%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM700^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:16:53 AM UTC 2026
% Result : Theorem 18.09s 2.99s
% Output : CNFRefutation 18.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 32
% Syntax : Number of formulae : 153 ( 78 unt; 0 typ; 0 def)
% Number of atoms : 1251 ( 273 equ; 0 cnn)
% Maximal formula atoms : 275 ( 8 avg)
% Number of connectives : 3297 ( 717 ~; 664 |; 70 &;1596 @)
% ( 0 <=>; 250 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 6 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 : 342 ( 178 ^; 164 !; 0 ?; 342 :)
% 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_200,type,
esk43_2: $i > $i > $i ).
thf(decl_215,type,
esk58_3: $i > $i > $i > $i ).
thf(decl_250,type,
esk93_2: $i > $i > $i ).
thf(decl_253,type,
esk96_0: $i ).
thf(decl_254,type,
esk97_0: $i ).
thf(decl_255,type,
esk98_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_is_of) ).
thf(def_non,axiom,
( non
= ( ^ [X1: $i,X2: $i > $o,X4: $i] : ( d_not @ ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_non) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X79: $o,X80: $o] : ( imp @ X79 @ ( d_not @ X80 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_l_some) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_e_is) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X81: $o,X82: $o] : ( d_not @ ( l_ec @ X81 @ X82 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_and3) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_iii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X505: $i] :
( ( in @ X505 @ nat )
=> ( ( Z0 @ X505 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_ec3) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_lessis) ).
thf(def_orec3,axiom,
( orec3
= ( ^ [X98: $o,X99: $o,X100: $o] : ( d_and @ ( or3 @ X98 @ X99 @ X100 ) @ ( ec3 @ X98 @ X99 @ X100 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_orec3) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_d_29_ii) ).
thf(satz26,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X331: $i] : ( in @ X331 @ nat )
@ ^ [X332: $i] :
( ( iii @ X332 @ ( n_pl @ X1 @ n_1 ) )
=> ( lessis @ X332 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz26) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_moreis) ).
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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz9) ).
thf(satz12,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X227: $i] : ( in @ X227 @ nat )
@ ^ [X228: $i] :
( ( iii @ X1 @ X228 )
=> ( d_29_ii @ X228 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz12) ).
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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz16d) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_nis) ).
thf(satz25a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X325: $i] : ( in @ X325 @ nat )
@ ^ [X326: $i] :
( ( d_29_ii @ X326 @ X1 )
=> ( moreis @ X326 @ ( ordsucc @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz25a) ).
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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz7) ).
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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz6) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',def_n_1) ).
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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',suc_p) ).
thf(satz4e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ X1 @ n_1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p',satz4e) ).
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] :
( ! [X478: $i] :
( ( in @ X478 @ Z0 )
=> ( ( Z1 @ X478 )
=> ~ $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] :
( ! [X478: $i] :
( ( in @ X478 @ Z0 )
=> ( ( Z1 @ X478 )
=> ~ $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,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X517: $i] :
( ( in @ X517 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X517 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_52,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X505: $i] :
( ( in @ X505 @ nat )
=> ( ( Z0 @ X505 )
=> ~ $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,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X521: $i] :
( ( in @ X521 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X521 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_59,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X517: $i] :
( ( in @ X517 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X517 ) )
=> ~ $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,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X516: $i] :
( ( in @ X516 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X516 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_64,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X331: $i] : ( in @ X331 @ nat )
@ ^ [X332: $i] :
( ( iii @ X332 @ ( n_pl @ X1 @ n_1 ) )
=> ( lessis @ X332 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[satz26]) ).
thf(c_0_65,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X521: $i] :
( ( in @ X521 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X521 ) )
=> ~ $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,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X520: $i] :
( ( in @ X520 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X520 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_68,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X516: $i] :
( ( in @ X516 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X516 ) )
=> ~ $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,
~ ! [X943: $i] :
( ( in @ X943 @ nat )
=> ! [X942: $i] :
( ( in @ X942 @ nat )
=> ( ( ! [X940: $i] :
( ( in @ X940 @ nat )
=> ( ( ( n_pl @ X943 @ n_1 )
= ( n_pl @ X942 @ X940 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ! [X941: $i] :
( ( in @ X941 @ nat )
=> ( ( X943
= ( n_pl @ X942 @ X941 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X942 = X943 ) ) ) ) ),
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,
! [X649: $i] :
( ( in @ X649 @ nat )
=> ! [X648: $i] :
( ( in @ X648 @ nat )
=> ( ( ( ( ( X649 = X648 )
=> ~ $true )
=> ( ( ( ! [X646: $i] :
( ( in @ X646 @ nat )
=> ( ( X649
= ( n_pl @ X648 @ X646 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( ! [X647: $i] :
( ( in @ X647 @ nat )
=> ( ( X648
= ( n_pl @ X649 @ X647 ) )
=> ~ $true ) )
=> ~ $true ) ) )
=> ( ( ( ( ( X649 = X648 )
=> ( ( ! [X646: $i] :
( ( in @ X646 @ nat )
=> ( ( X649
= ( n_pl @ X648 @ X646 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ( ( ! [X646: $i] :
( ( in @ X646 @ nat )
=> ( ( X649
= ( n_pl @ X648 @ X646 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ! [X647: $i] :
( ( in @ X647 @ nat )
=> ( ( X648
= ( n_pl @ X649 @ X647 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ! [X647: $i] :
( ( in @ X647 @ nat )
=> ( ( X648
= ( n_pl @ X649 @ X647 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( X649 = X648 )
=> ~ $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,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X520: $i] :
( ( in @ X520 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X520 ) )
=> ~ $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_72,plain,
! [X677: $i] :
( ( in @ X677 @ nat )
=> ! [X676: $i] :
( ( in @ X676 @ nat )
=> ( ( ! [X674: $i] :
( ( in @ X674 @ nat )
=> ( ( X676
= ( n_pl @ X677 @ X674 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ! [X675: $i] :
( ( in @ X675 @ nat )
=> ( ( X676
= ( n_pl @ X677 @ X675 ) )
=> ~ $true ) )
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz12]),c_0_40]),c_0_68]),c_0_59]) ).
thf(c_0_73,negated_conjecture,
! [X1747: $i] :
( ( in @ esk96_0 @ nat )
& ( in @ esk97_0 @ nat )
& ( ( in @ esk98_0 @ nat )
| ~ $true )
& ( ( ( n_pl @ esk96_0 @ n_1 )
= ( n_pl @ esk97_0 @ esk98_0 ) )
| ~ $true )
& ( $true
| ~ $true )
& ( ~ ( in @ X1747 @ nat )
| ( esk96_0
!= ( n_pl @ esk97_0 @ X1747 ) )
| ~ $true
| ~ $true )
& ( $true
| ~ $true )
& ( esk97_0 != esk96_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,
! [X1438: $i,X1439: $i,X1442: $i,X1443: $i,X1444: $i,X1445: $i] :
( ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| ( X1438
= ( n_pl @ X1439 @ ( esk34_2 @ X1438 @ X1439 ) ) )
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| ( X1438
= ( n_pl @ X1439 @ ( esk34_2 @ X1438 @ X1439 ) ) )
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ( X1438
= ( n_pl @ X1439 @ ( esk34_2 @ X1438 @ X1439 ) ) )
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| $true
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| $true
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| $true
| ( X1438 = X1439 )
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| ( X1438
= ( n_pl @ X1439 @ ( esk34_2 @ X1438 @ X1439 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| ( X1438
= ( n_pl @ X1439 @ ( esk34_2 @ X1438 @ X1439 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ( X1438
= ( n_pl @ X1439 @ ( esk34_2 @ X1438 @ X1439 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( in @ ( esk35_2 @ X1438 @ X1439 ) @ nat )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ( X1439
= ( n_pl @ X1438 @ ( esk35_2 @ X1438 @ X1439 ) ) )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ~ ( in @ X1442 @ nat )
| ( X1438
!= ( n_pl @ X1439 @ X1442 ) )
| ~ $true
| ~ $true
| ( X1438 != X1439 )
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ( X1438 != X1439 )
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ~ ( in @ X1444 @ nat )
| ( X1439
!= ( n_pl @ X1438 @ X1444 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1443 @ nat )
| ( X1438
!= ( n_pl @ X1439 @ X1443 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1443 @ nat )
| ( X1438
!= ( n_pl @ X1439 @ X1443 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ~ ( in @ X1444 @ nat )
| ( X1439
!= ( n_pl @ X1438 @ X1444 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( ~ ( in @ X1445 @ nat )
| ( X1439
!= ( n_pl @ X1438 @ X1445 ) )
| ~ $true
| ( X1438 != X1439 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ( X1438 != X1439 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1439 @ nat )
| ~ ( in @ X1438 @ 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,
! [X747: $i] :
( ( in @ X747 @ nat )
=> ! [X746: $i] :
( ( in @ X746 @ nat )
=> ! [X745: $i] :
( ( in @ X745 @ nat )
=> ( ( ! [X742: $i] :
( ( in @ X742 @ nat )
=> ( ( X747
= ( n_pl @ X746 @ X742 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ( ! [X743: $i] :
( ( in @ X743 @ nat )
=> ( ( X746
= ( n_pl @ X745 @ X743 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X746 = X745 ) )
=> ( ! [X744: $i] :
( ( in @ X744 @ nat )
=> ( ( X747
= ( n_pl @ X745 @ X744 ) )
=> ~ $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_68]),c_0_71]) ).
thf(c_0_76,plain,
! [X1478: $i,X1479: $i,X1480: $i] :
( ( ( in @ ( esk43_2 @ X1478 @ X1479 ) @ nat )
| ~ $true
| ~ ( in @ X1480 @ nat )
| ( X1479
!= ( n_pl @ X1478 @ X1480 ) )
| ~ $true
| ~ ( in @ X1479 @ nat )
| ~ ( in @ X1478 @ nat ) )
& ( ( X1479
= ( n_pl @ X1478 @ ( esk43_2 @ X1478 @ X1479 ) ) )
| ~ $true
| ~ ( in @ X1480 @ nat )
| ( X1479
!= ( n_pl @ X1478 @ X1480 ) )
| ~ $true
| ~ ( in @ X1479 @ nat )
| ~ ( in @ X1478 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1480 @ nat )
| ( X1479
!= ( n_pl @ X1478 @ X1480 ) )
| ~ $true
| ~ ( in @ X1479 @ nat )
| ~ ( in @ X1478 @ nat ) )
& ( ( in @ ( esk43_2 @ X1478 @ X1479 ) @ nat )
| ~ $true
| $true
| ~ ( in @ X1479 @ nat )
| ~ ( in @ X1478 @ nat ) )
& ( ( X1479
= ( n_pl @ X1478 @ ( esk43_2 @ X1478 @ X1479 ) ) )
| ~ $true
| $true
| ~ ( in @ X1479 @ nat )
| ~ ( in @ X1478 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ ( in @ X1479 @ nat )
| ~ ( in @ X1478 @ 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_77,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( esk96_0
!= ( n_pl @ esk97_0 @ X1 ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_78,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_79,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_80,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_81,plain,
! [X931: $i] :
( ( in @ X931 @ nat )
=> ! [X930: $i] :
( ( in @ X930 @ nat )
=> ( ( ! [X928: $i] :
( ( in @ X928 @ nat )
=> ( ( X930
= ( n_pl @ X931 @ X928 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ! [X929: $i] :
( ( in @ X929 @ nat )
=> ( ( X930
= ( n_pl @ ( ordsucc @ X931 ) @ X929 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X930
= ( ordsucc @ X931 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz25a]),c_0_40]),c_0_68]),c_0_71]) ).
thf(c_0_82,plain,
! [X1546: $i,X1547: $i,X1548: $i,X1549: $i,X1550: $i] :
( ( ( in @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) @ nat )
| ~ $true
| ~ ( in @ X1550 @ nat )
| ( X1547
!= ( n_pl @ X1548 @ X1550 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( X1546
= ( n_pl @ X1548 @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) ) )
| ~ $true
| ~ ( in @ X1550 @ nat )
| ( X1547
!= ( n_pl @ X1548 @ X1550 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1550 @ nat )
| ( X1547
!= ( n_pl @ X1548 @ X1550 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( in @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( X1546
= ( n_pl @ X1548 @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( in @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) @ nat )
| ~ $true
| ( X1547 != X1548 )
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( X1546
= ( n_pl @ X1548 @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) ) )
| ~ $true
| ( X1547 != X1548 )
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( $true
| ~ $true
| ( X1547 != X1548 )
| ~ ( in @ X1549 @ nat )
| ( X1546
!= ( n_pl @ X1547 @ X1549 ) )
| ~ $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( in @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) @ nat )
| ~ $true
| ~ ( in @ X1550 @ nat )
| ( X1547
!= ( n_pl @ X1548 @ X1550 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( X1546
= ( n_pl @ X1548 @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) ) )
| ~ $true
| ~ ( in @ X1550 @ nat )
| ( X1547
!= ( n_pl @ X1548 @ X1550 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1550 @ nat )
| ( X1547
!= ( n_pl @ X1548 @ X1550 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( in @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) @ nat )
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( X1546
= ( n_pl @ X1548 @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) ) )
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( in @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) @ nat )
| ~ $true
| ( X1547 != X1548 )
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( ( X1546
= ( n_pl @ X1548 @ ( esk58_3 @ X1546 @ X1547 @ X1548 ) ) )
| ~ $true
| ( X1547 != X1548 )
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ nat ) )
& ( $true
| ~ $true
| ( X1547 != X1548 )
| $true
| ~ ( in @ X1548 @ nat )
| ~ ( in @ X1547 @ nat )
| ~ ( in @ X1546 @ 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_75])])])])])]) ).
thf(c_0_83,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk43_2 @ X4 @ X1 ) ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_84,negated_conjecture,
! [X1: $i] :
( ( esk96_0
!= ( n_pl @ esk97_0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_77]) ).
thf(c_0_85,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_78]) ).
thf(c_0_86,negated_conjecture,
in @ esk97_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_87,negated_conjecture,
in @ esk96_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_88,negated_conjecture,
esk97_0 != esk96_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_89,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_90,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_79]) ).
thf(c_0_91,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_92,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk43_2 @ X1 @ X4 ) @ nat )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X4
!= ( n_pl @ X1 @ X5 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_93,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_80,c_0_37]),c_0_47]) ).
thf(c_0_94,plain,
! [X1732: $i,X1733: $i,X1734: $i] :
( ( ( in @ ( esk93_2 @ X1732 @ X1733 ) @ nat )
| ~ $true
| ( X1733
= ( ordsucc @ X1732 ) )
| ~ ( in @ X1734 @ nat )
| ( X1733
!= ( n_pl @ X1732 @ X1734 ) )
| ~ $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ nat ) )
& ( ( X1733
= ( n_pl @ ( ordsucc @ X1732 ) @ ( esk93_2 @ X1732 @ X1733 ) ) )
| ~ $true
| ( X1733
= ( ordsucc @ X1732 ) )
| ~ ( in @ X1734 @ nat )
| ( X1733
!= ( n_pl @ X1732 @ X1734 ) )
| ~ $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ nat ) )
& ( $true
| ~ $true
| ( X1733
= ( ordsucc @ X1732 ) )
| ~ ( in @ X1734 @ nat )
| ( X1733
!= ( n_pl @ X1732 @ X1734 ) )
| ~ $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ nat ) )
& ( $true
| ( X1733
= ( ordsucc @ X1732 ) )
| ~ ( in @ X1734 @ nat )
| ( X1733
!= ( n_pl @ X1732 @ X1734 ) )
| ~ $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ nat ) )
& ( ( in @ ( esk93_2 @ X1732 @ X1733 ) @ nat )
| ~ $true
| ( X1733
= ( ordsucc @ X1732 ) )
| $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ nat ) )
& ( ( X1733
= ( n_pl @ ( ordsucc @ X1732 ) @ ( esk93_2 @ X1732 @ X1733 ) ) )
| ~ $true
| ( X1733
= ( ordsucc @ X1732 ) )
| $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ nat ) )
& ( $true
| ~ $true
| ( X1733
= ( ordsucc @ X1732 ) )
| $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ nat ) )
& ( $true
| ( X1733
= ( ordsucc @ X1732 ) )
| $true
| ~ ( in @ X1733 @ nat )
| ~ ( in @ X1732 @ 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_81])])])])])]) ).
thf(c_0_95,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_82]) ).
thf(c_0_96,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1
= ( n_pl @ X4 @ ( esk43_2 @ X4 @ X1 ) ) )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_83]) ).
thf(c_0_97,negated_conjecture,
( ( ( n_pl @ esk96_0 @ ( esk34_2 @ esk97_0 @ esk96_0 ) )
= esk97_0 )
| ~ ( in @ ( esk35_2 @ esk97_0 @ esk96_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_84,c_0_85]),c_0_86])])]),c_0_87])]),c_0_88]) ).
thf(c_0_98,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_89]) ).
thf(c_0_99,negated_conjecture,
( ( in @ ( esk34_2 @ esk97_0 @ esk96_0 ) @ nat )
| ~ ( in @ ( esk35_2 @ esk97_0 @ esk96_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_84,c_0_90]),c_0_86])])]),c_0_87])]),c_0_88]) ).
thf(c_0_100,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_91]) ).
thf(c_0_101,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk43_2 @ X1 @ X4 ) @ nat )
| ( X4
!= ( n_pl @ X1 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_92]) ).
thf(c_0_102,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_82]) ).
thf(c_0_103,plain,
! [X635: $i] :
( ( in @ X635 @ nat )
=> ! [X634: $i] :
( ( in @ X634 @ nat )
=> ( ( X634
= ( n_pl @ X635 @ X634 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz7]),c_0_40]),c_0_93]) ).
thf(c_0_104,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( X1
= ( n_pl @ ( ordsucc @ X4 ) @ ( esk93_2 @ X4 @ X1 ) ) )
| ( X1
= ( ordsucc @ X4 ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
thf(c_0_105,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_95]) ).
thf(c_0_106,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ ( esk43_2 @ X1 @ ( n_pl @ X1 @ X4 ) ) )
= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[c_0_96]) ).
thf(c_0_107,negated_conjecture,
( ( n_pl @ esk96_0 @ ( esk34_2 @ esk97_0 @ esk96_0 ) )
= esk97_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_87]),c_0_86])]),c_0_88]) ).
thf(c_0_108,negated_conjecture,
in @ ( esk34_2 @ esk97_0 @ esk96_0 ) @ nat,
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_87]),c_0_86])]),c_0_88]) ).
thf(c_0_109,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk43_2 @ X1 @ ( n_pl @ X1 @ X4 ) ) @ nat )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[c_0_101]) ).
thf(c_0_110,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_102]) ).
thf(c_0_111,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk93_2 @ X1 @ X4 ) @ nat )
| ( X4
= ( ordsucc @ X1 ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X4
!= ( n_pl @ X1 @ X5 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
thf(c_0_112,plain,
! [X1426: $i,X1427: $i] :
( ~ ( in @ X1426 @ nat )
| ~ ( in @ X1427 @ nat )
| ( X1427
!= ( n_pl @ X1426 @ X1427 ) )
| ~ $true ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_103])])])]) ).
thf(c_0_113,plain,
! [X633: $i] :
( ( in @ X633 @ nat )
=> ! [X632: $i] :
( ( in @ X632 @ nat )
=> ( ( n_pl @ X633 @ X632 )
= ( n_pl @ X632 @ X633 ) ) ) ),
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_114,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_115,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1
= ( ordsucc @ X4 ) )
| ( X1
= ( n_pl @ ( ordsucc @ X4 ) @ ( esk93_2 @ X4 @ X1 ) ) )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_104]) ).
thf(c_0_116,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_105])]) ).
thf(c_0_117,negated_conjecture,
( ( n_pl @ esk96_0 @ ( esk43_2 @ esk96_0 @ esk97_0 ) )
= esk97_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_86]),c_0_108]),c_0_87])]) ).
thf(c_0_118,negated_conjecture,
in @ ( esk43_2 @ esk96_0 @ esk97_0 ) @ nat,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_107]),c_0_86]),c_0_108]),c_0_87])]) ).
thf(c_0_119,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_110])]) ).
thf(c_0_120,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X4
= ( ordsucc @ X1 ) )
| ( in @ ( esk93_2 @ X1 @ X4 ) @ nat )
| ( X4
!= ( n_pl @ X1 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_111]) ).
thf(c_0_121,plain,
! [X1: $i,X4: $i] :
( ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ( X4
!= ( n_pl @ X1 @ X4 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_122,plain,
! [X1424: $i,X1425: $i] :
( ~ ( in @ X1424 @ nat )
| ~ ( in @ X1425 @ nat )
| ( ( n_pl @ X1424 @ X1425 )
= ( n_pl @ X1425 @ X1424 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_113])])])]) ).
thf(c_0_123,negated_conjecture,
( ( ( n_pl @ esk96_0 @ n_1 )
= ( n_pl @ esk97_0 @ esk98_0 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_124,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_114]) ).
thf(c_0_125,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ ( ordsucc @ X1 ) @ ( esk93_2 @ X1 @ ( n_pl @ X1 @ X4 ) ) )
= ( n_pl @ X1 @ X4 ) )
| ( ( n_pl @ X1 @ X4 )
= ( ordsucc @ X1 ) )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[c_0_115]) ).
thf(c_0_126,negated_conjecture,
( ( n_pl @ esk96_0 @ ( esk58_3 @ esk97_0 @ esk96_0 @ esk96_0 ) )
= esk97_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_86]),c_0_118]),c_0_87])]) ).
thf(c_0_127,negated_conjecture,
in @ ( esk58_3 @ esk97_0 @ esk96_0 @ esk96_0 ) @ nat,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_107]),c_0_86]),c_0_108]),c_0_87])]) ).
thf(c_0_128,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ X4 )
= ( ordsucc @ X1 ) )
| ( in @ ( esk93_2 @ X1 @ ( n_pl @ X1 @ X4 ) ) @ nat )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[c_0_120]) ).
thf(c_0_129,plain,
! [X4: $i,X1: $i] :
( ( X4
!= ( n_pl @ X1 @ X4 ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_121]) ).
thf(c_0_130,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_122]) ).
thf(c_0_131,negated_conjecture,
( ( n_pl @ esk97_0 @ esk98_0 )
= ( n_pl @ esk96_0 @ n_1 ) ),
inference(cn,[status(thm)],[c_0_123]) ).
thf(c_0_132,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(split_conjunct,[status(thm)],[def_n_1]) ).
thf(c_0_133,negated_conjecture,
( ( in @ esk98_0 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_134,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_124]) ).
thf(c_0_135,negated_conjecture,
( ( ( n_pl @ ( ordsucc @ esk96_0 ) @ ( esk93_2 @ esk96_0 @ esk97_0 ) )
= esk97_0 )
| ( esk97_0
= ( ordsucc @ esk96_0 ) ) ),
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_126]),c_0_86]),c_0_127]),c_0_87])]) ).
thf(c_0_136,negated_conjecture,
( ( esk97_0
= ( ordsucc @ esk96_0 ) )
| ( in @ ( esk93_2 @ esk96_0 @ esk97_0 ) @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_117]),c_0_86]),c_0_118]),c_0_87])]) ).
thf(c_0_137,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
!= X1 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
thf(c_0_138,negated_conjecture,
( ( n_pl @ esk97_0 @ esk98_0 )
= ( n_pl @ esk96_0 @ ( ordsucc @ emptyset ) ) ),
inference(rw,[status(thm)],[c_0_131,c_0_132]) ).
thf(c_0_139,negated_conjecture,
in @ esk98_0 @ nat,
inference(cn,[status(thm)],[c_0_133]) ).
thf(c_0_140,negated_conjecture,
! [X1: $i] :
( ( esk97_0
= ( ordsucc @ esk96_0 ) )
| ( ( n_pl @ esk97_0 @ X1 )
!= ( ordsucc @ esk96_0 ) )
| ~ ( in @ ( ordsucc @ esk96_0 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_86])]),c_0_136]) ).
thf(c_0_141,plain,
! [X595: $i] :
( ( in @ X595 @ nat )
=> ( in @ ( ordsucc @ X595 ) @ 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_142,plain,
! [X623: $i] :
( ( in @ X623 @ nat )
=> ( ( ordsucc @ X623 )
= ( n_pl @ X623 @ 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_143,negated_conjecture,
( esk97_0
!= ( n_pl @ esk96_0 @ ( ordsucc @ emptyset ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_86]),c_0_139])]) ).
thf(c_0_144,negated_conjecture,
( ( esk97_0
= ( ordsucc @ esk96_0 ) )
| ( ( ordsucc @ esk96_0 )
!= ( n_pl @ esk96_0 @ ( ordsucc @ emptyset ) ) )
| ~ ( in @ ( ordsucc @ esk96_0 ) @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_138]),c_0_139])]) ).
thf(c_0_145,plain,
! [X1383: $i] :
( ~ ( in @ X1383 @ nat )
| ( in @ ( ordsucc @ X1383 ) @ nat ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_141])])]) ).
thf(c_0_146,plain,
! [X1415: $i] :
( ~ ( in @ X1415 @ nat )
| ( ( ordsucc @ X1415 )
= ( n_pl @ X1415 @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_142])])]) ).
thf(c_0_147,negated_conjecture,
( ( ( ordsucc @ esk96_0 )
!= ( n_pl @ esk96_0 @ ( ordsucc @ emptyset ) ) )
| ~ ( in @ ( ordsucc @ esk96_0 ) @ nat ) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
thf(c_0_148,plain,
! [X1: $i] :
( ( in @ ( ordsucc @ X1 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
thf(c_0_149,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ n_1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
thf(c_0_150,negated_conjecture,
( ( ordsucc @ esk96_0 )
!= ( n_pl @ esk96_0 @ ( ordsucc @ emptyset ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_87])]) ).
thf(c_0_151,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_149,c_0_132]) ).
thf(c_0_152,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM700^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:46:49 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.9N4fA7MiZv/E---3.1_291515.p
% 18.09/2.99 % Version: 3.5.1-ho
% 18.09/2.99 % Preprocessing class: HSLMSMSSLLLCHSA.
% 18.09/2.99 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 18.09/2.99 % Starting lpo1_fix with 900s (3) cores
% 18.09/2.99 % Starting full_lambda_9 with 300s (1) cores
% 18.09/2.99 % Starting almost_fo_4 with 300s (1) cores
% 18.09/2.99 % Starting new_ho_9 with 300s (1) cores
% 18.09/2.99 % Starting pre_casc_4 with 300s (1) cores
% 18.09/2.99 % Starting ho_unfolding_6 with 300s (1) cores
% 18.09/2.99 % lpo1_fix with pid 291550 completed with status 0
% 18.09/2.99 % Result found by lpo1_fix
% 18.09/2.99 % Preprocessing class: HSLMSMSSLLLCHSA.
% 18.09/2.99 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 18.09/2.99 % Starting lpo1_fix with 900s (3) cores
% 18.09/2.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.09/2.99 % No SInE strategy applied
% 18.09/2.99 % Search class: HGHSM-FSLM32-MHSMMSBN
% 18.09/2.99 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 18.09/2.99 % Starting SubtermCWHack with 91s (1) cores
% 18.09/2.99 % Starting full_lambda_5 with 82s (1) cores
% 18.09/2.99 % Starting new_ho_6 with 82s (1) cores
% 18.09/2.99 % full_lambda_5 with pid 291574 completed with status 0
% 18.09/2.99 % Result found by full_lambda_5
% 18.09/2.99 % Preprocessing class: HSLMSMSSLLLCHSA.
% 18.09/2.99 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 18.09/2.99 % Starting lpo1_fix with 900s (3) cores
% 18.09/2.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.09/2.99 % No SInE strategy applied
% 18.09/2.99 % Search class: HGHSM-FSLM32-MHSMMSBN
% 18.09/2.99 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 18.09/2.99 % Starting SubtermCWHack with 91s (1) cores
% 18.09/2.99 % Starting full_lambda_5 with 82s (1) cores
% 18.09/2.99 % Preprocessing time : 0.016 s
% 18.09/2.99 % Presaturation interreduction done
% 18.09/2.99
% 18.09/2.99 % Proof found!
% 18.09/2.99 % SZS status Theorem
% 18.09/2.99 % SZS output start CNFRefutation
% See solution above
% 18.09/2.99 % Parsed axioms : 405
% 18.09/2.99 % Removed by relevancy pruning/SinE : 0
% 18.09/2.99 % Initial clauses : 1208
% 18.09/2.99 % Removed in clause preprocessing : 745
% 18.09/2.99 % Initial clauses in saturation : 463
% 18.09/2.99 % Processed clauses : 2406
% 18.09/2.99 % ...of these trivial : 163
% 18.09/2.99 % ...subsumed : 574
% 18.09/2.99 % ...remaining for further processing : 1669
% 18.09/2.99 % Other redundant clauses eliminated : 1021
% 18.09/2.99 % Clauses deleted for lack of memory : 0
% 18.09/2.99 % Backward-subsumed : 34
% 18.09/2.99 % Backward-rewritten : 153
% 18.09/2.99 % Generated clauses : 36169
% 18.09/2.99 % ...of the previous two non-redundant : 34526
% 18.09/2.99 % ...aggressively subsumed : 0
% 18.09/2.99 % Contextual simplify-reflections : 18
% 18.09/2.99 % Paramodulations : 34886
% 18.09/2.99 % Factorizations : 2
% 18.09/2.99 % NegExts : 25
% 18.09/2.99 % Equation resolutions : 1033
% 18.09/2.99 % Disequality decompositions : 0
% 18.09/2.99 % Total rewrite steps : 18873
% 18.09/2.99 % ...of those cached : 18357
% 18.09/2.99 % Propositional unsat checks : 0
% 18.09/2.99 % Propositional check models : 0
% 18.09/2.99 % Propositional check unsatisfiable : 0
% 18.09/2.99 % Propositional clauses : 0
% 18.09/2.99 % Propositional clauses after purity: 0
% 18.09/2.99 % Propositional unsat core size : 0
% 18.09/2.99 % Propositional preprocessing time : 0.000
% 18.09/2.99 % Propositional encoding time : 0.000
% 18.09/2.99 % Propositional solver time : 0.000
% 18.09/2.99 % Success case prop preproc time : 0.000
% 18.09/2.99 % Success case prop encoding time : 0.000
% 18.09/2.99 % Success case prop solver time : 0.000
% 18.09/2.99 % Current number of processed clauses : 923
% 18.09/2.99 % Positive orientable unit clauses : 188
% 18.09/2.99 % Positive unorientable unit clauses: 7
% 18.09/2.99 % Negative unit clauses : 206
% 18.09/2.99 % Non-unit-clauses : 522
% 18.09/2.99 % Current number of unprocessed clauses: 32754
% 18.09/2.99 % ...number of literals in the above : 197209
% 18.09/2.99 % Current number of archived formulas : 0
% 18.09/2.99 % Current number of archived clauses : 612
% 18.09/2.99 % Clause-clause subsumption calls (NU) : 193114
% 18.09/2.99 % Rec. Clause-clause subsumption calls : 26957
% 18.09/2.99 % Non-unit clause-clause subsumptions : 348
% 18.09/2.99 % Unit Clause-clause subsumption calls : 38736
% 18.09/2.99 % Rewrite failures with RHS unbound : 0
% 18.09/2.99 % BW rewrite match attempts : 147
% 18.09/2.99 % BW rewrite match successes : 65
% 18.09/2.99 % Condensation attempts : 0
% 18.09/2.99 % Condensation successes : 0
% 18.09/2.99 % Termbank termtop insertions : 1162556
% 18.09/2.99 % Search garbage collected termcells : 49589
% 18.09/2.99
% 18.09/2.99 % -------------------------------------------------
% 18.09/2.99 % User time : 2.514 s
% 18.09/2.99 % System time : 0.088 s
% 18.09/2.99 % Total time : 2.602 s
% 18.09/2.99 % Maximum resident set size: 10716 pages
% 18.09/2.99
% 18.09/2.99 % -------------------------------------------------
% 18.09/2.99 % User time : 7.178 s
% 18.09/2.99 % System time : 0.286 s
% 18.09/2.99 % Total time : 7.464 s
% 18.09/2.99 % Maximum resident set size: 5632 pages
% 18.09/2.99 % E exiting
%------------------------------------------------------------------------------