TSTP Solution File: LCL129-1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : LCL129-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 : Tue May 21 00:04:46 EDT 2024
% Result : Unsatisfiable 103.39s 19.40s
% Output : Refutation 103.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 9
% Syntax : Number of formulae : 583 ( 326 unt; 6 typ; 0 def)
% Number of atoms : 1235 ( 550 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 14298 ( 731 ~; 310 |; 0 &;13257 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 2172 ( 0 ^2172 !; 0 ?;2172 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(equivalent_type,type,
equivalent: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(e_type,type,
e: $i ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_4) ).
thf(8,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
inference(cnf,[status(esa)],[6]) ).
thf(22,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ E )
| ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( M )),bind(B,$thf( Q )),bind(C,$thf( P )),bind(D,$thf( R )),bind(E,$thf( equivalent @ M @ ( equivalent @ Q @ P ) )),bind(F,$thf( equivalent @ ( equivalent @ M @ ( equivalent @ R @ P ) ) @ ( equivalent @ Q @ R ) ))]]) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(45,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ H @ F ) ) @ ( equivalent @ G @ H ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,29]) ).
thf(46,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( M )),bind(B,$thf( Q )),bind(C,$thf( P )),bind(D,$thf( R )),bind(E,$thf( equivalent @ M @ ( equivalent @ Q @ P ) )),bind(F,$thf( equivalent @ Q @ R )),bind(G,$thf( equivalent @ M @ ( equivalent @ R @ P ) )),bind(H,$thf( H ))]]) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(24,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ E @ F ) )
| ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(25,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( O )),bind(B,$thf( S )),bind(C,$thf( R )),bind(D,$thf( T )),bind(E,$thf( equivalent @ ( equivalent @ O @ ( equivalent @ S @ R ) ) @ ( equivalent @ ( equivalent @ O @ ( equivalent @ T @ R ) ) @ ( equivalent @ S @ T ) ) )),bind(F,$thf( F ))]]) ).
thf(30,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(simp,[status(thm)],[25]) ).
thf(380,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ I @ H ) ) @ ( equivalent @ ( equivalent @ G @ ( equivalent @ J @ H ) ) @ ( equivalent @ I @ J ) ) ) @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,30]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( equivalent @ U @ ( equivalent @ W @ X ) )),bind(B,$thf( U )),bind(C,$thf( X )),bind(D,$thf( D )),bind(E,$thf( W )),bind(F,$thf( equivalent @ ( equivalent @ U @ ( equivalent @ W @ X ) ) @ ( equivalent @ U @ ( equivalent @ W @ X ) ) )),bind(G,$thf( U )),bind(H,$thf( X )),bind(I,$thf( D )),bind(J,$thf( W ))]]) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(55,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ F )
| ( is_a_theorem @ G )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ G ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,7]) ).
thf(56,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( S )),bind(B,$thf( T )),bind(C,$thf( W )),bind(D,$thf( P )),bind(E,$thf( V )),bind(F,$thf( equivalent @ ( equivalent @ T @ ( equivalent @ P @ W ) ) @ ( equivalent @ S @ ( equivalent @ P @ V ) ) )),bind(G,$thf( equivalent @ ( equivalent @ T @ ( equivalent @ V @ W ) ) @ S ))]]) ).
thf(61,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(1530,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ E ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ D @ H ) ) @ ( equivalent @ E @ ( equivalent @ D @ G ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,61]) ).
thf(1531,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[1530:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A )),bind(F,$thf( A )),bind(G,$thf( C )),bind(H,$thf( C ))]]) ).
thf(1592,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) ),
inference(simp,[status(thm)],[1531]) ).
thf(1,negated_conjecture,
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_2) ).
thf(4,plain,
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,plain,
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,5]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ A @ ( equivalent @ D @ B ) )
!= a )
| ( ( equivalent @ C @ D )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ A @ ( equivalent @ D @ B ) )
!= a )
| ( C != a )
| ( D
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ a @ B ) ) )
| ( ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ) ),
inference(simp,[status(thm)],[87]) ).
thf(101,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ E @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ F ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,96]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ a @ C ) ) )
| ( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( a )),bind(D,$thf( I )),bind(E,$thf( equivalent @ G @ ( equivalent @ I @ J ) )),bind(F,$thf( I ))]]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ a @ C ) ) )
| ( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ) ),
inference(simp,[status(thm)],[102]) ).
thf(1614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ D ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,109]) ).
thf(1615,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(pattern_uni,[status(thm)],[1614:[bind(A,$thf( equivalent @ a @ K )),bind(B,$thf( I )),bind(C,$thf( equivalent @ ( equivalent @ a @ K ) @ ( equivalent @ I @ I ) )),bind(D,$thf( D )),bind(E,$thf( K ))]]) ).
thf(1665,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(simp,[status(thm)],[1615]) ).
thf(392,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ D @ ( equivalent @ G @ E ) ) @ ( equivalent @ F @ G ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ F @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,29]) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( equivalent @ H @ ( equivalent @ L @ M ) )),bind(E,$thf( equivalent @ L @ M )),bind(F,$thf( H )),bind(G,$thf( G ))]]) ).
thf(426,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ B @ A ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(464,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ E )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ B @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ H @ G ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ I @ G ) ) @ ( equivalent @ H @ I ) ) ) @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[426,30]) ).
thf(465,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[464:[bind(A,$thf( equivalent @ P @ ( equivalent @ S @ S ) )),bind(B,$thf( P )),bind(C,$thf( C )),bind(D,$thf( S )),bind(E,$thf( equivalent @ P @ ( equivalent @ P @ ( equivalent @ S @ S ) ) )),bind(F,$thf( P )),bind(G,$thf( S )),bind(H,$thf( C )),bind(I,$thf( S ))]]) ).
thf(477,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) ),
inference(simp,[status(thm)],[465]) ).
thf(488,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ F @ D ) ) @ ( equivalent @ E @ F ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ E @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,29]) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[488:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( equivalent @ H @ H )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(57,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ F @ G ) )
| ( is_a_theorem @ G )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ F ) ) ),
inference(paramod_ordered,[status(thm)],[51,7]) ).
thf(58,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ B @ F ) ) @ ( equivalent @ C @ ( equivalent @ B @ E ) ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ C ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( U )),bind(B,$thf( V )),bind(C,$thf( Y )),bind(D,$thf( R )),bind(E,$thf( X )),bind(F,$thf( equivalent @ ( equivalent @ ( equivalent @ V @ ( equivalent @ R @ Y ) ) @ ( equivalent @ U @ ( equivalent @ R @ X ) ) ) @ ( equivalent @ ( equivalent @ V @ ( equivalent @ X @ Y ) ) @ U ) )),bind(G,$thf( G ))]]) ).
thf(62,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ B @ F ) ) @ ( equivalent @ C @ ( equivalent @ B @ E ) ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ C ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(simp,[status(thm)],[58]) ).
thf(1955,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ D )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ E @ I ) ) @ ( equivalent @ F @ ( equivalent @ E @ H ) ) ) @ ( equivalent @ ( equivalent @ G @ ( equivalent @ H @ I ) ) @ F ) ) @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,62]) ).
thf(1956,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ B @ E ) ) @ ( equivalent @ ( equivalent @ A @ A ) @ ( equivalent @ B @ D ) ) ) @ ( equivalent @ C @ ( equivalent @ D @ E ) ) ) ),
inference(pattern_uni,[status(thm)],[1955:[bind(A,$thf( equivalent @ ( equivalent @ ZN @ ( equivalent @ ZL @ ZQ ) ) @ ( equivalent @ ( equivalent @ ZK @ ZK ) @ ( equivalent @ ZL @ ZP ) ) )),bind(B,$thf( equivalent @ ZN @ ( equivalent @ ZP @ ZQ ) )),bind(C,$thf( ZK )),bind(D,$thf( equivalent @ ( equivalent @ ( equivalent @ ZN @ ( equivalent @ ZL @ ZQ ) ) @ ( equivalent @ ( equivalent @ ZK @ ZK ) @ ( equivalent @ ZL @ ZP ) ) ) @ ( equivalent @ ZN @ ( equivalent @ ZP @ ZQ ) ) )),bind(E,$thf( ZL )),bind(F,$thf( equivalent @ ZK @ ZK )),bind(G,$thf( ZN )),bind(H,$thf( ZP )),bind(I,$thf( ZQ ))]]) ).
thf(1987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ B @ E ) ) @ ( equivalent @ ( equivalent @ A @ A ) @ ( equivalent @ B @ D ) ) ) @ ( equivalent @ C @ ( equivalent @ D @ E ) ) ) ),
inference(simp,[status(thm)],[1956]) ).
thf(6084,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ H @ ( equivalent @ I @ J ) ) @ G ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ B @ E ) ) @ ( equivalent @ ( equivalent @ A @ A ) @ ( equivalent @ B @ D ) ) ) @ ( equivalent @ C @ ( equivalent @ D @ E ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ H @ ( equivalent @ F @ J ) ) @ ( equivalent @ G @ ( equivalent @ F @ I ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1987,61]) ).
thf(6085,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[6084:[bind(A,$thf( T )),bind(B,$thf( Q )),bind(C,$thf( K )),bind(D,$thf( equivalent @ T @ T )),bind(E,$thf( N )),bind(F,$thf( equivalent @ T @ T )),bind(G,$thf( K )),bind(H,$thf( equivalent @ K @ ( equivalent @ Q @ N ) )),bind(I,$thf( N )),bind(J,$thf( equivalent @ Q @ ( equivalent @ T @ T ) ))]]) ).
thf(6205,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) ) @ A ) ),
inference(simp,[status(thm)],[6085]) ).
thf(53,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ I @ G ) ) @ ( equivalent @ H @ I ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ H @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,29]) ).
thf(54,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( P )),bind(B,$thf( T )),bind(C,$thf( W )),bind(D,$thf( R )),bind(E,$thf( V )),bind(F,$thf( equivalent @ ( equivalent @ T @ ( equivalent @ R @ W ) ) @ ( equivalent @ P @ ( equivalent @ R @ V ) ) )),bind(G,$thf( P )),bind(H,$thf( equivalent @ T @ ( equivalent @ V @ W ) )),bind(I,$thf( I ))]]) ).
thf(60,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(76,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ G )
| ( is_a_theorem @ H )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ G @ H ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,7]) ).
thf(77,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ A @ F ) ) @ ( equivalent @ B @ ( equivalent @ A @ E ) ) ) @ ( equivalent @ C @ B ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ C ) ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( X )),bind(B,$thf( V )),bind(C,$thf( S )),bind(D,$thf( Y )),bind(E,$thf( ZA )),bind(F,$thf( ZB )),bind(G,$thf( equivalent @ ( equivalent @ ( equivalent @ Y @ ( equivalent @ S @ ZB ) ) @ ( equivalent @ V @ ( equivalent @ S @ ZA ) ) ) @ ( equivalent @ X @ V ) )),bind(H,$thf( equivalent @ ( equivalent @ Y @ ( equivalent @ ZA @ ZB ) ) @ X ))]]) ).
thf(85,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ A @ F ) ) @ ( equivalent @ B @ ( equivalent @ A @ E ) ) ) @ ( equivalent @ C @ B ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ C ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(6435,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ H @ ( equivalent @ I @ J ) ) @ G ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ H @ ( equivalent @ E @ J ) ) @ ( equivalent @ F @ ( equivalent @ E @ I ) ) ) @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6205,85]) ).
thf(6436,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ ( equivalent @ A @ A ) @ C ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[6435:[bind(A,$thf( equivalent @ M @ N )),bind(B,$thf( N )),bind(C,$thf( C )),bind(D,$thf( L )),bind(E,$thf( C )),bind(F,$thf( N )),bind(G,$thf( M )),bind(H,$thf( equivalent @ M @ N )),bind(I,$thf( equivalent @ L @ L )),bind(J,$thf( N ))]]) ).
thf(6554,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ ( equivalent @ A @ A ) @ C ) ) @ B ) ),
inference(simp,[status(thm)],[6436]) ).
thf(6590,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ E ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ ( equivalent @ A @ A ) @ C ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ D @ H ) ) @ ( equivalent @ E @ ( equivalent @ D @ G ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6554,61]) ).
thf(6591,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ ( equivalent @ D @ D ) @ C ) ) @ A ) @ ( equivalent @ C @ A ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[6590:[bind(A,$thf( R )),bind(B,$thf( equivalent @ M @ ( equivalent @ ( equivalent @ R @ R ) @ P ) )),bind(C,$thf( J )),bind(D,$thf( equivalent @ R @ R )),bind(E,$thf( M )),bind(F,$thf( equivalent @ ( equivalent @ M @ ( equivalent @ ( equivalent @ R @ R ) @ P ) ) @ J )),bind(G,$thf( P )),bind(H,$thf( J ))]]) ).
thf(6712,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ ( equivalent @ D @ D ) @ C ) ) @ A ) @ ( equivalent @ C @ A ) ) @ B ) ),
inference(simp,[status(thm)],[6591]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,5]) ).
thf(518,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(41,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ~ ( is_a_theorem @ E )
| ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ D @ B ) ) )
| ( is_a_theorem @ ( equivalent @ C @ D ) ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( equivalent @ G @ ( equivalent @ L @ J ) )),bind(F,$thf( equivalent @ K @ L ))]]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ D @ B ) ) )
| ( is_a_theorem @ ( equivalent @ C @ D ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ D @ B ) ) )
| ( ( is_a_theorem @ ( equivalent @ C @ D ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,5]) ).
thf(725,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ a @ B ) ) )
| ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[724:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ))]]) ).
thf(1608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,725]) ).
thf(1609,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[1608:[bind(A,$thf( equivalent @ a @ J )),bind(B,$thf( H )),bind(C,$thf( equivalent @ ( equivalent @ a @ J ) @ ( equivalent @ H @ H ) )),bind(D,$thf( J ))]]) ).
thf(1663,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[1609]) ).
thf(2233,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ F ) @ ( equivalent @ E @ E ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,1663]) ).
thf(2234,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ A ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[2233:[bind(A,$thf( equivalent @ a @ B )),bind(B,$thf( B )),bind(C,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )),bind(D,$thf( B )),bind(E,$thf( B )),bind(F,$thf( B ))]]) ).
thf(2280,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ A ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) ) ),
inference(simp,[status(thm)],[2234]) ).
thf(2456,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2280]) ).
thf(2480,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[2456]) ).
thf(1610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,725]) ).
thf(1611,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ a @ B ) ) ),
inference(pattern_uni,[status(thm)],[1610:[bind(A,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ J )),bind(B,$thf( H )),bind(C,$thf( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ J ) @ ( equivalent @ H @ H ) )),bind(D,$thf( J ))]]) ).
thf(1664,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[1611]) ).
thf(2497,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ F ) @ ( equivalent @ E @ E ) ) @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,1664]) ).
thf(2498,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[2497:[bind(A,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( B )),bind(E,$thf( B )),bind(F,$thf( B ))]]) ).
thf(2544,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[2498]) ).
thf(514,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ C )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ F @ E ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ G @ E ) ) @ ( equivalent @ F @ G ) ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,30]) ).
thf(515,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ E @ E ) ) ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( equivalent @ ( equivalent @ ZF @ ( equivalent @ ZJ @ ZI ) ) @ ( equivalent @ ( equivalent @ ZF @ ( equivalent @ ZK @ ZI ) ) @ ( equivalent @ ZJ @ ZK ) ) )),bind(B,$thf( ZM )),bind(C,$thf( equivalent @ ( equivalent @ ( equivalent @ ZF @ ( equivalent @ ZJ @ ZI ) ) @ ( equivalent @ ( equivalent @ ZF @ ( equivalent @ ZK @ ZI ) ) @ ( equivalent @ ZJ @ ZK ) ) ) @ ( equivalent @ ZM @ ZM ) )),bind(D,$thf( ZF )),bind(E,$thf( ZI )),bind(F,$thf( ZJ )),bind(G,$thf( ZK ))]]) ).
thf(520,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ E @ E ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(3973,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ E @ E ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ I @ H ) ) @ ( equivalent @ ( equivalent @ G @ ( equivalent @ J @ H ) ) @ ( equivalent @ I @ J ) ) ) @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[520,30]) ).
thf(3974,plain,
! [A: $i] : ( is_a_theorem @ ( equivalent @ A @ A ) ),
inference(pattern_uni,[status(thm)],[3973:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( L )),bind(F,$thf( equivalent @ L @ L )),bind(G,$thf( A )),bind(H,$thf( B )),bind(I,$thf( C )),bind(J,$thf( D ))]]) ).
thf(4020,plain,
! [A: $i] : ( is_a_theorem @ ( equivalent @ A @ A ) ),
inference(simp,[status(thm)],[3974]) ).
thf(1595,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ F @ D ) ) @ ( equivalent @ E @ F ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ E @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,29]) ).
thf(1596,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[1595:[bind(A,$thf( equivalent @ K @ L )),bind(B,$thf( J )),bind(C,$thf( equivalent @ ( equivalent @ K @ L ) @ ( equivalent @ J @ J ) )),bind(D,$thf( L )),bind(E,$thf( K )),bind(F,$thf( F ))]]) ).
thf(1679,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) ),
inference(simp,[status(thm)],[1596]) ).
thf(1817,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ E )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ H @ G ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ I @ G ) ) @ ( equivalent @ H @ I ) ) ) @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[1679,30]) ).
thf(1818,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[1817:[bind(A,$thf( equivalent @ ( equivalent @ X @ ( equivalent @ ZC @ ZB ) ) @ ( equivalent @ ZB @ ZC ) )),bind(B,$thf( ZC )),bind(C,$thf( X )),bind(D,$thf( equivalent @ ZC @ ZB )),bind(E,$thf( equivalent @ X @ ( equivalent @ ( equivalent @ X @ ( equivalent @ ZC @ ZB ) ) @ ( equivalent @ ZB @ ZC ) ) )),bind(F,$thf( equivalent @ X @ ( equivalent @ ZC @ ZB ) )),bind(G,$thf( ZC )),bind(H,$thf( ZC )),bind(I,$thf( ZB ))]]) ).
thf(1845,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) ) ),
inference(simp,[status(thm)],[1818]) ).
thf(2014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1845,725]) ).
thf(2015,plain,
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2014:[bind(A,$thf( a )),bind(B,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(C,$thf( equivalent @ b @ c )),bind(D,$thf( a )),bind(E,$thf( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ))]]) ).
thf(2097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ D @ B ) ) )
| ( ( is_a_theorem @ ( equivalent @ C @ D ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,2015]) ).
thf(2098,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ a @ B ) ) )
| ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[2097:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ))]]) ).
thf(2644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2098]) ).
thf(2645,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2644:[bind(A,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )),bind(B,$thf( R )),bind(C,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )),bind(D,$thf( equivalent @ R @ R ))]]) ).
thf(2720,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ A ) ) ) ),
inference(simp,[status(thm)],[2645]) ).
thf(2892,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ F @ F ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,2720]) ).
thf(2893,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2892:[bind(A,$thf( A )),bind(B,$thf( equivalent @ a @ ( equivalent @ R @ R ) )),bind(C,$thf( a )),bind(D,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(E,$thf( equivalent @ b @ c )),bind(F,$thf( R ))]]) ).
thf(2941,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[2893]) ).
thf(4081,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ C ) ) @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2941]) ).
thf(4134,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ C ) ) @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[4081]) ).
thf(7071,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) )
| ( A
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ C ) ) @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[4134]) ).
thf(7072,plain,
! [B: $i,A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[7071]) ).
thf(4099,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ B @ ( equivalent @ E @ C ) )
!= a )
| ( ( equivalent @ D @ E )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ D @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,63]) ).
thf(4100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) )
!= a )
| ( ( equivalent @ B @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[4099:[bind(A,$thf( equivalent @ F @ G )),bind(B,$thf( equivalent @ F @ G )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(4166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) )
!= a )
| ( ( equivalent @ B @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[4100]) ).
thf(945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,725]) ).
thf(946,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[945:[bind(A,$thf( a )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( equivalent @ a @ ( equivalent @ H @ ( equivalent @ K @ K ) ) )),bind(E,$thf( H ))]]) ).
thf(1005,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) ) ),
inference(simp,[status(thm)],[946]) ).
thf(2562,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2544]) ).
thf(2590,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[2562]) ).
thf(955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,725]) ).
thf(956,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[955:[bind(A,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )),bind(B,$thf( R )),bind(C,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )),bind(D,$thf( equivalent @ R @ R ))]]) ).
thf(1010,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ A ) ) ) ),
inference(simp,[status(thm)],[956]) ).
thf(1528,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ F @ F ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,1010]) ).
thf(1529,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1528:[bind(A,$thf( A )),bind(B,$thf( equivalent @ a @ ( equivalent @ R @ R ) )),bind(C,$thf( a )),bind(D,$thf( equivalent @ b @ c )),bind(E,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(F,$thf( R ))]]) ).
thf(1591,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(4059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ D @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,29]) ).
thf(4060,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[4059:[bind(A,$thf( equivalent @ F @ G )),bind(B,$thf( equivalent @ F @ G )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(4178,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) ),
inference(simp,[status(thm)],[4060]) ).
thf(4262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4178,2098]) ).
thf(4263,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[4262:[bind(A,$thf( J )),bind(B,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )),bind(C,$thf( K )),bind(D,$thf( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ K ) @ ( equivalent @ J @ K ) )),bind(E,$thf( J ))]]) ).
thf(4326,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[4263]) ).
thf(2104,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,2015]) ).
thf(2123,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2104]) ).
thf(5257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2123]) ).
thf(5264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( A != a )
| ( ( equivalent @ B @ C )
!= ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[5257]) ).
thf(5265,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ A @ B ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[5264]) ).
thf(9,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,5]) ).
thf(10,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(165,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ F ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,109]) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ a @ D ) ) )
| ( ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( a )),bind(D,$thf( J )),bind(E,$thf( equivalent @ H @ ( equivalent @ J @ K ) )),bind(F,$thf( F )),bind(G,$thf( J ))]]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ a @ D ) ) )
| ( ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ) ),
inference(simp,[status(thm)],[166]) ).
thf(510,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ ( equivalent @ C @ E ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ C ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,175]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( a )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( a )),bind(E,$thf( E )),bind(F,$thf( equivalent @ H @ H ))]]) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(simp,[status(thm)],[511]) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,725]) ).
thf(954,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[953:[bind(A,$thf( a )),bind(B,$thf( F )),bind(C,$thf( a )),bind(D,$thf( equivalent @ F @ F ))]]) ).
thf(1009,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ A ) ) ) ),
inference(simp,[status(thm)],[954]) ).
thf(1648,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,1009]) ).
thf(1649,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1648]) ).
thf(4761,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= a )
| ( A
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1649]) ).
thf(4762,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ A ) )
!= a ),
inference(simp,[status(thm)],[4761]) ).
thf(2628,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,2098]) ).
thf(2629,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[2628:[bind(A,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ H @ ( equivalent @ K @ K ) ) )),bind(E,$thf( H ))]]) ).
thf(2712,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[2629]) ).
thf(2630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2098]) ).
thf(2631,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[2630:[bind(A,$thf( equivalent @ a @ J )),bind(B,$thf( H )),bind(C,$thf( equivalent @ ( equivalent @ a @ J ) @ ( equivalent @ H @ H ) )),bind(D,$thf( J ))]]) ).
thf(2713,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[2631]) ).
thf(3279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ F ) @ ( equivalent @ E @ E ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,2713]) ).
thf(3280,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ A ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[3279:[bind(A,$thf( equivalent @ a @ B )),bind(B,$thf( B )),bind(C,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )),bind(D,$thf( B )),bind(E,$thf( B )),bind(F,$thf( B ))]]) ).
thf(3325,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ A ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) ) ),
inference(simp,[status(thm)],[3280]) ).
thf(4097,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,3325]) ).
thf(4142,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[4097]) ).
thf(966,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,725]) ).
thf(967,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) ) ),
inference(pattern_uni,[status(thm)],[966:[bind(A,$thf( a )),bind(B,$thf( S )),bind(C,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(D,$thf( equivalent @ b @ c )),bind(E,$thf( equivalent @ a @ ( equivalent @ S @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )),bind(F,$thf( equivalent @ S @ ( equivalent @ b @ c ) ))]]) ).
thf(990,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[967]) ).
thf(1626,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,990]) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[1626]) ).
thf(4113,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,1010]) ).
thf(4156,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ B ) ) ) ),
inference(simp,[status(thm)],[4113]) ).
thf(2099,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2015]) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2099]) ).
thf(2133,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2124]) ).
thf(2134,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[2133]) ).
thf(2135,plain,
! [A: $i] :
( ( a != a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[2134]) ).
thf(2136,plain,
! [A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ),
inference(simp,[status(thm)],[2135]) ).
thf(6924,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ H @ ( equivalent @ I @ J ) ) @ G ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ ( equivalent @ D @ D ) @ C ) ) @ A ) @ ( equivalent @ C @ A ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ H @ ( equivalent @ E @ J ) ) @ ( equivalent @ F @ ( equivalent @ E @ I ) ) ) @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6712,85]) ).
thf(6925,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ ( equivalent @ A @ A ) @ D ) ) @ ( equivalent @ B @ B ) ) @ C ) ),
inference(pattern_uni,[status(thm)],[6924:[bind(A,$thf( equivalent @ Q @ R )),bind(B,$thf( equivalent @ S @ T )),bind(C,$thf( T )),bind(D,$thf( P )),bind(E,$thf( Q )),bind(F,$thf( T )),bind(G,$thf( S )),bind(H,$thf( equivalent @ ( equivalent @ S @ T ) @ ( equivalent @ ( equivalent @ P @ P ) @ T ) )),bind(I,$thf( R )),bind(J,$thf( R ))]]) ).
thf(7043,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ ( equivalent @ A @ A ) @ D ) ) @ ( equivalent @ B @ B ) ) @ C ) ),
inference(simp,[status(thm)],[6925]) ).
thf(2680,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ a @ G ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,2098]) ).
thf(2681,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[2680:[bind(A,$thf( N )),bind(B,$thf( a )),bind(C,$thf( equivalent @ b @ c )),bind(D,$thf( P )),bind(E,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(F,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ P @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ N @ ( equivalent @ P @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )),bind(G,$thf( N ))]]) ).
thf(2735,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[2681]) ).
thf(6592,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ G @ ( equivalent @ H @ I ) ) @ F ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ ( equivalent @ A @ A ) @ C ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ D @ I ) ) @ ( equivalent @ E @ ( equivalent @ D @ H ) ) ) @ ( equivalent @ F @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6554,85]) ).
thf(6593,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ C ) ) @ ( equivalent @ A @ A ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[6592:[bind(A,$thf( Q )),bind(B,$thf( equivalent @ N @ ( equivalent @ Q @ Q ) )),bind(C,$thf( equivalent @ J @ K )),bind(D,$thf( J )),bind(E,$thf( equivalent @ Q @ Q )),bind(F,$thf( N )),bind(G,$thf( equivalent @ N @ ( equivalent @ Q @ Q ) )),bind(H,$thf( K )),bind(I,$thf( K ))]]) ).
thf(6713,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ C ) ) @ ( equivalent @ A @ A ) ) @ B ) ),
inference(simp,[status(thm)],[6593]) ).
thf(74,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ G @ ( equivalent @ J @ H ) ) @ ( equivalent @ I @ J ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ G @ ( equivalent @ I @ H ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,29]) ).
thf(75,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( W )),bind(B,$thf( X )),bind(C,$thf( U )),bind(D,$thf( Y )),bind(E,$thf( ZA )),bind(F,$thf( ZB )),bind(G,$thf( equivalent @ ( equivalent @ ( equivalent @ Y @ ( equivalent @ U @ ZB ) ) @ ( equivalent @ X @ ( equivalent @ U @ ZA ) ) ) @ ( equivalent @ W @ X ) )),bind(H,$thf( W )),bind(I,$thf( equivalent @ Y @ ( equivalent @ ZA @ ZB ) )),bind(J,$thf( J ))]]) ).
thf(84,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(143,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ H )
| ( is_a_theorem @ I )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ H @ I ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,7]) ).
thf(144,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ A @ G ) ) @ ( equivalent @ B @ ( equivalent @ A @ F ) ) ) @ ( equivalent @ C @ B ) ) @ ( equivalent @ D @ C ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ D ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( ZC )),bind(B,$thf( V )),bind(C,$thf( ZA )),bind(D,$thf( Y )),bind(E,$thf( ZD )),bind(F,$thf( ZF )),bind(G,$thf( ZG )),bind(H,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZD @ ( equivalent @ V @ ZG ) ) @ ( equivalent @ Y @ ( equivalent @ V @ ZF ) ) ) @ ( equivalent @ ZA @ Y ) ) @ ( equivalent @ ZC @ ZA ) )),bind(I,$thf( equivalent @ ( equivalent @ ZD @ ( equivalent @ ZF @ ZG ) ) @ ZC ))]]) ).
thf(157,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ A @ G ) ) @ ( equivalent @ B @ ( equivalent @ A @ F ) ) ) @ ( equivalent @ C @ B ) ) @ ( equivalent @ D @ C ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ D ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(2094,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,2015]) ).
thf(2121,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2094]) ).
thf(5250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2121]) ).
thf(5255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) )
!= a )
| ( A != a )
| ( B
!= ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[5250]) ).
thf(5256,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) @ ( equivalent @ A @ A ) ) )
!= a ),
inference(simp,[status(thm)],[5255]) ).
thf(1641,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,1010]) ).
thf(1654,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1641]) ).
thf(4924,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( A
!= ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1654]) ).
thf(4925,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[4924]) ).
thf(4928,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ B ) )
!= a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[4925]) ).
thf(1999,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ D @ ( equivalent @ G @ E ) ) @ ( equivalent @ F @ G ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ F @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1845,29]) ).
thf(2000,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[1999:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( H )),bind(E,$thf( equivalent @ L @ M )),bind(F,$thf( equivalent @ H @ ( equivalent @ M @ L ) )),bind(G,$thf( G ))]]) ).
thf(2071,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ A ) ) ),
inference(simp,[status(thm)],[2000]) ).
thf(2836,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2071,2098]) ).
thf(2837,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[2836:[bind(A,$thf( I )),bind(B,$thf( a )),bind(C,$thf( equivalent @ b @ c )),bind(D,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(E,$thf( equivalent @ a @ ( equivalent @ I @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )),bind(F,$thf( I ))]]) ).
thf(2879,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[2837]) ).
thf(4133,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2879]) ).
thf(4160,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[4133]) ).
thf(4513,plain,
! [B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( A
!= ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[4160]) ).
thf(4514,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
!= ( equivalent @ a @ A ) ),
inference(simp,[status(thm)],[4513]) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,1010]) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1089]) ).
thf(1769,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ H @ F ) ) @ ( equivalent @ G @ H ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1679,29]) ).
thf(1770,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ E ) @ ( equivalent @ C @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[1769:[bind(A,$thf( Q )),bind(B,$thf( P )),bind(C,$thf( M )),bind(D,$thf( R )),bind(E,$thf( equivalent @ ( equivalent @ ( equivalent @ M @ R ) @ ( equivalent @ P @ P ) ) @ ( equivalent @ Q @ R ) )),bind(F,$thf( Q )),bind(G,$thf( M )),bind(H,$thf( H ))]]) ).
thf(1847,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ E ) @ ( equivalent @ C @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ B @ A ) ) ),
inference(simp,[status(thm)],[1770]) ).
thf(4755,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1100]) ).
thf(4756,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ B @ B ) ) ),
inference(simp,[status(thm)],[4755]) ).
thf(2642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2098]) ).
thf(2643,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2642:[bind(A,$thf( a )),bind(B,$thf( F )),bind(C,$thf( a )),bind(D,$thf( equivalent @ F @ F ))]]) ).
thf(2719,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ A ) ) ) ),
inference(simp,[status(thm)],[2643]) ).
thf(2750,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2719]) ).
thf(2772,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2750]) ).
thf(5432,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2772]) ).
thf(5433,plain,
! [B: $i,A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ A ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ B @ B ) ) ),
inference(simp,[status(thm)],[5432]) ).
thf(3076,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2879]) ).
thf(3105,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3076]) ).
thf(6226,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3105]) ).
thf(6227,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ B ) ),
inference(simp,[status(thm)],[6226]) ).
thf(2806,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2071,725]) ).
thf(2807,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[2806:[bind(A,$thf( I )),bind(B,$thf( a )),bind(C,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(D,$thf( equivalent @ b @ c )),bind(E,$thf( equivalent @ a @ ( equivalent @ I @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) )),bind(F,$thf( I ))]]) ).
thf(2888,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[2807]) ).
thf(3125,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2888]) ).
thf(3160,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3125]) ).
thf(6326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) )
| ( A
!= ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3160]) ).
thf(6327,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[6326]) ).
thf(6419,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ B )
!= a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[6327]) ).
thf(2840,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ E )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ ( equivalent @ C @ D ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ H @ G ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ I @ G ) ) @ ( equivalent @ H @ I ) ) ) @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[2071,30]) ).
thf(2841,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) @ ( equivalent @ B @ ( equivalent @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[2840:[bind(A,$thf( equivalent @ ZB @ ( equivalent @ ZD @ ZE ) )),bind(B,$thf( equivalent @ ZB @ ( equivalent @ ZA @ ZE ) )),bind(C,$thf( ZA )),bind(D,$thf( ZD )),bind(E,$thf( equivalent @ ( equivalent @ ( equivalent @ ZB @ ( equivalent @ ZA @ ZE ) ) @ ( equivalent @ ZD @ ZA ) ) @ ( equivalent @ ZB @ ( equivalent @ ZD @ ZE ) ) )),bind(F,$thf( ZB )),bind(G,$thf( ZE )),bind(H,$thf( ZA )),bind(I,$thf( ZD ))]]) ).
thf(2880,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) @ ( equivalent @ B @ ( equivalent @ C @ D ) ) ) ),
inference(simp,[status(thm)],[2841]) ).
thf(3129,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2888]) ).
thf(3152,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3129]) ).
thf(1599,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ D ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ C @ G ) ) @ ( equivalent @ D @ ( equivalent @ C @ F ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,61]) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[1599:[bind(A,$thf( equivalent @ H @ ( equivalent @ J @ K ) )),bind(B,$thf( J )),bind(C,$thf( J )),bind(D,$thf( H )),bind(E,$thf( equivalent @ H @ ( equivalent @ J @ K ) )),bind(F,$thf( K )),bind(G,$thf( J ))]]) ).
thf(1659,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A ) ),
inference(simp,[status(thm)],[1600]) ).
thf(2096,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1659,2015]) ).
thf(2127,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2096]) ).
thf(5258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) )
!= a )
| ( A
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2127]) ).
thf(5259,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ B @ A ) )
!= a ),
inference(simp,[status(thm)],[5258]) ).
thf(4053,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2280]) ).
thf(4147,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[4053]) ).
thf(103,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ G @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ H ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ G @ ( equivalent @ a @ H ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,96]) ).
thf(106,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ G @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ H ) )
!= a )
| ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) )
!= ( equivalent @ G @ ( equivalent @ a @ H ) ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(2460,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2280]) ).
thf(2483,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[2460]) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,1009]) ).
thf(1072,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1056]) ).
thf(2558,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2544]) ).
thf(2586,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[2558]) ).
thf(4752,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[1072]) ).
thf(4753,plain,
! [B: $i,A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ A ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ B @ B ) ) ),
inference(simp,[status(thm)],[4752]) ).
thf(502,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ D ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,109]) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(pattern_uni,[status(thm)],[502:[bind(A,$thf( a )),bind(B,$thf( G )),bind(C,$thf( a )),bind(D,$thf( D )),bind(E,$thf( equivalent @ G @ G ))]]) ).
thf(529,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(simp,[status(thm)],[503]) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2015]) ).
thf(2118,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2095]) ).
thf(1598,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,5]) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[1598]) ).
thf(1767,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= a )
| ( A
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[1657]) ).
thf(1768,plain,
! [A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ A ) )
!= a ),
inference(simp,[status(thm)],[1767]) ).
thf(2674,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,2098]) ).
thf(2675,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2674:[bind(A,$thf( a )),bind(B,$thf( S )),bind(C,$thf( equivalent @ b @ c )),bind(D,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(E,$thf( equivalent @ a @ ( equivalent @ S @ ( equivalent @ b @ c ) ) )),bind(F,$thf( equivalent @ S @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ))]]) ).
thf(2733,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[2675]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( equivalent @ A @ B ) )
!= ( is_a_theorem @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ ( is_a_theorem @ A )
| ( ( equivalent @ A @ B )
!= A ) ),
inference(simp,[status(thm)],[26]) ).
thf(149,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ H @ ( equivalent @ K @ I ) ) @ ( equivalent @ J @ K ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ H @ ( equivalent @ J @ I ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,47]) ).
thf(150,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ A ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( ZB )),bind(B,$thf( X )),bind(C,$thf( ZC )),bind(D,$thf( ZA )),bind(E,$thf( ZD )),bind(F,$thf( ZF )),bind(G,$thf( ZG )),bind(H,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZD @ ( equivalent @ X @ ZG ) ) @ ( equivalent @ ZA @ ( equivalent @ X @ ZF ) ) ) @ ( equivalent @ ZC @ ZA ) ) @ ( equivalent @ ZB @ ZC ) )),bind(I,$thf( ZB )),bind(J,$thf( equivalent @ ZD @ ( equivalent @ ZF @ ZG ) )),bind(K,$thf( K ))]]) ).
thf(160,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ A ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(1616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ D ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,96]) ).
thf(1617,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ),
inference(pattern_uni,[status(thm)],[1616:[bind(A,$thf( equivalent @ a @ J )),bind(B,$thf( H )),bind(C,$thf( equivalent @ ( equivalent @ a @ J ) @ ( equivalent @ H @ H ) )),bind(D,$thf( J ))]]) ).
thf(1666,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ),
inference(simp,[status(thm)],[1617]) ).
thf(64,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ ( equivalent @ E @ ( equivalent @ H @ F ) ) @ ( equivalent @ G @ H ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,47]) ).
thf(65,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ A @ E ) ) )
| ( ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( equivalent @ I @ ( equivalent @ K @ L ) )),bind(F,$thf( K )),bind(G,$thf( C )),bind(H,$thf( H ))]]) ).
thf(70,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ A @ E ) ) )
| ( ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(4103,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2888]) ).
thf(4136,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[4103]) ).
thf(4339,plain,
! [B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) )
| ( A
!= ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[4136]) ).
thf(4340,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) )
!= ( equivalent @ a @ A ) ),
inference(simp,[status(thm)],[4339]) ).
thf(4343,plain,
! [A: $i] :
( ( a != a )
| ( ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )
!= A ) ),
inference(simp,[status(thm)],[4340]) ).
thf(4344,plain,
! [A: $i] :
( ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )
!= A ),
inference(simp,[status(thm)],[4343]) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ D @ C ) )
!= a )
| ( ( equivalent @ B @ D )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ D @ C ) )
!= a )
| ( B
!= ( equivalent @ b @ c ) )
| ( D
!= ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ B ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ B ) )
!= a ) ),
inference(simp,[status(thm)],[13]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ B ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ B ) )
!= ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ B ) ) )
| ( a != a ) ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ B ) )
!= a )
| ( A != A )
| ( ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ B )
!= ( equivalent @ ( equivalent @ b @ c ) @ B ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ B ) )
!= a )
| ( ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ B )
!= ( equivalent @ ( equivalent @ b @ c ) @ B ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(2131,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= a )
| ( A
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2118]) ).
thf(2132,plain,
! [A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ A ) )
!= a ),
inference(simp,[status(thm)],[2131]) ).
thf(1022,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,990]) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[1022]) ).
thf(4043,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[1033]) ).
thf(4044,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[4043]) ).
thf(391,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,5]) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[422]) ).
thf(3072,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2879]) ).
thf(3090,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3072]) ).
thf(4052,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) @ ( equivalent @ a @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2544]) ).
thf(4155,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) @ ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[4052]) ).
thf(88,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ E @ ( equivalent @ H @ F ) )
!= a )
| ( ( equivalent @ G @ H )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,63]) ).
thf(89,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ A @ E ) ) )
| ( ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( equivalent @ I @ ( equivalent @ K @ L ) )),bind(F,$thf( K )),bind(G,$thf( C )),bind(H,$thf( H ))]]) ).
thf(97,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ A @ E ) ) )
| ( ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(39,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ H @ F ) ) @ ( equivalent @ G @ H ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,29]) ).
thf(40,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ A @ E ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( equivalent @ I @ ( equivalent @ K @ L ) )),bind(F,$thf( K )),bind(G,$thf( C )),bind(H,$thf( H ))]]) ).
thf(48,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ A @ E ) ) )
| ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(549,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ ( equivalent @ D @ F ) ) @ ( equivalent @ C @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ C @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,48]) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[549:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( F )),bind(G,$thf( equivalent @ I @ I ))]]) ).
thf(605,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ B ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(676,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ E @ ( equivalent @ H @ F ) ) @ ( equivalent @ G @ H ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[605,29]) ).
thf(677,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[676:[bind(A,$thf( K )),bind(B,$thf( Q )),bind(C,$thf( R )),bind(D,$thf( P )),bind(E,$thf( equivalent @ ( equivalent @ K @ ( equivalent @ R @ ( equivalent @ P @ P ) ) ) @ ( equivalent @ Q @ R ) )),bind(F,$thf( Q )),bind(G,$thf( K )),bind(H,$thf( H ))]]) ).
thf(710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ B @ A ) ) ),
inference(simp,[status(thm)],[677]) ).
thf(6321,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3152]) ).
thf(6322,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ B ) ),
inference(simp,[status(thm)],[6321]) ).
thf(6323,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) )
!= a )
| ( ( equivalent @ A @ A )
!= B ) ),
inference(simp,[status(thm)],[6322]) ).
thf(6324,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ ( equivalent @ A @ A ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) )
!= a ),
inference(simp,[status(thm)],[6323]) ).
thf(2101,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1845,2015]) ).
thf(2115,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2101]) ).
thf(2632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2098]) ).
thf(2633,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ a @ B ) ) ),
inference(pattern_uni,[status(thm)],[2632:[bind(A,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ J )),bind(B,$thf( H )),bind(C,$thf( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ J ) @ ( equivalent @ H @ H ) )),bind(D,$thf( J ))]]) ).
thf(2714,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[2633]) ).
thf(3385,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ F ) @ ( equivalent @ E @ E ) ) @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,2714]) ).
thf(3386,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[3385:[bind(A,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( B )),bind(E,$thf( B )),bind(F,$thf( B ))]]) ).
thf(3432,plain,
! [A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[3386]) ).
thf(3443,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,3432]) ).
thf(3482,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3443]) ).
thf(2954,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2733]) ).
thf(2973,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[2954]) ).
thf(947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,725]) ).
thf(948,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[947:[bind(A,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ H @ ( equivalent @ K @ K ) ) )),bind(E,$thf( H ))]]) ).
thf(1006,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[948]) ).
thf(1702,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ D @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ E ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1659,96]) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ B @ A ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ C ) )
!= a ),
inference(pattern_uni,[status(thm)],[1702:[bind(A,$thf( equivalent @ a @ O )),bind(B,$thf( M )),bind(C,$thf( L )),bind(D,$thf( equivalent @ ( equivalent @ ( equivalent @ a @ O ) @ ( equivalent @ M @ L ) ) @ ( equivalent @ L @ M ) )),bind(E,$thf( O ))]]) ).
thf(1755,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ B @ A ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ C ) )
!= a ),
inference(simp,[status(thm)],[1703]) ).
thf(4104,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ ( equivalent @ C @ E ) ) @ ( equivalent @ B @ C ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,48]) ).
thf(4105,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[4104:[bind(A,$thf( equivalent @ G @ H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( equivalent @ G @ H )),bind(E,$thf( E )),bind(F,$thf( H ))]]) ).
thf(4167,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ C @ A ) ) ),
inference(simp,[status(thm)],[4105]) ).
thf(668,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(669,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[668]) ).
thf(2901,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2720]) ).
thf(2927,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2901]) ).
thf(5898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) )
| ( A
!= ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2927]) ).
thf(5899,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[5898]) ).
thf(5900,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ B ) )
!= a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[5899]) ).
thf(4131,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ B @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,1009]) ).
thf(4135,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ B @ B ) ) ) ),
inference(simp,[status(thm)],[4131]) ).
thf(92,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ E @ ( equivalent @ H @ F ) )
!= a )
| ( ( equivalent @ G @ H )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ G @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,63]) ).
thf(93,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) )
!= a )
| ( ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( M )),bind(B,$thf( Q )),bind(C,$thf( P )),bind(D,$thf( R )),bind(E,$thf( equivalent @ M @ ( equivalent @ Q @ P ) )),bind(F,$thf( equivalent @ Q @ R )),bind(G,$thf( equivalent @ M @ ( equivalent @ R @ P ) )),bind(H,$thf( H ))]]) ).
thf(99,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) )
!= a )
| ( ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) )
!= a )
| ( ( equivalent @ B @ ( equivalent @ E @ C ) )
!= a )
| ( A
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ ( equivalent @ C @ D ) ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ D @ B ) )
!= a ) ),
inference(simp,[status(thm)],[236]) ).
thf(670,plain,
! [A: $i] :
( ( a != a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[669]) ).
thf(671,plain,
! [A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ),
inference(simp,[status(thm)],[670]) ).
thf(672,plain,
! [A: $i] :
( ( A
!= ( equivalent @ b @ c ) )
| ( A
!= ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(673,plain,
( ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )
!= ( equivalent @ b @ c ) ),
inference(simp,[status(thm)],[672]) ).
thf(674,plain,
( ( ( equivalent @ b @ e )
!= b )
| ( ( equivalent @ c @ e )
!= c ) ),
inference(simp,[status(thm)],[673]) ).
thf(504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ C @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ D ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,96]) ).
thf(505,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ ( equivalent @ A @ A ) ) )
!= a ),
inference(pattern_uni,[status(thm)],[504:[bind(A,$thf( a )),bind(B,$thf( F )),bind(C,$thf( a )),bind(D,$thf( equivalent @ F @ F ))]]) ).
thf(530,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ ( equivalent @ A @ A ) ) )
!= a ),
inference(simp,[status(thm)],[505]) ).
thf(5247,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[2115]) ).
thf(5248,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ A ) ) @ ( equivalent @ A @ B ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[5247]) ).
thf(5249,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ A ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[5248]) ).
thf(3732,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ E @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ F ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) @ ( equivalent @ B @ ( equivalent @ C @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2880,96]) ).
thf(3733,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ ( equivalent @ B @ C ) ) )
!= a ),
inference(pattern_uni,[status(thm)],[3732:[bind(A,$thf( N )),bind(B,$thf( a )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ N @ P ) ) @ ( equivalent @ O @ N ) )),bind(F,$thf( equivalent @ O @ P ))]]) ).
thf(3824,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ ( equivalent @ B @ C ) ) )
!= a ),
inference(simp,[status(thm)],[3733]) ).
thf(4076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ C ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ a @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,109]) ).
thf(4077,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(pattern_uni,[status(thm)],[4076:[bind(A,$thf( equivalent @ a @ F )),bind(B,$thf( equivalent @ a @ F )),bind(C,$thf( C )),bind(D,$thf( F ))]]) ).
thf(4184,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(simp,[status(thm)],[4077]) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( ( equivalent @ B @ D )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )
| ( ( equivalent @ A @ ( equivalent @ D @ C ) )
!= ( equivalent @ A @ ( equivalent @ B @ C ) ) )
| ( a != a ) ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ C @ B ) )
!= a )
| ( ( equivalent @ C @ C )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( A )),bind(B,$thf( D ))]]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ C @ B ) )
!= a )
| ( ( equivalent @ C @ C )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(1681,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ D @ ( equivalent @ G @ E ) ) @ ( equivalent @ F @ G ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ F @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1659,29]) ).
thf(1682,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ E ) @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ E ) ) @ ( equivalent @ D @ A ) ) ),
inference(pattern_uni,[status(thm)],[1681:[bind(A,$thf( equivalent @ P @ Q )),bind(B,$thf( O )),bind(C,$thf( N )),bind(D,$thf( equivalent @ ( equivalent @ ( equivalent @ P @ Q ) @ ( equivalent @ O @ N ) ) @ ( equivalent @ N @ O ) )),bind(E,$thf( Q )),bind(F,$thf( P )),bind(G,$thf( G ))]]) ).
thf(1747,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ E ) @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ E ) ) @ ( equivalent @ D @ A ) ) ),
inference(simp,[status(thm)],[1682]) ).
thf(6228,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
!= a )
| ( ( equivalent @ A @ A )
!= B ) ),
inference(simp,[status(thm)],[6227]) ).
thf(6229,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ ( equivalent @ A @ A ) @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
!= a ),
inference(simp,[status(thm)],[6228]) ).
thf(52,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,5]) ).
thf(59,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( equivalent @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(5514,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ E ) @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ E ) ) @ ( equivalent @ D @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ I @ H ) ) @ ( equivalent @ ( equivalent @ G @ ( equivalent @ J @ H ) ) @ ( equivalent @ I @ J ) ) ) @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[1747,30]) ).
thf(5515,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[5514:[bind(A,$thf( equivalent @ ( equivalent @ ( equivalent @ ZI @ ( equivalent @ ZN @ ZO ) ) @ ( equivalent @ ZP @ ZN ) ) @ ( equivalent @ ZO @ ZP ) )),bind(B,$thf( ZN )),bind(C,$thf( ZP )),bind(D,$thf( ZI )),bind(E,$thf( equivalent @ ZN @ ZO )),bind(F,$thf( equivalent @ ZI @ ( equivalent @ ( equivalent @ ( equivalent @ ZI @ ( equivalent @ ZN @ ZO ) ) @ ( equivalent @ ZP @ ZN ) ) @ ( equivalent @ ZO @ ZP ) ) )),bind(G,$thf( equivalent @ ( equivalent @ ZI @ ( equivalent @ ZN @ ZO ) ) @ ( equivalent @ ZP @ ZN ) )),bind(H,$thf( ZP )),bind(I,$thf( ZN )),bind(J,$thf( ZO ))]]) ).
thf(5567,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) ) ),
inference(simp,[status(thm)],[5515]) ).
thf(4063,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2733]) ).
thf(4149,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[4063]) ).
thf(78,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ G @ H ) )
| ( is_a_theorem @ H )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) )
!= ( is_a_theorem @ G ) ) ),
inference(paramod_ordered,[status(thm)],[60,7]) ).
thf(79,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ C @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ D ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( Z )),bind(B,$thf( X )),bind(C,$thf( U )),bind(D,$thf( ZA )),bind(E,$thf( ZC )),bind(F,$thf( ZD )),bind(G,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZA @ ( equivalent @ U @ ZD ) ) @ ( equivalent @ X @ ( equivalent @ U @ ZC ) ) ) @ ( equivalent @ Z @ X ) ) @ ( equivalent @ ( equivalent @ ZA @ ( equivalent @ ZC @ ZD ) ) @ Z ) )),bind(H,$thf( H ))]]) ).
thf(86,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ C @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ D ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(simp,[status(thm)],[79]) ).
thf(147,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ H @ ( equivalent @ K @ I ) )
!= a )
| ( ( equivalent @ J @ K )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ H @ ( equivalent @ J @ I ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,63]) ).
thf(148,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) )
!= a )
| ( ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( ZB )),bind(B,$thf( X )),bind(C,$thf( ZC )),bind(D,$thf( ZA )),bind(E,$thf( ZD )),bind(F,$thf( ZF )),bind(G,$thf( ZG )),bind(H,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZD @ ( equivalent @ X @ ZG ) ) @ ( equivalent @ ZA @ ( equivalent @ X @ ZF ) ) ) @ ( equivalent @ ZC @ ZA ) ) @ ( equivalent @ ZB @ ZC ) )),bind(I,$thf( ZB )),bind(J,$thf( equivalent @ ZD @ ( equivalent @ ZF @ ZG ) )),bind(K,$thf( K ))]]) ).
thf(159,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) )
!= a )
| ( ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(2905,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2720]) ).
thf(2931,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2905]) ).
thf(6058,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2931]) ).
thf(6059,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ B @ B ) ) ),
inference(simp,[status(thm)],[6058]) ).
thf(2002,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1845,5]) ).
thf(2054,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[2002]) ).
thf(5242,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[2054]) ).
thf(5243,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ A ) ) @ ( equivalent @ A @ B ) )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[5242]) ).
thf(5244,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ A ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[5243]) ).
thf(4120,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ B @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2719]) ).
thf(4154,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ B @ B ) ) ) ),
inference(simp,[status(thm)],[4120]) ).
thf(90,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ G @ ( equivalent @ J @ H ) )
!= a )
| ( ( equivalent @ I @ J )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ G @ ( equivalent @ I @ H ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,63]) ).
thf(91,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) )
!= a )
| ( ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( W )),bind(B,$thf( X )),bind(C,$thf( U )),bind(D,$thf( Y )),bind(E,$thf( ZA )),bind(F,$thf( ZB )),bind(G,$thf( equivalent @ ( equivalent @ ( equivalent @ Y @ ( equivalent @ U @ ZB ) ) @ ( equivalent @ X @ ( equivalent @ U @ ZA ) ) ) @ ( equivalent @ W @ X ) )),bind(H,$thf( W )),bind(I,$thf( equivalent @ Y @ ( equivalent @ ZA @ ZB ) )),bind(J,$thf( J ))]]) ).
thf(98,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) )
!= a )
| ( ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ C ) )
!= a )
| ( A != a )
| ( ( equivalent @ B @ C )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[484]) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ A @ B ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(534,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ A @ B ) )
!= a )
| ( A
!= ( equivalent @ b @ c ) )
| ( B
!= ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ),
inference(simp,[status(thm)],[486]) ).
thf(535,plain,
( ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )
!= a ),
inference(simp,[status(thm)],[534]) ).
thf(2746,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,2719]) ).
thf(2785,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2746]) ).
thf(142,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ H @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ I ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ H @ ( equivalent @ a @ I ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,96]) ).
thf(155,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ H @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ I ) )
!= a )
| ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) )
!= ( equivalent @ H @ ( equivalent @ a @ I ) ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(105,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ F @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ G ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ a @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,96]) ).
thf(108,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ F @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ G ) )
!= a )
| ( ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) )
!= ( equivalent @ F @ ( equivalent @ a @ G ) ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(113,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ E @ F ) )
!= ( is_a_theorem @ E ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[29,27]) ).
thf(114,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ D @ C ) ) )
| ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( equivalent @ ( equivalent @ I @ ( equivalent @ N @ L ) ) @ ( equivalent @ M @ N ) )),bind(F,$thf( F ))]]) ).
thf(130,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ D @ C ) ) )
| ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(3337,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,3325]) ).
thf(3362,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A )
!= ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[3337]) ).
thf(6737,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ C ) )
| ( A
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[3362]) ).
thf(6738,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ B ) ),
inference(simp,[status(thm)],[6737]) ).
thf(3341,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,3325]) ).
thf(3363,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[3341]) ).
thf(4494,plain,
! [B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) )
| ( A
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[4149]) ).
thf(4495,plain,
! [A: $i] :
( ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )
!= ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[4494]) ).
thf(4496,plain,
! [A: $i] :
( ( a != a )
| ( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) )
!= ( equivalent @ A @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[4495]) ).
thf(4497,plain,
! [A: $i] :
( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) )
!= ( equivalent @ A @ ( equivalent @ b @ c ) ) ),
inference(simp,[status(thm)],[4496]) ).
thf(4132,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) @ ( equivalent @ a @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,3432]) ).
thf(4158,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) @ ( equivalent @ a @ B ) ) ),
inference(simp,[status(thm)],[4132]) ).
thf(619,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ D @ ( equivalent @ G @ E ) ) @ ( equivalent @ F @ G ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ F @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,29]) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[619:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( equivalent @ H @ ( equivalent @ J @ ( equivalent @ M @ M ) ) )),bind(E,$thf( J )),bind(F,$thf( H )),bind(G,$thf( G ))]]) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) ),
inference(simp,[status(thm)],[620]) ).
thf(516,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ C @ ( equivalent @ F @ D ) ) @ ( equivalent @ E @ F ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ E @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,47]) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[516:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( equivalent @ H @ H )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[517]) ).
thf(3447,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,3432]) ).
thf(3480,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) @ ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3447]) ).
thf(5423,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ C ) )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[2483]) ).
thf(5424,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) ),
inference(simp,[status(thm)],[5423]) ).
thf(2945,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ F @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ F @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,2733]) ).
thf(2946,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[2945:[bind(A,$thf( A )),bind(B,$thf( equivalent @ a @ ( equivalent @ K @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )),bind(C,$thf( a )),bind(D,$thf( K )),bind(E,$thf( equivalent @ b @ c )),bind(F,$thf( K ))]]) ).
thf(2994,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ B ) ) ) ),
inference(simp,[status(thm)],[2946]) ).
thf(4221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4178,725]) ).
thf(4222,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[4221:[bind(A,$thf( J )),bind(B,$thf( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )),bind(C,$thf( K )),bind(D,$thf( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ K ) @ ( equivalent @ J @ K ) )),bind(E,$thf( J ))]]) ).
thf(4336,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[4222]) ).
thf(4045,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )
!= a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ B @ ( equivalent @ b @ c ) ) ) ),
inference(simp,[status(thm)],[4044]) ).
thf(6901,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ C ) )
| ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[3363]) ).
thf(6902,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) ),
inference(simp,[status(thm)],[6901]) ).
thf(4921,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( A
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[1650]) ).
thf(4922,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[4921]) ).
thf(5591,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= a )
| ( A
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ C @ C ) ) ) ),
inference(simp,[status(thm)],[2785]) ).
thf(5592,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ A ) )
!= a ),
inference(simp,[status(thm)],[5591]) ).
thf(5448,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ I @ ( equivalent @ J @ K ) ) @ H ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ E ) @ ( equivalent @ C @ B ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ E ) ) @ ( equivalent @ D @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ I @ ( equivalent @ F @ K ) ) @ ( equivalent @ G @ ( equivalent @ F @ J ) ) ) @ ( equivalent @ H @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1747,85]) ).
thf(5449,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ D ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ D @ B ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[5448:[bind(A,$thf( A )),bind(B,$thf( R )),bind(C,$thf( P )),bind(D,$thf( N )),bind(E,$thf( equivalent @ R @ S )),bind(F,$thf( R )),bind(G,$thf( A )),bind(H,$thf( N )),bind(I,$thf( equivalent @ ( equivalent @ N @ ( equivalent @ R @ S ) ) @ ( equivalent @ P @ R ) )),bind(J,$thf( S )),bind(K,$thf( P ))]]) ).
thf(5570,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ D ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ D @ B ) ) @ A ) ),
inference(simp,[status(thm)],[5449]) ).
thf(1685,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ E ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ D @ H ) ) @ ( equivalent @ E @ ( equivalent @ D @ G ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1659,61]) ).
thf(1686,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ D @ A ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[1685:[bind(A,$thf( equivalent @ M @ ( equivalent @ O @ P ) )),bind(B,$thf( K )),bind(C,$thf( O )),bind(D,$thf( O )),bind(E,$thf( M )),bind(F,$thf( equivalent @ ( equivalent @ M @ ( equivalent @ O @ P ) ) @ ( equivalent @ K @ O ) )),bind(G,$thf( P )),bind(H,$thf( K ))]]) ).
thf(1748,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ D @ A ) ) @ B ) ),
inference(simp,[status(thm)],[1686]) ).
thf(6067,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( A
!= ( equivalent @ a @ C ) ) ),
inference(simp,[status(thm)],[3090]) ).
thf(6068,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[6067]) ).
thf(6069,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ B )
!= a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[6068]) ).
thf(494,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ C @ ( equivalent @ F @ D ) )
!= a )
| ( ( equivalent @ E @ F )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ E @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,63]) ).
thf(495,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[494:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( A )),bind(D,$thf( equivalent @ H @ H )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) )
!= a )
| ( ( equivalent @ A @ B )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(3063,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ F @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,2879]) ).
thf(3064,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[3063:[bind(A,$thf( A )),bind(B,$thf( equivalent @ a @ R )),bind(C,$thf( a )),bind(D,$thf( R )),bind(E,$thf( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) )),bind(F,$thf( R ))]]) ).
thf(3112,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) ) ),
inference(simp,[status(thm)],[3064]) ).
thf(43,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ~ ( is_a_theorem @ ( equivalent @ E @ F ) )
| ( is_a_theorem @ F )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ E ) ) ),
inference(paramod_ordered,[status(thm)],[29,7]) ).
thf(44,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ D @ C ) ) )
| ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( equivalent @ ( equivalent @ I @ ( equivalent @ N @ L ) ) @ ( equivalent @ M @ N ) )),bind(F,$thf( F ))]]) ).
thf(50,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ D @ C ) ) )
| ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(simp,[status(thm)],[44]) ).
thf(4345,plain,
! [B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ B ) )
| ( A
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[4142]) ).
thf(4346,plain,
! [A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A )
!= ( equivalent @ a @ A ) ),
inference(simp,[status(thm)],[4345]) ).
thf(690,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ E @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ F ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ C @ ( equivalent @ D @ D ) ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[605,96]) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ A @ A ) ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ),
inference(pattern_uni,[status(thm)],[690:[bind(A,$thf( a )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( N )),bind(E,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ P @ ( equivalent @ N @ N ) ) ) @ ( equivalent @ O @ P ) )),bind(F,$thf( O ))]]) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ A @ A ) ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ),
inference(simp,[status(thm)],[691]) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1659,5]) ).
thf(1738,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[1684]) ).
thf(2958,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,2733]) ).
thf(2975,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ A @ ( equivalent @ A @ ( equivalent @ B @ B ) ) )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ C @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[2958]) ).
thf(2626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,2098]) ).
thf(2627,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[2626:[bind(A,$thf( a )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( equivalent @ a @ ( equivalent @ H @ ( equivalent @ K @ K ) ) )),bind(E,$thf( H ))]]) ).
thf(2711,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ B @ B ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) ) ),
inference(simp,[status(thm)],[2627]) ).
thf(68,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ F @ ( equivalent @ I @ G ) ) @ ( equivalent @ H @ I ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ H @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,47]) ).
thf(69,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( P )),bind(B,$thf( T )),bind(C,$thf( W )),bind(D,$thf( R )),bind(E,$thf( V )),bind(F,$thf( equivalent @ ( equivalent @ T @ ( equivalent @ R @ W ) ) @ ( equivalent @ P @ ( equivalent @ R @ V ) ) )),bind(G,$thf( P )),bind(H,$thf( equivalent @ T @ ( equivalent @ V @ W ) )),bind(I,$thf( I ))]]) ).
thf(72,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(4515,plain,
! [A: $i] :
( ( a != a )
| ( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )
!= A ) ),
inference(simp,[status(thm)],[4514]) ).
thf(4516,plain,
! [A: $i] :
( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) )
!= A ),
inference(simp,[status(thm)],[4515]) ).
thf(4078,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ B @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ C ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ B @ ( equivalent @ a @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,96]) ).
thf(4079,plain,
! [A: $i] :
( ( equivalent @ ( equivalent @ a @ A ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(pattern_uni,[status(thm)],[4078:[bind(A,$thf( equivalent @ a @ E )),bind(B,$thf( equivalent @ a @ E )),bind(C,$thf( E ))]]) ).
thf(4185,plain,
! [A: $i] :
( ( equivalent @ ( equivalent @ a @ A ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(simp,[status(thm)],[4079]) ).
thf(4260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4178,2098]) ).
thf(4261,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[4260:[bind(A,$thf( J )),bind(B,$thf( a )),bind(C,$thf( K )),bind(D,$thf( equivalent @ ( equivalent @ a @ K ) @ ( equivalent @ J @ K ) )),bind(E,$thf( J ))]]) ).
thf(4325,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ A ) ) ),
inference(simp,[status(thm)],[4261]) ).
thf(1633,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ ( equivalent @ D @ F ) ) @ ( equivalent @ C @ D ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ B ) ) @ A ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ C @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1592,48]) ).
thf(1634,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ E ) @ ( equivalent @ C @ C ) ) @ ( equivalent @ B @ E ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ D @ A ) ) ),
inference(pattern_uni,[status(thm)],[1633:[bind(A,$thf( equivalent @ L @ M )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( equivalent @ ( equivalent @ L @ M ) @ ( equivalent @ K @ K ) )),bind(F,$thf( F )),bind(G,$thf( M ))]]) ).
thf(1674,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ E ) @ ( equivalent @ C @ C ) ) @ ( equivalent @ B @ E ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ D @ A ) ) ),
inference(simp,[status(thm)],[1634]) ).
thf(176,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ C @ B ) ) )
| ( ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ ( equivalent @ E @ G ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ E ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ B ) ) @ ( equivalent @ C @ D ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ a @ H ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,175]) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ E ) ) )
| ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( a )),bind(D,$thf( K )),bind(E,$thf( E )),bind(F,$thf( equivalent @ I @ ( equivalent @ K @ L ) )),bind(G,$thf( G )),bind(H,$thf( K ))]]) ).
thf(186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ C @ ( equivalent @ a @ E ) ) )
| ( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ) ),
inference(simp,[status(thm)],[177]) ).
thf(1789,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ E @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ F ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ D ) @ ( equivalent @ B @ B ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ C @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1679,96]) ).
thf(1790,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ),
inference(pattern_uni,[status(thm)],[1789:[bind(A,$thf( O )),bind(B,$thf( N )),bind(C,$thf( a )),bind(D,$thf( P )),bind(E,$thf( equivalent @ ( equivalent @ ( equivalent @ a @ P ) @ ( equivalent @ N @ N ) ) @ ( equivalent @ O @ P ) )),bind(F,$thf( O ))]]) ).
thf(1854,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ a @ C ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ B ) )
!= a ),
inference(simp,[status(thm)],[1790]) ).
thf(145,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ H @ I ) )
| ( is_a_theorem @ I )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) )
!= ( is_a_theorem @ H ) ) ),
inference(paramod_ordered,[status(thm)],[84,7]) ).
thf(146,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ E @ D ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ E ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( ZE )),bind(B,$thf( X )),bind(C,$thf( ZC )),bind(D,$thf( ZA )),bind(E,$thf( ZF )),bind(F,$thf( ZH )),bind(G,$thf( ZI )),bind(H,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZF @ ( equivalent @ X @ ZI ) ) @ ( equivalent @ ZA @ ( equivalent @ X @ ZH ) ) ) @ ( equivalent @ ZC @ ZA ) ) @ ( equivalent @ ZE @ ZC ) ) @ ( equivalent @ ( equivalent @ ZF @ ( equivalent @ ZH @ ZI ) ) @ ZE ) )),bind(I,$thf( I ))]]) ).
thf(158,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ E @ D ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ E ) ) @ A ) )
| ( is_a_theorem @ A ) ),
inference(simp,[status(thm)],[146]) ).
thf(639,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ ( equivalent @ E @ G ) ) @ ( equivalent @ D @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ C @ C ) ) ) @ ( equivalent @ A @ B ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ D @ H ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,48]) ).
thf(640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ ( equivalent @ E @ E ) ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( I )),bind(E,$thf( E )),bind(F,$thf( equivalent @ I @ ( equivalent @ K @ ( equivalent @ N @ N ) ) )),bind(G,$thf( G )),bind(H,$thf( K ))]]) ).
thf(652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ ( equivalent @ E @ E ) ) ) @ ( equivalent @ B @ D ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ C @ A ) ) ),
inference(simp,[status(thm)],[640]) ).
thf(5086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ C @ B ) )
!= a )
| ( A
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[1738]) ).
thf(5087,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ B @ A ) )
!= a ),
inference(simp,[status(thm)],[5086]) ).
thf(140,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ H @ ( equivalent @ K @ I ) ) @ ( equivalent @ J @ K ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ H @ ( equivalent @ J @ I ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,29]) ).
thf(141,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( ZB )),bind(B,$thf( X )),bind(C,$thf( ZC )),bind(D,$thf( ZA )),bind(E,$thf( ZD )),bind(F,$thf( ZF )),bind(G,$thf( ZG )),bind(H,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZD @ ( equivalent @ X @ ZG ) ) @ ( equivalent @ ZA @ ( equivalent @ X @ ZF ) ) ) @ ( equivalent @ ZC @ ZA ) ) @ ( equivalent @ ZB @ ZC ) )),bind(I,$thf( ZB )),bind(J,$thf( equivalent @ ZD @ ( equivalent @ ZF @ ZG ) )),bind(K,$thf( K ))]]) ).
thf(163,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ A ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(188,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ I @ ( equivalent @ L @ J ) ) @ ( equivalent @ K @ L ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ F @ ( equivalent @ B @ H ) ) @ ( equivalent @ C @ ( equivalent @ B @ G ) ) ) @ ( equivalent @ E @ C ) ) @ ( equivalent @ D @ E ) ) @ ( equivalent @ A @ D ) ) @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ I @ ( equivalent @ K @ J ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[163,29]) ).
thf(189,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ B @ I ) ) @ ( equivalent @ C @ ( equivalent @ B @ H ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ F @ D ) ) @ ( equivalent @ E @ F ) ) @ ( equivalent @ A @ E ) ) @ ( equivalent @ ( equivalent @ G @ ( equivalent @ H @ I ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( ZG )),bind(B,$thf( ZA )),bind(C,$thf( ZD )),bind(D,$thf( ZH )),bind(E,$thf( ZF )),bind(F,$thf( ZI )),bind(G,$thf( ZK )),bind(H,$thf( ZL )),bind(I,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZI @ ( equivalent @ ZA @ ZL ) ) @ ( equivalent @ ZD @ ( equivalent @ ZA @ ZK ) ) ) @ ( equivalent @ ZF @ ZD ) ) @ ( equivalent @ ZH @ ZF ) ) @ ( equivalent @ ZG @ ZH ) )),bind(J,$thf( ZG )),bind(K,$thf( equivalent @ ZI @ ( equivalent @ ZK @ ZL ) )),bind(L,$thf( L ))]]) ).
thf(214,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ B @ I ) ) @ ( equivalent @ C @ ( equivalent @ B @ H ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ F @ D ) ) @ ( equivalent @ E @ F ) ) @ ( equivalent @ A @ E ) ) @ ( equivalent @ ( equivalent @ G @ ( equivalent @ H @ I ) ) @ A ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ D @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ E ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,96]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ ( equivalent @ A @ B ) ) )
!= a ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( a )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( equivalent @ a @ ( equivalent @ J @ K ) )),bind(E,$thf( equivalent @ J @ K ))]]) ).
thf(433,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ ( equivalent @ A @ B ) ) )
!= a ),
inference(simp,[status(thm)],[409]) ).
thf(4068,plain,
! [A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2015]) ).
thf(4153,plain,
! [A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[4068]) ).
thf(406,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ E ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,109]) ).
thf(407,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(pattern_uni,[status(thm)],[406:[bind(A,$thf( a )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( equivalent @ a @ ( equivalent @ K @ L ) )),bind(E,$thf( E )),bind(F,$thf( equivalent @ K @ L ))]]) ).
thf(432,plain,
! [C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ C ) ) @ ( equivalent @ A @ ( equivalent @ B @ C ) ) ) @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ A ) )
!= a ),
inference(simp,[status(thm)],[407]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ B ) )
!= a )
| ( ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ B ) )
!= ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ c ) @ B ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(3116,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ F @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,2888]) ).
thf(3117,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[3116:[bind(A,$thf( A )),bind(B,$thf( equivalent @ a @ R )),bind(C,$thf( a )),bind(D,$thf( R )),bind(E,$thf( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) )),bind(F,$thf( R ))]]) ).
thf(3164,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) ) ),
inference(simp,[status(thm)],[3117]) ).
thf(4055,plain,
! [A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,5]) ).
thf(4146,plain,
! [A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[4055]) ).
thf(104,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ E @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ F ) )
!= a )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) ) )
!= ( is_a_theorem @ ( equivalent @ E @ ( equivalent @ a @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,96]) ).
thf(107,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ E @ ( equivalent @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) @ F ) )
!= a )
| ( ( equivalent @ ( equivalent @ A @ ( equivalent @ B @ C ) ) @ ( equivalent @ ( equivalent @ A @ ( equivalent @ D @ C ) ) @ ( equivalent @ B @ D ) ) )
!= ( equivalent @ E @ ( equivalent @ a @ F ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(4349,plain,
! [B: $i,A: $i] :
( ( A
!= ( equivalent @ a @ B ) )
| ( A
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[4147]) ).
thf(4350,plain,
! [A: $i] :
( ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A )
!= ( equivalent @ a @ A ) ),
inference(simp,[status(thm)],[4349]) ).
thf(4092,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,990]) ).
thf(4157,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[4092]) ).
thf(4192,plain,
! [A: $i] :
( ( A != a )
| ( A
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) ) ),
inference(simp,[status(thm)],[4153]) ).
thf(4193,plain,
( ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) )
!= a ),
inference(simp,[status(thm)],[4192]) ).
thf(258,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ J @ ( equivalent @ M @ K ) ) @ ( equivalent @ L @ M ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ G @ ( equivalent @ B @ I ) ) @ ( equivalent @ C @ ( equivalent @ B @ H ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ F @ D ) ) @ ( equivalent @ E @ F ) ) @ ( equivalent @ A @ E ) ) @ ( equivalent @ ( equivalent @ G @ ( equivalent @ H @ I ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ J @ ( equivalent @ L @ K ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[214,29]) ).
thf(259,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ H @ ( equivalent @ B @ J ) ) @ ( equivalent @ C @ ( equivalent @ B @ I ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ E @ D ) ) @ ( equivalent @ G @ E ) ) @ ( equivalent @ F @ G ) ) @ ( equivalent @ A @ F ) ) @ ( equivalent @ ( equivalent @ H @ ( equivalent @ I @ J ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( ZL )),bind(B,$thf( ZD )),bind(C,$thf( ZG )),bind(D,$thf( ZI )),bind(E,$thf( ZM )),bind(F,$thf( ZK )),bind(G,$thf( ZN )),bind(H,$thf( ZP )),bind(I,$thf( ZQ )),bind(J,$thf( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ZN @ ( equivalent @ ZD @ ZQ ) ) @ ( equivalent @ ZG @ ( equivalent @ ZD @ ZP ) ) ) @ ( equivalent @ ZI @ ZG ) ) @ ( equivalent @ ZK @ ZI ) ) @ ( equivalent @ ZM @ ZK ) ) @ ( equivalent @ ZL @ ZM ) )),bind(K,$thf( ZL )),bind(L,$thf( equivalent @ ZN @ ( equivalent @ ZP @ ZQ ) )),bind(M,$thf( M ))]]) ).
thf(283,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ H @ ( equivalent @ B @ J ) ) @ ( equivalent @ C @ ( equivalent @ B @ I ) ) ) @ ( equivalent @ D @ C ) ) @ ( equivalent @ E @ D ) ) @ ( equivalent @ G @ E ) ) @ ( equivalent @ F @ G ) ) @ ( equivalent @ A @ F ) ) @ ( equivalent @ ( equivalent @ H @ ( equivalent @ I @ J ) ) @ A ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(4923,plain,
! [B: $i,A: $i] :
( ( ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) )
!= a )
| ( ( equivalent @ A @ A )
!= ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ),
inference(simp,[status(thm)],[4922]) ).
thf(1508,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ A @ E ) ) @ ( equivalent @ B @ ( equivalent @ A @ D ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ C @ ( equivalent @ D @ E ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ F @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ a @ ( equivalent @ F @ ( equivalent @ b @ c ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,990]) ).
thf(1509,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1508:[bind(A,$thf( A )),bind(B,$thf( equivalent @ a @ ( equivalent @ O @ ( equivalent @ b @ c ) ) )),bind(C,$thf( a )),bind(D,$thf( O )),bind(E,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(F,$thf( O ))]]) ).
thf(1582,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ A @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ A @ B ) ) ) ),
inference(simp,[status(thm)],[1509]) ).
thf(972,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ a @ G ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,725]) ).
thf(973,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(pattern_uni,[status(thm)],[972:[bind(A,$thf( N )),bind(B,$thf( a )),bind(C,$thf( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) )),bind(D,$thf( P )),bind(E,$thf( equivalent @ b @ c )),bind(F,$thf( equivalent @ ( equivalent @ a @ ( equivalent @ P @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ N @ ( equivalent @ P @ ( equivalent @ b @ c ) ) ) )),bind(G,$thf( N ))]]) ).
thf(992,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ B @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ ( equivalent @ A @ ( equivalent @ B @ ( equivalent @ b @ c ) ) ) ) @ ( equivalent @ a @ A ) ) ),
inference(simp,[status(thm)],[973]) ).
thf(4219,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ E ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ D @ ( equivalent @ a @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4178,725]) ).
thf(4220,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[4219:[bind(A,$thf( J )),bind(B,$thf( a )),bind(C,$thf( K )),bind(D,$thf( equivalent @ ( equivalent @ a @ K ) @ ( equivalent @ J @ K ) )),bind(E,$thf( J ))]]) ).
thf(4335,plain,
! [B: $i,A: $i] :
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ B ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ A ) ) ),
inference(simp,[status(thm)],[4220]) ).
thf(80,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ G @ ( equivalent @ J @ H ) ) @ ( equivalent @ I @ J ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) ) @ ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ G @ ( equivalent @ I @ H ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,47]) ).
thf(81,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( W )),bind(B,$thf( X )),bind(C,$thf( U )),bind(D,$thf( Y )),bind(E,$thf( ZA )),bind(F,$thf( ZB )),bind(G,$thf( equivalent @ ( equivalent @ ( equivalent @ Y @ ( equivalent @ U @ ZB ) ) @ ( equivalent @ X @ ( equivalent @ U @ ZA ) ) ) @ ( equivalent @ W @ X ) )),bind(H,$thf( W )),bind(I,$thf( equivalent @ Y @ ( equivalent @ ZA @ ZB ) )),bind(J,$thf( J ))]]) ).
thf(83,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ E @ ( equivalent @ B @ G ) ) @ ( equivalent @ D @ ( equivalent @ B @ F ) ) ) @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ ( equivalent @ E @ ( equivalent @ F @ G ) ) @ A ) )
!= ( equivalent @ a @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(4102,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ A @ A ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4020,2720]) ).
thf(4161,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ A )
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) @ ( equivalent @ b @ c ) ) ) @ ( equivalent @ a @ ( equivalent @ B @ B ) ) ) ),
inference(simp,[status(thm)],[4102]) ).
thf(5260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( equivalent @ A @ ( equivalent @ B @ B ) )
!= ( equivalent @ a @ C ) )
| ( A
!= ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ C ) ) ),
inference(simp,[status(thm)],[2480]) ).
thf(5261,plain,
! [B: $i,A: $i] :
( ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) @ B ) @ ( equivalent @ A @ A ) )
!= ( equivalent @ a @ B ) ),
inference(simp,[status(thm)],[5260]) ).
thf(6753,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ G @ H ) ) @ E ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ C ) ) @ ( equivalent @ A @ A ) ) @ B ) )
!= ( is_a_theorem @ ( equivalent @ ( equivalent @ F @ ( equivalent @ D @ H ) ) @ ( equivalent @ E @ ( equivalent @ D @ G ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6713,61]) ).
thf(6754,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ D @ C ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[6753:[bind(A,$thf( O )),bind(B,$thf( equivalent @ M @ ( equivalent @ O @ P ) )),bind(C,$thf( L )),bind(D,$thf( O )),bind(E,$thf( M )),bind(F,$thf( equivalent @ ( equivalent @ M @ ( equivalent @ O @ P ) ) @ ( equivalent @ L @ L ) )),bind(G,$thf( P )),bind(H,$thf( O ))]]) ).
thf(6886,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ C @ D ) ) @ ( equivalent @ A @ A ) ) @ ( equivalent @ D @ C ) ) @ B ) ),
inference(simp,[status(thm)],[6754]) ).
thf(94,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ F @ ( equivalent @ I @ G ) )
!= a )
| ( ( equivalent @ H @ I )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) )
| ( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ B @ ( equivalent @ D @ C ) ) @ ( equivalent @ A @ ( equivalent @ D @ E ) ) ) @ ( equivalent @ ( equivalent @ B @ ( equivalent @ E @ C ) ) @ A ) ) )
!= ( is_a_theorem @ ( equivalent @ F @ ( equivalent @ H @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,63]) ).
thf(95,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) )
!= a )
| ( ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( P )),bind(B,$thf( T )),bind(C,$thf( W )),bind(D,$thf( R )),bind(E,$thf( V )),bind(F,$thf( equivalent @ ( equivalent @ T @ ( equivalent @ R @ W ) ) @ ( equivalent @ P @ ( equivalent @ R @ V ) ) )),bind(G,$thf( P )),bind(H,$thf( equivalent @ T @ ( equivalent @ V @ W ) )),bind(I,$thf( I ))]]) ).
thf(100,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( equivalent @ ( equivalent @ ( equivalent @ D @ ( equivalent @ C @ F ) ) @ ( equivalent @ B @ ( equivalent @ C @ E ) ) ) @ ( equivalent @ A @ B ) )
!= a )
| ( ( equivalent @ ( equivalent @ D @ ( equivalent @ E @ F ) ) @ A )
!= ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ c ) @ ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(8085,plain,
$false,
inference(e,[status(thm)],[1665,6712,518,2480,2544,7072,2280,4166,1005,2590,5,1591,4326,5265,10,533,4762,5257,2712,4142,1650,4156,2136,7043,2735,6713,157,2713,5256,4928,4514,1100,1847,4756,29,5433,1664,6227,6419,2880,4134,84,3152,5259,4147,106,61,2483,1072,2772,6327,2586,6,60,4753,529,85,2118,1768,4925,2733,28,160,1666,70,4344,21,2132,4160,2015,4044,484,3090,4155,97,522,710,6324,2115,3482,2973,725,1006,1755,3105,1592,109,1659,4167,669,96,5900,4135,605,237,674,1663,530,5249,3824,4184,2121,4340,17,1747,2941,6229,59,2134,27,12,5567,4149,49,86,159,6059,5244,990,7,4154,98,3160,477,535,520,2785,155,108,130,6738,5248,2931,3363,3325,4497,4158,658,521,3480,2054,5424,4136,2994,2124,2927,4336,4045,1845,63,6902,4922,5592,2720,2888,5570,1748,48,6069,525,5250,3112,50,4346,673,1987,717,1679,1738,4020,16,2975,2711,11,72,175,4516,1649,671,6068,1654,4185,1010,2071,4325,99,6322,2098,1674,5899,186,1854,158,652,4495,5087,5243,8,6554,214,433,4153,2123,432,2719,30,51,19,422,3164,4146,107,4350,1657,4157,1033,2714,4193,283,4178,4,4923,2127,3362,1582,6205,992,47,163,62,4335,83,1009,4161,5261,3432,6886,100,486,2879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL129-1 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 00:45:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (104ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 1.67/1.20 % [INFO] eprover registered as external prover.
% 1.67/1.21 % [INFO] cvc4 registered as external prover.
% 1.67/1.21 % [INFO] Scanning for conjecture ...
% 1.67/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.87/1.28 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.87/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.29 % [INFO] Type checking passed.
% 1.87/1.29 % [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 ...
% 103.39/19.40 % External prover 'e' found a proof!
% 103.39/19.40 % [INFO] Killing All external provers ...
% 103.39/19.40 % Time passed: 18861ms (effective reasoning time: 18408ms)
% 103.39/19.40 % Axioms used in derivation (2): s_4, condensed_detachment
% 103.39/19.40 % No. of inferences in proof: 577
% 103.39/19.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18861 ms resp. 18408 ms w/o parsing
% 103.89/19.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 103.89/19.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------