%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM659^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:16:44 AM UTC 2026
% Result : Theorem 0.22s 0.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 340 ( 94 equ; 0 cnn)
% Maximal formula atoms : 63 ( 5 avg)
% Number of connectives : 752 ( 113 ~; 102 |; 14 &; 465 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 154 ( 110 ^; 44 !; 0 ?; 154 :)
% 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_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_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_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_153,type,
lessis: $i > $i > $o ).
thf(decl_154,type,
esk1_0: $i ).
thf(decl_155,type,
esk2_0: $i ).
thf(decl_160,type,
esk7_2: $i > $i > $i ).
thf(decl_161,type,
esk8_2: $i > $i > $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_imp) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_e_is) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X1: $i,X2: $i > $o] :
( d_not
@ ( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ( non @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_l_some) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_l_or) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_iii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X307: $i] :
( ( in @ X307 @ nat )
=> ( non @ nat @ Z0 @ X307 ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.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/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_lessis) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',def_d_29_ii) ).
thf(satz10k,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X249: $i] : ( in @ X249 @ nat )
@ ^ [X250: $i] :
( ( d_not @ ( lessis @ X1 @ X250 ) )
=> ( d_29_ii @ X1 @ X250 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',satz10k) ).
thf(satz10e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X239: $i] : ( in @ X239 @ nat )
@ ^ [X240: $i] :
( ( d_not @ ( d_29_ii @ X1 @ X240 ) )
=> ( lessis @ X1 @ X240 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p',satz10e) ).
thf(c_0_15,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_16,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_17,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_18,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_19,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_20,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X306: $i] :
( ( in @ X306 @ Z0 )
=> ( non @ Z0 @ Z1 @ X306 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_21,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_22,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_24,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_19]) ).
thf(c_0_25,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X306: $i] :
( ( in @ X306 @ Z0 )
=> ( non @ Z0 @ Z1 @ X306 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_26,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_27,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X309: $i] :
( ( in @ X309 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X309 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_28,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_29,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X307: $i] :
( ( in @ X307 @ nat )
=> ( non @ nat @ Z0 @ X307 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_25]) ).
thf(c_0_30,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X311: $i] :
( ( in @ X311 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X311 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_31,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26,c_0_16]),c_0_21]) ).
thf(c_0_32,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X309: $i] :
( ( in @ X309 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X309 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_33,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X308: $i] :
( ( in @ X308 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X308 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_34,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X311: $i] :
( ( in @ X311 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X311 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_24]),c_0_31]),c_0_32]) ).
thf(c_0_35,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X308: $i] :
( ( in @ X308 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X308 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_28]),c_0_29]) ).
thf(c_0_36,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X249: $i] : ( in @ X249 @ nat )
@ ^ [X250: $i] :
( ( d_not @ ( lessis @ X1 @ X250 ) )
=> ( d_29_ii @ X1 @ X250 ) ) ) ),
inference(assume_negation,[status(cth)],[satz10k]) ).
thf(c_0_37,plain,
! [X339: $i] :
( ( in @ X339 @ nat )
=> ! [X338: $i] :
( ( in @ X338 @ nat )
=> ( ( ( ! [X336: $i] :
( ( in @ X336 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X339
= ( n_pl @ X338 @ Z0 ) )
@ X336 ) )
=> ~ $true )
=> ~ $true )
=> ( ( ( ! [X337: $i] :
( ( in @ X337 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X338
= ( n_pl @ X339 @ Z0 ) )
@ X337 ) )
=> ~ $true )
=> ~ $true )
=> ( X339 = X338 ) ) ) ) ),
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)],[satz10e]),c_0_34]),c_0_21]),c_0_35]),c_0_22]) ).
thf(c_0_38,negated_conjecture,
~ ! [X315: $i] :
( ( in @ X315 @ nat )
=> ! [X314: $i] :
( ( in @ X314 @ nat )
=> ( ( ( ( ( ! [X312: $i] :
( ( in @ X312 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X314
= ( n_pl @ X315 @ Z0 ) )
@ X312 ) )
=> ~ $true )
=> ~ $true )
=> ( X315 = X314 ) )
=> ~ $true )
=> ( ! [X313: $i] :
( ( in @ X313 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X315
= ( n_pl @ X314 @ Z0 ) )
@ X313 ) )
=> ~ $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)],[c_0_36]),c_0_34]),c_0_21]),c_0_35]),c_0_22]) ).
thf(c_0_39,plain,
! [X458: $i,X459: $i] :
( ( ( in @ ( esk8_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ( X458 = X459 )
| ( in @ ( esk7_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X459
= ( n_pl @ X458 @ Z0 ) )
@ ( esk8_2 @ X458 @ X459 ) )
| ~ $true
| ( X458 = X459 )
| ( in @ ( esk7_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( $true
| ( X458 = X459 )
| ( in @ ( esk7_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ( in @ ( esk8_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ( X458 = X459 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X458
= ( n_pl @ X459 @ Z0 ) )
@ ( esk7_2 @ X458 @ X459 ) )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X459
= ( n_pl @ X458 @ Z0 ) )
@ ( esk8_2 @ X458 @ X459 ) )
| ~ $true
| ( X458 = X459 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X458
= ( n_pl @ X459 @ Z0 ) )
@ ( esk7_2 @ X458 @ X459 ) )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( $true
| ( X458 = X459 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X458
= ( n_pl @ X459 @ Z0 ) )
@ ( esk7_2 @ X458 @ X459 ) )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ( in @ ( esk8_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ( X458 = X459 )
| $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X459
= ( n_pl @ X458 @ Z0 ) )
@ ( esk8_2 @ X458 @ X459 ) )
| ~ $true
| ( X458 = X459 )
| $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( $true
| ( X458 = X459 )
| $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ 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_37])])])])])]) ).
thf(c_0_40,negated_conjecture,
! [X436: $i,X437: $i] :
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( ~ ( in @ X436 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X436 )
| ~ $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true )
& ( ( esk1_0 != esk2_0 )
| ~ $true )
& ( ~ ( in @ X437 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ X437 ) )
& $true ),
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_38])])])])])]) ).
thf(c_0_41,plain,
! [X1: $i,X4: $i] :
( ( X4 = X1 )
| ( in @ ( esk7_2 @ X4 @ X1 ) @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_42,negated_conjecture,
( ( esk1_0 != esk2_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_43,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( in @ ( esk7_2 @ X4 @ X1 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_41]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_45,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_46,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_47,negated_conjecture,
esk2_0 != esk1_0,
inference(cn,[status(thm)],[c_0_42]) ).
thf(c_0_48,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ( X1 = X4 )
| ( in @ ( esk7_2 @ X1 @ X4 ) @ nat )
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_49,plain,
! [X1: $i,X4: $i] :
( ( X4 = X1 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X4
= ( n_pl @ X1 @ Z0 ) )
@ ( esk7_2 @ X4 @ X1 ) )
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_51,negated_conjecture,
( ( in @ ( esk7_2 @ esk2_0 @ esk1_0 ) @ nat )
| ~ ( in @ ( esk8_2 @ esk2_0 @ esk1_0 ) @ nat ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).
thf(c_0_52,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( in @ ( esk7_2 @ X1 @ X4 ) @ nat )
| ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_53,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ( X1 = X4 )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk7_2 @ X1 @ X4 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_54,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X4
= ( n_pl @ X1 @ Z0 ) )
@ ( esk7_2 @ X4 @ X1 ) )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_49]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_50]) ).
thf(c_0_56,negated_conjecture,
in @ ( esk7_2 @ esk2_0 @ esk1_0 ) @ nat,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_46]),c_0_45])]),c_0_47]) ).
thf(c_0_57,plain,
! [X1: $i,X4: $i] :
( ( X1 = X4 )
| ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk7_2 @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_53]) ).
thf(c_0_58,negated_conjecture,
~ ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ ( esk8_2 @ esk2_0 @ esk1_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_54,c_0_55]),c_0_45]),c_0_46]),c_0_56])]),c_0_47]) ).
thf(c_0_59,negated_conjecture,
in @ ( esk8_2 @ esk2_0 @ esk1_0 ) @ nat,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_46]),c_0_45])]),c_0_47]),c_0_56])]) ).
thf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_44]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM659^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n010.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 12:33:18 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.23 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.OF59umdFze/E---3.1_2785902.p
% 0.22/0.40 % Version: 3.5.1-ho
% 0.22/0.40 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.40 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.40 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.40 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.40 % Starting almost_fo_4 with 300s (1) cores
% 0.22/0.40 % Starting new_ho_9 with 300s (1) cores
% 0.22/0.40 % Starting pre_casc_4 with 300s (1) cores
% 0.22/0.40 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.40 % pre_casc_4 with pid 2785937 completed with status 0
% 0.22/0.40 % Result found by pre_casc_4
% 0.22/0.40 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.40 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.40 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.40 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.40 % Starting almost_fo_4 with 300s (1) cores
% 0.22/0.40 % Starting new_ho_9 with 300s (1) cores
% 0.22/0.40 % Starting pre_casc_4 with 300s (1) cores
% 0.22/0.40 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.22/0.40 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.40 % Search class: HGHSM-FSLM31-DHSMMSBN
% 0.22/0.40 % partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.22/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.40 % SubtermCWHack with pid 2785947 completed with status 0
% 0.22/0.40 % Result found by SubtermCWHack
% 0.22/0.40 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.40 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.40 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.40 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.40 % Starting almost_fo_4 with 300s (1) cores
% 0.22/0.40 % Starting new_ho_9 with 300s (1) cores
% 0.22/0.40 % Starting pre_casc_4 with 300s (1) cores
% 0.22/0.40 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.22/0.40 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.40 % Search class: HGHSM-FSLM31-DHSMMSBN
% 0.22/0.40 % partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.22/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.40 % Preprocessing time : 0.005 s
% 0.22/0.40
% 0.22/0.40 % Proof found!
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start CNFRefutation
% See solution above
% 0.22/0.40 % Parsed axioms : 358
% 0.22/0.40 % Removed by relevancy pruning/SinE : 273
% 0.22/0.40 % Initial clauses : 203
% 0.22/0.40 % Removed in clause preprocessing : 73
% 0.22/0.40 % Initial clauses in saturation : 130
% 0.22/0.40 % Processed clauses : 862
% 0.22/0.40 % ...of these trivial : 214
% 0.22/0.40 % ...subsumed : 315
% 0.22/0.40 % ...remaining for further processing : 333
% 0.22/0.40 % Other redundant clauses eliminated : 31
% 0.22/0.40 % Clauses deleted for lack of memory : 0
% 0.22/0.40 % Backward-subsumed : 3
% 0.22/0.40 % Backward-rewritten : 32
% 0.22/0.40 % Generated clauses : 2223
% 0.22/0.40 % ...of the previous two non-redundant : 1686
% 0.22/0.40 % ...aggressively subsumed : 0
% 0.22/0.40 % Contextual simplify-reflections : 3
% 0.22/0.40 % Paramodulations : 2187
% 0.22/0.40 % Factorizations : 2
% 0.22/0.40 % NegExts : 0
% 0.22/0.40 % Equation resolutions : 33
% 0.22/0.40 % Disequality decompositions : 0
% 0.22/0.40 % Total rewrite steps : 1972
% 0.22/0.40 % ...of those cached : 1866
% 0.22/0.40 % Propositional unsat checks : 0
% 0.22/0.40 % Propositional check models : 0
% 0.22/0.40 % Propositional check unsatisfiable : 0
% 0.22/0.40 % Propositional clauses : 0
% 0.22/0.40 % Propositional clauses after purity: 0
% 0.22/0.40 % Propositional unsat core size : 0
% 0.22/0.40 % Propositional preprocessing time : 0.000
% 0.22/0.40 % Propositional encoding time : 0.000
% 0.22/0.40 % Propositional solver time : 0.000
% 0.22/0.40 % Success case prop preproc time : 0.000
% 0.22/0.40 % Success case prop encoding time : 0.000
% 0.22/0.40 % Success case prop solver time : 0.000
% 0.22/0.40 % Current number of processed clauses : 293
% 0.22/0.40 % Positive orientable unit clauses : 107
% 0.22/0.40 % Positive unorientable unit clauses: 0
% 0.22/0.40 % Negative unit clauses : 31
% 0.22/0.40 % Non-unit-clauses : 155
% 0.22/0.40 % Current number of unprocessed clauses: 935
% 0.22/0.40 % ...number of literals in the above : 3921
% 0.22/0.40 % Current number of archived formulas : 0
% 0.22/0.40 % Current number of archived clauses : 35
% 0.22/0.40 % Clause-clause subsumption calls (NU) : 12372
% 0.22/0.40 % Rec. Clause-clause subsumption calls : 3396
% 0.22/0.40 % Non-unit clause-clause subsumptions : 136
% 0.22/0.40 % Unit Clause-clause subsumption calls : 749
% 0.22/0.40 % Rewrite failures with RHS unbound : 0
% 0.22/0.40 % BW rewrite match attempts : 132
% 0.22/0.40 % BW rewrite match successes : 20
% 0.22/0.40 % Condensation attempts : 0
% 0.22/0.40 % Condensation successes : 0
% 0.22/0.40 % Termbank termtop insertions : 64874
% 0.22/0.40 % Search garbage collected termcells : 10723
% 0.22/0.40
% 0.22/0.40 % -------------------------------------------------
% 0.22/0.40 % User time : 0.109 s
% 0.22/0.40 % System time : 0.008 s
% 0.22/0.40 % Total time : 0.117 s
% 0.22/0.40 % Maximum resident set size: 5708 pages
% 0.22/0.40
% 0.22/0.40 % -------------------------------------------------
% 0.22/0.40 % User time : 0.116 s
% 0.22/0.40 % System time : 0.016 s
% 0.22/0.40 % Total time : 0.132 s
% 0.22/0.40 % Maximum resident set size: 5376 pages
% 0.22/0.40 % E exiting
%------------------------------------------------------------------------------