%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV571+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 08:48:12 AM UTC 2026
% Result : Theorem 265.47s 78.15s
% Output : Refutation 256.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 43
% Syntax : Number of formulae : 1428 ( 523 unt; 0 typ; 17 def)
% Number of atoms : 4096 (1400 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 20110 (2212 ~;1319 |; 281 &;16183 @)
% ( 21 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 42 usr; 4 con; 0-2 aty)
% Number of variables : 2769 ( 19 ^;2652 !; 81 ?;2769 :)
% ( 0 !>; 0 ?*; 0 @-; 17 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subq_decl,type,
subq: $i > $i > $o ).
thf(u_decl,type,
u: $i > $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(n_decl,type,
n: $i > $i ).
thf(e_decl,type,
e: $i ).
thf(a_decl,type,
a: $i > $i > $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/sandbox/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(10,axiom,
! [A: $i] :
( ( A @ n )
= ( A @ ( A @ a ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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(10077,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(10078,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)],[10077]) ).
thf(10079,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10078:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ s ))]]) ).
thf(10128,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10079]) ).
thf(10167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ s @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,10128]) ).
thf(10168,plain,
! [A: $i] : ( A @ s @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[10167:[bind(A,$thf( F @ s )),bind(B,$thf( F @ s @ s )),bind(C,$thf( F ))]]) ).
thf(10183,plain,
! [A: $i] : ( A @ s @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[10168]) ).
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(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subq ) )
<=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( B @ ( C @ mem ) ) ) ),
file('/export/starexec/sandbox/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(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ m ) @ ( A @ mem ) )
<=> ( ~ ( C @ ( A @ mem ) )
& ( B @ ( A @ mem ) ) ) ),
file('/export/starexec/sandbox/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(665,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(666,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)],[665]) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$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(687,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk17 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ subq ) ) ),
inference(simp,[status(thm)],[667]) ).
thf(8262,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)],[687,69]) ).
thf(8263,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)],[8262]) ).
thf(8264,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( e @ m ) @ subq ) ),
inference(pattern_uni,[status(thm)],[8263:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( H )),bind(D,$thf( H @ ( e @ m ) @ ( E @ sk17 ) ))]]) ).
thf(8299,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( e @ m ) @ subq ) ),
inference(simp,[status(thm)],[8264]) ).
thf(677,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(678,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk17 ) @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ( B @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[677]) ).
thf(679,plain,
! [A: $i] : ( A @ ( e @ subq ) ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( e )),bind(B,$thf( D )),bind(C,$thf( e @ ( D @ sk17 ) ))]]) ).
thf(685,plain,
! [A: $i] : ( A @ ( e @ subq ) ),
inference(simp,[status(thm)],[679]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subq ) )
=> ( ( A @ ( B @ subq ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/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(3000,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ~ ( B @ ( C @ subq ) )
| ~ $true
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[685,55]) ).
thf(3001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ~ ( B @ ( C @ subq ) )
| ( B = C ) ),
inference(simp,[status(thm)],[3000]) ).
thf(3002,plain,
! [A: $i] :
( ~ ( e @ ( A @ subq ) )
| ( e = A ) ),
inference(pattern_uni,[status(thm)],[3001:[bind(A,$thf( A )),bind(B,$thf( e )),bind(C,$thf( A ))]]) ).
thf(8799,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ subq ) ) )
| ~ $true
| ( e = C ) ),
inference(paramod_ordered,[status(thm)],[8299,3002]) ).
thf(8800,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ subq ) ) )
| ( e = C ) ),
inference(simp,[status(thm)],[8799]) ).
thf(8801,plain,
! [A: $i] :
( ( A @ ( e @ m ) )
= e ),
inference(pattern_uni,[status(thm)],[8800:[bind(A,$thf( e )),bind(B,$thf( E )),bind(C,$thf( E @ ( e @ m ) ))]]) ).
thf(8835,plain,
! [A: $i] :
( ( A @ ( e @ m ) )
= e ),
inference(simp,[status(thm)],[8801]) ).
thf(8864,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)],[8835,687]) ).
thf(8865,plain,
! [B: $i,A: $i] :
( ( e @ ( e @ ( B @ sk17 ) @ mem ) )
| ( B @ ( A @ ( e @ m ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[8864:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( e )),bind(D,$thf( A ))]]) ).
thf(9134,plain,
! [A: $i] :
( $false
| ( A @ ( e @ subq ) ) ),
inference(rewrite,[status(thm)],[8865,8835,69]) ).
thf(9135,plain,
! [A: $i] : ( A @ ( e @ subq ) ),
inference(simp,[status(thm)],[9134]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ p @ ( A @ mem ) )
<=> ( B @ ( A @ subq ) ) ),
file('/export/starexec/sandbox/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(19064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9135,118]) ).
thf(19065,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19064]) ).
thf(19066,plain,
! [A: $i] : ( A @ p @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19065:[bind(A,$thf( A )),bind(B,$thf( e )),bind(C,$thf( A ))]]) ).
thf(19214,plain,
! [A: $i] : ( A @ p @ ( e @ mem ) ),
inference(simp,[status(thm)],[19066]) ).
thf(19216,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19214,69]) ).
thf(19217,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[19216]) ).
thf(19281,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[19217]) ).
thf(19296,plain,
! [A: $i] :
( ( A @ p )
!= e ),
inference(simp,[status(thm)],[19281]) ).
thf(19314,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p ) )
| ( B != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19296]) ).
thf(19315,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( A @ s @ ( B @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19314:[bind(A,$thf( D @ p )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(19325,plain,
! [A: $i] :
~ ( e @ s @ ( A @ p @ mem ) ),
inference(simp,[status(thm)],[19315]) ).
thf(19492,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10183,19325]) ).
thf(19493,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19492]) ).
thf(19560,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19493]) ).
thf(19597,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19560]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ atleast11p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast10p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(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(34614,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk14 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast11p ) ),
inference(paramod_ordered,[status(thm)],[9135,179]) ).
thf(34615,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk14 @ ( B @ subq ) ) )
| ~ ( B @ atleast11p ) ),
inference(simp,[status(thm)],[34614]) ).
thf(34616,plain,
~ ( e @ atleast11p ),
inference(pattern_uni,[status(thm)],[34615:[bind(A,$thf( e @ sk14 )),bind(B,$thf( e ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ atleast16p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast15p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(19316,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p ) )
| ( A != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19296]) ).
thf(19317,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( B @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19316:[bind(A,$thf( A )),bind(B,$thf( D @ p )),bind(C,$thf( D ))]]) ).
thf(19326,plain,
! [A: $i] :
~ ( A @ p @ s @ ( e @ mem ) ),
inference(simp,[status(thm)],[19317]) ).
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(41173,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(41174,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)],[41173]) ).
thf(41175,plain,
! [A: $i] :
( ( A @ ( A @ subq ) )
| ( A @ ( A @ subq ) ) ),
inference(pattern_uni,[status(thm)],[41174:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(41333,plain,
! [A: $i] : ( A @ ( A @ subq ) ),
inference(simp,[status(thm)],[41175]) ).
thf(41387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41333,118]) ).
thf(41388,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subq ) )
!= ( C @ ( B @ subq ) ) )
| ( C @ p @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[41387]) ).
thf(41389,plain,
! [A: $i] : ( A @ p @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[41388:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
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(7353,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ( e != e )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3002,209]) ).
thf(7354,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[7353]) ).
thf(7355,plain,
! [A: $i] :
~ ( e @ ( A @ s @ subq ) ),
inference(pattern_uni,[status(thm)],[7354:[bind(A,$thf( C @ s )),bind(B,$thf( C ))]]) ).
thf(8109,plain,
! [A: $i] :
~ ( e @ ( A @ s @ subq ) ),
inference(simp,[status(thm)],[7355]) ).
thf(8791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ s @ subq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8299,8109]) ).
thf(8792,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( e @ m ) @ subq ) )
!= ( e @ ( C @ s @ subq ) ) ),
inference(simp,[status(thm)],[8791]) ).
thf(8834,plain,
! [C: $i,B: $i,A: $i] :
( ( A != e )
| ( ( B @ ( e @ m ) )
!= ( C @ s ) ) ),
inference(simp,[status(thm)],[8792]) ).
thf(8837,plain,
! [B: $i,A: $i] :
( ( A @ ( e @ m ) )
!= ( B @ s ) ),
inference(simp,[status(thm)],[8834]) ).
thf(9118,plain,
! [A: $i] :
( ( A @ s )
!= e ),
inference(rewrite,[status(thm)],[8837,8835]) ).
thf(13521,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s ) )
| ( A != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,9118]) ).
thf(13522,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( B @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[13521:[bind(A,$thf( (@) )),bind(B,$thf( D @ s )),bind(C,$thf( D ))]]) ).
thf(15332,plain,
! [A: $i] :
~ ( A @ s @ s @ ( e @ mem ) ),
inference(simp,[status(thm)],[13522]) ).
thf(41542,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,15332]) ).
thf(41543,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[41542]) ).
thf(41570,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[41543]) ).
thf(41617,plain,
! [A: $i] :
( ( e @ p )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[41570]) ).
thf(41649,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ( B
!= ( C @ s @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41617]) ).
thf(41650,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ~ ( A @ s @ ( e @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41649:[bind(A,$thf( e @ p )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(41699,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ p @ mem ) ),
inference(simp,[status(thm)],[41650]) ).
thf(48191,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,41699]) ).
thf(48192,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[48191]) ).
thf(48248,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[48192]) ).
thf(48339,plain,
! [A: $i] :
( ( e @ p @ s )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[48248]) ).
thf(10205,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)],[10183,87]) ).
thf(10206,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)],[10205]) ).
thf(10207,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10206:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ s @ n )),bind(D,$thf( D ))]]) ).
thf(10247,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10207]) ).
thf(10432,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)],[210,10247]) ).
thf(10433,plain,
! [A: $i] : ( A @ s @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[10432:[bind(A,$thf( H @ s @ n )),bind(B,$thf( H @ s @ n @ s )),bind(C,$thf( H ))]]) ).
thf(10439,plain,
! [A: $i] : ( A @ s @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[10433]) ).
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(10510,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(10511,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)],[10510]) ).
thf(10512,plain,
! [B: $i,A: $i] : ( B @ s @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10511:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ s ))]]) ).
thf(10545,plain,
! [B: $i,A: $i] : ( B @ s @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10512]) ).
thf(10859,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( C @ s @ ( B @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,10545]) ).
thf(10860,plain,
! [A: $i] : ( A @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[10859:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(10966,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,69]) ).
thf(10967,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[10966]) ).
thf(11001,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[10967]) ).
thf(11014,plain,
! [A: $i] :
( ( A @ n )
!= e ),
inference(simp,[status(thm)],[11001]) ).
thf(11521,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n ) )
| ( A != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,11014]) ).
thf(11522,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( B @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[11521:[bind(A,$thf( A )),bind(B,$thf( D @ n )),bind(C,$thf( D ))]]) ).
thf(15772,plain,
! [A: $i] :
~ ( A @ n @ s @ ( e @ mem ) ),
inference(simp,[status(thm)],[11522]) ).
thf(16438,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10439,15772]) ).
thf(16439,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16438]) ).
thf(16473,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16439]) ).
thf(16501,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[16473]) ).
thf(41544,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)],[41389,87]) ).
thf(41545,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)],[41544]) ).
thf(41546,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[41545:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ p ))]]) ).
thf(41608,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[41546]) ).
thf(44273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,41608]) ).
thf(44274,plain,
! [A: $i] : ( A @ p @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[44273:[bind(A,$thf( F @ p )),bind(B,$thf( F @ p @ s )),bind(C,$thf( F ))]]) ).
thf(44347,plain,
! [A: $i] : ( A @ p @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[44274]) ).
thf(45704,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44347,15772]) ).
thf(45705,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[45704]) ).
thf(45746,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[45705]) ).
thf(45790,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[45746]) ).
thf(45712,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44347,19325]) ).
thf(45713,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[45712]) ).
thf(45773,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[45713]) ).
thf(45818,plain,
! [A: $i] :
( ( A @ p @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[45773]) ).
thf(10980,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)],[10860,87]) ).
thf(10981,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)],[10980]) ).
thf(10982,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10981:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ n ))]]) ).
thf(11005,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10982]) ).
thf(11201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ n @ u ) ) )
| ( A @ n @ ( C @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,11005]) ).
thf(11202,plain,
! [A: $i] : ( A @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[11201:[bind(A,$thf( F @ n )),bind(B,$thf( F @ n @ s )),bind(C,$thf( F ))]]) ).
thf(11209,plain,
! [A: $i] : ( A @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[11202]) ).
thf(11365,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)],[11209,87]) ).
thf(11366,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)],[11365]) ).
thf(11367,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[11366:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ n @ n )),bind(D,$thf( D ))]]) ).
thf(11395,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[11367]) ).
thf(16982,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)],[210,11395]) ).
thf(16983,plain,
! [A: $i] : ( A @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[16982:[bind(A,$thf( H @ n @ n )),bind(B,$thf( H @ n @ n @ s )),bind(C,$thf( H ))]]) ).
thf(17003,plain,
! [A: $i] : ( A @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[16983]) ).
thf(13519,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s ) )
| ( B != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,9118]) ).
thf(13520,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( A @ s @ ( B @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[13519:[bind(A,$thf( D @ s )),bind(B,$thf( A )),bind(C,$thf( D ))]]) ).
thf(15331,plain,
! [A: $i] :
~ ( e @ s @ ( A @ s @ mem ) ),
inference(simp,[status(thm)],[13520]) ).
thf(17905,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17003,15331]) ).
thf(17906,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[17905]) ).
thf(17971,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[17906]) ).
thf(17998,plain,
! [A: $i] :
( ( A @ s @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17971]) ).
thf(41469,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,19326]) ).
thf(41470,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[41469]) ).
thf(41586,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[41470]) ).
thf(41633,plain,
! [A: $i] :
( ( e @ p )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[41586]) ).
thf(41803,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ( B
!= ( C @ p @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41633]) ).
thf(41804,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ p @ s ) )
| ~ ( A @ s @ ( e @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41803:[bind(A,$thf( e @ p )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(41851,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ p @ mem ) ),
inference(simp,[status(thm)],[41804]) ).
thf(52023,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,41851]) ).
thf(52024,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[52023]) ).
thf(52096,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[52024]) ).
thf(52125,plain,
! [A: $i] :
( ( e @ p @ s )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[52096]) ).
thf(41540,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,19325]) ).
thf(41541,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[41540]) ).
thf(41597,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[41541]) ).
thf(41646,plain,
! [A: $i] :
( ( A @ p @ p )
!= ( e @ s ) ),
inference(simp,[status(thm)],[41597]) ).
thf(11162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ n @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11005,69]) ).
thf(11163,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ n @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[11162]) ).
thf(11204,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ n @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[11163]) ).
thf(11211,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ n @ u ) )
!= e ),
inference(simp,[status(thm)],[11204]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ atleast10p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast9p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(5,axiom,
! [A: $i] :
( ( A @ atleast9p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast8p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(870,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk2 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[685,50]) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk2 @ ( B @ subq ) ) )
| ~ ( B @ atleast9p ) ),
inference(simp,[status(thm)],[870]) ).
thf(872,plain,
~ ( e @ atleast9p ),
inference(pattern_uni,[status(thm)],[871:[bind(A,$thf( e @ sk2 )),bind(B,$thf( e ))]]) ).
thf(891,plain,
! [A: $i] :
( ( ( A @ sk8 @ atleast9p )
!= ( e @ atleast9p ) )
| ~ $true
| ~ ( A @ atleast10p ) ),
inference(paramod_ordered,[status(thm)],[130,872]) ).
thf(892,plain,
! [A: $i] :
( ( ( A @ sk8 @ atleast9p )
!= ( e @ atleast9p ) )
| ~ ( A @ atleast10p ) ),
inference(simp,[status(thm)],[891]) ).
thf(893,plain,
! [A: $i] :
( ( ( A @ sk8 )
!= e )
| ~ ( A @ atleast10p ) ),
inference(simp,[status(thm)],[892]) ).
thf(11519,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n ) )
| ( B != e )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,11014]) ).
thf(11520,plain,
! [B: $i,A: $i] :
( ( A != e )
| ~ ( A @ s @ ( B @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[11519:[bind(A,$thf( D @ n )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(15771,plain,
! [A: $i] :
~ ( e @ s @ ( A @ n @ mem ) ),
inference(simp,[status(thm)],[11520]) ).
thf(16315,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,15771]) ).
thf(16316,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[16315]) ).
thf(16345,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[16316]) ).
thf(16372,plain,
! [A: $i] :
( ( A @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16345]) ).
thf(19257,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)],[19214,87]) ).
thf(19258,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)],[19257]) ).
thf(19259,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19258:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( E @ p ))]]) ).
thf(19311,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[19259]) ).
thf(20196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( B @ ( C @ p @ u ) ) )
| ( A @ n @ ( e @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[210,19311]) ).
thf(20197,plain,
! [A: $i] : ( A @ p @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20196:[bind(A,$thf( F @ p )),bind(B,$thf( F @ p @ s )),bind(C,$thf( F ))]]) ).
thf(20224,plain,
! [A: $i] : ( A @ p @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[20197]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ atleast2p )
<=> ? [B: $i] :
( ~ ( B @ p @ ( A @ subq ) )
& ( A @ ( B @ mem ) ) ) ),
file('/export/starexec/sandbox/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(21269,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)],[20224,125]) ).
thf(21270,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)],[21269]) ).
thf(21271,plain,
! [A: $i] :
( ( A @ p @ n @ atleast2p )
| ( e @ p @ ( A @ p @ n @ subq ) ) ),
inference(pattern_uni,[status(thm)],[21270:[bind(A,$thf( E )),bind(B,$thf( E @ p @ n )),bind(C,$thf( e ))]]) ).
thf(21353,plain,
! [A: $i] :
( ( A @ p @ n @ atleast2p )
| ( e @ p @ ( A @ p @ n @ subq ) ) ),
inference(simp,[status(thm)],[21271]) ).
thf(16855,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ n ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16372]) ).
thf(16856,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ n @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16855:[bind(A,$thf( A )),bind(B,$thf( E @ n @ n )),bind(C,$thf( E ))]]) ).
thf(16877,plain,
! [A: $i] :
~ ( A @ n @ n @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[16856]) ).
thf(25287,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16877]) ).
thf(25288,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[25287]) ).
thf(25343,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[25288]) ).
thf(25415,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ n @ s ) ),
inference(simp,[status(thm)],[25343]) ).
thf(1,conjecture,
~ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ ( e @ n @ s @ s @ a ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nsubq_2508_2504) ).
thf(2,negated_conjecture,
~ ~ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ ( e @ n @ s @ s @ a ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(28,plain,
~ ~ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ ( e @ n @ s @ s @ a ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,plain,
e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ ( e @ n @ s @ s @ a ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(211,plain,
e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ),
inference(rewrite,[status(thm)],[29,66]) ).
thf(226,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( A @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(262,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s ) )
| ( A
!= ( e @ n @ s @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( A @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(276,plain,
( ( ( e @ n @ n @ n @ s )
!= ( e @ n @ s @ s @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ s @ s @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(41532,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,15772]) ).
thf(41533,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[41532]) ).
thf(41579,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[41533]) ).
thf(41626,plain,
! [A: $i] :
( ( e @ p )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[41579]) ).
thf(41711,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ( B
!= ( C @ n @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41626]) ).
thf(41712,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n @ s ) )
| ~ ( A @ s @ ( e @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41711:[bind(A,$thf( e @ p )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(41760,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ p @ mem ) ),
inference(simp,[status(thm)],[41712]) ).
thf(49877,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,41760]) ).
thf(49878,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[49877]) ).
thf(49959,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[49878]) ).
thf(50001,plain,
! [A: $i] :
( ( e @ p @ s )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[49959]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ atleast5p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast4p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(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(876,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk10 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast5p ) ),
inference(paramod_ordered,[status(thm)],[685,147]) ).
thf(877,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk10 @ ( B @ subq ) ) )
| ~ ( B @ atleast5p ) ),
inference(simp,[status(thm)],[876]) ).
thf(878,plain,
~ ( e @ atleast5p ),
inference(pattern_uni,[status(thm)],[877:[bind(A,$thf( e @ sk10 )),bind(B,$thf( e ))]]) ).
thf(20975,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)],[20224,87]) ).
thf(20976,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)],[20975]) ).
thf(20977,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20976:[bind(A,$thf( F )),bind(B,$thf( e )),bind(C,$thf( F @ p @ n )),bind(D,$thf( D ))]]) ).
thf(21038,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20977]) ).
thf(22337,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)],[210,21038]) ).
thf(22338,plain,
! [A: $i] : ( A @ p @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[22337:[bind(A,$thf( H @ p @ n )),bind(B,$thf( H @ p @ n @ s )),bind(C,$thf( H ))]]) ).
thf(22353,plain,
! [A: $i] : ( A @ p @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[22338]) ).
thf(22887,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)],[22353,87]) ).
thf(22888,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)],[22887]) ).
thf(22889,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[22888:[bind(A,$thf( G )),bind(B,$thf( e )),bind(C,$thf( G @ p @ n @ n )),bind(D,$thf( D ))]]) ).
thf(22955,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[22889]) ).
thf(25745,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)],[210,22955]) ).
thf(25746,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[25745:[bind(A,$thf( J @ p @ n @ n )),bind(B,$thf( J @ p @ n @ n @ s )),bind(C,$thf( J ))]]) ).
thf(25778,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[25746]) ).
thf(27167,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)],[25778,88]) ).
thf(27168,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)],[27167]) ).
thf(27169,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[27168:[bind(A,$thf( H )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( H @ p @ n @ n @ n ))]]) ).
thf(27327,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[27169]) ).
thf(41476,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,15331]) ).
thf(41477,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[41476]) ).
thf(41591,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[41477]) ).
thf(41640,plain,
! [A: $i] :
( ( A @ s @ p )
!= ( e @ s ) ),
inference(simp,[status(thm)],[41591]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ atleast15p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast14p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(170,plain,
! [A: $i] :
( ( A @ sk13 @ atleast14p )
| ~ ( A @ atleast15p ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(16186,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,15332]) ).
thf(16187,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16186]) ).
thf(16215,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16187]) ).
thf(16242,plain,
! [A: $i] :
( ( e @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[16215]) ).
thf(16793,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16242]) ).
thf(16794,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16793:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(16845,plain,
! [A: $i] :
~ ( e @ n @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[16794]) ).
thf(20119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19311,69]) ).
thf(20120,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ p @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[20119]) ).
thf(20206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p @ u ) )
!= e )
| ( e != C ) ),
inference(simp,[status(thm)],[20120]) ).
thf(20235,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ p @ u ) )
!= e ),
inference(simp,[status(thm)],[20206]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ atleast8p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast7p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(17938,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17003,15772]) ).
thf(17939,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17938]) ).
thf(17974,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17939]) ).
thf(18001,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[17974]) ).
thf(229,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( A @ n @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(256,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ s @ n ) )
| ( A
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( A @ n @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(270,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(333,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( A @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,270]) ).
thf(340,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ s @ n ) )
| ( A
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( A @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[333]) ).
thf(352,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(373,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( A @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,352]) ).
thf(388,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( A
!= ( e @ n @ n @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( A @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[373]) ).
thf(394,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(544,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ n @ s @ u ) ) )
| ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,394]) ).
thf(556,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( A
!= ( e @ n @ n @ s ) )
| ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[544]) ).
thf(568,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(706,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( ( A @ n )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,568]) ).
thf(712,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n ) )
| ( A
!= ( e @ n @ s @ n @ s ) )
| ( ( A @ n )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[706]) ).
thf(724,plain,
( ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ s @ n @ s @ n )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[712]) ).
thf(999,plain,
( ( ( e @ n @ s @ n @ s @ s )
!= ( e @ n @ n @ s @ s ) )
| ( ( e @ n @ s @ n @ s @ n )
!= ( e @ n @ n @ s @ n ) )
| ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(eqfactor_ordered,[status(thm)],[724]) ).
thf(1008,plain,
( ( ( e @ n @ s @ n @ s )
!= ( e @ n @ n @ s ) )
| ( ( e @ n @ s @ n @ s )
!= ( e @ n @ n @ s ) )
| ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[999]) ).
thf(1023,plain,
( ( ( e @ n @ s @ n @ s )
!= ( e @ n @ n @ s ) )
| ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[1008]) ).
thf(1077,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n @ n ) )
| ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[1023]) ).
thf(1180,plain,
( ( ( e @ n @ s @ n @ s @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(eqfactor_ordered,[status(thm)],[1077]) ).
thf(1205,plain,
( ( ( e @ n @ s @ n @ s )
!= ( e @ n ) )
| ( ( e @ n @ n @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[1180]) ).
thf(5488,plain,
( ( ( e @ n )
!= ( e @ n ) )
| ( ( e @ n @ s @ n @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ n @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(eqfactor_ordered,[status(thm)],[1205]) ).
thf(5520,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[5488]) ).
thf(5799,plain,
( ( ( e @ n @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ s @ n )
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(eqfactor_ordered,[status(thm)],[5520]) ).
thf(5856,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[5799]) ).
thf(5959,plain,
( ( ( e @ n @ s @ n )
!= ( e @ n ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[5856]) ).
thf(17459,plain,
( ( ( e @ n )
!= ( e @ n ) )
| ( ( e @ n @ s @ n )
!= ( e @ n @ n ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(eqfactor_ordered,[status(thm)],[5959]) ).
thf(17470,plain,
( ( ( e @ n @ s )
!= ( e @ n ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[17459]) ).
thf(17577,plain,
( ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[17470]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ atleast3p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast2p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(153,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ subq ) )
| ~ ( A @ atleast3p ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(16323,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,15771]) ).
thf(16324,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[16323]) ).
thf(16355,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[16324]) ).
thf(16387,plain,
! [A: $i] :
( ( A @ n @ s )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16355]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ atleast13p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast12p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(19218,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)],[19214,88]) ).
thf(19219,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)],[19218]) ).
thf(19220,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19219:[bind(A,$thf( E )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( E @ p ))]]) ).
thf(19298,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[19220]) ).
thf(19810,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)],[19298,87]) ).
thf(19811,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)],[19810]) ).
thf(19812,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ p @ ( B @ u ) @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19811:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( H @ p @ ( F @ u ) )),bind(E,$thf( E ))]]) ).
thf(19869,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ p @ ( B @ u ) @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[19812]) ).
thf(67379,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)],[210,19869]) ).
thf(67380,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[67379:[bind(A,$thf( K @ p @ ( I @ u ) )),bind(B,$thf( K @ p @ ( I @ u ) @ s )),bind(C,$thf( I )),bind(D,$thf( K ))]]) ).
thf(67446,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[67380]) ).
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(212,plain,
! [A: $i] :
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ 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 @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk3 @ ( A @ subq ) ) )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[212]) ).
thf(216,plain,
! [A: $i] :
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( A @ sk3 ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= A )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[213]) ).
thf(218,plain,
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[216]) ).
thf(233,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( A @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(251,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s ) )
| ( A
!= ( e @ n @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( A @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[233]) ).
thf(288,plain,
( ( ( e @ n @ n @ n @ s )
!= ( e @ n @ s @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ s @ s @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[251]) ).
thf(16170,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10183,15332]) ).
thf(16171,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16170]) ).
thf(16233,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16171]) ).
thf(16265,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[16233]) ).
thf(18858,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ( B
!= ( C @ s @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16265]) ).
thf(18859,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ~ ( A @ s @ ( e @ s @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18858:[bind(A,$thf( e @ s @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(18925,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ s @ n @ mem ) ),
inference(simp,[status(thm)],[18859]) ).
thf(16059,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,15331]) ).
thf(16060,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[16059]) ).
thf(16092,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[16060]) ).
thf(16121,plain,
! [A: $i] :
( ( A @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16092]) ).
thf(16727,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ n ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16121]) ).
thf(16728,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ s @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16727:[bind(A,$thf( E @ s @ n )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(16751,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ s @ n @ mem ) ),
inference(simp,[status(thm)],[16728]) ).
thf(41503,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16751]) ).
thf(41504,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[41503]) ).
thf(41574,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[41504]) ).
thf(41621,plain,
! [A: $i] :
( ( A @ s @ n @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41574]) ).
thf(10609,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)],[10439,87]) ).
thf(10610,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)],[10609]) ).
thf(10611,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10610:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G @ s @ n @ n )),bind(D,$thf( D ))]]) ).
thf(10654,plain,
! [B: $i,A: $i] : ( A @ ( B @ s @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10611]) ).
thf(57322,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)],[210,10654]) ).
thf(57323,plain,
! [A: $i] : ( A @ s @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[57322:[bind(A,$thf( J @ s @ n @ n )),bind(B,$thf( J @ s @ n @ n @ s )),bind(C,$thf( J ))]]) ).
thf(57423,plain,
! [A: $i] : ( A @ s @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[57323]) ).
thf(19512,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,19325]) ).
thf(19513,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19512]) ).
thf(19548,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19513]) ).
thf(19586,plain,
! [A: $i] :
( ( A @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19548]) ).
thf(19993,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ n ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19586]) ).
thf(19994,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ p @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19993:[bind(A,$thf( E @ p @ n )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(20018,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ p @ n @ mem ) ),
inference(simp,[status(thm)],[19994]) ).
thf(29271,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,20018]) ).
thf(29272,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[29271]) ).
thf(29331,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[29272]) ).
thf(29366,plain,
! [A: $i] :
( ( A @ p @ n @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[29331]) ).
thf(11017,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n ) )
| ( e != e )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3002,11014]) ).
thf(11018,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[11017]) ).
thf(11019,plain,
! [A: $i] :
~ ( e @ ( A @ n @ subq ) ),
inference(pattern_uni,[status(thm)],[11018:[bind(A,$thf( C @ n )),bind(B,$thf( C ))]]) ).
thf(11024,plain,
! [A: $i] :
~ ( e @ ( A @ n @ subq ) ),
inference(simp,[status(thm)],[11019]) ).
thf(16426,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10183,15772]) ).
thf(16427,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16426]) ).
thf(16477,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16427]) ).
thf(16507,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[16477]) ).
thf(21173,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ s @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16507]) ).
thf(21174,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[21173:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(21239,plain,
! [A: $i] :
~ ( e @ s @ n @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[21174]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disj ) )
<=> ~ ? [C: $i] :
( ( B @ ( C @ mem ) )
& ( A @ ( C @ mem ) ) ) ),
file('/export/starexec/sandbox/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(41807,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41633]) ).
thf(41808,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41807:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(41855,plain,
! [A: $i] :
~ ( e @ p @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[41808]) ).
thf(52239,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41855]) ).
thf(52240,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[52239]) ).
thf(52375,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ p @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[52240]) ).
thf(52416,plain,
! [A: $i] :
( ( A @ p @ s @ p )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[52375]) ).
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(41471,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)],[41389,88]) ).
thf(41472,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)],[41471]) ).
thf(41473,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[41472:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ p ))]]) ).
thf(41604,plain,
! [B: $i,A: $i] : ( B @ p @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[41473]) ).
thf(43186,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ p ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41640]) ).
thf(43187,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ s @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[43186:[bind(A,$thf( A )),bind(B,$thf( E @ s @ p )),bind(C,$thf( E ))]]) ).
thf(43204,plain,
! [A: $i] :
~ ( A @ s @ p @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[43187]) ).
thf(54586,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,43204]) ).
thf(54587,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[54586]) ).
thf(54716,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[54587]) ).
thf(54782,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ s @ p @ s ) ),
inference(simp,[status(thm)],[54716]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ atleast12p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast11p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(45716,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)],[44347,87]) ).
thf(45717,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)],[45716]) ).
thf(45718,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[45717:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ p @ n )),bind(D,$thf( D ))]]) ).
thf(45782,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[45718]) ).
thf(50439,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)],[210,45782]) ).
thf(50440,plain,
! [A: $i] : ( A @ p @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[50439:[bind(A,$thf( H @ p @ n )),bind(B,$thf( H @ p @ n @ s )),bind(C,$thf( H ))]]) ).
thf(50481,plain,
! [A: $i] : ( A @ p @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[50440]) ).
thf(52473,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50481,15331]) ).
thf(52474,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[52473]) ).
thf(52627,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[52474]) ).
thf(52666,plain,
! [A: $i] :
( ( A @ s @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[52627]) ).
thf(19318,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ p ) )
| ( e != e )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3002,19296]) ).
thf(19319,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ p ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(simp,[status(thm)],[19318]) ).
thf(19320,plain,
! [A: $i] :
~ ( e @ ( A @ p @ subq ) ),
inference(pattern_uni,[status(thm)],[19319:[bind(A,$thf( C @ p )),bind(B,$thf( C ))]]) ).
thf(19327,plain,
! [A: $i] :
~ ( e @ ( A @ p @ subq ) ),
inference(simp,[status(thm)],[19320]) ).
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(49,plain,
! [A: $i] :
( ( A @ sk2 @ atleast8p )
| ~ ( A @ atleast9p ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk3 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[685,61]) ).
thf(880,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk3 @ ( B @ subq ) ) )
| ~ ( B @ atleast8p ) ),
inference(simp,[status(thm)],[879]) ).
thf(881,plain,
~ ( e @ atleast8p ),
inference(pattern_uni,[status(thm)],[880:[bind(A,$thf( e @ sk3 )),bind(B,$thf( e ))]]) ).
thf(900,plain,
! [A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( e @ atleast8p ) )
| ~ $true
| ~ ( A @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[49,881]) ).
thf(901,plain,
! [A: $i] :
( ( ( A @ sk2 @ atleast8p )
!= ( e @ atleast8p ) )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[900]) ).
thf(902,plain,
! [A: $i] :
( ( ( A @ sk2 )
!= e )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[901]) ).
thf(22826,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22353,69]) ).
thf(22827,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[22826]) ).
thf(22918,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[22827]) ).
thf(22938,plain,
! [A: $i] :
( ( A @ p @ n @ n )
!= e ),
inference(simp,[status(thm)],[22918]) ).
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(41509,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,15771]) ).
thf(41510,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[41509]) ).
thf(41585,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[41510]) ).
thf(41632,plain,
! [A: $i] :
( ( A @ n @ p )
!= ( e @ s ) ),
inference(simp,[status(thm)],[41585]) ).
thf(41777,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ p ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41632]) ).
thf(41778,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ n @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41777:[bind(A,$thf( A )),bind(B,$thf( E @ n @ p )),bind(C,$thf( E ))]]) ).
thf(41795,plain,
! [A: $i] :
~ ( A @ n @ p @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[41778]) ).
thf(51465,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,41795]) ).
thf(51466,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[51465]) ).
thf(51531,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ n @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[51466]) ).
thf(51599,plain,
! [A: $i] :
( ( A @ n @ p @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[51531]) ).
thf(16851,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ n ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16372]) ).
thf(16852,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ n @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16851:[bind(A,$thf( E @ n @ n )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(16873,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ n @ n @ mem ) ),
inference(simp,[status(thm)],[16852]) ).
thf(234,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(247,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( A
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[234]) ).
thf(284,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ n @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[247]) ).
thf(41715,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41626]) ).
thf(41716,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41715:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(41764,plain,
! [A: $i] :
~ ( e @ p @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[41716]) ).
thf(19520,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,19325]) ).
thf(19521,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19520]) ).
thf(19549,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19521]) ).
thf(19587,plain,
! [A: $i] :
( ( A @ p @ s )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19549]) ).
thf(20024,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ s ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19587]) ).
thf(20025,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ p @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[20024:[bind(A,$thf( E @ p @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(20049,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[20025]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ atleast6p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast5p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(13,axiom,
! [A: $i] :
( ( A @ atleast7p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast6p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(93,plain,
! [A: $i] :
( ( A @ sk5 @ atleast6p )
| ~ ( A @ atleast7p ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(16801,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ s ) )
| ( A
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16242]) ).
thf(16802,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( B @ s @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16801:[bind(A,$thf( A )),bind(B,$thf( E @ s @ s )),bind(C,$thf( E ))]]) ).
thf(16832,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ n @ mem ) ),
inference(simp,[status(thm)],[16802]) ).
thf(24491,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,16832]) ).
thf(24492,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[24491]) ).
thf(24560,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[24492]) ).
thf(24609,plain,
! [A: $i] :
( ( e @ n @ s )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[24560]) ).
thf(225,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( e @ n @ n @ n @ s @ ( A @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(252,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( A
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s ) )
| ( e @ n @ n @ n @ s @ ( A @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(289,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[252]) ).
thf(18085,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ( B
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17577]) ).
thf(18086,plain,
! [A: $i] :
( ( A
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( A @ s @ ( e @ n @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18085:[bind(A,$thf( e @ n @ n )),bind(B,$thf( B ))]]) ).
thf(18481,plain,
( ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ n @ s @ ( e @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[18086]) ).
thf(25926,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( e @ n @ n @ mem ) ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,18481]) ).
thf(25927,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( e @ n @ n @ mem ) ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[25926]) ).
thf(26009,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ s ) )
| ( A
!= ( e @ n @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[25927]) ).
thf(26036,plain,
( ( ( e @ n @ n @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[26009]) ).
thf(10593,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)],[10439,88]) ).
thf(10594,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)],[10593]) ).
thf(10595,plain,
! [B: $i,A: $i] : ( B @ s @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10594:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ s @ n @ n ))]]) ).
thf(10641,plain,
! [B: $i,A: $i] : ( B @ s @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10595]) ).
thf(45643,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44347,15331]) ).
thf(45644,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[45643]) ).
thf(45751,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[45644]) ).
thf(45795,plain,
! [A: $i] :
( ( A @ s @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[45751]) ).
thf(20028,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ s ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19587]) ).
thf(20029,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ p @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[20028:[bind(A,$thf( A )),bind(B,$thf( E @ p @ s )),bind(C,$thf( E ))]]) ).
thf(20053,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[20029]) ).
thf(41489,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,20053]) ).
thf(41490,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41489]) ).
thf(41592,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41490]) ).
thf(41641,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[41592]) ).
thf(17902,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)],[17003,88]) ).
thf(17903,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)],[17902]) ).
thf(17904,plain,
! [B: $i,A: $i] : ( B @ n @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[17903:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ n @ n @ n ))]]) ).
thf(17994,plain,
! [B: $i,A: $i] : ( B @ n @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[17904]) ).
thf(19686,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17003,19326]) ).
thf(19687,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19686]) ).
thf(19703,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19687]) ).
thf(19749,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19703]) ).
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(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(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(465,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(466,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)],[465]) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ m ) @ sk1 ) @ mem ) )
| ( C @ ( B @ m ) @ ( A @ disj ) ) ),
inference(pattern_uni,[status(thm)],[466:[bind(A,$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(480,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ m ) @ sk1 ) @ mem ) )
| ( C @ ( B @ m ) @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[467]) ).
thf(27250,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)],[25778,87]) ).
thf(27251,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)],[27250]) ).
thf(27252,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[27251:[bind(A,$thf( H )),bind(B,$thf( e )),bind(C,$thf( H @ p @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(27352,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[27252]) ).
thf(239,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(266,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n ) )
| ( A
!= ( e @ n @ s @ n @ s ) )
| ( ( e @ n @ n @ n @ s @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[239]) ).
thf(280,plain,
( ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ n @ s @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[266]) ).
thf(16210,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11209,15332]) ).
thf(16211,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16210]) ).
thf(16222,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16211]) ).
thf(16252,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[16222]) ).
thf(18781,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ( B
!= ( C @ s @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16252]) ).
thf(18782,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ~ ( A @ s @ ( e @ n @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18781:[bind(A,$thf( e @ n @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(18842,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ n @ n @ mem ) ),
inference(simp,[status(thm)],[18782]) ).
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(16882,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16387]) ).
thf(16883,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16882:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(16905,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[16883]) ).
thf(25494,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16905]) ).
thf(25495,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[25494]) ).
thf(25537,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[25495]) ).
thf(25587,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[25537]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ mem ) )
| ~ ( C @ ( B @ m ) @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(409,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(410,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)],[409]) ).
thf(411,plain,
! [B: $i,A: $i] :
~ ( B @ s @ ( A @ m ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[410:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ s ))]]) ).
thf(418,plain,
! [B: $i,A: $i] :
~ ( B @ s @ ( A @ m ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[411]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( C @ s @ ( B @ m ) @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,418]) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( C @ s @ ( B @ m ) @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[423]) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( C @ s @ ( B @ m ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[424]) ).
thf(428,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ m ) )
!= ( B @ s ) ),
inference(simp,[status(thm)],[426]) ).
thf(10968,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)],[10860,88]) ).
thf(10969,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)],[10968]) ).
thf(10970,plain,
! [B: $i,A: $i] : ( B @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10969:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ n ))]]) ).
thf(11015,plain,
! [B: $i,A: $i] : ( B @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10970]) ).
thf(11453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ n @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11015,69]) ).
thf(11454,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ n @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[11453]) ).
thf(11496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ n @ ( A @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[11454]) ).
thf(11505,plain,
! [B: $i,A: $i] :
( ( B @ n @ ( A @ u ) )
!= e ),
inference(simp,[status(thm)],[11496]) ).
thf(18864,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ s @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16265]) ).
thf(18865,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18864:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18928,plain,
! [A: $i] :
~ ( e @ s @ n @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[18865]) ).
thf(19763,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)],[19298,88]) ).
thf(19764,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)],[19763]) ).
thf(19765,plain,
! [C: $i,B: $i,A: $i] : ( C @ p @ ( B @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[19764:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( D )),bind(E,$thf( H @ p @ ( F @ u ) ))]]) ).
thf(19877,plain,
! [C: $i,B: $i,A: $i] : ( C @ p @ ( B @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[19765]) ).
thf(45636,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44347,19326]) ).
thf(45637,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[45636]) ).
thf(45764,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[45637]) ).
thf(45808,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[45764]) ).
thf(48131,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41699]) ).
thf(48132,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[48131]) ).
thf(48287,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[48132]) ).
thf(48308,plain,
! [A: $i] :
( ( e @ p @ p )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[48287]) ).
thf(60,plain,
! [A: $i] :
( ( A @ sk3 @ atleast7p )
| ~ ( A @ atleast8p ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(94,plain,
! [A: $i] :
( ~ ( A @ sk5 @ ( A @ subq ) )
| ~ ( A @ atleast7p ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk5 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast7p ) ),
inference(paramod_ordered,[status(thm)],[685,94]) ).
thf(886,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk5 @ ( B @ subq ) ) )
| ~ ( B @ atleast7p ) ),
inference(simp,[status(thm)],[885]) ).
thf(887,plain,
~ ( e @ atleast7p ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( e @ sk5 )),bind(B,$thf( e ))]]) ).
thf(1065,plain,
! [A: $i] :
( ( ( A @ sk3 @ atleast7p )
!= ( e @ atleast7p ) )
| ~ $true
| ~ ( A @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[60,887]) ).
thf(1066,plain,
! [A: $i] :
( ( ( A @ sk3 @ atleast7p )
!= ( e @ atleast7p ) )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[1065]) ).
thf(1067,plain,
! [A: $i] :
( ( ( A @ sk3 )
!= e )
| ~ ( A @ atleast8p ) ),
inference(simp,[status(thm)],[1066]) ).
thf(24487,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16832]) ).
thf(24488,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[24487]) ).
thf(24554,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[24488]) ).
thf(24603,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[24554]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ mem ) )
| ~ ( A @ ( C @ mem ) )
| ~ ( B @ ( A @ subq ) ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(16886,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ s ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16387]) ).
thf(16887,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ n @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16886:[bind(A,$thf( A )),bind(B,$thf( E @ n @ s )),bind(C,$thf( E ))]]) ).
thf(16909,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[16887]) ).
thf(26610,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16909]) ).
thf(26611,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[26610]) ).
thf(26663,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[26611]) ).
thf(26703,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[26663]) ).
thf(41534,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16905]) ).
thf(41535,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[41534]) ).
thf(41601,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[41535]) ).
thf(41605,plain,
! [A: $i] :
( ( A @ n @ s @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41601]) ).
thf(43212,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ p @ p ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41646]) ).
thf(43213,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ p @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[43212:[bind(A,$thf( E @ p @ p )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(43238,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ p @ p @ mem ) ),
inference(simp,[status(thm)],[43213]) ).
thf(55493,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,43238]) ).
thf(55494,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) ),
inference(simp,[status(thm)],[55493]) ).
thf(55592,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ p ) ) ),
inference(simp,[status(thm)],[55494]) ).
thf(55625,plain,
! [A: $i] :
( ( A @ p @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[55592]) ).
thf(19662,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,19326]) ).
thf(19663,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19662]) ).
thf(19698,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19663]) ).
thf(19744,plain,
! [A: $i] :
( ( e @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19698]) ).
thf(20063,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( e @ n ) )
| ( A
!= ( C @ p @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19744]) ).
thf(20064,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ p @ s ) )
| ~ ( e @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[20063:[bind(A,$thf( A )),bind(B,$thf( e @ n )),bind(C,$thf( C ))]]) ).
thf(20097,plain,
! [A: $i] :
~ ( e @ n @ s @ ( A @ p @ s @ mem ) ),
inference(simp,[status(thm)],[20064]) ).
thf(41517,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,20097]) ).
thf(41518,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[41517]) ).
thf(41583,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[41518]) ).
thf(41630,plain,
! [A: $i] :
( ( A @ p @ s @ p )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[41583]) ).
thf(16731,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ n ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16121]) ).
thf(16732,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ s @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16731:[bind(A,$thf( A )),bind(B,$thf( E @ s @ n )),bind(C,$thf( E ))]]) ).
thf(16755,plain,
! [A: $i] :
~ ( A @ s @ n @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[16732]) ).
thf(41536,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16755]) ).
thf(41537,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41536]) ).
thf(41578,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41537]) ).
thf(41625,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ s @ n @ s ) ),
inference(simp,[status(thm)],[41578]) ).
thf(41653,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ p ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41617]) ).
thf(41654,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ p ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41653:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(41703,plain,
! [A: $i] :
~ ( e @ p @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[41654]) ).
thf(48459,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41703]) ).
thf(48460,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[48459]) ).
thf(48545,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ p @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[48460]) ).
thf(48581,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[48545]) ).
thf(16067,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,15331]) ).
thf(16068,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[16067]) ).
thf(16097,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[16068]) ).
thf(16128,plain,
! [A: $i] :
( ( A @ s @ s )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16097]) ).
thf(16762,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ s @ s ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16128]) ).
thf(16763,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ s @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16762:[bind(A,$thf( A )),bind(B,$thf( E @ s @ s )),bind(C,$thf( E ))]]) ).
thf(16786,plain,
! [A: $i] :
~ ( A @ s @ s @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[16763]) ).
thf(24280,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16786]) ).
thf(24281,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[24280]) ).
thf(24335,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[24281]) ).
thf(24367,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[24335]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ atleast4p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast3p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(41773,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ p ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41632]) ).
thf(41774,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ n @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[41773:[bind(A,$thf( E @ n @ p )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(41801,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ n @ p @ mem ) ),
inference(simp,[status(thm)],[41774]) ).
thf(16758,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16128]) ).
thf(16759,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[16758:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(16782,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[16759]) ).
thf(23959,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16782]) ).
thf(23960,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[23959]) ).
thf(24010,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[23960]) ).
thf(24059,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24010]) ).
thf(245,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(261,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n ) )
| ( A
!= ( e @ n @ s @ n @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[245]) ).
thf(275,plain,
( ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ s @ n @ s @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[261]) ).
thf(137,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ subq ) )
| ~ ( A @ atleast16p ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(92,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ subq ) )
| ~ ( A @ atleast7p ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ atleast14p )
<=> ? [B: $i] :
( ~ ( B @ ( A @ subq ) )
& ( B @ atleast13p )
& ( A @ ( B @ subq ) ) ) ),
file('/export/starexec/sandbox/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(17900,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17003,69]) ).
thf(17901,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[17900]) ).
thf(17976,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[17901]) ).
thf(18004,plain,
! [A: $i] :
( ( A @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[17976]) ).
thf(20123,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)],[19311,88]) ).
thf(20124,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)],[20123]) ).
thf(20125,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ p @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20124:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ p @ u ) ))]]) ).
thf(20220,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ p @ u ) @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20125]) ).
thf(21183,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ n @ s ) )
| ( A
!= ( e @ s @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16507]) ).
thf(21184,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s @ n ) )
| ~ ( B @ n @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[21183:[bind(A,$thf( A )),bind(B,$thf( E @ n @ s )),bind(C,$thf( E ))]]) ).
thf(21219,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ s @ n @ mem ) ),
inference(simp,[status(thm)],[21184]) ).
thf(45714,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44347,15332]) ).
thf(45715,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[45714]) ).
thf(45760,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[45715]) ).
thf(45804,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[45760]) ).
thf(19997,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ n ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19586]) ).
thf(19998,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ p @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[19997:[bind(A,$thf( A )),bind(B,$thf( E @ p @ n )),bind(C,$thf( E ))]]) ).
thf(20022,plain,
! [A: $i] :
~ ( A @ p @ n @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[19998]) ).
thf(29482,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,20022]) ).
thf(29483,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[29482]) ).
thf(29537,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[29483]) ).
thf(29593,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ n @ s ) ),
inference(simp,[status(thm)],[29537]) ).
thf(30601,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,20053]) ).
thf(30602,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[30601]) ).
thf(30663,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[30602]) ).
thf(30708,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[30663]) ).
thf(19759,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19298,69]) ).
thf(19760,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ p @ ( A @ u ) @ ( e @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[19759]) ).
thf(19842,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ p @ ( A @ u ) )
!= e )
| ( e != C ) ),
inference(simp,[status(thm)],[19760]) ).
thf(19854,plain,
! [B: $i,A: $i] :
( ( B @ p @ ( A @ u ) )
!= e ),
inference(simp,[status(thm)],[19842]) ).
thf(30387,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,20049]) ).
thf(30388,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[30387]) ).
thf(30440,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[30388]) ).
thf(30494,plain,
! [A: $i] :
( ( A @ p @ s @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[30440]) ).
thf(43216,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ p ) )
| ( A
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41646]) ).
thf(43217,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( B @ p @ p @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[43216:[bind(A,$thf( A )),bind(B,$thf( E @ p @ p )),bind(C,$thf( E ))]]) ).
thf(43232,plain,
! [A: $i] :
~ ( A @ p @ p @ s @ ( e @ s @ mem ) ),
inference(simp,[status(thm)],[43217]) ).
thf(31337,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)],[210,27352]) ).
thf(31338,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[31337:[bind(A,$thf( L @ p @ n @ n @ n )),bind(B,$thf( L @ p @ n @ n @ n @ s )),bind(C,$thf( L ))]]) ).
thf(31403,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[31338]) ).
thf(32374,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)],[31403,87]) ).
thf(32375,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)],[32374]) ).
thf(32376,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[32375:[bind(A,$thf( I )),bind(B,$thf( e )),bind(C,$thf( I @ p @ n @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(32498,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[32376]) ).
thf(36334,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)],[210,32498]) ).
thf(36335,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[36334:[bind(A,$thf( N @ p @ n @ n @ n @ n )),bind(B,$thf( N @ p @ n @ n @ n @ n @ s )),bind(C,$thf( N ))]]) ).
thf(36409,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[36335]) ).
thf(36790,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)],[36409,87]) ).
thf(36791,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)],[36790]) ).
thf(36792,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[36791:[bind(A,$thf( J )),bind(B,$thf( e )),bind(C,$thf( J @ p @ n @ n @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(36887,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ n @ n @ n @ n @ n @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[36792]) ).
thf(17940,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17003,15332]) ).
thf(17941,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[17940]) ).
thf(17972,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[17941]) ).
thf(17999,plain,
! [A: $i] :
( ( e @ n @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[17972]) ).
thf(187,plain,
! [A: $i] :
( ~ ( A @ sk15 @ ( A @ subq ) )
| ~ ( A @ atleast13p ) ),
inference(cnfConj,[status(thm)],[184]) ).
thf(36428,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk15 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast13p ) ),
inference(paramod_ordered,[status(thm)],[9135,187]) ).
thf(36429,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk15 @ ( B @ subq ) ) )
| ~ ( B @ atleast13p ) ),
inference(simp,[status(thm)],[36428]) ).
thf(36430,plain,
~ ( e @ atleast13p ),
inference(pattern_uni,[status(thm)],[36429:[bind(A,$thf( e @ sk15 )),bind(B,$thf( e ))]]) ).
thf(169,plain,
! [A: $i] :
( ( A @ ( A @ sk13 @ subq ) )
| ~ ( A @ atleast15p ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(16442,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,15772]) ).
thf(16443,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16442]) ).
thf(16475,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16443]) ).
thf(16504,plain,
! [A: $i] :
( ( e @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[16475]) ).
thf(16466,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11209,15772]) ).
thf(16467,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16466]) ).
thf(16487,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16467]) ).
thf(16519,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[16487]) ).
thf(23752,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16755]) ).
thf(23753,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[23752]) ).
thf(23817,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[23753]) ).
thf(23837,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ n @ s ) ),
inference(simp,[status(thm)],[23817]) ).
thf(55434,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,43238]) ).
thf(55435,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ p @ mem ) ) ),
inference(simp,[status(thm)],[55434]) ).
thf(55545,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ p ) ) ),
inference(simp,[status(thm)],[55435]) ).
thf(55653,plain,
! [A: $i] :
( ( A @ p @ p @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[55545]) ).
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(867,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk6 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast12p ) ),
inference(paramod_ordered,[status(thm)],[685,110]) ).
thf(868,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk6 @ ( B @ subq ) ) )
| ~ ( B @ atleast12p ) ),
inference(simp,[status(thm)],[867]) ).
thf(869,plain,
~ ( e @ atleast12p ),
inference(pattern_uni,[status(thm)],[868:[bind(A,$thf( e @ sk6 )),bind(B,$thf( e ))]]) ).
thf(109,plain,
! [A: $i] :
( ( A @ sk6 @ atleast11p )
| ~ ( A @ atleast12p ) ),
inference(cnfConj,[status(thm)],[107]) ).
thf(49815,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41760]) ).
thf(49816,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[49815]) ).
thf(49921,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[49816]) ).
thf(49977,plain,
! [A: $i] :
( ( e @ p @ p )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[49921]) ).
thf(10131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ s @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10128,69]) ).
thf(10132,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ s @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[10131]) ).
thf(10170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ s @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[10132]) ).
thf(10185,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ s @ u ) )
!= e ),
inference(simp,[status(thm)],[10170]) ).
thf(77,plain,
! [A: $i] :
( ( A @ sk4 @ atleast5p )
| ~ ( A @ atleast6p ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(193,plain,
! [A: $i] :
( ( A @ ( A @ sk16 @ subq ) )
| ~ ( A @ atleast14p ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(19536,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17003,19325]) ).
thf(19537,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19536]) ).
thf(19564,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19537]) ).
thf(19603,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19564]) ).
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(58954,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[57423,69]) ).
thf(58955,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[58954]) ).
thf(59125,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[58955]) ).
thf(59217,plain,
! [A: $i] :
( ( A @ s @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[59125]) ).
thf(139,plain,
! [A: $i] :
( ~ ( A @ sk9 @ ( A @ subq ) )
| ~ ( A @ atleast16p ) ),
inference(cnfConj,[status(thm)],[136]) ).
thf(882,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk9 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast16p ) ),
inference(paramod_ordered,[status(thm)],[685,139]) ).
thf(883,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk9 @ ( B @ subq ) ) )
| ~ ( B @ atleast16p ) ),
inference(simp,[status(thm)],[882]) ).
thf(884,plain,
~ ( e @ atleast16p ),
inference(pattern_uni,[status(thm)],[883:[bind(A,$thf( e @ sk9 )),bind(B,$thf( e ))]]) ).
thf(41483,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16873]) ).
thf(41484,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[41483]) ).
thf(41575,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[41484]) ).
thf(41622,plain,
! [A: $i] :
( ( A @ n @ n @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41575]) ).
thf(18151,plain,
! [B: $i,A: $i] :
( ( B
!= ( e @ n @ n ) )
| ( A
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17577]) ).
thf(18152,plain,
! [A: $i] :
( ( A
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ n @ n @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18151:[bind(A,$thf( A )),bind(B,$thf( e @ n @ n ))]]) ).
thf(18485,plain,
( ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ n @ n @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[18152]) ).
thf(55152,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,43232]) ).
thf(55153,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[55152]) ).
thf(55297,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[55153]) ).
thf(55318,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ p @ p @ s ) ),
inference(simp,[status(thm)],[55297]) ).
thf(18200,plain,
! [A: $i] :
( ( A
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3002,17577]) ).
thf(18201,plain,
( ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[18200:[bind(A,$thf( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ))]]) ).
thf(16055,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10439,15331]) ).
thf(16056,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[16055]) ).
thf(16100,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[16056]) ).
thf(16132,plain,
! [A: $i] :
( ( A @ s @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16100]) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( A @ sk8 @ subq ) )
| ~ ( A @ atleast10p ) ),
inference(cnfConj,[status(thm)],[128]) ).
thf(39558,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)],[210,36887]) ).
thf(39559,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[39558:[bind(A,$thf( P @ p @ n @ n @ n @ n @ n )),bind(B,$thf( P @ p @ n @ n @ n @ n @ n @ s )),bind(C,$thf( P ))]]) ).
thf(39597,plain,
! [A: $i] : ( A @ p @ n @ n @ n @ n @ n @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[39559]) ).
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(18787,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ s ) )
| ( B
!= ( e @ n @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16252]) ).
thf(18788,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n @ n ) )
| ~ ( A @ s @ ( B @ s @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18787:[bind(A,$thf( E @ s @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(18845,plain,
! [A: $i] :
~ ( e @ n @ n @ s @ ( A @ s @ s @ mem ) ),
inference(simp,[status(thm)],[18788]) ).
thf(51961,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41851]) ).
thf(51962,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[51961]) ).
thf(52119,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[51962]) ).
thf(52143,plain,
! [A: $i] :
( ( e @ p @ p )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[52119]) ).
thf(17942,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)],[17003,87]) ).
thf(17943,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)],[17942]) ).
thf(17944,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ n @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[17943:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( G @ n @ n @ n )),bind(D,$thf( D ))]]) ).
thf(17984,plain,
! [B: $i,A: $i] : ( A @ ( B @ n @ n @ n @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[17944]) ).
thf(19508,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10439,19325]) ).
thf(19509,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19508]) ).
thf(19567,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19509]) ).
thf(19607,plain,
! [A: $i] :
( ( A @ p @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19567]) ).
thf(23545,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16751]) ).
thf(23546,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[23545]) ).
thf(23604,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[23546]) ).
thf(23644,plain,
! [A: $i] :
( ( A @ s @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23604]) ).
thf(48402,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41703]) ).
thf(48403,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[48402]) ).
thf(48521,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ p @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[48403]) ).
thf(48568,plain,
! [A: $i] :
( ( A @ s @ s @ p )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[48521]) ).
thf(8862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( e @ m ) )
!= ( D @ ( C @ m ) ) )
| ( C @ ( B @ ( e @ sk1 ) @ mem ) )
| ( D @ ( C @ m ) @ ( B @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[8835,480]) ).
thf(8863,plain,
! [B: $i,A: $i] :
( ( e @ ( B @ ( e @ sk1 ) @ mem ) )
| ( A @ ( e @ m ) @ ( B @ disj ) ) ),
inference(pattern_uni,[status(thm)],[8862:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( e )),bind(D,$thf( A ))]]) ).
thf(8988,plain,
! [A: $i] :
( $false
| ( e @ ( A @ disj ) ) ),
inference(rewrite,[status(thm)],[8863,8835,69]) ).
thf(8989,plain,
! [A: $i] : ( e @ ( A @ disj ) ),
inference(simp,[status(thm)],[8988]) ).
thf(20170,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)],[19311,87]) ).
thf(20171,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)],[20170]) ).
thf(20172,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ p @ u ) @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20171:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( e )),bind(D,$thf( G @ ( H @ p @ u ) )),bind(E,$thf( E ))]]) ).
thf(20212,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ p @ u ) @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20172]) ).
thf(11349,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11209,69]) ).
thf(11350,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[11349]) ).
thf(11390,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[11350]) ).
thf(11407,plain,
! [A: $i] :
( ( A @ n @ n )
!= e ),
inference(simp,[status(thm)],[11390]) ).
thf(41478,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16877]) ).
thf(41479,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41478]) ).
thf(41571,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41479]) ).
thf(41618,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ n @ n @ s ) ),
inference(simp,[status(thm)],[41571]) ).
thf(52519,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50481,15771]) ).
thf(52520,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[52519]) ).
thf(52620,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[52520]) ).
thf(52656,plain,
! [A: $i] :
( ( A @ n @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[52620]) ).
thf(41143,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)],[687,205]) ).
thf(41144,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)],[41143]) ).
thf(41145,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ m ) @ subq ) )
| ( A @ ( B @ ( A @ m ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[41144:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ m ) )),bind(E,$thf( F ))]]) ).
thf(41319,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ m ) @ subq ) ),
inference(simp,[status(thm)],[41145]) ).
thf(41865,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ n @ subq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41319,11024]) ).
thf(41866,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ n @ subq ) ) ),
inference(simp,[status(thm)],[41865]) ).
thf(41977,plain,
! [C: $i,B: $i,A: $i] :
( ( A != e )
| ( ( B @ ( A @ m ) )
!= ( C @ n ) ) ),
inference(simp,[status(thm)],[41866]) ).
thf(42021,plain,
! [B: $i,A: $i] :
( ( A @ ( e @ m ) )
!= ( B @ n ) ),
inference(simp,[status(thm)],[41977]) ).
thf(68642,plain,
! [A: $i] :
( ( A @ n )
!= e ),
inference(rewrite,[status(thm)],[42021,8835]) ).
thf(17834,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ( B
!= ( C @ n @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16504]) ).
thf(17835,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ n @ s ) )
| ~ ( A @ s @ ( e @ n @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17834:[bind(A,$thf( e @ n )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(17881,plain,
! [A: $i] :
~ ( A @ n @ s @ s @ ( e @ n @ mem ) ),
inference(simp,[status(thm)],[17835]) ).
thf(26824,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,17881]) ).
thf(26825,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[26824]) ).
thf(26888,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[26825]) ).
thf(26910,plain,
! [A: $i] :
( ( e @ n @ s )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[26888]) ).
thf(161,plain,
! [A: $i] :
( ( A @ ( A @ sk12 @ subq ) )
| ~ ( A @ atleast4p ) ),
inference(cnfConj,[status(thm)],[160]) ).
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(10820,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ s @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10545,69]) ).
thf(10821,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ s @ ( A @ u ) @ ( B @ mem ) )
!= ( e @ ( C @ mem ) ) ),
inference(simp,[status(thm)],[10820]) ).
thf(10862,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ s @ ( A @ u ) )
!= e )
| ( B != C ) ),
inference(simp,[status(thm)],[10821]) ).
thf(10872,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ u ) )
!= e ),
inference(simp,[status(thm)],[10862]) ).
thf(21263,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)],[19214,125]) ).
thf(21264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[21263]) ).
thf(21265,plain,
! [A: $i] :
( ( A @ p @ atleast2p )
| ( e @ p @ ( A @ p @ subq ) ) ),
inference(pattern_uni,[status(thm)],[21264:[bind(A,$thf( D )),bind(B,$thf( D @ p )),bind(C,$thf( e ))]]) ).
thf(21349,plain,
! [A: $i] :
( ( A @ p @ atleast2p )
| ( e @ p @ ( A @ p @ subq ) ) ),
inference(simp,[status(thm)],[21265]) ).
thf(246,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ( ( A @ n @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(265,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( A
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( ( A @ n @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[246]) ).
thf(279,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ s )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ n @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[265]) ).
thf(61778,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)],[210,17984]) ).
thf(61779,plain,
! [A: $i] : ( A @ n @ n @ n @ n @ ( A @ mem ) ),
inference(pattern_uni,[status(thm)],[61778:[bind(A,$thf( J @ n @ n @ n )),bind(B,$thf( J @ n @ n @ n @ s )),bind(C,$thf( J ))]]) ).
thf(61854,plain,
! [A: $i] : ( A @ n @ n @ n @ n @ ( A @ mem ) ),
inference(simp,[status(thm)],[61779]) ).
thf(18079,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( B
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,17577]) ).
thf(18080,plain,
! [A: $i] :
( ( ( e @ n @ n )
!= ( e @ n ) )
| ( A
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( A @ s @ ( e @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[18079:[bind(A,$thf( e @ n @ s )),bind(B,$thf( B ))]]) ).
thf(18478,plain,
( ( ( e @ n @ n )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ n @ s @ ( e @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[18080]) ).
thf(22499,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( e @ n @ s @ mem ) ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,18478]) ).
thf(22500,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( e @ n @ s @ mem ) ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[22499]) ).
thf(22611,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ s ) )
| ( A
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[22500]) ).
thf(22683,plain,
( ( ( e @ n @ s @ s )
!= ( e @ n @ s ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[22611]) ).
thf(238,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( A @ n @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(249,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( A
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s ) )
| ( ( e @ n @ n @ n @ s @ ( A @ n @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[238]) ).
thf(286,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ n @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[249]) ).
thf(873,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk4 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast6p ) ),
inference(paramod_ordered,[status(thm)],[685,78]) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk4 @ ( B @ subq ) ) )
| ~ ( B @ atleast6p ) ),
inference(simp,[status(thm)],[873]) ).
thf(875,plain,
~ ( e @ atleast6p ),
inference(pattern_uni,[status(thm)],[874:[bind(A,$thf( e @ sk4 )),bind(B,$thf( e ))]]) ).
thf(240,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ( ( A @ n )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(254,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s ) )
| ( A
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( ( A @ n )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[240]) ).
thf(291,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ s )
!= ( e @ n @ n @ n @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ n ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[254]) ).
thf(25080,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16873]) ).
thf(25081,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[25080]) ).
thf(25135,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[25081]) ).
thf(25177,plain,
! [A: $i] :
( ( A @ n @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[25135]) ).
thf(19069,plain,
! [B: $i,A: $i] :
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
!= ( B @ ( A @ subq ) ) )
| ( B @ p @ ( A @ mem ) )
| ~ $true
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) ) ),
inference(paramod_ordered,[status(thm)],[17577,118]) ).
thf(19070,plain,
! [B: $i,A: $i] :
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
!= ( B @ ( A @ subq ) ) )
| ( B @ p @ ( A @ mem ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[19069]) ).
thf(19071,plain,
( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ p @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ mem ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) ) ),
inference(pattern_uni,[status(thm)],[19070:[bind(A,$thf( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) )),bind(B,$thf( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) ))]]) ).
thf(59,plain,
! [A: $i] :
( ( A @ ( A @ sk3 @ subq ) )
| ~ ( A @ atleast8p ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(43182,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ s @ p ) )
| ( B
!= ( e @ s ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,41640]) ).
thf(43183,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ s ) )
| ~ ( A @ s @ ( B @ s @ p @ mem ) ) ),
inference(pattern_uni,[status(thm)],[43182:[bind(A,$thf( E @ s @ p )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(43210,plain,
! [A: $i] :
~ ( e @ s @ s @ ( A @ s @ p @ mem ) ),
inference(simp,[status(thm)],[43183]) ).
thf(18202,plain,
! [A: $i] :
( ( A
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) ) )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ ( A @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[3002,17577]) ).
thf(18203,plain,
( ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[18202:[bind(A,$thf( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) ))]]) ).
thf(59493,plain,
! [A: $i] :
( ( ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
!= ( e @ ( A @ subq ) ) )
| ~ $true
| ( e = A )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ~ ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[18203,3002]) ).
thf(59494,plain,
! [A: $i] :
( ( ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
!= ( e @ ( A @ subq ) ) )
| ( e = A )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ~ ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[59493]) ).
thf(59495,plain,
( ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) )
= e )
| ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ~ ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(pattern_uni,[status(thm)],[59494:[bind(A,$thf( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) ))]]) ).
thf(63547,plain,
( ( ( e @ n @ n )
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ~ ( e @ ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simplifyReflect,[status(thm)],[59495,11211]) ).
thf(242,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(267,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( A
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[242]) ).
thf(281,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ n @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[267]) ).
thf(51461,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41795]) ).
thf(51462,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[51461]) ).
thf(51538,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[51462]) ).
thf(51602,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ n @ p @ s ) ),
inference(simp,[status(thm)],[51538]) ).
thf(50148,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41764]) ).
thf(50149,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[50148]) ).
thf(50239,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ p @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[50149]) ).
thf(50285,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[50239]) ).
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(41528,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16909]) ).
thf(41529,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41528]) ).
thf(41594,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41529]) ).
thf(41643,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[41594]) ).
thf(19658,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10439,19326]) ).
thf(19659,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19658]) ).
thf(19695,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19659]) ).
thf(19741,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19695]) ).
thf(54868,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,43210]) ).
thf(54869,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) ),
inference(simp,[status(thm)],[54868]) ).
thf(55000,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ p ) ) ),
inference(simp,[status(thm)],[54869]) ).
thf(55072,plain,
! [A: $i] :
( ( A @ s @ p @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[55000]) ).
thf(55214,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,43232]) ).
thf(55215,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[55214]) ).
thf(55304,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ p @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[55215]) ).
thf(55324,plain,
! [A: $i] :
( ( A @ p @ p @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[55304]) ).
thf(214,plain,
! [A: $i] :
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk2 @ ( A @ subq ) ) )
| ~ $true
| ~ ( A @ atleast9p ) ),
inference(paramod_ordered,[status(thm)],[211,50]) ).
thf(215,plain,
! [A: $i] :
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) )
!= ( A @ sk2 @ ( A @ subq ) ) )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[214]) ).
thf(217,plain,
! [A: $i] :
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( A @ sk2 ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= A )
| ~ ( A @ atleast9p ) ),
inference(simp,[status(thm)],[215]) ).
thf(219,plain,
( ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk2 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast9p ) ),
inference(simp,[status(thm)],[217]) ).
thf(230,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(260,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n ) )
| ( A
!= ( e @ n @ s @ n @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(274,plain,
( ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ s @ n @ s @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(19642,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10183,19326]) ).
thf(19643,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19642]) ).
thf(19706,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19643]) ).
thf(19752,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19706]) ).
thf(76,plain,
! [A: $i] :
( ( A @ ( A @ sk4 @ subq ) )
| ~ ( A @ atleast6p ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(224,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( A
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(271,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) )
!= ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ s ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(195,plain,
! [A: $i] :
( ~ ( A @ sk16 @ ( A @ subq ) )
| ~ ( A @ atleast14p ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(38621,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk16 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast14p ) ),
inference(paramod_ordered,[status(thm)],[9135,195]) ).
thf(38622,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk16 @ ( B @ subq ) ) )
| ~ ( B @ atleast14p ) ),
inference(simp,[status(thm)],[38621]) ).
thf(38623,plain,
~ ( e @ atleast14p ),
inference(pattern_uni,[status(thm)],[38622:[bind(A,$thf( e @ sk16 )),bind(B,$thf( e ))]]) ).
thf(10490,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)],[10183,88]) ).
thf(10491,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)],[10490]) ).
thf(10492,plain,
! [B: $i,A: $i] : ( B @ s @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[10491:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ s @ n ))]]) ).
thf(10565,plain,
! [B: $i,A: $i] : ( B @ s @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[10492]) ).
thf(23114,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)],[21349,118]) ).
thf(23115,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)],[23114]) ).
thf(23116,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ mem ) )
| ( A @ p @ atleast2p ) ),
inference(pattern_uni,[status(thm)],[23115:[bind(A,$thf( D )),bind(B,$thf( D @ p )),bind(C,$thf( e @ p ))]]) ).
thf(23189,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ mem ) )
| ( A @ p @ atleast2p ) ),
inference(simp,[status(thm)],[23116]) ).
thf(36685,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)],[36409,88]) ).
thf(36686,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)],[36685]) ).
thf(36687,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[36686:[bind(A,$thf( J )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( J @ p @ n @ n @ n @ n @ n ))]]) ).
thf(36897,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[36687]) ).
thf(41920,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)],[41319,118]) ).
thf(41921,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)],[41920]) ).
thf(41922,plain,
! [B: $i,A: $i] : ( A @ p @ ( B @ ( A @ m ) @ mem ) ),
inference(pattern_uni,[status(thm)],[41921:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ m ) )),bind(D,$thf( E ))]]) ).
thf(41990,plain,
! [B: $i,A: $i] : ( A @ p @ ( B @ ( A @ m ) @ mem ) ),
inference(simp,[status(thm)],[41922]) ).
thf(52558,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50481,19325]) ).
thf(52559,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[52558]) ).
thf(52615,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[52559]) ).
thf(52651,plain,
! [A: $i] :
( ( A @ p @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[52615]) ).
thf(19632,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19214,19326]) ).
thf(19633,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19632]) ).
thf(19701,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s ) )
| ( e != e ) ),
inference(simp,[status(thm)],[19633]) ).
thf(19747,plain,
! [B: $i,A: $i] :
( ( A @ p )
!= ( B @ p @ s ) ),
inference(simp,[status(thm)],[19701]) ).
thf(155,plain,
! [A: $i] :
( ~ ( A @ sk11 @ ( A @ subq ) )
| ~ ( A @ atleast3p ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(108,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ subq ) )
| ~ ( A @ atleast12p ) ),
inference(cnfConj,[status(thm)],[107]) ).
thf(41511,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16786]) ).
thf(41512,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41511]) ).
thf(41581,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41512]) ).
thf(41628,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[41581]) ).
thf(131,plain,
! [A: $i] :
( ~ ( A @ sk8 @ ( A @ subq ) )
| ~ ( A @ atleast10p ) ),
inference(cnfConj,[status(thm)],[128]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk8 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast10p ) ),
inference(paramod_ordered,[status(thm)],[685,131]) ).
thf(889,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk8 @ ( B @ subq ) ) )
| ~ ( B @ atleast10p ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
~ ( e @ atleast10p ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( e @ sk8 )),bind(B,$thf( e ))]]) ).
thf(16299,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10183,15771]) ).
thf(16300,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[16299]) ).
thf(16351,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[16300]) ).
thf(16381,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16351]) ).
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(316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ~ $true
| ( B @ ( A @ disj ) ) ),
inference(paramod_ordered,[status(thm)],[43,69]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk1 ) @ mem ) )
!= ( e @ ( C @ mem ) ) )
| ( B @ ( A @ disj ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
! [A: $i] : ( A @ ( e @ disj ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( e )),bind(B,$thf( D )),bind(C,$thf( e @ ( D @ sk1 ) ))]]) ).
thf(323,plain,
! [A: $i] : ( A @ ( e @ disj ) ),
inference(simp,[status(thm)],[318]) ).
thf(26820,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,17881]) ).
thf(26821,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[26820]) ).
thf(26896,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[26821]) ).
thf(26918,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[26896]) ).
thf(25084,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,16873]) ).
thf(25085,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ n @ mem ) ) ),
inference(simp,[status(thm)],[25084]) ).
thf(25144,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ n ) ) ),
inference(simp,[status(thm)],[25085]) ).
thf(25184,plain,
! [A: $i] :
( ( A @ n @ n @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[25144]) ).
thf(17838,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ n @ s ) )
| ( B
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,16504]) ).
thf(17839,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( A @ s @ ( B @ n @ s @ mem ) ) ),
inference(pattern_uni,[status(thm)],[17838:[bind(A,$thf( E @ n @ s )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(17885,plain,
! [A: $i] :
~ ( e @ n @ s @ ( A @ n @ s @ mem ) ),
inference(simp,[status(thm)],[17839]) ).
thf(41563,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,17885]) ).
thf(41564,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[41563]) ).
thf(41590,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[41564]) ).
thf(41638,plain,
! [A: $i] :
( ( A @ n @ s @ p )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[41590]) ).
thf(20067,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ p @ s ) )
| ( A
!= ( e @ n ) )
| ~ ( B @ s @ ( A @ mem ) ) ),
inference(paramod_ordered,[status(thm)],[102,19744]) ).
thf(20068,plain,
! [B: $i,A: $i] :
( ( A
!= ( e @ n ) )
| ~ ( B @ p @ s @ s @ ( A @ mem ) ) ),
inference(pattern_uni,[status(thm)],[20067:[bind(A,$thf( A )),bind(B,$thf( E @ p @ s )),bind(C,$thf( E ))]]) ).
thf(20100,plain,
! [A: $i] :
~ ( A @ p @ s @ s @ ( e @ n @ mem ) ),
inference(simp,[status(thm)],[20068]) ).
thf(30823,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,20097]) ).
thf(30824,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[30823]) ).
thf(30893,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[30824]) ).
thf(30935,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[30893]) ).
thf(29951,plain,
! [A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ n @ s @ ( e @ n @ mem ) ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,18485]) ).
thf(29952,plain,
! [A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ n @ s @ ( e @ n @ mem ) ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[29951]) ).
thf(30021,plain,
! [A: $i] :
( ( ( A @ n )
!= ( e @ n @ n @ s ) )
| ( A
!= ( e @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[29952]) ).
thf(30079,plain,
( ( ( e @ n @ n @ s )
!= ( e @ n @ n ) )
| ( ( e @ n @ s )
!= ( e @ n ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ u ) @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[30021]) ).
thf(41474,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16845]) ).
thf(41475,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[41474]) ).
thf(41572,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ n @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[41475]) ).
thf(41619,plain,
! [A: $i] :
( ( A @ s @ s @ p )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[41572]) ).
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(51681,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41801]) ).
thf(51682,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) ),
inference(simp,[status(thm)],[51681]) ).
thf(51820,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ p ) ) ),
inference(simp,[status(thm)],[51682]) ).
thf(51891,plain,
! [A: $i] :
( ( A @ n @ p @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[51820]) ).
thf(11351,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)],[11209,88]) ).
thf(11352,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)],[11351]) ).
thf(11353,plain,
! [B: $i,A: $i] : ( B @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[11352:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ n @ n ))]]) ).
thf(11402,plain,
! [B: $i,A: $i] : ( B @ n @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[11353]) ).
thf(52019,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41851]) ).
thf(52020,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[52019]) ).
thf(52091,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[52020]) ).
thf(52178,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[52091]) ).
thf(220,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(221,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)],[220]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( D @ ( C @ m ) ) )
| ( A != B )
| ( C @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s )
!= ( C @ ( B @ m ) ) )
| ( B @ ( A @ mem ) ) ),
inference(simp,[status(thm)],[222]) ).
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(598,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(599,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)],[598]) ).
thf(600,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ s @ m ) @ ( B @ mem ) )
| ( A @ ( B @ mem ) ) ),
inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ s ))]]) ).
thf(608,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ s @ m ) @ ( B @ mem ) )
| ( A @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[600]) ).
thf(162,plain,
! [A: $i] :
( ( A @ sk12 @ atleast3p )
| ~ ( A @ atleast4p ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(20925,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20224,69]) ).
thf(20926,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[20925]) ).
thf(21006,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[20926]) ).
thf(21022,plain,
! [A: $i] :
( ( A @ p @ n )
!= e ),
inference(simp,[status(thm)],[21006]) ).
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(123,plain,
! [A: $i] :
( ~ ( A @ sk7 @ p @ ( A @ subq ) )
| ~ ( A @ atleast2p ) ),
inference(cnfConj,[status(thm)],[121]) ).
thf(34024,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)],[21353,118]) ).
thf(34025,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)],[34024]) ).
thf(34026,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ n @ mem ) )
| ( A @ p @ n @ atleast2p ) ),
inference(pattern_uni,[status(thm)],[34025:[bind(A,$thf( E )),bind(B,$thf( E @ p @ n )),bind(C,$thf( e @ p ))]]) ).
thf(34141,plain,
! [A: $i] :
( ( e @ p @ p @ ( A @ p @ n @ mem ) )
| ( A @ p @ n @ atleast2p ) ),
inference(simp,[status(thm)],[34026]) ).
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(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(32271,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31403,69]) ).
thf(32272,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[32271]) ).
thf(32440,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[32272]) ).
thf(32482,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[32440]) ).
thf(227,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ( A @ n @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(268,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s ) )
| ( A
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( A @ n @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(282,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ s )
!= ( e @ n @ n @ n @ s ) )
| ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ n @ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ subq ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(50089,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41764]) ).
thf(50090,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[50089]) ).
thf(50233,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ p @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[50090]) ).
thf(50281,plain,
! [A: $i] :
( ( A @ n @ s @ p )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[50233]) ).
thf(52298,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41855]) ).
thf(52299,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ p @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[52298]) ).
thf(52393,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ p @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[52299]) ).
thf(52430,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ p @ s ) ),
inference(simp,[status(thm)],[52393]) ).
thf(41565,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,20022]) ).
thf(41566,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ n @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[41565]) ).
thf(41576,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ n @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[41566]) ).
thf(41623,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ p @ n @ s ) ),
inference(simp,[status(thm)],[41576]) ).
thf(29263,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,20018]) ).
thf(29264,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[29263]) ).
thf(29318,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[29264]) ).
thf(29354,plain,
! [A: $i] :
( ( A @ p @ n @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[29318]) ).
thf(23963,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,16782]) ).
thf(23964,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[23963]) ).
thf(24013,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[23964]) ).
thf(24062,plain,
! [A: $i] :
( ( A @ s @ s @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[24013]) ).
thf(45638,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)],[44347,88]) ).
thf(45639,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)],[45638]) ).
thf(45640,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(pattern_uni,[status(thm)],[45639:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ p @ n ))]]) ).
thf(45812,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( B @ mem ) ),
inference(simp,[status(thm)],[45640]) ).
thf(52548,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50481,15772]) ).
thf(52549,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[52548]) ).
thf(52634,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( B @ n @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[52549]) ).
thf(52676,plain,
! [A: $i] :
( ( e @ p @ n @ n )
!= ( A @ n @ s ) ),
inference(simp,[status(thm)],[52634]) ).
thf(19255,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19214,15332]) ).
thf(19256,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19255]) ).
thf(19283,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s ) )
| ( e != e ) ),
inference(simp,[status(thm)],[19256]) ).
thf(19297,plain,
! [B: $i,A: $i] :
( ( A @ p )
!= ( B @ s @ s ) ),
inference(simp,[status(thm)],[19283]) ).
thf(30831,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,20097]) ).
thf(30832,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[30831]) ).
thf(30871,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ n @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[30832]) ).
thf(30915,plain,
! [A: $i] :
( ( A @ p @ s @ s )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[30871]) ).
thf(72343,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)],[210,20212]) ).
thf(72344,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ n @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[72343:[bind(A,$thf( J @ ( K @ p @ u ) )),bind(B,$thf( J @ ( K @ p @ u ) @ s )),bind(C,$thf( J )),bind(D,$thf( K ))]]) ).
thf(72406,plain,
! [B: $i,A: $i] : ( A @ ( B @ p @ u ) @ n @ ( e @ mem ) ),
inference(simp,[status(thm)],[72344]) ).
thf(51740,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41801]) ).
thf(51741,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ p @ mem ) ) ),
inference(simp,[status(thm)],[51740]) ).
thf(51812,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ p ) ) ),
inference(simp,[status(thm)],[51741]) ).
thf(51885,plain,
! [A: $i] :
( ( A @ n @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[51812]) ).
thf(16311,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10439,15771]) ).
thf(16312,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[16311]) ).
thf(16353,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[16312]) ).
thf(16384,plain,
! [A: $i] :
( ( A @ n @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16353]) ).
thf(32275,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)],[31403,88]) ).
thf(32276,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)],[32275]) ).
thf(32277,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[32276:[bind(A,$thf( I )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( I @ p @ n @ n @ n @ n ))]]) ).
thf(32464,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[32277]) ).
thf(41485,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,20049]) ).
thf(41486,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[41485]) ).
thf(41602,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[41486]) ).
thf(41606,plain,
! [A: $i] :
( ( A @ p @ s @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41602]) ).
thf(177,plain,
! [A: $i] :
( ( A @ ( A @ sk14 @ subq ) )
| ~ ( A @ atleast11p ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(54644,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,43204]) ).
thf(54645,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[54644]) ).
thf(54748,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[54645]) ).
thf(54803,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ s @ p @ s ) ),
inference(simp,[status(thm)],[54748]) ).
thf(31045,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,20100]) ).
thf(31046,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[31045]) ).
thf(31097,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[31046]) ).
thf(31181,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[31097]) ).
thf(19253,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( e @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19214,15772]) ).
thf(19254,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( e @ mem ) )
!= ( B @ n @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19253]) ).
thf(19279,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s ) )
| ( e != e ) ),
inference(simp,[status(thm)],[19254]) ).
thf(19295,plain,
! [B: $i,A: $i] :
( ( A @ p )
!= ( B @ n @ s ) ),
inference(simp,[status(thm)],[19279]) ).
thf(54927,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,43210]) ).
thf(54928,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ p @ mem ) ) ),
inference(simp,[status(thm)],[54927]) ).
thf(54987,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ p ) ) ),
inference(simp,[status(thm)],[54928]) ).
thf(55061,plain,
! [A: $i] :
( ( A @ s @ p @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[54987]) ).
thf(52562,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50481,15332]) ).
thf(52563,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[52562]) ).
thf(52636,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[52563]) ).
thf(52679,plain,
! [A: $i] :
( ( e @ p @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[52636]) ).
thf(17925,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17003,15771]) ).
thf(17926,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[17925]) ).
thf(17970,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[17926]) ).
thf(17997,plain,
! [A: $i] :
( ( A @ n @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[17970]) ).
thf(154,plain,
! [A: $i] :
( ( A @ sk11 @ atleast2p )
| ~ ( A @ atleast3p ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(41513,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16832]) ).
thf(41514,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[41513]) ).
thf(41580,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[41514]) ).
thf(41627,plain,
! [A: $i] :
( ( e @ n @ p )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[41580]) ).
thf(25498,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,16905]) ).
thf(25499,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[25498]) ).
thf(25550,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[25499]) ).
thf(25596,plain,
! [A: $i] :
( ( A @ n @ s @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[25550]) ).
thf(23549,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,16751]) ).
thf(23550,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ n @ mem ) ) ),
inference(simp,[status(thm)],[23549]) ).
thf(23589,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ n ) ) ),
inference(simp,[status(thm)],[23550]) ).
thf(23634,plain,
! [A: $i] :
( ( A @ s @ n @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[23589]) ).
thf(16339,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11209,15771]) ).
thf(16340,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[16339]) ).
thf(16343,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[16340]) ).
thf(16369,plain,
! [A: $i] :
( ( A @ n @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16343]) ).
thf(10192,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10183,69]) ).
thf(10193,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[10192]) ).
thf(10229,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[10193]) ).
thf(10241,plain,
! [A: $i] :
( ( A @ s @ n )
!= e ),
inference(simp,[status(thm)],[10229]) ).
thf(24695,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,16845]) ).
thf(24696,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[24695]) ).
thf(24770,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[24696]) ).
thf(24814,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[24770]) ).
thf(19688,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11209,19326]) ).
thf(19689,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[19688]) ).
thf(19717,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[19689]) ).
thf(19725,plain,
! [A: $i] :
( ( e @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[19717]) ).
thf(49873,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41760]) ).
thf(49874,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[49873]) ).
thf(49969,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[49874]) ).
thf(50010,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[49969]) ).
thf(41547,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,17881]) ).
thf(41548,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[41547]) ).
thf(41593,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[41548]) ).
thf(41642,plain,
! [A: $i] :
( ( e @ n @ p )
!= ( A @ n @ s @ s ) ),
inference(simp,[status(thm)],[41593]) ).
thf(894,plain,
! [A: $i] :
( ( ( A @ sk5 @ atleast6p )
!= ( e @ atleast6p ) )
| ~ $true
| ~ ( A @ atleast7p ) ),
inference(paramod_ordered,[status(thm)],[93,875]) ).
thf(895,plain,
! [A: $i] :
( ( ( A @ sk5 @ atleast6p )
!= ( e @ atleast6p ) )
| ~ ( A @ atleast7p ) ),
inference(simp,[status(thm)],[894]) ).
thf(896,plain,
! [A: $i] :
( ( ( A @ sk5 )
!= e )
| ~ ( A @ atleast7p ) ),
inference(simp,[status(thm)],[895]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ mem ) )
| ~ ( A @ ( C @ mem ) )
| ~ ( B @ ( A @ disj ) ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(16083,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11209,15331]) ).
thf(16084,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[16083]) ).
thf(16102,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[16084]) ).
thf(16134,plain,
! [A: $i] :
( ( A @ s @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16102]) ).
thf(171,plain,
! [A: $i] :
( ~ ( A @ sk13 @ ( A @ subq ) )
| ~ ( A @ atleast15p ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(186,plain,
! [A: $i] :
( ( A @ sk15 @ atleast12p )
| ~ ( A @ atleast13p ) ),
inference(cnfConj,[status(thm)],[184]) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ mem ) )
| ~ ( A @ atleast2p ) ),
inference(cnfConj,[status(thm)],[121]) ).
thf(19882,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true
| ~ ( A @ atleast2p ) ),
inference(paramod_ordered,[status(thm)],[122,69]) ).
thf(19883,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ ( A @ atleast2p ) ),
inference(simp,[status(thm)],[19882]) ).
thf(19884,plain,
~ ( e @ atleast2p ),
inference(pattern_uni,[status(thm)],[19883:[bind(A,$thf( e )),bind(B,$thf( e @ sk7 ))]]) ).
thf(51403,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,41795]) ).
thf(51404,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ n @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[51403]) ).
thf(51515,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ n @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[51404]) ).
thf(51588,plain,
! [A: $i] :
( ( e @ s @ p )
!= ( A @ n @ p @ s ) ),
inference(simp,[status(thm)],[51515]) ).
thf(63271,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61854,69]) ).
thf(63272,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[63271]) ).
thf(63440,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[63272]) ).
thf(63508,plain,
! [A: $i] :
( ( A @ n @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[63440]) ).
thf(30379,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,20049]) ).
thf(30380,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ s @ mem ) ) ),
inference(simp,[status(thm)],[30379]) ).
thf(30451,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ s ) ) ),
inference(simp,[status(thm)],[30380]) ).
thf(30505,plain,
! [A: $i] :
( ( A @ p @ s @ n )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[30451]) ).
thf(236,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(253,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ s @ n ) )
| ( A
!= ( e @ n @ s @ n @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( A @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[236]) ).
thf(290,plain,
( ( ( e @ n @ n @ s @ n )
!= ( e @ n @ s @ n @ s @ s ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ s @ n @ s @ n @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[253]) ).
thf(237,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( A @ n @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(258,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( A
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( A @ n @ atleast8p ) ),
inference(simp,[status(thm)],[237]) ).
thf(272,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ s )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 ) )
| ~ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ n @ atleast8p ) ),
inference(simp,[status(thm)],[258]) ).
thf(897,plain,
! [A: $i] :
( ( ( A @ sk4 @ atleast5p )
!= ( e @ atleast5p ) )
| ~ $true
| ~ ( A @ atleast6p ) ),
inference(paramod_ordered,[status(thm)],[77,878]) ).
thf(898,plain,
! [A: $i] :
( ( ( A @ sk4 @ atleast5p )
!= ( e @ atleast5p ) )
| ~ ( A @ atleast6p ) ),
inference(simp,[status(thm)],[897]) ).
thf(899,plain,
! [A: $i] :
( ( ( A @ sk4 )
!= e )
| ~ ( A @ atleast6p ) ),
inference(simp,[status(thm)],[898]) ).
thf(19538,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11209,19325]) ).
thf(19539,plain,
! [B: $i,A: $i] :
( ( A @ n @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ p @ mem ) ) ),
inference(simp,[status(thm)],[19538]) ).
thf(19552,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ n )
!= ( e @ s ) )
| ( A
!= ( B @ p ) ) ),
inference(simp,[status(thm)],[19539]) ).
thf(19590,plain,
! [A: $i] :
( ( A @ p @ n @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[19552]) ).
thf(163,plain,
! [A: $i] :
( ~ ( A @ sk12 @ ( A @ subq ) )
| ~ ( A @ atleast4p ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(28927,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk12 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast4p ) ),
inference(paramod_ordered,[status(thm)],[9135,163]) ).
thf(28928,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk12 @ ( B @ subq ) ) )
| ~ ( B @ atleast4p ) ),
inference(simp,[status(thm)],[28927]) ).
thf(28929,plain,
~ ( e @ atleast4p ),
inference(pattern_uni,[status(thm)],[28928:[bind(A,$thf( e @ sk12 )),bind(B,$thf( e ))]]) ).
thf(54648,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,43204]) ).
thf(54649,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ mem ) )
!= ( B @ s @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[54648]) ).
thf(54717,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= ( B @ s @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[54649]) ).
thf(54783,plain,
! [A: $i] :
( ( A @ s @ p @ s )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[54717]) ).
thf(243,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( ( A @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(paramod_ordered,[status(thm)],[210,218]) ).
thf(250,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s ) )
| ( A
!= ( e @ n @ s @ s ) )
| ( ( A @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[243]) ).
thf(287,plain,
( ( ( e @ n @ n @ n @ s )
!= ( e @ n @ s @ s @ s ) )
| ( ( e @ n @ s @ s @ n @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ sk3 )
!= ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ~ ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ atleast8p ) ),
inference(simp,[status(thm)],[250]) ).
thf(32508,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk13 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast15p ) ),
inference(paramod_ordered,[status(thm)],[9135,171]) ).
thf(32509,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk13 @ ( B @ subq ) ) )
| ~ ( B @ atleast15p ) ),
inference(simp,[status(thm)],[32508]) ).
thf(32510,plain,
~ ( e @ atleast15p ),
inference(pattern_uni,[status(thm)],[32509:[bind(A,$thf( e @ sk13 )),bind(B,$thf( e ))]]) ).
thf(41538,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,20100]) ).
thf(41539,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( B @ p @ s @ s @ ( e @ n @ mem ) ) ),
inference(simp,[status(thm)],[41538]) ).
thf(41573,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( B @ p @ s @ s ) )
| ( A
!= ( e @ n ) ) ),
inference(simp,[status(thm)],[41539]) ).
thf(41620,plain,
! [A: $i] :
( ( e @ n @ p )
!= ( A @ p @ s @ s ) ),
inference(simp,[status(thm)],[41573]) ).
thf(55210,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,43232]) ).
thf(55211,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ p @ p @ s @ ( e @ s @ mem ) ) ),
inference(simp,[status(thm)],[55210]) ).
thf(55282,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ p @ p @ s ) )
| ( A
!= ( e @ s ) ) ),
inference(simp,[status(thm)],[55211]) ).
thf(55365,plain,
! [A: $i] :
( ( e @ s @ n )
!= ( A @ p @ p @ s ) ),
inference(simp,[status(thm)],[55282]) ).
thf(27026,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,17885]) ).
thf(27027,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( e @ n @ s @ ( B @ n @ s @ mem ) ) ),
inference(simp,[status(thm)],[27026]) ).
thf(27102,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( e @ n @ s ) )
| ( A
!= ( B @ n @ s ) ) ),
inference(simp,[status(thm)],[27027]) ).
thf(27148,plain,
! [A: $i] :
( ( A @ n @ s @ n )
!= ( e @ n @ s ) ),
inference(simp,[status(thm)],[27102]) ).
thf(22830,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)],[22353,88]) ).
thf(22831,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)],[22830]) ).
thf(22832,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[22831:[bind(A,$thf( G )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( G @ p @ n @ n ))]]) ).
thf(22958,plain,
! [B: $i,A: $i] : ( B @ p @ n @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[22832]) ).
thf(146,plain,
! [A: $i] :
( ( A @ sk10 @ atleast4p )
| ~ ( A @ atleast5p ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(52466,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50481,19326]) ).
thf(52467,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ ( A @ mem ) )
!= ( B @ p @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[52466]) ).
thf(52639,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n )
!= ( B @ p @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[52467]) ).
thf(52682,plain,
! [A: $i] :
( ( e @ p @ n @ n )
!= ( A @ p @ s ) ),
inference(simp,[status(thm)],[52639]) ).
thf(10591,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10439,69]) ).
thf(10592,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[10591]) ).
thf(10637,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= e )
| ( A != B ) ),
inference(simp,[status(thm)],[10592]) ).
thf(10649,plain,
! [A: $i] :
( ( A @ s @ n @ n )
!= e ),
inference(simp,[status(thm)],[10637]) ).
thf(20929,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)],[20224,88]) ).
thf(20930,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)],[20929]) ).
thf(20931,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(pattern_uni,[status(thm)],[20930:[bind(A,$thf( F )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( F @ p @ n ))]]) ).
thf(21015,plain,
! [B: $i,A: $i] : ( B @ p @ n @ ( A @ u ) @ ( e @ mem ) ),
inference(simp,[status(thm)],[20931]) ).
thf(48187,plain,
! [B: $i,A: $i] :
( ( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10860,41699]) ).
thf(48188,plain,
! [B: $i,A: $i] :
( ( A @ n @ ( A @ mem ) )
!= ( B @ s @ s @ s @ ( e @ p @ mem ) ) ),
inference(simp,[status(thm)],[48187]) ).
thf(48288,plain,
! [B: $i,A: $i] :
( ( ( A @ n )
!= ( B @ s @ s @ s ) )
| ( A
!= ( e @ p ) ) ),
inference(simp,[status(thm)],[48188]) ).
thf(48310,plain,
! [A: $i] :
( ( e @ p @ n )
!= ( A @ s @ s @ s ) ),
inference(simp,[status(thm)],[48288]) ).
thf(16182,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10439,15332]) ).
thf(16183,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ n @ ( A @ mem ) )
!= ( B @ s @ s @ ( e @ mem ) ) ),
inference(simp,[status(thm)],[16182]) ).
thf(16223,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ n )
!= ( B @ s @ s ) )
| ( A != e ) ),
inference(simp,[status(thm)],[16183]) ).
thf(16254,plain,
! [A: $i] :
( ( e @ s @ n @ n )
!= ( A @ s @ s ) ),
inference(simp,[status(thm)],[16223]) ).
thf(41872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ p @ subq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41319,19327]) ).
thf(41873,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ m ) @ subq ) )
!= ( e @ ( C @ p @ subq ) ) ),
inference(simp,[status(thm)],[41872]) ).
thf(41987,plain,
! [C: $i,B: $i,A: $i] :
( ( A != e )
| ( ( B @ ( A @ m ) )
!= ( C @ p ) ) ),
inference(simp,[status(thm)],[41873]) ).
thf(41992,plain,
! [B: $i,A: $i] :
( ( A @ ( e @ m ) )
!= ( B @ p ) ),
inference(simp,[status(thm)],[41987]) ).
thf(68625,plain,
! [A: $i] :
( ( A @ p )
!= e ),
inference(rewrite,[status(thm)],[41992,8835]) ).
thf(232,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ u ) )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( A @ n @ subq ) ) ),
inference(paramod_ordered,[status(thm)],[210,211]) ).
thf(269,plain,
! [A: $i] :
( ( ( A @ s )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( A
!= ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( A @ n @ subq ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(283,plain,
( ( ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ s )
!= ( e @ n @ n @ n @ s @ ( e @ n @ s @ s @ u ) ) )
| ( e @ n @ n @ n @ s @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ u ) @ ( e @ n @ n @ s @ n @ ( e @ n @ s @ n @ s @ u ) @ ( e @ n @ s @ n @ ( e @ n @ u ) @ s @ u ) @ n @ subq ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(178,plain,
! [A: $i] :
( ( A @ sk14 @ atleast10p )
| ~ ( A @ atleast11p ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(41561,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,20018]) ).
thf(41562,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ p @ n @ mem ) ) ),
inference(simp,[status(thm)],[41561]) ).
thf(41577,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ p @ n ) ) ),
inference(simp,[status(thm)],[41562]) ).
thf(41624,plain,
! [A: $i] :
( ( A @ p @ n @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41577]) ).
thf(27163,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25778,69]) ).
thf(27164,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ n @ n @ ( e @ mem ) )
!= ( e @ ( B @ mem ) ) ),
inference(simp,[status(thm)],[27163]) ).
thf(27304,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ n @ n )
!= e )
| ( e != B ) ),
inference(simp,[status(thm)],[27164]) ).
thf(27331,plain,
! [A: $i] :
( ( A @ p @ n @ n @ n )
!= e ),
inference(simp,[status(thm)],[27304]) ).
thf(45679,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44347,15771]) ).
thf(45680,plain,
! [B: $i,A: $i] :
( ( A @ p @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ n @ mem ) ) ),
inference(simp,[status(thm)],[45679]) ).
thf(45765,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ n )
!= ( e @ s ) )
| ( A
!= ( B @ n ) ) ),
inference(simp,[status(thm)],[45680]) ).
thf(45809,plain,
! [A: $i] :
( ( A @ n @ p @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[45765]) ).
thf(1323,plain,
! [A: $i] :
( ( ( A @ sk14 @ atleast10p )
!= ( e @ atleast10p ) )
| ~ $true
| ~ ( A @ atleast11p ) ),
inference(paramod_ordered,[status(thm)],[178,890]) ).
thf(1324,plain,
! [A: $i] :
( ( ( A @ sk14 @ atleast10p )
!= ( e @ atleast10p ) )
| ~ ( A @ atleast11p ) ),
inference(simp,[status(thm)],[1323]) ).
thf(1331,plain,
! [A: $i] :
( ( ( A @ sk14 )
!= e )
| ~ ( A @ atleast11p ) ),
inference(simp,[status(thm)],[1324]) ).
thf(319,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(320,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)],[319]) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$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(322,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ m ) @ ( A @ sk1 ) @ mem ) )
| ( A @ ( C @ ( B @ m ) @ disj ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(16043,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10183,15331]) ).
thf(16044,plain,
! [B: $i,A: $i] :
( ( A @ s @ n @ ( A @ mem ) )
!= ( e @ s @ ( B @ s @ mem ) ) ),
inference(simp,[status(thm)],[16043]) ).
thf(16095,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ n )
!= ( e @ s ) )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[16044]) ).
thf(16125,plain,
! [A: $i] :
( ( A @ s @ s @ n )
!= ( e @ s ) ),
inference(simp,[status(thm)],[16095]) ).
thf(5171,plain,
! [A: $i] :
( ( ( A @ sk15 @ atleast12p )
!= ( e @ atleast12p ) )
| ~ $true
| ~ ( A @ atleast13p ) ),
inference(paramod_ordered,[status(thm)],[186,869]) ).
thf(5172,plain,
! [A: $i] :
( ( ( A @ sk15 @ atleast12p )
!= ( e @ atleast12p ) )
| ~ ( A @ atleast13p ) ),
inference(simp,[status(thm)],[5171]) ).
thf(5183,plain,
! [A: $i] :
( ( ( A @ sk15 )
!= e )
| ~ ( A @ atleast13p ) ),
inference(simp,[status(thm)],[5172]) ).
thf(21314,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(21315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ s @ ( A @ mem ) )
!= ( B @ ( C @ mem ) ) )
| ( B @ atleast2p )
| ( C @ p @ ( B @ subq ) ) ),
inference(simp,[status(thm)],[21314]) ).
thf(21316,plain,
! [A: $i] :
( ( A @ s @ atleast2p )
| ( A @ p @ ( A @ s @ subq ) ) ),
inference(pattern_uni,[status(thm)],[21315:[bind(A,$thf( D )),bind(B,$thf( D @ s )),bind(C,$thf( D ))]]) ).
thf(21340,plain,
! [A: $i] :
( ( A @ s @ atleast2p )
| ( A @ p @ ( A @ s @ subq ) ) ),
inference(simp,[status(thm)],[21316]) ).
thf(41530,plain,
! [B: $i,A: $i] :
( ( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41389,16782]) ).
thf(41531,plain,
! [B: $i,A: $i] :
( ( A @ p @ ( A @ mem ) )
!= ( e @ s @ s @ ( B @ s @ s @ mem ) ) ),
inference(simp,[status(thm)],[41530]) ).
thf(41600,plain,
! [B: $i,A: $i] :
( ( ( A @ p )
!= ( e @ s @ s ) )
| ( A
!= ( B @ s @ s ) ) ),
inference(simp,[status(thm)],[41531]) ).
thf(41603,plain,
! [A: $i] :
( ( A @ s @ s @ p )
!= ( e @ s @ s ) ),
inference(simp,[status(thm)],[41600]) ).
thf(27361,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk11 @ ( B @ subq ) ) )
| ~ $true
| ~ ( B @ atleast3p ) ),
inference(paramod_ordered,[status(thm)],[9135,155]) ).
thf(27362,plain,
! [B: $i,A: $i] :
( ( ( A @ ( e @ subq ) )
!= ( B @ sk11 @ ( B @ subq ) ) )
| ~ ( B @ atleast3p ) ),
inference(simp,[status(thm)],[27361]) ).
thf(27363,plain,
~ ( e @ atleast3p ),
inference(pattern_uni,[status(thm)],[27362:[bind(A,$thf( e @ sk11 )),bind(B,$thf( e ))]]) ).
thf(100362,plain,
$false,
inference(e,[status(thm)],[69,19597,34616,138,19326,48339,16501,45790,45818,17998,88,52125,41646,11211,893,16372,21353,25415,276,50001,878,9135,27327,41640,170,16845,20235,56,41608,142,11014,18001,15331,17577,153,41626,174,16387,185,67446,10545,16877,288,18925,41621,57423,29366,11024,21239,37,52416,52,41604,22353,54782,110,125,52666,22955,19327,157,902,22938,189,51599,16873,284,881,41764,20049,78,93,24609,289,26036,8109,10641,45795,211,41641,17994,19749,84,480,27352,179,147,687,280,61,18842,20053,89,133,116,25587,428,11505,18928,19877,11395,45808,48308,102,1067,60,24603,201,26703,41605,41851,55625,41630,11015,41625,48581,24367,165,41801,33,19744,24059,28,70,16751,275,137,92,197,18004,97,20220,10247,21219,45804,16252,18481,15771,29593,30708,19854,19214,30494,43232,36887,17999,36430,169,44347,16242,16504,41333,16519,50481,23837,53,55653,141,869,109,8835,49977,10185,77,16786,193,16832,20224,19603,96,59217,884,41622,18485,41389,55318,21038,18201,16132,129,39597,173,25778,18845,20097,134,52143,73,105,41855,17984,19607,23644,48568,8989,205,20212,11407,41618,52656,68642,43204,26910,166,34,45,161,149,10872,16265,21349,279,64,61854,22683,44,286,875,291,25177,19071,59,118,19296,43210,63547,281,51602,204,50285,36409,10183,49,41319,181,16909,16782,41643,19741,55072,3002,55324,113,219,274,19752,9118,76,271,41633,38623,10565,23189,41795,187,36897,15772,81,41990,52651,16128,19747,155,198,108,41628,890,16381,323,26918,66,25184,16905,41638,130,16755,20100,19587,30935,30079,41619,80,51891,11402,52178,223,608,162,21022,209,112,123,41632,34141,194,145,48,63,32482,282,150,887,50281,52430,41617,41623,29354,24062,45812,52676,19297,872,30915,72406,50,67,51885,16384,19325,32464,10439,41606,177,182,54803,31181,19295,41699,10128,11005,43,55061,52679,17997,15332,154,41760,41627,25596,10860,23634,16369,10241,24814,87,218,104,19725,50010,16121,17881,41642,896,40,158,16134,55,171,418,20018,186,19884,139,51588,63508,30505,17885,290,119,45782,272,899,19590,28929,19869,54783,287,32510,41620,55365,27148,22958,146,52682,190,20022,19311,36,30,16507,10649,210,21015,126,11209,19586,48310,16254,94,195,17003,43238,68625,283,31403,41703,131,178,32498,19298,41624,27331,45809,163,1331,322,122,16125,5183,10654,21340,41603,27363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV571+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 11:17:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.18 % [INFO] Parsing done (206ms).
% 1.40/1.20 % [INFO] Running in sequential loop mode.
% 1.85/1.60 % [INFO] eprover registered as external prover.
% 2.07/1.60 % [INFO] Scanning for conjecture ...
% 2.24/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 25 axioms. Running axiom selection ...
% 2.24/1.77 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 2.43/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.43/1.84 % [INFO] Type checking passed.
% 2.43/1.84 % [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 ...
% 265.47/78.15 % External prover 'e' found a proof!
% 265.47/78.15 % [INFO] Killing All external provers ...
% 265.47/78.15 % Time passed: 77640ms (effective reasoning time: 76946ms)
% 265.47/78.15 % 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)>
% 265.47/78.15 % 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
% 265.47/78.15 % No. of inferences in proof: 1411
% 265.47/78.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 77640 ms resp. 76946 ms w/o parsing
% 256.54/78.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 256.54/78.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------