%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL067-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:50:43 AM UTC 2026
% Result : Unsatisfiable 262.82s 76.33s
% Output : Refutation 254.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 5
% Syntax : Number of formulae : 611 ( 247 unt; 0 typ; 0 def)
% Number of atoms : 1754 ( 914 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 10643 (1093 ~; 699 |; 0 &;8851 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 2747 ( 0 ^;2747 !; 0 ?;2747 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_19) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(cnf,[status(esa)],[8]) ).
thf(58,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(59,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ is_a_theorem )
| ~ ( C @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ ( H @ implies ) @ implies ) )),bind(E,$thf( K @ ( J @ implies ) ))]]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ is_a_theorem )
| ~ ( C @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[60]) ).
thf(97,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,83]) ).
thf(98,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( I @ ( G @ implies ) )),bind(E,$thf( J )),bind(F,$thf( J @ ( I @ implies ) ))]]) ).
thf(101,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[99]) ).
thf(107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,83]) ).
thf(108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( C @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( H )),bind(B,$thf( K @ ( J @ implies ) )),bind(C,$thf( J )),bind(D,$thf( K )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) ))]]) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[109]) ).
thf(158,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,83]) ).
thf(159,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( N @ ( M @ implies ) )),bind(D,$thf( M )),bind(E,$thf( N )),bind(F,$thf( N @ ( M @ implies ) @ ( K @ implies ) @ ( I @ implies ) ))]]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[160]) ).
thf(243,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( G @ ( F @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( G @ ( F @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,83]) ).
thf(244,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( G @ ( F @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( G @ ( F @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[243]) ).
thf(245,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( E @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( Q @ ( P @ implies ) )),bind(E,$thf( P )),bind(F,$thf( Q )),bind(G,$thf( Q @ ( P @ implies ) @ ( N @ implies ) @ ( L @ implies ) @ ( J @ implies ) ))]]) ).
thf(253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( E @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[245]) ).
thf(259,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( E @ implies ) @ is_a_theorem )
!= ( H @ ( G @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( H @ ( G @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[253,83]) ).
thf(260,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( E @ implies ) @ is_a_theorem )
!= ( H @ ( G @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( H @ ( G @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[259]) ).
thf(261,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( F @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( Q )),bind(E,$thf( T @ ( S @ implies ) )),bind(F,$thf( S )),bind(G,$thf( T )),bind(H,$thf( T @ ( S @ implies ) @ ( Q @ implies ) @ ( O @ implies ) @ ( M @ implies ) @ ( K @ implies ) ))]]) ).
thf(269,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( F @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[261]) ).
thf(276,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( F @ implies ) @ is_a_theorem )
!= ( I @ ( H @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( I @ ( H @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,83]) ).
thf(277,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( F @ implies ) @ is_a_theorem )
!= ( I @ ( H @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( I @ ( H @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( G @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( R )),bind(E,$thf( T )),bind(F,$thf( W @ ( V @ implies ) )),bind(G,$thf( V )),bind(H,$thf( W )),bind(I,$thf( W @ ( V @ implies ) @ ( T @ implies ) @ ( R @ implies ) @ ( P @ implies ) @ ( N @ implies ) @ ( L @ implies ) ))]]) ).
thf(286,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( G @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[278]) ).
thf(339,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( G @ implies ) @ is_a_theorem )
!= ( J @ ( I @ ( H @ implies ) @ implies ) @ is_a_theorem ) )
| ( J @ ( I @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[286,83]) ).
thf(340,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( G @ implies ) @ is_a_theorem )
!= ( J @ ( I @ ( H @ implies ) @ implies ) @ is_a_theorem ) )
| ( J @ ( I @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[339]) ).
thf(341,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( H @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( M )),bind(B,$thf( O )),bind(C,$thf( Q )),bind(D,$thf( S )),bind(E,$thf( U )),bind(F,$thf( W )),bind(G,$thf( Z @ ( Y @ implies ) )),bind(H,$thf( Y )),bind(I,$thf( Z )),bind(J,$thf( Z @ ( Y @ implies ) @ ( W @ implies ) @ ( U @ implies ) @ ( S @ implies ) @ ( Q @ implies ) @ ( O @ implies ) @ ( M @ implies ) ))]]) ).
thf(344,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( H @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[341]) ).
thf(417,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( H @ implies ) @ is_a_theorem )
!= ( K @ ( J @ ( I @ implies ) @ implies ) @ is_a_theorem ) )
| ( K @ ( J @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[344,83]) ).
thf(418,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( H @ implies ) @ is_a_theorem )
!= ( K @ ( J @ ( I @ implies ) @ implies ) @ is_a_theorem ) )
| ( K @ ( J @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[417]) ).
thf(419,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( I @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[418:[bind(A,$thf( N )),bind(B,$thf( P )),bind(C,$thf( R )),bind(D,$thf( T )),bind(E,$thf( V )),bind(F,$thf( X )),bind(G,$thf( Z )),bind(H,$thf( ZC @ ( ZB @ implies ) )),bind(I,$thf( ZB )),bind(J,$thf( ZC )),bind(K,$thf( ZC @ ( ZB @ implies ) @ ( Z @ implies ) @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) @ ( R @ implies ) @ ( P @ implies ) @ ( N @ implies ) ))]]) ).
thf(422,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( I @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[419]) ).
thf(451,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] :
( ( ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( I @ implies ) @ is_a_theorem )
!= ( L @ ( K @ ( J @ implies ) @ implies ) @ is_a_theorem ) )
| ( L @ ( K @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[422,83]) ).
thf(452,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] :
( ( ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( I @ implies ) @ is_a_theorem )
!= ( L @ ( K @ ( J @ implies ) @ implies ) @ is_a_theorem ) )
| ( L @ ( K @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[451]) ).
thf(453,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( J @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[452:[bind(A,$thf( O )),bind(B,$thf( Q )),bind(C,$thf( S )),bind(D,$thf( U )),bind(E,$thf( W )),bind(F,$thf( Y )),bind(G,$thf( ZA )),bind(H,$thf( ZC )),bind(I,$thf( ZF @ ( ZE @ implies ) )),bind(J,$thf( ZE )),bind(K,$thf( ZF )),bind(L,$thf( ZF @ ( ZE @ implies ) @ ( ZC @ implies ) @ ( ZA @ implies ) @ ( Y @ implies ) @ ( W @ implies ) @ ( U @ implies ) @ ( S @ implies ) @ ( Q @ implies ) @ ( O @ implies ) ))]]) ).
thf(456,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( J @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[453]) ).
thf(477,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] :
( ( ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( J @ implies ) @ is_a_theorem )
!= ( M @ ( L @ ( K @ implies ) @ implies ) @ is_a_theorem ) )
| ( M @ ( L @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[456,83]) ).
thf(478,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] :
( ( ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( J @ implies ) @ is_a_theorem )
!= ( M @ ( L @ ( K @ implies ) @ implies ) @ is_a_theorem ) )
| ( M @ ( L @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[477]) ).
thf(479,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( K @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[478:[bind(A,$thf( P )),bind(B,$thf( R )),bind(C,$thf( T )),bind(D,$thf( V )),bind(E,$thf( X )),bind(F,$thf( Z )),bind(G,$thf( ZB )),bind(H,$thf( ZD )),bind(I,$thf( ZF )),bind(J,$thf( ZI @ ( ZH @ implies ) )),bind(K,$thf( ZH )),bind(L,$thf( ZI )),bind(M,$thf( ZI @ ( ZH @ implies ) @ ( ZF @ implies ) @ ( ZD @ implies ) @ ( ZB @ implies ) @ ( Z @ implies ) @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) @ ( R @ implies ) @ ( P @ implies ) ))]]) ).
thf(483,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( K @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[479]) ).
thf(541,plain,
! [N: $i,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] :
( ( ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( K @ implies ) @ is_a_theorem )
!= ( N @ ( M @ ( L @ implies ) @ implies ) @ is_a_theorem ) )
| ( N @ ( M @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,83]) ).
thf(542,plain,
! [N: $i,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] :
( ( ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( K @ implies ) @ is_a_theorem )
!= ( N @ ( M @ ( L @ implies ) @ implies ) @ is_a_theorem ) )
| ( N @ ( M @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[541]) ).
thf(543,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( L @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[542:[bind(A,$thf( Q )),bind(B,$thf( S )),bind(C,$thf( U )),bind(D,$thf( W )),bind(E,$thf( Y )),bind(F,$thf( ZA )),bind(G,$thf( ZC )),bind(H,$thf( ZE )),bind(I,$thf( ZG )),bind(J,$thf( ZI )),bind(K,$thf( ZL @ ( ZK @ implies ) )),bind(L,$thf( ZK )),bind(M,$thf( ZL )),bind(N,$thf( ZL @ ( ZK @ implies ) @ ( ZI @ implies ) @ ( ZG @ implies ) @ ( ZE @ implies ) @ ( ZC @ implies ) @ ( ZA @ implies ) @ ( Y @ implies ) @ ( W @ implies ) @ ( U @ implies ) @ ( S @ implies ) @ ( Q @ implies ) ))]]) ).
thf(547,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] : ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( L @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[543]) ).
thf(575,plain,
! [O: $i,N: $i,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] :
( ( ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( L @ implies ) @ is_a_theorem )
!= ( O @ ( N @ ( M @ implies ) @ implies ) @ is_a_theorem ) )
| ( O @ ( N @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[547,83]) ).
thf(576,plain,
! [O: $i,N: $i,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] :
( ( ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( L @ implies ) @ is_a_theorem )
!= ( O @ ( N @ ( M @ implies ) @ implies ) @ is_a_theorem ) )
| ( O @ ( N @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[575]) ).
thf(577,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: $i] : ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( M @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( R )),bind(B,$thf( T )),bind(C,$thf( V )),bind(D,$thf( X )),bind(E,$thf( Z )),bind(F,$thf( ZB )),bind(G,$thf( ZD )),bind(H,$thf( ZF )),bind(I,$thf( ZH )),bind(J,$thf( ZJ )),bind(K,$thf( ZL )),bind(L,$thf( ZO @ ( ZN @ implies ) )),bind(M,$thf( ZN )),bind(N,$thf( ZO )),bind(O,$thf( ZO @ ( ZN @ implies ) @ ( ZL @ implies ) @ ( ZJ @ implies ) @ ( ZH @ implies ) @ ( ZF @ implies ) @ ( ZD @ implies ) @ ( ZB @ implies ) @ ( Z @ implies ) @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) @ ( R @ implies ) ))]]) ).
thf(579,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] : ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( M @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[577]) ).
thf(1,negated_conjecture,
~ ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_1) ).
thf(6,plain,
~ ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(622,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] :
( ( ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( M @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[579,7]) ).
thf(623,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] :
( ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( M @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[622]) ).
thf(633,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] :
( ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( M @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[623]) ).
thf(1001,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] :
( ( ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( M
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[633]) ).
thf(1002,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] :
( ( b @ ( a @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1102,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] :
( ( ( b @ ( a @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[1002]) ).
thf(1103,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[1102]) ).
thf(1104,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[1103]) ).
thf(1105,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[1104]) ).
thf(469,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( J @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[456,7]) ).
thf(470,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( J @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[469]) ).
thf(480,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( J @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[470]) ).
thf(620,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( J
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[480]) ).
thf(621,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[620]) ).
thf(665,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[621]) ).
thf(666,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,9]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[112]) ).
thf(2618,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[117,7]) ).
thf(2619,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2618]) ).
thf(2620,plain,
~ ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2619:[bind(A,$thf( b @ ( a @ implies ) )),bind(B,$thf( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ))]]) ).
thf(2747,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[117,2620]) ).
thf(2748,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2747]) ).
thf(2749,plain,
~ ( c @ ( a @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2748:[bind(A,$thf( c @ ( b @ implies ) )),bind(B,$thf( c @ ( a @ implies ) ))]]) ).
thf(2905,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,2749]) ).
thf(2906,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2905]) ).
thf(2942,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2906]) ).
thf(3680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ( C != a ) ),
inference(simp,[status(thm)],[2942]) ).
thf(3681,plain,
! [B: $i,A: $i] :
( ( a @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3680]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_37) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(70,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(71,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[70]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ ( B @ ( A @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( L )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( K @ ( I @ ( L @ implies ) @ implies ) )),bind(E,$thf( K @ ( L @ not @ implies ) ))]]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ ( B @ ( A @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[72]) ).
thf(1614,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,81]) ).
thf(1615,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1614]) ).
thf(1616,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1615:[bind(A,$thf( K )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( J )),bind(E,$thf( J @ ( K @ not @ implies ) )),bind(F,$thf( H @ ( K @ implies ) ))]]) ).
thf(1641,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1616]) ).
thf(2858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1641,2749]) ).
thf(2859,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2858]) ).
thf(2940,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2859]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( C @ ( B @ ( A @ implies ) @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[22]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= C )
| ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[27]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( b @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[32]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( B @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( B != b )
| ( A != B )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[210]) ).
thf(238,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[221]) ).
thf(3838,plain,
( ( ( b @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( b @ implies ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[238]) ).
thf(3848,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != b )
| ( b != a )
| ( ( b @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3838]) ).
thf(3858,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != a )
| ( ( b @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3848]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_59) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(64,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(65,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ not @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( O )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( N @ ( O @ not @ implies ) )),bind(E,$thf( N @ ( P @ ( O @ implies ) @ implies ) @ ( N @ ( P @ implies ) @ implies ) ))]]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[66]) ).
thf(1146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( C @ ( E @ ( D @ implies ) @ implies ) @ ( C @ ( E @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,79]) ).
thf(1147,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( C @ ( E @ ( D @ implies ) @ implies ) @ ( C @ ( E @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1146]) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1147:[bind(A,$thf( G )),bind(B,$thf( I @ not )),bind(C,$thf( I @ not @ ( G @ implies ) )),bind(D,$thf( I )),bind(E,$thf( E ))]]) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1148]) ).
thf(1579,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1242,81]) ).
thf(1580,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1579]) ).
thf(1581,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( A @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1580:[bind(A,$thf( M )),bind(B,$thf( N )),bind(C,$thf( P )),bind(D,$thf( P @ not @ ( N @ implies ) )),bind(E,$thf( P @ not @ ( N @ implies ) @ ( M @ ( P @ implies ) @ implies ) )),bind(F,$thf( M ))]]) ).
thf(1655,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( A @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1581]) ).
thf(2864,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[117,2749]) ).
thf(2865,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2864]) ).
thf(2866,plain,
~ ( c @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2865:[bind(A,$thf( a )),bind(B,$thf( c ))]]) ).
thf(2967,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1655,2866]) ).
thf(2968,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( A @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2967]) ).
thf(3040,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( A @ not @ implies ) )
!= c ),
inference(simp,[status(thm)],[2968]) ).
thf(2911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,2749]) ).
thf(2912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2911]) ).
thf(2953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2912]) ).
thf(73,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(74,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( N )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( M @ ( N @ not @ implies ) @ ( M @ ( K @ ( N @ implies ) @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(82,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( D @ not @ implies ) @ ( C @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[75]) ).
thf(1866,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( G @ not @ implies ) @ ( F @ ( E @ ( G @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1242,82]) ).
thf(1867,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( G @ not @ implies ) @ ( F @ ( E @ ( G @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1866]) ).
thf(1868,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ not @ implies ) @ ( C @ not @ ( A @ ( B @ implies ) @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1867:[bind(A,$thf( Z @ not @ ( U @ ( Y @ implies ) @ implies ) )),bind(B,$thf( Y @ not )),bind(C,$thf( Z )),bind(D,$thf( Z @ not @ ( Y @ not @ implies ) @ ( Z @ not @ ( U @ ( Y @ implies ) @ implies ) @ ( Z @ implies ) @ implies ) )),bind(E,$thf( U )),bind(F,$thf( Z @ not )),bind(G,$thf( Y ))]]) ).
thf(1939,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ not @ implies ) @ ( C @ not @ ( A @ ( B @ implies ) @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1868]) ).
thf(257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( E @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[253,7]) ).
thf(258,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( E @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[257]) ).
thf(268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( E @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(406,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( E
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[406]) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[407]) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[437]) ).
thf(439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[438]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[439]) ).
thf(67,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(68,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[67]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( D @ implies ) @ implies ) @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( Q )),bind(B,$thf( P )),bind(C,$thf( R )),bind(D,$thf( P @ ( R @ ( Q @ implies ) @ implies ) @ ( P @ ( R @ implies ) @ implies ) @ ( P @ ( Q @ not @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( D @ implies ) @ implies ) @ ( B @ ( C @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(1340,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( F @ ( E @ implies ) @ implies ) @ ( D @ ( F @ implies ) @ implies ) @ ( D @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,80]) ).
thf(1341,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( D @ ( F @ ( E @ implies ) @ implies ) @ ( D @ ( F @ implies ) @ implies ) @ ( D @ ( E @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[1340]) ).
thf(1342,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( D @ implies ) @ implies ) @ ( B @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1341:[bind(A,$thf( T )),bind(B,$thf( ZF @ ( ZH @ ( ZG @ implies ) @ implies ) @ ( ZF @ ( ZH @ implies ) @ implies ) @ ( ZF @ ( ZG @ not @ implies ) @ implies ) )),bind(C,$thf( ZF @ ( ZH @ ( ZG @ implies ) @ implies ) @ ( ZF @ ( ZH @ implies ) @ implies ) @ ( ZF @ ( ZG @ not @ implies ) @ implies ) @ ( T @ implies ) )),bind(D,$thf( ZF )),bind(E,$thf( ZG )),bind(F,$thf( ZH ))]]) ).
thf(1426,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ implies ) @ implies ) @ ( B @ ( D @ implies ) @ implies ) @ ( B @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1342]) ).
thf(1567,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,81]) ).
thf(1568,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1567]) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1568:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J )),bind(E,$thf( J @ ( I @ implies ) )),bind(F,$thf( I @ ( G @ implies ) ))]]) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1569]) ).
thf(2543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1650,117]) ).
thf(2544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2543]) ).
thf(2545,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( C @ ( B @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2544:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( L @ ( K @ implies ) @ ( K @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(2712,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( C @ ( B @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2545]) ).
thf(2525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,117]) ).
thf(2526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2525]) ).
thf(2527,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2526:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(2694,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2527]) ).
thf(3097,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2694,2749]) ).
thf(3098,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3097]) ).
thf(3121,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3098]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( C @ ( B @ ( A @ implies ) @ implies ) ) )
| ( C != b )
| ( B != a )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[27]) ).
thf(56,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ ( A @ implies ) @ implies ) ) )
| ( ( a @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[30]) ).
thf(533,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( K @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,7]) ).
thf(534,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( K @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[533]) ).
thf(544,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( K @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[534]) ).
thf(669,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( K
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[544]) ).
thf(670,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[669]) ).
thf(1561,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ ( C @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,81]) ).
thf(1562,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( D @ ( C @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1561]) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1562:[bind(A,$thf( H )),bind(B,$thf( K @ ( J @ implies ) )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ implies ) @ ( H @ implies ) )),bind(E,$thf( J ))]]) ).
thf(1646,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1563]) ).
thf(2981,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[117,2866]) ).
thf(2982,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2981]) ).
thf(3051,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[2982]) ).
thf(3229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1646,3051]) ).
thf(3230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3229]) ).
thf(3231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( C @ not @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3230:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( L @ ( K @ implies ) @ ( I @ implies ) @ ( K @ not @ implies ) ))]]) ).
thf(3276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( C @ not @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3231]) ).
thf(3172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[117,3051]) ).
thf(3173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3172]) ).
thf(3174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3173:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(3281,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3174]) ).
thf(1623,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( G @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,81]) ).
thf(1624,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( G @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1623]) ).
thf(1625,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1624:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( Q @ ( P @ implies ) )),bind(E,$thf( Q )),bind(F,$thf( Q @ ( P @ implies ) @ ( N @ implies ) @ ( L @ implies ) @ ( J @ implies ) )),bind(G,$thf( P ))]]) ).
thf(1645,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1625]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( c @ ( a @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(52,plain,
! [A: $i] :
( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(3163,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1641,3051]) ).
thf(3164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3163]) ).
thf(3165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( B @ ( D @ implies ) @ not @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3164:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( L @ ( M @ not @ implies ) @ ( J @ ( M @ implies ) @ not @ implies ) ))]]) ).
thf(3275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ not @ implies ) @ ( B @ ( D @ implies ) @ not @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3165]) ).
thf(443,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( I @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[422,7]) ).
thf(444,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( I @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[443]) ).
thf(454,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( I @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[444]) ).
thf(565,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( I
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(566,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[565]) ).
thf(616,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[566]) ).
thf(617,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[616]) ).
thf(618,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[617]) ).
thf(619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[618]) ).
thf(3235,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,3051]) ).
thf(3236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3235]) ).
thf(3237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3236:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) @ ( K @ implies ) ))]]) ).
thf(3280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3237]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= C )
| ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( C != b )
| ( B != a )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(43,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(174,plain,
! [A: $i] :
( ( ( b @ ( a @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( A @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[43]) ).
thf(180,plain,
! [A: $i] :
( ( b != a )
| ( a != A )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != A ) ),
inference(simp,[status(thm)],[174]) ).
thf(196,plain,
( ( b != a )
| ( ( b @ ( a @ ( b @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[180]) ).
thf(3839,plain,
( ( ( b @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( b @ implies ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[238]) ).
thf(3844,plain,
( ( b != b )
| ( b != a )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != b )
| ( b != a )
| ( ( b @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3839]) ).
thf(3855,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != a )
| ( ( b @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3844]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[22]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( C != C )
| ( ( B @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(2840,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,2749]) ).
thf(2841,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2840]) ).
thf(2929,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2841]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= C )
| ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[76]) ).
thf(717,plain,
! [B: $i,A: $i] :
( ( c != B )
| ( b != A )
| ( ( c @ ( a @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(789,plain,
( ( ( c @ ( a @ implies ) @ ( c @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[717]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,7]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[105]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( B
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(121,plain,
! [A: $i] :
( ( b @ ( a @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(61,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(62,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[63]) ).
thf(146,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(147,plain,
( ( c @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(1558,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,81]) ).
thf(1559,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1558]) ).
thf(1560,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( N @ ( M @ implies ) )),bind(D,$thf( N )),bind(E,$thf( N @ ( M @ implies ) @ ( K @ implies ) @ ( I @ implies ) )),bind(F,$thf( M ))]]) ).
thf(1644,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1560]) ).
thf(2991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1644,2866]) ).
thf(2992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2991]) ).
thf(3068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) )
!= c ),
inference(simp,[status(thm)],[2992]) ).
thf(2784,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1646,2620]) ).
thf(2785,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2784]) ).
thf(2833,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2785]) ).
thf(179,plain,
! [A: $i] :
( ( b != a )
| ( a != A )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( A @ implies ) ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(195,plain,
( ( b != a )
| ( ( b @ ( a @ ( a @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(674,plain,
( ( ( c @ ( b @ implies ) )
!= ( a @ ( a @ implies ) ) )
| ( ( b @ ( a @ ( a @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( b != a )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[195]) ).
thf(680,plain,
( ( c != a )
| ( b != a )
| ( ( b @ ( a @ ( a @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( b != a )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[674]) ).
thf(692,plain,
( ( ( b @ ( a @ ( a @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[680]) ).
thf(567,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] :
( ( ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( L @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[547,7]) ).
thf(568,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] :
( ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( L @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[567]) ).
thf(578,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] :
( ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( L @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[568]) ).
thf(838,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] :
( ( ( L @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( L
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[578]) ).
thf(839,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[838]) ).
thf(997,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[839]) ).
thf(998,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[997]) ).
thf(2901,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1646,2749]) ).
thf(2902,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2901]) ).
thf(2954,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2902]) ).
thf(2957,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,2866]) ).
thf(2958,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2957]) ).
thf(3054,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= c ),
inference(simp,[status(thm)],[2958]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[101,9]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ implies ) @ ( H @ implies ) )),bind(D,$thf( D ))]]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[115]) ).
thf(3326,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1242,118]) ).
thf(3327,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[3326]) ).
thf(3328,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3327:[bind(A,$thf( O @ not )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( O @ not @ ( M @ implies ) @ ( O @ not @ ( O @ implies ) @ implies ) )),bind(E,$thf( M )),bind(F,$thf( O @ not ))]]) ).
thf(3418,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3328]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( B @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( B != b )
| ( A != a )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( B @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != b )
| ( B != a )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[209]) ).
thf(233,plain,
( ( b != a )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( a @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[215]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(2723,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,2620]) ).
thf(2724,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2723]) ).
thf(2823,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2724]) ).
thf(3607,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[2823]) ).
thf(3608,plain,
! [A: $i] :
( ( c @ ( b @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3607]) ).
thf(3609,plain,
! [A: $i] :
( ( ( c @ ( b @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[3608]) ).
thf(3610,plain,
( ( c @ ( b @ implies ) )
!= c ),
inference(simp,[status(thm)],[3609]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( B @ ( A @ not @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(3659,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,2866]) ).
thf(3660,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3659]) ).
thf(3664,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[3660]) ).
thf(3296,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= c )
| ( B != a ) ),
inference(simp,[status(thm)],[2929]) ).
thf(3297,plain,
! [A: $i] :
( ( a @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3296]) ).
thf(1842,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( F @ not @ implies ) @ ( E @ ( D @ ( F @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,82]) ).
thf(1843,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( F @ not @ implies ) @ ( E @ ( D @ ( F @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[1842]) ).
thf(1844,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( C @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1843:[bind(A,$thf( P )),bind(B,$thf( Y @ ( Z @ not @ implies ) @ ( Y @ ( W @ ( Z @ implies ) @ implies ) @ implies ) )),bind(C,$thf( Y @ ( Z @ not @ implies ) @ ( Y @ ( W @ ( Z @ implies ) @ implies ) @ implies ) @ ( P @ implies ) )),bind(D,$thf( W )),bind(E,$thf( Y )),bind(F,$thf( Z ))]]) ).
thf(1951,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( C @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1844]) ).
thf(630,plain,
! [P: $i,O: $i,N: $i,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] :
( ( ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( M @ implies ) @ is_a_theorem )
!= ( P @ ( O @ ( N @ implies ) @ implies ) @ is_a_theorem ) )
| ( P @ ( O @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[579,83]) ).
thf(631,plain,
! [P: $i,O: $i,N: $i,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] :
( ( ( M @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( M @ implies ) @ is_a_theorem )
!= ( P @ ( O @ ( N @ implies ) @ implies ) @ is_a_theorem ) )
| ( P @ ( O @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[630]) ).
thf(632,plain,
! [N: $i,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: $i] : ( N @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( N @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( S )),bind(B,$thf( U )),bind(C,$thf( W )),bind(D,$thf( Y )),bind(E,$thf( ZA )),bind(F,$thf( ZC )),bind(G,$thf( ZE )),bind(H,$thf( ZG )),bind(I,$thf( ZI )),bind(J,$thf( ZK )),bind(K,$thf( ZM )),bind(L,$thf( ZO )),bind(M,$thf( ZR @ ( ZQ @ implies ) )),bind(N,$thf( ZQ )),bind(O,$thf( ZR )),bind(P,$thf( ZR @ ( ZQ @ implies ) @ ( ZO @ implies ) @ ( ZM @ implies ) @ ( ZK @ implies ) @ ( ZI @ implies ) @ ( ZG @ implies ) @ ( ZE @ implies ) @ ( ZC @ implies ) @ ( ZA @ implies ) @ ( Y @ implies ) @ ( W @ implies ) @ ( U @ implies ) @ ( S @ implies ) ))]]) ).
thf(636,plain,
! [N: $i,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] : ( N @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( N @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[632]) ).
thf(707,plain,
! [Q: $i,P: $i,O: $i,N: $i,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] :
( ( ( N @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( N @ implies ) @ is_a_theorem )
!= ( Q @ ( P @ ( O @ implies ) @ implies ) @ is_a_theorem ) )
| ( Q @ ( P @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,83]) ).
thf(708,plain,
! [Q: $i,P: $i,O: $i,N: $i,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] :
( ( ( N @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( N @ implies ) @ is_a_theorem )
!= ( Q @ ( P @ ( O @ implies ) @ implies ) @ is_a_theorem ) )
| ( Q @ ( P @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
! [O: $i,N: $i,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: $i] : ( O @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( O @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( T )),bind(B,$thf( V )),bind(C,$thf( X )),bind(D,$thf( Z )),bind(E,$thf( ZB )),bind(F,$thf( ZD )),bind(G,$thf( ZF )),bind(H,$thf( ZH )),bind(I,$thf( ZJ )),bind(J,$thf( ZL )),bind(K,$thf( ZN )),bind(L,$thf( ZP )),bind(M,$thf( ZR )),bind(N,$thf( ZU @ ( ZT @ implies ) )),bind(O,$thf( ZT )),bind(P,$thf( ZU )),bind(Q,$thf( ZU @ ( ZT @ implies ) @ ( ZR @ implies ) @ ( ZP @ implies ) @ ( ZN @ implies ) @ ( ZL @ implies ) @ ( ZJ @ implies ) @ ( ZH @ implies ) @ ( ZF @ implies ) @ ( ZD @ implies ) @ ( ZB @ implies ) @ ( Z @ implies ) @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) ))]]) ).
thf(712,plain,
! [O: $i,N: $i,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] : ( O @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( O @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[709]) ).
thf(849,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,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] :
( ( ( O @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( O @ implies ) @ is_a_theorem )
!= ( R @ ( Q @ ( P @ implies ) @ implies ) @ is_a_theorem ) )
| ( R @ ( Q @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[712,83]) ).
thf(850,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,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] :
( ( ( O @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( O @ implies ) @ is_a_theorem )
!= ( R @ ( Q @ ( P @ implies ) @ implies ) @ is_a_theorem ) )
| ( R @ ( Q @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[849]) ).
thf(851,plain,
! [P: $i,O: $i,N: $i,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: $i] : ( P @ ( O @ implies ) @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( P @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[850:[bind(A,$thf( U )),bind(B,$thf( W )),bind(C,$thf( Y )),bind(D,$thf( ZA )),bind(E,$thf( ZC )),bind(F,$thf( ZE )),bind(G,$thf( ZG )),bind(H,$thf( ZI )),bind(I,$thf( ZK )),bind(J,$thf( ZM )),bind(K,$thf( ZO )),bind(L,$thf( ZQ )),bind(M,$thf( ZS )),bind(N,$thf( ZU )),bind(O,$thf( ZX @ ( ZW @ implies ) )),bind(P,$thf( ZW )),bind(Q,$thf( ZX )),bind(R,$thf( ZX @ ( ZW @ implies ) @ ( ZU @ implies ) @ ( ZS @ implies ) @ ( ZQ @ implies ) @ ( ZO @ implies ) @ ( ZM @ implies ) @ ( ZK @ implies ) @ ( ZI @ implies ) @ ( ZG @ implies ) @ ( ZE @ implies ) @ ( ZC @ implies ) @ ( ZA @ implies ) @ ( Y @ implies ) @ ( W @ implies ) @ ( U @ implies ) ))]]) ).
thf(854,plain,
! [P: $i,O: $i,N: $i,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] : ( P @ ( O @ implies ) @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( P @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[851]) ).
thf(1019,plain,
! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,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] :
( ( ( P @ ( O @ implies ) @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( P @ implies ) @ is_a_theorem )
!= ( S @ ( R @ ( Q @ implies ) @ implies ) @ is_a_theorem ) )
| ( S @ ( R @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[854,83]) ).
thf(1020,plain,
! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,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] :
( ( ( P @ ( O @ implies ) @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( P @ implies ) @ is_a_theorem )
!= ( S @ ( R @ ( Q @ implies ) @ implies ) @ is_a_theorem ) )
| ( S @ ( R @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1019]) ).
thf(1021,plain,
! [Q: $i,P: $i,O: $i,N: $i,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: $i] : ( Q @ ( P @ implies ) @ ( O @ implies ) @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( Q @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1020:[bind(A,$thf( V )),bind(B,$thf( X )),bind(C,$thf( Z )),bind(D,$thf( ZB )),bind(E,$thf( ZD )),bind(F,$thf( ZF )),bind(G,$thf( ZH )),bind(H,$thf( ZJ )),bind(I,$thf( ZL )),bind(J,$thf( ZN )),bind(K,$thf( ZP )),bind(L,$thf( ZR )),bind(M,$thf( ZT )),bind(N,$thf( ZV )),bind(O,$thf( ZX )),bind(P,$thf( ZZA @ ( ZZ @ implies ) )),bind(Q,$thf( ZZ )),bind(R,$thf( ZZA )),bind(S,$thf( ZZA @ ( ZZ @ implies ) @ ( ZX @ implies ) @ ( ZV @ implies ) @ ( ZT @ implies ) @ ( ZR @ implies ) @ ( ZP @ implies ) @ ( ZN @ implies ) @ ( ZL @ implies ) @ ( ZJ @ implies ) @ ( ZH @ implies ) @ ( ZF @ implies ) @ ( ZD @ implies ) @ ( ZB @ implies ) @ ( Z @ implies ) @ ( X @ implies ) @ ( V @ implies ) ))]]) ).
thf(1027,plain,
! [Q: $i,P: $i,O: $i,N: $i,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] : ( Q @ ( P @ implies ) @ ( O @ implies ) @ ( N @ implies ) @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( Q @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1021]) ).
thf(2963,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,2866]) ).
thf(2964,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2963]) ).
thf(3050,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[2964]) ).
thf(699,plain,
! [N: $i,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] :
( ( ( N @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( N @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,7]) ).
thf(700,plain,
! [N: $i,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] :
( ( N @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( N @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[699]) ).
thf(710,plain,
! [N: $i,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] :
( ( N @ ( M @ implies ) @ ( L @ implies ) @ ( K @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( N @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[700]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,7]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[156]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( C
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(324,plain,
! [A: $i] :
( ( b @ ( a @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( F @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,7]) ).
thf(275,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( F @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[274]) ).
thf(285,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( F @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,7]) ).
thf(242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[241]) ).
thf(252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(3154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1650,3051]) ).
thf(3155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3154]) ).
thf(3156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ ( B @ implies ) @ not @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3155:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( L @ ( K @ implies ) @ ( K @ ( I @ implies ) @ not @ implies ) ))]]) ).
thf(3269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( C @ ( B @ implies ) @ not @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3156]) ).
thf(675,plain,
( ( ( c @ ( b @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( b @ ( a @ ( a @ implies ) @ implies ) )
!= ( a @ ( a @ implies ) ) )
| ( b != a )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[195]) ).
thf(686,plain,
( ( b != a )
| ( ( a @ ( a @ implies ) )
!= a )
| ( b != a )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[675]) ).
thf(697,plain,
( ( ( a @ ( a @ implies ) )
!= a )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[686]) ).
thf(3104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2694,2620]) ).
thf(3105,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3104]) ).
thf(3122,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[3105]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( c @ ( a @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[22]) ).
thf(53,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[25]) ).
thf(161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,9]) ).
thf(162,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( I )),bind(E,$thf( I @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[163]) ).
thf(409,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( H @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[344,7]) ).
thf(410,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( H @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[409]) ).
thf(420,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( H @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(498,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( H
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(499,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[498]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( D
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[252]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[328]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[402]) ).
thf(2648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,117]) ).
thf(2649,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2648]) ).
thf(2650,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2649:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( H @ implies ) @ ( K @ implies ) ))]]) ).
thf(2692,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2650]) ).
thf(1498,plain,
( ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[789]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[76]) ).
thf(176,plain,
! [A: $i] :
( ( ( b @ ( a @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != A ) ),
inference(simp,[status(thm)],[174]) ).
thf(193,plain,
( ( ( a @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( a @ ( b @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[176]) ).
thf(1386,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( G @ ( F @ implies ) @ implies ) @ ( E @ ( G @ implies ) @ implies ) @ ( E @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,80]) ).
thf(1387,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( G @ ( F @ implies ) @ implies ) @ ( E @ ( G @ implies ) @ implies ) @ ( E @ ( F @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1386]) ).
thf(1388,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1387:[bind(A,$thf( ZA @ not )),bind(B,$thf( Z )),bind(C,$thf( Z @ ( ZB @ ( ZA @ implies ) @ implies ) @ ( Z @ ( ZB @ implies ) @ implies ) )),bind(D,$thf( Z @ ( ZB @ ( ZA @ implies ) @ implies ) @ ( Z @ ( ZB @ implies ) @ implies ) @ ( ZA @ not @ not @ implies ) )),bind(E,$thf( Z )),bind(F,$thf( ZA )),bind(G,$thf( ZB ))]]) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ implies ) @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( B @ not @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1388]) ).
thf(3621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,117]) ).
thf(3622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3621]) ).
thf(3623,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( C @ not @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3622:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( L @ not @ ( J @ implies ) @ ( L @ not @ ( L @ implies ) @ implies ) ))]]) ).
thf(3671,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( C @ not @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3623]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( c @ ( a @ implies ) ) )
| ( ( A @ not )
!= ( c @ ( b @ implies ) ) )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[86]) ).
thf(2317,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( A @ not )
!= ( c @ ( b @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2293]) ).
thf(834,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[670]) ).
thf(835,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[834]) ).
thf(836,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[835]) ).
thf(837,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[836]) ).
thf(3760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) )
!= c )
| ( ( A @ ( C @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[2940]) ).
thf(2735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1650,2620]) ).
thf(2736,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2735]) ).
thf(2815,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2736]) ).
thf(4361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) @ not )
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[2815]) ).
thf(2788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,2620]) ).
thf(2789,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2788]) ).
thf(2827,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2789]) ).
thf(4194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( C
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[2827]) ).
thf(4195,plain,
! [B: $i,A: $i] :
( ( c @ ( b @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[4194]) ).
thf(1500,plain,
( ( ( b @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( c @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[789]) ).
thf(1510,plain,
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[1500]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( C != C )
| ( ( B @ ( A @ implies ) )
!= B )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[26]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= B )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[37]) ).
thf(427,plain,
! [B: $i,A: $i] :
( ( B != a )
| ( ( B @ ( A @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[47]) ).
thf(430,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( a @ ( A @ implies ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[427:[bind(A,$thf( A )),bind(B,$thf( a ))]]) ).
thf(2118,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,84]) ).
thf(2119,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[2118]) ).
thf(2120,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2119:[bind(A,$thf( P )),bind(B,$thf( R )),bind(C,$thf( ZA @ ( Z @ implies ) @ ( ZA @ ( Z @ ( X @ implies ) @ implies ) @ implies ) )),bind(D,$thf( ZA @ ( Z @ implies ) @ ( ZA @ ( Z @ ( X @ implies ) @ implies ) @ implies ) @ ( R @ implies ) @ ( P @ implies ) )),bind(E,$thf( X )),bind(F,$thf( Z )),bind(G,$thf( ZA ))]]) ).
thf(2149,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2120]) ).
thf(723,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[57]) ).
thf(758,plain,
! [B: $i,A: $i] :
( ( b != B )
| ( a != A )
| ( ( c @ ( a @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( c != B )
| ( b != A )
| ( ( c @ ( a @ implies ) )
!= b )
| ( B != a ) ),
inference(simp,[status(thm)],[723]) ).
thf(824,plain,
( ( b != a )
| ( ( c @ ( a @ implies ) @ ( a @ ( b @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( c != a )
| ( ( c @ ( a @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[758]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[26]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( B @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[35]) ).
thf(3184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2694,3051]) ).
thf(3185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3184]) ).
thf(3186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3185:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(3289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3186]) ).
thf(148,plain,
( ( c != b )
| ( a != a ) ),
inference(simp,[status(thm)],[147]) ).
thf(149,plain,
c != b,
inference(simp,[status(thm)],[148]) ).
thf(561,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[499]) ).
thf(562,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[561]) ).
thf(172,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != A )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(191,plain,
( ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( ( b @ ( a @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= C )
| ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( C != b )
| ( B != a )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[27]) ).
thf(44,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( a @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[34]) ).
thf(2852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1650,2749]) ).
thf(2853,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2852]) ).
thf(2952,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2853]) ).
thf(3758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= c )
| ( ( B @ ( A @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[2952]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( C @ ( B @ ( A @ implies ) @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[27]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( B @ ( A @ implies ) @ implies ) ) )
| ( ( b @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[28]) ).
thf(1206,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ ( F @ not @ implies ) @ is_a_theorem ) )
| ( E @ ( G @ ( F @ implies ) @ implies ) @ ( E @ ( G @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,79]) ).
thf(1207,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( E @ ( F @ not @ implies ) @ is_a_theorem ) )
| ( E @ ( G @ ( F @ implies ) @ implies ) @ ( E @ ( G @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1206]) ).
thf(1208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ not @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( E @ implies ) @ implies ) @ ( E @ not @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1207:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O @ not )),bind(E,$thf( O @ not @ ( M @ implies ) @ ( K @ implies ) @ ( I @ implies ) )),bind(F,$thf( O )),bind(G,$thf( G ))]]) ).
thf(1239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ not @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( E @ implies ) @ implies ) @ ( E @ not @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1208]) ).
thf(3118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2694,2866]) ).
thf(3119,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3118]) ).
thf(3123,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3119]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( C != C )
| ( ( B @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(331,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( G @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[286,7]) ).
thf(332,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( G @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[331]) ).
thf(342,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( G @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(465,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( G
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[342]) ).
thf(466,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[465]) ).
thf(4272,plain,
! [B: $i,A: $i] :
( ( ( c @ ( b @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[4195]) ).
thf(4273,plain,
! [A: $i] :
( ( c @ ( b @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[4272]) ).
thf(3013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,2866]) ).
thf(3014,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3013]) ).
thf(3038,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ not @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[3014]) ).
thf(2846,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,2749]) ).
thf(2847,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2846]) ).
thf(2955,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2847]) ).
thf(3483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[117,3281]) ).
thf(3484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3483]) ).
thf(3485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3484:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(3586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[3485]) ).
thf(3027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,2866]) ).
thf(3028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3027]) ).
thf(3055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= c ),
inference(simp,[status(thm)],[3028]) ).
thf(667,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[666]) ).
thf(668,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[667]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( c != B )
| ( b != A )
| ( ( b @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[42]) ).
thf(227,plain,
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( c @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[207]) ).
thf(329,plain,
( ( ( c @ ( a @ implies ) )
!= b )
| ( b != b )
| ( c != a )
| ( ( c @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[227]) ).
thf(330,plain,
( ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( ( c @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[329]) ).
thf(441,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( F
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[441]) ).
thf(461,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[442]) ).
thf(462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(4276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ( D != a ) ),
inference(simp,[status(thm)],[2953]) ).
thf(4277,plain,
! [C: $i,B: $i,A: $i] :
( ( a @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[4276]) ).
thf(3759,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ( ( B @ not )
!= a ) ),
inference(simp,[status(thm)],[2954]) ).
thf(999,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( J @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[998]) ).
thf(1000,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( I @ implies ) @ ( H @ implies ) @ ( G @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[999]) ).
thf(684,plain,
( ( ( b @ ( a @ ( a @ implies ) @ implies ) )
!= ( a @ ( a @ implies ) ) )
| ( b != a )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[675]) ).
thf(695,plain,
( ( ( b @ ( a @ ( a @ implies ) @ implies ) )
!= ( a @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[684]) ).
thf(2071,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1242,84]) ).
thf(2072,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[2071]) ).
thf(2073,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( C @ not @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2072:[bind(A,$thf( X @ not @ ( V @ ( S @ implies ) @ implies ) )),bind(B,$thf( V )),bind(C,$thf( X )),bind(D,$thf( X @ not @ ( V @ implies ) @ ( X @ not @ ( V @ ( S @ implies ) @ implies ) @ ( X @ implies ) @ implies ) )),bind(E,$thf( S )),bind(F,$thf( V )),bind(G,$thf( X @ not ))]]) ).
thf(2156,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ implies ) @ ( C @ not @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2073]) ).
thf(721,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( B @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[57]) ).
thf(728,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( B @ implies ) ) )
| ( c != B )
| ( b != A )
| ( ( c @ ( a @ implies ) )
!= b )
| ( B != a ) ),
inference(simp,[status(thm)],[721]) ).
thf(795,plain,
( ( ( c @ ( a @ implies ) @ ( a @ ( b @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( a @ implies ) ) )
| ( c != a )
| ( ( c @ ( a @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[728]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( B != b )
| ( A != a )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( B @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[209]) ).
thf(232,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[214]) ).
thf(2454,plain,
( ( ( b @ ( b @ implies ) )
!= ( b @ ( b @ implies ) ) )
| ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( b @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[232]) ).
thf(2456,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != b )
| ( b != a )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2454]) ).
thf(2471,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != a )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2456]) ).
thf(2975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1641,2866]) ).
thf(2976,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2975]) ).
thf(3048,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) )
!= c ),
inference(simp,[status(thm)],[2976]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[26]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( b @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( B @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[39]) ).
thf(3082,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2694,117]) ).
thf(3083,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3082]) ).
thf(3084,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3083:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(3129,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3084]) ).
thf(2552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1641,117]) ).
thf(2553,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ not @ implies ) @ ( A @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2552]) ).
thf(2554,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( B @ ( D @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2553:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( L @ ( M @ not @ implies ) @ ( J @ ( M @ implies ) @ not @ implies ) ))]]) ).
thf(2720,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ not @ implies ) @ ( B @ ( D @ implies ) @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2554]) ).
thf(2642,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1646,117]) ).
thf(2643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2642]) ).
thf(2644,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( C @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2643:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( L @ ( K @ implies ) @ ( I @ implies ) @ ( K @ not @ implies ) ))]]) ).
thf(2689,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( C @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2644]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( C != C )
| ( ( B @ ( A @ implies ) )
!= B )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[26]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= B )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[41]) ).
thf(175,plain,
! [A: $i] :
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= ( a @ ( A @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[43]) ).
thf(183,plain,
! [A: $i] :
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( a @ ( A @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != A ) ),
inference(simp,[status(thm)],[175]) ).
thf(199,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( a @ ( b @ implies ) @ implies ) )
!= ( a @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[183]) ).
thf(3786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3129,2749]) ).
thf(3787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3786]) ).
thf(3818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3787]) ).
thf(719,plain,
! [B: $i,A: $i] :
( ( c != B )
| ( b != A )
| ( ( c @ ( a @ implies ) )
!= b )
| ( B != a )
| ( ( c @ ( a @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(791,plain,
( ( c != a )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( a @ implies ) @ ( a @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[719]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( B @ ( A @ implies ) @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[38]) ).
thf(127,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( b ))]]) ).
thf(2969,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1650,2866]) ).
thf(2970,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[2969]) ).
thf(3041,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= c ),
inference(simp,[status(thm)],[2970]) ).
thf(2450,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != b )
| ( b != a )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[232]) ).
thf(2468,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( b != a )
| ( ( b @ ( a @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2450]) ).
thf(762,plain,
! [B: $i,A: $i] :
( ( b != B )
| ( a != A )
| ( ( c @ ( a @ implies ) )
!= c )
| ( ( B @ ( A @ implies ) )
!= b )
| ( c != B )
| ( b != A )
| ( ( c @ ( a @ implies ) )
!= b )
| ( B != a ) ),
inference(simp,[status(thm)],[723]) ).
thf(828,plain,
( ( b != a )
| ( ( c @ ( a @ implies ) )
!= c )
| ( ( a @ ( b @ implies ) )
!= b )
| ( c != a )
| ( ( c @ ( a @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[762]) ).
thf(1137,plain,
( ( b != b )
| ( ( a @ ( b @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( b != a )
| ( ( c @ ( a @ implies ) )
!= c )
| ( c != a )
| ( ( c @ ( a @ implies ) )
!= b ) ),
inference(eqfactor_ordered,[status(thm)],[828]) ).
thf(1139,plain,
( ( c != a )
| ( b != a )
| ( b != a )
| ( ( c @ ( a @ implies ) )
!= c )
| ( c != a )
| ( ( c @ ( a @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[1137]) ).
thf(1140,plain,
( ( b != a )
| ( ( c @ ( a @ implies ) )
!= c )
| ( c != a )
| ( ( c @ ( a @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[1139]) ).
thf(1143,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( D @ ( F @ ( E @ implies ) @ implies ) @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,79]) ).
thf(1144,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( D @ ( E @ not @ implies ) @ is_a_theorem ) )
| ( D @ ( F @ ( E @ implies ) @ implies ) @ ( D @ ( F @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1143]) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1144:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L @ not )),bind(D,$thf( L @ not @ ( J @ implies ) @ ( H @ implies ) )),bind(E,$thf( L )),bind(F,$thf( F ))]]) ).
thf(1240,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1145]) ).
thf(494,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) ) ) ),
inference(simp,[status(thm)],[466]) ).
thf(495,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[494]) ).
thf(496,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[495]) ).
thf(497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[496]) ).
thf(4278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= c )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2955]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( ( B @ ( A @ not @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(103,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != A )
| ( ( a @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[44]) ).
thf(104,plain,
( ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( ( a @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[103]) ).
thf(2875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1644,2749]) ).
thf(2876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2875]) ).
thf(2919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( C @ not @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[2876]) ).
thf(2045,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( E @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,84]) ).
thf(2046,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( C @ ( F @ ( E @ implies ) @ ( F @ ( E @ ( D @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[2045]) ).
thf(2047,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2046:[bind(A,$thf( O )),bind(B,$thf( X @ ( W @ implies ) @ ( X @ ( W @ ( U @ implies ) @ implies ) @ implies ) )),bind(C,$thf( X @ ( W @ implies ) @ ( X @ ( W @ ( U @ implies ) @ implies ) @ implies ) @ ( O @ implies ) )),bind(D,$thf( U )),bind(E,$thf( W )),bind(F,$thf( X ))]]) ).
thf(2167,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2047]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( C @ ( B @ ( A @ implies ) @ implies ) ) )
| ( C != b )
| ( B != a )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(55,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ ( A @ implies ) @ implies ) ) )
| ( ( b @ ( a @ ( A @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(1678,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1646,7]) ).
thf(1679,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1678]) ).
thf(1689,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1679]) ).
thf(3640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,3051]) ).
thf(3641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3640]) ).
thf(3642,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( B @ implies ) @ ( C @ not @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(pattern_uni,[status(thm)],[3641:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( L @ not @ ( J @ implies ) @ ( L @ not @ ( L @ implies ) @ implies ) ))]]) ).
thf(3677,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( B @ implies ) @ ( C @ not @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[3642]) ).
thf(3636,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,2749]) ).
thf(3637,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3636]) ).
thf(3669,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( B @ not @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3637]) ).
thf(3761,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ implies ) )
!= c )
| ( ( B @ not @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3669]) ).
thf(150,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( b != b )
| ( ( a @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[127]) ).
thf(151,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a )
| ( ( a @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[150]) ).
thf(1617,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( G @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1240,81]) ).
thf(1618,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ ( E @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( F @ ( G @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1617]) ).
thf(1619,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( A @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1618:[bind(A,$thf( P )),bind(B,$thf( Q )),bind(C,$thf( S )),bind(D,$thf( U )),bind(E,$thf( U @ not @ ( S @ implies ) @ ( Q @ implies ) )),bind(F,$thf( U @ not @ ( S @ implies ) @ ( Q @ implies ) @ ( P @ ( U @ implies ) @ implies ) )),bind(G,$thf( P ))]]) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( A @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1619]) ).
thf(1714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1650,7]) ).
thf(1715,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1714]) ).
thf(1725,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1715]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( C != b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[22]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ( b @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( c @ ( b @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[23]) ).
thf(404,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[403]) ).
thf(405,plain,
! [A: $i] :
( ( b @ ( a @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[404]) ).
thf(718,plain,
! [B: $i,A: $i] :
( ( c != B )
| ( b != A )
| ( ( c @ ( a @ implies ) @ ( B @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( B @ ( A @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[57]) ).
thf(790,plain,
( ( ( c @ ( a @ implies ) @ ( c @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( c @ ( a @ implies ) )
!= b )
| ( ( c @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[718]) ).
thf(563,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( F @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[562]) ).
thf(564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[563]) ).
thf(325,plain,
! [A: $i] :
( ( ( b @ ( a @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
( ( b @ ( a @ implies ) )
!= c ),
inference(simp,[status(thm)],[325]) ).
thf(463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[462]) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( b @ ( a @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c ),
inference(simp,[status(thm)],[463]) ).
thf(3017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1646,2866]) ).
thf(3018,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3017]) ).
thf(3057,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( B @ not @ implies ) )
!= c ),
inference(simp,[status(thm)],[3018]) ).
thf(185,plain,
! [A: $i] :
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( b != a )
| ( ( a @ ( A @ implies ) )
!= A )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a )
| ( b != A ) ),
inference(simp,[status(thm)],[175]) ).
thf(200,plain,
( ( ( c @ ( b @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( b != a )
| ( ( a @ ( b @ implies ) )
!= b )
| ( ( c @ ( a @ implies ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[185]) ).
thf(3710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2692,2749]) ).
thf(3711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3710]) ).
thf(3740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[3711]) ).
thf(4363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= c )
| ( ( C @ not )
!= a ) ),
inference(simp,[status(thm)],[2919]) ).
thf(1389,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( H @ ( G @ implies ) @ implies ) @ ( F @ ( H @ implies ) @ implies ) @ ( F @ ( G @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1240,80]) ).
thf(1390,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ ( D @ implies ) @ implies ) @ ( D @ not @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( F @ ( H @ ( G @ implies ) @ implies ) @ ( F @ ( H @ implies ) @ implies ) @ ( F @ ( G @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[1389]) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ ( A @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ implies ) @ ( C @ not @ ( A @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1390:[bind(A,$thf( ZH @ not @ ( ZF @ not @ implies ) )),bind(B,$thf( ZH @ not @ ( ZG @ implies ) )),bind(C,$thf( ZG @ ( ZF @ implies ) )),bind(D,$thf( ZH )),bind(E,$thf( ZH @ not @ ( ZG @ ( ZF @ implies ) @ implies ) @ ( ZH @ not @ ( ZG @ implies ) @ implies ) @ ( ZH @ not @ ( ZF @ not @ implies ) @ ( ZH @ implies ) @ implies ) )),bind(F,$thf( ZH @ not )),bind(G,$thf( ZF )),bind(H,$thf( ZG ))]]) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( B @ ( A @ implies ) @ implies ) @ ( C @ not @ ( B @ implies ) @ implies ) @ ( C @ not @ ( A @ not @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1391]) ).
thf(3021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,2866]) ).
thf(3022,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( c @ is_a_theorem ) ),
inference(simp,[status(thm)],[3021]) ).
thf(3052,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= c ),
inference(simp,[status(thm)],[3022]) ).
thf(14890,plain,
$false,
inference(e,[status(thm)],[101,1105,666,3681,2940,3858,3040,2953,1939,440,269,10,1426,2712,3121,56,1655,670,3276,42,3281,1650,1645,52,3275,619,344,3280,196,3855,46,2929,1641,57,78,789,253,238,121,84,480,147,3068,2833,692,998,116,1242,2954,117,3054,3418,233,6,38,3610,407,21,3664,566,3297,1951,1027,3050,710,456,324,285,252,3269,578,697,3122,2694,53,169,420,499,403,2692,1498,9,328,77,193,1414,3671,1644,2317,547,837,1002,3760,4361,2749,4195,633,1510,430,1103,2149,824,45,3289,149,562,191,22,44,286,3758,579,118,2827,12,54,3051,1239,3123,49,466,4273,86,3038,81,2955,7,3586,3055,483,668,330,462,4277,621,3759,2620,1000,80,167,636,695,2156,438,2952,795,2471,342,3048,617,2942,48,712,18,3129,2720,3608,2689,50,199,3818,791,127,3041,2468,544,11,1140,1240,497,43,4278,87,495,104,2919,1646,2167,2823,55,8,1689,119,3677,3761,82,151,1642,1725,51,405,273,168,835,2815,854,422,790,564,326,268,79,195,839,464,3057,47,15,200,3740,442,4363,227,83,2866,1416,3052,454,232,3669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL067-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.21/0.45 % Computer : n004.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Fri Sep 25 21:48:21 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.96/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.28 % [INFO] Parsing done (268ms).
% 1.66/1.30 % [INFO] Running in sequential loop mode.
% 2.50/1.90 % [INFO] eprover registered as external prover.
% 2.50/1.92 % [INFO] Scanning for conjecture ...
% 2.50/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.50/2.02 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.50/2.03 % [INFO] Problem is propositional (TPTP CNF).
% 2.50/2.04 % [INFO] Type checking passed.
% 2.50/2.04 % [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 ...
% 262.82/76.32 % External prover 'e' found a proof!
% 262.82/76.32 % [INFO] Killing All external provers ...
% 262.82/76.33 % Time passed: 75694ms (effective reasoning time: 75018ms)
% 262.82/76.33 % Axioms used in derivation (4): cn_19, condensed_detachment, cn_37, cn_59
% 262.82/76.33 % No. of inferences in proof: 611
% 262.82/76.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 75694 ms resp. 75018 ms w/o parsing
% 254.00/76.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 254.00/76.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------