%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM702^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Wed Sep 30 08:17:30 AM UTC 2026
% Result : Theorem 23.25s 3.77s
% Output : CNFRefutation 23.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 32
% Syntax : Number of formulae : 155 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 1631 ( 371 equ; 0 cnn)
% Maximal formula atoms : 375 ( 10 avg)
% Number of connectives : 4385 (1000 ~; 998 |; 100 &;2025 @)
% ( 0 <=>; 262 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 8 con; 0-3 aty)
% Number of variables : 361 ( 180 ^; 181 !; 0 ?; 361 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_28,type,
emptyset: $i ).
thf(decl_48,type,
ordsucc: $i > $i ).
thf(decl_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
thf(decl_66,type,
l_ec: $o > $o > $o ).
thf(decl_67,type,
d_and: $o > $o > $o ).
thf(decl_68,type,
l_or: $o > $o > $o ).
thf(decl_72,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(decl_73,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_74,type,
or3: $o > $o > $o > $o ).
thf(decl_75,type,
and3: $o > $o > $o > $o ).
thf(decl_76,type,
ec3: $o > $o > $o > $o ).
thf(decl_77,type,
orec3: $o > $o > $o > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_126,type,
nis: $i > $i > $o ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_131,type,
n_1: $i ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_152,type,
moreis: $i > $i > $o ).
thf(decl_153,type,
lessis: $i > $i > $o ).
thf(decl_191,type,
esk34_2: $i > $i > $i ).
thf(decl_192,type,
esk35_2: $i > $i > $i ).
thf(decl_215,type,
esk58_3: $i > $i > $i > $i ).
thf(decl_216,type,
esk59_3: $i > $i > $i > $i ).
thf(decl_251,type,
esk94_2: $i > $i > $i ).
thf(decl_255,type,
esk98_0: $i ).
thf(decl_256,type,
esk99_0: $i ).
thf(decl_257,type,
esk100_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_imp) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_is_of) ).
thf(def_non,axiom,
( non
= ( ^ [X1: $i,X2: $i > $o,X4: $i] : ( d_not @ ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_non) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X79: $o,X80: $o] : ( imp @ X79 @ ( d_not @ X80 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_l_ec) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X1: $i,X2: $i > $o] :
( d_not
@ ( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ( non @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_l_some) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_e_is) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X81: $o,X82: $o] : ( d_not @ ( l_ec @ X81 @ X82 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_d_and) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_l_or) ).
thf(def_and3,axiom,
( and3
= ( ^ [X92: $o,X93: $o,X94: $o] : ( d_and @ X92 @ ( d_and @ X93 @ X94 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_and3) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_d_29_ii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X509: $i] :
( ( in @ X509 @ nat )
=> ( ( Z0 @ X509 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_n_some) ).
thf(def_or3,axiom,
( or3
= ( ^ [X89: $o,X90: $o,X91: $o] : ( l_or @ X89 @ ( l_or @ X90 @ X91 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_or3) ).
thf(def_ec3,axiom,
( ec3
= ( ^ [X95: $o,X96: $o,X97: $o] : ( and3 @ ( l_ec @ X95 @ X96 ) @ ( l_ec @ X96 @ X97 ) @ ( l_ec @ X97 @ X95 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_ec3) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_moreis) ).
thf(def_orec3,axiom,
( orec3
= ( ^ [X98: $o,X99: $o,X100: $o] : ( d_and @ ( or3 @ X98 @ X99 @ X100 ) @ ( ec3 @ X98 @ X99 @ X100 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_orec3) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_iii) ).
thf(satz26b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X335: $i] : ( in @ X335 @ nat )
@ ^ [X336: $i] :
( ( d_29_ii @ ( n_pl @ X336 @ n_1 ) @ X1 )
=> ( moreis @ X336 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz26b) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_lessis) ).
thf(satz9,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X213: $i] : ( in @ X213 @ nat )
@ ^ [X214: $i] :
( orec3 @ ( n_is @ X1 @ X214 )
@ ( n_some
@ ^ [X4: $i] : ( n_is @ X1 @ ( n_pl @ X214 @ X4 ) ) )
@ ( n_some
@ ^ [X4: $i] : ( n_is @ X214 @ ( n_pl @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz9) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_nis) ).
thf(satz16d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X259: $i] : ( in @ X259 @ nat )
@ ^ [X260: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( d_29_ii @ X1 @ X260 )
=> ( ( moreis @ X260 @ X4 )
=> ( d_29_ii @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz16d) ).
thf(satz17,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X261: $i] : ( in @ X261 @ nat )
@ ^ [X262: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( lessis @ X1 @ X262 )
=> ( ( lessis @ X262 @ X4 )
=> ( lessis @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz17) ).
thf(satz7,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X200: $i] : ( in @ X200 @ nat )
@ ^ [X201: $i] : ( nis @ X201 @ ( n_pl @ X1 @ X201 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz7) ).
thf(satz25b,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X327: $i] : ( in @ X327 @ nat )
@ ^ [X328: $i] :
( ( iii @ X328 @ X1 )
=> ( lessis @ ( n_pl @ X328 @ n_1 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz25b) ).
thf(satz6,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X197: $i] : ( in @ X197 @ nat )
@ ^ [X198: $i] : ( n_is @ ( n_pl @ X1 @ X198 ) @ ( n_pl @ X198 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz6) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',def_n_1) ).
thf(satz4e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ X1 @ n_1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',satz4e) ).
thf(suc_p,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( is_of @ ( ordsucc @ X1 )
@ ^ [X166: $i] : ( in @ X166 @ nat ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p',suc_p) ).
thf(c_0_32,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_33,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_34,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_35,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_36,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_37,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_38,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[def_l_ec]) ).
thf(c_0_39,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X482: $i] :
( ( in @ X482 @ Z0 )
=> ( ( Z1 @ X482 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_40,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_41,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_42,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_43,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_and]) ).
thf(c_0_44,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_38,c_0_33]),c_0_37]) ).
thf(c_0_45,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X482: $i] :
( ( in @ X482 @ Z0 )
=> ( ( Z1 @ X482 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_39,c_0_40]),c_0_37]),c_0_41]) ).
thf(c_0_46,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_47,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_42]) ).
thf(c_0_48,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_49,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_and3]) ).
thf(c_0_50,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_43,c_0_37]),c_0_44]) ).
thf(c_0_51,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X520: $i] :
( ( in @ X520 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X520 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_52,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X509: $i] :
( ( in @ X509 @ nat )
=> ( ( Z0 @ X509 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_45]) ).
thf(c_0_53,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_54,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_or3]) ).
thf(c_0_55,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_48,c_0_33]),c_0_37]) ).
thf(c_0_56,plain,
( ec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_ec3]) ).
thf(c_0_57,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_58,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X524: $i] :
( ( in @ X524 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X524 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_59,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X520: $i] :
( ( in @ X520 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X520 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
thf(c_0_60,plain,
( orec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) )
=> ( ( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_orec3]) ).
thf(c_0_61,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_62,plain,
( ec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_56,c_0_44]),c_0_57]) ).
thf(c_0_63,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X521: $i] :
( ( in @ X521 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X521 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_64,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X335: $i] : ( in @ X335 @ nat )
@ ^ [X336: $i] :
( ( d_29_ii @ ( n_pl @ X336 @ n_1 ) @ X1 )
=> ( moreis @ X336 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[satz26b]) ).
thf(c_0_65,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X524: $i] :
( ( in @ X524 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X524 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_58,c_0_55]),c_0_47]),c_0_59]) ).
thf(c_0_66,plain,
( orec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) )
=> ( ( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_60,c_0_50]),c_0_61]),c_0_62]) ).
thf(c_0_67,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X525: $i] :
( ( in @ X525 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X525 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_68,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X521: $i] :
( ( in @ X521 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X521 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_63,c_0_52]),c_0_53]) ).
thf(c_0_69,negated_conjecture,
~ ! [X955: $i] :
( ( in @ X955 @ nat )
=> ! [X954: $i] :
( ( in @ X954 @ nat )
=> ( ( ! [X952: $i] :
( ( in @ X952 @ nat )
=> ( ( ( n_pl @ X954 @ n_1 )
= ( n_pl @ X955 @ X952 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ! [X953: $i] :
( ( in @ X953 @ nat )
=> ( ( X954
= ( n_pl @ X955 @ X953 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X954 = X955 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_64]),c_0_40]),c_0_59]),c_0_65]) ).
thf(c_0_70,plain,
! [X653: $i] :
( ( in @ X653 @ nat )
=> ! [X652: $i] :
( ( in @ X652 @ nat )
=> ( ( ( ( ( X653 = X652 )
=> ~ $true )
=> ( ( ( ! [X650: $i] :
( ( in @ X650 @ nat )
=> ( ( X653
= ( n_pl @ X652 @ X650 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( ! [X651: $i] :
( ( in @ X651 @ nat )
=> ( ( X652
= ( n_pl @ X653 @ X651 ) )
=> ~ $true ) )
=> ~ $true ) ) )
=> ( ( ( ( ( X653 = X652 )
=> ( ( ! [X650: $i] :
( ( in @ X650 @ nat )
=> ( ( X653
= ( n_pl @ X652 @ X650 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ( ( ! [X650: $i] :
( ( in @ X650 @ nat )
=> ( ( X653
= ( n_pl @ X652 @ X650 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ! [X651: $i] :
( ( in @ X651 @ nat )
=> ( ( X652
= ( n_pl @ X653 @ X651 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ! [X651: $i] :
( ( in @ X651 @ nat )
=> ( ( X652
= ( n_pl @ X653 @ X651 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( X653 = X652 )
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz9]),c_0_40]),c_0_66]),c_0_47]),c_0_52]) ).
thf(c_0_71,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_72,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X525: $i] :
( ( in @ X525 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X525 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_67,c_0_55]),c_0_47]),c_0_68]) ).
thf(c_0_73,plain,
! [X751: $i] :
( ( in @ X751 @ nat )
=> ! [X750: $i] :
( ( in @ X750 @ nat )
=> ! [X749: $i] :
( ( in @ X749 @ nat )
=> ( ( ! [X746: $i] :
( ( in @ X746 @ nat )
=> ( ( X751
= ( n_pl @ X750 @ X746 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ( ! [X747: $i] :
( ( in @ X747 @ nat )
=> ( ( X750
= ( n_pl @ X749 @ X747 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X750 = X749 ) )
=> ( ! [X748: $i] :
( ( in @ X748 @ nat )
=> ( ( X751
= ( n_pl @ X749 @ X748 ) )
=> ~ $true ) )
=> ~ $true ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz16d]),c_0_40]),c_0_59]),c_0_65]) ).
thf(c_0_74,negated_conjecture,
! [X1767: $i] :
( ( in @ esk98_0 @ nat )
& ( in @ esk99_0 @ nat )
& ( ( in @ esk100_0 @ nat )
| ~ $true )
& ( ( ( n_pl @ esk99_0 @ n_1 )
= ( n_pl @ esk98_0 @ esk100_0 ) )
| ~ $true )
& ( $true
| ~ $true )
& ( ~ ( in @ X1767 @ nat )
| ( esk99_0
!= ( n_pl @ esk98_0 @ X1767 ) )
| ~ $true
| ~ $true )
& ( $true
| ~ $true )
& ( esk99_0 != esk98_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])])])]) ).
thf(c_0_75,plain,
! [X1450: $i,X1451: $i,X1454: $i,X1455: $i,X1456: $i,X1457: $i] :
( ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| ( X1450
= ( n_pl @ X1451 @ ( esk34_2 @ X1450 @ X1451 ) ) )
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| ( X1450
= ( n_pl @ X1451 @ ( esk34_2 @ X1450 @ X1451 ) ) )
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ( X1450
= ( n_pl @ X1451 @ ( esk34_2 @ X1450 @ X1451 ) ) )
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| $true
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| $true
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| $true
| ( X1450 = X1451 )
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| ( X1450
= ( n_pl @ X1451 @ ( esk34_2 @ X1450 @ X1451 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| ( X1450
= ( n_pl @ X1451 @ ( esk34_2 @ X1450 @ X1451 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ( X1450
= ( n_pl @ X1451 @ ( esk34_2 @ X1450 @ X1451 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( in @ ( esk35_2 @ X1450 @ X1451 ) @ nat )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ( X1451
= ( n_pl @ X1450 @ ( esk35_2 @ X1450 @ X1451 ) ) )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ~ ( in @ X1454 @ nat )
| ( X1450
!= ( n_pl @ X1451 @ X1454 ) )
| ~ $true
| ~ $true
| ( X1450 != X1451 )
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ( X1450 != X1451 )
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ~ ( in @ X1456 @ nat )
| ( X1451
!= ( n_pl @ X1450 @ X1456 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1455 @ nat )
| ( X1450
!= ( n_pl @ X1451 @ X1455 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1455 @ nat )
| ( X1450
!= ( n_pl @ X1451 @ X1455 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ~ ( in @ X1456 @ nat )
| ( X1451
!= ( n_pl @ X1450 @ X1456 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( ~ ( in @ X1457 @ nat )
| ( X1451
!= ( n_pl @ X1450 @ X1457 ) )
| ~ $true
| ( X1450 != X1451 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ( X1450 != X1451 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1451 @ nat )
| ~ ( in @ X1450 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])])])]) ).
thf(c_0_76,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_71,c_0_37]),c_0_47]) ).
thf(c_0_77,plain,
! [X757: $i] :
( ( in @ X757 @ nat )
=> ! [X756: $i] :
( ( in @ X756 @ nat )
=> ! [X755: $i] :
( ( in @ X755 @ nat )
=> ( ( ( ( ! [X752: $i] :
( ( in @ X752 @ nat )
=> ( ( X756
= ( n_pl @ X757 @ X752 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X757 = X756 ) )
=> ( ( ( ( ! [X753: $i] :
( ( in @ X753 @ nat )
=> ( ( X755
= ( n_pl @ X756 @ X753 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X756 = X755 ) )
=> ( ( ( ! [X754: $i] :
( ( in @ X754 @ nat )
=> ( ( X755
= ( n_pl @ X757 @ X754 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X757 = X755 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz17]),c_0_40]),c_0_72]) ).
thf(c_0_78,plain,
! [X1558: $i,X1559: $i,X1560: $i,X1561: $i,X1562: $i] :
( ( ( in @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) @ nat )
| ~ $true
| ~ ( in @ X1562 @ nat )
| ( X1559
!= ( n_pl @ X1560 @ X1562 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( X1558
= ( n_pl @ X1560 @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) ) )
| ~ $true
| ~ ( in @ X1562 @ nat )
| ( X1559
!= ( n_pl @ X1560 @ X1562 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1562 @ nat )
| ( X1559
!= ( n_pl @ X1560 @ X1562 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( in @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( X1558
= ( n_pl @ X1560 @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( in @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) @ nat )
| ~ $true
| ( X1559 != X1560 )
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( X1558
= ( n_pl @ X1560 @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) ) )
| ~ $true
| ( X1559 != X1560 )
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( $true
| ~ $true
| ( X1559 != X1560 )
| ~ ( in @ X1561 @ nat )
| ( X1558
!= ( n_pl @ X1559 @ X1561 ) )
| ~ $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( in @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) @ nat )
| ~ $true
| ~ ( in @ X1562 @ nat )
| ( X1559
!= ( n_pl @ X1560 @ X1562 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( X1558
= ( n_pl @ X1560 @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) ) )
| ~ $true
| ~ ( in @ X1562 @ nat )
| ( X1559
!= ( n_pl @ X1560 @ X1562 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1562 @ nat )
| ( X1559
!= ( n_pl @ X1560 @ X1562 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( in @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) @ nat )
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( X1558
= ( n_pl @ X1560 @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) ) )
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( in @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) @ nat )
| ~ $true
| ( X1559 != X1560 )
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( ( X1558
= ( n_pl @ X1560 @ ( esk58_3 @ X1558 @ X1559 @ X1560 ) ) )
| ~ $true
| ( X1559 != X1560 )
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) )
& ( $true
| ~ $true
| ( X1559 != X1560 )
| $true
| ~ ( in @ X1560 @ nat )
| ~ ( in @ X1559 @ nat )
| ~ ( in @ X1558 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])])])])]) ).
thf(c_0_79,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( esk99_0
!= ( n_pl @ esk98_0 @ X1 ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_80,plain,
! [X1: $i,X4: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk35_2 @ X4 @ X1 ) ) )
| ( X4
= ( n_pl @ X1 @ ( esk34_2 @ X4 @ X1 ) ) )
| ( X4 = X1 )
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_81,plain,
! [X1: $i,X4: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk35_2 @ X4 @ X1 ) ) )
| ( in @ ( esk34_2 @ X4 @ X1 ) @ nat )
| ( X4 = X1 )
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_82,plain,
! [X639: $i] :
( ( in @ X639 @ nat )
=> ! [X638: $i] :
( ( in @ X638 @ nat )
=> ( ( X638
= ( n_pl @ X639 @ X638 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz7]),c_0_40]),c_0_76]) ).
thf(c_0_83,plain,
! [X939: $i] :
( ( in @ X939 @ nat )
=> ! [X938: $i] :
( ( in @ X938 @ nat )
=> ( ( ! [X936: $i] :
( ( in @ X936 @ nat )
=> ( ( X939
= ( n_pl @ X938 @ X936 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ! [X937: $i] :
( ( in @ X937 @ nat )
=> ( ( X939
= ( n_pl @ ( n_pl @ X938 @ n_1 ) @ X937 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( ( n_pl @ X938 @ n_1 )
= X939 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz25b]),c_0_40]),c_0_68]),c_0_72]) ).
thf(c_0_84,plain,
! [X1564: $i,X1565: $i,X1566: $i,X1567: $i,X1568: $i] :
( ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ~ ( in @ X1567 @ nat )
| ( X1565
!= ( n_pl @ X1564 @ X1567 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| $true
| ~ $true
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| ~ ( in @ X1568 @ nat )
| ( X1566
!= ( n_pl @ X1565 @ X1568 ) )
| ~ $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| $true
| ~ $true
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( in @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) @ nat )
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( ( X1566
= ( n_pl @ X1564 @ ( esk59_3 @ X1564 @ X1565 @ X1566 ) ) )
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ~ $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) )
& ( $true
| ( X1564 = X1566 )
| ( X1565 != X1566 )
| ( X1564 != X1565 )
| ~ ( in @ X1566 @ nat )
| ~ ( in @ X1565 @ nat )
| ~ ( in @ X1564 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])])])])]) ).
thf(c_0_85,plain,
! [X1: $i,X4: $i,X5: $i] :
( ~ ( in @ X1 @ nat )
| ( X4
!= ( n_pl @ X5 @ X1 ) )
| ~ $true
| ( X5 != X4 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_86,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk58_3 @ X1 @ X5 @ X4 ) ) )
| ~ $true
| ( X5 != X4 )
| ~ ( in @ X6 @ nat )
| ( X1
!= ( n_pl @ X5 @ X6 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_87,negated_conjecture,
! [X1: $i] :
( ( esk99_0
!= ( n_pl @ esk98_0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_79]) ).
thf(c_0_88,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( X4
= ( n_pl @ X1 @ ( esk34_2 @ X4 @ X1 ) ) )
| ( X1
= ( n_pl @ X4 @ ( esk35_2 @ X4 @ X1 ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_80]) ).
thf(c_0_89,negated_conjecture,
in @ esk98_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_90,negated_conjecture,
in @ esk99_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_91,negated_conjecture,
esk99_0 != esk98_0,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_92,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk35_2 @ X1 @ X4 ) @ nat )
| ( X1
= ( n_pl @ X4 @ ( esk34_2 @ X1 @ X4 ) ) )
| ( X1 = X4 )
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_93,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( X1
= ( n_pl @ X4 @ ( esk35_2 @ X4 @ X1 ) ) )
| ( in @ ( esk34_2 @ X4 @ X1 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_81]) ).
thf(c_0_94,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk35_2 @ X1 @ X4 ) @ nat )
| ( in @ ( esk34_2 @ X1 @ X4 ) @ nat )
| ( X1 = X4 )
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_95,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk58_3 @ X1 @ X4 @ X5 ) @ nat )
| ~ $true
| ( X4 != X5 )
| ~ ( in @ X6 @ nat )
| ( X1
!= ( n_pl @ X4 @ X6 ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_96,plain,
! [X1438: $i,X1439: $i] :
( ~ ( in @ X1438 @ nat )
| ~ ( in @ X1439 @ nat )
| ( X1439
!= ( n_pl @ X1438 @ X1439 ) )
| ~ $true ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])]) ).
thf(c_0_97,plain,
! [X637: $i] :
( ( in @ X637 @ nat )
=> ! [X636: $i] :
( ( in @ X636 @ nat )
=> ( ( n_pl @ X637 @ X636 )
= ( n_pl @ X636 @ X637 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_40]),c_0_47]) ).
thf(c_0_98,plain,
! [X1748: $i,X1749: $i,X1750: $i] :
( ( ( in @ ( esk94_2 @ X1748 @ X1749 ) @ nat )
| ~ $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| ~ ( in @ X1750 @ nat )
| ( X1748
!= ( n_pl @ X1749 @ X1750 ) )
| ~ $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) )
& ( ( X1748
= ( n_pl @ ( n_pl @ X1749 @ n_1 ) @ ( esk94_2 @ X1748 @ X1749 ) ) )
| ~ $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| ~ ( in @ X1750 @ nat )
| ( X1748
!= ( n_pl @ X1749 @ X1750 ) )
| ~ $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) )
& ( $true
| ~ $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| ~ ( in @ X1750 @ nat )
| ( X1748
!= ( n_pl @ X1749 @ X1750 ) )
| ~ $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) )
& ( $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| ~ ( in @ X1750 @ nat )
| ( X1748
!= ( n_pl @ X1749 @ X1750 ) )
| ~ $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) )
& ( ( in @ ( esk94_2 @ X1748 @ X1749 ) @ nat )
| ~ $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) )
& ( ( X1748
= ( n_pl @ ( n_pl @ X1749 @ n_1 ) @ ( esk94_2 @ X1748 @ X1749 ) ) )
| ~ $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) )
& ( $true
| ~ $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) )
& ( $true
| ( ( n_pl @ X1749 @ n_1 )
= X1748 )
| $true
| ~ ( in @ X1749 @ nat )
| ~ ( in @ X1748 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])])])]) ).
thf(c_0_99,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk59_3 @ X4 @ X5 @ X1 ) ) )
| ( X4 = X1 )
| ~ $true
| ( X5 != X1 )
| ~ ( in @ X6 @ nat )
| ( X5
!= ( n_pl @ X4 @ X6 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_100,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X4 != X5 )
| ( X4
!= ( n_pl @ X5 @ X1 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_85]) ).
thf(c_0_101,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk58_3 @ X1 @ X5 @ X4 ) ) )
| ( X4 != X5 )
| ( X1
!= ( n_pl @ X5 @ X6 ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_86]) ).
thf(c_0_102,negated_conjecture,
( ( ( n_pl @ esk99_0 @ ( esk34_2 @ esk98_0 @ esk99_0 ) )
= esk98_0 )
| ~ ( in @ ( esk35_2 @ esk98_0 @ esk99_0 ) @ nat ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])])]),c_0_90])]),c_0_91]) ).
thf(c_0_103,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( X1
= ( n_pl @ X4 @ ( esk34_2 @ X1 @ X4 ) ) )
| ( in @ ( esk35_2 @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_92]) ).
thf(c_0_104,negated_conjecture,
( ( in @ ( esk34_2 @ esk98_0 @ esk99_0 ) @ nat )
| ~ ( in @ ( esk35_2 @ esk98_0 @ esk99_0 ) @ nat ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_93]),c_0_89])])]),c_0_90])]),c_0_91]) ).
thf(c_0_105,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( in @ ( esk34_2 @ X1 @ X4 ) @ nat )
| ( in @ ( esk35_2 @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_94]) ).
thf(c_0_106,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk58_3 @ X1 @ X4 @ X5 ) @ nat )
| ( X4 != X5 )
| ( X1
!= ( n_pl @ X4 @ X6 ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_95]) ).
thf(c_0_107,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk59_3 @ X1 @ X4 @ X5 ) @ nat )
| ( X1 = X5 )
| ~ $true
| ( X4 != X5 )
| ~ ( in @ X6 @ nat )
| ( X4
!= ( n_pl @ X1 @ X6 ) )
| ~ $true
| ~ $true
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_108,plain,
! [X1: $i,X4: $i] :
( ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ( X4
!= ( n_pl @ X1 @ X4 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
thf(c_0_109,plain,
! [X1436: $i,X1437: $i] :
( ~ ( in @ X1436 @ nat )
| ~ ( in @ X1437 @ nat )
| ( ( n_pl @ X1436 @ X1437 )
= ( n_pl @ X1437 @ X1436 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])])]) ).
thf(c_0_110,negated_conjecture,
( ( ( n_pl @ esk99_0 @ n_1 )
= ( n_pl @ esk98_0 @ esk100_0 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_111,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ~ ( in @ X1 @ nat )
| ( X4
!= ( n_pl @ X5 @ X1 ) )
| ~ $true
| ~ $true
| ~ ( in @ X6 @ nat )
| ( X5
!= ( n_pl @ X4 @ X6 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_112,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1
= ( n_pl @ ( n_pl @ X4 @ n_1 ) @ ( esk94_2 @ X1 @ X4 ) ) )
| ( ( n_pl @ X4 @ n_1 )
= X1 )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
thf(c_0_113,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( X1 = X4 )
| ( X1
= ( n_pl @ X4 @ ( esk59_3 @ X4 @ X5 @ X1 ) ) )
| ( X1 != X5 )
| ( X5
!= ( n_pl @ X4 @ X6 ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_99]) ).
thf(c_0_114,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
!= X1 )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(er,[status(thm)],[c_0_100]) ).
thf(c_0_115,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ ( esk58_3 @ ( n_pl @ X1 @ X4 ) @ X1 @ X1 ) )
= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_101])]) ).
thf(c_0_116,negated_conjecture,
( ( n_pl @ esk99_0 @ ( esk34_2 @ esk98_0 @ esk99_0 ) )
= esk98_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_90]),c_0_89])]),c_0_91]) ).
thf(c_0_117,negated_conjecture,
in @ ( esk34_2 @ esk98_0 @ esk99_0 ) @ nat,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_90]),c_0_89])]),c_0_91]) ).
thf(c_0_118,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk58_3 @ ( n_pl @ X1 @ X4 ) @ X1 @ X1 ) @ nat )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_106])]) ).
thf(c_0_119,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( X1 = X5 )
| ( in @ ( esk59_3 @ X1 @ X4 @ X5 ) @ nat )
| ( X4 != X5 )
| ( X4
!= ( n_pl @ X1 @ X6 ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_107]) ).
thf(c_0_120,plain,
! [X4: $i,X1: $i] :
( ( X4
!= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_108]) ).
thf(c_0_121,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
= ( n_pl @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
thf(c_0_122,negated_conjecture,
( ( n_pl @ esk99_0 @ n_1 )
= ( n_pl @ esk98_0 @ esk100_0 ) ),
inference(cn,[status(thm)],[c_0_110]) ).
thf(c_0_123,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(split_conjunct,[status(thm)],[def_n_1]) ).
thf(c_0_124,negated_conjecture,
( ( in @ esk100_0 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_125,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk94_2 @ X1 @ X4 ) @ nat )
| ( ( n_pl @ X4 @ n_1 )
= X1 )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
thf(c_0_126,plain,
! [X627: $i] :
( ( in @ X627 @ nat )
=> ( ( ordsucc @ X627 )
= ( n_pl @ X627 @ n_1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4e]),c_0_40]),c_0_47]) ).
thf(c_0_127,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( X5
!= ( n_pl @ X4 @ X6 ) )
| ( X4
!= ( n_pl @ X5 @ X1 ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_111]) ).
thf(c_0_128,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( ( n_pl @ X4 @ n_1 )
= X1 )
| ( X1
= ( n_pl @ ( n_pl @ X4 @ n_1 ) @ ( esk94_2 @ X1 @ X4 ) ) )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_112]) ).
thf(c_0_129,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ ( esk59_3 @ X1 @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X1 @ X4 ) ) )
= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_113])]),c_0_114]) ).
thf(c_0_130,negated_conjecture,
( ( n_pl @ esk99_0 @ ( esk58_3 @ esk98_0 @ esk99_0 @ esk99_0 ) )
= esk98_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_89]),c_0_117]),c_0_90])]) ).
thf(c_0_131,negated_conjecture,
in @ ( esk58_3 @ esk98_0 @ esk99_0 @ esk99_0 ) @ nat,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_116]),c_0_89]),c_0_117]),c_0_90])]) ).
thf(c_0_132,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk59_3 @ X1 @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X1 @ X4 ) ) @ nat )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_119])]),c_0_114]) ).
thf(c_0_133,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
!= X1 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
thf(c_0_134,negated_conjecture,
( ( n_pl @ esk98_0 @ esk100_0 )
= ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) ) ),
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
thf(c_0_135,negated_conjecture,
in @ esk100_0 @ nat,
inference(cn,[status(thm)],[c_0_124]) ).
thf(c_0_136,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( ( n_pl @ X4 @ n_1 )
= X1 )
| ( in @ ( esk94_2 @ X1 @ X4 ) @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_125]) ).
thf(c_0_137,plain,
! [X599: $i] :
( ( in @ X599 @ nat )
=> ( in @ ( ordsucc @ X599 ) @ nat ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[suc_p]),c_0_35]),c_0_40]) ).
thf(c_0_138,plain,
! [X1427: $i] :
( ~ ( in @ X1427 @ nat )
| ( ( ordsucc @ X1427 )
= ( n_pl @ X1427 @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])]) ).
thf(c_0_139,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( ( n_pl @ ( n_pl @ X1 @ X4 ) @ X5 )
!= X1 )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(er,[status(thm)],[c_0_127]) ).
thf(c_0_140,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) @ ( esk94_2 @ ( n_pl @ X1 @ X4 ) @ X1 ) )
= ( n_pl @ X1 @ X4 ) )
| ( ( n_pl @ X1 @ ( ordsucc @ emptyset ) )
= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_123]),c_0_123])]) ).
thf(c_0_141,negated_conjecture,
( ( n_pl @ esk99_0 @ ( esk59_3 @ esk99_0 @ esk98_0 @ esk98_0 ) )
= esk98_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_89]),c_0_131]),c_0_90])]) ).
thf(c_0_142,negated_conjecture,
in @ ( esk59_3 @ esk99_0 @ esk98_0 @ esk98_0 ) @ nat,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_130]),c_0_89]),c_0_131]),c_0_90])]) ).
thf(c_0_143,negated_conjecture,
( ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) )
!= esk98_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_89]),c_0_135])]) ).
thf(c_0_144,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ ( ordsucc @ emptyset ) )
= ( n_pl @ X1 @ X4 ) )
| ( in @ ( esk94_2 @ ( n_pl @ X1 @ X4 ) @ X1 ) @ nat )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_123])]) ).
thf(c_0_145,plain,
! [X1395: $i] :
( ~ ( in @ X1395 @ nat )
| ( in @ ( ordsucc @ X1395 ) @ nat ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])]) ).
thf(c_0_146,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ n_1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_147,negated_conjecture,
! [X1: $i] :
( ( ( n_pl @ ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) ) @ X1 )
!= esk98_0 )
| ~ ( in @ ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_134]),c_0_135]),c_0_89])]) ).
thf(c_0_148,negated_conjecture,
( ( n_pl @ ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) ) @ ( esk94_2 @ esk98_0 @ esk99_0 ) )
= esk98_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_89]),c_0_142]),c_0_90])]),c_0_143]) ).
thf(c_0_149,negated_conjecture,
in @ ( esk94_2 @ esk98_0 @ esk99_0 ) @ nat,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_130]),c_0_89]),c_0_131]),c_0_90])]),c_0_143]) ).
thf(c_0_150,plain,
! [X1: $i] :
( ( in @ ( ordsucc @ X1 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
thf(c_0_151,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_146,c_0_123]) ).
thf(c_0_152,negated_conjecture,
~ ( in @ ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) ) @ nat ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149])]) ).
thf(c_0_153,plain,
! [X1: $i] :
( ( in @ ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
thf(c_0_154,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_90])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM702^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:41:17 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.23/0.32 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.AAllCDAfLQ/E---3.1_2045948.p
% 23.25/3.77 % Version: 3.5.1-ho
% 23.25/3.77 % Preprocessing class: HSLMSMSSLLLCHSA.
% 23.25/3.77 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 23.25/3.77 % Starting lpo1_fix with 900s (3) cores
% 23.25/3.77 % Starting full_lambda_9 with 300s (1) cores
% 23.25/3.77 % Starting almost_fo_4 with 300s (1) cores
% 23.25/3.77 % Starting new_ho_9 with 300s (1) cores
% 23.25/3.77 % Starting pre_casc_4 with 300s (1) cores
% 23.25/3.77 % Starting ho_unfolding_6 with 300s (1) cores
% 23.25/3.77 % lpo1_fix with pid 2045961 completed with status 0
% 23.25/3.77 % Result found by lpo1_fix
% 23.25/3.77 % Preprocessing class: HSLMSMSSLLLCHSA.
% 23.25/3.77 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 23.25/3.77 % Starting lpo1_fix with 900s (3) cores
% 23.25/3.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.25/3.77 % No SInE strategy applied
% 23.25/3.77 % Search class: HGHSM-FSLM32-MHSMMSBN
% 23.25/3.77 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 23.25/3.77 % Starting SubtermCWHack with 91s (1) cores
% 23.25/3.77 % Starting full_lambda_5 with 82s (1) cores
% 23.25/3.77 % Starting new_ho_6 with 82s (1) cores
% 23.25/3.77 % full_lambda_5 with pid 2045971 completed with status 0
% 23.25/3.77 % Result found by full_lambda_5
% 23.25/3.77 % Preprocessing class: HSLMSMSSLLLCHSA.
% 23.25/3.77 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 23.25/3.77 % Starting lpo1_fix with 900s (3) cores
% 23.25/3.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.25/3.77 % No SInE strategy applied
% 23.25/3.77 % Search class: HGHSM-FSLM32-MHSMMSBN
% 23.25/3.77 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 23.25/3.77 % Starting SubtermCWHack with 91s (1) cores
% 23.25/3.77 % Starting full_lambda_5 with 82s (1) cores
% 23.25/3.77 % Preprocessing time : 0.023 s
% 23.25/3.77 % Presaturation interreduction done
% 23.25/3.77
% 23.25/3.77 % Proof found!
% 23.25/3.77 % SZS status Theorem
% 23.25/3.77 % SZS output start CNFRefutation
% See solution above
% 23.25/3.78 % Parsed axioms : 407
% 23.25/3.78 % Removed by relevancy pruning/SinE : 0
% 23.25/3.78 % Initial clauses : 1224
% 23.25/3.78 % Removed in clause preprocessing : 757
% 23.25/3.78 % Initial clauses in saturation : 467
% 23.25/3.78 % Processed clauses : 3578
% 23.25/3.78 % ...of these trivial : 268
% 23.25/3.78 % ...subsumed : 1200
% 23.25/3.78 % ...remaining for further processing : 2110
% 23.25/3.78 % Other redundant clauses eliminated : 1382
% 23.25/3.78 % Clauses deleted for lack of memory : 0
% 23.25/3.78 % Backward-subsumed : 92
% 23.25/3.78 % Backward-rewritten : 182
% 23.25/3.78 % Generated clauses : 49691
% 23.25/3.78 % ...of the previous two non-redundant : 47176
% 23.25/3.78 % ...aggressively subsumed : 0
% 23.25/3.78 % Contextual simplify-reflections : 22
% 23.25/3.78 % Paramodulations : 48005
% 23.25/3.78 % Factorizations : 2
% 23.25/3.78 % NegExts : 42
% 23.25/3.78 % Equation resolutions : 1396
% 23.25/3.78 % Disequality decompositions : 0
% 23.25/3.78 % Total rewrite steps : 20869
% 23.25/3.78 % ...of those cached : 20136
% 23.25/3.78 % Propositional unsat checks : 0
% 23.25/3.78 % Propositional check models : 0
% 23.25/3.78 % Propositional check unsatisfiable : 0
% 23.25/3.78 % Propositional clauses : 0
% 23.25/3.78 % Propositional clauses after purity: 0
% 23.25/3.78 % Propositional unsat core size : 0
% 23.25/3.78 % Propositional preprocessing time : 0.000
% 23.25/3.78 % Propositional encoding time : 0.000
% 23.25/3.78 % Propositional solver time : 0.000
% 23.25/3.78 % Success case prop preproc time : 0.000
% 23.25/3.78 % Success case prop encoding time : 0.000
% 23.25/3.78 % Success case prop solver time : 0.000
% 23.25/3.78 % Current number of processed clauses : 1269
% 23.25/3.78 % Positive orientable unit clauses : 279
% 23.25/3.78 % Positive unorientable unit clauses: 8
% 23.25/3.78 % Negative unit clauses : 240
% 23.25/3.78 % Non-unit-clauses : 742
% 23.25/3.78 % Current number of unprocessed clauses: 43196
% 23.25/3.78 % ...number of literals in the above : 235385
% 23.25/3.78 % Current number of archived formulas : 0
% 23.25/3.78 % Current number of archived clauses : 707
% 23.25/3.78 % Clause-clause subsumption calls (NU) : 229605
% 23.25/3.78 % Rec. Clause-clause subsumption calls : 55794
% 23.25/3.78 % Non-unit clause-clause subsumptions : 386
% 23.25/3.78 % Unit Clause-clause subsumption calls : 22697
% 23.25/3.78 % Rewrite failures with RHS unbound : 41
% 23.25/3.78 % BW rewrite match attempts : 279
% 23.25/3.78 % BW rewrite match successes : 87
% 23.25/3.78 % Condensation attempts : 0
% 23.25/3.78 % Condensation successes : 0
% 23.25/3.78 % Termbank termtop insertions : 1390424
% 23.25/3.78 % Search garbage collected termcells : 50507
% 23.25/3.78
% 23.25/3.78 % -------------------------------------------------
% 23.25/3.78 % User time : 3.211 s
% 23.25/3.78 % System time : 0.103 s
% 23.25/3.78 % Total time : 3.314 s
% 23.25/3.78 % Maximum resident set size: 10480 pages
% 23.25/3.78
% 23.25/3.78 % -------------------------------------------------
% 23.25/3.78 % User time : 9.344 s
% 23.25/3.78 % System time : 0.337 s
% 23.25/3.78 % Total time : 9.681 s
% 23.25/3.78 % Maximum resident set size: 5632 pages
% 23.25/3.78 % E exiting
%------------------------------------------------------------------------------