%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL031-1 : 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 : n014.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 07:50:37 AM UTC 2026
% Result : Unsatisfiable 134.85s 33.06s
% Output : Refutation 123.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 6
% Syntax : Number of formulae : 1082 ( 497 unt; 0 typ; 0 def)
% Number of atoms : 3045 (1242 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 13950 (1670 ~; 855 |; 0 &;11425 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 3635 ( 0 ^;3635 !; 0 ?;3635 :)
% 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(falsehood_decl,type,
falsehood: $i ).
thf(e_decl,type,
e: $i ).
thf(5,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
~ ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c0_CAMeredith) ).
thf(7,plain,
~ ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
~ ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,8]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[17]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( A
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(69,plain,
! [A: $i] :
( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( A @ ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_1) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_2) ).
thf(12,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(9,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(10,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(cnf,[status(esa)],[9]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[48]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ implies ) @ ( H @ implies ) )),bind(D,$thf( D ))]]) ).
thf(60,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)],[50]) ).
thf(306,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,60]) ).
thf(307,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( O )),bind(B,$thf( O @ ( M @ implies ) )),bind(C,$thf( P )),bind(D,$thf( P @ ( O @ implies ) @ ( P @ ( O @ ( M @ implies ) @ implies ) @ implies ) )),bind(E,$thf( M )),bind(F,$thf( O ))]]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[308]) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[42]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[44]) ).
thf(1131,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,65]) ).
thf(1132,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( E @ ( F @ ( E @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1133,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( H @ ( J @ implies ) )),bind(B,$thf( J )),bind(C,$thf( J )),bind(D,$thf( J @ ( J @ implies ) )),bind(E,$thf( J )),bind(F,$thf( H ))]]) ).
thf(1183,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1133]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[45]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,66]) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1235,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1234:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1266,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1235]) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(52,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[51]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( L )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( J @ ( L @ implies ) )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) ))]]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[53]) ).
thf(1282,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1266,61]) ).
thf(1283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1282]) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1283:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ implies ) )),bind(D,$thf( A )),bind(E,$thf( E ))]]) ).
thf(1341,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1284]) ).
thf(2024,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1341,66]) ).
thf(2025,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2026,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2025:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2060,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2026]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( falsehood @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_4) ).
thf(14,plain,
! [A: $i] : ( A @ ( falsehood @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,66]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[188]) ).
thf(190,plain,
! [B: $i,A: $i] : ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( falsehood @ implies ) ))]]) ).
thf(214,plain,
! [B: $i,A: $i] : ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[190]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[214,10]) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[265]) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) )),bind(D,$thf( D ))]]) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[267]) ).
thf(6988,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( falsehood @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2060,299]) ).
thf(6989,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( falsehood @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[6988]) ).
thf(6990,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[6989:[bind(A,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) )),bind(B,$thf( Q )),bind(C,$thf( R )),bind(D,$thf( S )),bind(E,$thf( S @ ( R @ implies ) @ ( S @ ( Q @ ( Q @ implies ) @ implies ) @ implies ) )),bind(F,$thf( H )),bind(G,$thf( K ))]]) ).
thf(7037,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[6990]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,8]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
~ ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )),bind(B,$thf( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ))]]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,199]) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[473]) ).
thf(475,plain,
~ ( falsehood @ ( c @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( falsehood )),bind(B,$thf( c )),bind(C,$thf( a ))]]) ).
thf(7248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7037,475]) ).
thf(7249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[7248]) ).
thf(7353,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[7249]) ).
thf(7427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= falsehood )
| ( ( C @ ( A @ ( A @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[7353]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,199]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[223]) ).
thf(225,plain,
~ ( a @ ( c @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( a @ ( falsehood @ implies ) )),bind(B,$thf( a @ ( c @ implies ) ))]]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,225]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[238]) ).
thf(240,plain,
~ ( a @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( c )),bind(B,$thf( a ))]]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,240]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[253]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[254]) ).
thf(1145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,259]) ).
thf(1146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1145]) ).
thf(1147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1146:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1147]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,199]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[215]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(2340,plain,
! [B: $i,A: $i] :
( ( A
!= ( a @ ( c @ implies ) ) )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(2341,plain,
! [A: $i] :
( ( a @ ( c @ implies ) @ ( A @ ( a @ ( c @ implies ) @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ),
inference(simp,[status(thm)],[2340]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
! [A: $i] :
( ( A @ is_a_theorem )
| ~ ( falsehood @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( falsehood )),bind(C,$thf( A ))]]) ).
thf(90,plain,
! [A: $i] :
( ( ( A @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( falsehood @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[35,8]) ).
thf(91,plain,
! [A: $i] :
( ( ( A @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
~ ( falsehood @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ))]]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,92]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[177]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[178]) ).
thf(326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,206]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[326]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) ))]]) ).
thf(347,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[328]) ).
thf(431,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,61]) ).
thf(432,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[431]) ).
thf(433,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[432:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( G )),bind(D,$thf( G @ ( I @ ( G @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(501,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[433]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true
| ~ ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( E )),bind(B,$thf( E @ ( falsehood @ implies ) )),bind(C,$thf( C ))]]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(2699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[501,62]) ).
thf(2700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[2699]) ).
thf(2701,plain,
! [B: $i,A: $i] : ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( G )),bind(B,$thf( falsehood )),bind(C,$thf( K )),bind(D,$thf( G @ ( falsehood @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(E,$thf( G ))]]) ).
thf(2715,plain,
! [B: $i,A: $i] : ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2701]) ).
thf(2780,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,199]) ).
thf(2781,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2780]) ).
thf(2796,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2781]) ).
thf(2920,plain,
! [B: $i,A: $i] :
( ( A
!= ( a @ ( c @ implies ) ) )
| ( ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[2796]) ).
thf(2921,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ),
inference(simp,[status(thm)],[2920]) ).
thf(478,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,61]) ).
thf(479,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[478]) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[479:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( falsehood @ implies ) )),bind(D,$thf( A )),bind(E,$thf( E ))]]) ).
thf(492,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[480]) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,240]) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[945]) ).
thf(962,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[946]) ).
thf(1153,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,66]) ).
thf(1154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1153]) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1154:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1179,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)],[1155]) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,475]) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[910]) ).
thf(961,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[911]) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= falsehood )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[961]) ).
thf(54,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(55,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[56]) ).
thf(1156,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,63]) ).
thf(1157,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( G @ ( F @ implies ) @ ( G @ ( E @ implies ) @ implies ) @ ( E @ ( F @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1156]) ).
thf(1158,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1157:[bind(A,$thf( T )),bind(B,$thf( R )),bind(C,$thf( U @ ( T @ implies ) @ ( U @ ( R @ implies ) @ implies ) )),bind(D,$thf( U @ ( T @ implies ) @ ( U @ ( R @ implies ) @ implies ) @ ( R @ implies ) )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( U ))]]) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1158]) ).
thf(1830,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1181,92]) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1879,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1831]) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1266,199]) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1321]) ).
thf(1337,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1322]) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,199]) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1159]) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1160]) ).
thf(6563,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[1177]) ).
thf(6568,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( falsehood @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[6563]) ).
thf(6570,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( falsehood @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( C != a )
| ( ( B @ ( A @ implies ) )
!= c )
| ( ( C @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[6568]) ).
thf(6587,plain,
! [B: $i,A: $i] :
( ( ( a @ ( falsehood @ implies ) )
!= ( a @ ( B @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= c )
| ( ( a @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[6570]) ).
thf(1126,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,60]) ).
thf(1127,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[1126]) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1127:[bind(A,$thf( Q )),bind(B,$thf( R )),bind(C,$thf( R @ ( Q @ implies ) @ ( O @ implies ) )),bind(D,$thf( R @ ( Q @ implies ) @ ( O @ implies ) @ ( R @ implies ) )),bind(E,$thf( O )),bind(F,$thf( R @ ( Q @ implies ) ))]]) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1128]) ).
thf(1481,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,199]) ).
thf(1482,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1481]) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1482]) ).
thf(2509,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( C
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[1495]) ).
thf(2510,plain,
! [B: $i,A: $i] :
( ( a @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2509]) ).
thf(2511,plain,
! [B: $i,A: $i] :
( ( ( a @ ( falsehood @ implies ) @ ( B @ implies ) )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[2510]) ).
thf(2512,plain,
! [A: $i] :
( ( a @ ( falsehood @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2511]) ).
thf(7262,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7037,92]) ).
thf(7263,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[7262]) ).
thf(7358,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[7263]) ).
thf(1824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1181,206]) ).
thf(1825,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1824]) ).
thf(1826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1825:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( J @ implies ) ))]]) ).
thf(1882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1826]) ).
thf(412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,259]) ).
thf(413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[412]) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[414]) ).
thf(2760,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,423]) ).
thf(2761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2760]) ).
thf(2762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2761:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( falsehood @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2762]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,66]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[182]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[184]) ).
thf(671,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)],[211,66]) ).
thf(672,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)],[671]) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[672:[bind(A,$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(696,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)],[673]) ).
thf(1655,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[696,66]) ).
thf(1656,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1655]) ).
thf(1657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1656:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ implies ) @ ( N @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(1692,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1657]) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,225]) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1173,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1135]) ).
thf(915,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,206]) ).
thf(916,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[915]) ).
thf(917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[916:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[917]) ).
thf(57,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)],[10]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[57]) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,59]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[155]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[157]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,66]) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) ))]]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[277]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,199]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[374]) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(2652,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ 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)],[501,60]) ).
thf(2653,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( F @ ( E @ implies ) @ ( F @ implies ) @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[2652]) ).
thf(2654,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2653:[bind(A,$thf( P @ ( O @ implies ) )),bind(B,$thf( P )),bind(C,$thf( N )),bind(D,$thf( P @ ( O @ implies ) @ ( P @ ( N @ ( P @ implies ) @ implies ) @ implies ) )),bind(E,$thf( O )),bind(F,$thf( P ))]]) ).
thf(2721,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2654]) ).
thf(3279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2721,92]) ).
thf(3280,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[3279]) ).
thf(3332,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3280]) ).
thf(3269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2721,475]) ).
thf(3270,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3269]) ).
thf(3338,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[3270]) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,423]) ).
thf(1220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1219]) ).
thf(1221,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1220:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1221]) ).
thf(1315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1266,66]) ).
thf(1316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1315]) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1316:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ implies ) @ ( E @ implies ) ))]]) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1317]) ).
thf(1443,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 @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,61]) ).
thf(1444,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 @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1443]) ).
thf(1445,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1444:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ implies ) @ ( G @ implies ) )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(1503,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1445]) ).
thf(5645,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( F @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1503,60]) ).
thf(5646,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ implies ) @ ( A @ ( D @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ ( G @ ( F @ implies ) @ ( G @ implies ) @ implies ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[5645]) ).
thf(5647,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[5646:[bind(A,$thf( Y @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) )),bind(B,$thf( V )),bind(C,$thf( X )),bind(D,$thf( Y )),bind(E,$thf( Y @ ( X @ implies ) @ ( V @ implies ) @ ( T @ implies ) @ ( Y @ implies ) )),bind(F,$thf( T )),bind(G,$thf( Y @ ( X @ implies ) @ ( V @ implies ) ))]]) ).
thf(5745,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)],[5647]) ).
thf(6267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5745,225]) ).
thf(6268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6267]) ).
thf(6351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[6268]) ).
thf(6390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( D != c ) ),
inference(simp,[status(thm)],[6351]) ).
thf(6391,plain,
! [C: $i,B: $i,A: $i] :
( ( c @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[6390]) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,8]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[376]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,66]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[179]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) ))]]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[181]) ).
thf(1063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[210,66]) ).
thf(1064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1063]) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1064:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( I @ ( I @ ( M @ ( I @ implies ) @ implies ) @ implies ) @ ( F @ implies ) ))]]) ).
thf(1095,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1065]) ).
thf(1563,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1342,66]) ).
thf(1564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1563]) ).
thf(1565,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1564:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( K @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(1602,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1565]) ).
thf(2183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1602,225]) ).
thf(2184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2184]) ).
thf(763,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,423]) ).
thf(764,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[763]) ).
thf(765,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[764:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( falsehood @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(782,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[765]) ).
thf(6564,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( C != a )
| ( ( B @ ( A @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[6563]) ).
thf(6583,plain,
! [B: $i,A: $i] :
( ( ( a @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[6564]) ).
thf(1530,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1342,61]) ).
thf(1531,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1530]) ).
thf(1532,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1531:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( J )),bind(D,$thf( J @ ( J @ implies ) @ ( G @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(1601,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( D @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1532]) ).
thf(2743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,206]) ).
thf(2744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[2743]) ).
thf(2745,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[2744:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2819,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2745]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,240]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[249]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[250]) ).
thf(19,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(20,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[19]) ).
thf(23,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(24,plain,
! [A: $i] :
( ( A
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) )
| ( ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
( ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[24]) ).
thf(1215,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,225]) ).
thf(1216,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1215]) ).
thf(1254,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1216]) ).
thf(2775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,66]) ).
thf(2776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2775]) ).
thf(2777,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2776:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2812,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2777]) ).
thf(2871,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2812,66]) ).
thf(2872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2871]) ).
thf(2873,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2872:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( I @ ( falsehood @ ( M @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( F @ implies ) ))]]) ).
thf(2916,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2873]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= ( a @ ( falsehood @ implies ) ) )
| ( B != falsehood )
| ( A
!= ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(1021,plain,
! [A: $i] :
( ( ( A @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( A @ ( falsehood @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[991]) ).
thf(1773,plain,
! [A: $i] :
( ( ( A @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( A != a )
| ( falsehood != falsehood ) ),
inference(simp,[status(thm)],[1021]) ).
thf(1792,plain,
( ( a @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1773]) ).
thf(457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,225]) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[457]) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[458]) ).
thf(7922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,488]) ).
thf(7923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[7922]) ).
thf(7924,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(pattern_uni,[status(thm)],[7923:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( falsehood ))]]) ).
thf(8089,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[7924]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,225]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[230]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[243]) ).
thf(785,plain,
! [A: $i] :
( ( a @ ( A @ ( a @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[784]) ).
thf(942,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,66]) ).
thf(943,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[942]) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[943:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[944]) ).
thf(2539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[975,225]) ).
thf(2540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2539]) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2540]) ).
thf(4760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[2584]) ).
thf(4761,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[4760]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,66]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[196]) ).
thf(3615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[209,475]) ).
thf(3616,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3615]) ).
thf(3776,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3616]) ).
thf(8006,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,488]) ).
thf(8007,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[8006]) ).
thf(8008,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(pattern_uni,[status(thm)],[8007:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( falsehood @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(8069,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[8008]) ).
thf(2847,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2812,225]) ).
thf(2848,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2847]) ).
thf(2897,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2848]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,92]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[105]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[106]) ).
thf(2681,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[501,240]) ).
thf(2682,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[2681]) ).
thf(2708,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[2682]) ).
thf(338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,206]) ).
thf(339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[338]) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[340]) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,345]) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1228]) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1229:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ implies ) ))]]) ).
thf(1264,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1230]) ).
thf(6262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5745,92]) ).
thf(6263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[6262]) ).
thf(6350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[6263]) ).
thf(2002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1341,225]) ).
thf(2003,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2002]) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2003]) ).
thf(1457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,225]) ).
thf(1458,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1457]) ).
thf(1494,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1458]) ).
thf(1608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ( C != c ) ),
inference(simp,[status(thm)],[1494]) ).
thf(1609,plain,
! [B: $i,A: $i] :
( ( c @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1608]) ).
thf(70,plain,
! [A: $i] :
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( ( A @ ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(72,plain,
! [A: $i] :
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( A != e )
| ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(73,plain,
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(147,plain,
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( ( falsehood @ ( c @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( a @ ( falsehood @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(150,plain,
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( falsehood != a )
| ( c != c )
| ( b != a )
| ( falsehood != a ) ),
inference(simp,[status(thm)],[147]) ).
thf(152,plain,
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( b != a )
| ( falsehood != a ) ),
inference(simp,[status(thm)],[150]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,199]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[217]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[218]) ).
thf(452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,61]) ).
thf(453,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[452]) ).
thf(454,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[453:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( J )),bind(D,$thf( J @ ( falsehood @ implies ) @ ( G @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(495,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[454]) ).
thf(2260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[495,475]) ).
thf(2261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2260]) ).
thf(2321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2261]) ).
thf(4632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= falsehood )
| ( ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[2321]) ).
thf(1854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1181,240]) ).
thf(1855,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1854]) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1855]) ).
thf(236,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,225]) ).
thf(237,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[236]) ).
thf(242,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(260,plain,
! [A: $i] :
( ( A != a )
| ( falsehood != c ) ),
inference(simp,[status(thm)],[242]) ).
thf(261,plain,
falsehood != c,
inference(simp,[status(thm)],[260]) ).
thf(7994,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,488]) ).
thf(7995,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[7994]) ).
thf(7996,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[7995:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(8065,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[7996]) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,92]) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[921]) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[922]) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1266,475]) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1280]) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1281]) ).
thf(989,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) )
| ( B != falsehood )
| ( A
!= ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(1020,plain,
! [A: $i] :
( ( A @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[989]) ).
thf(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,206]) ).
thf(330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[329]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[331]) ).
thf(577,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,345]) ).
thf(578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[577]) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[578:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( G @ implies ) @ implies ) @ implies ) ))]]) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[579]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,199]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[280]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,225]) ).
thf(661,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[660]) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[661]) ).
thf(987,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[691]) ).
thf(988,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= a ),
inference(simp,[status(thm)],[987]) ).
thf(1558,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1342,345]) ).
thf(1559,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1558]) ).
thf(1560,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( L @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(1600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1560]) ).
thf(7931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,488]) ).
thf(7932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[7931]) ).
thf(7933,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(pattern_uni,[status(thm)],[7932:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(8092,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[7933]) ).
thf(8094,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[8092]) ).
thf(514,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,475]) ).
thf(515,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[514]) ).
thf(527,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(2016,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1341,259]) ).
thf(2017,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2016]) ).
thf(2018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2017:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2018]) ).
thf(1301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1266,423]) ).
thf(1302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1301]) ).
thf(1303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1302:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ ( I @ implies ) @ ( F @ implies ) ))]]) ).
thf(1351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1303]) ).
thf(446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,206]) ).
thf(447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[446]) ).
thf(448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[447:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ ( H @ implies ) @ implies ) ))]]) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( B @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[448]) ).
thf(8888,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,491]) ).
thf(8889,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[8888]) ).
thf(8890,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[8889:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( falsehood ))]]) ).
thf(9035,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[8890]) ).
thf(2523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[975,475]) ).
thf(2524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2523]) ).
thf(2586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2524]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,240]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[278]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[279]) ).
thf(4589,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= falsehood )
| ( ( C @ ( A @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3338]) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,475]) ).
thf(509,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[508]) ).
thf(529,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[509]) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,475]) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1118]) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1119]) ).
thf(2621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= falsehood )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1171]) ).
thf(2833,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2812,61]) ).
thf(2834,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2833]) ).
thf(2835,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2834:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( L )),bind(D,$thf( H @ ( falsehood @ ( L @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(2905,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2835]) ).
thf(711,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( A
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(712,plain,
! [A: $i] :
( ( a @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[711]) ).
thf(713,plain,
! [A: $i] :
( ( ( a @ ( falsehood @ implies ) )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[712]) ).
thf(714,plain,
( ( a @ ( falsehood @ implies ) )
!= a ),
inference(simp,[status(thm)],[713]) ).
thf(2782,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,8]) ).
thf(2783,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2782]) ).
thf(2805,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2783]) ).
thf(1199,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,475]) ).
thf(1200,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1199]) ).
thf(1255,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1200]) ).
thf(7266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7037,225]) ).
thf(7267,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[7266]) ).
thf(7359,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[7267]) ).
thf(7428,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= a )
| ( ( C @ ( A @ ( A @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[7359]) ).
thf(3655,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[209,225]) ).
thf(3656,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3655]) ).
thf(3778,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[3656]) ).
thf(1856,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1181,66]) ).
thf(1857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1856]) ).
thf(1858,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1857:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( J @ implies ) ))]]) ).
thf(1883,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[1858]) ).
thf(369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,66]) ).
thf(370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[369]) ).
thf(371,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[370:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(394,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[371]) ).
thf(825,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,66]) ).
thf(826,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[825]) ).
thf(827,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( falsehood @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(862,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[827]) ).
thf(332,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,206]) ).
thf(333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[332]) ).
thf(334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[334]) ).
thf(1620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[696,475]) ).
thf(1621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1620]) ).
thf(1676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1621]) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,240]) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[471]) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= a )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[472]) ).
thf(5407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,487]) ).
thf(5408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[5407]) ).
thf(5409,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[5408:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( falsehood @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(5455,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[5409]) ).
thf(1470,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,345]) ).
thf(1471,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1470]) ).
thf(1472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1471:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( I @ implies ) @ ( L @ implies ) ))]]) ).
thf(1502,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1472]) ).
thf(397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,259]) ).
thf(398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[397]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) ))]]) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[399]) ).
thf(3204,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2916,66]) ).
thf(3205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3204]) ).
thf(3206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3205:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( P )),bind(E,$thf( E )),bind(F,$thf( L @ ( falsehood @ ( P @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(3239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3206]) ).
thf(3180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2916,225]) ).
thf(3181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3180]) ).
thf(3233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[3181]) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,199]) ).
thf(680,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[679]) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(6248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5745,475]) ).
thf(6249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[6248]) ).
thf(6356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[6249]) ).
thf(1475,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)],[1182,66]) ).
thf(1476,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)],[1475]) ).
thf(1477,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[1476:[bind(A,$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(1504,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)],[1477]) ).
thf(2075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1504,475]) ).
thf(2076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2075]) ).
thf(2132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2076]) ).
thf(2352,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[862,475]) ).
thf(2353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2352]) ).
thf(2414,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2353]) ).
thf(221,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,199]) ).
thf(222,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[221]) ).
thf(229,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(6397,plain,
! [B: $i,A: $i] :
( ( A
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) )
| ( ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[2805]) ).
thf(6398,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[6397]) ).
thf(6399,plain,
! [A: $i] :
( ( falsehood != falsehood )
| ( ( A @ ( falsehood @ implies ) )
!= ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[6398]) ).
thf(6400,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[6399]) ).
thf(6401,plain,
! [A: $i] :
( ( A != e )
| ( ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[6400]) ).
thf(6402,plain,
( ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[6401]) ).
thf(2167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1602,475]) ).
thf(2168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2167]) ).
thf(2228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2168]) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[210,225]) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1046]) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1047]) ).
thf(301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,60]) ).
thf(302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[301]) ).
thf(317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[302]) ).
thf(2752,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,225]) ).
thf(2753,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2752]) ).
thf(2801,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2753]) ).
thf(1775,plain,
! [A: $i] :
( ( A != a )
| ( ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) )
!= c )
| ( A != a )
| ( falsehood != falsehood ) ),
inference(simp,[status(thm)],[1021]) ).
thf(1794,plain,
( ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[1775]) ).
thf(2877,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2812,199]) ).
thf(2878,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2877]) ).
thf(2895,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2878]) ).
thf(925,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,225]) ).
thf(926,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[925]) ).
thf(965,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[926]) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[965]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= B )
| ~ $true
| ( C @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[14,59]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= B )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( B @ ( falsehood @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( E )),bind(B,$thf( E @ ( falsehood @ implies ) )),bind(C,$thf( C ))]]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( falsehood @ implies ) @ implies ) )
!= ( B @ ( falsehood @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[166]) ).
thf(3164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2916,475]) ).
thf(3165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3164]) ).
thf(3237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[3165]) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,240]) ).
thf(1474,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1473]) ).
thf(1498,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= a ),
inference(simp,[status(thm)],[1474]) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1342,199]) ).
thf(1570,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1569]) ).
thf(1587,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1570]) ).
thf(748,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,423]) ).
thf(749,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[748]) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[749:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( G @ ( K @ ( G @ implies ) @ implies ) @ implies ) ))]]) ).
thf(783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( C @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[750]) ).
thf(403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,259]) ).
thf(404,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[403]) ).
thf(405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[405]) ).
thf(2773,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,240]) ).
thf(2774,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[2773]) ).
thf(2798,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[2774]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,225]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[232]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(536,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[241]) ).
thf(537,plain,
! [A: $i] :
( ( c @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[536]) ).
thf(1987,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1341,475]) ).
thf(1988,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1987]) ).
thf(2045,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1988]) ).
thf(3596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= falsehood )
| ( ( B @ ( C @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[2045]) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,475]) ).
thf(519,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[518]) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[519]) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,92]) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[455]) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= falsehood )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[456]) ).
thf(2271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[495,92]) ).
thf(2272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[2271]) ).
thf(2317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2272]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,92]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[103]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[104]) ).
thf(251,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,240]) ).
thf(252,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[251]) ).
thf(256,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= a ),
inference(simp,[status(thm)],[252]) ).
thf(58,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)],[57]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,58]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) ))]]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[202]) ).
thf(665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,259]) ).
thf(666,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[665]) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$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(706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[667]) ).
thf(366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[297,59]) ).
thf(367,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[366]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) )
!= ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[367:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) )
!= ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[368]) ).
thf(1992,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1341,206]) ).
thf(1993,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1992]) ).
thf(1994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1993:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( K @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1994]) ).
thf(3306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2721,66]) ).
thf(3307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3306]) ).
thf(3308,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[3307:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( M @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3354,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[3308]) ).
thf(592,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 ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,345]) ).
thf(593,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 ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[592]) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[593:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[594]) ).
thf(1734,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,601]) ).
thf(1735,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[1734]) ).
thf(1736,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( E @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[1735:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( G @ implies ) ))]]) ).
thf(1759,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ~ ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[1736]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,35]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[82]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood )
| ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[83]) ).
thf(1391,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(paramod_ordered,[status(thm)],[95,259]) ).
thf(1392,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ implies ) )
!= a )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(pattern_uni,[status(thm)],[1392:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C ))]]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,225]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[234]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[210,475]) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1030]) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1031]) ).
thf(2022,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1341,240]) ).
thf(2023,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[2022]) ).
thf(2043,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[2023]) ).
thf(5395,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= a )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,487]) ).
thf(5396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[5395]) ).
thf(5397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5396:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(5447,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[5397]) ).
thf(1467,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,259]) ).
thf(1468,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1467]) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1468:[bind(A,$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(1515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1469]) ).
thf(1848,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1181,259]) ).
thf(1849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1848]) ).
thf(1850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1849:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( J @ implies ) @ implies ) @ ( J @ implies ) ))]]) ).
thf(1895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1850]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,475]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[523]) ).
thf(530,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[524]) ).
thf(950,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,199]) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[950]) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[951]) ).
thf(4463,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[967]) ).
thf(4592,plain,
! [C: $i,B: $i,A: $i] :
( ( B != a )
| ( A != c )
| ( ( B @ ( C @ ( falsehood @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[4463]) ).
thf(4613,plain,
! [A: $i] :
( ( a @ ( A @ ( falsehood @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ),
inference(simp,[status(thm)],[4592]) ).
thf(1272,plain,
! [A: $i] :
( ( A != a )
| ( A != c ) ),
inference(simp,[status(thm)],[1254]) ).
thf(1273,plain,
c != a,
inference(simp,[status(thm)],[1272]) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(40,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( F @ ( H @ ( F @ implies ) @ implies ) )),bind(D,$thf( F ))]]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[41]) ).
thf(1549,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1342,423]) ).
thf(1550,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1549]) ).
thf(1551,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1550:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( L @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(1595,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1551]) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[214,59]) ).
thf(273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) )
!= ( C @ ( falsehood @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) )),bind(D,$thf( D ))]]) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ implies ) )
!= ( C @ ( falsehood @ implies ) @ ( B @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[274]) ).
thf(2831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2812,475]) ).
thf(2832,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2831]) ).
thf(2894,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2832]) ).
thf(8290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= a )
| ( ( C @ ( B @ implies ) )
!= c )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[8065]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) )
| ( A
!= ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(30,plain,
! [A: $i] :
( ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( A
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
( ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(5344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,487]) ).
thf(5345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[5344]) ).
thf(5346,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[5345:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(5456,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[5346]) ).
thf(647,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,475]) ).
thf(648,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[647]) ).
thf(694,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[648]) ).
thf(808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,225]) ).
thf(809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[808]) ).
thf(843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[809]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,8]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[282]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(3283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2721,225]) ).
thf(3284,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3283]) ).
thf(3341,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[3284]) ).
thf(4590,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= a )
| ( ( C @ ( A @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[3341]) ).
thf(1210,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,92]) ).
thf(1211,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1210]) ).
thf(1256,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1211]) ).
thf(1369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(paramod_ordered,[status(thm)],[95,206]) ).
thf(1370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1369]) ).
thf(1371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ implies ) )
!= falsehood )
| ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ) ),
inference(pattern_uni,[status(thm)],[1370:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C ))]]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[13,58]) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( F @ ( F @ ( J @ ( F @ implies ) @ implies ) @ implies ) )),bind(D,$thf( D ))]]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[122]) ).
thf(3304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2721,240]) ).
thf(3305,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[3304]) ).
thf(3340,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[3305]) ).
thf(1239,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,199]) ).
thf(1240,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1258,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1240]) ).
thf(3539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,240]) ).
thf(3540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[3539]) ).
thf(3568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[3540]) ).
thf(2296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[495,240]) ).
thf(2297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[2296]) ).
thf(2319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[2297]) ).
thf(1636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[696,225]) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1636]) ).
thf(1675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1637]) ).
thf(356,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,206]) ).
thf(357,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[358]) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1181,225]) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1835]) ).
thf(1876,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(3486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[1876]) ).
thf(3487,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( c @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[3486]) ).
thf(7976,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,488]) ).
thf(7977,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[7976]) ).
thf(7978,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(pattern_uni,[status(thm)],[7977:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) )),bind(D,$thf( G ))]]) ).
thf(8059,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[7978]) ).
thf(1241,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,8]) ).
thf(1242,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1241]) ).
thf(1253,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1242]) ).
thf(2623,plain,
! [A: $i] :
( ( A
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) )
| ( A
!= ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[1253]) ).
thf(2624,plain,
( ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[2623]) ).
thf(2629,plain,
( ( ( a @ ( c @ implies ) )
!= falsehood )
| ( ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[2624]) ).
thf(2634,plain,
( ( ( a @ ( c @ implies ) )
!= falsehood )
| ( e != a )
| ( ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[2629]) ).
thf(2635,plain,
( ( falsehood != falsehood )
| ( ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( a @ ( c @ implies ) )
!= falsehood )
| ( e != a ) ),
inference(eqfactor_ordered,[status(thm)],[2634]) ).
thf(2637,plain,
( ( ( falsehood @ ( c @ implies ) )
!= a )
| ( ( b @ ( a @ implies ) )
!= c )
| ( ( a @ ( c @ implies ) )
!= falsehood )
| ( e != a ) ),
inference(simp,[status(thm)],[2635]) ).
thf(400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,259]) ).
thf(401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[400]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[402]) ).
thf(5788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,489]) ).
thf(5789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[5788]) ).
thf(5790,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[5789:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(5901,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[5790]) ).
thf(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,60]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ is_a_theorem ) )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[309]) ).
thf(318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) )
!= ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) ) )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[310]) ).
thf(2738,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,475]) ).
thf(2739,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2738]) ).
thf(2802,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2739]) ).
thf(191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,59]) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[191]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) ))]]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) ) )
| ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[193]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,92]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1130]) ).
thf(580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,345]) ).
thf(581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[580]) ).
thf(582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ ( H @ implies ) @ ( I @ implies ) ))]]) ).
thf(604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[582]) ).
thf(3297,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2721,259]) ).
thf(3298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[3297]) ).
thf(3299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[3298:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( M @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[3299]) ).
thf(8972,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,491]) ).
thf(8973,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[8972]) ).
thf(8974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[8973:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) )),bind(F,$thf( F ))]]) ).
thf(9015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[8974]) ).
thf(4031,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,3778]) ).
thf(4032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[4031]) ).
thf(4033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[4032:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(4073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[4033]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,225]) ).
thf(365,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[364]) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(5842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,489]) ).
thf(5843,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[5842]) ).
thf(5844,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[5843:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(5894,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[5844]) ).
thf(322,plain,
! [A: $i] :
( ( A
!= ( a @ ( c @ implies ) ) )
| ( ( a @ ( falsehood @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[229]) ).
thf(323,plain,
( ( a @ ( falsehood @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[322]) ).
thf(5380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,487]) ).
thf(5381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[5380]) ).
thf(5382,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[5381:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) )),bind(D,$thf( G ))]]) ).
thf(5439,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[5382]) ).
thf(3898,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 ) )
!= ( falsehood @ ( c @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,3776]) ).
thf(3899,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 ) )
!= ( falsehood @ ( c @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[3898]) ).
thf(3900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3899:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(3971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[3900]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,92]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[101]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[102]) ).
thf(2655,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[501,92]) ).
thf(2656,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[2655]) ).
thf(2710,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2656]) ).
thf(8589,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( C @ implies ) )
!= a )
| ( ( E @ ( D @ implies ) )
!= c )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,8290]) ).
thf(8590,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( C @ implies ) )
!= a )
| ( ( E @ ( D @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[8589]) ).
thf(8591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) )
!= c ) ),
inference(pattern_uni,[status(thm)],[8590:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( G @ ( falsehood @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(8633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[8591]) ).
thf(1296,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1266,225]) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1296]) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1297]) ).
thf(6314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5745,240]) ).
thf(6315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[6314]) ).
thf(6353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ ( D @ implies ) )
!= a ),
inference(simp,[status(thm)],[6315]) ).
thf(3509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,92]) ).
thf(3510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[3509]) ).
thf(3572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3510]) ).
thf(185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,66]) ).
thf(186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[185]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(213,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[187]) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,475]) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[795]) ).
thf(848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[796]) ).
thf(649,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,61]) ).
thf(650,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[649]) ).
thf(651,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[650:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ implies ) @ ( J @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(700,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ ( D @ ( C @ implies ) @ ( D @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[651]) ).
thf(2368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[862,225]) ).
thf(2369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2368]) ).
thf(2410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2369]) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( A != falsehood )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[529]) ).
thf(983,plain,
! [A: $i] :
( ( falsehood @ ( A @ ( falsehood @ implies ) @ implies ) )
!= c ),
inference(simp,[status(thm)],[982]) ).
thf(6393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ( D != c ) ),
inference(simp,[status(thm)],[6356]) ).
thf(6394,plain,
! [C: $i,B: $i,A: $i] :
( ( c @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[6393]) ).
thf(757,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,423]) ).
thf(758,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[757]) ).
thf(759,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( L @ implies ) @ ( G @ implies ) ))]]) ).
thf(780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[759]) ).
thf(2748,plain,
! [B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,92]) ).
thf(2749,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[2748]) ).
thf(2797,plain,
! [B: $i,A: $i] :
( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2749]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ~ $true
| ( D @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[12,59]) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= C )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ implies ) @ ( H @ implies ) )),bind(D,$thf( D ))]]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[160]) ).
thf(2505,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( A
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[693]) ).
thf(2506,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2505]) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,240]) ).
thf(1152,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1151]) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[1152]) ).
thf(589,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,345]) ).
thf(590,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[589]) ).
thf(591,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[590:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( falsehood @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(608,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( falsehood @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[591]) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[61,8]) ).
thf(477,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[476]) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ ( falsehood @ ( e @ ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ implies ) @ implies ) ) )
| ~ ( A @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[477]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,240]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[247]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[248]) ).
thf(1310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1266,345]) ).
thf(1311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1311:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ ( I @ implies ) @ ( F @ implies ) ))]]) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1312]) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,475]) ).
thf(1442,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1441]) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1442]) ).
thf(1610,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood )
| ( C != c ) ),
inference(simp,[status(thm)],[1500]) ).
thf(1611,plain,
! [B: $i,A: $i] :
( ( c @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1610]) ).
thf(3833,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( C @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[2049]) ).
thf(1231,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,240]) ).
thf(1232,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[1231]) ).
thf(1252,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1232]) ).
thf(8096,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ implies ) )
!= a )
| ( ( A @ ( C @ ( B @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[8059]) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,206]) ).
thf(1205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1204]) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1205:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1267,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1206]) ).
thf(8993,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,491]) ).
thf(8994,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( E @ implies ) @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( F @ ( D @ implies ) @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[8993]) ).
thf(8995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[8994:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( falsehood @ implies ) )),bind(E,$thf( A )),bind(F,$thf( F ))]]) ).
thf(9022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[8995]) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,475]) ).
thf(511,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[510]) ).
thf(525,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(668,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,345]) ).
thf(669,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[668]) ).
thf(670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[669:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( L @ implies ) @ ( G @ implies ) ))]]) ).
thf(707,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( E @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[670]) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,92]) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1452]) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1453]) ).
thf(1431,plain,
! [A: $i] :
( ( A
!= ( a @ ( c @ implies ) ) )
| ( A
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[1258]) ).
thf(1432,plain,
( ( a @ ( falsehood @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1431]) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,259]) ).
thf(1226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ ( B @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1225]) ).
thf(1227,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1226:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(1262,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1227]) ).
thf(7313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7037,240]) ).
thf(7314,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[7313]) ).
thf(7351,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( A @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[7314]) ).
thf(1998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1341,92]) ).
thf(1999,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[1998]) ).
thf(2044,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( C @ ( C @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1999]) ).
thf(5335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,487]) ).
thf(5336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[5335]) ).
thf(5337,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[5336:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( falsehood ))]]) ).
thf(5450,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[5337]) ).
thf(5854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,489]) ).
thf(5855,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[5854]) ).
thf(5856,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[5855:[bind(A,$thf( A )),bind(B,$thf( I )),bind(C,$thf( A )),bind(D,$thf( falsehood @ ( I @ ( falsehood @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(5902,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[5856]) ).
thf(1022,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) )
!= falsehood )
| ( A != c ) ),
inference(simp,[status(thm)],[694]) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1022]) ).
thf(2276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[495,225]) ).
thf(2277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2276]) ).
thf(2320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2277]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= falsehood )
| ( A != c ) ),
inference(simp,[status(thm)],[525]) ).
thf(571,plain,
! [A: $i] :
( ( c @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[570]) ).
thf(5779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,489]) ).
thf(5780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( B @ ( C @ implies ) @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[5779]) ).
thf(5781,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[5780:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( falsehood ))]]) ).
thf(5895,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[5781]) ).
thf(1544,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1342,225]) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1544]) ).
thf(1585,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1545]) ).
thf(372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,240]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[372]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[373]) ).
thf(1819,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1181,475]) ).
thf(1820,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1819]) ).
thf(1881,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(2757,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,601]) ).
thf(2758,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[2757]) ).
thf(2759,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[2758:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( falsehood @ ( L @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2807,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2759]) ).
thf(833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,199]) ).
thf(834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[833]) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[834]) ).
thf(1123,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[320,206]) ).
thf(1124,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1124:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( L @ ( J @ implies ) @ implies ) @ implies ) ))]]) ).
thf(1180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1125]) ).
thf(4762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood )
| ( A != c ) ),
inference(simp,[status(thm)],[2586]) ).
thf(4763,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ ( falsehood @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[4762]) ).
thf(2626,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) )
!= a )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[210,199]) ).
thf(1072,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1071]) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[1072]) ).
thf(2342,plain,
! [A: $i] :
( ( ( a @ ( c @ implies ) )
!= a )
| ( ( A @ ( a @ ( c @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[2341]) ).
thf(2091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1504,225]) ).
thf(2092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2091]) ).
thf(2135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[2092]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,240]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[245]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[246]) ).
thf(353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[297,10]) ).
thf(354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[353]) ).
thf(355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) )),bind(E,$thf( E ))]]) ).
thf(390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[355]) ).
thf(2770,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,345]) ).
thf(2771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[2770]) ).
thf(2772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[2771:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( falsehood @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[2772]) ).
thf(3210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2916,199]) ).
thf(3211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3210]) ).
thf(3235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ ( D @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[3211]) ).
thf(6565,plain,
! [C: $i,B: $i,A: $i] :
( ( C != a )
| ( B != c )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ) ),
inference(simp,[status(thm)],[6563]) ).
thf(6584,plain,
! [A: $i] :
( ( a @ ( c @ ( A @ implies ) @ implies ) )
!= ( a @ ( falsehood @ implies ) ) ),
inference(simp,[status(thm)],[6565]) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true
| ~ ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,10]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( D @ ( C @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[174]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) ))]]) ).
thf(207,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[176]) ).
thf(341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,206]) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[341]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( falsehood @ implies ) @ ( E @ implies ) ))]]) ).
thf(346,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[343]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,92]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[268]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[269]) ).
thf(149,plain,
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( falsehood != a )
| ( c != c )
| ( ( a @ ( falsehood @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(151,plain,
( ( ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) )
!= falsehood )
| ( falsehood != a )
| ( ( a @ ( falsehood @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(1461,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,423]) ).
thf(1462,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) @ ( C @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[1461]) ).
thf(1463,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[1462:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L @ ( K @ implies ) @ ( I @ implies ) @ ( L @ implies ) ))]]) ).
thf(1512,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[1463]) ).
thf(161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ~ $true
| ( E @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[11,59]) ).
thf(162,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= D )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[163]) ).
thf(766,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[66,423]) ).
thf(767,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[766]) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[767:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ implies ) ))]]) ).
thf(775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[768]) ).
thf(2792,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,775]) ).
thf(2793,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( ( F @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2792]) ).
thf(2794,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2793:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ ( falsehood @ ( L @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2815,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ ( E @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2794]) ).
thf(5824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,489]) ).
thf(5825,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[5824]) ).
thf(5826,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[5825:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) )),bind(D,$thf( G ))]]) ).
thf(5884,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ ( C @ ( B @ implies ) @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[5826]) ).
thf(409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,259]) ).
thf(410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( falsehood @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[409]) ).
thf(411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[410:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( falsehood @ implies ) @ ( H @ implies ) @ ( F @ implies ) ))]]) ).
thf(422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[411]) ).
thf(2636,plain,
( ( ( falsehood @ ( c @ implies ) @ ( b @ ( a @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) ) )
| ( ( a @ ( c @ implies ) )
!= falsehood )
| ( e != a ) ),
inference(simp,[status(thm)],[2635]) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,92]) ).
thf(100,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) @ is_a_theorem )
!= ( falsehood @ is_a_theorem ) ),
inference(simp,[status(thm)],[99]) ).
thf(107,plain,
! [A: $i] :
( ( A @ ( falsehood @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[100]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,225]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[270]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( B @ ( falsehood @ implies ) @ ( A @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(3274,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2721,206]) ).
thf(3275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[3274]) ).
thf(3276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[3275:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( M @ implies ) @ implies ) @ implies ) ))]]) ).
thf(3347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( D @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3276]) ).
thf(4631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ( ( B @ ( D @ ( falsehood @ implies ) @ ( C @ implies ) @ implies ) )
!= c ) ),
inference(simp,[status(thm)],[2320]) ).
thf(2766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2715,259]) ).
thf(2767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( falsehood @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ ( C @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[2766]) ).
thf(2768,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[2767:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( F @ ( falsehood @ ( J @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(2810,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( falsehood @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[2768]) ).
thf(8897,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1183,491]) ).
thf(8898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ implies ) @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) @ ( E @ ( C @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ) ),
inference(simp,[status(thm)],[8897]) ).
thf(8899,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[8898:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(9038,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( B @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[8899]) ).
thf(1528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1342,475]) ).
thf(1529,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( falsehood @ ( c @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1528]) ).
thf(1582,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) )
!= ( falsehood @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(3488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) )
!= falsehood )
| ( A != c ) ),
inference(simp,[status(thm)],[1881]) ).
thf(3489,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ ( c @ implies ) @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[3488]) ).
thf(1446,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 ) )
!= falsehood )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1182,206]) ).
thf(1447,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 ) )
!= falsehood ) ),
inference(simp,[status(thm)],[1446]) ).
thf(1448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(pattern_uni,[status(thm)],[1447:[bind(A,$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(1505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) )
!= falsehood ),
inference(simp,[status(thm)],[1448]) ).
thf(2113,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1504,66]) ).
thf(2114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ implies ) @ ( B @ implies ) @ ( D @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2113]) ).
thf(2115,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2114:[bind(A,$thf( G )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( M @ implies ) @ ( K @ implies ) @ ( N @ implies ) @ ( G @ implies ) ))]]) ).
thf(2138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ implies ) @ ( C @ implies ) @ ( E @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2115]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,199]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[219]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( c @ implies ) @ ( a @ ( falsehood @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(936,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[492,259]) ).
thf(937,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ ( C @ ( falsehood @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( E @ ( D @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[936]) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(pattern_uni,[status(thm)],[937:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( M @ ( L @ implies ) @ ( M @ ( K @ ( falsehood @ implies ) @ implies ) @ implies ) ))]]) ).
thf(972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ implies ) @ ( D @ ( B @ ( falsehood @ implies ) @ implies ) @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[938]) ).
thf(2205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1602,66]) ).
thf(2206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( F @ ( E @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2205]) ).
thf(2207,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[2206:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( N )),bind(E,$thf( E )),bind(F,$thf( N @ ( N @ implies ) @ ( K @ implies ) @ ( I @ implies ) @ ( G @ implies ) ))]]) ).
thf(2238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( E @ implies ) @ ( D @ implies ) @ ( C @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[2207]) ).
thf(23419,plain,
$false,
inference(e,[status(thm)],[69,7427,1190,2341,347,2921,962,1179,1110,1879,1337,6587,2512,7358,1882,2808,1692,1173,977,170,10,384,3332,3338,1260,1342,6391,385,1095,2227,782,5745,6583,1601,320,2819,257,25,1254,14,2916,1792,8089,785,4761,3776,8069,2897,110,2708,1264,6350,2049,1609,152,228,4632,1494,1875,261,475,492,8065,966,1183,1334,211,1020,348,602,61,293,988,243,1600,8094,527,147,2058,1351,9035,206,2586,292,60,4589,529,7037,2621,2905,714,2805,1021,7353,1255,7428,3778,1883,862,349,28,1676,5455,1502,297,70,424,3239,3233,693,21,6356,2132,2414,92,229,1602,65,6402,2228,1089,317,2801,1794,2895,1111,169,3237,1498,9,1587,783,420,2798,488,225,1182,537,3596,526,489,2317,109,256,212,706,393,13,2052,1266,3354,1759,1393,73,244,1086,2043,5447,1515,1895,6400,530,965,4613,1273,64,1595,296,2894,601,8290,32,975,5456,423,694,22,843,291,59,8092,4590,1256,259,12,1371,144,3340,1258,3568,2319,1675,71,391,1503,3487,8059,2624,2637,419,5901,7,318,2802,208,1175,2510,604,2721,3352,9015,4073,387,2812,345,5894,323,5439,3971,1177,108,2710,8633,1339,6353,3572,213,848,700,66,240,2410,1171,983,6394,780,394,2797,299,226,241,167,2506,1176,608,490,255,2629,1340,1181,209,487,712,2715,63,1611,95,3833,1252,8096,1267,9022,525,2060,707,1499,199,1432,1262,7351,2044,5450,5902,1023,2320,11,1504,571,5895,2584,1585,386,1881,2807,845,2045,1180,4763,495,2626,1084,2342,4463,1253,961,1341,7359,2135,258,390,2811,3235,23,6584,8,207,346,214,2796,290,58,151,1512,967,168,6563,30,1876,2815,5884,422,2636,210,107,242,294,1495,3347,4631,6398,696,6351,2810,9038,1582,3489,1500,62,691,1505,501,2138,3341,227,2321,491,972,2238,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % 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
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 21:44:47 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 1.27/1.27 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.79/1.55 % [INFO] Parsing done (276ms).
% 1.79/1.58 % [INFO] Running in sequential loop mode.
% 2.89/2.22 % [INFO] eprover registered as external prover.
% 2.89/2.23 % [INFO] Scanning for conjecture ...
% 3.08/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 3.23/2.42 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 3.23/2.44 % [INFO] Problem is propositional (TPTP CNF).
% 3.23/2.44 % [INFO] Type checking passed.
% 3.23/2.45 % [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 ...
% 133.92/33.05 % External prover 'e' found a proof!
% 133.92/33.05 % [INFO] Killing All external provers ...
% 134.85/33.06 % Time passed: 32455ms (effective reasoning time: 31472ms)
% 134.85/33.06 % Axioms used in derivation (5): c0_4, condensed_detachment, c0_1, c0_3, c0_2
% 134.85/33.06 % No. of inferences in proof: 1082
% 134.85/33.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 32455 ms resp. 31472 ms w/o parsing
% 123.83/33.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 123.83/33.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------