%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM698^4 : 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 : n010.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 08:16:52 AM UTC 2026
% Result : Theorem 18.09s 2.96s
% Output : CNFRefutation 18.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 27
% Syntax : Number of formulae : 132 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 1559 ( 355 equ; 0 cnn)
% Maximal formula atoms : 375 ( 11 avg)
% Number of connectives : 4181 ( 974 ~; 978 |; 100 &;1876 @)
% ( 0 <=>; 253 =>; 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 : 38 ( 35 usr; 8 con; 0-3 aty)
% Number of variables : 319 ( 161 ^; 158 !; 0 ?; 319 :)
% 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_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_131,type,
n_1: $i ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_152,type,
moreis: $i > $i > $o ).
thf(decl_153,type,
lessis: $i > $i > $o ).
thf(decl_191,type,
esk34_2: $i > $i > $i ).
thf(decl_192,type,
esk35_2: $i > $i > $i ).
thf(decl_215,type,
esk58_3: $i > $i > $i > $i ).
thf(decl_216,type,
esk59_3: $i > $i > $i > $i ).
thf(decl_249,type,
esk92_2: $i > $i > $i ).
thf(decl_251,type,
esk94_0: $i ).
thf(decl_252,type,
esk95_0: $i ).
thf(decl_253,type,
esk96_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_imp) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X79: $o,X80: $o] : ( imp @ X79 @ ( d_not @ X80 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_l_ec) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X81: $o,X82: $o] : ( d_not @ ( l_ec @ X81 @ X82 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_d_and) ).
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.XKgyoByQWj/E---3.1_2796015.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.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.XKgyoByQWj/E---3.1_2796015.p',def_non) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.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.XKgyoByQWj/E---3.1_2796015.p',def_and3) ).
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.XKgyoByQWj/E---3.1_2796015.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.XKgyoByQWj/E---3.1_2796015.p',def_e_is) ).
thf(def_or3,axiom,
( or3
= ( ^ [X89: $o,X90: $o,X91: $o] : ( l_or @ X89 @ ( l_or @ X90 @ X91 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.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.XKgyoByQWj/E---3.1_2796015.p',def_ec3) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_n_is) ).
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.XKgyoByQWj/E---3.1_2796015.p',def_orec3) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_iii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X501: $i] :
( ( in @ X501 @ nat )
=> ( ( Z0 @ X501 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_n_some) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_lessis) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_d_29_ii) ).
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.XKgyoByQWj/E---3.1_2796015.p',satz9) ).
thf(satz25b,conjecture,
( 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.XKgyoByQWj/E---3.1_2796015.p',satz25b) ).
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.XKgyoByQWj/E---3.1_2796015.p',def_moreis) ).
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.XKgyoByQWj/E---3.1_2796015.p',satz16d) ).
thf(satz17,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X261: $i] : ( in @ X261 @ nat )
@ ^ [X262: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( lessis @ X1 @ X262 )
=> ( ( lessis @ X262 @ X4 )
=> ( lessis @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',satz17) ).
thf(satz25,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X323: $i] : ( in @ X323 @ nat )
@ ^ [X324: $i] :
( ( d_29_ii @ X324 @ X1 )
=> ( moreis @ X324 @ ( n_pl @ X1 @ n_1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',satz25) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.XKgyoByQWj/E---3.1_2796015.p',def_n_1) ).
thf(c_0_27,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_28,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_29,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[def_l_ec]) ).
thf(c_0_30,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_31,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_and]) ).
thf(c_0_32,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_28]),c_0_30]) ).
thf(c_0_33,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_34,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_35,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_36,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_37,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_38,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_31,c_0_30]),c_0_32]) ).
thf(c_0_39,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X474: $i] :
( ( in @ X474 @ Z0 )
=> ( ( Z1 @ X474 )
=> ~ $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_33,c_0_34]) ).
thf(c_0_41,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_35,c_0_30]) ).
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,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_or3]) ).
thf(c_0_44,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36,c_0_28]),c_0_30]) ).
thf(c_0_45,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_46,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_47,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X474: $i] :
( ( in @ X474 @ Z0 )
=> ( ( Z1 @ X474 )
=> ~ $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_30]),c_0_41]) ).
thf(c_0_48,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_49,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_42]) ).
thf(c_0_50,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_51,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_52,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_45,c_0_32]),c_0_46]) ).
thf(c_0_53,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X513: $i] :
( ( in @ X513 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X513 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_54,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X501: $i] :
( ( in @ X501 @ nat )
=> ( ( Z0 @ X501 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_47]) ).
thf(c_0_55,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_56,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_50,c_0_38]),c_0_51]),c_0_52]) ).
thf(c_0_57,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X517: $i] :
( ( in @ X517 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X517 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_58,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X513: $i] :
( ( in @ X513 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X513 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
thf(c_0_59,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X512: $i] :
( ( in @ X512 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X512 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_60,plain,
! [X645: $i] :
( ( in @ X645 @ nat )
=> ! [X644: $i] :
( ( in @ X644 @ nat )
=> ( ( ( ( ( X645 = X644 )
=> ~ $true )
=> ( ( ( ! [X642: $i] :
( ( in @ X642 @ nat )
=> ( ( X645
= ( n_pl @ X644 @ X642 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( ! [X643: $i] :
( ( in @ X643 @ nat )
=> ( ( X644
= ( n_pl @ X645 @ X643 ) )
=> ~ $true ) )
=> ~ $true ) ) )
=> ( ( ( ( ( X645 = X644 )
=> ( ( ! [X642: $i] :
( ( in @ X642 @ nat )
=> ( ( X645
= ( n_pl @ X644 @ X642 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ( ( ! [X642: $i] :
( ( in @ X642 @ nat )
=> ( ( X645
= ( n_pl @ X644 @ X642 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ! [X643: $i] :
( ( in @ X643 @ nat )
=> ( ( X644
= ( n_pl @ X645 @ X643 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ! [X643: $i] :
( ( in @ X643 @ nat )
=> ( ( X644
= ( n_pl @ X645 @ X643 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( X645 = X644 )
=> ~ $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_56]),c_0_49]),c_0_54]) ).
thf(c_0_61,negated_conjecture,
~ ( 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 ) ) ) ),
inference(assume_negation,[status(cth)],[satz25b]) ).
thf(c_0_62,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X517: $i] :
( ( in @ X517 @ nat )
=> ( ( Z1
= ( n_pl @ Z0 @ X517 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_57,c_0_44]),c_0_49]),c_0_58]) ).
thf(c_0_63,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X516: $i] :
( ( in @ X516 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X516 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_64,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X512: $i] :
( ( in @ X512 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X512 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_59,c_0_54]),c_0_55]) ).
thf(c_0_65,plain,
! [X1426: $i,X1427: $i,X1430: $i,X1431: $i,X1432: $i,X1433: $i] :
( ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| ( X1426
= ( n_pl @ X1427 @ ( esk34_2 @ X1426 @ X1427 ) ) )
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| ( X1426
= ( n_pl @ X1427 @ ( esk34_2 @ X1426 @ X1427 ) ) )
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ( X1426
= ( n_pl @ X1427 @ ( esk34_2 @ X1426 @ X1427 ) ) )
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| $true
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| $true
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| $true
| ( X1426 = X1427 )
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| ( X1426
= ( n_pl @ X1427 @ ( esk34_2 @ X1426 @ X1427 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| ( X1426
= ( n_pl @ X1427 @ ( esk34_2 @ X1426 @ X1427 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ( X1426
= ( n_pl @ X1427 @ ( esk34_2 @ X1426 @ X1427 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( in @ ( esk35_2 @ X1426 @ X1427 ) @ nat )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ( X1427
= ( n_pl @ X1426 @ ( esk35_2 @ X1426 @ X1427 ) ) )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ~ ( in @ X1430 @ nat )
| ( X1426
!= ( n_pl @ X1427 @ X1430 ) )
| ~ $true
| ~ $true
| ( X1426 != X1427 )
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ( X1426 != X1427 )
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ~ ( in @ X1432 @ nat )
| ( X1427
!= ( n_pl @ X1426 @ X1432 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1431 @ nat )
| ( X1426
!= ( n_pl @ X1427 @ X1431 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1431 @ nat )
| ( X1426
!= ( n_pl @ X1427 @ X1431 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ~ ( in @ X1432 @ nat )
| ( X1427
!= ( n_pl @ X1426 @ X1432 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( ~ ( in @ X1433 @ nat )
| ( X1427
!= ( n_pl @ X1426 @ X1433 ) )
| ~ $true
| ( X1426 != X1427 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ( X1426 != X1427 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1427 @ nat )
| ~ ( in @ X1426 @ 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_60])])])])])]) ).
thf(c_0_66,negated_conjecture,
~ ! [X931: $i] :
( ( in @ X931 @ nat )
=> ! [X930: $i] :
( ( in @ X930 @ nat )
=> ( ( ! [X928: $i] :
( ( in @ X928 @ nat )
=> ( ( X931
= ( n_pl @ X930 @ X928 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ! [X929: $i] :
( ( in @ X929 @ nat )
=> ( ( X931
= ( n_pl @ ( n_pl @ X930 @ n_1 ) @ X929 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( ( n_pl @ X930 @ n_1 )
= X931 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_61]),c_0_40]),c_0_58]),c_0_62]) ).
thf(c_0_67,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X516: $i] :
( ( in @ X516 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X516 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_63,c_0_44]),c_0_49]),c_0_64]) ).
thf(c_0_68,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_65]) ).
thf(c_0_69,negated_conjecture,
! [X1727: $i] :
( ( in @ esk94_0 @ nat )
& ( in @ esk95_0 @ nat )
& ( ( in @ esk96_0 @ nat )
| ~ $true )
& ( ( esk94_0
= ( n_pl @ esk95_0 @ esk96_0 ) )
| ~ $true )
& ( $true
| ~ $true )
& ( ~ ( in @ X1727 @ nat )
| ( esk94_0
!= ( n_pl @ ( n_pl @ esk95_0 @ n_1 ) @ X1727 ) )
| ~ $true
| ~ $true )
& ( $true
| ~ $true )
& ( ( n_pl @ esk95_0 @ n_1 )
!= esk94_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_66])])])])])]) ).
thf(c_0_70,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_65]) ).
thf(c_0_71,plain,
! [X743: $i] :
( ( in @ X743 @ nat )
=> ! [X742: $i] :
( ( in @ X742 @ nat )
=> ! [X741: $i] :
( ( in @ X741 @ nat )
=> ( ( ! [X738: $i] :
( ( in @ X738 @ nat )
=> ( ( X743
= ( n_pl @ X742 @ X738 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ( ! [X739: $i] :
( ( in @ X739 @ nat )
=> ( ( X742
= ( n_pl @ X741 @ X739 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X742 = X741 ) )
=> ( ! [X740: $i] :
( ( in @ X740 @ nat )
=> ( ( X743
= ( n_pl @ X741 @ X740 ) )
=> ~ $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_64]),c_0_67]) ).
thf(c_0_72,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_68]) ).
thf(c_0_73,negated_conjecture,
( ( esk94_0
= ( n_pl @ esk95_0 @ esk96_0 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_74,negated_conjecture,
( ( in @ esk96_0 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_75,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_70]) ).
thf(c_0_76,plain,
! [X749: $i] :
( ( in @ X749 @ nat )
=> ! [X748: $i] :
( ( in @ X748 @ nat )
=> ! [X747: $i] :
( ( in @ X747 @ nat )
=> ( ( ( ( ! [X744: $i] :
( ( in @ X744 @ nat )
=> ( ( X748
= ( n_pl @ X749 @ X744 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X749 = X748 ) )
=> ( ( ( ( ! [X745: $i] :
( ( in @ X745 @ nat )
=> ( ( X747
= ( n_pl @ X748 @ X745 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X748 = X747 ) )
=> ( ( ( ! [X746: $i] :
( ( in @ X746 @ nat )
=> ( ( X747
= ( n_pl @ X749 @ X746 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X749 = X747 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz17]),c_0_40]),c_0_62]) ).
thf(c_0_77,plain,
! [X1534: $i,X1535: $i,X1536: $i,X1537: $i,X1538: $i] :
( ( ( in @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) @ nat )
| ~ $true
| ~ ( in @ X1538 @ nat )
| ( X1535
!= ( n_pl @ X1536 @ X1538 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( X1534
= ( n_pl @ X1536 @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) ) )
| ~ $true
| ~ ( in @ X1538 @ nat )
| ( X1535
!= ( n_pl @ X1536 @ X1538 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1538 @ nat )
| ( X1535
!= ( n_pl @ X1536 @ X1538 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( in @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( X1534
= ( n_pl @ X1536 @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( in @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) @ nat )
| ~ $true
| ( X1535 != X1536 )
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( X1534
= ( n_pl @ X1536 @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) ) )
| ~ $true
| ( X1535 != X1536 )
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( $true
| ~ $true
| ( X1535 != X1536 )
| ~ ( in @ X1537 @ nat )
| ( X1534
!= ( n_pl @ X1535 @ X1537 ) )
| ~ $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( in @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) @ nat )
| ~ $true
| ~ ( in @ X1538 @ nat )
| ( X1535
!= ( n_pl @ X1536 @ X1538 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( X1534
= ( n_pl @ X1536 @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) ) )
| ~ $true
| ~ ( in @ X1538 @ nat )
| ( X1535
!= ( n_pl @ X1536 @ X1538 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1538 @ nat )
| ( X1535
!= ( n_pl @ X1536 @ X1538 ) )
| ~ $true
| ~ $true
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( in @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) @ nat )
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( X1534
= ( n_pl @ X1536 @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) ) )
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( in @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) @ nat )
| ~ $true
| ( X1535 != X1536 )
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( ( X1534
= ( n_pl @ X1536 @ ( esk58_3 @ X1534 @ X1535 @ X1536 ) ) )
| ~ $true
| ( X1535 != X1536 )
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ nat ) )
& ( $true
| ~ $true
| ( X1535 != X1536 )
| $true
| ~ ( in @ X1536 @ nat )
| ~ ( in @ X1535 @ nat )
| ~ ( in @ X1534 @ 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_71])])])])])]) ).
thf(c_0_78,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_72]) ).
thf(c_0_79,negated_conjecture,
( esk94_0
= ( n_pl @ esk95_0 @ esk96_0 ) ),
inference(cn,[status(thm)],[c_0_73]) ).
thf(c_0_80,negated_conjecture,
in @ esk94_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_81,negated_conjecture,
in @ esk96_0 @ nat,
inference(cn,[status(thm)],[c_0_74]) ).
thf(c_0_82,negated_conjecture,
in @ esk95_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_83,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_65]) ).
thf(c_0_84,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_75]) ).
thf(c_0_85,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_65]) ).
thf(c_0_86,plain,
! [X923: $i] :
( ( in @ X923 @ nat )
=> ! [X922: $i] :
( ( in @ X922 @ nat )
=> ( ( ! [X920: $i] :
( ( in @ X920 @ nat )
=> ( ( X922
= ( n_pl @ X923 @ X920 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ( ! [X921: $i] :
( ( in @ X921 @ nat )
=> ( ( X922
= ( n_pl @ ( n_pl @ X923 @ n_1 ) @ X921 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X922
= ( n_pl @ X923 @ n_1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz25]),c_0_40]),c_0_64]),c_0_67]) ).
thf(c_0_87,plain,
! [X1540: $i,X1541: $i,X1542: $i,X1543: $i,X1544: $i] :
( ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ~ ( in @ X1543 @ nat )
| ( X1541
!= ( n_pl @ X1540 @ X1543 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| $true
| ~ $true
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| ~ ( in @ X1544 @ nat )
| ( X1542
!= ( n_pl @ X1541 @ X1544 ) )
| ~ $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| $true
| ~ $true
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( in @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) @ nat )
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( ( X1542
= ( n_pl @ X1540 @ ( esk59_3 @ X1540 @ X1541 @ X1542 ) ) )
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ~ $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ nat ) )
& ( $true
| ( X1540 = X1542 )
| ( X1541 != X1542 )
| ( X1540 != X1541 )
| ~ ( in @ X1542 @ nat )
| ~ ( in @ X1541 @ nat )
| ~ ( in @ X1540 @ 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_88,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_77]) ).
thf(c_0_89,negated_conjecture,
! [X1: $i] :
( ( ( n_pl @ esk94_0 @ X1 )
!= esk95_0 )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_81]),c_0_82])]) ).
thf(c_0_90,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_83]) ).
thf(c_0_91,negated_conjecture,
esk95_0 != esk94_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_79]),c_0_80]),c_0_82]),c_0_81])]) ).
thf(c_0_92,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk35_2 @ X1 @ X4 ) @ nat )
| ( X1
= ( n_pl @ X4 @ ( esk34_2 @ X1 @ X4 ) ) )
| ( X1 = X4 )
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_93,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( X1
= ( n_pl @ X4 @ ( esk35_2 @ X4 @ X1 ) ) )
| ( in @ ( esk34_2 @ X4 @ X1 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_85]) ).
thf(c_0_94,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk35_2 @ X1 @ X4 ) @ nat )
| ( in @ ( esk34_2 @ X1 @ X4 ) @ nat )
| ( X1 = X4 )
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_95,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk58_3 @ X1 @ X4 @ X5 ) @ nat )
| ~ $true
| ( X4 != X5 )
| ~ ( in @ X6 @ nat )
| ( X1
!= ( n_pl @ X4 @ X6 ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_96,plain,
! [X1716: $i,X1717: $i,X1718: $i] :
( ( ( in @ ( esk92_2 @ X1716 @ X1717 ) @ nat )
| ~ $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| ~ ( in @ X1718 @ nat )
| ( X1717
!= ( n_pl @ X1716 @ X1718 ) )
| ~ $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ nat ) )
& ( ( X1717
= ( n_pl @ ( n_pl @ X1716 @ n_1 ) @ ( esk92_2 @ X1716 @ X1717 ) ) )
| ~ $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| ~ ( in @ X1718 @ nat )
| ( X1717
!= ( n_pl @ X1716 @ X1718 ) )
| ~ $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ nat ) )
& ( $true
| ~ $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| ~ ( in @ X1718 @ nat )
| ( X1717
!= ( n_pl @ X1716 @ X1718 ) )
| ~ $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ nat ) )
& ( $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| ~ ( in @ X1718 @ nat )
| ( X1717
!= ( n_pl @ X1716 @ X1718 ) )
| ~ $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ nat ) )
& ( ( in @ ( esk92_2 @ X1716 @ X1717 ) @ nat )
| ~ $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ nat ) )
& ( ( X1717
= ( n_pl @ ( n_pl @ X1716 @ n_1 ) @ ( esk92_2 @ X1716 @ X1717 ) ) )
| ~ $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ nat ) )
& ( $true
| ~ $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ nat ) )
& ( $true
| ( X1717
= ( n_pl @ X1716 @ n_1 ) )
| $true
| ~ ( in @ X1717 @ nat )
| ~ ( in @ X1716 @ 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_86])])])])])]) ).
thf(c_0_97,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_87]) ).
thf(c_0_98,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_88]) ).
thf(c_0_99,negated_conjecture,
( ( ( n_pl @ esk95_0 @ ( esk34_2 @ esk94_0 @ esk95_0 ) )
= esk94_0 )
| ~ ( in @ ( esk35_2 @ esk94_0 @ esk95_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_89,c_0_90]),c_0_80])])]),c_0_82])]),c_0_91]) ).
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_92]) ).
thf(c_0_101,negated_conjecture,
( ( in @ ( esk34_2 @ esk94_0 @ esk95_0 ) @ nat )
| ~ ( in @ ( esk35_2 @ esk94_0 @ esk95_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_89,c_0_93]),c_0_80])])]),c_0_82])]),c_0_91]) ).
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_94]) ).
thf(c_0_103,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk58_3 @ X1 @ X4 @ X5 ) @ nat )
| ( X4 != X5 )
| ( X1
!= ( n_pl @ X4 @ X6 ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_95]) ).
thf(c_0_104,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_87]) ).
thf(c_0_105,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( X1
= ( n_pl @ ( n_pl @ X4 @ n_1 ) @ ( esk92_2 @ X4 @ X1 ) ) )
| ( X1
= ( n_pl @ X4 @ n_1 ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
thf(c_0_106,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_97]) ).
thf(c_0_107,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_98])]) ).
thf(c_0_108,negated_conjecture,
( ( n_pl @ esk95_0 @ ( esk34_2 @ esk94_0 @ esk95_0 ) )
= esk94_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_82]),c_0_80])]),c_0_91]) ).
thf(c_0_109,negated_conjecture,
in @ ( esk34_2 @ esk94_0 @ esk95_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_82]),c_0_80])]),c_0_91]) ).
thf(c_0_110,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_103])]) ).
thf(c_0_111,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_104]) ).
thf(c_0_112,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk92_2 @ X1 @ X4 ) @ nat )
| ( X4
= ( n_pl @ X1 @ n_1 ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ( X4
!= ( n_pl @ X1 @ X5 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
thf(c_0_113,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( esk94_0
!= ( n_pl @ ( n_pl @ esk95_0 @ n_1 ) @ X1 ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_114,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1
= ( n_pl @ X4 @ n_1 ) )
| ( X1
= ( n_pl @ ( n_pl @ X4 @ n_1 ) @ ( esk92_2 @ X4 @ X1 ) ) )
| ( X1
!= ( n_pl @ X4 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_105]) ).
thf(c_0_115,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(split_conjunct,[status(thm)],[def_n_1]) ).
thf(c_0_116,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_106])]),c_0_84]) ).
thf(c_0_117,negated_conjecture,
( ( n_pl @ esk95_0 @ ( esk58_3 @ esk94_0 @ esk95_0 @ esk95_0 ) )
= esk94_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_80]),c_0_109]),c_0_82])]) ).
thf(c_0_118,negated_conjecture,
in @ ( esk58_3 @ esk94_0 @ esk95_0 @ esk95_0 ) @ nat,
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_79]),c_0_80]),c_0_81]),c_0_82])]) ).
thf(c_0_119,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_111])]),c_0_84]) ).
thf(c_0_120,negated_conjecture,
( ( n_pl @ esk95_0 @ n_1 )
!= esk94_0 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_121,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X4
= ( n_pl @ X1 @ n_1 ) )
| ( in @ ( esk92_2 @ X1 @ X4 ) @ nat )
| ( X4
!= ( n_pl @ X1 @ X5 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_112]) ).
thf(c_0_122,negated_conjecture,
! [X1: $i] :
( ( esk94_0
!= ( n_pl @ ( n_pl @ esk95_0 @ n_1 ) @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_113]) ).
thf(c_0_123,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) @ ( esk92_2 @ X1 @ ( n_pl @ X1 @ X4 ) ) )
= ( n_pl @ X1 @ X4 ) )
| ( ( n_pl @ X1 @ X4 )
= ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) )
| ~ ( 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_114,c_0_115]),c_0_115])]) ).
thf(c_0_124,negated_conjecture,
( ( n_pl @ esk95_0 @ ( esk59_3 @ esk95_0 @ esk94_0 @ esk94_0 ) )
= esk94_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_80]),c_0_118]),c_0_82])]) ).
thf(c_0_125,negated_conjecture,
in @ ( esk59_3 @ esk95_0 @ esk94_0 @ esk94_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_117]),c_0_80]),c_0_118]),c_0_82])]) ).
thf(c_0_126,negated_conjecture,
( ( n_pl @ esk95_0 @ ( ordsucc @ emptyset ) )
!= esk94_0 ),
inference(rw,[status(thm)],[c_0_120,c_0_115]) ).
thf(c_0_127,plain,
! [X4: $i,X1: $i] :
( ( ( n_pl @ X1 @ X4 )
= ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) )
| ( in @ ( esk92_2 @ X1 @ ( n_pl @ X1 @ X4 ) ) @ nat )
| ~ ( in @ ( n_pl @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_115])]) ).
thf(c_0_128,negated_conjecture,
! [X1: $i] :
( ( ( n_pl @ ( n_pl @ esk95_0 @ ( ordsucc @ emptyset ) ) @ X1 )
!= esk94_0 )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_122,c_0_115]) ).
thf(c_0_129,negated_conjecture,
( ( n_pl @ ( n_pl @ esk95_0 @ ( ordsucc @ emptyset ) ) @ ( esk92_2 @ esk95_0 @ esk94_0 ) )
= esk94_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_123,c_0_124]),c_0_80]),c_0_125]),c_0_82])]),c_0_126]) ).
thf(c_0_130,negated_conjecture,
in @ ( esk92_2 @ esk95_0 @ esk94_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_127,c_0_117]),c_0_80]),c_0_118]),c_0_82])]),c_0_126]) ).
thf(c_0_131,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM698^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n010.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 12:41:33 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.23/0.26 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.XKgyoByQWj/E---3.1_2796015.p
% 18.09/2.96 % Version: 3.5.1-ho
% 18.09/2.96 % Preprocessing class: HSLMSMSSLLLCHSA.
% 18.09/2.96 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 18.09/2.96 % Starting lpo1_fix with 900s (3) cores
% 18.09/2.96 % Starting full_lambda_9 with 300s (1) cores
% 18.09/2.96 % Starting almost_fo_4 with 300s (1) cores
% 18.09/2.96 % Starting new_ho_9 with 300s (1) cores
% 18.09/2.96 % Starting pre_casc_4 with 300s (1) cores
% 18.09/2.96 % Starting ho_unfolding_6 with 300s (1) cores
% 18.09/2.96 % lpo1_fix with pid 2796063 completed with status 0
% 18.09/2.96 % Result found by lpo1_fix
% 18.09/2.96 % Preprocessing class: HSLMSMSSLLLCHSA.
% 18.09/2.96 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 18.09/2.96 % Starting lpo1_fix with 900s (3) cores
% 18.09/2.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.09/2.96 % No SInE strategy applied
% 18.09/2.96 % Search class: HGHSM-FSLM32-MHSMMSBN
% 18.09/2.96 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 18.09/2.96 % Starting SubtermCWHack with 91s (1) cores
% 18.09/2.96 % Starting full_lambda_5 with 82s (1) cores
% 18.09/2.96 % Starting new_ho_6 with 82s (1) cores
% 18.09/2.96 % full_lambda_5 with pid 2796103 completed with status 0
% 18.09/2.96 % Result found by full_lambda_5
% 18.09/2.96 % Preprocessing class: HSLMSMSSLLLCHSA.
% 18.09/2.96 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 18.09/2.96 % Starting lpo1_fix with 900s (3) cores
% 18.09/2.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.09/2.96 % No SInE strategy applied
% 18.09/2.96 % Search class: HGHSM-FSLM32-MHSMMSBN
% 18.09/2.96 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 18.09/2.96 % Starting SubtermCWHack with 91s (1) cores
% 18.09/2.96 % Starting full_lambda_5 with 82s (1) cores
% 18.09/2.96 % Preprocessing time : 0.015 s
% 18.09/2.96 % Presaturation interreduction done
% 18.09/2.96
% 18.09/2.96 % Proof found!
% 18.09/2.96 % SZS status Theorem
% 18.09/2.96 % SZS output start CNFRefutation
% See solution above
% 18.09/2.97 % Parsed axioms : 403
% 18.09/2.97 % Removed by relevancy pruning/SinE : 0
% 18.09/2.97 % Initial clauses : 1192
% 18.09/2.97 % Removed in clause preprocessing : 733
% 18.09/2.97 % Initial clauses in saturation : 459
% 18.09/2.97 % Processed clauses : 2361
% 18.09/2.97 % ...of these trivial : 132
% 18.09/2.97 % ...subsumed : 517
% 18.09/2.97 % ...remaining for further processing : 1712
% 18.09/2.97 % Other redundant clauses eliminated : 863
% 18.09/2.97 % Clauses deleted for lack of memory : 0
% 18.09/2.97 % Backward-subsumed : 43
% 18.09/2.97 % Backward-rewritten : 212
% 18.09/2.97 % Generated clauses : 36605
% 18.09/2.97 % ...of the previous two non-redundant : 35299
% 18.09/2.97 % ...aggressively subsumed : 0
% 18.09/2.97 % Contextual simplify-reflections : 48
% 18.09/2.97 % Paramodulations : 35529
% 18.09/2.97 % Factorizations : 2
% 18.09/2.97 % NegExts : 11
% 18.09/2.97 % Equation resolutions : 877
% 18.09/2.97 % Disequality decompositions : 0
% 18.09/2.97 % Total rewrite steps : 19919
% 18.09/2.97 % ...of those cached : 19436
% 18.09/2.97 % Propositional unsat checks : 0
% 18.09/2.97 % Propositional check models : 0
% 18.09/2.97 % Propositional check unsatisfiable : 0
% 18.09/2.97 % Propositional clauses : 0
% 18.09/2.97 % Propositional clauses after purity: 0
% 18.09/2.97 % Propositional unsat core size : 0
% 18.09/2.97 % Propositional preprocessing time : 0.000
% 18.09/2.97 % Propositional encoding time : 0.000
% 18.09/2.97 % Propositional solver time : 0.000
% 18.09/2.97 % Success case prop preproc time : 0.000
% 18.09/2.97 % Success case prop encoding time : 0.000
% 18.09/2.97 % Success case prop solver time : 0.000
% 18.09/2.97 % Current number of processed clauses : 906
% 18.09/2.97 % Positive orientable unit clauses : 191
% 18.09/2.97 % Positive unorientable unit clauses: 5
% 18.09/2.97 % Negative unit clauses : 181
% 18.09/2.97 % Non-unit-clauses : 529
% 18.09/2.97 % Current number of unprocessed clauses: 33407
% 18.09/2.97 % ...number of literals in the above : 198860
% 18.09/2.97 % Current number of archived formulas : 0
% 18.09/2.97 % Current number of archived clauses : 676
% 18.09/2.97 % Clause-clause subsumption calls (NU) : 214333
% 18.09/2.97 % Rec. Clause-clause subsumption calls : 41778
% 18.09/2.97 % Non-unit clause-clause subsumptions : 297
% 18.09/2.97 % Unit Clause-clause subsumption calls : 14887
% 18.09/2.97 % Rewrite failures with RHS unbound : 0
% 18.09/2.97 % BW rewrite match attempts : 161
% 18.09/2.97 % BW rewrite match successes : 65
% 18.09/2.97 % Condensation attempts : 0
% 18.09/2.97 % Condensation successes : 0
% 18.09/2.97 % Termbank termtop insertions : 1206865
% 18.09/2.97 % Search garbage collected termcells : 48668
% 18.09/2.97
% 18.09/2.97 % -------------------------------------------------
% 18.09/2.97 % User time : 2.506 s
% 18.09/2.97 % System time : 0.082 s
% 18.09/2.97 % Total time : 2.588 s
% 18.09/2.97 % Maximum resident set size: 10456 pages
% 18.09/2.97
% 18.09/2.97 % -------------------------------------------------
% 18.09/2.97 % User time : 7.096 s
% 18.09/2.97 % System time : 0.243 s
% 18.09/2.97 % Total time : 7.338 s
% 18.09/2.97 % Maximum resident set size: 5632 pages
% 18.09/2.97 % E exiting
%------------------------------------------------------------------------------