%------------------------------------------------------------------------------
% File : E---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 : 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 : Wed Sep 30 08:16:54 AM UTC 2026
% Result : Theorem 16.34s 2.75s
% Output : CNFRefutation 16.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 33
% Syntax : Number of formulae : 174 ( 84 unt; 0 typ; 0 def)
% Number of atoms : 1765 ( 402 equ; 0 cnn)
% Maximal formula atoms : 375 ( 10 avg)
% Number of connectives : 4853 (1093 ~;1094 |; 105 &;2289 @)
% ( 0 <=>; 272 =>; 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 : 40 ( 37 usr; 8 con; 0-3 aty)
% Number of variables : 408 ( 184 ^; 224 !; 0 ?; 408 :)
% 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_199,type,
esk42_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.gWrsU9wKgB/E---3.1_1605917.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.p',def_orec3) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.p',satz26b) ).
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.gWrsU9wKgB/E---3.1_1605917.p',satz9) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.p',def_lessis) ).
thf(satz11,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X225: $i] : ( in @ X225 @ nat )
@ ^ [X226: $i] :
( ( d_29_ii @ X1 @ X226 )
=> ( iii @ X226 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.p',satz11) ).
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.gWrsU9wKgB/E---3.1_1605917.p',satz16d) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.p',def_nis) ).
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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.p',satz6) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.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.gWrsU9wKgB/E---3.1_1605917.p',suc_p) ).
thf(c_0_33,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_34,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_35,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_36,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_37,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_38,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_39,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[def_l_ec]) ).
thf(c_0_40,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_41,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_42,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_43,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_44,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_and]) ).
thf(c_0_45,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_39,c_0_34]),c_0_38]) ).
thf(c_0_46,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_40,c_0_41]),c_0_38]),c_0_42]) ).
thf(c_0_47,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_48,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_43]) ).
thf(c_0_49,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_50,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_51,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_44,c_0_38]),c_0_45]) ).
thf(c_0_52,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_53,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_46]) ).
thf(c_0_54,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_55,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_or3]) ).
thf(c_0_56,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_49,c_0_34]),c_0_38]) ).
thf(c_0_57,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_58,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_59,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_60,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_52,c_0_53]),c_0_54]) ).
thf(c_0_61,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_62,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_63,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_57,c_0_45]),c_0_58]) ).
thf(c_0_64,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_65,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_66,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_59,c_0_56]),c_0_48]),c_0_60]) ).
thf(c_0_67,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_61,c_0_51]),c_0_62]),c_0_63]) ).
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_64,c_0_53]),c_0_54]) ).
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_65]),c_0_41]),c_0_60]),c_0_66]) ).
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_41]),c_0_67]),c_0_48]),c_0_53]) ).
thf(c_0_71,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_72,plain,
! [X677: $i] :
( ( in @ X677 @ nat )
=> ! [X676: $i] :
( ( in @ X676 @ nat )
=> ( ( ! [X674: $i] :
( ( in @ X674 @ nat )
=> ( ( X677
= ( n_pl @ X676 @ X674 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ! [X675: $i] :
( ( in @ X675 @ nat )
=> ( ( X677
= ( n_pl @ X676 @ X675 ) )
=> ~ $true ) )
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz11]),c_0_41]),c_0_60]),c_0_68]) ).
thf(c_0_73,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_74,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_75,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_71,c_0_56]),c_0_48]),c_0_68]) ).
thf(c_0_76,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_41]),c_0_60]),c_0_66]) ).
thf(c_0_77,plain,
! [X1486: $i,X1487: $i,X1488: $i] :
( ( ( in @ ( esk42_2 @ X1486 @ X1487 ) @ nat )
| ~ $true
| ~ ( in @ X1488 @ nat )
| ( X1486
!= ( n_pl @ X1487 @ X1488 ) )
| ~ $true
| ~ ( in @ X1487 @ nat )
| ~ ( in @ X1486 @ nat ) )
& ( ( X1486
= ( n_pl @ X1487 @ ( esk42_2 @ X1486 @ X1487 ) ) )
| ~ $true
| ~ ( in @ X1488 @ nat )
| ( X1486
!= ( n_pl @ X1487 @ X1488 ) )
| ~ $true
| ~ ( in @ X1487 @ nat )
| ~ ( in @ X1486 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1488 @ nat )
| ( X1486
!= ( n_pl @ X1487 @ X1488 ) )
| ~ $true
| ~ ( in @ X1487 @ nat )
| ~ ( in @ X1486 @ nat ) )
& ( ( in @ ( esk42_2 @ X1486 @ X1487 ) @ nat )
| ~ $true
| $true
| ~ ( in @ X1487 @ nat )
| ~ ( in @ X1486 @ nat ) )
& ( ( X1486
= ( n_pl @ X1487 @ ( esk42_2 @ X1486 @ X1487 ) ) )
| ~ $true
| $true
| ~ ( in @ X1487 @ nat )
| ~ ( in @ X1486 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ ( in @ X1487 @ nat )
| ~ ( in @ X1486 @ 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_72])])])])])]) ).
thf(c_0_78,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( esk99_0
!= ( n_pl @ esk98_0 @ X1 ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_79,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_74]) ).
thf(c_0_80,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_74]) ).
thf(c_0_81,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_82,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_41]),c_0_75]) ).
thf(c_0_83,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_76])])])])])]) ).
thf(c_0_84,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk42_2 @ X1 @ X4 ) ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_85,negated_conjecture,
! [X1: $i] :
( ( esk99_0
!= ( n_pl @ esk98_0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_78]) ).
thf(c_0_86,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_79]) ).
thf(c_0_87,negated_conjecture,
in @ esk98_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_88,negated_conjecture,
in @ esk99_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_89,negated_conjecture,
esk99_0 != esk98_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_90,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_74]) ).
thf(c_0_91,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_80]) ).
thf(c_0_92,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_74]) ).
thf(c_0_93,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk42_2 @ X1 @ X4 ) @ nat )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_94,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_81,c_0_38]),c_0_48]) ).
thf(c_0_95,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_82])])])])])]) ).
thf(c_0_96,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_74]) ).
thf(c_0_97,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_83]) ).
thf(c_0_98,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk42_2 @ X1 @ X4 ) ) )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_84]) ).
thf(c_0_99,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_85,c_0_86]),c_0_87])])]),c_0_88])]),c_0_89]) ).
thf(c_0_100,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_90]) ).
thf(c_0_101,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_85,c_0_91]),c_0_87])])]),c_0_88])]),c_0_89]) ).
thf(c_0_102,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_92]) ).
thf(c_0_103,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk42_2 @ X1 @ X4 ) @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_93]) ).
thf(c_0_104,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_83]) ).
thf(c_0_105,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_41]),c_0_94]) ).
thf(c_0_106,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_41]),c_0_68]),c_0_75]) ).
thf(c_0_107,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk59_3 @ X4 @ X5 @ X1 ) ) )
| ( X4 = X1 )
| ~ $true
| ~ ( in @ X6 @ nat )
| ( X1
!= ( n_pl @ X5 @ X6 ) )
| ~ $true
| ~ $true
| ( X4 != X5 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
thf(c_0_108,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_96]) ).
thf(c_0_109,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_97]) ).
thf(c_0_110,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ ( esk42_2 @ ( n_pl @ X1 @ X4 ) @ X1 ) )
= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[c_0_98]) ).
thf(c_0_111,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_99,c_0_100]),c_0_88]),c_0_87])]),c_0_89]) ).
thf(c_0_112,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_101,c_0_102]),c_0_88]),c_0_87])]),c_0_89]) ).
thf(c_0_113,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk42_2 @ ( n_pl @ X1 @ X4 ) @ X1 ) @ nat )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[c_0_103]) ).
thf(c_0_114,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_104]) ).
thf(c_0_115,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk59_3 @ X1 @ X4 @ X5 ) @ nat )
| ( X1 = X5 )
| ~ $true
| ~ ( in @ X6 @ nat )
| ( X5
!= ( n_pl @ X4 @ X6 ) )
| ~ $true
| ~ $true
| ( X1 != X4 )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
thf(c_0_116,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_105])])])]) ).
thf(c_0_117,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_41]),c_0_48]) ).
thf(c_0_118,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_106])])])])])]) ).
thf(c_0_119,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_95]) ).
thf(c_0_120,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( X1 = X4 )
| ( X1
= ( n_pl @ X4 @ ( esk59_3 @ X4 @ X5 @ X1 ) ) )
| ( 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_107]) ).
thf(c_0_121,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_108]) ).
thf(c_0_122,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_109])]) ).
thf(c_0_123,negated_conjecture,
( ( n_pl @ esk99_0 @ ( esk42_2 @ esk98_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_110,c_0_111]),c_0_87]),c_0_112]),c_0_88])]) ).
thf(c_0_124,negated_conjecture,
in @ ( esk42_2 @ esk98_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_113,c_0_111]),c_0_87]),c_0_112]),c_0_88])]) ).
thf(c_0_125,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_114])]) ).
thf(c_0_126,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( X1 = X5 )
| ( in @ ( esk59_3 @ X1 @ X4 @ X5 ) @ nat )
| ( X1 != X4 )
| ( X5
!= ( n_pl @ X4 @ X6 ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_115]) ).
thf(c_0_127,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_95]) ).
thf(c_0_128,plain,
! [X1: $i,X4: $i] :
( ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ( X4
!= ( n_pl @ X1 @ X4 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
thf(c_0_129,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_117])])])]) ).
thf(c_0_130,negated_conjecture,
( ( ( n_pl @ esk99_0 @ n_1 )
= ( n_pl @ esk98_0 @ esk100_0 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_131,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_74]) ).
thf(c_0_132,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_118]) ).
thf(c_0_133,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_119]) ).
thf(c_0_134,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ ( esk59_3 @ X1 @ X1 @ ( 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_120])]),c_0_121]) ).
thf(c_0_135,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_122,c_0_123]),c_0_87]),c_0_124]),c_0_88])]) ).
thf(c_0_136,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_125,c_0_111]),c_0_87]),c_0_112]),c_0_88])]) ).
thf(c_0_137,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk59_3 @ X1 @ X1 @ ( 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_126])]),c_0_121]) ).
thf(c_0_138,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_127]) ).
thf(c_0_139,plain,
! [X4: $i,X1: $i] :
( ( X4
!= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_128]) ).
thf(c_0_140,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_129]) ).
thf(c_0_141,negated_conjecture,
( ( n_pl @ esk99_0 @ n_1 )
= ( n_pl @ esk98_0 @ esk100_0 ) ),
inference(cn,[status(thm)],[c_0_130]) ).
thf(c_0_142,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(split_conjunct,[status(thm)],[def_n_1]) ).
thf(c_0_143,negated_conjecture,
( ( in @ esk100_0 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_144,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_118]) ).
thf(c_0_145,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_41]),c_0_48]) ).
thf(c_0_146,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_131]) ).
thf(c_0_147,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_132]) ).
thf(c_0_148,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_133])]),c_0_121]) ).
thf(c_0_149,negated_conjecture,
( ( n_pl @ esk99_0 @ ( esk59_3 @ esk99_0 @ esk99_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_134,c_0_135]),c_0_87]),c_0_136]),c_0_88])]) ).
thf(c_0_150,negated_conjecture,
in @ ( esk59_3 @ esk99_0 @ esk99_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_137,c_0_135]),c_0_87]),c_0_136]),c_0_88])]) ).
thf(c_0_151,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_138])]),c_0_121]) ).
thf(c_0_152,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
!= X1 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
thf(c_0_153,negated_conjecture,
( ( n_pl @ esk98_0 @ esk100_0 )
= ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) ) ),
inference(rw,[status(thm)],[c_0_141,c_0_142]) ).
thf(c_0_154,negated_conjecture,
in @ esk100_0 @ nat,
inference(cn,[status(thm)],[c_0_143]) ).
thf(c_0_155,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_144]) ).
thf(c_0_156,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_36]),c_0_41]) ).
thf(c_0_157,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_145])])]) ).
thf(c_0_158,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_146]) ).
thf(c_0_159,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_147,c_0_142]),c_0_142])]) ).
thf(c_0_160,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_148,c_0_149]),c_0_87]),c_0_150]),c_0_88])]) ).
thf(c_0_161,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_151,c_0_135]),c_0_87]),c_0_136]),c_0_88])]) ).
thf(c_0_162,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_152,c_0_153]),c_0_87]),c_0_154])]) ).
thf(c_0_163,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_155,c_0_142])]) ).
thf(c_0_164,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_156])])]) ).
thf(c_0_165,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ n_1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
thf(c_0_166,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_158,c_0_153]),c_0_154]),c_0_87])]) ).
thf(c_0_167,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_159,c_0_160]),c_0_87]),c_0_161]),c_0_88])]),c_0_162]) ).
thf(c_0_168,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_163,c_0_135]),c_0_87]),c_0_136]),c_0_88])]),c_0_162]) ).
thf(c_0_169,plain,
! [X1: $i] :
( ( in @ ( ordsucc @ X1 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
thf(c_0_170,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_165,c_0_142]) ).
thf(c_0_171,negated_conjecture,
~ ( in @ ( n_pl @ esk99_0 @ ( ordsucc @ emptyset ) ) @ nat ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168])]) ).
thf(c_0_172,plain,
! [X1: $i] :
( ( in @ ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
thf(c_0_173,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_88])]),
[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
% 0.08/0.21 % Computer : n005.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 12:41:42 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running higher-order theorem proving
% 0.24/0.33 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.gWrsU9wKgB/E---3.1_1605917.p
% 16.34/2.75 % Version: 3.5.1-ho
% 16.34/2.75 % Preprocessing class: HSLMSMSSLLLCHSA.
% 16.34/2.75 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 16.34/2.75 % Starting lpo1_fix with 900s (3) cores
% 16.34/2.75 % Starting full_lambda_9 with 300s (1) cores
% 16.34/2.75 % Starting almost_fo_4 with 300s (1) cores
% 16.34/2.75 % Starting new_ho_9 with 300s (1) cores
% 16.34/2.75 % Starting pre_casc_4 with 300s (1) cores
% 16.34/2.75 % Starting ho_unfolding_6 with 300s (1) cores
% 16.34/2.75 % lpo1_fix with pid 1605930 completed with status 0
% 16.34/2.75 % Result found by lpo1_fix
% 16.34/2.75 % Preprocessing class: HSLMSMSSLLLCHSA.
% 16.34/2.75 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 16.34/2.75 % Starting lpo1_fix with 900s (3) cores
% 16.34/2.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.34/2.75 % No SInE strategy applied
% 16.34/2.75 % Search class: HGHSM-FSLM32-MHSMMSBN
% 16.34/2.75 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 16.34/2.75 % Starting SubtermCWHack with 91s (1) cores
% 16.34/2.75 % Starting full_lambda_5 with 82s (1) cores
% 16.34/2.75 % Starting new_ho_6 with 82s (1) cores
% 16.34/2.75 % full_lambda_5 with pid 1605938 completed with status 0
% 16.34/2.75 % Result found by full_lambda_5
% 16.34/2.75 % Preprocessing class: HSLMSMSSLLLCHSA.
% 16.34/2.75 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 16.34/2.75 % Starting lpo1_fix with 900s (3) cores
% 16.34/2.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.34/2.75 % No SInE strategy applied
% 16.34/2.75 % Search class: HGHSM-FSLM32-MHSMMSBN
% 16.34/2.75 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 16.34/2.75 % Starting SubtermCWHack with 91s (1) cores
% 16.34/2.75 % Starting full_lambda_5 with 82s (1) cores
% 16.34/2.75 % Preprocessing time : 0.017 s
% 16.34/2.75 % Presaturation interreduction done
% 16.34/2.75
% 16.34/2.75 % Proof found!
% 16.34/2.75 % SZS status Theorem
% 16.34/2.75 % SZS output start CNFRefutation
% See solution above
% 16.34/2.76 % Parsed axioms : 407
% 16.34/2.76 % Removed by relevancy pruning/SinE : 0
% 16.34/2.76 % Initial clauses : 1224
% 16.34/2.76 % Removed in clause preprocessing : 757
% 16.34/2.76 % Initial clauses in saturation : 467
% 16.34/2.76 % Processed clauses : 3535
% 16.34/2.76 % ...of these trivial : 249
% 16.34/2.76 % ...subsumed : 1172
% 16.34/2.76 % ...remaining for further processing : 2114
% 16.34/2.76 % Other redundant clauses eliminated : 1382
% 16.34/2.76 % Clauses deleted for lack of memory : 0
% 16.34/2.76 % Backward-subsumed : 93
% 16.34/2.76 % Backward-rewritten : 182
% 16.34/2.76 % Generated clauses : 49965
% 16.34/2.76 % ...of the previous two non-redundant : 47408
% 16.34/2.76 % ...aggressively subsumed : 0
% 16.34/2.76 % Contextual simplify-reflections : 22
% 16.34/2.76 % Paramodulations : 48277
% 16.34/2.76 % Factorizations : 2
% 16.34/2.76 % NegExts : 44
% 16.34/2.76 % Equation resolutions : 1396
% 16.34/2.76 % Disequality decompositions : 0
% 16.34/2.76 % Total rewrite steps : 20918
% 16.34/2.76 % ...of those cached : 20174
% 16.34/2.76 % Propositional unsat checks : 0
% 16.34/2.76 % Propositional check models : 0
% 16.34/2.76 % Propositional check unsatisfiable : 0
% 16.34/2.76 % Propositional clauses : 0
% 16.34/2.76 % Propositional clauses after purity: 0
% 16.34/2.76 % Propositional unsat core size : 0
% 16.34/2.76 % Propositional preprocessing time : 0.000
% 16.34/2.76 % Propositional encoding time : 0.000
% 16.34/2.76 % Propositional solver time : 0.000
% 16.34/2.76 % Success case prop preproc time : 0.000
% 16.34/2.76 % Success case prop encoding time : 0.000
% 16.34/2.76 % Success case prop solver time : 0.000
% 16.34/2.76 % Current number of processed clauses : 1272
% 16.34/2.76 % Positive orientable unit clauses : 287
% 16.34/2.76 % Positive unorientable unit clauses: 8
% 16.34/2.76 % Negative unit clauses : 234
% 16.34/2.76 % Non-unit-clauses : 743
% 16.34/2.76 % Current number of unprocessed clauses: 43468
% 16.34/2.76 % ...number of literals in the above : 236092
% 16.34/2.76 % Current number of archived formulas : 0
% 16.34/2.76 % Current number of archived clauses : 708
% 16.34/2.76 % Clause-clause subsumption calls (NU) : 229524
% 16.34/2.76 % Rec. Clause-clause subsumption calls : 55881
% 16.34/2.76 % Non-unit clause-clause subsumptions : 388
% 16.34/2.76 % Unit Clause-clause subsumption calls : 22821
% 16.34/2.76 % Rewrite failures with RHS unbound : 43
% 16.34/2.76 % BW rewrite match attempts : 404
% 16.34/2.76 % BW rewrite match successes : 90
% 16.34/2.76 % Condensation attempts : 0
% 16.34/2.76 % Condensation successes : 0
% 16.34/2.76 % Termbank termtop insertions : 1398353
% 16.34/2.76 % Search garbage collected termcells : 50507
% 16.34/2.76
% 16.34/2.76 % -------------------------------------------------
% 16.34/2.76 % User time : 2.205 s
% 16.34/2.76 % System time : 0.071 s
% 16.34/2.76 % Total time : 2.276 s
% 16.34/2.76 % Maximum resident set size: 10684 pages
% 16.34/2.76
% 16.34/2.76 % -------------------------------------------------
% 16.34/2.76 % User time : 6.532 s
% 16.34/2.76 % System time : 0.239 s
% 16.34/2.76 % Total time : 6.770 s
% 16.34/2.76 % Maximum resident set size: 5632 pages
% 16.34/2.76 % E exiting
%------------------------------------------------------------------------------