%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM654^4 : 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 : n020.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 08:16:43 AM UTC 2026
% Result : Theorem 0.59s 0.39s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 382 ( 98 equ; 0 cnn)
% Maximal formula atoms : 90 ( 5 avg)
% Number of connectives : 874 ( 133 ~; 121 |; 17 &; 538 @)
% ( 0 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 169 ( 124 ^; 45 !; 0 ?; 169 :)
% 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_74,type,
or3: $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_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.ItqTcFSFxG/E---3.1_986627.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.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.ItqTcFSFxG/E---3.1_986627.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.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.ItqTcFSFxG/E---3.1_986627.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.ItqTcFSFxG/E---3.1_986627.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.ItqTcFSFxG/E---3.1_986627.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',def_l_or) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',def_iii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X297: $i] :
( ( in @ X297 @ nat )
=> ( non @ nat @ Z0 @ X297 ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',def_n_some) ).
thf(def_or3,axiom,
( or3
= ( ^ [X89: $o,X90: $o,X91: $o] : ( l_or @ X89 @ ( l_or @ X90 @ X91 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',def_or3) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',def_d_29_ii) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',def_lessis) ).
thf(satz10e,conjecture,
( 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.ItqTcFSFxG/E---3.1_986627.p',satz10e) ).
thf(satz9a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X215: $i] : ( in @ X215 @ nat )
@ ^ [X216: $i] : ( or3 @ ( n_is @ X1 @ X216 ) @ ( n_some @ ( diffprop @ X1 @ X216 ) ) @ ( n_some @ ( diffprop @ X216 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ItqTcFSFxG/E---3.1_986627.p',satz9a) ).
thf(c_0_16,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_17,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_18,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_19,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_20,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_21,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X296: $i] :
( ( in @ X296 @ Z0 )
=> ( non @ Z0 @ Z1 @ X296 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_22,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_25,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_20]) ).
thf(c_0_26,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X296: $i] :
( ( in @ X296 @ Z0 )
=> ( non @ Z0 @ Z1 @ X296 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_27,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_28,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X299: $i] :
( ( in @ X299 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X299 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_29,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_30,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X297: $i] :
( ( in @ X297 @ nat )
=> ( non @ nat @ Z0 @ X297 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_26]) ).
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_27,c_0_17]),c_0_22]) ).
thf(c_0_33,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X298: $i] :
( ( in @ X298 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X298 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_34,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X300: $i] :
( ( in @ X300 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X300 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_35,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X299: $i] :
( ( in @ X299 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X299 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
thf(c_0_36,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_37,negated_conjecture,
~ ( 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 ) ) ) ),
inference(assume_negation,[status(cth)],[satz10e]) ).
thf(c_0_38,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X298: $i] :
( ( in @ X298 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X298 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_29]),c_0_30]) ).
thf(c_0_39,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X300: $i] :
( ( in @ X300 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X300 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_34,c_0_35]),c_0_25]),c_0_32]) ).
thf(c_0_40,plain,
! [X325: $i] :
( ( in @ X325 @ nat )
=> ! [X324: $i] :
( ( in @ X324 @ nat )
=> ( ( ( X325 = X324 )
=> ~ $true )
=> ( ( ( ! [X322: $i] :
( ( in @ X322 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X325
= ( n_pl @ X324 @ Z0 ) )
@ X322 ) )
=> ~ $true )
=> ~ $true )
=> ( ! [X323: $i] :
( ( in @ X323 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X324
= ( n_pl @ X325 @ Z0 ) )
@ X323 ) )
=> ~ $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)],[satz9a]),c_0_36]),c_0_29]),c_0_30]),c_0_25]),c_0_23]) ).
thf(c_0_41,negated_conjecture,
~ ! [X304: $i] :
( ( in @ X304 @ nat )
=> ! [X303: $i] :
( ( in @ X303 @ nat )
=> ( ( ( ! [X301: $i] :
( ( in @ X301 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X304
= ( n_pl @ X303 @ Z0 ) )
@ X301 ) )
=> ~ $true )
=> ~ $true )
=> ( ( ( ! [X302: $i] :
( ( in @ X302 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X303
= ( n_pl @ X304 @ Z0 ) )
@ X302 ) )
=> ~ $true )
=> ~ $true )
=> ( X304 = X303 ) ) ) ) ),
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_37]),c_0_38]),c_0_22]),c_0_39]),c_0_23]) ).
thf(c_0_42,plain,
! [X418: $i,X419: $i] :
( ( ( in @ ( esk8_2 @ X418 @ X419 ) @ nat )
| ~ $true
| ( in @ ( esk7_2 @ X418 @ X419 ) @ nat )
| ~ $true
| ( X418 = X419 )
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X419
= ( n_pl @ X418 @ Z0 ) )
@ ( esk8_2 @ X418 @ X419 ) )
| ~ $true
| ( in @ ( esk7_2 @ X418 @ X419 ) @ nat )
| ~ $true
| ( X418 = X419 )
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ( in @ ( esk8_2 @ X418 @ X419 ) @ nat )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X418
= ( n_pl @ X419 @ Z0 ) )
@ ( esk7_2 @ X418 @ X419 ) )
| ~ $true
| ( X418 = X419 )
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X419
= ( n_pl @ X418 @ Z0 ) )
@ ( esk8_2 @ X418 @ X419 ) )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X418
= ( n_pl @ X419 @ Z0 ) )
@ ( esk7_2 @ X418 @ X419 ) )
| ~ $true
| ( X418 = X419 )
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ( in @ ( esk8_2 @ X418 @ X419 ) @ nat )
| ~ $true
| $true
| ( X418 = X419 )
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X419
= ( n_pl @ X418 @ Z0 ) )
@ ( esk8_2 @ X418 @ X419 ) )
| ~ $true
| $true
| ( X418 = X419 )
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ( in @ ( esk8_2 @ X418 @ X419 ) @ nat )
| ~ $true
| ( in @ ( esk7_2 @ X418 @ X419 ) @ nat )
| ~ $true
| $true
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X419
= ( n_pl @ X418 @ Z0 ) )
@ ( esk8_2 @ X418 @ X419 ) )
| ~ $true
| ( in @ ( esk7_2 @ X418 @ X419 ) @ nat )
| ~ $true
| $true
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ( in @ ( esk8_2 @ X418 @ X419 ) @ nat )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X418
= ( n_pl @ X419 @ Z0 ) )
@ ( esk7_2 @ X418 @ X419 ) )
| ~ $true
| $true
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X419
= ( n_pl @ X418 @ Z0 ) )
@ ( esk8_2 @ X418 @ X419 ) )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X418
= ( n_pl @ X419 @ Z0 ) )
@ ( esk7_2 @ X418 @ X419 ) )
| ~ $true
| $true
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ( in @ ( esk8_2 @ X418 @ X419 ) @ nat )
| ~ $true
| $true
| $true
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X419
= ( n_pl @ X418 @ Z0 ) )
@ ( esk8_2 @ X418 @ X419 ) )
| ~ $true
| $true
| $true
| ~ ( in @ X419 @ nat )
| ~ ( in @ X418 @ 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_40])])])])])]) ).
thf(c_0_43,negated_conjecture,
! [X393: $i,X394: $i] :
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( ~ ( in @ X393 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ X393 )
| ~ $true )
& ( $true
| ~ $true )
& ( ~ ( in @ X394 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X394 )
| ~ $true )
& ( $true
| ~ $true )
& ( esk1_0 != esk2_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_41])])])])])]) ).
thf(c_0_44,plain,
! [X1: $i,X4: $i] :
( ( in @ ( esk7_2 @ X4 @ X1 ) @ nat )
| ( X4 = X1 )
| ~ ( 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_42]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_46,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_44]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_45]) ).
thf(c_0_48,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_49,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_51,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ( in @ ( esk7_2 @ X1 @ X4 ) @ nat )
| ( X1 = X4 )
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_52,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_42]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_54,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_46,c_0_47]),c_0_48]),c_0_49])]),c_0_50]) ).
thf(c_0_55,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_51]) ).
thf(c_0_56,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_42]) ).
thf(c_0_57,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_52]) ).
thf(c_0_58,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_53]) ).
thf(c_0_59,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_54,c_0_55]),c_0_49]),c_0_48])]),c_0_50]) ).
thf(c_0_60,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_56]) ).
thf(c_0_61,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_57,c_0_58]),c_0_48]),c_0_49]),c_0_59])]),c_0_50]) ).
thf(c_0_62,negated_conjecture,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_58]),c_0_49]),c_0_48]),c_0_59])]),c_0_50]) ).
thf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM654^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:33:19 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.20/0.27 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.ItqTcFSFxG/E---3.1_986627.p
% 0.59/0.39 % Version: 3.5.1-ho
% 0.59/0.39 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.59/0.39 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.39 % Starting lpo1_fix with 900s (3) cores
% 0.59/0.39 % Starting full_lambda_9 with 300s (1) cores
% 0.59/0.39 % Starting almost_fo_4 with 300s (1) cores
% 0.59/0.39 % Starting new_ho_9 with 300s (1) cores
% 0.59/0.39 % Starting pre_casc_4 with 300s (1) cores
% 0.59/0.39 % Starting ho_unfolding_6 with 300s (1) cores
% 0.59/0.39 % pre_casc_4 with pid 986667 completed with status 0
% 0.59/0.39 % Result found by pre_casc_4
% 0.59/0.39 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.59/0.39 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.39 % Starting lpo1_fix with 900s (3) cores
% 0.59/0.39 % Starting full_lambda_9 with 300s (1) cores
% 0.59/0.39 % Starting almost_fo_4 with 300s (1) cores
% 0.59/0.39 % Starting new_ho_9 with 300s (1) cores
% 0.59/0.39 % Starting pre_casc_4 with 300s (1) cores
% 0.59/0.39 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.59/0.39 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.59/0.39 % Search class: HGHSM-FFMM31-DHSMMSBN
% 0.59/0.39 % partial match(2): HGHSM-FFMM31-SHSSMSBN
% 0.59/0.39 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.39 % Starting SubtermCWHack with 28s (1) cores
% 0.59/0.39 % SubtermCWHack with pid 986680 completed with status 0
% 0.59/0.39 % Result found by SubtermCWHack
% 0.59/0.39 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.59/0.39 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.39 % Starting lpo1_fix with 900s (3) cores
% 0.59/0.39 % Starting full_lambda_9 with 300s (1) cores
% 0.59/0.39 % Starting almost_fo_4 with 300s (1) cores
% 0.59/0.39 % Starting new_ho_9 with 300s (1) cores
% 0.59/0.39 % Starting pre_casc_4 with 300s (1) cores
% 0.59/0.39 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.59/0.39 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.59/0.39 % Search class: HGHSM-FFMM31-DHSMMSBN
% 0.59/0.39 % partial match(2): HGHSM-FFMM31-SHSSMSBN
% 0.59/0.39 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.39 % Starting SubtermCWHack with 28s (1) cores
% 0.59/0.39 % Preprocessing time : 0.004 s
% 0.59/0.39
% 0.59/0.39 % Proof found!
% 0.59/0.39 % SZS status Theorem
% 0.59/0.39 % SZS output start CNFRefutation
% See solution above
% 0.59/0.39 % Parsed axioms : 353
% 0.59/0.39 % Removed by relevancy pruning/SinE : 277
% 0.59/0.39 % Initial clauses : 141
% 0.59/0.39 % Removed in clause preprocessing : 33
% 0.59/0.39 % Initial clauses in saturation : 108
% 0.59/0.39 % Processed clauses : 519
% 0.59/0.39 % ...of these trivial : 43
% 0.59/0.39 % ...subsumed : 189
% 0.59/0.39 % ...remaining for further processing : 287
% 0.59/0.39 % Other redundant clauses eliminated : 24
% 0.59/0.39 % Clauses deleted for lack of memory : 0
% 0.59/0.39 % Backward-subsumed : 3
% 0.59/0.39 % Backward-rewritten : 18
% 0.59/0.39 % Generated clauses : 1489
% 0.59/0.39 % ...of the previous two non-redundant : 1254
% 0.59/0.39 % ...aggressively subsumed : 0
% 0.59/0.39 % Contextual simplify-reflections : 3
% 0.59/0.39 % Paramodulations : 1459
% 0.59/0.39 % Factorizations : 2
% 0.59/0.39 % NegExts : 0
% 0.59/0.39 % Equation resolutions : 26
% 0.59/0.39 % Disequality decompositions : 0
% 0.59/0.39 % Total rewrite steps : 347
% 0.59/0.39 % ...of those cached : 270
% 0.59/0.39 % Propositional unsat checks : 0
% 0.59/0.39 % Propositional check models : 0
% 0.59/0.39 % Propositional check unsatisfiable : 0
% 0.59/0.39 % Propositional clauses : 0
% 0.59/0.39 % Propositional clauses after purity: 0
% 0.59/0.39 % Propositional unsat core size : 0
% 0.59/0.39 % Propositional preprocessing time : 0.000
% 0.59/0.39 % Propositional encoding time : 0.000
% 0.59/0.39 % Propositional solver time : 0.000
% 0.59/0.39 % Success case prop preproc time : 0.000
% 0.59/0.39 % Success case prop encoding time : 0.000
% 0.59/0.39 % Success case prop solver time : 0.000
% 0.59/0.39 % Current number of processed clauses : 264
% 0.59/0.39 % Positive orientable unit clauses : 63
% 0.59/0.39 % Positive unorientable unit clauses: 0
% 0.59/0.39 % Negative unit clauses : 23
% 0.59/0.39 % Non-unit-clauses : 178
% 0.59/0.39 % Current number of unprocessed clauses: 832
% 0.59/0.39 % ...number of literals in the above : 2802
% 0.59/0.39 % Current number of archived formulas : 0
% 0.59/0.39 % Current number of archived clauses : 21
% 0.59/0.39 % Clause-clause subsumption calls (NU) : 4772
% 0.59/0.39 % Rec. Clause-clause subsumption calls : 2485
% 0.59/0.39 % Non-unit clause-clause subsumptions : 110
% 0.59/0.39 % Unit Clause-clause subsumption calls : 287
% 0.59/0.39 % Rewrite failures with RHS unbound : 0
% 0.59/0.39 % BW rewrite match attempts : 281
% 0.59/0.39 % BW rewrite match successes : 17
% 0.59/0.39 % Condensation attempts : 0
% 0.59/0.39 % Condensation successes : 0
% 0.59/0.39 % Termbank termtop insertions : 48202
% 0.59/0.39 % Search garbage collected termcells : 7599
% 0.59/0.39
% 0.59/0.39 % -------------------------------------------------
% 0.59/0.39 % User time : 0.064 s
% 0.59/0.39 % System time : 0.015 s
% 0.59/0.39 % Total time : 0.080 s
% 0.59/0.39 % Maximum resident set size: 5436 pages
% 0.59/0.39
% 0.59/0.39 % -------------------------------------------------
% 0.59/0.39 % User time : 0.074 s
% 0.59/0.39 % System time : 0.020 s
% 0.59/0.39 % Total time : 0.094 s
% 0.59/0.39 % Maximum resident set size: 5376 pages
% 0.59/0.39 % E exiting
%------------------------------------------------------------------------------