%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV570+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 08:48:11 AM UTC 2026
% Result : Theorem 212.00s 60.29s
% Output : Refutation 205.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 43
% Syntax : Number of formulae : 1738 ( 680 unt; 0 typ; 17 def)
% Number of atoms : 4794 (1596 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 18695 (2534 ~;1391 |; 281 &;14374 @)
% ( 21 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 3 con; 0-2 aty)
% Number of variables : 3522 ( 19 ^;3405 !; 81 ?;3522 :)
% ( 0 !>; 0 ?*; 0 @-; 17 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subq_decl,type,
subq: $i > $i > $o ).
thf(u_decl,type,
u: $i > $i > $i ).
thf(a_decl,type,
a: $i > $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(n_decl,type,
n: $i > $i ).
thf(e_decl,type,
e: $i ).
thf(mem_decl,type,
mem: $i > $i > $o ).
thf(m_decl,type,
m: $i > $i > $i ).
thf(disj_decl,type,
disj: $i > $i > $o ).
thf(atleast9p_decl,type,
atleast9p: $i > $o ).
thf(atleast8p_decl,type,
atleast8p: $i > $o ).
thf(atleast7p_decl,type,
atleast7p: $i > $o ).
thf(atleast6p_decl,type,
atleast6p: $i > $o ).
thf(atleast5p_decl,type,
atleast5p: $i > $o ).
thf(atleast12p_decl,type,
atleast12p: $i > $o ).
thf(atleast11p_decl,type,
atleast11p: $i > $o ).
thf(p_decl,type,
p: $i > $i ).
thf(atleast2p_decl,type,
atleast2p: $i > $o ).
thf(atleast10p_decl,type,
atleast10p: $i > $o ).
thf(atleast16p_decl,type,
atleast16p: $i > $o ).
thf(atleast15p_decl,type,
atleast15p: $i > $o ).
thf(atleast4p_decl,type,
atleast4p: $i > $o ).
thf(atleast3p_decl,type,
atleast3p: $i > $o ).
thf(atleast14p_decl,type,
atleast14p: $i > $o ).
thf(atleast13p_decl,type,
atleast13p: $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( C @ mem ) )
& ( B @ ( C @ mem ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast8p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast7p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast5p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast6p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast11p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ p @ ( A @ subq ) )
& ( A @ ( B @ mem ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast9p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast15p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast4p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast2p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast3p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast14p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast10p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast12p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast13p )
& ( A @ ( B @ subq ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ mem ) )
=> ( A @ ( C @ mem ) ) ) ) ) ).
thf(9,axiom,
! [A: $i] :
~ ( e @ ( A @ mem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_ax) ).
thf(67,plain,
! [A: $i] :
~ ( e @ ( A @ mem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(68,plain,
~ ? [A: $i] : ( e @ ( A @ mem ) ),
inference(miniscope,[status(thm)],[67]) ).
thf(69,plain,
! [A: $i] :
~ ( e @ ( A @ mem ) ),
inference(cnf,[status(esa)],[68]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ atleast16p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast15p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast16p_def) ).
thf(134,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast15p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast16p ) )
& ( ( A @ atleast16p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast15p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(135,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast15p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast16p ) )
& ! [A: $i] :
( ( A @ atleast16p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast15p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[134]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast16p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast15p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk9 @ ( A @ subq ) )
| ~ ( A @ atleast16p ) )
& ( ( A @ sk9 @ atleast15p )
| ~ ( A @ atleast16p ) )
& ( ( A @ ( A @ sk9 @ subq ) )
| ~ ( A @ atleast16p ) ) ),
inference(cnf,[status(esa)],[135]) ).
thf(138,plain,
! [A: $i] :
( ( A @ sk9 @ atleast15p )
| ~ ( A @ atleast16p ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ n )
= ( A @ ( A @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_def) ).
thf(70,plain,
! [A: $i] :
( ( A @ n )
= ( A @ ( A @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(71,plain,
! [A: $i] :
( ( A @ n )
= ( A @ ( A @ a ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(72,plain,
! [A: $i] :
( ( A @ ( A @ a ) )
= ( A @ n ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ a ) )
= ( B @ s @ ( A @ u ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_def) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ a ) )
= ( B @ s @ ( A @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ a ) )
= ( B @ s @ ( A @ u ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ a ) )
= ( B @ s @ ( A @ u ) ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(210,plain,
! [A: $i] :
( ( A @ s @ ( A @ u ) )
= ( A @ n ) ),
inference(rewrite,[status(thm)],[72,66]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ mem ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_ax) ).
thf(97,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( B @ s @ ( A @ mem ) ) )
& ( ( B @ s @ ( A @ mem ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(98,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( B @ s @ ( A @ mem ) ) )
& ! [A: $i,B: $i] :
( ( B @ s @ ( A @ mem ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[97]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ s @ ( C @ mem ) )
| ( C != D ) )
& ( ( A = B )
| ~ ( B @ s @ ( A @ mem ) ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ mem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ mem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(104,plain,
! [A: $i] : ( A @ s @ ( A @ mem ) ),
inference(simp,[status(thm)],[103]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ u ) @ ( A @ mem ) )
<=> ( ( C @ ( A @ mem ) )
| ( B @ ( A @ mem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_ax) ).
thf(81,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ mem ) )
| ( B @ ( A @ mem ) ) )
=> ( C @ ( B @ u ) @ ( A @ mem ) ) )
& ( ( C @ ( B @ u ) @ ( A @ mem ) )
=> ( ( C @ ( A @ mem ) )
| ( B @ ( A @ mem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(82,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ mem ) )
| ( B @ ( A @ mem ) ) )
=> ( C @ ( B @ u ) @ ( A @ mem ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ u ) @ ( A @ mem ) )
=> ( ( C @ ( A @ mem ) )
| ( B @ ( A @ mem ) ) ) ) ),
inference(miniscope,[status(thm)],[81]) ).
thf(83,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ u ) @ ( D @ mem ) )
| ~ ( F @ ( D @ mem ) ) )
& ( ( F @ ( E @ u ) @ ( D @ mem ) )
| ~ ( E @ ( D @ mem ) ) )
& ( ( C @ ( A @ mem ) )
| ( B @ ( A @ mem ) )
| ~ ( C @ ( B @ u ) @ ( A @ mem ) ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ u ) @ ( A @ mem ) )
| ~ ( B @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ u ) @ ( A @ mem ) )
| ~ ( B @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(10974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,87]) ).
thf(10975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[10974]) ).
thf(10976,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10975:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ s ))]]) ).
thf(11004,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10976]) ).
thf(11064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ s @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,11004]) ).
thf(11065,plain,
! [A: $i] : ( A @ s @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[11064:[bind(A,$thf( F @ s )),bind(B,$thf( F @ s @ s )),bind(C,$thf( F ))]]) ).
thf(11080,plain,
! [A: $i] : ( A @ s @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[11065]) ).
thf(11102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,87]) ).
thf(11103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[11102]) ).
thf(11104,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[11103:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ s @ n )),bind(D,$thf( D ))]]) ).
thf(11129,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[11104]) ).
thf(11353,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ s @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,11129]) ).
thf(11354,plain,
! [A: $i] : ( A @ s @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[11353:[bind(A,$thf( H @ s @ n )),bind(B,$thf( H @ s @ n @ s )),bind(C,$thf( H ))]]) ).
thf(11372,plain,
! [A: $i] : ( A @ s @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[11354]) ).
thf(1,conjecture,
~ ( e @ n @ n @ ( e @ n @ s @ a ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ a ) @ ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ ( e @ n @ s @ n @ s @ a ) @ u ) @ subq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nsubq_1216_1152) ).
thf(2,negated_conjecture,
~ ~ ( e @ n @ n @ ( e @ n @ s @ a ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ a ) @ ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ ( e @ n @ s @ n @ s @ a ) @ u ) @ subq ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(28,plain,
~ ~ ( e @ n @ n @ ( e @ n @ s @ a ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ a ) @ ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ ( e @ n @ s @ n @ s @ a ) @ u ) @ subq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,plain,
e @ n @ n @ ( e @ n @ s @ a ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ a ) @ ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ ( e @ n @ s @ n @ s @ a ) @ u ) @ subq ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(211,plain,
e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ),
inference(rewrite,[status(thm)],[29,66]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ atleast9p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast8p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast9p_def) ).
thf(45,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast8p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast9p ) )
& ( ( A @ atleast9p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast8p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast8p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast9p ) )
& ! [A: $i] :
( ( A @ atleast9p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast8p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[45]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast9p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast8p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk2 @ ( A @ subq ) )
| ~ ( A @ atleast9p ) )
& ( ( A @ sk2 @ atleast8p )
| ~ ( A @ atleast9p ) )
& ( ( A @ ( A @ sk2 @ subq ) )
| ~ ( A @ atleast9p ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(50,plain,
! [A: $i] :
( ~ ( A @ sk2 @ ( A @ subq ) )
| ~ ( A @ atleast9p ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(216,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk2 @ ( A @ subq ) ) )
| ~ $true
| ~ ( A @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[211,50]) ).
thf(217,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk2 @ ( A @ subq ) ) )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[216]) ).
thf(219,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( A @ sk2 ) )
| ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) )
!= A )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[217]) ).
thf(221,plain,
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk2 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast9p ) ),
inference(simp,[status(thm)],[219]) ).
thf(38711,plain,
( ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk2 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast9p ) ),
inference(rewrite,[status(thm)],[221,66]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ ( B @ s @ ( A @ mem ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ u ) @ ( A @ mem ) )
| ~ ( C @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ u ) @ ( A @ mem ) )
| ~ ( C @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(12118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,88]) ).
thf(12119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[12118]) ).
thf(12120,plain,
! [B: $i,A: $i] : ( B @ s @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[12119:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ s ))]]) ).
thf(12156,plain,
! [B: $i,A: $i] : ( B @ s @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[12120]) ).
thf(12497,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( C @ s @ ( B @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,12156]) ).
thf(12498,plain,
! [A: $i] : ( A @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[12497:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(13336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,87]) ).
thf(13337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[13336]) ).
thf(13338,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[13337:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ n ))]]) ).
thf(13371,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[13338]) ).
thf(13904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,13371]) ).
thf(13905,plain,
! [A: $i] : ( A @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[13904:[bind(A,$thf( F @ n )),bind(B,$thf( F @ n @ s )),bind(C,$thf( F ))]]) ).
thf(13918,plain,
! [A: $i] : ( A @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[13905]) ).
thf(13327,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,69]) ).
thf(13328,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[13327]) ).
thf(13358,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[13328]) ).
thf(13368,plain,
! [A: $i] :
( ( A @ n )
!= e ),
inference(simp,[status(thm)],[13358]) ).
thf(15200,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n ) )
| ( A != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,13368]) ).
thf(15201,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( B @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[15200:[bind(A,$thf( A )),bind(B,$thf( D @ n )),bind(C,$thf( D ))]]) ).
thf(16681,plain,
! [A: $i] :
~ ( A @ n @ s @ ( e @ mem ) ),
inference(simp,[status(thm)],[15201]) ).
thf(17723,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,16681]) ).
thf(17724,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17723]) ).
thf(17728,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17724]) ).
thf(17737,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[17728]) ).
thf(18845,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ( B
!= ( C @ n @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17737]) ).
thf(18846,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n @ s ) )
| ~ ( A @ s @ ( e @ n @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18845:[bind(A,$thf( e @ n @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(18906,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ n @ n @ mem ) ),
inference(simp,[status(thm)],[18846]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subq ) )
<=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( B @ ( C @ mem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subq_def) ).
thf(198,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( B @ ( C @ mem ) ) )
=> ( B @ ( A @ subq ) ) )
& ( ( B @ ( A @ subq ) )
=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( B @ ( C @ mem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(199,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( B @ ( C @ mem ) ) )
=> ( B @ ( A @ subq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subq ) )
=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( B @ ( C @ mem ) ) ) ) ),
inference(miniscope,[status(thm)],[198]) ).
thf(200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subq ) )
| ~ ( E @ ( D @ ( E @ sk17 ) @ mem ) ) )
& ( ( E @ ( D @ subq ) )
| ( D @ ( D @ ( E @ sk17 ) @ mem ) ) )
& ( ( B @ ( C @ mem ) )
| ~ ( A @ ( C @ mem ) )
| ~ ( B @ ( A @ subq ) ) ) ),
inference(cnf,[status(esa)],[199]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subq ) )
| ( A @ ( A @ ( B @ sk17 ) @ mem ) ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subq ) )
| ( A @ ( A @ ( B @ sk17 ) @ mem ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subq ) )
| ~ ( B @ ( A @ ( B @ sk17 ) @ mem ) ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subq ) )
| ~ ( B @ ( A @ ( B @ sk17 ) @ mem ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(36534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk17 ) @ mem ) )
!= ( D @ ( C @ ( D @ sk17 ) @ mem ) ) )
| ( D @ ( C @ subq ) )
| ~ $true
| ( B @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[204,205]) ).
thf(36535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk17 ) @ mem ) )
!= ( D @ ( C @ ( D @ sk17 ) @ mem ) ) )
| ( D @ ( C @ subq ) )
| ( B @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[36534]) ).
thf(36536,plain,
! [A: $i] :
( ( A @ ( A @ subq ) )
| ( A @ ( A @ subq ) ) ),
inference(pattern_uni,[status(thm)],[36535:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(36653,plain,
! [A: $i] : ( A @ ( A @ subq ) ),
inference(simp,[status(thm)],[36536]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ p @ ( A @ mem ) )
<=> ( B @ ( A @ subq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_ax) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subq ) )
=> ( B @ p @ ( A @ mem ) ) )
& ( ( B @ p @ ( A @ mem ) )
=> ( B @ ( A @ subq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(114,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subq ) )
=> ( B @ p @ ( A @ mem ) ) )
& ! [A: $i,B: $i] :
( ( B @ p @ ( A @ mem ) )
=> ( B @ ( A @ subq ) ) ) ),
inference(miniscope,[status(thm)],[113]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ p @ ( C @ mem ) )
| ~ ( D @ ( C @ subq ) ) )
& ( ( B @ ( A @ subq ) )
| ~ ( B @ p @ ( A @ mem ) ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ p @ ( A @ mem ) )
| ~ ( B @ ( A @ subq ) ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B @ p @ ( A @ mem ) )
| ~ ( B @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(36727,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36653,118]) ).
thf(36728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[36727]) ).
thf(36729,plain,
! [A: $i] : ( A @ p @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[36728:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(36888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,87]) ).
thf(36889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[36888]) ).
thf(36890,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[36889:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ p ))]]) ).
thf(36961,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[36890]) ).
thf(40483,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,36961]) ).
thf(40484,plain,
! [A: $i] : ( A @ p @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[40483:[bind(A,$thf( F @ p )),bind(B,$thf( F @ p @ s )),bind(C,$thf( F ))]]) ).
thf(40528,plain,
! [A: $i] : ( A @ p @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[40484]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ m ) @ ( A @ mem ) )
<=> ( ~ ( C @ ( A @ mem ) )
& ( B @ ( A @ mem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_ax) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ mem ) )
& ( B @ ( A @ mem ) ) )
=> ( C @ ( B @ m ) @ ( A @ mem ) ) )
& ( ( C @ ( B @ m ) @ ( A @ mem ) )
=> ( ~ ( C @ ( A @ mem ) )
& ( B @ ( A @ mem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(31,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( A @ mem ) )
& ( B @ ( A @ mem ) ) )
=> ( C @ ( B @ m ) @ ( A @ mem ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ m ) @ ( A @ mem ) )
=> ( ~ ( C @ ( A @ mem ) )
& ( B @ ( A @ mem ) ) ) ) ),
inference(miniscope,[status(thm)],[30]) ).
thf(32,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ m ) @ ( D @ mem ) )
| ( F @ ( D @ mem ) )
| ~ ( E @ ( D @ mem ) ) )
& ( ~ ( C @ ( A @ mem ) )
| ~ ( C @ ( B @ m ) @ ( A @ mem ) ) )
& ( ( B @ ( A @ mem ) )
| ~ ( C @ ( B @ m ) @ ( A @ mem ) ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ mem ) )
| ~ ( C @ ( B @ m ) @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk17 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ( D @ ( C @ mem ) )
| ~ $true
| ( B @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[204,33]) ).
thf(695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk17 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ( D @ ( C @ mem ) )
| ( B @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[694]) ).
thf(696,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[695:[bind(A,$thf( I @ ( H @ m ) )),bind(B,$thf( F )),bind(C,$thf( I @ ( H @ m ) @ ( F @ sk17 ) )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(simp,[status(thm)],[696]) ).
thf(7071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
!= ( e @ ( D @ mem ) ) )
| ~ $true
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[715,69]) ).
thf(7072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
!= ( e @ ( D @ mem ) ) )
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(simp,[status(thm)],[7071]) ).
thf(7073,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( e @ m ) @ subq ) ),
inference(pattern_uni,[status(thm)],[7072:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( H )),bind(D,$thf( H @ ( e @ m ) @ ( E @ sk17 ) ))]]) ).
thf(7107,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( e @ m ) @ subq ) ),
inference(simp,[status(thm)],[7073]) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk17 ) @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true
| ( B @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[204,69]) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk17 ) @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ( B @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[706]) ).
thf(708,plain,
! [A: $i] : ( A @ ( e @ subq ) ),
inference(pattern_uni,[status(thm)],[707:[bind(A,$thf( e )),bind(B,$thf( D )),bind(C,$thf( e @ ( D @ sk17 ) ))]]) ).
thf(713,plain,
! [A: $i] : ( A @ ( e @ subq ) ),
inference(simp,[status(thm)],[708]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subq ) )
=> ( ( A @ ( B @ subq ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subq ) )
=> ( ( A @ ( B @ subq ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subq ) )
| ~ ( B @ ( A @ subq ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subq ) )
| ~ ( B @ ( A @ subq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(3036,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ~ ( B @ ( C @ subq ) )
| ~ $true
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[713,55]) ).
thf(3037,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ~ ( B @ ( C @ subq ) )
| ( B = C ) ),
inference(simp,[status(thm)],[3036]) ).
thf(3038,plain,
! [A: $i] :
( ~ ( e @ ( A @ subq ) )
| ( e = A ) ),
inference(pattern_uni,[status(thm)],[3037:[bind(A,$thf( A )),bind(B,$thf( e )),bind(C,$thf( A ))]]) ).
thf(7629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ subq ) ) )
| ~ $true
| ( e = C ) ),
inference(paramod_ordered,[status(thm)],[7107,3038]) ).
thf(7630,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ subq ) ) )
| ( e = C ) ),
inference(simp,[status(thm)],[7629]) ).
thf(7631,plain,
! [A: $i] :
( ( A @ ( e @ m ) )
= e ),
inference(pattern_uni,[status(thm)],[7630:[bind(A,$thf( e )),bind(B,$thf( E )),bind(C,$thf( E @ ( e @ m ) ))]]) ).
thf(7681,plain,
! [A: $i] :
( ( A @ ( e @ m ) )
= e ),
inference(simp,[status(thm)],[7631]) ).
thf(7775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ m ) )
!= ( D @ ( C @ m ) ) )
| ( C @ ( e @ ( B @ sk17 ) @ mem ) )
| ( B @ ( D @ ( C @ m ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[7681,715]) ).
thf(7776,plain,
! [B: $i,A: $i] :
( ( e @ ( e @ ( B @ sk17 ) @ mem ) )
| ( B @ ( A @ ( e @ m ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[7775:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( e )),bind(D,$thf( A ))]]) ).
thf(8580,plain,
! [A: $i] :
( $false
| ( A @ ( e @ subq ) ) ),
inference(rewrite,[status(thm)],[7776,7681,69]) ).
thf(8581,plain,
! [A: $i] : ( A @ ( e @ subq ) ),
inference(simp,[status(thm)],[8580]) ).
thf(19090,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8581,118]) ).
thf(19091,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19090]) ).
thf(19092,plain,
! [A: $i] : ( A @ p @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19091:[bind(A,$thf( A )),bind(B,$thf( e )),bind(C,$thf( A ))]]) ).
thf(19169,plain,
! [A: $i] : ( A @ p @ ( e @ mem ) ),
inference(simp,[status(thm)],[19092]) ).
thf(19186,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,69]) ).
thf(19187,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19186]) ).
thf(19249,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[19187]) ).
thf(19274,plain,
! [A: $i] :
( ( A @ p )
!= e ),
inference(simp,[status(thm)],[19249]) ).
thf(19284,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p ) )
| ( B != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19274]) ).
thf(19285,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( A @ s @ ( B @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19284:[bind(A,$thf( D @ p )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(19295,plain,
! [A: $i] :
~ ( e @ s @ ( A @ p @ mem ) ),
inference(simp,[status(thm)],[19285]) ).
thf(19468,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,19295]) ).
thf(19469,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19468]) ).
thf(19511,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19469]) ).
thf(19548,plain,
! [A: $i] :
( ( A @ p @ s )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19511]) ).
thf(19964,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19548]) ).
thf(19965,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19964:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(19992,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[19965]) ).
thf(41044,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,19992]) ).
thf(41045,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[41044]) ).
thf(41094,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[41045]) ).
thf(41127,plain,
! [A: $i] :
( ( A @ p @ s @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41094]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ atleast15p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast14p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast15p_def) ).
thf(166,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast14p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast15p ) )
& ( ( A @ atleast15p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast14p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(167,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast14p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast15p ) )
& ! [A: $i] :
( ( A @ atleast15p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast14p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[166]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast15p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast14p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk13 @ ( A @ subq ) )
| ~ ( A @ atleast15p ) )
& ( ( A @ sk13 @ atleast14p )
| ~ ( A @ atleast15p ) )
& ( ( A @ ( A @ sk13 @ subq ) )
| ~ ( A @ atleast15p ) ) ),
inference(cnf,[status(esa)],[167]) ).
thf(171,plain,
! [A: $i] :
( ~ ( A @ sk13 @ ( A @ subq ) )
| ~ ( A @ atleast15p ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(29803,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk13 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast15p ) ),
inference(paramod_ordered,[status(thm)],[8581,171]) ).
thf(29804,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk13 @ ( B @ subq ) ) )
| ~ ( B @ atleast15p ) ),
inference(simp,[status(thm)],[29803]) ).
thf(29805,plain,
~ ( e @ atleast15p ),
inference(pattern_uni,[status(thm)],[29804:[bind(A,$thf( e @ sk13 )),bind(B,$thf( e ))]]) ).
thf(15198,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n ) )
| ( B != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,13368]) ).
thf(15199,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( A @ s @ ( B @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[15198:[bind(A,$thf( D @ n )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(16680,plain,
! [A: $i] :
~ ( e @ s @ ( A @ n @ mem ) ),
inference(simp,[status(thm)],[15199]) ).
thf(17225,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,16680]) ).
thf(17226,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[17225]) ).
thf(17255,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[17226]) ).
thf(17282,plain,
! [A: $i] :
( ( A @ n @ s )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17255]) ).
thf(17921,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ s ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17282]) ).
thf(17922,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ n @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17921:[bind(A,$thf( A )),bind(B,$thf( E @ n @ s )),bind(C,$thf( E ))]]) ).
thf(17940,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[17922]) ).
thf(23184,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,17940]) ).
thf(23185,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[23184]) ).
thf(23233,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[23185]) ).
thf(23272,plain,
! [A: $i] :
( ( A @ n @ s @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23233]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,69]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[207]) ).
thf(209,plain,
! [A: $i] :
( ( A @ s )
!= e ),
inference(simp,[status(thm)],[208]) ).
thf(15466,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s ) )
| ( B != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,209]) ).
thf(15467,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( A @ s @ ( B @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[15466:[bind(A,$thf( D @ s )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(16774,plain,
! [A: $i] :
~ ( e @ s @ ( A @ s @ mem ) ),
inference(simp,[status(thm)],[15467]) ).
thf(17471,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,16774]) ).
thf(17472,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[17471]) ).
thf(17495,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[17472]) ).
thf(17520,plain,
! [A: $i] :
( ( A @ s @ s )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17495]) ).
thf(18011,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17520]) ).
thf(18012,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18011:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18038,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[18012]) ).
thf(24583,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,18038]) ).
thf(24584,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[24583]) ).
thf(24723,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[24584]) ).
thf(24747,plain,
! [A: $i] :
( ( A @ s @ s @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24723]) ).
thf(36864,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,18038]) ).
thf(36865,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[36864]) ).
thf(36934,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[36865]) ).
thf(36949,plain,
! [A: $i] :
( ( A @ s @ s @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[36934]) ).
thf(17241,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,16680]) ).
thf(17242,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[17241]) ).
thf(17246,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[17242]) ).
thf(17271,plain,
! [A: $i] :
( ( A @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17246]) ).
thf(17890,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ n ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17271]) ).
thf(17891,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ n @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17890:[bind(A,$thf( A )),bind(B,$thf( E @ n @ n )),bind(C,$thf( E ))]]) ).
thf(17908,plain,
! [A: $i] :
~ ( A @ n @ n @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[17891]) ).
thf(41023,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,17908]) ).
thf(41024,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41023]) ).
thf(41111,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41024]) ).
thf(41144,plain,
! [A: $i] :
( ( e @ s @ p @ n )
!= ( A @ n @ n @ s ) ),
inference(simp,[status(thm)],[41111]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ atleast3p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast2p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast3p_def) ).
thf(150,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast2p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast3p ) )
& ( ( A @ atleast3p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast2p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(151,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast2p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast3p ) )
& ! [A: $i] :
( ( A @ atleast3p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast2p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[150]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast3p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast2p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk11 @ ( A @ subq ) )
| ~ ( A @ atleast3p ) )
& ( ( A @ sk11 @ atleast2p )
| ~ ( A @ atleast3p ) )
& ( ( A @ ( A @ sk11 @ subq ) )
| ~ ( A @ atleast3p ) ) ),
inference(cnf,[status(esa)],[151]) ).
thf(155,plain,
! [A: $i] :
( ~ ( A @ sk11 @ ( A @ subq ) )
| ~ ( A @ atleast3p ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(25620,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk11 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast3p ) ),
inference(paramod_ordered,[status(thm)],[8581,155]) ).
thf(25621,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk11 @ ( B @ subq ) ) )
| ~ ( B @ atleast3p ) ),
inference(simp,[status(thm)],[25620]) ).
thf(25622,plain,
~ ( e @ atleast3p ),
inference(pattern_uni,[status(thm)],[25621:[bind(A,$thf( e @ sk11 )),bind(B,$thf( e ))]]) ).
thf(19286,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p ) )
| ( A != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19274]) ).
thf(19287,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( B @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19286:[bind(A,$thf( A )),bind(B,$thf( D @ p )),bind(C,$thf( D ))]]) ).
thf(19296,plain,
! [A: $i] :
~ ( A @ p @ s @ ( e @ mem ) ),
inference(simp,[status(thm)],[19287]) ).
thf(36866,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,19296]) ).
thf(36867,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[36866]) ).
thf(36913,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[36867]) ).
thf(36971,plain,
! [A: $i] :
( ( e @ p )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[36913]) ).
thf(19223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,87]) ).
thf(19224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19223]) ).
thf(19225,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19224:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( E @ p ))]]) ).
thf(19266,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[19225]) ).
thf(20132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,19266]) ).
thf(20133,plain,
! [A: $i] : ( A @ p @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20132:[bind(A,$thf( F @ p )),bind(B,$thf( F @ p @ s )),bind(C,$thf( F ))]]) ).
thf(20165,plain,
! [A: $i] : ( A @ p @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[20133]) ).
thf(20384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20165,87]) ).
thf(20385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[20384]) ).
thf(20386,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20385:[bind(A,$thf( F )),bind(B,$thf( e )),bind(C,$thf( F @ p @ n )),bind(D,$thf( D ))]]) ).
thf(20445,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20386]) ).
thf(21348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,20445]) ).
thf(21349,plain,
! [A: $i] : ( A @ p @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[21348:[bind(A,$thf( H @ p @ n )),bind(B,$thf( H @ p @ n @ s )),bind(C,$thf( H ))]]) ).
thf(21386,plain,
! [A: $i] : ( A @ p @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[21349]) ).
thf(21599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21386,87]) ).
thf(21600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[21599]) ).
thf(21601,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[21600:[bind(A,$thf( G )),bind(B,$thf( e )),bind(C,$thf( G @ p @ n @ n )),bind(D,$thf( D ))]]) ).
thf(21665,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[21601]) ).
thf(24389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ n @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,21665]) ).
thf(24390,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[24389:[bind(A,$thf( J @ p @ n @ n )),bind(B,$thf( J @ p @ n @ n @ s )),bind(C,$thf( J ))]]) ).
thf(24434,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[24390]) ).
thf(25401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24434,88]) ).
thf(25402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[25401]) ).
thf(25403,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[25402:[bind(A,$thf( H )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( H @ p @ n @ n @ n ))]]) ).
thf(25563,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[25403]) ).
thf(15468,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s ) )
| ( A != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,209]) ).
thf(15469,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( B @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[15468:[bind(A,$thf( A )),bind(B,$thf( D @ s )),bind(C,$thf( D ))]]) ).
thf(16775,plain,
! [A: $i] :
~ ( A @ s @ s @ ( e @ mem ) ),
inference(simp,[status(thm)],[15469]) ).
thf(41092,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,16775]) ).
thf(41093,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[41092]) ).
thf(41117,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[41093]) ).
thf(41150,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[41117]) ).
thf(49,plain,
! [A: $i] :
( ( A @ sk2 @ atleast8p )
| ~ ( A @ atleast9p ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ atleast8p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast7p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast8p_def) ).
thf(56,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast7p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast8p ) )
& ( ( A @ atleast8p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast7p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(57,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast7p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast8p ) )
& ! [A: $i] :
( ( A @ atleast8p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast7p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[56]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast8p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast7p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk3 @ ( A @ subq ) )
| ~ ( A @ atleast8p ) )
& ( ( A @ sk3 @ atleast7p )
| ~ ( A @ atleast8p ) )
& ( ( A @ ( A @ sk3 @ subq ) )
| ~ ( A @ atleast8p ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(61,plain,
! [A: $i] :
( ~ ( A @ sk3 @ ( A @ subq ) )
| ~ ( A @ atleast8p ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( B @ atleast8p ) )
| ~ ( B @ sk3 @ ( B @ subq ) )
| ~ $true
| ~ ( A @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[49,61]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( B @ atleast8p ) )
| ~ ( B @ sk3 @ ( B @ subq ) )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [A: $i] :
( ~ ( A @ sk2 @ sk3 @ ( A @ sk2 @ subq ) )
| ~ ( A @ atleast9p ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( C )),bind(B,$thf( C @ sk2 ))]]) ).
thf(276,plain,
! [A: $i] :
( ~ ( A @ sk2 @ sk3 @ ( A @ sk2 @ subq ) )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[275]) ).
thf(17487,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,16774]) ).
thf(17488,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[17487]) ).
thf(17497,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[17488]) ).
thf(17522,plain,
! [A: $i] :
( ( A @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17497]) ).
thf(18292,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ n ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17522]) ).
thf(18293,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ s @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18292:[bind(A,$thf( A )),bind(B,$thf( E @ s @ n )),bind(C,$thf( E ))]]) ).
thf(18312,plain,
! [A: $i] :
~ ( A @ s @ n @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[18293]) ).
thf(36834,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,18312]) ).
thf(36835,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[36834]) ).
thf(36923,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[36835]) ).
thf(36981,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ s @ n @ s ) ),
inference(simp,[status(thm)],[36923]) ).
thf(17302,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,16681]) ).
thf(17303,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17302]) ).
thf(17376,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17303]) ).
thf(17402,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[17376]) ).
thf(18652,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ s @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17402]) ).
thf(18653,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18652:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18706,plain,
! [A: $i] :
~ ( e @ s @ n @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[18653]) ).
thf(12204,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,69]) ).
thf(12205,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[12204]) ).
thf(12245,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[12205]) ).
thf(12261,plain,
! [A: $i] :
( ( A @ s @ n @ n )
!= e ),
inference(simp,[status(thm)],[12245]) ).
thf(36884,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,19295]) ).
thf(36885,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[36884]) ).
thf(36939,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[36885]) ).
thf(36955,plain,
! [A: $i] :
( ( A @ p @ p )
!= ( e @ s ) ),
inference(simp,[status(thm)],[36939]) ).
thf(37049,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ p ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36955]) ).
thf(37050,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ p @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[37049:[bind(A,$thf( E @ p @ p )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(37074,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ p @ p @ mem ) ),
inference(simp,[status(thm)],[37050]) ).
thf(44249,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37074]) ).
thf(44250,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) ),
inference(simp,[status(thm)],[44249]) ).
thf(44275,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ p ) ) ),
inference(simp,[status(thm)],[44250]) ).
thf(44357,plain,
! [A: $i] :
( ( A @ p @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[44275]) ).
thf(17886,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ n ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17271]) ).
thf(17887,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ n @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17886:[bind(A,$thf( E @ n @ n )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(17914,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ n @ n @ mem ) ),
inference(simp,[status(thm)],[17887]) ).
thf(22906,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,17914]) ).
thf(22907,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[22906]) ).
thf(23047,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[22907]) ).
thf(23056,plain,
! [A: $i] :
( ( A @ n @ n @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23047]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ atleast2p )
<=> ? [B: $i] :
( ~ ( B @ p @ ( A @ subq ) )
& ( A @ ( B @ mem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast2p_def) ).
thf(119,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ p @ ( A @ subq ) )
& ( A @ ( B @ mem ) ) )
=> ( A @ atleast2p ) )
& ( ( A @ atleast2p )
=> ? [B: $i] :
( ~ ( B @ p @ ( A @ subq ) )
& ( A @ ( B @ mem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(120,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ p @ ( A @ subq ) )
& ( A @ ( B @ mem ) ) )
=> ( A @ atleast2p ) )
& ! [A: $i] :
( ( A @ atleast2p )
=> ? [B: $i] :
( ~ ( B @ p @ ( A @ subq ) )
& ( A @ ( B @ mem ) ) ) ) ),
inference(miniscope,[status(thm)],[119]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) )
| ~ ( B @ ( C @ mem ) ) )
& ( ~ ( A @ sk7 @ p @ ( A @ subq ) )
| ~ ( A @ atleast2p ) )
& ( ( A @ ( A @ sk7 @ mem ) )
| ~ ( A @ atleast2p ) ) ),
inference(cnf,[status(esa)],[120]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( A @ atleast2p )
| ( B @ p @ ( A @ subq ) )
| ~ ( A @ ( B @ mem ) ) ),
inference(cnfConj,[status(thm)],[121]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( A @ atleast2p )
| ( B @ p @ ( A @ subq ) )
| ~ ( A @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(20765,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20165,125]) ).
thf(20766,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[20765]) ).
thf(20767,plain,
! [A: $i] :
( ( A @ p @ n @ atleast2p )
| ( e @ p @ ( A @ p @ n @ subq ) ) ),
inference(pattern_uni,[status(thm)],[20766:[bind(A,$thf( E )),bind(B,$thf( E @ p @ n )),bind(C,$thf( e ))]]) ).
thf(20846,plain,
! [A: $i] :
( ( A @ p @ n @ atleast2p )
| ( e @ p @ ( A @ p @ n @ subq ) ) ),
inference(simp,[status(thm)],[20767]) ).
thf(31084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( e @ p @ ( A @ p @ n @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ~ $true
| ( A @ p @ n @ atleast2p ) ),
inference(paramod_ordered,[status(thm)],[20846,118]) ).
thf(31085,plain,
! [C: $i,B: $i,A: $i] :
( ( ( e @ p @ ( A @ p @ n @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ( A @ p @ n @ atleast2p ) ),
inference(simp,[status(thm)],[31084]) ).
thf(31086,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ n @ mem ) )
| ( A @ p @ n @ atleast2p ) ),
inference(pattern_uni,[status(thm)],[31085:[bind(A,$thf( E )),bind(B,$thf( E @ p @ n )),bind(C,$thf( e @ p ))]]) ).
thf(31207,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ n @ mem ) )
| ( A @ p @ n @ atleast2p ) ),
inference(simp,[status(thm)],[31086]) ).
thf(170,plain,
! [A: $i] :
( ( A @ sk13 @ atleast14p )
| ~ ( A @ atleast15p ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(17298,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,16681]) ).
thf(17299,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17298]) ).
thf(17379,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17299]) ).
thf(17407,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[17379]) ).
thf(23106,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,17940]) ).
thf(23107,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[23106]) ).
thf(23229,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[23107]) ).
thf(23268,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[23229]) ).
thf(20340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20165,88]) ).
thf(20341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[20340]) ).
thf(20342,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20341:[bind(A,$thf( F )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( F @ p @ n ))]]) ).
thf(20453,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20342]) ).
thf(21787,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20453,87]) ).
thf(21788,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[21787]) ).
thf(21789,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ p @ n @ ( B @ u ) @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[21788:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( e )),bind(D,$thf( I @ p @ n @ ( F @ u ) )),bind(E,$thf( E ))]]) ).
thf(21850,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ p @ n @ ( B @ u ) @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[21789]) ).
thf(69299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( D @ p @ n @ ( C @ u ) @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,21850]) ).
thf(69300,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[69299:[bind(A,$thf( M @ p @ n @ ( J @ u ) )),bind(B,$thf( M @ p @ n @ ( J @ u ) @ s )),bind(C,$thf( J )),bind(D,$thf( M ))]]) ).
thf(69388,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[69300]) ).
thf(22523,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,17908]) ).
thf(22524,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[22523]) ).
thf(22558,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[22524]) ).
thf(22599,plain,
! [A: $i] :
( ( A @ n @ n @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[22558]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ atleast5p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast4p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast5p_def) ).
thf(142,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast4p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast5p ) )
& ( ( A @ atleast5p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast4p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(41006,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,18312]) ).
thf(41007,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41006]) ).
thf(41112,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ s @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41007]) ).
thf(41145,plain,
! [A: $i] :
( ( e @ s @ p @ n )
!= ( A @ s @ n @ s ) ),
inference(simp,[status(thm)],[41112]) ).
thf(41066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,87]) ).
thf(41067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[41066]) ).
thf(41068,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[41067:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ p @ n )),bind(D,$thf( D ))]]) ).
thf(41169,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[41068]) ).
thf(47396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,41169]) ).
thf(47397,plain,
! [A: $i] : ( A @ p @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[47396:[bind(A,$thf( H @ p @ n )),bind(B,$thf( H @ p @ n @ s )),bind(C,$thf( H ))]]) ).
thf(47454,plain,
! [A: $i] : ( A @ p @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[47397]) ).
thf(49280,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,16775]) ).
thf(49281,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[49280]) ).
thf(49313,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[49281]) ).
thf(49364,plain,
! [A: $i] :
( ( e @ p @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[49313]) ).
thf(19968,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ s ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19548]) ).
thf(19969,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ p @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19968:[bind(A,$thf( A )),bind(B,$thf( E @ p @ s )),bind(C,$thf( E ))]]) ).
thf(19986,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[19969]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ atleast12p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast11p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast12p_def) ).
thf(105,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast11p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast12p ) )
& ( ( A @ atleast12p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast11p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(106,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast11p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast12p ) )
& ! [A: $i] :
( ( A @ atleast12p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast11p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[105]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast12p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast11p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk6 @ ( A @ subq ) )
| ~ ( A @ atleast12p ) )
& ( ( A @ sk6 @ atleast11p )
| ~ ( A @ atleast12p ) )
& ( ( A @ ( A @ sk6 @ subq ) )
| ~ ( A @ atleast12p ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(110,plain,
! [A: $i] :
( ~ ( A @ sk6 @ ( A @ subq ) )
| ~ ( A @ atleast12p ) ),
inference(cnfConj,[status(thm)],[107]) ).
thf(911,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk6 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast12p ) ),
inference(paramod_ordered,[status(thm)],[713,110]) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk6 @ ( B @ subq ) ) )
| ~ ( B @ atleast12p ) ),
inference(simp,[status(thm)],[911]) ).
thf(913,plain,
~ ( e @ atleast12p ),
inference(pattern_uni,[status(thm)],[912:[bind(A,$thf( e @ sk6 )),bind(B,$thf( e ))]]) ).
thf(23108,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,17940]) ).
thf(23109,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[23108]) ).
thf(23247,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[23109]) ).
thf(23283,plain,
! [A: $i] :
( ( e @ s @ s @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[23247]) ).
thf(22445,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,17908]) ).
thf(22446,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[22445]) ).
thf(22561,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[22446]) ).
thf(22602,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ n @ n @ s ) ),
inference(simp,[status(thm)],[22561]) ).
thf(153,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ subq ) )
| ~ ( A @ atleast3p ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(19484,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,19295]) ).
thf(19485,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19484]) ).
thf(19489,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19485]) ).
thf(19522,plain,
! [A: $i] :
( ( A @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19489]) ).
thf(19937,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ n ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19522]) ).
thf(19938,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ p @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19937:[bind(A,$thf( A )),bind(B,$thf( E @ p @ n )),bind(C,$thf( E ))]]) ).
thf(19955,plain,
! [A: $i] :
~ ( A @ p @ n @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[19938]) ).
thf(36822,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,19955]) ).
thf(36823,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[36822]) ).
thf(36927,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[36823]) ).
thf(36986,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ p @ n @ s ) ),
inference(simp,[status(thm)],[36927]) ).
thf(17917,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17282]) ).
thf(17918,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17917:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(17946,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[17918]) ).
thf(28296,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,19986]) ).
thf(28297,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[28296]) ).
thf(28335,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[28297]) ).
thf(28366,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[28335]) ).
thf(19188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,88]) ).
thf(19189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19188]) ).
thf(19190,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19189:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( E @ p ))]]) ).
thf(19278,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[19190]) ).
thf(20612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19278,69]) ).
thf(20613,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[20612]) ).
thf(20698,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) )
!= e )
| ( e != C ) ),
inference(simp,[status(thm)],[20613]) ).
thf(20722,plain,
! [B: $i,A: $i] :
( ( B @ p @ ( A @ u ) )
!= e ),
inference(simp,[status(thm)],[20698]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ atleast11p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast10p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast11p_def) ).
thf(174,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast10p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast11p ) )
& ( ( A @ atleast11p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast10p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19630,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,19296]) ).
thf(19631,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19630]) ).
thf(19651,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19631]) ).
thf(19662,plain,
! [A: $i] :
( ( e @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19651]) ).
thf(19999,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19662]) ).
thf(20000,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19999:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(20037,plain,
! [A: $i] :
~ ( e @ n @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[20000]) ).
thf(28696,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,20037]) ).
thf(28697,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[28696]) ).
thf(28739,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[28697]) ).
thf(28786,plain,
! [A: $i] :
( ( A @ p @ s @ s )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[28739]) ).
thf(17364,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,16681]) ).
thf(17365,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17364]) ).
thf(17374,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17365]) ).
thf(17399,plain,
! [A: $i] :
( ( e @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[17374]) ).
thf(17952,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17399]) ).
thf(17953,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17952:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(17990,plain,
! [A: $i] :
~ ( e @ n @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[17953]) ).
thf(23616,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,17990]) ).
thf(23617,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[23616]) ).
thf(23638,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[23617]) ).
thf(23682,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[23638]) ).
thf(37121,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ s ) )
| ( A
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36971]) ).
thf(37122,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( B @ p @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[37121:[bind(A,$thf( A )),bind(B,$thf( E @ p @ s )),bind(C,$thf( E ))]]) ).
thf(37152,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ p @ mem ) ),
inference(simp,[status(thm)],[37122]) ).
thf(45328,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37152]) ).
thf(45329,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[45328]) ).
thf(45382,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[45329]) ).
thf(45431,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[45382]) ).
thf(36870,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,16774]) ).
thf(36871,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[36870]) ).
thf(36912,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[36871]) ).
thf(36970,plain,
! [A: $i] :
( ( A @ s @ p )
!= ( e @ s ) ),
inference(simp,[status(thm)],[36912]) ).
thf(37079,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ p ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36970]) ).
thf(37080,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ s @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[37079:[bind(A,$thf( E @ s @ p )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(37103,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ s @ p @ mem ) ),
inference(simp,[status(thm)],[37080]) ).
thf(44693,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37103]) ).
thf(44694,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) ),
inference(simp,[status(thm)],[44693]) ).
thf(44839,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ p ) ) ),
inference(simp,[status(thm)],[44694]) ).
thf(44885,plain,
! [A: $i] :
( ( A @ s @ p @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[44839]) ).
thf(23308,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,17946]) ).
thf(23309,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[23308]) ).
thf(23421,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[23309]) ).
thf(23502,plain,
! [A: $i] :
( ( A @ n @ s @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23421]) ).
thf(37053,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ p ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36955]) ).
thf(37054,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ p @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[37053:[bind(A,$thf( A )),bind(B,$thf( E @ p @ p )),bind(C,$thf( E ))]]) ).
thf(37078,plain,
! [A: $i] :
~ ( A @ p @ p @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[37054]) ).
thf(44519,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37078]) ).
thf(44520,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[44519]) ).
thf(44565,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[44520]) ).
thf(44596,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ p @ s ) ),
inference(simp,[status(thm)],[44565]) ).
thf(41042,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,19296]) ).
thf(41043,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[41042]) ).
thf(41099,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[41043]) ).
thf(41132,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[41099]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disj ) )
<=> ~ ? [C: $i] :
( ( B @ ( C @ mem ) )
& ( A @ ( C @ mem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disj_def) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( C @ mem ) )
& ( A @ ( C @ mem ) ) )
=> ( B @ ( A @ disj ) ) )
& ( ( B @ ( A @ disj ) )
=> ~ ? [C: $i] :
( ( B @ ( C @ mem ) )
& ( A @ ( C @ mem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17421,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,16774]) ).
thf(17422,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[17421]) ).
thf(17505,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[17422]) ).
thf(17534,plain,
! [A: $i] :
( ( A @ s @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17505]) ).
thf(41090,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,16681]) ).
thf(41091,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[41090]) ).
thf(41104,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[41091]) ).
thf(41137,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[41104]) ).
thf(41511,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ p @ n ) )
| ( B
!= ( C @ n @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41137]) ).
thf(41512,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n @ s ) )
| ~ ( A @ s @ ( e @ p @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41511:[bind(A,$thf( e @ p @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(41577,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ p @ n @ mem ) ),
inference(simp,[status(thm)],[41512]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ atleast13p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast12p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast13p_def) ).
thf(182,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast12p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast13p ) )
& ( ( A @ atleast13p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast12p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(183,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast12p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast13p ) )
& ! [A: $i] :
( ( A @ atleast13p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast12p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[182]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast13p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast12p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk15 @ ( A @ subq ) )
| ~ ( A @ atleast13p ) )
& ( ( A @ sk15 @ atleast12p )
| ~ ( A @ atleast13p ) )
& ( ( A @ ( A @ sk15 @ subq ) )
| ~ ( A @ atleast13p ) ) ),
inference(cnf,[status(esa)],[183]) ).
thf(185,plain,
! [A: $i] :
( ( A @ ( A @ sk15 @ subq ) )
| ~ ( A @ atleast13p ) ),
inference(cnfConj,[status(thm)],[184]) ).
thf(49220,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,16774]) ).
thf(49221,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[49220]) ).
thf(49287,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[49221]) ).
thf(49332,plain,
! [A: $i] :
( ( A @ s @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[49287]) ).
thf(36910,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,16775]) ).
thf(36911,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[36910]) ).
thf(36936,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[36911]) ).
thf(36951,plain,
! [A: $i] :
( ( e @ p )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[36936]) ).
thf(36991,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36951]) ).
thf(36992,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[36991:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(37029,plain,
! [A: $i] :
~ ( e @ p @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[36992]) ).
thf(42858,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37029]) ).
thf(42859,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[42858]) ).
thf(42972,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ p @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[42859]) ).
thf(43042,plain,
! [A: $i] :
( ( A @ s @ s @ p )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[42972]) ).
thf(21318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20445,87]) ).
thf(21319,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[21318]) ).
thf(21320,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ p @ n @ u ) @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[21319:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( e )),bind(D,$thf( G @ ( I @ p @ n @ u ) )),bind(E,$thf( E ))]]) ).
thf(21368,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ p @ n @ u ) @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[21320]) ).
thf(67237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ ( D @ p @ n @ u ) @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,21368]) ).
thf(67238,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[67237:[bind(A,$thf( K @ ( M @ p @ n @ u ) )),bind(B,$thf( K @ ( M @ p @ n @ u ) @ s )),bind(C,$thf( K )),bind(D,$thf( M ))]]) ).
thf(67324,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[67238]) ).
thf(17610,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,16775]) ).
thf(17611,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17610]) ).
thf(17629,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17611]) ).
thf(17657,plain,
! [A: $i] :
( ( e @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[17629]) ).
thf(18322,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17657]) ).
thf(18323,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18322:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18371,plain,
! [A: $i] :
~ ( e @ n @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[18323]) ).
thf(25793,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,18371]) ).
thf(25794,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[25793]) ).
thf(25921,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[25794]) ).
thf(25961,plain,
! [A: $i] :
( ( A @ s @ s @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[25921]) ).
thf(27649,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,19955]) ).
thf(27650,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[27649]) ).
thf(27684,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[27650]) ).
thf(27731,plain,
! [A: $i] :
( ( A @ p @ n @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[27684]) ).
thf(36908,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,16681]) ).
thf(36909,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[36908]) ).
thf(36914,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[36909]) ).
thf(36972,plain,
! [A: $i] :
( ( e @ p )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[36914]) ).
thf(38311,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36972]) ).
thf(38312,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[38311:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(38355,plain,
! [A: $i] :
~ ( e @ p @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[38312]) ).
thf(47040,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,38355]) ).
thf(47041,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[47040]) ).
thf(47188,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ p @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[47041]) ).
thf(47244,plain,
! [A: $i] :
( ( A @ n @ s @ p )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[47188]) ).
thf(28396,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,19992]) ).
thf(28397,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[28396]) ).
thf(28550,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[28397]) ).
thf(28559,plain,
! [A: $i] :
( ( A @ p @ s @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[28550]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ atleast7p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast6p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast7p_def) ).
thf(89,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast6p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast7p ) )
& ( ( A @ atleast7p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast6p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(90,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast6p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast7p ) )
& ! [A: $i] :
( ( A @ atleast7p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast6p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[89]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast7p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast6p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk5 @ ( A @ subq ) )
| ~ ( A @ atleast7p ) )
& ( ( A @ sk5 @ atleast6p )
| ~ ( A @ atleast7p ) )
& ( ( A @ ( A @ sk5 @ subq ) )
| ~ ( A @ atleast7p ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(94,plain,
! [A: $i] :
( ~ ( A @ sk5 @ ( A @ subq ) )
| ~ ( A @ atleast7p ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk5 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast7p ) ),
inference(paramod_ordered,[status(thm)],[713,94]) ).
thf(933,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk5 @ ( B @ subq ) ) )
| ~ ( B @ atleast7p ) ),
inference(simp,[status(thm)],[932]) ).
thf(934,plain,
~ ( e @ atleast7p ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( e @ sk5 )),bind(B,$thf( e ))]]) ).
thf(49242,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,19295]) ).
thf(49243,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[49242]) ).
thf(49297,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[49243]) ).
thf(49342,plain,
! [A: $i] :
( ( A @ p @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[49297]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ atleast6p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast5p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast6p_def) ).
thf(73,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast5p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast6p ) )
& ( ( A @ atleast6p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast5p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(74,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast5p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast6p ) )
& ! [A: $i] :
( ( A @ atleast6p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast5p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[73]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast6p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast5p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk4 @ ( A @ subq ) )
| ~ ( A @ atleast6p ) )
& ( ( A @ sk4 @ atleast5p )
| ~ ( A @ atleast6p ) )
& ( ( A @ ( A @ sk4 @ subq ) )
| ~ ( A @ atleast6p ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(78,plain,
! [A: $i] :
( ~ ( A @ sk4 @ ( A @ subq ) )
| ~ ( A @ atleast6p ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(281,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk4 @ ( A @ subq ) ) )
| ~ $true
| ~ ( A @ atleast6p ) ),
inference(paramod_ordered,[status(thm)],[211,78]) ).
thf(282,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk4 @ ( A @ subq ) ) )
| ~ ( A @ atleast6p ) ),
inference(simp,[status(thm)],[281]) ).
thf(285,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( A @ sk4 ) )
| ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) )
!= A )
| ~ ( A @ atleast6p ) ),
inference(simp,[status(thm)],[282]) ).
thf(287,plain,
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk4 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast6p ) ),
inference(simp,[status(thm)],[285]) ).
thf(54347,plain,
( ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk4 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast6p ) ),
inference(rewrite,[status(thm)],[287,66]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A @ atleast3p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast2p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( A @ atleast3p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast2p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ atleast9p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast8p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A @ atleast9p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast8p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(20614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19278,88]) ).
thf(20615,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[20614]) ).
thf(20616,plain,
! [C: $i,B: $i,A: $i] : ( C @ p @ ( B @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20615:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( D )),bind(E,$thf( H @ p @ ( F @ u ) ))]]) ).
thf(20707,plain,
! [C: $i,B: $i,A: $i] : ( C @ p @ ( B @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20616]) ).
thf(44423,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37078]) ).
thf(44424,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[44423]) ).
thf(44572,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[44424]) ).
thf(44601,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ p @ p @ s ) ),
inference(simp,[status(thm)],[44572]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( A @ atleast13p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast12p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[184]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A @ atleast13p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast12p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(41062,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,19295]) ).
thf(41063,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[41062]) ).
thf(41103,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[41063]) ).
thf(41136,plain,
! [A: $i] :
( ( A @ p @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[41103]) ).
thf(20819,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,125]) ).
thf(20820,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[20819]) ).
thf(20821,plain,
! [A: $i] :
( ( A @ n @ atleast2p )
| ( A @ p @ ( A @ n @ subq ) ) ),
inference(pattern_uni,[status(thm)],[20820:[bind(A,$thf( D )),bind(B,$thf( D @ n )),bind(C,$thf( D ))]]) ).
thf(20841,plain,
! [A: $i] :
( ( A @ n @ atleast2p )
| ( A @ p @ ( A @ n @ subq ) ) ),
inference(simp,[status(thm)],[20821]) ).
thf(21546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21386,88]) ).
thf(21547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[21546]) ).
thf(21548,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[21547:[bind(A,$thf( G )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( G @ p @ n @ n ))]]) ).
thf(21669,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[21548]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ a ) )
!= ( e @ n @ n @ ( e @ n @ s @ a ) ) )
| ( B @ s @ ( A @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[66,211]) ).
thf(215,plain,
e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( e @ n @ s )),bind(B,$thf( e @ n @ n ))]]) ).
thf(246,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) ) )
| ( A @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,215]) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s ) )
| ( A
!= ( e @ n @ s ) )
| ( A @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(261,plain,
( ( ( e @ n @ n @ s )
!= ( e @ n @ s @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(93,plain,
! [A: $i] :
( ( A @ sk5 @ atleast6p )
| ~ ( A @ atleast7p ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(11316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ s @ n @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11129,69]) ).
thf(11317,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ s @ n @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[11316]) ).
thf(11358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ s @ n @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[11317]) ).
thf(11378,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ s @ n @ u ) )
!= e ),
inference(simp,[status(thm)],[11358]) ).
thf(11094,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,69]) ).
thf(11095,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[11094]) ).
thf(11125,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[11095]) ).
thf(11139,plain,
! [A: $i] :
( ( A @ s @ n )
!= e ),
inference(simp,[status(thm)],[11125]) ).
thf(28398,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,19992]) ).
thf(28399,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[28398]) ).
thf(28528,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[28399]) ).
thf(28591,plain,
! [A: $i] :
( ( A @ p @ s @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[28528]) ).
thf(25901,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,18371]) ).
thf(25902,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[25901]) ).
thf(25926,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[25902]) ).
thf(25965,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[25926]) ).
thf(25482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24434,87]) ).
thf(25483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[25482]) ).
thf(25484,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[25483:[bind(A,$thf( H )),bind(B,$thf( e )),bind(C,$thf( H @ p @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(25544,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[25484]) ).
thf(28962,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ n @ n @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,25544]) ).
thf(28963,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[28962:[bind(A,$thf( L @ p @ n @ n @ n )),bind(B,$thf( L @ p @ n @ n @ n @ s )),bind(C,$thf( L ))]]) ).
thf(29014,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[28963]) ).
thf(29638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29014,87]) ).
thf(29639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[29638]) ).
thf(29640,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[29639:[bind(A,$thf( I )),bind(B,$thf( e )),bind(C,$thf( I @ p @ n @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(29734,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[29640]) ).
thf(32094,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ n @ n @ n @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,29734]) ).
thf(32095,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[32094:[bind(A,$thf( N @ p @ n @ n @ n @ n )),bind(B,$thf( N @ p @ n @ n @ n @ n @ s )),bind(C,$thf( N ))]]) ).
thf(32159,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[32095]) ).
thf(32652,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32159,69]) ).
thf(32653,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[32652]) ).
thf(32828,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[32653]) ).
thf(32876,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[32828]) ).
thf(22447,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,17908]) ).
thf(22448,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[22447]) ).
thf(22568,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[22448]) ).
thf(22608,plain,
! [A: $i] :
( ( e @ s @ s @ n )
!= ( A @ n @ n @ s ) ),
inference(simp,[status(thm)],[22568]) ).
thf(18646,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ( B
!= ( C @ n @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17402]) ).
thf(18647,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n @ s ) )
| ~ ( A @ s @ ( e @ s @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18646:[bind(A,$thf( e @ s @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(18703,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ s @ n @ mem ) ),
inference(simp,[status(thm)],[18647]) ).
thf(41025,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,17990]) ).
thf(41026,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[41025]) ).
thf(41107,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[41026]) ).
thf(41140,plain,
! [A: $i] :
( ( A @ n @ s @ p @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[41107]) ).
thf(175,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast10p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast11p ) )
& ! [A: $i] :
( ( A @ atleast11p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast10p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[174]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast11p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast10p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk14 @ ( A @ subq ) )
| ~ ( A @ atleast11p ) )
& ( ( A @ sk14 @ atleast10p )
| ~ ( A @ atleast11p ) )
& ( ( A @ ( A @ sk14 @ subq ) )
| ~ ( A @ atleast11p ) ) ),
inference(cnf,[status(esa)],[175]) ).
thf(179,plain,
! [A: $i] :
( ~ ( A @ sk14 @ ( A @ subq ) )
| ~ ( A @ atleast11p ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(13373,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n ) )
| ( e != e )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3038,13368]) ).
thf(13374,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[13373]) ).
thf(13375,plain,
! [A: $i] :
~ ( e @ ( A @ n @ subq ) ),
inference(pattern_uni,[status(thm)],[13374:[bind(A,$thf( C @ n )),bind(B,$thf( C ))]]) ).
thf(13382,plain,
! [A: $i] :
~ ( e @ ( A @ n @ subq ) ),
inference(simp,[status(thm)],[13375]) ).
thf(17676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,88]) ).
thf(17677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[17676]) ).
thf(17678,plain,
! [B: $i,A: $i] : ( B @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[17677:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ n @ n ))]]) ).
thf(17747,plain,
! [B: $i,A: $i] : ( B @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[17678]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ mem ) )
| ( B @ ( A @ mem ) )
| ~ ( C @ ( B @ u ) @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(18015,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ s ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17520]) ).
thf(18016,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ s @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18015:[bind(A,$thf( A )),bind(B,$thf( E @ s @ s )),bind(C,$thf( E ))]]) ).
thf(18032,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[18016]) ).
thf(24159,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,18032]) ).
thf(24160,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[24159]) ).
thf(24203,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[24160]) ).
thf(24233,plain,
! [A: $i] :
( ( A @ s @ s @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24203]) ).
thf(239,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( A @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(258,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s ) )
| ( A
!= ( e @ n @ s ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( A @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(262,plain,
( ( ( e @ n @ n @ s )
!= ( e @ n @ s @ s ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(510,plain,
( ( ( e @ n @ n @ s )
!= ( e @ n @ s @ s ) )
| ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(rewrite,[status(thm)],[262,66]) ).
thf(527,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) ) )
| ( ( e @ n @ n @ s )
!= ( e @ n @ s @ s ) )
| ( A @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,510]) ).
thf(531,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s ) )
| ( A
!= ( e @ n @ s ) )
| ( ( e @ n @ n @ s )
!= ( e @ n @ s @ s ) )
| ( A @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[527]) ).
thf(566,plain,
( ( ( e @ n @ n @ s )
!= ( e @ n @ s @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[531]) ).
thf(736,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) ) )
| ( ( e @ n @ n @ s )
!= ( e @ n @ s @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( A @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,566]) ).
thf(775,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ s @ n ) )
| ( A
!= ( e @ n ) )
| ( ( e @ n @ n )
!= ( e @ n @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( A @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[736]) ).
thf(784,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[775]) ).
thf(996,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n @ s ) )
| ( e @ n @ s @ n @ s @ ( A @ n @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,784]) ).
thf(1011,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ s @ n ) )
| ( A
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n @ s ) )
| ( e @ n @ s @ n @ s @ ( A @ n @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[996]) ).
thf(1023,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[1011]) ).
thf(1045,plain,
( ( ( e @ n @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ n ) )
| ( ( e @ n @ n )
!= ( e @ n @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(eqfactor_ordered,[status(thm)],[1023]) ).
thf(1056,plain,
( ( ( e @ n @ s )
!= ( e @ n ) )
| ( ( e @ n @ n )
!= ( e @ n @ s ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[1045]) ).
thf(1140,plain,
( ( ( e @ n @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(eqfactor_ordered,[status(thm)],[1056]) ).
thf(1151,plain,
( ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ u ) @ ( e @ n @ s @ n @ s @ ( e @ n @ n @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[1140]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ atleast10p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast9p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast10p_def) ).
thf(126,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast9p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast10p ) )
& ( ( A @ atleast10p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast9p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(127,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast9p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast10p ) )
& ! [A: $i] :
( ( A @ atleast10p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast9p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[126]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast10p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast9p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk8 @ ( A @ subq ) )
| ~ ( A @ atleast10p ) )
& ( ( A @ sk8 @ atleast9p )
| ~ ( A @ atleast10p ) )
& ( ( A @ ( A @ sk8 @ subq ) )
| ~ ( A @ atleast10p ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(130,plain,
! [A: $i] :
( ( A @ sk8 @ atleast9p )
| ~ ( A @ atleast10p ) ),
inference(cnfConj,[status(thm)],[128]) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk2 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[713,50]) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk2 @ ( B @ subq ) ) )
| ~ ( B @ atleast9p ) ),
inference(simp,[status(thm)],[914]) ).
thf(916,plain,
~ ( e @ atleast9p ),
inference(pattern_uni,[status(thm)],[915:[bind(A,$thf( e @ sk2 )),bind(B,$thf( e ))]]) ).
thf(935,plain,
! [A: $i] :
( ( ( A @ sk8 @ atleast9p )
!= ( e @ atleast9p ) )
| ~ $true
| ~ ( A @ atleast10p ) ),
inference(paramod_ordered,[status(thm)],[130,916]) ).
thf(936,plain,
! [A: $i] :
( ( ( A @ sk8 @ atleast9p )
!= ( e @ atleast9p ) )
| ~ ( A @ atleast10p ) ),
inference(simp,[status(thm)],[935]) ).
thf(937,plain,
! [A: $i] :
( ( ( A @ sk8 )
!= e )
| ~ ( A @ atleast10p ) ),
inference(simp,[status(thm)],[936]) ).
thf(60,plain,
! [A: $i] :
( ( A @ sk3 @ atleast7p )
| ~ ( A @ atleast8p ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( B @ atleast8p ) )
| ( B @ sk3 @ atleast7p )
| ~ $true
| ~ ( A @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[49,60]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( B @ atleast8p ) )
| ( B @ sk3 @ atleast7p )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[277]) ).
thf(279,plain,
! [A: $i] :
( ( A @ sk2 @ sk3 @ atleast7p )
| ~ ( A @ atleast9p ) ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( C )),bind(B,$thf( C @ sk2 ))]]) ).
thf(280,plain,
! [A: $i] :
( ( A @ sk2 @ sk3 @ atleast7p )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[279]) ).
thf(24691,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,18038]) ).
thf(24692,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[24691]) ).
thf(24701,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[24692]) ).
thf(24779,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24701]) ).
thf(20007,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ s ) )
| ( A
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19662]) ).
thf(20008,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( B @ p @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[20007:[bind(A,$thf( A )),bind(B,$thf( E @ p @ s )),bind(C,$thf( E ))]]) ).
thf(20044,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ n @ mem ) ),
inference(simp,[status(thm)],[20008]) ).
thf(36880,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,20044]) ).
thf(36881,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[36880]) ).
thf(36919,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[36881]) ).
thf(36977,plain,
! [A: $i] :
( ( e @ n @ p )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[36919]) ).
thf(41389,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ p @ n ) )
| ( B
!= ( C @ p @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41132]) ).
thf(41390,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ p @ s ) )
| ~ ( A @ s @ ( e @ p @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41389:[bind(A,$thf( e @ p @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(41457,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ p @ n @ mem ) ),
inference(simp,[status(thm)],[41390]) ).
thf(143,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast4p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast5p ) )
& ! [A: $i] :
( ( A @ atleast5p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast4p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[142]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast5p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast4p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk10 @ ( A @ subq ) )
| ~ ( A @ atleast5p ) )
& ( ( A @ sk10 @ atleast4p )
| ~ ( A @ atleast5p ) )
& ( ( A @ ( A @ sk10 @ subq ) )
| ~ ( A @ atleast5p ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(147,plain,
! [A: $i] :
( ~ ( A @ sk10 @ ( A @ subq ) )
| ~ ( A @ atleast5p ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( A @ atleast10p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast9p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[128]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( A @ atleast10p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast9p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subq ) )
| ~ ( B @ p @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(41054,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,17914]) ).
thf(41055,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[41054]) ).
thf(41121,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[41055]) ).
thf(41155,plain,
! [A: $i] :
( ( A @ n @ n @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41121]) ).
thf(36999,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ s ) )
| ( A
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36951]) ).
thf(37000,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( B @ s @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[36999:[bind(A,$thf( A )),bind(B,$thf( E @ s @ s )),bind(C,$thf( E ))]]) ).
thf(37036,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ p @ mem ) ),
inference(simp,[status(thm)],[37000]) ).
thf(17960,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ s ) )
| ( A
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17399]) ).
thf(17961,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( B @ n @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17960:[bind(A,$thf( A )),bind(B,$thf( E @ n @ s )),bind(C,$thf( E ))]]) ).
thf(17997,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ n @ mem ) ),
inference(simp,[status(thm)],[17961]) ).
thf(23878,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,17997]) ).
thf(23879,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[23878]) ).
thf(24015,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[23879]) ).
thf(24052,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[24015]) ).
thf(21264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20445,88]) ).
thf(21265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[21264]) ).
thf(21266,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ p @ n @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[21265:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( e )),bind(D,$thf( D )),bind(E,$thf( G @ ( I @ p @ n @ u ) ))]]) ).
thf(21371,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ p @ n @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[21266]) ).
thf(17548,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,16775]) ).
thf(17549,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17548]) ).
thf(17622,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17549]) ).
thf(17646,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[17622]) ).
thf(18774,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ s @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17646]) ).
thf(18775,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18774:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18825,plain,
! [A: $i] :
~ ( e @ s @ n @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[18775]) ).
thf(38,plain,
( ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( B @ ( C @ mem ) )
& ( A @ ( C @ mem ) ) )
=> ( B @ ( A @ disj ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ disj ) )
=> ~ ? [C: $i] :
( ( B @ ( C @ mem ) )
& ( A @ ( C @ mem ) ) ) ) ),
inference(miniscope,[status(thm)],[37]) ).
thf(39,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ disj ) )
| ( E @ ( D @ ( E @ sk1 ) @ mem ) ) )
& ( ( E @ ( D @ disj ) )
| ( D @ ( D @ ( E @ sk1 ) @ mem ) ) )
& ( ~ ( B @ ( C @ mem ) )
| ~ ( A @ ( C @ mem ) )
| ~ ( B @ ( A @ disj ) ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disj ) )
| ( A @ ( A @ ( B @ sk1 ) @ mem ) ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disj ) )
| ( A @ ( A @ ( B @ sk1 ) @ mem ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ( D @ ( C @ mem ) )
| ~ $true
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[43,33]) ).
thf(305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ( D @ ( C @ mem ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( I @ ( H @ m ) )),bind(B,$thf( F )),bind(C,$thf( I @ ( H @ m ) @ ( F @ sk1 ) )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( C @ m ) @ ( B @ mem ) ) )
| ( C @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,33]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( C @ m ) @ ( B @ mem ) ) )
| ( C @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( D @ ( C @ m ) ) )
| ( A != B )
| ( C @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( C @ ( B @ m ) ) )
| ( B @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(923,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk10 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast5p ) ),
inference(paramod_ordered,[status(thm)],[713,147]) ).
thf(924,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk10 @ ( B @ subq ) ) )
| ~ ( B @ atleast5p ) ),
inference(simp,[status(thm)],[923]) ).
thf(925,plain,
~ ( e @ atleast5p ),
inference(pattern_uni,[status(thm)],[924:[bind(A,$thf( e @ sk10 )),bind(B,$thf( e ))]]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ mem ) )
| ~ ( A @ ( C @ mem ) )
| ~ ( B @ ( A @ subq ) ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(36827,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,16680]) ).
thf(36828,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[36827]) ).
thf(36920,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[36828]) ).
thf(36978,plain,
! [A: $i] :
( ( A @ n @ p )
!= ( e @ s ) ),
inference(simp,[status(thm)],[36920]) ).
thf(38369,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ p ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36978]) ).
thf(38370,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ n @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[38369:[bind(A,$thf( E @ n @ p )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(38390,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ n @ p @ mem ) ),
inference(simp,[status(thm)],[38370]) ).
thf(18288,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ n ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17522]) ).
thf(18289,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ s @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18288:[bind(A,$thf( E @ s @ n )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18308,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ s @ n @ mem ) ),
inference(simp,[status(thm)],[18289]) ).
thf(41027,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,18308]) ).
thf(41028,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[41027]) ).
thf(41116,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[41028]) ).
thf(41149,plain,
! [A: $i] :
( ( A @ s @ n @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41116]) ).
thf(28724,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,20037]) ).
thf(28725,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[28724]) ).
thf(28763,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[28725]) ).
thf(28807,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[28763]) ).
thf(36820,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,17946]) ).
thf(36821,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[36820]) ).
thf(36924,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[36821]) ).
thf(36982,plain,
! [A: $i] :
( ( A @ n @ s @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[36924]) ).
thf(18851,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ n @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17737]) ).
thf(18852,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18851:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18909,plain,
! [A: $i] :
~ ( e @ n @ n @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[18852]) ).
thf(25101,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,18312]) ).
thf(25102,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[25101]) ).
thf(25114,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[25102]) ).
thf(25151,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ n @ s ) ),
inference(simp,[status(thm)],[25114]) ).
thf(12080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,88]) ).
thf(12081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[12080]) ).
thf(12082,plain,
! [B: $i,A: $i] : ( B @ s @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[12081:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ s @ n ))]]) ).
thf(12169,plain,
! [B: $i,A: $i] : ( B @ s @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[12082]) ).
thf(49248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,87]) ).
thf(49249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[49248]) ).
thf(49250,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[49249:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G @ p @ n @ n )),bind(D,$thf( D ))]]) ).
thf(49382,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[49250]) ).
thf(11033,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ s @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11004,69]) ).
thf(11034,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ s @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[11033]) ).
thf(11069,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ s @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[11034]) ).
thf(11085,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ s @ u ) )
!= e ),
inference(simp,[status(thm)],[11069]) ).
thf(12175,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ s @ u ) ) )
| ( e != e )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3038,11085]) ).
thf(12176,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ s @ u ) ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[12175]) ).
thf(12177,plain,
! [B: $i,A: $i] :
~ ( e @ ( A @ ( B @ s @ u ) @ subq ) ),
inference(pattern_uni,[status(thm)],[12176:[bind(A,$thf( E @ ( F @ s @ u ) )),bind(B,$thf( E )),bind(C,$thf( F ))]]) ).
thf(12190,plain,
! [B: $i,A: $i] :
~ ( e @ ( A @ ( B @ s @ u ) @ subq ) ),
inference(simp,[status(thm)],[12177]) ).
thf(41031,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,18371]) ).
thf(41032,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[41031]) ).
thf(41095,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[41032]) ).
thf(41128,plain,
! [A: $i] :
( ( A @ s @ s @ p @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[41095]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ mem ) )
| ~ ( C @ ( B @ m ) @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ m ) @ ( A @ mem ) )
!= ( C @ ( A @ mem ) ) )
| ~ ( C @ ( A @ mem ) ) ),
inference(eqfactor_ordered,[status(thm)],[34]) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ m ) )
!= C )
| ( A != A )
| ~ ( C @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ m ) )
!= C )
| ~ ( C @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[389]) ).
thf(137,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ subq ) )
| ~ ( A @ atleast16p ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ atleast4p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast3p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast4p_def) ).
thf(158,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast3p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast4p ) )
& ( ( A @ atleast4p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast3p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(159,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast3p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast4p ) )
& ! [A: $i] :
( ( A @ atleast4p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast3p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[158]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast4p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast3p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk12 @ ( A @ subq ) )
| ~ ( A @ atleast4p ) )
& ( ( A @ sk12 @ atleast3p )
| ~ ( A @ atleast4p ) )
& ( ( A @ ( A @ sk12 @ subq ) )
| ~ ( A @ atleast4p ) ) ),
inference(cnf,[status(esa)],[159]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( A @ atleast4p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast3p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A @ atleast4p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast3p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(28510,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,19992]) ).
thf(28511,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[28510]) ).
thf(28518,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[28511]) ).
thf(28583,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[28518]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ m ) @ ( A @ mem ) )
| ( C @ ( A @ mem ) )
| ~ ( B @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ m ) @ ( A @ mem ) )
| ( C @ ( A @ mem ) )
| ~ ( B @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(19242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ m ) @ ( B @ mem ) )
| ( D @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,36]) ).
thf(19243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ m ) @ ( B @ mem ) )
| ( D @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19242]) ).
thf(19244,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ p @ m ) @ ( e @ mem ) )
| ( A @ ( e @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19243:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( E @ p ))]]) ).
thf(19273,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ p @ m ) @ ( e @ mem ) )
| ( A @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19244]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ atleast14p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast13p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast14p_def) ).
thf(190,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast13p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast14p ) )
& ( ( A @ atleast14p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast13p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(191,plain,
( ! [A: $i] :
( ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast13p )
& ( A @ ( B @ subq ) ) )
=> ( A @ atleast14p ) )
& ! [A: $i] :
( ( A @ atleast14p )
=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast13p )
& ( A @ ( B @ subq ) ) ) ) ),
inference(miniscope,[status(thm)],[190]) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ atleast14p )
| ( C @ ( B @ subq ) )
| ~ ( C @ atleast13p )
| ~ ( B @ ( C @ subq ) ) )
& ( ~ ( A @ sk16 @ ( A @ subq ) )
| ~ ( A @ atleast14p ) )
& ( ( A @ sk16 @ atleast13p )
| ~ ( A @ atleast14p ) )
& ( ( A @ ( A @ sk16 @ subq ) )
| ~ ( A @ atleast14p ) ) ),
inference(cnf,[status(esa)],[191]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( A @ atleast14p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast13p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A @ atleast14p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast13p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(41060,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,18032]) ).
thf(41061,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41060]) ).
thf(41115,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41061]) ).
thf(41148,plain,
! [A: $i] :
( ( e @ s @ p @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[41115]) ).
thf(20061,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19266,88]) ).
thf(20062,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[20061]) ).
thf(20063,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ p @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20062:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ p @ u ) ))]]) ).
thf(20161,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ p @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20063]) ).
thf(27563,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,19955]) ).
thf(27564,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[27563]) ).
thf(27690,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[27564]) ).
thf(27737,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ p @ n @ s ) ),
inference(simp,[status(thm)],[27690]) ).
thf(41517,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ p @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41137]) ).
thf(41518,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p @ n ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41517:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(41580,plain,
! [A: $i] :
~ ( e @ p @ n @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[41518]) ).
thf(18318,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ( B
!= ( C @ s @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17657]) ).
thf(18319,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ~ ( A @ s @ ( e @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18318:[bind(A,$thf( e @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(18367,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ n @ mem ) ),
inference(simp,[status(thm)],[18319]) ).
thf(36874,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,18367]) ).
thf(36875,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[36874]) ).
thf(36942,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[36875]) ).
thf(36958,plain,
! [A: $i] :
( ( e @ n @ p )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[36942]) ).
thf(38307,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ( B
!= ( C @ n @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36972]) ).
thf(38308,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n @ s ) )
| ~ ( A @ s @ ( e @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[38307:[bind(A,$thf( e @ p )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(38351,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ p @ mem ) ),
inference(simp,[status(thm)],[38308]) ).
thf(46766,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,38351]) ).
thf(46767,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[46766]) ).
thf(46891,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[46767]) ).
thf(46950,plain,
! [A: $i] :
( ( e @ p @ p )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[46891]) ).
thf(17701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,87]) ).
thf(17702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[17701]) ).
thf(17703,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[17702:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ n @ n )),bind(D,$thf( D ))]]) ).
thf(17754,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[17703]) ).
thf(18989,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ n @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,17754]) ).
thf(18990,plain,
! [A: $i] : ( A @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[18989:[bind(A,$thf( H @ n @ n )),bind(B,$thf( H @ n @ n @ s )),bind(C,$thf( H ))]]) ).
thf(19022,plain,
! [A: $i] : ( A @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[18990]) ).
thf(19769,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,16681]) ).
thf(19770,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19769]) ).
thf(19785,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19770]) ).
thf(19800,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[19785]) ).
thf(92,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ subq ) )
| ~ ( A @ atleast7p ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(36878,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,17940]) ).
thf(36879,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[36878]) ).
thf(36937,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[36879]) ).
thf(36953,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[36937]) ).
thf(41046,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,16774]) ).
thf(41047,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[41046]) ).
thf(41098,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[41047]) ).
thf(41131,plain,
! [A: $i] :
( ( A @ s @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[41098]) ).
thf(36492,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
!= ( E @ ( D @ ( E @ sk17 ) @ mem ) ) )
| ( E @ ( D @ subq ) )
| ~ $true
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[715,205]) ).
thf(36493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
!= ( E @ ( D @ ( E @ sk17 ) @ mem ) ) )
| ( E @ ( D @ subq ) )
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(simp,[status(thm)],[36492]) ).
thf(36494,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ m ) @ subq ) )
| ( A @ ( B @ ( A @ m ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[36493:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ m ) )),bind(E,$thf( F ))]]) ).
thf(36643,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ m ) @ subq ) ),
inference(simp,[status(thm)],[36494]) ).
thf(38554,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ n @ subq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36643,13382]) ).
thf(38555,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ n @ subq ) ) ),
inference(simp,[status(thm)],[38554]) ).
thf(38659,plain,
! [C: $i,B: $i,A: $i] :
( ( A != e )
| ( ( B @ ( A @ m ) )
!= ( C @ n ) ) ),
inference(simp,[status(thm)],[38555]) ).
thf(38670,plain,
! [B: $i,A: $i] :
( ( A @ ( e @ m ) )
!= ( B @ n ) ),
inference(simp,[status(thm)],[38659]) ).
thf(54065,plain,
! [A: $i] :
( ( A @ n )
!= e ),
inference(rewrite,[status(thm)],[38670,7681]) ).
thf(19558,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,19296]) ).
thf(19559,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19558]) ).
thf(19656,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19559]) ).
thf(19667,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19656]) ).
thf(21111,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ s @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19667]) ).
thf(21112,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[21111:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(21178,plain,
! [A: $i] :
~ ( e @ s @ n @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[21112]) ).
thf(64575,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,49382]) ).
thf(64576,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[64575:[bind(A,$thf( J @ p @ n @ n )),bind(B,$thf( J @ p @ n @ n @ s )),bind(C,$thf( J ))]]) ).
thf(64656,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[64576]) ).
thf(24083,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,18032]) ).
thf(24084,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[24083]) ).
thf(24210,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[24084]) ).
thf(24240,plain,
! [A: $i] :
( ( e @ s @ s @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[24210]) ).
thf(1109,plain,
! [A: $i] :
( ( ( A @ sk3 @ atleast7p )
!= ( e @ atleast7p ) )
| ~ $true
| ~ ( A @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[60,934]) ).
thf(1110,plain,
! [A: $i] :
( ( ( A @ sk3 @ atleast7p )
!= ( e @ atleast7p ) )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[1109]) ).
thf(1111,plain,
! [A: $i] :
( ( ( A @ sk3 )
!= e )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[1110]) ).
thf(19743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,87]) ).
thf(19744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19743]) ).
thf(19745,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[19744:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(19806,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[19745]) ).
thf(51852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ n @ n @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,19806]) ).
thf(51853,plain,
! [A: $i] : ( A @ n @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[51852:[bind(A,$thf( J @ n @ n @ n )),bind(B,$thf( J @ n @ n @ n @ s )),bind(C,$thf( J ))]]) ).
thf(51908,plain,
! [A: $i] : ( A @ n @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[51853]) ).
thf(52251,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[51908,69]) ).
thf(52252,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[52251]) ).
thf(52443,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[52252]) ).
thf(52510,plain,
! [A: $i] :
( ( A @ n @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[52443]) ).
thf(169,plain,
! [A: $i] :
( ( A @ ( A @ sk13 @ subq ) )
| ~ ( A @ atleast15p ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(37083,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ p ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36970]) ).
thf(37084,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ s @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[37083:[bind(A,$thf( A )),bind(B,$thf( E @ s @ p )),bind(C,$thf( E ))]]) ).
thf(37107,plain,
! [A: $i] :
~ ( A @ s @ p @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[37084]) ).
thf(45059,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37107]) ).
thf(45060,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[45059]) ).
thf(45100,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[45060]) ).
thf(45152,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ p @ s ) ),
inference(simp,[status(thm)],[45100]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( A @ atleast16p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast15p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( A @ atleast16p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast15p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ m ) @ ( A @ mem ) )
!= ( C @ ( A @ mem ) ) )
| ~ ( C @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(109,plain,
! [A: $i] :
( ( A @ sk6 @ atleast11p )
| ~ ( A @ atleast12p ) ),
inference(cnfConj,[status(thm)],[107]) ).
thf(19247,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,16775]) ).
thf(19248,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19247]) ).
thf(19252,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s ) )
| ( e != e ) ),
inference(simp,[status(thm)],[19248]) ).
thf(19277,plain,
! [B: $i,A: $i] :
( ( A @ p )
!= ( B @ s @ s ) ),
inference(simp,[status(thm)],[19252]) ).
thf(46834,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,38351]) ).
thf(46835,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[46834]) ).
thf(46877,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[46835]) ).
thf(46937,plain,
! [A: $i] :
( ( e @ p @ s )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[46877]) ).
thf(17725,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,16775]) ).
thf(17726,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17725]) ).
thf(17733,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17726]) ).
thf(17742,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[17733]) ).
thf(40995,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,19955]) ).
thf(40996,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[40995]) ).
thf(41118,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[40996]) ).
thf(41152,plain,
! [A: $i] :
( ( e @ s @ p @ n )
!= ( A @ p @ n @ s ) ),
inference(simp,[status(thm)],[41118]) ).
thf(32759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32159,87]) ).
thf(32760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[32759]) ).
thf(32761,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[32760:[bind(A,$thf( J )),bind(B,$thf( e )),bind(C,$thf( J @ p @ n @ n @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(32888,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[32761]) ).
thf(36380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ n @ n @ n @ n @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,32888]) ).
thf(36381,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[36380:[bind(A,$thf( P @ p @ n @ n @ n @ n @ n )),bind(B,$thf( P @ p @ n @ n @ n @ n @ n @ s )),bind(C,$thf( P ))]]) ).
thf(36437,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[36381]) ).
thf(77,plain,
! [A: $i] :
( ( A @ sk4 @ atleast5p )
| ~ ( A @ atleast6p ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(19933,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ n ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19522]) ).
thf(19934,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ p @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19933:[bind(A,$thf( E @ p @ n )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(19961,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ p @ n @ mem ) ),
inference(simp,[status(thm)],[19934]) ).
thf(36891,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,19961]) ).
thf(36892,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[36891]) ).
thf(36931,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[36892]) ).
thf(36946,plain,
! [A: $i] :
( ( A @ p @ n @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[36931]) ).
thf(193,plain,
! [A: $i] :
( ( A @ ( A @ sk16 @ subq ) )
| ~ ( A @ atleast14p ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(17425,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,16774]) ).
thf(17426,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[17425]) ).
thf(17503,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[17426]) ).
thf(17531,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17503]) ).
thf(44219,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,37074]) ).
thf(44220,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) ),
inference(simp,[status(thm)],[44219]) ).
thf(44305,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ p ) ) ),
inference(simp,[status(thm)],[44220]) ).
thf(44319,plain,
! [A: $i] :
( ( A @ p @ p @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[44305]) ).
thf(163,plain,
! [A: $i] :
( ~ ( A @ sk12 @ ( A @ subq ) )
| ~ ( A @ atleast4p ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(27359,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk12 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast4p ) ),
inference(paramod_ordered,[status(thm)],[8581,163]) ).
thf(27360,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk12 @ ( B @ subq ) ) )
| ~ ( B @ atleast4p ) ),
inference(simp,[status(thm)],[27359]) ).
thf(27361,plain,
~ ( e @ atleast4p ),
inference(pattern_uni,[status(thm)],[27360:[bind(A,$thf( e @ sk12 )),bind(B,$thf( e ))]]) ).
thf(41033,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,20037]) ).
thf(41034,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[41033]) ).
thf(41102,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[41034]) ).
thf(41135,plain,
! [A: $i] :
( ( A @ p @ s @ p @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[41102]) ).
thf(41052,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,18367]) ).
thf(41053,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[41052]) ).
thf(41108,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[41053]) ).
thf(41141,plain,
! [A: $i] :
( ( e @ n @ p @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[41108]) ).
thf(27891,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,19961]) ).
thf(27892,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[27891]) ).
thf(27908,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[27892]) ).
thf(27937,plain,
! [A: $i] :
( ( A @ p @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[27908]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( A @ atleast7p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast6p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( A @ atleast7p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast6p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ~ ( E @ ( C @ mem ) )
| ~ $true
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[43,34]) ).
thf(376,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ~ ( E @ ( C @ mem ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(pattern_uni,[status(thm)],[376:[bind(A,$thf( I @ ( H @ m ) )),bind(B,$thf( F )),bind(C,$thf( I @ ( H @ m ) @ ( F @ sk1 ) )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(178,plain,
! [A: $i] :
( ( A @ sk14 @ atleast10p )
| ~ ( A @ atleast11p ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(131,plain,
! [A: $i] :
( ~ ( A @ sk8 @ ( A @ subq ) )
| ~ ( A @ atleast10p ) ),
inference(cnfConj,[status(thm)],[128]) ).
thf(917,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk8 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast10p ) ),
inference(paramod_ordered,[status(thm)],[713,131]) ).
thf(918,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk8 @ ( B @ subq ) ) )
| ~ ( B @ atleast10p ) ),
inference(simp,[status(thm)],[917]) ).
thf(919,plain,
~ ( e @ atleast10p ),
inference(pattern_uni,[status(thm)],[918:[bind(A,$thf( e @ sk8 )),bind(B,$thf( e ))]]) ).
thf(1289,plain,
! [A: $i] :
( ( ( A @ sk14 @ atleast10p )
!= ( e @ atleast10p ) )
| ~ $true
| ~ ( A @ atleast11p ) ),
inference(paramod_ordered,[status(thm)],[178,919]) ).
thf(1290,plain,
! [A: $i] :
( ( ( A @ sk14 @ atleast10p )
!= ( e @ atleast10p ) )
| ~ ( A @ atleast11p ) ),
inference(simp,[status(thm)],[1289]) ).
thf(1297,plain,
! [A: $i] :
( ( ( A @ sk14 )
!= e )
| ~ ( A @ atleast11p ) ),
inference(simp,[status(thm)],[1290]) ).
thf(49142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,88]) ).
thf(49143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[49142]) ).
thf(49144,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[49143:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ p @ n @ n ))]]) ).
thf(49390,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[49144]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( A @ atleast15p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast14p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( A @ atleast15p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast14p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( A @ sk8 @ subq ) )
| ~ ( A @ atleast10p ) ),
inference(cnfConj,[status(thm)],[128]) ).
thf(20490,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ( B
!= ( C @ s @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17742]) ).
thf(20491,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ~ ( A @ s @ ( e @ n @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[20490:[bind(A,$thf( e @ n @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(20542,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ n @ n @ mem ) ),
inference(simp,[status(thm)],[20491]) ).
thf(19552,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,19296]) ).
thf(19553,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19552]) ).
thf(19643,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19553]) ).
thf(19694,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19643]) ).
thf(29539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29014,88]) ).
thf(29540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[29539]) ).
thf(29541,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[29540:[bind(A,$thf( I )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( I @ p @ n @ n @ n @ n ))]]) ).
thf(29746,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[29541]) ).
thf(41395,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ p @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41132]) ).
thf(41396,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p @ n ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41395:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(41460,plain,
! [A: $i] :
~ ( e @ p @ n @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[41396]) ).
thf(29305,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,20044]) ).
thf(29306,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[29305]) ).
thf(29345,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[29306]) ).
thf(29377,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[29345]) ).
thf(44153,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37074]) ).
thf(44154,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) ),
inference(simp,[status(thm)],[44153]) ).
thf(44276,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ p ) ) ),
inference(simp,[status(thm)],[44154]) ).
thf(44359,plain,
! [A: $i] :
( ( A @ p @ p @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[44276]) ).
thf(73905,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
!= ( F @ ( F @ ( E @ m ) @ ( D @ sk1 ) @ mem ) ) )
| ~ $true
| ( D @ ( F @ ( E @ m ) @ disj ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[307,393]) ).
thf(73906,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
!= ( F @ ( F @ ( E @ m ) @ ( D @ sk1 ) @ mem ) ) )
| ( D @ ( F @ ( E @ m ) @ disj ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(simp,[status(thm)],[73905]) ).
thf(73907,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ m ) @ disj ) )
| ( A @ ( B @ ( B @ m ) @ disj ) ) ),
inference(pattern_uni,[status(thm)],[73906:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( B ))]]) ).
thf(74248,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ m ) @ disj ) ),
inference(simp,[status(thm)],[73907]) ).
thf(20106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19266,87]) ).
thf(20107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[20106]) ).
thf(20108,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ p @ u ) @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20107:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( G @ ( H @ p @ u ) )),bind(E,$thf( E ))]]) ).
thf(20153,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ p @ u ) @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20108]) ).
thf(17175,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,16680]) ).
thf(17176,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[17175]) ).
thf(17262,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[17176]) ).
thf(17293,plain,
! [A: $i] :
( ( A @ n @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17262]) ).
thf(19288,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ p ) )
| ( e != e )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3038,19274]) ).
thf(19289,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ p ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[19288]) ).
thf(19290,plain,
! [A: $i] :
~ ( e @ ( A @ p @ subq ) ),
inference(pattern_uni,[status(thm)],[19289:[bind(A,$thf( C @ p )),bind(B,$thf( C ))]]) ).
thf(19297,plain,
! [A: $i] :
~ ( e @ ( A @ p @ subq ) ),
inference(simp,[status(thm)],[19290]) ).
thf(38618,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ p @ subq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36643,19297]) ).
thf(38619,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ p @ subq ) ) ),
inference(simp,[status(thm)],[38618]) ).
thf(38662,plain,
! [C: $i,B: $i,A: $i] :
( ( A != e )
| ( ( B @ ( A @ m ) )
!= ( C @ p ) ) ),
inference(simp,[status(thm)],[38619]) ).
thf(38673,plain,
! [B: $i,A: $i] :
( ( A @ ( e @ m ) )
!= ( B @ p ) ),
inference(simp,[status(thm)],[38662]) ).
thf(54082,plain,
! [A: $i] :
( ( A @ p )
!= e ),
inference(rewrite,[status(thm)],[38673,7681]) ).
thf(43129,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37036]) ).
thf(43130,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[43129]) ).
thf(43277,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[43130]) ).
thf(43293,plain,
! [A: $i] :
( ( e @ p @ p )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[43277]) ).
thf(36868,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,19992]) ).
thf(36869,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[36868]) ).
thf(36935,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[36869]) ).
thf(36950,plain,
! [A: $i] :
( ( A @ p @ s @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[36935]) ).
thf(20798,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,125]) ).
thf(20799,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[20798]) ).
thf(20800,plain,
! [A: $i] :
( ( A @ p @ atleast2p )
| ( e @ p @ ( A @ p @ subq ) ) ),
inference(pattern_uni,[status(thm)],[20799:[bind(A,$thf( D )),bind(B,$thf( D @ p )),bind(C,$thf( e ))]]) ).
thf(20828,plain,
! [A: $i] :
( ( A @ p @ atleast2p )
| ( e @ p @ ( A @ p @ subq ) ) ),
inference(simp,[status(thm)],[20800]) ).
thf(22679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( e @ p @ ( A @ p @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ~ $true
| ( A @ p @ atleast2p ) ),
inference(paramod_ordered,[status(thm)],[20828,118]) ).
thf(22680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( e @ p @ ( A @ p @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ( A @ p @ atleast2p ) ),
inference(simp,[status(thm)],[22679]) ).
thf(22681,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ mem ) )
| ( A @ p @ atleast2p ) ),
inference(pattern_uni,[status(thm)],[22680:[bind(A,$thf( D )),bind(B,$thf( D @ p )),bind(C,$thf( e @ p ))]]) ).
thf(22768,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ mem ) )
| ( A @ p @ atleast2p ) ),
inference(simp,[status(thm)],[22681]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 @ atleast7p )
!= ( B @ atleast7p ) )
| ~ ( B @ sk5 @ ( B @ subq ) )
| ~ $true
| ~ ( A @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[60,94]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( ( A @ sk3 @ atleast7p )
!= ( B @ atleast7p ) )
| ~ ( B @ sk5 @ ( B @ subq ) )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[291]) ).
thf(293,plain,
! [A: $i] :
( ~ ( A @ sk3 @ sk5 @ ( A @ sk3 @ subq ) )
| ~ ( A @ atleast8p ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( C )),bind(B,$thf( C @ sk3 ))]]) ).
thf(298,plain,
! [A: $i] :
( ~ ( A @ sk3 @ sk5 @ ( A @ sk3 @ subq ) )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[293]) ).
thf(43225,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37036]) ).
thf(43226,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[43225]) ).
thf(43286,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[43226]) ).
thf(43300,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[43286]) ).
thf(23010,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,17914]) ).
thf(23011,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[23010]) ).
thf(23020,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[23011]) ).
thf(23085,plain,
! [A: $i] :
( ( A @ n @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23020]) ).
thf(19701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,88]) ).
thf(19702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19701]) ).
thf(19703,plain,
! [B: $i,A: $i] : ( B @ n @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[19702:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ n @ n @ n ))]]) ).
thf(19815,plain,
! [B: $i,A: $i] : ( B @ n @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[19703]) ).
thf(25200,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,18367]) ).
thf(25201,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[25200]) ).
thf(25331,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[25201]) ).
thf(25388,plain,
! [A: $i] :
( ( e @ n @ s @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[25331]) ).
thf(161,plain,
! [A: $i] :
( ( A @ ( A @ sk12 @ subq ) )
| ~ ( A @ atleast4p ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(23212,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,17940]) ).
thf(23213,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[23212]) ).
thf(23239,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[23213]) ).
thf(23276,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[23239]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( A @ atleast5p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast4p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( A @ atleast5p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast4p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(28182,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,19986]) ).
thf(28183,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[28182]) ).
thf(28326,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[28183]) ).
thf(28355,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[28326]) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ mem ) )
| ~ ( A @ atleast2p ) ),
inference(cnfConj,[status(thm)],[121]) ).
thf(19854,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true
| ~ ( A @ atleast2p ) ),
inference(paramod_ordered,[status(thm)],[122,16774]) ).
thf(19855,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19854]) ).
thf(19889,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ( ( A @ sk7 )
!= ( B @ s ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19855]) ).
thf(19909,plain,
! [A: $i] :
( ( ( e @ s @ sk7 )
!= ( A @ s ) )
| ~ ( e @ s @ atleast2p ) ),
inference(simp,[status(thm)],[19889]) ).
thf(37173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36437,88]) ).
thf(37174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[37173]) ).
thf(37175,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[37174:[bind(A,$thf( K )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( K @ p @ n @ n @ n @ n @ n @ n ))]]) ).
thf(37386,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[37175]) ).
thf(44963,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37107]) ).
thf(44964,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[44963]) ).
thf(45116,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[44964]) ).
thf(45159,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ s @ p @ s ) ),
inference(simp,[status(thm)],[45116]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disj ) )
| ( B @ ( A @ ( B @ sk1 ) @ mem ) ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disj ) )
| ( B @ ( A @ ( B @ sk1 ) @ mem ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(19731,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,19296]) ).
thf(19732,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19731]) ).
thf(19773,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19732]) ).
thf(19817,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19773]) ).
thf(25278,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,18367]) ).
thf(25279,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[25278]) ).
thf(25316,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[25279]) ).
thf(25376,plain,
! [A: $i] :
( ( e @ n @ s )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[25316]) ).
thf(383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ~ $true
| ~ ( D @ ( C @ m ) @ ( B @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[104,34]) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ~ ( D @ ( C @ m ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(385,plain,
! [B: $i,A: $i] :
~ ( B @ s @ ( A @ m ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ s ))]]) ).
thf(390,plain,
! [B: $i,A: $i] :
~ ( B @ s @ ( A @ m ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[385]) ).
thf(395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( D @ s @ ( C @ m ) @ ( D @ mem ) ) )
| ~ $true
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[43,390]) ).
thf(396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( D @ s @ ( C @ m ) @ ( D @ mem ) ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[395]) ).
thf(399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( D @ s @ ( C @ m ) ) )
| ( ( A @ ( B @ sk1 ) )
!= D )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[396]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk1 ) @ s @ ( C @ m ) )
!= A )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[399]) ).
thf(19771,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,16775]) ).
thf(19772,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19771]) ).
thf(19783,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19772]) ).
thf(19797,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[19783]) ).
thf(13329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,88]) ).
thf(13330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[13329]) ).
thf(13331,plain,
! [B: $i,A: $i] : ( B @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[13330:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ n ))]]) ).
thf(13369,plain,
! [B: $i,A: $i] : ( B @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[13331]) ).
thf(13514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ n @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13369,69]) ).
thf(13515,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ n @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[13514]) ).
thf(13551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ n @ ( A @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[13515]) ).
thf(13563,plain,
! [B: $i,A: $i] :
( ( B @ n @ ( A @ u ) )
!= e ),
inference(simp,[status(thm)],[13551]) ).
thf(23588,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,17990]) ).
thf(23589,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[23588]) ).
thf(23644,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[23589]) ).
thf(23687,plain,
! [A: $i] :
( ( A @ n @ s @ s )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[23644]) ).
thf(59,plain,
! [A: $i] :
( ( A @ ( A @ sk3 @ subq ) )
| ~ ( A @ atleast8p ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(37113,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36971]) ).
thf(37114,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[37113:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(37165,plain,
! [A: $i] :
~ ( e @ p @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[37114]) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( C @ m ) @ ( B @ mem ) ) )
| ~ ( D @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,34]) ).
thf(382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( D @ ( C @ m ) @ ( B @ mem ) ) )
| ~ ( D @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( D @ ( C @ m ) ) )
| ( A != B )
| ~ ( D @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(391,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( C @ ( B @ m ) ) )
| ~ ( C @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[387]) ).
thf(24995,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,18312]) ).
thf(24996,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[24995]) ).
thf(25107,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ s @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[24996]) ).
thf(25145,plain,
! [A: $i] :
( ( e @ s @ s @ n )
!= ( A @ s @ n @ s ) ),
inference(simp,[status(thm)],[25107]) ).
thf(17695,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,16774]) ).
thf(17696,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[17695]) ).
thf(17735,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[17696]) ).
thf(17744,plain,
! [A: $i] :
( ( A @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17735]) ).
thf(18768,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ( B
!= ( C @ s @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17646]) ).
thf(18769,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ~ ( A @ s @ ( e @ s @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18768:[bind(A,$thf( e @ s @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(18822,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ s @ n @ mem ) ),
inference(simp,[status(thm)],[18769]) ).
thf(25306,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,18367]) ).
thf(25307,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[25306]) ).
thf(25319,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[25307]) ).
thf(25378,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[25319]) ).
thf(36847,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,17908]) ).
thf(36848,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[36847]) ).
thf(36940,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[36848]) ).
thf(36956,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ n @ n @ s ) ),
inference(simp,[status(thm)],[36940]) ).
thf(46491,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37165]) ).
thf(46492,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[46491]) ).
thf(46627,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ p @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[46492]) ).
thf(46677,plain,
! [A: $i] :
( ( A @ p @ s @ p )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[46627]) ).
thf(48418,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,38390]) ).
thf(48419,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) ),
inference(simp,[status(thm)],[48418]) ).
thf(48458,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ p ) ) ),
inference(simp,[status(thm)],[48419]) ).
thf(48523,plain,
! [A: $i] :
( ( A @ n @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[48458]) ).
thf(46589,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37165]) ).
thf(46590,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[46589]) ).
thf(46605,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ p @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[46590]) ).
thf(46662,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[46605]) ).
thf(49214,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,19296]) ).
thf(49215,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[49214]) ).
thf(49288,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[49215]) ).
thf(49333,plain,
! [A: $i] :
( ( e @ p @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[49288]) ).
thf(12217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,87]) ).
thf(12218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[12217]) ).
thf(12219,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[12218:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G @ s @ n @ n )),bind(D,$thf( D ))]]) ).
thf(12266,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[12219]) ).
thf(50370,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ s @ n @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,12266]) ).
thf(50371,plain,
! [A: $i] : ( A @ s @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[50370:[bind(A,$thf( J @ s @ n @ n )),bind(B,$thf( J @ s @ n @ n @ s )),bind(C,$thf( J ))]]) ).
thf(50438,plain,
! [A: $i] : ( A @ s @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[50371]) ).
thf(51163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50438,87]) ).
thf(51164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[51163]) ).
thf(51165,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[51164:[bind(A,$thf( H )),bind(B,$thf( H )),bind(C,$thf( H @ s @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(51303,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[51165]) ).
thf(72227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ s @ n @ n @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,51303]) ).
thf(72228,plain,
! [A: $i] : ( A @ s @ n @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[72227:[bind(A,$thf( L @ s @ n @ n @ n )),bind(B,$thf( L @ s @ n @ n @ n @ s )),bind(C,$thf( L ))]]) ).
thf(72316,plain,
! [A: $i] : ( A @ s @ n @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[72228]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( A @ atleast11p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast10p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( A @ atleast11p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast10p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(187,plain,
! [A: $i] :
( ~ ( A @ sk15 @ ( A @ subq ) )
| ~ ( A @ atleast13p ) ),
inference(cnfConj,[status(thm)],[184]) ).
thf(7779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ m ) )
!= ( D @ ( C @ m ) ) )
| ( C @ ( e @ ( B @ sk1 ) @ mem ) )
| ( B @ ( D @ ( C @ m ) @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[7681,307]) ).
thf(7780,plain,
! [B: $i,A: $i] :
( ( e @ ( e @ ( B @ sk1 ) @ mem ) )
| ( B @ ( A @ ( e @ m ) @ disj ) ) ),
inference(pattern_uni,[status(thm)],[7779:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( e )),bind(D,$thf( A ))]]) ).
thf(10235,plain,
! [A: $i] :
( $false
| ( A @ ( e @ disj ) ) ),
inference(rewrite,[status(thm)],[7780,7681,69]) ).
thf(10236,plain,
! [A: $i] : ( A @ ( e @ disj ) ),
inference(simp,[status(thm)],[10235]) ).
thf(37289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36437,87]) ).
thf(37290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[37289]) ).
thf(37291,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[37290:[bind(A,$thf( K )),bind(B,$thf( e )),bind(C,$thf( K @ p @ n @ n @ n @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(37382,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[37291]) ).
thf(36851,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,18308]) ).
thf(36852,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[36851]) ).
thf(36925,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[36852]) ).
thf(36983,plain,
! [A: $i] :
( ( A @ s @ n @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[36925]) ).
thf(20807,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,125]) ).
thf(20808,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[20807]) ).
thf(20809,plain,
! [A: $i] :
( ( A @ s @ atleast2p )
| ( A @ p @ ( A @ s @ subq ) ) ),
inference(pattern_uni,[status(thm)],[20808:[bind(A,$thf( D )),bind(B,$thf( D @ s )),bind(C,$thf( D ))]]) ).
thf(20833,plain,
! [A: $i] :
( ( A @ s @ atleast2p )
| ( A @ p @ ( A @ s @ subq ) ) ),
inference(simp,[status(thm)],[20809]) ).
thf(24790,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,18308]) ).
thf(24791,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[24790]) ).
thf(24902,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[24791]) ).
thf(24951,plain,
! [A: $i] :
( ( A @ s @ n @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24902]) ).
thf(19245,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,16681]) ).
thf(19246,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19245]) ).
thf(19251,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s ) )
| ( e != e ) ),
inference(simp,[status(thm)],[19246]) ).
thf(19276,plain,
! [B: $i,A: $i] :
( ( A @ p )
!= ( B @ n @ s ) ),
inference(simp,[status(thm)],[19251]) ).
thf(53846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ ( D @ p @ u ) @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,20153]) ).
thf(53847,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[53846:[bind(A,$thf( J @ ( K @ p @ u ) )),bind(B,$thf( J @ ( K @ p @ u ) @ s )),bind(C,$thf( J )),bind(D,$thf( K ))]]) ).
thf(53917,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[53847]) ).
thf(27779,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,19961]) ).
thf(27780,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[27779]) ).
thf(27931,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[27780]) ).
thf(27957,plain,
! [A: $i] :
( ( A @ p @ n @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[27931]) ).
thf(19822,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true
| ~ ( A @ atleast2p ) ),
inference(paramod_ordered,[status(thm)],[122,69]) ).
thf(19823,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19822]) ).
thf(19824,plain,
~ ( e @ atleast2p ),
inference(pattern_uni,[status(thm)],[19823:[bind(A,$thf( e )),bind(B,$thf( e @ sk7 ))]]) ).
thf(41056,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,17940]) ).
thf(41057,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41056]) ).
thf(41097,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41057]) ).
thf(41130,plain,
! [A: $i] :
( ( e @ s @ p @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[41097]) ).
thf(76,plain,
! [A: $i] :
( ( A @ ( A @ sk4 @ subq ) )
| ~ ( A @ atleast6p ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(36855,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,18371]) ).
thf(36856,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[36855]) ).
thf(36916,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ n @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[36856]) ).
thf(36974,plain,
! [A: $i] :
( ( A @ s @ s @ p )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[36916]) ).
thf(19410,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,19295]) ).
thf(19411,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19410]) ).
thf(19490,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19411]) ).
thf(19523,plain,
! [A: $i] :
( ( A @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19490]) ).
thf(21544,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21386,69]) ).
thf(21545,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[21544]) ).
thf(21640,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[21545]) ).
thf(21657,plain,
! [A: $i] :
( ( A @ p @ n @ n )
!= e ),
inference(simp,[status(thm)],[21640]) ).
thf(41069,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,19961]) ).
thf(41070,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[41069]) ).
thf(41123,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[41070]) ).
thf(41157,plain,
! [A: $i] :
( ( A @ p @ n @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41123]) ).
thf(25791,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,18371]) ).
thf(25792,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[25791]) ).
thf(25910,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[25792]) ).
thf(25955,plain,
! [A: $i] :
( ( A @ s @ s @ n @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[25910]) ).
thf(27677,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,19955]) ).
thf(27678,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[27677]) ).
thf(27694,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[27678]) ).
thf(27738,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ n @ s ) ),
inference(simp,[status(thm)],[27694]) ).
thf(941,plain,
! [A: $i] :
( ( ( A @ sk4 @ atleast5p )
!= ( e @ atleast5p ) )
| ~ $true
| ~ ( A @ atleast6p ) ),
inference(paramod_ordered,[status(thm)],[77,925]) ).
thf(942,plain,
! [A: $i] :
( ( ( A @ sk4 @ atleast5p )
!= ( e @ atleast5p ) )
| ~ ( A @ atleast6p ) ),
inference(simp,[status(thm)],[941]) ).
thf(943,plain,
! [A: $i] :
( ( ( A @ sk4 )
!= e )
| ~ ( A @ atleast6p ) ),
inference(simp,[status(thm)],[942]) ).
thf(108,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ subq ) )
| ~ ( A @ atleast12p ) ),
inference(cnfConj,[status(thm)],[107]) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[44,69]) ).
thf(448,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[447]) ).
thf(449,plain,
! [A: $i] : ( e @ ( A @ disj ) ),
inference(pattern_uni,[status(thm)],[448:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( E @ ( e @ sk1 ) ))]]) ).
thf(462,plain,
! [A: $i] : ( e @ ( A @ disj ) ),
inference(simp,[status(thm)],[449]) ).
thf(40991,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,19986]) ).
thf(40992,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[40991]) ).
thf(41114,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[40992]) ).
thf(41147,plain,
! [A: $i] :
( ( e @ s @ p @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[41114]) ).
thf(36876,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,17914]) ).
thf(36877,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[36876]) ).
thf(36921,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[36877]) ).
thf(36979,plain,
! [A: $i] :
( ( A @ n @ n @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[36921]) ).
thf(20659,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19278,87]) ).
thf(20660,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( D @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[20659]) ).
thf(20661,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ p @ ( B @ u ) @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20660:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( H @ p @ ( F @ u ) )),bind(E,$thf( E ))]]) ).
thf(20731,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ p @ ( B @ u ) @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20661]) ).
thf(378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ~ $true
| ~ ( E @ ( D @ m ) @ ( C @ mem ) )
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[43,34]) ).
thf(379,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ~ ( E @ ( D @ m ) @ ( C @ mem ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[378]) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ m ) @ ( C @ ( B @ sk1 ) @ mem ) )
| ( B @ ( C @ disj ) ) ),
inference(pattern_uni,[status(thm)],[379:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ sk1 ) )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).
thf(394,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ m ) @ ( C @ ( B @ sk1 ) @ mem ) )
| ( B @ ( C @ disj ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(44759,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,37103]) ).
thf(44760,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) ),
inference(simp,[status(thm)],[44759]) ).
thf(44826,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ p ) ) ),
inference(simp,[status(thm)],[44760]) ).
thf(44878,plain,
! [A: $i] :
( ( A @ s @ p @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[44826]) ).
thf(21549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21386,125]) ).
thf(21550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[21549]) ).
thf(21551,plain,
! [A: $i] :
( ( A @ p @ n @ n @ atleast2p )
| ( e @ p @ ( A @ p @ n @ n @ subq ) ) ),
inference(pattern_uni,[status(thm)],[21550:[bind(A,$thf( F )),bind(B,$thf( F @ p @ n @ n )),bind(C,$thf( e ))]]) ).
thf(21671,plain,
! [A: $i] :
( ( A @ p @ n @ n @ atleast2p )
| ( e @ p @ ( A @ p @ n @ n @ subq ) ) ),
inference(simp,[status(thm)],[21551]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( A @ atleast6p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast5p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( A @ atleast6p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast5p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk4 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast6p ) ),
inference(paramod_ordered,[status(thm)],[713,78]) ).
thf(921,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk4 @ ( B @ subq ) ) )
| ~ ( B @ atleast6p ) ),
inference(simp,[status(thm)],[920]) ).
thf(922,plain,
~ ( e @ atleast6p ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( e @ sk4 )),bind(B,$thf( e ))]]) ).
thf(38373,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ p ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,36978]) ).
thf(38374,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ n @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[38373:[bind(A,$thf( A )),bind(B,$thf( E @ n @ p )),bind(C,$thf( E ))]]) ).
thf(38394,plain,
! [A: $i] :
~ ( A @ n @ p @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[38374]) ).
thf(48598,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,38394]) ).
thf(48599,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[48598]) ).
thf(48744,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[48599]) ).
thf(48803,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ n @ p @ s ) ),
inference(simp,[status(thm)],[48744]) ).
thf(62562,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ n @ n @ n @ n @ n @ n @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,37382]) ).
thf(62563,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[62562:[bind(A,$thf( R @ p @ n @ n @ n @ n @ n @ n )),bind(B,$thf( R @ p @ n @ n @ n @ n @ n @ n @ s )),bind(C,$thf( R ))]]) ).
thf(62656,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[62563]) ).
thf(41000,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,16680]) ).
thf(41001,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[41000]) ).
thf(41119,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[41001]) ).
thf(41153,plain,
! [A: $i] :
( ( A @ n @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[41119]) ).
thf(162,plain,
! [A: $i] :
( ( A @ sk12 @ atleast3p )
| ~ ( A @ atleast4p ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(23310,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,17946]) ).
thf(23311,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[23310]) ).
thf(23442,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[23311]) ).
thf(23466,plain,
! [A: $i] :
( ( A @ n @ s @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23442]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( A @ atleast12p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast11p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[107]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( A @ atleast12p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast11p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(36886,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,17997]) ).
thf(36887,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[36886]) ).
thf(36915,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[36887]) ).
thf(36973,plain,
! [A: $i] :
( ( e @ n @ p )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[36915]) ).
thf(47138,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,38355]) ).
thf(47139,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[47138]) ).
thf(47180,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ p @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[47139]) ).
thf(47242,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[47180]) ).
thf(19733,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,16774]) ).
thf(19734,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[19733]) ).
thf(19778,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[19734]) ).
thf(19789,plain,
! [A: $i] :
( ( A @ s @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19778]) ).
thf(123,plain,
! [A: $i] :
( ~ ( A @ sk7 @ p @ ( A @ subq ) )
| ~ ( A @ atleast2p ) ),
inference(cnfConj,[status(thm)],[121]) ).
thf(40988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,88]) ).
thf(40989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[40988]) ).
thf(40990,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[40989:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ p @ n ))]]) ).
thf(41151,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[40990]) ).
thf(194,plain,
! [A: $i] :
( ( A @ sk16 @ atleast13p )
| ~ ( A @ atleast14p ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(145,plain,
! [A: $i] :
( ( A @ ( A @ sk10 @ subq ) )
| ~ ( A @ atleast5p ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(42954,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37029]) ).
thf(42955,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[42954]) ).
thf(42978,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ p @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[42955]) ).
thf(43051,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[42978]) ).
thf(48,plain,
! [A: $i] :
( ( A @ ( A @ sk2 @ subq ) )
| ~ ( A @ atleast9p ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( A @ atleast8p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast7p )
| ~ ( A @ ( B @ subq ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A @ atleast8p )
| ( B @ ( A @ subq ) )
| ~ ( B @ atleast7p )
| ~ ( A @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(20496,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ n @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17742]) ).
thf(20497,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[20496:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(20545,plain,
! [A: $i] :
~ ( e @ n @ n @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[20497]) ).
thf(19858,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true
| ~ ( A @ atleast2p ) ),
inference(paramod_ordered,[status(thm)],[122,19295]) ).
thf(19859,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19858]) ).
thf(19887,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ( ( A @ sk7 )
!= ( B @ p ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19859]) ).
thf(19907,plain,
! [A: $i] :
( ( ( e @ s @ sk7 )
!= ( A @ p ) )
| ~ ( e @ s @ atleast2p ) ),
inference(simp,[status(thm)],[19887]) ).
thf(23510,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,17990]) ).
thf(23511,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[23510]) ).
thf(23639,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[23511]) ).
thf(23683,plain,
! [A: $i] :
( ( A @ n @ s @ n @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[23639]) ).
thf(25198,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,18367]) ).
thf(25199,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[25198]) ).
thf(25312,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[25199]) ).
thf(25372,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[25312]) ).
thf(19828,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true
| ~ ( A @ atleast2p ) ),
inference(paramod_ordered,[status(thm)],[122,16680]) ).
thf(19829,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19828]) ).
thf(19890,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ( ( A @ sk7 )
!= ( B @ n ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19829]) ).
thf(19910,plain,
! [A: $i] :
( ( ( e @ s @ sk7 )
!= ( A @ n ) )
| ~ ( e @ s @ atleast2p ) ),
inference(simp,[status(thm)],[19890]) ).
thf(242,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( A @ n @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,215]) ).
thf(259,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s ) )
| ( A
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s ) )
| ( A @ n @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(263,plain,
( ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ s ) )
| ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ n @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(56738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( D @ p @ ( C @ u ) @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,20731]) ).
thf(56739,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[56738:[bind(A,$thf( K @ p @ ( I @ u ) )),bind(B,$thf( K @ p @ ( I @ u ) @ s )),bind(C,$thf( I )),bind(D,$thf( K ))]]) ).
thf(56805,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[56739]) ).
thf(20338,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20165,69]) ).
thf(20339,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[20338]) ).
thf(20425,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[20339]) ).
thf(20438,plain,
! [A: $i] :
( ( A @ p @ n )
!= e ),
inference(simp,[status(thm)],[20425]) ).
thf(17679,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,16680]) ).
thf(17680,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[17679]) ).
thf(17736,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[17680]) ).
thf(17745,plain,
! [A: $i] :
( ( A @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17736]) ).
thf(212,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk3 @ ( A @ subq ) ) )
| ~ $true
| ~ ( A @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[211,61]) ).
thf(213,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk3 @ ( A @ subq ) ) )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[212]) ).
thf(218,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( A @ sk3 ) )
| ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) )
!= A )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[213]) ).
thf(220,plain,
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[218]) ).
thf(37434,plain,
( ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast8p ) ),
inference(rewrite,[status(thm)],[220,66]) ).
thf(12206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,88]) ).
thf(12207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[12206]) ).
thf(12208,plain,
! [B: $i,A: $i] : ( B @ s @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[12207:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ s @ n @ n ))]]) ).
thf(12256,plain,
! [B: $i,A: $i] : ( B @ s @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[12208]) ).
thf(177,plain,
! [A: $i] :
( ( A @ ( A @ sk14 @ subq ) )
| ~ ( A @ atleast11p ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(24868,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,18308]) ).
thf(24869,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[24868]) ).
thf(24928,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[24869]) ).
thf(24969,plain,
! [A: $i] :
( ( A @ s @ n @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24928]) ).
thf(40993,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,17946]) ).
thf(40994,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[40993]) ).
thf(41105,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[40994]) ).
thf(41138,plain,
! [A: $i] :
( ( A @ n @ s @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41105]) ).
thf(21121,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ s ) )
| ( A
!= ( e @ s @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19667]) ).
thf(21122,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ~ ( B @ p @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[21121:[bind(A,$thf( A )),bind(B,$thf( E @ p @ s )),bind(C,$thf( E ))]]) ).
thf(21158,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ s @ n @ mem ) ),
inference(simp,[status(thm)],[21122]) ).
thf(450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ( D @ ( C @ mem ) )
| ~ $true
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[44,33]) ).
thf(451,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( D @ m ) @ ( C @ mem ) ) )
| ( D @ ( C @ mem ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ m ) @ sk1 ) @ mem ) )
| ( C @ ( B @ m ) @ ( A @ disj ) ) ),
inference(pattern_uni,[status(thm)],[451:[bind(A,$thf( G )),bind(B,$thf( I @ ( H @ m ) )),bind(C,$thf( G @ ( I @ ( H @ m ) @ sk1 ) )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).
thf(463,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ m ) @ sk1 ) @ mem ) )
| ( C @ ( B @ m ) @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(234,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( A @ n @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(247,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s ) )
| ( A
!= ( e @ n @ s @ n @ s ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( A @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(264,plain,
( ( ( e @ n @ s @ n @ ( e @ n @ u ) @ s )
!= ( e @ n @ s @ n @ s @ s ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(47513,plain,
( ( ( e @ n @ s @ n @ ( e @ n @ u ) @ s )
!= ( e @ n @ s @ n @ s @ s ) )
| ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ s @ n @ u ) @ subq ) ) ),
inference(rewrite,[status(thm)],[264,66]) ).
thf(19412,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,19295]) ).
thf(19413,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19412]) ).
thf(19512,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19413]) ).
thf(19549,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19512]) ).
thf(195,plain,
! [A: $i] :
( ~ ( A @ sk16 @ ( A @ subq ) )
| ~ ( A @ atleast14p ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(34609,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk16 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast14p ) ),
inference(paramod_ordered,[status(thm)],[8581,195]) ).
thf(34610,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk16 @ ( B @ subq ) ) )
| ~ ( B @ atleast14p ) ),
inference(simp,[status(thm)],[34609]) ).
thf(34611,plain,
~ ( e @ atleast14p ),
inference(pattern_uni,[status(thm)],[34610:[bind(A,$thf( e @ sk16 )),bind(B,$thf( e ))]]) ).
thf(154,plain,
! [A: $i] :
( ( A @ sk11 @ atleast2p )
| ~ ( A @ atleast3p ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(32932,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk15 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast13p ) ),
inference(paramod_ordered,[status(thm)],[8581,187]) ).
thf(32933,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk15 @ ( B @ subq ) ) )
| ~ ( B @ atleast13p ) ),
inference(simp,[status(thm)],[32932]) ).
thf(32934,plain,
~ ( e @ atleast13p ),
inference(pattern_uni,[status(thm)],[32933:[bind(A,$thf( e @ sk15 )),bind(B,$thf( e ))]]) ).
thf(19704,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,16680]) ).
thf(19705,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[19704]) ).
thf(19779,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[19705]) ).
thf(19791,plain,
! [A: $i] :
( ( A @ n @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19779]) ).
thf(24585,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,18038]) ).
thf(24586,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[24585]) ).
thf(24722,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[24586]) ).
thf(24746,plain,
! [A: $i] :
( ( A @ s @ s @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24722]) ).
thf(24187,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,18032]) ).
thf(24188,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[24187]) ).
thf(24201,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[24188]) ).
thf(24231,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[24201]) ).
thf(48388,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,38390]) ).
thf(48389,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) ),
inference(simp,[status(thm)],[48388]) ).
thf(48443,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ p ) ) ),
inference(simp,[status(thm)],[48389]) ).
thf(48514,plain,
! [A: $i] :
( ( A @ n @ p @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[48443]) ).
thf(24896,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,18308]) ).
thf(24897,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[24896]) ).
thf(24923,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[24897]) ).
thf(24965,plain,
! [A: $i] :
( ( A @ s @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24923]) ).
thf(139,plain,
! [A: $i] :
( ~ ( A @ sk9 @ ( A @ subq ) )
| ~ ( A @ atleast16p ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(929,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk9 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast16p ) ),
inference(paramod_ordered,[status(thm)],[713,139]) ).
thf(930,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk9 @ ( B @ subq ) ) )
| ~ ( B @ atleast16p ) ),
inference(simp,[status(thm)],[929]) ).
thf(931,plain,
~ ( e @ atleast16p ),
inference(pattern_uni,[status(thm)],[930:[bind(A,$thf( e @ sk9 )),bind(B,$thf( e ))]]) ).
thf(41040,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,18038]) ).
thf(41041,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[41040]) ).
thf(41110,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[41041]) ).
thf(41143,plain,
! [A: $i] :
( ( A @ s @ s @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41110]) ).
thf(17179,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,16680]) ).
thf(17180,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[17179]) ).
thf(17263,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[17180]) ).
thf(17294,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17263]) ).
thf(17674,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,69]) ).
thf(17675,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[17674]) ).
thf(17734,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[17675]) ).
thf(17743,plain,
! [A: $i] :
( ( A @ n @ n )
!= e ),
inference(simp,[status(thm)],[17734]) ).
thf(926,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk3 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[713,61]) ).
thf(927,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk3 @ ( B @ subq ) ) )
| ~ ( B @ atleast8p ) ),
inference(simp,[status(thm)],[926]) ).
thf(928,plain,
~ ( e @ atleast8p ),
inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( e @ sk3 )),bind(B,$thf( e ))]]) ).
thf(1106,plain,
! [A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( e @ atleast8p ) )
| ~ $true
| ~ ( A @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[49,928]) ).
thf(1107,plain,
! [A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( e @ atleast8p ) )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[1106]) ).
thf(1108,plain,
! [A: $i] :
( ( ( A @ sk2 )
!= e )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[1107]) ).
thf(19699,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,69]) ).
thf(19700,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19699]) ).
thf(19784,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[19700]) ).
thf(19798,plain,
! [A: $i] :
( ( A @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[19784]) ).
thf(23512,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,17990]) ).
thf(23513,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[23512]) ).
thf(23643,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[23513]) ).
thf(23686,plain,
! [A: $i] :
( ( A @ n @ s @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[23643]) ).
thf(38590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( D @ ( C @ subq ) ) )
| ( D @ p @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36643,118]) ).
thf(38591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( D @ ( C @ subq ) ) )
| ( D @ p @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[38590]) ).
thf(38592,plain,
! [B: $i,A: $i] : ( A @ p @ ( B @ ( A @ m ) @ mem ) ),
inference(pattern_uni,[status(thm)],[38591:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ m ) )),bind(D,$thf( E ))]]) ).
thf(38665,plain,
! [B: $i,A: $i] : ( A @ p @ ( B @ ( A @ m ) @ mem ) ),
inference(simp,[status(thm)],[38592]) ).
thf(28184,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,19986]) ).
thf(28185,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[28184]) ).
thf(28331,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[28185]) ).
thf(28361,plain,
! [A: $i] :
( ( e @ s @ s @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[28331]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ mem ) )
| ~ ( A @ ( C @ mem ) )
| ~ ( B @ ( A @ disj ) ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(13868,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ n @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13371,69]) ).
thf(13869,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ n @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[13868]) ).
thf(13906,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ n @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[13869]) ).
thf(13919,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ n @ u ) )
!= e ),
inference(simp,[status(thm)],[13906]) ).
thf(73512,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72316,69]) ).
thf(73513,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[73512]) ).
thf(73723,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[73513]) ).
thf(73861,plain,
! [A: $i] :
( ( A @ s @ n @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[73723]) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( C @ s @ ( B @ m ) @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,390]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( C @ s @ ( B @ m ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( C @ s @ ( B @ m ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[398]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ m ) )
!= ( B @ s ) ),
inference(simp,[status(thm)],[400]) ).
thf(49154,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,16680]) ).
thf(49155,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[49154]) ).
thf(49311,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[49155]) ).
thf(49361,plain,
! [A: $i] :
( ( A @ n @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[49311]) ).
thf(45232,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,37152]) ).
thf(45233,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[45232]) ).
thf(45385,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[45233]) ).
thf(45432,plain,
! [A: $i] :
( ( e @ p @ p )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[45385]) ).
thf(235,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( A @ n @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(256,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s ) )
| ( A
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( A @ n @ subq ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(260,plain,
( ( ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ s )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s ) )
| ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ n @ subq ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(41880,plain,
( ( ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ s )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s ) )
| ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ n @ subq ) ) ),
inference(rewrite,[status(thm)],[260,66]) ).
thf(12463,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ s @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12156,69]) ).
thf(12464,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ s @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[12463]) ).
thf(12502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ s @ ( A @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[12464]) ).
thf(12516,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ u ) )
!= e ),
inference(simp,[status(thm)],[12502]) ).
thf(19608,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19169,19296]) ).
thf(19609,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19608]) ).
thf(19638,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s ) )
| ( e != e ) ),
inference(simp,[status(thm)],[19609]) ).
thf(19686,plain,
! [B: $i,A: $i] :
( ( A @ p )
!= ( B @ p @ s ) ),
inference(simp,[status(thm)],[19638]) ).
thf(186,plain,
! [A: $i] :
( ( A @ sk15 @ atleast12p )
| ~ ( A @ atleast13p ) ),
inference(cnfConj,[status(thm)],[184]) ).
thf(22904,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,17914]) ).
thf(22905,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[22904]) ).
thf(23035,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[22905]) ).
thf(23096,plain,
! [A: $i] :
( ( A @ n @ n @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23035]) ).
thf(24993,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,18312]) ).
thf(24994,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[24993]) ).
thf(25133,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ s @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[24994]) ).
thf(25163,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ s @ n @ s ) ),
inference(simp,[status(thm)],[25133]) ).
thf(29191,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,20044]) ).
thf(29192,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[29191]) ).
thf(29336,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[29192]) ).
thf(29367,plain,
! [A: $i] :
( ( e @ n @ s @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[29336]) ).
thf(6229,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ( e != e )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3038,209]) ).
thf(6230,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[6229]) ).
thf(6231,plain,
! [A: $i] :
~ ( e @ ( A @ s @ subq ) ),
inference(pattern_uni,[status(thm)],[6230:[bind(A,$thf( C @ s )),bind(B,$thf( C ))]]) ).
thf(6889,plain,
! [A: $i] :
~ ( e @ ( A @ s @ subq ) ),
inference(simp,[status(thm)],[6231]) ).
thf(7661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ s @ subq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7107,6889]) ).
thf(7662,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ s @ subq ) ) ),
inference(simp,[status(thm)],[7661]) ).
thf(7670,plain,
! [C: $i,B: $i,A: $i] :
( ( A != e )
| ( ( B @ ( e @ m ) )
!= ( C @ s ) ) ),
inference(simp,[status(thm)],[7662]) ).
thf(7687,plain,
! [B: $i,A: $i] :
( ( A @ ( e @ m ) )
!= ( B @ s ) ),
inference(simp,[status(thm)],[7670]) ).
thf(9470,plain,
! [A: $i] :
( ( A @ s )
!= e ),
inference(rewrite,[status(thm)],[7687,7681]) ).
thf(4579,plain,
! [A: $i] :
( ( ( A @ sk15 @ atleast12p )
!= ( e @ atleast12p ) )
| ~ $true
| ~ ( A @ atleast13p ) ),
inference(paramod_ordered,[status(thm)],[186,913]) ).
thf(4580,plain,
! [A: $i] :
( ( ( A @ sk15 @ atleast12p )
!= ( e @ atleast12p ) )
| ~ ( A @ atleast13p ) ),
inference(simp,[status(thm)],[4579]) ).
thf(4591,plain,
! [A: $i] :
( ( ( A @ sk15 )
!= e )
| ~ ( A @ atleast13p ) ),
inference(simp,[status(thm)],[4580]) ).
thf(25399,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24434,69]) ).
thf(25400,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[25399]) ).
thf(25533,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[25400]) ).
thf(25564,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[25533]) ).
thf(48320,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,38390]) ).
thf(48321,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) ),
inference(simp,[status(thm)],[48320]) ).
thf(48453,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ p ) ) ),
inference(simp,[status(thm)],[48321]) ).
thf(48519,plain,
! [A: $i] :
( ( A @ n @ p @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[48453]) ).
thf(24788,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,18308]) ).
thf(24789,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[24788]) ).
thf(24903,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[24789]) ).
thf(24952,plain,
! [A: $i] :
( ( A @ s @ n @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24903]) ).
thf(22551,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,17908]) ).
thf(22552,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[22551]) ).
thf(22577,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[22552]) ).
thf(22615,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ n @ s ) ),
inference(simp,[status(thm)],[22577]) ).
thf(21733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20453,88]) ).
thf(21734,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) )
!= ( E @ ( C @ mem ) ) )
| ( E @ ( D @ u ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[21733]) ).
thf(21735,plain,
! [C: $i,B: $i,A: $i] : ( C @ p @ n @ ( B @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[21734:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( e )),bind(D,$thf( D )),bind(E,$thf( I @ p @ n @ ( F @ u ) ))]]) ).
thf(21853,plain,
! [C: $i,B: $i,A: $i] : ( C @ p @ n @ ( B @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[21735]) ).
thf(36882,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,18032]) ).
thf(36883,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[36882]) ).
thf(36926,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[36883]) ).
thf(36984,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[36926]) ).
thf(28612,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,20037]) ).
thf(28613,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[28612]) ).
thf(28761,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[28613]) ).
thf(28805,plain,
! [A: $i] :
( ( A @ p @ s @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[28761]) ).
thf(146,plain,
! [A: $i] :
( ( A @ sk10 @ atleast4p )
| ~ ( A @ atleast5p ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(51049,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50438,69]) ).
thf(51050,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[51049]) ).
thf(51207,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[51050]) ).
thf(51252,plain,
! [A: $i] :
( ( A @ s @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[51207]) ).
thf(19556,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,19296]) ).
thf(19557,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19556]) ).
thf(19645,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19557]) ).
thf(19696,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19645]) ).
thf(21198,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ s ) )
| ( A
!= ( e @ n @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19696]) ).
thf(21199,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ~ ( B @ p @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[21198:[bind(A,$thf( A )),bind(B,$thf( E @ p @ s )),bind(C,$thf( E ))]]) ).
thf(21241,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ n @ n @ mem ) ),
inference(simp,[status(thm)],[21199]) ).
thf(49278,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47454,16681]) ).
thf(49279,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[49278]) ).
thf(49305,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[49279]) ).
thf(49352,plain,
! [A: $i] :
( ( e @ p @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[49305]) ).
thf(28268,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,19986]) ).
thf(28269,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[28268]) ).
thf(28338,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[28269]) ).
thf(28370,plain,
! [A: $i] :
( ( A @ p @ s @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[28338]) ).
thf(45298,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,37152]) ).
thf(45299,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[45298]) ).
thf(45377,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[45299]) ).
thf(45428,plain,
! [A: $i] :
( ( e @ p @ s )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[45377]) ).
thf(23880,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,17997]) ).
thf(23881,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[23880]) ).
thf(24008,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[23881]) ).
thf(24046,plain,
! [A: $i] :
( ( e @ n @ s @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[24008]) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ m ) @ ( B @ mem ) )
| ( D @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,36]) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( C @ ( B @ mem ) ) )
| ( D @ ( C @ m ) @ ( B @ mem ) )
| ( D @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[607]) ).
thf(609,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ s @ m ) @ ( B @ mem ) )
| ( A @ ( B @ mem ) ) ),
inference(pattern_uni,[status(thm)],[608:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ s ))]]) ).
thf(620,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ s @ m ) @ ( B @ mem ) )
| ( A @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[609]) ).
thf(23414,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,17946]) ).
thf(23415,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[23414]) ).
thf(23420,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[23415]) ).
thf(23501,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23420]) ).
thf(29189,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,20044]) ).
thf(29190,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[29189]) ).
thf(29319,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[29190]) ).
thf(29355,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[29319]) ).
thf(23984,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,17997]) ).
thf(23985,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[23984]) ).
thf(24013,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[23985]) ).
thf(24051,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[24013]) ).
thf(20059,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19266,69]) ).
thf(20060,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[20059]) ).
thf(20140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) )
!= e )
| ( e != C ) ),
inference(simp,[status(thm)],[20060]) ).
thf(20170,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ p @ u ) )
!= e ),
inference(simp,[status(thm)],[20140]) ).
thf(17544,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,16775]) ).
thf(17545,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17544]) ).
thf(17624,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17545]) ).
thf(17649,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[17624]) ).
thf(32654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32159,88]) ).
thf(32655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[32654]) ).
thf(32656,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[32655:[bind(A,$thf( J )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( J @ p @ n @ n @ n @ n @ n ))]]) ).
thf(32845,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[32656]) ).
thf(73968,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( E @ ( D @ m ) @ ( C @ sk1 ) @ mem ) ) )
| ~ $true
| ( C @ ( E @ ( D @ m ) @ disj ) )
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[44,393]) ).
thf(73969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( E @ ( E @ ( D @ m ) @ ( C @ sk1 ) @ mem ) ) )
| ( C @ ( E @ ( D @ m ) @ disj ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[73968]) ).
thf(73970,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ m ) @ disj ) )
| ( A @ ( A @ ( B @ m ) @ disj ) ) ),
inference(pattern_uni,[status(thm)],[73969:[bind(A,$thf( B @ ( F @ m ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F )),bind(E,$thf( B ))]]) ).
thf(74257,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ m ) @ disj ) ),
inference(simp,[status(thm)],[73970]) ).
thf(36857,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,20037]) ).
thf(36858,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[36857]) ).
thf(36933,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[36858]) ).
thf(36948,plain,
! [A: $i] :
( ( A @ p @ s @ p )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[36933]) ).
thf(19741,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19022,19295]) ).
thf(19742,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19741]) ).
thf(19780,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19742]) ).
thf(19792,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19780]) ).
thf(21188,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ n @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19696]) ).
thf(21189,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[21188:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(21236,plain,
! [A: $i] :
~ ( e @ n @ n @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[21189]) ).
thf(46864,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,38351]) ).
thf(46865,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[46864]) ).
thf(46884,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[46865]) ).
thf(46942,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[46884]) ).
thf(24081,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,18032]) ).
thf(24082,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[24081]) ).
thf(24196,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[24082]) ).
thf(24227,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[24196]) ).
thf(36849,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,17990]) ).
thf(36850,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[36849]) ).
thf(36918,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[36850]) ).
thf(36976,plain,
! [A: $i] :
( ( A @ n @ s @ p )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[36918]) ).
thf(289,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk5 @ ( A @ subq ) ) )
| ~ $true
| ~ ( A @ atleast7p ) ),
inference(paramod_ordered,[status(thm)],[211,94]) ).
thf(290,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk5 @ ( A @ subq ) ) )
| ~ ( A @ atleast7p ) ),
inference(simp,[status(thm)],[289]) ).
thf(296,plain,
! [A: $i] :
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( A @ sk5 ) )
| ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) )
!= A )
| ~ ( A @ atleast7p ) ),
inference(simp,[status(thm)],[290]) ).
thf(299,plain,
( ( ( e @ n @ n @ ( e @ n @ s @ a ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk5 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast7p ) ),
inference(simp,[status(thm)],[296]) ).
thf(56833,plain,
( ( ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) )
!= ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ sk5 ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ s @ u ) @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ ( e @ n @ s @ n @ s @ u ) @ u ) @ atleast7p ) ),
inference(rewrite,[status(thm)],[299,66]) ).
thf(42924,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,37029]) ).
thf(42925,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[42924]) ).
thf(42995,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ p @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[42925]) ).
thf(43065,plain,
! [A: $i] :
( ( A @ s @ s @ s )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[42995]) ).
thf(938,plain,
! [A: $i] :
( ( ( A @ sk5 @ atleast6p )
!= ( e @ atleast6p ) )
| ~ $true
| ~ ( A @ atleast7p ) ),
inference(paramod_ordered,[status(thm)],[93,922]) ).
thf(939,plain,
! [A: $i] :
( ( ( A @ sk5 @ atleast6p )
!= ( e @ atleast6p ) )
| ~ ( A @ atleast7p ) ),
inference(simp,[status(thm)],[938]) ).
thf(940,plain,
! [A: $i] :
( ( ( A @ sk5 )
!= e )
| ~ ( A @ atleast7p ) ),
inference(simp,[status(thm)],[939]) ).
thf(36818,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,19986]) ).
thf(36819,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[36818]) ).
thf(36929,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[36819]) ).
thf(36944,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[36929]) ).
thf(48696,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,38394]) ).
thf(48697,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[48696]) ).
thf(48758,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[48697]) ).
thf(48812,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ p @ s ) ),
inference(simp,[status(thm)],[48758]) ).
thf(31256,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk14 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast11p ) ),
inference(paramod_ordered,[status(thm)],[8581,179]) ).
thf(31257,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk14 @ ( B @ subq ) ) )
| ~ ( B @ atleast11p ) ),
inference(simp,[status(thm)],[31256]) ).
thf(31258,plain,
~ ( e @ atleast11p ),
inference(pattern_uni,[status(thm)],[31257:[bind(A,$thf( e @ sk14 )),bind(B,$thf( e ))]]) ).
thf(19406,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11372,19295]) ).
thf(19407,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19406]) ).
thf(19508,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19407]) ).
thf(19545,plain,
! [A: $i] :
( ( A @ p @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19508]) ).
thf(28610,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,20037]) ).
thf(28611,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[28610]) ).
thf(28745,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[28611]) ).
thf(28791,plain,
! [A: $i] :
( ( A @ p @ s @ n @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[28745]) ).
thf(27777,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13918,19961]) ).
thf(27778,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[27777]) ).
thf(27911,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[27778]) ).
thf(27939,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[27911]) ).
thf(29537,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29014,69]) ).
thf(29538,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[29537]) ).
thf(29702,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[29538]) ).
thf(29719,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[29702]) ).
thf(44789,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12498,37103]) ).
thf(44790,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) ),
inference(simp,[status(thm)],[44789]) ).
thf(44825,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ p ) ) ),
inference(simp,[status(thm)],[44790]) ).
thf(44877,plain,
! [A: $i] :
( ( A @ s @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[44825]) ).
thf(36815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36729,88]) ).
thf(36816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( D @ ( B @ mem ) ) )
| ( D @ ( C @ u ) @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[36815]) ).
thf(36817,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[36816:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ p ))]]) ).
thf(36959,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[36817]) ).
thf(27565,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11080,19955]) ).
thf(27566,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[27565]) ).
thf(27702,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[27566]) ).
thf(27743,plain,
! [A: $i] :
( ( e @ s @ s @ n )
!= ( A @ p @ n @ s ) ),
inference(simp,[status(thm)],[27702]) ).
thf(41064,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,17997]) ).
thf(41065,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[41064]) ).
thf(41120,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[41065]) ).
thf(41154,plain,
! [A: $i] :
( ( e @ n @ p @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[41120]) ).
thf(41058,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40528,20044]) ).
thf(41059,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[41058]) ).
thf(41106,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[41059]) ).
thf(41139,plain,
! [A: $i] :
( ( e @ n @ p @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[41106]) ).
thf(90107,plain,
$false,
inference(e,[status(thm)],[69,138,11372,38711,18906,88,41127,29805,23272,24747,36949,41144,25622,36971,21386,25563,41150,276,36981,18706,19274,12261,13918,44357,23056,31207,170,11080,17407,23268,56,69388,22599,142,41145,49364,19986,913,23283,22602,153,36986,715,17946,28366,20722,174,28786,19955,23682,45431,44885,23502,44596,41132,37,17534,41577,185,49332,43042,67324,25961,110,27731,47244,125,28559,934,49342,54347,157,52,20707,44601,20445,189,41136,20841,21669,78,261,93,11378,11139,28591,25965,32876,22608,18703,41140,179,13382,17747,211,16680,38355,84,24233,1151,937,280,61,24779,36977,41457,21665,11004,147,89,133,116,41155,37036,24052,21371,18825,307,233,37078,18312,925,201,38390,41149,28807,36982,102,18909,60,25151,12169,36970,49382,28,12190,41128,392,70,137,165,28583,33,566,19273,197,41148,20161,27737,41169,41580,36958,36653,46950,19800,92,36953,916,41131,97,54065,17908,21178,64656,36729,24240,1111,52510,169,45152,141,17990,19667,388,53,109,19277,46937,17742,41152,36437,77,36946,193,17531,17402,44319,36643,25544,20165,27361,41135,41141,37103,27937,96,17399,393,11129,1297,49390,173,21368,129,20542,19694,29746,41460,134,73,18308,29377,205,18371,20037,44359,41137,74248,36978,17646,105,20153,36961,17293,37074,54082,43293,36950,22768,298,17271,43300,23085,37029,19815,25388,166,34,45,161,24434,23276,149,28355,19662,17282,19909,37386,64,45159,13368,44,19817,25376,8581,204,32888,402,19797,18038,13563,23687,17737,59,118,19296,29014,37165,391,25145,17744,18822,25378,19992,36956,46677,48523,46662,49,49333,72316,919,181,11085,187,10236,113,37382,16774,36983,20833,17754,24951,19276,53917,37152,27957,51908,19824,17522,3038,41130,81,18367,37107,76,36974,19523,21657,36951,41157,25955,17914,66,27738,943,155,198,108,462,29734,41147,19548,36979,20731,394,44878,17940,21671,80,922,48803,20828,62656,130,32159,13371,41153,162,23466,209,7681,47454,12156,19806,112,36973,47242,19789,123,41151,194,145,43051,48,63,20545,150,19907,23683,25372,19910,263,12266,56805,19297,40528,67,13369,19022,20438,17745,37434,18032,12256,50,177,24969,182,41138,20044,21158,463,19295,36972,17997,47513,19549,34611,154,19169,32934,19791,24746,43,24231,21850,48514,38351,20453,24965,17657,931,87,51303,41143,17294,17743,104,1108,19798,36955,23686,38665,19961,28361,40,13919,73861,38394,55,401,139,49361,45432,41880,20846,158,12516,19686,390,186,19522,171,23096,25163,29367,9470,119,510,4591,19278,25564,48519,24952,22615,21853,36984,28805,50438,36,146,30,19266,51252,21241,49352,28370,190,45428,24046,19696,12498,620,23501,210,29355,126,24051,195,20170,17649,6889,32845,94,928,74257,36948,19792,21236,46942,131,163,178,24227,36976,56833,43065,940,36944,48812,215,31258,19545,17520,16775,28791,27939,29719,44877,36959,27743,122,41154,16681,41139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV570+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n018.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 11:20:06 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.20 % [INFO] Parsing done (206ms).
% 1.44/1.21 % [INFO] Running in sequential loop mode.
% 2.05/1.61 % [INFO] eprover registered as external prover.
% 2.05/1.62 % [INFO] Scanning for conjecture ...
% 2.22/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 25 axioms. Running axiom selection ...
% 2.22/1.78 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 2.38/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.85 % [INFO] Type checking passed.
% 2.38/1.85 % [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 ...
% 212.00/60.28 % External prover 'e' found a proof!
% 212.00/60.28 % [INFO] Killing All external provers ...
% 212.00/60.28 % Time passed: 59736ms (effective reasoning time: 59062ms)
% 212.00/60.28 % Solved by 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)>
% 212.00/60.29 % Axioms used in derivation (25): atleast15p_def, p_ax, atleast6p_def, atleast10p_def, atleast4p_def, atleast9p_def, u_ax, n_def, atleast7p_def, e_ax, a_def, atleast13p_def, atleast8p_def, atleast5p_def, atleast11p_def, atleast14p_def, atleast2p_def, disj_def, setext, subq_def, atleast3p_def, m_ax, atleast16p_def, s_ax, atleast12p_def
% 212.00/60.29 % No. of inferences in proof: 1721
% 212.00/60.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 59736 ms resp. 59062 ms w/o parsing
% 205.33/61.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 205.33/61.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------