%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM651^4 : 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 : n018.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 08:16:42 AM UTC 2026
% Result : Theorem 1.00s 0.56s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 98 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 2012 ( 360 equ; 0 cnn)
% Maximal formula atoms : 1256 ( 20 avg)
% Number of connectives : 4138 (1124 ~;1456 |; 216 &;1160 @)
% ( 0 <=>; 182 =>; 0 <=; 0 <~>)
% Maximal formula depth : 190 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 9 con; 0-3 aty)
% Number of variables : 168 ( 121 ^; 47 !; 0 ?; 168 :)
% 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_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_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_189,type,
esk34_2: $i > $i > $i ).
thf(decl_190,type,
esk35_2: $i > $i > $i ).
thf(decl_193,type,
esk38_0: $i ).
thf(decl_194,type,
esk39_0: $i ).
thf(decl_195,type,
esk40_0: $i ).
thf(decl_196,type,
esk41_0: $i ).
thf(decl_197,type,
esk42_0: $i ).
thf(decl_198,type,
esk43_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.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.2aWuu1Civc/E---3.1_12657.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.2aWuu1Civc/E---3.1_12657.p',def_d_and) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.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.2aWuu1Civc/E---3.1_12657.p',def_and3) ).
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.2aWuu1Civc/E---3.1_12657.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.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.2aWuu1Civc/E---3.1_12657.p',def_non) ).
thf(def_or3,axiom,
( or3
= ( ^ [X89: $o,X90: $o,X91: $o] : ( l_or @ X89 @ ( l_or @ X90 @ X91 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.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.2aWuu1Civc/E---3.1_12657.p',def_ec3) ).
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.2aWuu1Civc/E---3.1_12657.p',def_l_some) ).
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.2aWuu1Civc/E---3.1_12657.p',def_orec3) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.p',def_e_is) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.p',def_n_is) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X391: $i] :
( ( in @ X391 @ nat )
=> ( ( Z0 @ X391 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.p',def_n_some) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.p',def_diffprop) ).
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.2aWuu1Civc/E---3.1_12657.p',satz9) ).
thf(satz9b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X217: $i] : ( in @ X217 @ nat )
@ ^ [X218: $i] : ( ec3 @ ( n_is @ X1 @ X218 ) @ ( n_some @ ( diffprop @ X1 @ X218 ) ) @ ( n_some @ ( diffprop @ X218 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aWuu1Civc/E---3.1_12657.p',satz9b) ).
thf(c_0_19,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_20,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_21,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[def_l_ec]) ).
thf(c_0_22,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_and]) ).
thf(c_0_24,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).
thf(c_0_25,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_26,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_27,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
thf(c_0_28,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_29,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_30,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_31,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_or3]) ).
thf(c_0_32,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_20]),c_0_22]) ).
thf(c_0_33,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_34,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_35,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X364: $i] :
( ( in @ X364 @ Z0 )
=> ( ( Z1 @ X364 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_36,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_37,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_30,c_0_22]) ).
thf(c_0_38,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_39,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_40,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_33,c_0_24]),c_0_34]) ).
thf(c_0_41,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_42,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X364: $i] :
( ( in @ X364 @ Z0 )
=> ( ( Z1 @ X364 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_35,c_0_36]),c_0_22]),c_0_37]) ).
thf(c_0_43,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_38,c_0_27]),c_0_39]),c_0_40]) ).
thf(c_0_44,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_41]) ).
thf(c_0_45,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X391: $i] :
( ( in @ X391 @ nat )
=> ( ( Z0 @ X391 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_42]) ).
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,plain,
! [X533: $i] :
( ( in @ X533 @ nat )
=> ! [X532: $i] :
( ( in @ X532 @ nat )
=> ( ( ( ( ( X533 = X532 )
=> ~ $true )
=> ( ( ( ! [X530: $i] :
( ( in @ X530 @ nat )
=> ( ( X533
= ( n_pl @ X532 @ X530 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( ! [X531: $i] :
( ( in @ X531 @ nat )
=> ( ( X532
= ( n_pl @ X533 @ X531 ) )
=> ~ $true ) )
=> ~ $true ) ) )
=> ( ( ( ( ( X533 = X532 )
=> ( ( ! [X530: $i] :
( ( in @ X530 @ nat )
=> ( ( X533
= ( n_pl @ X532 @ X530 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ( ( ! [X530: $i] :
( ( in @ X530 @ nat )
=> ( ( X533
= ( n_pl @ X532 @ X530 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ! [X531: $i] :
( ( in @ X531 @ nat )
=> ( ( X532
= ( n_pl @ X533 @ X531 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ! [X531: $i] :
( ( in @ X531 @ nat )
=> ( ( X532
= ( n_pl @ X533 @ X531 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( X533 = X532 )
=> ~ $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_36]),c_0_43]),c_0_44]),c_0_45]) ).
thf(c_0_48,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X217: $i] : ( in @ X217 @ nat )
@ ^ [X218: $i] : ( ec3 @ ( n_is @ X1 @ X218 ) @ ( n_some @ ( diffprop @ X1 @ X218 ) ) @ ( n_some @ ( diffprop @ X218 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz9b]) ).
thf(c_0_49,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_46,c_0_44]) ).
thf(c_0_50,plain,
! [X1036: $i,X1037: $i,X1040: $i,X1041: $i,X1042: $i,X1043: $i] :
( ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| ( X1036
= ( n_pl @ X1037 @ ( esk34_2 @ X1036 @ X1037 ) ) )
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| ( X1036
= ( n_pl @ X1037 @ ( esk34_2 @ X1036 @ X1037 ) ) )
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ( X1036
= ( n_pl @ X1037 @ ( esk34_2 @ X1036 @ X1037 ) ) )
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| $true
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| $true
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| $true
| ( X1036 = X1037 )
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| ( in @ ( esk34_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| ( in @ ( esk34_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ( in @ ( esk34_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| ( X1036
= ( n_pl @ X1037 @ ( esk34_2 @ X1036 @ X1037 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| ( X1036
= ( n_pl @ X1037 @ ( esk34_2 @ X1036 @ X1037 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ( X1036
= ( n_pl @ X1037 @ ( esk34_2 @ X1036 @ X1037 ) ) )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( in @ ( esk35_2 @ X1036 @ X1037 ) @ nat )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ( X1037
= ( n_pl @ X1036 @ ( esk35_2 @ X1036 @ X1037 ) ) )
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| $true
| $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ~ ( in @ X1040 @ nat )
| ( X1036
!= ( n_pl @ X1037 @ X1040 ) )
| ~ $true
| ~ $true
| ( X1036 != X1037 )
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ( X1036 != X1037 )
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ~ ( in @ X1042 @ nat )
| ( X1037
!= ( n_pl @ X1036 @ X1042 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1041 @ nat )
| ( X1036
!= ( n_pl @ X1037 @ X1041 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1041 @ nat )
| ( X1036
!= ( n_pl @ X1037 @ X1041 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ~ ( in @ X1042 @ nat )
| ( X1037
!= ( n_pl @ X1036 @ X1042 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( ~ ( in @ X1043 @ nat )
| ( X1037
!= ( n_pl @ X1036 @ X1043 ) )
| ~ $true
| ( X1036 != X1037 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ( X1036 != X1037 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ nat ) )
& ( $true
| ~ $true
| ~ ( in @ X1037 @ nat )
| ~ ( in @ X1036 @ 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_47])])])])])]) ).
thf(c_0_51,negated_conjecture,
~ ! [X541: $i] :
( ( in @ X541 @ nat )
=> ! [X540: $i] :
( ( in @ X540 @ nat )
=> ( ( ( ( X541 = X540 )
=> ( ( ! [X538: $i] :
( ( in @ X538 @ nat )
=> ( ( X541
= ( n_pl @ X540 @ X538 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ( ( ! [X538: $i] :
( ( in @ X538 @ nat )
=> ( ( X541
= ( n_pl @ X540 @ X538 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( ! [X539: $i] :
( ( in @ X539 @ nat )
=> ( ( X540
= ( n_pl @ X541 @ X539 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ( ( ( ! [X539: $i] :
( ( in @ X539 @ nat )
=> ( ( X540
= ( n_pl @ X541 @ X539 ) )
=> ~ $true ) )
=> ~ $true )
=> ( ( X541 = X540 )
=> ~ $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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_48]),c_0_36]),c_0_40]),c_0_44]),c_0_45]),c_0_49]) ).
thf(c_0_52,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_50]) ).
thf(c_0_53,negated_conjecture,
( ( in @ esk38_0 @ nat )
& ( in @ esk39_0 @ nat )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( $true
| ~ $true
| ( esk38_0 = esk39_0 ) )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( $true
| ~ $true
| ( in @ esk40_0 @ nat )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ $true
| $true
| ~ $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ( in @ esk41_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ~ $true
| ~ $true
| $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ( in @ esk42_0 @ nat )
| ~ $true
| ~ $true
| $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ~ $true
| ~ $true
| $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ $true
| $true )
& ( ( in @ esk43_0 @ nat )
| ~ $true
| ~ $true
| $true
| ~ $true
| $true )
& ( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ~ $true
| ~ $true
| $true
| ~ $true
| $true )
& ( $true
| ~ $true
| ~ $true
| $true
| ~ $true
| $true )
& ( ( esk38_0 = esk39_0 )
| ~ $true
| $true
| ~ $true
| $true )
& ( $true
| ~ $true
| $true
| ~ $true
| $true )
& ( $true
| ~ $true
| $true )
& $true ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])])]) ).
thf(c_0_54,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_52]) ).
thf(c_0_55,negated_conjecture,
( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_56,negated_conjecture,
( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ( in @ esk41_0 @ nat )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_57,negated_conjecture,
( ( in @ esk43_0 @ nat )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_58,negated_conjecture,
( ( in @ esk43_0 @ nat )
| ( in @ esk41_0 @ nat )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_59,negated_conjecture,
( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( in @ esk40_0 @ nat )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_60,negated_conjecture,
( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ( in @ esk41_0 @ nat )
| ( in @ esk40_0 @ nat )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_61,negated_conjecture,
( ( in @ esk43_0 @ nat )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( in @ esk40_0 @ nat )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_62,negated_conjecture,
( ( in @ esk43_0 @ nat )
| ( in @ esk41_0 @ nat )
| ( in @ esk40_0 @ nat )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_63,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_54]) ).
thf(c_0_64,negated_conjecture,
( ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) ) ),
inference(cn,[status(thm)],[c_0_55]) ).
thf(c_0_65,negated_conjecture,
in @ esk38_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_66,negated_conjecture,
in @ esk39_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_67,negated_conjecture,
( ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ( in @ esk41_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_56]) ).
thf(c_0_68,negated_conjecture,
( ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( in @ esk43_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_57]) ).
thf(c_0_69,negated_conjecture,
( ( esk38_0
= ( n_pl @ esk39_0 @ esk40_0 ) )
| ( in @ esk41_0 @ nat )
| ( in @ esk43_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_58]) ).
thf(c_0_70,negated_conjecture,
( ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ( in @ esk40_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_59]) ).
thf(c_0_71,negated_conjecture,
( ( esk39_0
= ( n_pl @ esk38_0 @ esk43_0 ) )
| ( in @ esk40_0 @ nat )
| ( in @ esk41_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_60]) ).
thf(c_0_72,negated_conjecture,
( ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( in @ esk40_0 @ nat )
| ( in @ esk43_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_61]) ).
thf(c_0_73,negated_conjecture,
( ( in @ esk40_0 @ nat )
| ( in @ esk41_0 @ nat )
| ( in @ esk43_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_62]) ).
thf(c_0_74,negated_conjecture,
( ( ( n_pl @ esk38_0 @ esk43_0 )
= esk39_0 )
| ( ( n_pl @ esk39_0 @ esk40_0 )
= esk38_0 )
| ( esk39_0 != esk38_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66])]),c_0_67]) ).
thf(c_0_75,negated_conjecture,
( ( ( n_pl @ esk39_0 @ esk40_0 )
= esk38_0 )
| ( in @ esk43_0 @ nat )
| ( esk39_0 != esk38_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_68]),c_0_65]),c_0_66])]),c_0_69]) ).
thf(c_0_76,negated_conjecture,
( ( ( n_pl @ esk38_0 @ esk43_0 )
= esk39_0 )
| ( in @ esk40_0 @ nat )
| ( esk39_0 != esk38_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_70]),c_0_65]),c_0_66])]),c_0_71]) ).
thf(c_0_77,negated_conjecture,
( ( in @ esk43_0 @ nat )
| ( in @ esk40_0 @ nat )
| ( esk39_0 != esk38_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_72]),c_0_65]),c_0_66])]),c_0_73]) ).
thf(c_0_78,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_50]) ).
thf(c_0_79,negated_conjecture,
( ( esk38_0 = esk39_0 )
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) )
| ( esk38_0 = esk39_0 )
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_80,negated_conjecture,
( ( ( n_pl @ esk39_0 @ esk40_0 )
= esk38_0 )
| ( esk39_0 != esk38_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_74]),c_0_66]),c_0_65])]),c_0_75]) ).
thf(c_0_81,negated_conjecture,
( ( in @ esk40_0 @ nat )
| ( esk39_0 != esk38_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_76]),c_0_66]),c_0_65])]),c_0_77]) ).
thf(c_0_82,negated_conjecture,
( ( esk38_0 = esk39_0 )
| ( in @ esk42_0 @ nat )
| ( esk38_0 = esk39_0 )
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_83,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_78]) ).
thf(c_0_84,negated_conjecture,
( ( esk39_0 = esk38_0 )
| ( esk39_0
= ( n_pl @ esk38_0 @ esk42_0 ) ) ),
inference(cn,[status(thm)],[c_0_79]) ).
thf(c_0_85,negated_conjecture,
esk39_0 != esk38_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_80]),c_0_65]),c_0_66])]),c_0_81]) ).
thf(c_0_86,negated_conjecture,
( ( esk39_0 = esk38_0 )
| ( in @ esk42_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_82]) ).
thf(c_0_87,negated_conjecture,
( ( esk38_0 = esk39_0 )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) )
| ( esk38_0 = esk39_0 )
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_88,negated_conjecture,
( ( esk38_0 = esk39_0 )
| ( in @ esk41_0 @ nat )
| ( esk38_0 = esk39_0 )
| ~ $true
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_89,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_83]) ).
thf(c_0_90,negated_conjecture,
( ( n_pl @ esk38_0 @ esk42_0 )
= esk39_0 ),
inference(sr,[status(thm)],[c_0_84,c_0_85]) ).
thf(c_0_91,negated_conjecture,
in @ esk42_0 @ nat,
inference(sr,[status(thm)],[c_0_86,c_0_85]) ).
thf(c_0_92,negated_conjecture,
( ( esk39_0 = esk38_0 )
| ( esk38_0
= ( n_pl @ esk39_0 @ esk41_0 ) ) ),
inference(cn,[status(thm)],[c_0_87]) ).
thf(c_0_93,negated_conjecture,
( ( esk39_0 = esk38_0 )
| ( in @ esk41_0 @ nat ) ),
inference(cn,[status(thm)],[c_0_88]) ).
thf(c_0_94,negated_conjecture,
! [X1: $i] :
( ( ( n_pl @ esk39_0 @ X1 )
!= esk38_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_89,c_0_90]),c_0_66]),c_0_91]),c_0_65])]) ).
thf(c_0_95,negated_conjecture,
( ( n_pl @ esk39_0 @ esk41_0 )
= esk38_0 ),
inference(sr,[status(thm)],[c_0_92,c_0_85]) ).
thf(c_0_96,negated_conjecture,
in @ esk41_0 @ nat,
inference(sr,[status(thm)],[c_0_93,c_0_85]) ).
thf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM651^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n018.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 12:34:11 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.35 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.2aWuu1Civc/E---3.1_12657.p
% 1.00/0.56 % Version: 3.5.1-ho
% 1.00/0.56 % Preprocessing class: HSLMSMSSLLLCHSA.
% 1.00/0.56 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.00/0.56 % Starting lpo1_fix with 900s (3) cores
% 1.00/0.56 % Starting full_lambda_9 with 300s (1) cores
% 1.00/0.56 % Starting almost_fo_4 with 300s (1) cores
% 1.00/0.56 % Starting new_ho_9 with 300s (1) cores
% 1.00/0.56 % Starting pre_casc_4 with 300s (1) cores
% 1.00/0.56 % Starting ho_unfolding_6 with 300s (1) cores
% 1.00/0.56 % lpo1_fix with pid 12670 completed with status 0
% 1.00/0.56 % Result found by lpo1_fix
% 1.00/0.56 % Preprocessing class: HSLMSMSSLLLCHSA.
% 1.00/0.56 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.00/0.56 % Starting lpo1_fix with 900s (3) cores
% 1.00/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.00/0.56 % No SInE strategy applied
% 1.00/0.56 % Search class: HGHSM-FSLM32-MHSMMSBN
% 1.00/0.56 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 1.00/0.56 % Starting SubtermCWHack with 91s (1) cores
% 1.00/0.56 % Starting full_lambda_5 with 82s (1) cores
% 1.00/0.56 % Starting new_ho_6 with 82s (1) cores
% 1.00/0.56 % full_lambda_5 with pid 12680 completed with status 0
% 1.00/0.56 % Result found by full_lambda_5
% 1.00/0.56 % Preprocessing class: HSLMSMSSLLLCHSA.
% 1.00/0.56 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.00/0.56 % Starting lpo1_fix with 900s (3) cores
% 1.00/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.00/0.56 % No SInE strategy applied
% 1.00/0.56 % Search class: HGHSM-FSLM32-MHSMMSBN
% 1.00/0.56 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 1.00/0.56 % Starting SubtermCWHack with 91s (1) cores
% 1.00/0.56 % Starting full_lambda_5 with 82s (1) cores
% 1.00/0.56 % Preprocessing time : 0.010 s
% 1.00/0.56 % Presaturation interreduction done
% 1.00/0.56
% 1.00/0.56 % Proof found!
% 1.00/0.56 % SZS status Theorem
% 1.00/0.56 % SZS output start CNFRefutation
% See solution above
% 1.00/0.57 % Parsed axioms : 339
% 1.00/0.57 % Removed by relevancy pruning/SinE : 0
% 1.00/0.57 % Initial clauses : 710
% 1.00/0.57 % Removed in clause preprocessing : 378
% 1.00/0.57 % Initial clauses in saturation : 332
% 1.00/0.57 % Processed clauses : 596
% 1.00/0.57 % ...of these trivial : 4
% 1.00/0.57 % ...subsumed : 47
% 1.00/0.57 % ...remaining for further processing : 545
% 1.00/0.57 % Other redundant clauses eliminated : 65
% 1.00/0.57 % Clauses deleted for lack of memory : 0
% 1.00/0.57 % Backward-subsumed : 35
% 1.00/0.57 % Backward-rewritten : 8
% 1.00/0.57 % Generated clauses : 675
% 1.00/0.57 % ...of the previous two non-redundant : 601
% 1.00/0.57 % ...aggressively subsumed : 0
% 1.00/0.57 % Contextual simplify-reflections : 17
% 1.00/0.57 % Paramodulations : 526
% 1.00/0.57 % Factorizations : 0
% 1.00/0.57 % NegExts : 8
% 1.00/0.57 % Equation resolutions : 68
% 1.00/0.57 % Disequality decompositions : 0
% 1.00/0.57 % Total rewrite steps : 201
% 1.00/0.57 % ...of those cached : 128
% 1.00/0.57 % Propositional unsat checks : 0
% 1.00/0.57 % Propositional check models : 0
% 1.00/0.57 % Propositional check unsatisfiable : 0
% 1.00/0.57 % Propositional clauses : 0
% 1.00/0.57 % Propositional clauses after purity: 0
% 1.00/0.57 % Propositional unsat core size : 0
% 1.00/0.57 % Propositional preprocessing time : 0.000
% 1.00/0.57 % Propositional encoding time : 0.000
% 1.00/0.57 % Propositional solver time : 0.000
% 1.00/0.57 % Success case prop preproc time : 0.000
% 1.00/0.57 % Success case prop encoding time : 0.000
% 1.00/0.57 % Success case prop solver time : 0.000
% 1.00/0.57 % Current number of processed clauses : 183
% 1.00/0.57 % Positive orientable unit clauses : 75
% 1.00/0.57 % Positive unorientable unit clauses: 3
% 1.00/0.57 % Negative unit clauses : 12
% 1.00/0.57 % Non-unit-clauses : 93
% 1.00/0.57 % Current number of unprocessed clauses: 612
% 1.00/0.57 % ...number of literals in the above : 1712
% 1.00/0.57 % Current number of archived formulas : 0
% 1.00/0.57 % Current number of archived clauses : 341
% 1.00/0.57 % Clause-clause subsumption calls (NU) : 12877
% 1.00/0.57 % Rec. Clause-clause subsumption calls : 4396
% 1.00/0.57 % Non-unit clause-clause subsumptions : 66
% 1.00/0.57 % Unit Clause-clause subsumption calls : 1651
% 1.00/0.57 % Rewrite failures with RHS unbound : 0
% 1.00/0.57 % BW rewrite match attempts : 75
% 1.00/0.57 % BW rewrite match successes : 23
% 1.00/0.57 % Condensation attempts : 0
% 1.00/0.57 % Condensation successes : 0
% 1.00/0.57 % Termbank termtop insertions : 69751
% 1.00/0.57 % Search garbage collected termcells : 16605
% 1.00/0.57
% 1.00/0.57 % -------------------------------------------------
% 1.00/0.57 % User time : 0.146 s
% 1.00/0.57 % System time : 0.018 s
% 1.00/0.57 % Total time : 0.164 s
% 1.00/0.57 % Maximum resident set size: 7176 pages
% 1.00/0.57
% 1.00/0.57 % -------------------------------------------------
% 1.00/0.57 % User time : 0.378 s
% 1.00/0.57 % System time : 0.051 s
% 1.00/0.57 % Total time : 0.428 s
% 1.00/0.57 % Maximum resident set size: 5376 pages
% 1.00/0.57 % E exiting
%------------------------------------------------------------------------------