( not @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[6912]) ).
thf(11198,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[6747,10861]) ).
thf(11241,plain,
! [B: $i,A: $i] :
( ( or @ ( or @ A @ B ) @ ( not @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11198]) ).
thf(15613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( or @ C @ D ) @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,11241]) ).
thf(15618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( B != r )
| ( ( not @ A )
!= ( or @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[15613]) ).
thf(15621,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
| ( ( not @ B )
!= r ) ),
inference(simp,[status(thm)],[15618]) ).
thf(16028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
| ( ( not @ D )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,15621]) ).
thf(16029,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
| ( ( not @ A )
!= r ) ),
inference(pattern_uni,[status(thm)],[16028:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(16030,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[16029]) ).
thf(22369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ D @ C )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,22042]) ).
thf(22370,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ ( not @ B ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ B @ A )
!= r ) ),
inference(pattern_uni,[status(thm)],[22369:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(22372,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ ( not @ B ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ B @ A )
!= r ) ),
inference(simp,[status(thm)],[22370]) ).
thf(4812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[1139,334]) ).
thf(4813,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( implies @ ( or @ B @ B ) @ B ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[4812:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( implies @ ( or @ F @ F ) @ F ))]]) ).
thf(4998,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( implies @ ( or @ B @ B ) @ B ) ) @ true )
= true ),
inference(simp,[status(thm)],[4813]) ).
thf(28176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27953,11295]) ).
thf(28177,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28176:[bind(A,$thf( E )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( or @ I @ ( not @ I ) ) ))]]) ).
thf(28278,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[28177]) ).
thf(11432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ C @ D ) @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,11304]) ).
thf(11433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[11432]) ).
thf(11434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ ( not @ C ) )
!= r )
| ( ( not @ A )
!= ( implies @ B @ C ) ) ),
inference(simp,[status(thm)],[11433]) ).
thf(27725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ B )
!= true )
| ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ B ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1046,11295]) ).
thf(27726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( implies @ A @ ( or @ B @ C ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[27725:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( or @ E @ F ))]]) ).
thf(27902,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
!= true )
| ( ( implies @ A @ ( or @ B @ C ) )
!= r ) ),
inference(simp,[status(thm)],[27726]) ).
thf(21888,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ ( implies @ D @ E ) ) )
!= r )
| ( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[15623,12137]) ).
thf(21889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( implies @ ( not @ D ) @ ( not @ D ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[21888:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( implies @ ( not @ I ) @ ( not @ I ) ))]]) ).
thf(21974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( implies @ ( not @ D ) @ ( not @ D ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[21889]) ).
thf(23241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23082,11295]) ).
thf(23242,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[23241:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( not @ ( not @ ( implies @ I @ I ) ) ) ) ))]]) ).
thf(23349,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[23242]) ).
thf(22769,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ E @ ( implies @ A @ B ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11248]) ).
thf(22770,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[22769:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(22772,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[22770]) ).
thf(1158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( implies @ C @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1139,847]) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[1158]) ).
thf(33446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ C ) )
= true )
| ( ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(rewrite,[status(thm)],[1194,16]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= ( implies @ ( and @ p @ q ) @ r ) )
| ( B
!= ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(205,plain,
! [A: $i] :
( ( ( implies @ A @ ( implies @ ( and @ p @ q ) @ r ) )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(498,plain,
! [A: $i] :
( ( ( implies @ A @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(rewrite,[status(thm)],[205,260]) ).
thf(11277,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[82,11181]) ).
thf(11291,plain,
! [A: $i] :
( ( implies @ ( or @ A @ A ) @ A )
!= r ),
inference(simp,[status(thm)],[11277]) ).
thf(12730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[12715,11399]) ).
thf(12731,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12730:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( implies @ F @ F ))]]) ).
thf(12936,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(simp,[status(thm)],[12731]) ).
thf(25707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25544,11399]) ).
thf(25708,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( not @ ( not @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[25707:[bind(A,$thf( L )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ ( not @ ( not @ ( not @ ( implies @ L @ ( not @ ( not @ L ) ) ) ) ) ) ))]]) ).
thf(25973,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( not @ ( not @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[25708]) ).
thf(16158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16032,11295]) ).
thf(16159,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[16158:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ G @ G ) ) ))]]) ).
thf(16246,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) )
!= r ),
inference(simp,[status(thm)],[16159]) ).
thf(11261,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[375,11181]) ).
thf(11301,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[11261]) ).
thf(13495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ C ) @ true @ ( theorem @ D ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[12710,334]) ).
thf(13496,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( implies @ B @ B ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[13495:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( implies @ F @ F ))]]) ).
thf(13673,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( implies @ B @ B ) ) @ true )
= true ),
inference(simp,[status(thm)],[13496]) ).
thf(11190,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[1627,10861]) ).
thf(11237,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11190]) ).
thf(25454,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25250,30]) ).
thf(25455,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[25454:[bind(A,$thf( I )),bind(B,$thf( not @ ( not @ ( not @ ( not @ ( or @ I @ ( not @ I ) ) ) ) ) ))]]) ).
thf(25542,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[25455]) ).
thf(15473,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[14172,10861]) ).
thf(15530,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ B ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[15473]) ).
thf(12091,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[6747,11399]) ).
thf(12092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ ( or @ C @ D ) @ ( not @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12091:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( or @ ( or @ H @ J ) @ ( not @ J ) ))]]) ).
thf(12160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ ( or @ C @ D ) @ ( not @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[12092]) ).
thf(22396,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ ( or @ ( implies @ A @ B ) @ ( not @ F ) ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[28,12160]) ).
thf(22397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ C @ ( or @ ( implies @ D @ A ) @ ( not @ A ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[22396:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( not @ G )),bind(F,$thf( B ))]]) ).
thf(22399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ C @ ( or @ ( implies @ D @ A ) @ ( not @ A ) ) ) )
!= r ),
inference(simp,[status(thm)],[22397]) ).
thf(28325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[12710,27844]) ).
thf(28326,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28325:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( implies @ H @ H ) ))]]) ).
thf(28484,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(simp,[status(thm)],[28326]) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= r )
| ( B
!= ( not @ q ) ) ),
inference(simp,[status(thm)],[1278]) ).
thf(1282,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ q ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= r ) ),
inference(simp,[status(thm)],[1280]) ).
thf(7201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ D @ C ) @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,6916]) ).
thf(7203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( not @ A )
!= ( implies @ D @ C ) )
| ( B
!= ( not @ C ) ) ),
inference(simp,[status(thm)],[7201]) ).
thf(7206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ ( not @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( not @ A )
!= ( implies @ C @ B ) ) ),
inference(simp,[status(thm)],[7203]) ).
thf(28405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17926,27844]) ).
thf(28406,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28405:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ I @ ( not @ ( not @ I ) ) ) ) ))]]) ).
thf(28529,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28406]) ).
thf(17323,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17156,14435]) ).
thf(17324,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[17323:[bind(A,$thf( G )),bind(B,$thf( or @ ( not @ ( not @ G ) ) @ ( not @ G ) ))]]) ).
thf(17390,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[17324]) ).
thf(24632,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[17390,16]) ).
thf(24836,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24632,30]) ).
thf(24837,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[24836:[bind(A,$thf( I )),bind(B,$thf( not @ ( not @ ( or @ ( not @ ( not @ I ) ) @ ( not @ I ) ) ) ))]]) ).
thf(24895,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[24837]) ).
thf(26320,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) ) @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[24895,28]) ).
thf(21848,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ ( implies @ E @ ( implies @ A @ B ) ) @ C )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11236]) ).
thf(21849,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[21848:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(21854,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[21849]) ).
thf(11268,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[1325,11181]) ).
thf(11306,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ C @ ( or @ B @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11268]) ).
thf(6208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( B
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= ( implies @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[6205]) ).
thf(6209,plain,
! [B: $i,A: $i] :
( ( ( not @ ( implies @ q @ r ) )
!= ( implies @ A @ B ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ B ) ) ),
inference(simp,[status(thm)],[6208]) ).
thf(6212,plain,
! [B: $i,A: $i] :
( ( ( not @ ( implies @ q @ r ) )
!= ( implies @ A @ B ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ B ) )
| ( ( not @ B )
!= ( not @ ( implies @ q @ r ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[6209]) ).
thf(6213,plain,
! [B: $i,A: $i] :
( ( ( not @ ( implies @ q @ r ) )
!= ( implies @ A @ B ) )
| ( ( not @ ( implies @ p @ ( not @ q ) ) )
!= A )
| ( r != B )
| ( ( not @ B )
!= ( not @ ( implies @ q @ r ) ) ) ),
inference(simp,[status(thm)],[6212]) ).
thf(6216,plain,
( ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( not @ ( implies @ q @ r ) )
!= ( not @ r ) ) ),
inference(simp,[status(thm)],[6213]) ).
thf(23250,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[23082,11181]) ).
thf(23314,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[23250]) ).
thf(11449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ D @ C ) @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,11445]) ).
thf(11450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ D @ C ) )
| ( B
!= ( not @ C ) ) ),
inference(simp,[status(thm)],[11449]) ).
thf(11451,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ ( not @ B ) )
!= r )
| ( ( not @ A )
!= ( implies @ C @ B ) ) ),
inference(simp,[status(thm)],[11450]) ).
thf(6214,plain,
! [B: $i,A: $i] :
( ( ( not @ ( implies @ q @ r ) )
!= ( implies @ A @ B ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ B ) )
| ( B
!= ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[6212]) ).
thf(6217,plain,
! [A: $i] :
( ( ( implies @ A @ ( implies @ q @ r ) )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( implies @ q @ r ) ) ) ),
inference(simp,[status(thm)],[6214]) ).
thf(11339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) @ A ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3569,11295]) ).
thf(11340,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ ( implies @ C @ ( not @ C ) ) @ ( not @ C ) ) @ B ) )
!= r ),
inference(pattern_uni,[status(thm)],[11339:[bind(A,$thf( F )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( or @ ( implies @ ( implies @ L @ ( not @ L ) ) @ ( not @ L ) ) @ F ))]]) ).
thf(11406,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ ( implies @ C @ ( not @ C ) ) @ ( not @ C ) ) @ B ) )
!= r ),
inference(simp,[status(thm)],[11340]) ).
thf(4106,plain,
! [A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( ( not @ ( implies @ A @ ( not @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[4091]) ).
thf(4107,plain,
( ( not @ ( implies @ ( implies @ q @ r ) @ ( not @ ( implies @ q @ r ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[4106]) ).
thf(2624,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[2614,261]) ).
thf(2687,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[2624]) ).
thf(5816,plain,
! [B: $i,A: $i] :
( ( ( or @ B @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[2687]) ).
thf(11945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ E @ ( implies @ A @ B ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11306]) ).
thf(11946,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11945:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(11947,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= r ),
inference(simp,[status(thm)],[11946]) ).
thf(16894,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[16247,261]) ).
thf(17066,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[16894]) ).
thf(27660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ B @ C ) )
= true )
| ( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17682,1046]) ).
thf(27661,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[27660:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( or @ H @ ( not @ H ) ) ) ))]]) ).
thf(27870,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) )
= true ),
inference(simp,[status(thm)],[27661]) ).
thf(12499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[12485,11399]) ).
thf(12500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ C @ ( implies @ D @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12499:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( or @ F @ ( implies @ I @ I ) ))]]) ).
thf(12697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ C @ ( implies @ D @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[12500]) ).
thf(4383,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( not @ ( implies @ A @ ( not @ A ) ) ) @ ( not @ A ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4308,30]) ).
thf(4384,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ ( implies @ A @ ( not @ A ) ) ) @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[4383:[bind(A,$thf( I )),bind(B,$thf( or @ ( not @ ( implies @ I @ ( not @ I ) ) ) @ ( not @ I ) ))]]) ).
thf(4401,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ ( implies @ A @ ( not @ A ) ) ) @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[4384]) ).
thf(4420,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[4401,28]) ).
thf(27701,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ B @ C ) )
= true )
| ( ( theorem @ ( or @ ( not @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17156,1046]) ).
thf(27702,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( or @ ( not @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[27701:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( or @ ( not @ ( not @ H ) ) @ ( not @ H ) ))]]) ).
thf(27888,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( or @ ( not @ ( not @ B ) ) @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[27702]) ).
thf(31541,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) )
= true ),
inference(rewrite,[status(thm)],[27888,28]) ).
thf(1159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1139,32]) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1159:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( implies @ E @ ( implies @ ( or @ H @ H ) @ H ) )),bind(D,$thf( D ))]]) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[1160]) ).
thf(34763,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[1199,16]) ).
thf(28339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23685,27844]) ).
thf(28340,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ ( implies @ C @ C ) @ B ) )
!= r ),
inference(pattern_uni,[status(thm)],[28339:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( or @ ( implies @ H @ H ) @ F ))]]) ).
thf(28496,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ ( implies @ C @ C ) @ B ) )
!= r ),
inference(simp,[status(thm)],[28340]) ).
thf(28361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[12485,27844]) ).
thf(28362,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28361:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( implies @ H @ H ) ))]]) ).
thf(28507,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(simp,[status(thm)],[28362]) ).
thf(22036,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ ( implies @ E @ ( implies @ A @ B ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11237]) ).
thf(22037,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[22036:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(22040,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[22037]) ).
thf(267,plain,
! [A: $i] :
( ( implies @ ( or @ A @ A ) @ A )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(rewrite,[status(thm)],[127,260]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ B @ C ) ) @ true @ ( ifeq @ ( theorem @ B ) @ true @ true @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[82,32]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ true @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( implies @ ( or @ E @ E ) @ E ))]]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ true @ true ) @ true )
= true ),
inference(simp,[status(thm)],[308]) ).
thf(585,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ ( implies @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,574]) ).
thf(586,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[585:[bind(A,$thf( E )),bind(B,$thf( or @ E @ E )),bind(C,$thf( E ))]]) ).
thf(627,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[586]) ).
thf(5693,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[341,627]) ).
thf(25739,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[25544,261]) ).
thf(25935,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[25739]) ).
thf(6689,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6578,30]) ).
thf(6690,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[6689:[bind(A,$thf( G )),bind(B,$thf( or @ G @ ( not @ ( or @ G @ G ) ) ))]]) ).
thf(6730,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( not @ ( or @ A @ A ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[6690]) ).
thf(11252,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[10153,11181]) ).
thf(11310,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[11252]) ).
thf(11206,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[3725,10861]) ).
thf(11219,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11206]) ).
thf(21507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ E @ ( implies @ D @ E ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,11219]) ).
thf(21510,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( B != r )
| ( ( not @ A )
!= ( implies @ E @ ( implies @ D @ E ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[21507]) ).
thf(21513,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= ( implies @ B @ ( implies @ A @ B ) ) ),
inference(simp,[status(thm)],[21510]) ).
thf(1187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1139,30]) ).
thf(1188,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( D )),bind(B,$thf( G )),bind(C,$thf( implies @ D @ ( implies @ ( or @ G @ G ) @ G ) ))]]) ).
thf(1198,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[1188]) ).
thf(11189,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[1552,10861]) ).
thf(11220,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11189]) ).
thf(11209,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[2003,10861]) ).
thf(11245,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[11209]) ).
thf(5239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ ( or @ D @ D ) @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,3563]) ).
thf(5244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( B
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( not @ A )
!= ( implies @ ( or @ D @ D ) @ D ) )
| ( B != C ) ),
inference(simp,[status(thm)],[5239]) ).
thf(5248,plain,
! [A: $i] :
( ( implies @ ( or @ A @ A ) @ A )
!= ( not @ ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[5244]) ).
thf(924,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ B ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ ( implies @ B @ ( not @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,847]) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ B ) ) @ true )
= true )
| ( ( implies @ ( or @ A @ A ) @ A )
!= ( implies @ B @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[924]) ).
thf(24575,plain,
! [B: $i,A: $i] :
( ( ( theorem @ ( not @ B ) )
= true )
| ( ( implies @ ( or @ A @ A ) @ A )
!= ( implies @ B @ ( not @ B ) ) ) ),
inference(rewrite,[status(thm)],[965,16]) ).
thf(17962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[17926,11399]) ).
thf(17963,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[17962:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ ( not @ ( implies @ J @ ( not @ ( not @ J ) ) ) ) ))]]) ).
thf(18173,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ C @ ( not @ ( not @ C ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[17963]) ).
thf(12637,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12485,30]) ).
thf(12638,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ B @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[12637:[bind(A,$thf( D )),bind(B,$thf( G )),bind(C,$thf( or @ D @ ( implies @ G @ G ) ))]]) ).
thf(12701,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ B @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[12638]) ).
thf(12867,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[12715,11181]) ).
thf(12922,plain,
! [A: $i] :
( ( implies @ A @ A )
!= r ),
inference(simp,[status(thm)],[12867]) ).
thf(1899,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1890,261]) ).
thf(1948,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1899]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[377,261]) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[475]) ).
thf(11276,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[4006,11181]) ).
thf(11316,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) )
!= r ),
inference(simp,[status(thm)],[11276]) ).
thf(29684,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[27903,10861]) ).
thf(29771,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[29684]) ).
thf(28421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22793,27844]) ).
thf(28422,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28421:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ ( not @ I ) @ ( not @ I ) ) ) ))]]) ).
thf(28466,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( implies @ ( not @ B ) @ ( not @ B ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28422]) ).
thf(806,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ B ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
!= ( theorem @ ( or @ B @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,785]) ).
thf(836,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ B ) @ true )
= true )
| ( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( or @ B @ B ) ) ),
inference(simp,[status(thm)],[806]) ).
thf(16290,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
= true )
| ( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( or @ B @ B ) ) ),
inference(rewrite,[status(thm)],[836,16]) ).
thf(15767,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[15623,11181]) ).
thf(15817,plain,
! [A: $i] :
( ( implies @ ( not @ A ) @ ( not @ A ) )
!= r ),
inference(simp,[status(thm)],[15767]) ).
thf(940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( ( ifeq @ A @ A @ B @ C )
!= ( ifeq @ ( theorem @ ( implies @ D @ ( not @ D ) ) ) @ true @ ( theorem @ ( not @ D ) ) @ true ) ) ),
inference(paramod_ordered,[status(thm)],[16,847]) ).
thf(968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( A
!= ( theorem @ ( implies @ D @ ( not @ D ) ) ) )
| ( A != true )
| ( B
!= ( theorem @ ( not @ D ) ) )
| ( C != true ) ),
inference(simp,[status(thm)],[940]) ).
thf(971,plain,
! [A: $i] :
( ( ( theorem @ ( not @ A ) )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ A ) ) )
!= true ) ),
inference(simp,[status(thm)],[968]) ).
thf(303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ D @ E ) ) @ true @ B @ true )
= true )
| ( ( ifeq @ A @ A @ B @ C )
!= ( ifeq @ ( theorem @ D ) @ true @ ( theorem @ E ) @ true ) ) ),
inference(paramod_ordered,[status(thm)],[16,32]) ).
thf(320,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ D @ E ) ) @ true @ B @ true )
= true )
| ( A
!= ( theorem @ D ) )
| ( A != true )
| ( B
!= ( theorem @ E ) )
| ( C != true ) ),
inference(simp,[status(thm)],[303]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( theorem @ B ) @ true )
= true )
| ( ( theorem @ A )
!= true ) ),
inference(simp,[status(thm)],[320]) ).
thf(16067,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[16032,261]) ).
thf(16221,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ A ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[16067]) ).
thf(11952,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ ( implies @ E @ ( implies @ A @ B ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11312]) ).
thf(11953,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11952:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(11956,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= r ),
inference(simp,[status(thm)],[11953]) ).
thf(17131,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( or @ D @ ( implies @ F @ ( implies @ A @ B ) ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[28,11410]) ).
thf(17132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( or @ C @ ( implies @ A @ ( implies @ D @ A ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[17131:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( not @ G )),bind(F,$thf( B ))]]) ).
thf(17134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( or @ C @ ( implies @ A @ ( implies @ D @ A ) ) ) )
!= r ),
inference(simp,[status(thm)],[17132]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[80,14]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( and @ p @ q ) @ r ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(rewrite,[status(thm)],[116,260]) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1552,261]) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ C @ ( implies @ B @ C ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1562]) ).
thf(23107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23082,11399]) ).
thf(23108,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[23107:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ ( not @ ( not @ ( not @ ( implies @ J @ J ) ) ) ) ))]]) ).
thf(23345,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[23108]) ).
thf(16048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16032,11399]) ).
thf(16049,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[16048:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ ( not @ ( implies @ H @ H ) ) ))]]) ).
thf(16249,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[16049]) ).
thf(17588,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( or @ ( not @ A ) @ A ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17424,14435]) ).
thf(17589,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ ( not @ A ) @ A ) ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[17588:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ ( or @ ( not @ F ) @ F ) ) ))]]) ).
thf(17658,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ ( not @ A ) @ A ) ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[17589]) ).
thf(24941,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ ( not @ A ) @ A ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[17658,16]) ).
thf(1406,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1391,261]) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ ( implies @ C @ A ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1406]) ).
thf(716,plain,
! [A: $i] :
( ( A != q )
| ( ( not @ A )
!= r )
| ( ( not @ A )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(717,plain,
( ( ( not @ q )
!= r )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ q ) ) ),
inference(simp,[status(thm)],[716]) ).
thf(11270,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[2614,11181]) ).
thf(11297,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ B @ ( not @ A ) ) @ ( implies @ A @ B ) )
!= r ),
inference(simp,[status(thm)],[11270]) ).
thf(157,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( or @ C @ ( or @ D @ E ) ) @ ( or @ D @ ( implies @ A @ B ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,24]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ ( not @ C ) @ ( or @ B @ A ) ) @ ( or @ B @ ( implies @ C @ A ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( not @ F )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(180,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ ( not @ C ) @ ( or @ B @ A ) ) @ ( or @ B @ ( implies @ C @ A ) ) ) )
= true ),
inference(simp,[status(thm)],[158]) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ C @ ( or @ B @ A ) ) @ ( or @ B @ ( implies @ C @ A ) ) ) )
= true ),
inference(rewrite,[status(thm)],[180,28]) ).
thf(32217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ E )
!= true )
| ( ( or @ C @ ( implies @ A @ B ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,28499]) ).
thf(32218,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( or @ B @ ( implies @ C @ A ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[32217:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(32386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( or @ B @ ( implies @ C @ A ) )
!= r ) ),
inference(simp,[status(thm)],[32218]) ).
thf(22045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ ( or @ D @ C ) @ ( implies @ A @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,11238]) ).
thf(22046,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[22045:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(22048,plain,
! [B: $i,A: $i] :
( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[22046]) ).
thf(11385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2003,11295]) ).
thf(11386,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ ( or @ C @ C ) @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11385:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( implies @ ( or @ H @ H ) @ H ) ))]]) ).
thf(11429,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ ( or @ C @ C ) @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11386]) ).
thf(15733,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( or @ B @ ( not @ C ) ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ ( implies @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[15623,8198]) ).
thf(15734,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ A ) @ ( not @ ( not @ A ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[15733:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(15869,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ A ) @ ( not @ ( not @ A ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[15734]) ).
thf(18206,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ A ) @ ( not @ ( not @ A ) ) ) )
= true ),
inference(rewrite,[status(thm)],[15869,16]) ).
thf(18379,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ B ) ) ) @ true )
= true )
| ( ( theorem @ ( or @ ( not @ A ) @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18206,14435]) ).
thf(18380,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ ( not @ A ) @ ( not @ ( not @ A ) ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[18379:[bind(A,$thf( G )),bind(B,$thf( or @ ( not @ G ) @ ( not @ ( not @ G ) ) ))]]) ).
thf(18454,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( not @ ( not @ ( or @ ( not @ A ) @ ( not @ ( not @ A ) ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[18380]) ).
thf(25999,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( or @ ( not @ A ) @ ( not @ ( not @ A ) ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[18454,16]) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[1197,261]) ).
thf(1262,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1218]) ).
thf(11967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ ( implies @ A @ B ) @ ( implies @ C @ D ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,11297]) ).
thf(11968,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ ( not @ B ) ) @ ( implies @ B @ ( not @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11967:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( F )),bind(D,$thf( not @ E ))]]) ).
thf(11969,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ ( not @ B ) ) @ ( implies @ B @ ( not @ A ) ) )
!= r ),
inference(simp,[status(thm)],[11968]) ).
thf(14123,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ A @ ( not @ A ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13962,30]) ).
thf(14124,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[14123:[bind(A,$thf( E )),bind(B,$thf( or @ E @ ( not @ E ) ))]]) ).
thf(14179,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( not @ A ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[14124]) ).
thf(15341,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( implies @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[14172,11399]) ).
thf(15342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( or @ D @ ( not @ D ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[15341:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( implies @ F @ ( or @ J @ ( not @ J ) ) ))]]) ).
thf(15580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( or @ D @ ( not @ D ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[15342]) ).
thf(5451,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ ( implies @ A @ B ) @ C )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,5248]) ).
thf(5452,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( not @ ( implies @ q @ r ) ) ),
inference(pattern_uni,[status(thm)],[5451:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(5453,plain,
! [A: $i] :
( ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) )
!= ( not @ ( implies @ q @ r ) ) ),
inference(simp,[status(thm)],[5452]) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
!= ( theorem @ ( implies @ C @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[80,847]) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( implies @ B @ ( implies @ A @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[936]) ).
thf(22401,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ C ) )
= true )
| ( ( implies @ B @ ( implies @ A @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(rewrite,[status(thm)],[954,16]) ).
thf(15756,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15623,11295]) ).
thf(15757,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[15756:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( implies @ ( not @ G ) @ ( not @ G ) ))]]) ).
thf(15841,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[15757]) ).
thf(33965,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ A ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[33717,11181]) ).
thf(34034,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ A ) )
!= r ),
inference(simp,[status(thm)],[33965]) ).
thf(29316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27897,11295]) ).
thf(29317,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[29316:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( not @ ( not @ ( implies @ J @ J ) ) ) ))]]) ).
thf(29423,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[29317]) ).
thf(28445,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25250,27844]) ).
thf(28446,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28445:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( not @ ( not @ ( or @ J @ ( not @ J ) ) ) ) ) ))]]) ).
thf(28478,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28446]) ).
thf(21858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ ( implies @ A @ B ) )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,21857]) ).
thf(21859,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(pattern_uni,[status(thm)],[21858:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(21860,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(simp,[status(thm)],[21859]) ).
thf(858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ D ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( or @ D @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[855,785]) ).
thf(898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ D ) @ true )
= true )
| ( ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) )
!= ( or @ D @ D ) ) ),
inference(simp,[status(thm)],[858]) ).
thf(18797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ D )
= true )
| ( ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) )
!= ( or @ D @ D ) ) ),
inference(rewrite,[status(thm)],[898,16]) ).
thf(1814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ D ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ B @ ( implies @ A @ ( implies @ C @ A ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1694,30]) ).
thf(1815,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[1814:[bind(A,$thf( J )),bind(B,$thf( E )),bind(C,$thf( I )),bind(D,$thf( or @ E @ ( implies @ J @ ( implies @ I @ J ) ) ))]]) ).
thf(1834,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[1815]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) )
= true ),
inference(lifteq,[status(thm)],[25]) ).
thf(213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ C @ D ) @ ( implies @ ( implies @ A @ B ) @ ( or @ E @ D ) ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,26]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ C @ A ) @ ( or @ ( not @ C ) @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( not @ F ))]]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ C @ A ) @ ( or @ ( not @ C ) @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[214]) ).
thf(1844,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) ) )
= true ),
inference(rewrite,[status(thm)],[229,28]) ).
thf(11351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[375,11295]) ).
thf(11352,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11351:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( implies @ ( implies @ K @ I ) @ ( or @ I @ ( not @ K ) ) ))]]) ).
thf(11412,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[11352]) ).
thf(3257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ ( or @ ( implies @ E @ ( implies @ A @ B ) ) @ C ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,3238]) ).
thf(3258,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B ) )
= true ),
inference(pattern_uni,[status(thm)],[3257:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(3334,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B ) )
= true ),
inference(simp,[status(thm)],[3258]) ).
thf(3380,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[3334,261]) ).
thf(3452,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ A @ ( implies @ C @ A ) ) @ B )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[3380]) ).
thf(23710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( or @ ( implies @ B @ B ) @ A ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[23685,11399]) ).
thf(23711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ ( implies @ D @ D ) @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[23710:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( or @ ( implies @ I @ I ) @ G ))]]) ).
thf(23965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( or @ ( implies @ D @ D ) @ C ) ) )
!= r ),
inference(simp,[status(thm)],[23711]) ).
thf(14371,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ A ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14188,30]) ).
thf(14372,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[14371:[bind(A,$thf( F )),bind(B,$thf( implies @ F @ ( not @ ( not @ F ) ) ))]]) ).
thf(14425,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[14372]) ).
thf(23131,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[23082,261]) ).
thf(23313,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[23131]) ).
thf(28407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27953,27844]) ).
thf(28408,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28407:[bind(A,$thf( E )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( or @ I @ ( not @ I ) ) ))]]) ).
thf(28530,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( or @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[28408]) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ C @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,847]) ).
thf(958,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[946]) ).
thf(22775,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ C ) )
= true )
| ( ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(rewrite,[status(thm)],[958,16]) ).
thf(17982,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[17926,261]) ).
thf(18166,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[17982]) ).
thf(859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( implies @ D @ E ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[855,574]) ).
thf(860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[859:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( implies @ ( or @ N @ ( or @ L @ O ) ) @ ( or @ L @ ( or @ N @ O ) ) ))]]) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[860]) ).
thf(21518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ ( or @ C @ ( or @ B @ D ) ) @ ( or @ B @ ( or @ C @ D ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[908,16]) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[377,785]) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( or @ C @ C ) ) ),
inference(simp,[status(thm)],[809]) ).
thf(15315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( or @ C @ C ) ) ),
inference(rewrite,[status(thm)],[828,16]) ).
thf(14456,plain,
! [A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( not @ ( not @ A ) )
!= r ) ),
inference(simp,[status(thm)],[14203]) ).
thf(14457,plain,
( ( not @ ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[14456]) ).
thf(19251,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( not @ E ) )
!= r )
| ( ( implies @ A @ B )
!= ( not @ C ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11446]) ).
thf(19252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= r )
| ( ( implies @ C @ A )
!= ( not @ B ) ) ),
inference(pattern_uni,[status(thm)],[19251:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(19253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= r )
| ( ( implies @ C @ A )
!= ( not @ B ) ) ),
inference(simp,[status(thm)],[19252]) ).
thf(2133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2070,30]) ).
thf(2134,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[2133:[bind(A,$thf( D )),bind(B,$thf( K )),bind(C,$thf( or @ D @ ( implies @ ( implies @ K @ ( not @ K ) ) @ ( not @ K ) ) ))]]) ).
thf(2152,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ ( implies @ B @ ( not @ B ) ) @ ( not @ B ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[2134]) ).
thf(478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[377,32]) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[478:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( implies @ ( or @ K @ ( not @ J ) ) @ ( implies @ J @ K ) )),bind(D,$thf( D ))]]) ).
thf(495,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[479]) ).
thf(9102,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( or @ C @ ( not @ B ) ) @ ( implies @ B @ C ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[495,16]) ).
thf(25860,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[25544,10861]) ).
thf(25939,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ ( not @ ( not @ A ) ) ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[25860]) ).
thf(12513,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[12485,261]) ).
thf(12662,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[12513]) ).
thf(28373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16247,27844]) ).
thf(28374,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28373:[bind(A,$thf( E )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( not @ ( not @ ( implies @ J @ J ) ) ) ))]]) ).
thf(28513,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( not @ ( not @ ( implies @ C @ C ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28374]) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( theorem @ ( implies @ C @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[377,847]) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[934]) ).
thf(24008,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ C ) )
= true )
| ( ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(rewrite,[status(thm)],[963,16]) ).
thf(5690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ ( implies @ A @ B ) @ ( implies @ D @ C ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,490]) ).
thf(5691,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ ( not @ B ) ) @ ( implies @ B @ ( not @ A ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[5690:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(5692,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ ( not @ B ) ) @ ( implies @ B @ ( not @ A ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[5691]) ).
thf(28419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16032,27844]) ).
thf(28420,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28419:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( implies @ G @ G ) ) ))]]) ).
thf(28465,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) )
!= r ),
inference(simp,[status(thm)],[28420]) ).
thf(13590,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[12710,10861]) ).
thf(13642,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[13590]) ).
thf(13456,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[12710,11399]) ).
thf(13457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( implies @ D @ D ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[13456:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( implies @ F @ ( implies @ I @ I ) ))]]) ).
thf(13659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( implies @ D @ D ) ) ) )
!= r ),
inference(simp,[status(thm)],[13457]) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[855,261]) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ ( or @ B @ ( or @ A @ C ) ) @ ( or @ A @ ( or @ B @ C ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[865]) ).
thf(11363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( or @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6747,11295]) ).
thf(11364,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( or @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11363:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( or @ ( or @ G @ I ) @ ( not @ I ) ))]]) ).
thf(11418,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( or @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11364]) ).
thf(11337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ ( implies @ A @ B ) @ ( not @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6054,11295]) ).
thf(11338,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11337:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( or @ ( implies @ G @ I ) @ ( not @ I ) ))]]) ).
thf(11405,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ ( implies @ B @ C ) @ ( not @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11338]) ).
thf(2012,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[2003,261]) ).
thf(2066,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[2012]) ).
thf(16872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( implies @ A @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[16247,11399]) ).
thf(16873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( not @ ( implies @ D @ D ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[16872:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( implies @ F @ ( not @ ( not @ ( implies @ K @ K ) ) ) ))]]) ).
thf(17116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( not @ ( not @ ( implies @ D @ D ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[16873]) ).
thf(28337,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23082,27844]) ).
thf(28338,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28337:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( not @ ( not @ ( implies @ I @ I ) ) ) ) ))]]) ).
thf(28495,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( not @ ( not @ ( not @ ( not @ ( implies @ B @ B ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[28338]) ).
thf(30992,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ E )
!= true )
| ( ( implies @ C @ ( implies @ A @ B ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,27902]) ).
thf(30993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( implies @ B @ ( implies @ C @ A ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[30992:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(31104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ A )
!= true )
| ( ( implies @ B @ ( implies @ C @ A ) )
!= r ) ),
inference(simp,[status(thm)],[30993]) ).
thf(12236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( or @ ( implies @ A @ B ) @ ( not @ E ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11418]) ).
thf(12237,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( or @ ( implies @ C @ A ) @ ( not @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12236:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(12240,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( or @ ( implies @ C @ A ) @ ( not @ A ) ) )
!= r ),
inference(simp,[status(thm)],[12237]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( or @ A @ B ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(rewrite,[status(thm)],[108,260]) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,785]) ).
thf(835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) )
!= ( or @ C @ C ) ) ),
inference(simp,[status(thm)],[803]) ).
thf(16271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) )
!= ( or @ C @ C ) ) ),
inference(rewrite,[status(thm)],[835,16]) ).
thf(27003,plain,
! [B: $i,A: $i] :
( ( ( or @ B @ ( not @ A ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ A @ B )
!= r ) ),
inference(simp,[status(thm)],[11223]) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ C @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,847]) ).
thf(962,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[930]) ).
thf(23535,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ C ) )
= true )
| ( ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(rewrite,[status(thm)],[962,16]) ).
thf(7027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ D ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,6919]) ).
thf(7028,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ A ) ) ),
inference(pattern_uni,[status(thm)],[7027:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(7029,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ A )
!= ( not @ ( implies @ q @ r ) ) )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( not @ A ) ) ),
inference(simp,[status(thm)],[7028]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( or @ D @ C ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,22]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[88]) ).
thf(397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ D @ C ) @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,100]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[398]) ).
thf(12616,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[12485,10861]) ).
thf(12681,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[12616]) ).
thf(1969,plain,
! [B: $i,A: $i] :
( ( ( implies @ B @ ( not @ A ) )
!= ( implies @ q @ r ) )
| ( A != q )
| ( ( not @ B )
!= r )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ B @ ( not @ A ) ) ) ),
inference(simp,[status(thm)],[1967]) ).
thf(1986,plain,
! [A: $i] :
( ( ( implies @ A @ ( not @ q ) )
!= ( implies @ q @ r ) )
| ( ( not @ A )
!= r )
| ( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ A @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[1969]) ).
thf(13694,plain,
! [A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( A
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[12913]) ).
thf(13695,plain,
( ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r )
!= ( implies @ q @ r ) ),
inference(simp,[status(thm)],[13694]) ).
thf(23274,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23082,30]) ).
thf(23275,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[23274:[bind(A,$thf( H )),bind(B,$thf( not @ ( not @ ( not @ ( not @ ( implies @ H @ H ) ) ) ) ))]]) ).
thf(23357,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[23275]) ).
thf(14206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ A @ B ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,14171]) ).
thf(14207,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[14206:[bind(A,$thf( G )),bind(B,$thf( not @ ( not @ G ) )),bind(C,$thf( C )),bind(D,$thf( not @ G ))]]) ).
thf(14208,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) )
!= r ),
inference(simp,[status(thm)],[14207]) ).
thf(547,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,261]) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(15614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ ( implies @ A @ B ) @ ( not @ D ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,11241]) ).
thf(15615,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ A ) @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[15614:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(15622,plain,
! [B: $i,A: $i] :
( ( or @ ( implies @ B @ A ) @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[15615]) ).
thf(268,plain,
! [A: $i] :
( ( implies @ A @ ( implies @ q @ r ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(rewrite,[status(thm)],[139,260]) ).
thf(11357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1139,11295]) ).
thf(11358,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[11357:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( implies @ ( or @ H @ H ) @ H ) ))]]) ).
thf(11415,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11358]) ).
thf(12246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ C @ D ) @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,11234]) ).
thf(12249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( B != r )
| ( ( not @ A )
!= ( implies @ C @ D ) )
| ( B
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[12246]) ).
thf(12252,plain,
! [B: $i,A: $i] :
( ( ( not @ ( not @ ( implies @ p @ ( not @ q ) ) ) )
!= ( implies @ A @ B ) )
| ( ( not @ B )
!= r ) ),
inference(simp,[status(thm)],[12249]) ).
thf(17821,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ B @ C )
!= r )
| ( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17682,11295]) ).
thf(17822,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[17821:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( not @ ( not @ ( or @ H @ ( not @ H ) ) ) ))]]) ).
thf(17910,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( not @ ( not @ ( or @ B @ ( not @ B ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[17822]) ).
thf(22390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ D @ C )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,22372]) ).
thf(22391,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ ( not @ B ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ B @ ( not @ A ) )
!= r ) ),
inference(pattern_uni,[status(thm)],[22390:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(22392,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ ( not @ B ) )
!= ( not @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( implies @ B @ ( not @ A ) )
!= r ) ),
inference(simp,[status(thm)],[22391]) ).
thf(16191,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( not @ ( not @ ( implies @ A @ A ) ) ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16032,30]) ).
thf(16192,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[16191:[bind(A,$thf( F )),bind(B,$thf( not @ ( not @ ( implies @ F @ F ) ) ))]]) ).
thf(16256,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[16192]) ).
thf(25429,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[25250,10861]) ).
thf(25511,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[25429]) ).
thf(548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[463,32]) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[548:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( implies @ ( implies @ L @ ( not @ J ) ) @ ( implies @ J @ ( not @ L ) ) )),bind(D,$thf( D ))]]) ).
thf(566,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[549]) ).
thf(9431,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ C @ ( not @ B ) ) @ ( implies @ B @ ( not @ C ) ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[566,16]) ).
thf(1675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ D ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1627,30]) ).
thf(1676,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[1675:[bind(A,$thf( E )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( or @ E @ ( implies @ J @ ( or @ I @ J ) ) ))]]) ).
thf(1693,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ A @ ( implies @ C @ ( or @ B @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[1676]) ).
thf(11275,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[3725,11181]) ).
thf(11309,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( implies @ C @ ( implies @ B @ C ) ) @ A )
!= r ),
inference(simp,[status(thm)],[11275]) ).
thf(11948,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ E @ ( implies @ D @ E ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,11309]) ).
thf(11949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ E @ ( implies @ D @ E ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[11948]) ).
thf(11950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ D @ ( implies @ C @ D ) ) ) ),
inference(simp,[status(thm)],[11949]) ).
thf(1470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ q @ r ) )
| ( ( implies @ D @ C )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,781]) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ ( not @ B ) )
!= ( implies @ q @ r ) )
| ( ( implies @ B @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(pattern_uni,[status(thm)],[1470:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(1473,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ ( not @ B ) )
!= ( implies @ q @ r ) )
| ( ( implies @ B @ ( not @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1471]) ).
thf(12888,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ A @ A ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12715,30]) ).
thf(12889,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ A ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[12888:[bind(A,$thf( D )),bind(B,$thf( implies @ D @ D ))]]) ).
thf(12944,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ A @ A ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[12889]) ).
thf(28359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ B @ C )
!= r )
| ( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15623,27844]) ).
thf(28360,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28359:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( implies @ ( not @ G ) @ ( not @ G ) ))]]) ).
thf(28506,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ ( not @ B ) @ ( not @ B ) ) )
!= r ),
inference(simp,[status(thm)],[28360]) ).
thf(23249,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[23082,10861]) ).
thf(23322,plain,
! [A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( implies @ A @ A ) ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[23249]) ).
thf(2897,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( implies @ q @ r ) )
| ( ( implies @ C @ ( implies @ B @ C ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[1611]) ).
thf(2898,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( implies @ A @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[2897]) ).
thf(15641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ B @ ( implies @ C @ D ) )
!= r )
| ( ( theorem @ ( implies @ ( not @ A ) @ ( not @ A ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15623,11399]) ).
thf(15642,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ ( not @ C ) @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[15641:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( implies @ ( not @ H ) @ ( not @ H ) ))]]) ).
thf(15845,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ ( not @ C ) @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[15642]) ).
thf(16707,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ ( or @ E @ D ) @ ( implies @ A @ B ) ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[28,11287]) ).
thf(16708,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ ( or @ A @ ( not @ C ) ) @ ( implies @ C @ A ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[16707:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not @ F )),bind(E,$thf( B ))]]) ).
thf(16711,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ B @ ( implies @ ( or @ A @ ( not @ C ) ) @ ( implies @ C @ A ) ) )
!= r ),
inference(simp,[status(thm)],[16708]) ).
thf(453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[375,32]) ).
thf(454,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[453:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( implies @ ( implies @ K @ I ) @ ( or @ I @ ( not @ K ) ) )),bind(D,$thf( D ))]]) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[454]) ).
thf(7493,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ ( implies @ ( implies @ C @ B ) @ ( or @ B @ ( not @ C ) ) ) @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[464,16]) ).
thf(28437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ D )
!= r )
| ( ( theorem @ ( implies @ A @ ( or @ B @ ( not @ B ) ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[14172,27844]) ).
thf(28438,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28437:[bind(A,$thf( E )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( or @ I @ ( not @ I ) ) ))]]) ).
thf(28474,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( or @ C @ ( not @ C ) ) ) )
!= r ),
inference(simp,[status(thm)],[28438]) ).
thf(11932,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ E @ ( or @ D @ E ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,11296]) ).
thf(11933,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ E @ ( or @ D @ E ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[11932]) ).
thf(11935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= r )
| ( ( not @ A )
!= ( implies @ D @ ( or @ C @ D ) ) ) ),
inference(simp,[status(thm)],[11933]) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ C @ ( not @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,847]) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ ( not @ C ) ) @ true )
= true )
| ( ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[942]) ).
thf(22054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( not @ C ) )
= true )
| ( ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) )
!= ( implies @ C @ ( not @ C ) ) ) ),
inference(rewrite,[status(thm)],[952,16]) ).
thf(13696,plain,
( ( ( not @ ( implies @ p @ ( not @ q ) ) )
!= q )
| ( r != r ) ),
inference(simp,[status(thm)],[13695]) ).
thf(13697,plain,
( ( not @ ( implies @ p @ ( not @ q ) ) )
!= q ),
inference(simp,[status(thm)],[13696]) ).
thf(11253,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[1890,11181]) ).
thf(11298,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ A @ ( implies @ C @ ( implies @ B @ C ) ) )
!= r ),
inference(simp,[status(thm)],[11253]) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ ( implies @ C @ D ) ) @ true @ ( ifeq @ ( theorem @ C ) @ true @ true @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1139,32]) ).
thf(1162,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ true @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[1161:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( implies @ E @ ( implies @ ( or @ H @ H ) @ H ) ))]]) ).
thf(1200,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ true @ true ) @ true )
= true ),
inference(simp,[status(thm)],[1162]) ).
thf(35351,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ ( implies @ B @ ( implies @ ( or @ C @ C ) @ C ) ) ) ) @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[1200,627]) ).
thf(11278,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) ) )
!= ( theorem @ r ) ),
inference(paramod_ordered,[status(thm)],[2003,11181]) ).
thf(11286,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ ( or @ B @ B ) @ B ) )
!= r ),
inference(simp,[status(thm)],[11278]) ).
thf(794,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ B ) @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ ( or @ B @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,785]) ).
thf(837,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ B ) @ true )
= true )
| ( ( implies @ ( or @ A @ A ) @ A )
!= ( or @ B @ B ) ) ),
inference(simp,[status(thm)],[794]) ).
thf(16430,plain,
! [B: $i,A: $i] :
( ( ( theorem @ B )
= true )
| ( ( implies @ ( or @ A @ A ) @ A )
!= ( or @ B @ B ) ) ),
inference(rewrite,[status(thm)],[837,16]) ).
thf(16474,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[14414,261]) ).
thf(16654,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[16474]) ).
thf(16455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( implies @ D @ E ) )
!= r )
| ( ( theorem @ ( implies @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) ) )
!= ( theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[14414,11399]) ).
thf(16456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( implies @ D @ ( not @ ( not @ D ) ) ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[16455:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( implies @ F @ ( implies @ K @ ( not @ ( not @ K ) ) ) ))]]) ).
thf(16681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ ( implies @ C @ ( implies @ D @ ( not @ ( not @ D ) ) ) ) ) )
!= r ),
inference(simp,[status(thm)],[16456]) ).
thf(22960,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) ) )
!= ( theorem @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[22793,10861]) ).
thf(23022,plain,
! [A: $i] :
( ( not @ ( not @ ( implies @ ( not @ A ) @ ( not @ A ) ) ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[22960]) ).
thf(28317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ C @ ( implies @ A @ B ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,28266]) ).
thf(28318,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[28317:[bind(A,$thf( G )),bind(B,$thf( not @ ( not @ G ) )),bind(C,$thf( C )),bind(D,$thf( not @ G ))]]) ).
thf(28320,plain,
! [B: $i,A: $i] :
( ( or @ A @ ( implies @ B @ ( not @ ( not @ B ) ) ) )
!= r ),
inference(simp,[status(thm)],[28318]) ).
thf(207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( theorem @ D )
= true )
| ( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) )
!= ( axiom @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26,69]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( or @ B @ A ) @ ( or @ B @ C ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( M )),bind(D,$thf( implies @ ( implies @ L @ N ) @ ( implies @ ( or @ M @ L ) @ ( or @ M @ N ) ) ))]]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( or @ B @ A ) @ ( or @ B @ C ) ) ) )
= true ),
inference(simp,[status(thm)],[208]) ).
thf(12606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ D )
!= r )
| ( ( theorem @ ( or @ A @ ( implies @ B @ B ) ) )
!= ( theorem @ D ) ) ),
inference(paramod_ordered,[status(thm)],[12485,11295]) ).
thf(12607,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(pattern_uni,[status(thm)],[12606:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( or @ E @ ( implies @ H @ H ) ))]]) ).
thf(12694,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( or @ B @ ( implies @ C @ C ) ) )
!= r ),
inference(simp,[status(thm)],[12607]) ).
thf(5580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) )
!= ( theorem @ ( implies @ ( implies @ ( or @ D @ D ) @ D ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,5475]) ).
thf(5581,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( not @ ( or @ ( not @ A ) @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[5580:[bind(A,$thf( N )),bind(B,$thf( or @ ( not @ N ) @ ( not @ N ) )),bind(C,$thf( implies @ N @ ( not @ ( or @ ( not @ N ) @ ( not @ N ) ) ) )),bind(D,$thf( not @ N ))]]) ).
thf(5665,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ A @ ( not @ ( or @ ( not @ A ) @ ( not @ A ) ) ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[5581]) ).
thf(10618,plain,
! [A: $i] :
( ( theorem @ ( implies @ A @ ( not @ ( or @ ( not @ A ) @ ( not @ A ) ) ) ) )
= true ),
inference(rewrite,[status(thm)],[5665,16]) ).
thf(17722,plain,
! [A: $i] :
( ( theorem @ ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[17682,261]) ).
thf(17893,plain,
! [A: $i] :
( ( not @ ( not @ ( or @ A @ ( not @ A ) ) ) )
!= ( implies @ ( implies @ q @ r ) @ ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ) ),
inference(simp,[status(thm)],[17722]) ).
thf(2348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ D @ ( implies @ A @ B ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,2345]) ).
thf(2349,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(pattern_uni,[status(thm)],[2348:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(2351,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ ( not @ ( implies @ p @ ( not @ q ) ) ) @ r ) ),
inference(simp,[status(thm)],[2349]) ).
thf(18616,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( or @ ( implies @ F @ ( implies @ A @ B ) ) @ D ) )
!= r )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[28,11416]) ).
thf(18617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( or @ ( implies @ A @ ( implies @ D @ A ) ) @ C ) )
!= r ),
inference(pattern_uni,[status(thm)],[18616:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( not @ G )),bind(F,$thf( B ))]]) ).
thf(18620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( implies @ B @ ( or @ ( implies @ A @ ( implies @ D @ A ) ) @ C ) )
!= r ),
inference(simp,[status(thm)],[18617]) ).
thf(4038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ C ) @ true ) @ true )
= true )
| ( ( theorem @ ( implies @ A @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) )
!= ( theorem @ ( implies @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[4006,32]) ).
thf(4039,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[4038:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( not @ ( implies @ G @ ( not @ G ) ) ))]]) ).
thf(4095,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[4039]) ).
thf(4552,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ ( not @ ( implies @ A @ ( not @ A ) ) ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[4095,16]) ).
thf(43276,plain,
$false,
inference(e,[status(thm)],[4188,25489,2072,17903,11318,1549,14419,18180,69,629,28526,20432,12710,23996,11445,33707,29830,101,1454,14171,32465,6918,14414,28504,6883,24173,6219,11409,7322,17424,16229,14200,14399,22424,11224,408,34117,11308,28499,1073,17907,20145,28266,12714,4097,27391,11303,21857,22300,11399,18482,11288,2141,11962,23082,17126,11228,21517,14203,14168,15590,23019,24,15870,12770,23685,14188,18171,10153,25,4511,15823,28482,1046,9379,24192,11426,22752,1985,11421,785,11431,11299,11944,1264,838,15881,1826,28486,16712,19851,1191,11416,1462,2356,11453,11696,15601,1890,18624,12137,152,17884,4507,261,29,1379,12920,11934,20,22389,24609,25980,11404,11215,6054,3569,11446,15623,25526,6187,24001,11398,574,6717,1283,981,11312,23042,28253,13668,3676,411,17938,23368,265,1843,12485,11413,29398,14162,28473,6183,11307,17919,7037,27392,12132,11292,1074,14661,11324,3318,11410,11424,18168,334,11238,260,11223,15531,4091,32476,12715,33,23053,28,28515,30199,34048,11217,21,3816,847,15886,5465,1888,16247,25534,461,2345,16652,1392,12147,13639,27897,11284,11234,22428,3831,23341,6919,29440,11304,5475,23049,11221,10398,11929,16031,15599,1683,22306,17942,193,17912,23974,25544,1889,11248,14174,8599,1099,1552,129,22042,16237,11300,17069,8980,1627,22432,28748,1060,6211,21119,11315,13436,29798,28519,28521,12913,5249,4308,266,3563,31179,11296,12155,22371,33169,11311,11427,17,375,412,25551,23938,32,264,8728,6578,29785,6916,16030,22372,8015,4998,28278,11434,6870,1884,22,27902,21974,27,23349,22772,1139,12,33446,498,11291,12936,25973,16246,11301,33717,13673,11237,25542,14151,15530,22399,28484,1282,3238,5827,3106,28511,7206,28529,26320,21854,11306,6216,23314,11451,6217,81,11406,4107,5816,11947,11419,17682,17066,27870,12697,8198,4420,31541,34763,6747,1325,17926,2350,28496,780,28507,15814,22040,267,5693,25935,6730,11310,21513,1198,11220,11245,5248,27953,80,24575,18173,8731,2614,374,1277,12701,27045,22689,12922,1948,490,11316,29771,1472,28466,16290,17156,15817,48,855,18,971,327,16221,11956,17134,263,1611,16032,23345,22793,16249,24941,1452,717,11295,11297,463,9911,1285,31,32386,16,22048,11429,25999,3475,10861,12160,1262,11969,14179,11181,23933,15580,5453,22401,15841,34034,29423,28478,11302,21860,99,18797,1834,1844,3725,4006,27903,11412,3452,627,23965,14425,23313,1276,14172,28530,22775,23940,18166,21518,15315,14457,19253,781,23,2152,9102,25939,12662,26,28513,11287,27867,24008,5692,28465,13642,28527,13659,899,11418,82,11405,2066,17116,15621,14435,28495,31104,18206,12240,12658,262,30,25250,2003,16271,27003,23535,25481,11219,7029,405,12681,1986,13695,19,23357,14208,564,15622,268,79,11415,12252,17910,22392,16256,25511,720,9431,11246,1693,2070,11950,1197,1473,12944,11236,27331,28506,23322,2898,15845,16711,6209,7493,2687,28474,1885,11309,47,15,24632,11935,22054,13697,11298,27844,35351,11286,16430,4547,16654,13962,16681,23022,11294,28320,227,11241,12694,10618,17893,2351,18620,4552,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL250-10 : TPTP v8.2.0. Released v7.3.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 13:06:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (101ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.74/1.25 % [INFO] eprover registered as external prover.
% 1.74/1.26 % [INFO] Scanning for conjecture ...
% 1.91/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.91/1.34 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.91/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.36 % [INFO] Type checking passed.
% 1.91/1.36 % [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 ...
% 136.87/38.16 % External prover 'e' found a proof!
% 136.87/38.16 % [INFO] Killing All external provers ...
% 136.87/38.16 % Time passed: 37643ms (effective reasoning time: 37175ms)
% 136.87/38.16 % Axioms used in derivation (10): axiom_1_5, ifeq_axiom, and_defn, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 136.87/38.16 % No. of inferences in proof: 1502
% 136.87/38.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 37643 ms resp. 37175 ms w/o parsing
% 137.66/38.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 137.66/38.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------