%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM693^4 : 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 : n013.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 08:16:51 AM UTC 2026
% Result : Theorem 2.17s 0.61s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 75 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 266 ( 87 equ; 0 cnn)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 470 ( 83 ~; 50 |; 8 &; 270 @)
% ( 0 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 6 con; 0-3 aty)
% Number of variables : 129 ( 91 ^; 38 !; 0 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_28,type,
emptyset: $i ).
thf(decl_48,type,
ordsucc: $i > $i ).
thf(decl_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
thf(decl_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_126,type,
nis: $i > $i > $o ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_131,type,
n_1: $i ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_152,type,
moreis: $i > $i > $o ).
thf(decl_186,type,
esk29_1: $i > $i ).
thf(decl_245,type,
esk88_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.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/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.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.uqDM4qFkoy/E---3.1_2043654.p',def_non) ).
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.uqDM4qFkoy/E---3.1_2043654.p',def_l_some) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_e_is) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_l_or) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_d_29_ii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X495: $i] :
( ( in @ X495 @ nat )
=> ( ( Z0 @ X495 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_n_some) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_moreis) ).
thf(satz24,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( moreis @ X1 @ n_1 ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',satz24) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_nis) ).
thf(satz6,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X197: $i] : ( in @ X197 @ nat )
@ ^ [X198: $i] : ( n_is @ ( n_pl @ X1 @ X198 ) @ ( n_pl @ X198 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',satz6) ).
thf(n_1_p,axiom,
( is_of @ n_1
@ ^ [X1: $i] : ( in @ X1 @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',n_1_p) ).
thf(satz4e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ X1 @ n_1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',satz4e) ).
thf(satz3,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( nis @ X1 @ n_1 )
=> ( n_some
@ ^ [X175: $i] : ( n_is @ X1 @ ( ordsucc @ X175 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',satz3) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.uqDM4qFkoy/E---3.1_2043654.p',def_n_1) ).
thf(c_0_20,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_21,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_22,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_23,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_24,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_25,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_26,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X468: $i] :
( ( in @ X468 @ Z0 )
=> ( ( Z1 @ X468 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_27,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_28,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_29,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_30,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X468: $i] :
( ( in @ X468 @ Z0 )
=> ( ( Z1 @ X468 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26,c_0_27]),c_0_25]),c_0_28]) ).
thf(c_0_31,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_32,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_29]) ).
thf(c_0_33,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_34,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X506: $i] :
( ( in @ X506 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X506 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_35,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X495: $i] :
( ( in @ X495 @ nat )
=> ( ( Z0 @ X495 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_30]) ).
thf(c_0_36,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_37,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X510: $i] :
( ( in @ X510 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X510 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_38,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_21]),c_0_25]) ).
thf(c_0_39,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X506: $i] :
( ( in @ X506 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X506 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
thf(c_0_40,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( moreis @ X1 @ n_1 ) ),
inference(assume_negation,[status(cth)],[satz24]) ).
thf(c_0_41,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X510: $i] :
( ( in @ X510 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X510 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_37,c_0_38]),c_0_32]),c_0_39]) ).
thf(c_0_42,negated_conjecture,
~ ! [X907: $i] :
( ( in @ X907 @ nat )
=> ( ( ( ! [X906: $i] :
( ( in @ X906 @ nat )
=> ( ( X907
= ( n_pl @ n_1 @ X906 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true )
=> ( X907 = n_1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_40]),c_0_27]),c_0_41]) ).
thf(c_0_43,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_44,negated_conjecture,
! [X1685: $i] :
( ( in @ esk88_0 @ nat )
& ( ~ ( in @ X1685 @ nat )
| ( esk88_0
!= ( n_pl @ n_1 @ X1685 ) )
| ~ $true
| ~ $true )
& ( $true
| ~ $true )
& ( esk88_0 != n_1 ) ),
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_42])])])])])]) ).
thf(c_0_45,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_43,c_0_25]),c_0_32]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( esk88_0
!= ( n_pl @ n_1 @ X1 ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_47,plain,
! [X623: $i] :
( ( in @ X623 @ nat )
=> ! [X622: $i] :
( ( in @ X622 @ nat )
=> ( ( n_pl @ X623 @ X622 )
= ( n_pl @ X622 @ X623 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_27]),c_0_32]) ).
thf(c_0_48,plain,
in @ n_1 @ nat,
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[n_1_p]),c_0_23]) ).
thf(c_0_49,plain,
! [X613: $i] :
( ( in @ X613 @ nat )
=> ( ( ordsucc @ X613 )
= ( n_pl @ X613 @ n_1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4e]),c_0_27]),c_0_32]) ).
thf(c_0_50,plain,
! [X596: $i] :
( ( in @ X596 @ nat )
=> ( ( ( X596 = n_1 )
=> ~ $true )
=> ( ! [X595: $i] :
( ( in @ X595 @ nat )
=> ( ( X596
= ( ordsucc @ X595 ) )
=> ~ $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)],[satz3]),c_0_27]),c_0_32]),c_0_45]),c_0_35]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i] :
( ( esk88_0
!= ( n_pl @ n_1 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_46]) ).
thf(c_0_52,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(split_conjunct,[status(thm)],[def_n_1]) ).
thf(c_0_53,plain,
! [X1388: $i,X1389: $i] :
( ~ ( in @ X1388 @ nat )
| ~ ( in @ X1389 @ nat )
| ( ( n_pl @ X1388 @ X1389 )
= ( n_pl @ X1389 @ X1388 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
thf(c_0_54,plain,
in @ n_1 @ nat,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_55,plain,
! [X1379: $i] :
( ~ ( in @ X1379 @ nat )
| ( ( ordsucc @ X1379 )
= ( n_pl @ X1379 @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
thf(c_0_56,plain,
! [X1357: $i] :
( ( ( in @ ( esk29_1 @ X1357 ) @ nat )
| ~ $true
| ( X1357 = n_1 )
| ~ ( in @ X1357 @ nat ) )
& ( ( X1357
= ( ordsucc @ ( esk29_1 @ X1357 ) ) )
| ~ $true
| ( X1357 = n_1 )
| ~ ( in @ X1357 @ nat ) )
& ( $true
| ~ $true
| ( X1357 = n_1 )
| ~ ( in @ X1357 @ nat ) )
& ( ( in @ ( esk29_1 @ X1357 ) @ nat )
| ~ $true
| $true
| ~ ( in @ X1357 @ nat ) )
& ( ( X1357
= ( ordsucc @ ( esk29_1 @ X1357 ) ) )
| ~ $true
| $true
| ~ ( in @ X1357 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ ( in @ X1357 @ nat ) ) ),
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_50])])])])]) ).
thf(c_0_57,negated_conjecture,
! [X1: $i] :
( ( esk88_0
!= ( n_pl @ ( ordsucc @ emptyset ) @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_58,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
= ( n_pl @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_59,plain,
in @ ( ordsucc @ emptyset ) @ nat,
inference(rw,[status(thm)],[c_0_54,c_0_52]) ).
thf(c_0_60,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ n_1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_61,plain,
! [X1: $i] :
( ( X1
= ( ordsucc @ ( esk29_1 @ X1 ) ) )
| ( X1 = n_1 )
| ~ $true
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i] :
( ( esk88_0
!= ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
thf(c_0_63,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ ( ordsucc @ emptyset ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_60,c_0_52]) ).
thf(c_0_64,plain,
! [X1: $i] :
( ( X1 = n_1 )
| ( X1
= ( ordsucc @ ( esk29_1 @ X1 ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_61]) ).
thf(c_0_65,negated_conjecture,
esk88_0 != n_1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_66,plain,
! [X1: $i] :
( ( in @ ( esk29_1 @ X1 ) @ nat )
| ( X1 = n_1 )
| ~ $true
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i] :
( ( esk88_0
!= ( ordsucc @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_68,plain,
! [X1: $i] :
( ( ( ordsucc @ ( esk29_1 @ X1 ) )
= X1 )
| ( X1
= ( ordsucc @ emptyset ) )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_64,c_0_52]) ).
thf(c_0_69,negated_conjecture,
in @ esk88_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_70,negated_conjecture,
( esk88_0
!= ( ordsucc @ emptyset ) ),
inference(rw,[status(thm)],[c_0_65,c_0_52]) ).
thf(c_0_71,plain,
! [X1: $i] :
( ( X1 = n_1 )
| ( in @ ( esk29_1 @ X1 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_66]) ).
thf(c_0_72,negated_conjecture,
~ ( in @ ( esk29_1 @ esk88_0 ) @ nat ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68])]),c_0_69])]),c_0_70]) ).
thf(c_0_73,plain,
! [X1: $i] :
( ( X1
= ( ordsucc @ emptyset ) )
| ( in @ ( esk29_1 @ X1 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(rw,[status(thm)],[c_0_71,c_0_52]) ).
thf(c_0_74,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_69])]),c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM693^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n013.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 12:40:16 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.24 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.uqDM4qFkoy/E---3.1_2043654.p
% 2.17/0.61 % Version: 3.5.1-ho
% 2.17/0.61 % Preprocessing class: HSLMSMSSLLLCHSA.
% 2.17/0.61 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 2.17/0.61 % Starting lpo1_fix with 900s (3) cores
% 2.17/0.61 % Starting full_lambda_9 with 300s (1) cores
% 2.17/0.61 % Starting almost_fo_4 with 300s (1) cores
% 2.17/0.61 % Starting new_ho_9 with 300s (1) cores
% 2.17/0.61 % Starting pre_casc_4 with 300s (1) cores
% 2.17/0.61 % Starting ho_unfolding_6 with 300s (1) cores
% 2.17/0.61 % lpo1_fix with pid 2043695 completed with status 0
% 2.17/0.61 % Result found by lpo1_fix
% 2.17/0.61 % Preprocessing class: HSLMSMSSLLLCHSA.
% 2.17/0.61 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 2.17/0.61 % Starting lpo1_fix with 900s (3) cores
% 2.17/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.17/0.61 % No SInE strategy applied
% 2.17/0.61 % Search class: HGHSM-FSLM32-MHSMMSBN
% 2.17/0.61 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 2.17/0.61 % Starting SubtermCWHack with 91s (1) cores
% 2.17/0.61 % Starting full_lambda_5 with 82s (1) cores
% 2.17/0.61 % Starting new_ho_6 with 82s (1) cores
% 2.17/0.61 % full_lambda_5 with pid 2043733 completed with status 0
% 2.17/0.61 % Result found by full_lambda_5
% 2.17/0.61 % Preprocessing class: HSLMSMSSLLLCHSA.
% 2.17/0.61 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 2.17/0.61 % Starting lpo1_fix with 900s (3) cores
% 2.17/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.17/0.61 % No SInE strategy applied
% 2.17/0.61 % Search class: HGHSM-FSLM32-MHSMMSBN
% 2.17/0.61 % Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 2.17/0.61 % Starting SubtermCWHack with 91s (1) cores
% 2.17/0.61 % Starting full_lambda_5 with 82s (1) cores
% 2.17/0.61 % Preprocessing time : 0.011 s
% 2.17/0.61 % Presaturation interreduction done
% 2.17/0.61
% 2.17/0.61 % Proof found!
% 2.17/0.61 % SZS status Theorem
% 2.17/0.61 % SZS output start CNFRefutation
% See solution above
% 2.17/0.61 % Parsed axioms : 397
% 2.17/0.61 % Removed by relevancy pruning/SinE : 0
% 2.17/0.61 % Initial clauses : 1158
% 2.17/0.61 % Removed in clause preprocessing : 714
% 2.17/0.61 % Initial clauses in saturation : 444
% 2.17/0.61 % Processed clauses : 971
% 2.17/0.61 % ...of these trivial : 5
% 2.17/0.61 % ...subsumed : 83
% 2.17/0.61 % ...remaining for further processing : 883
% 2.17/0.61 % Other redundant clauses eliminated : 297
% 2.17/0.61 % Clauses deleted for lack of memory : 0
% 2.17/0.61 % Backward-subsumed : 3
% 2.17/0.61 % Backward-rewritten : 9
% 2.17/0.61 % Generated clauses : 3259
% 2.17/0.61 % ...of the previous two non-redundant : 3061
% 2.17/0.61 % ...aggressively subsumed : 0
% 2.17/0.61 % Contextual simplify-reflections : 13
% 2.17/0.61 % Paramodulations : 2855
% 2.17/0.61 % Factorizations : 2
% 2.17/0.61 % NegExts : 10
% 2.17/0.61 % Equation resolutions : 303
% 2.17/0.61 % Disequality decompositions : 0
% 2.17/0.61 % Total rewrite steps : 465
% 2.17/0.61 % ...of those cached : 311
% 2.17/0.61 % Propositional unsat checks : 0
% 2.17/0.61 % Propositional check models : 0
% 2.17/0.61 % Propositional check unsatisfiable : 0
% 2.17/0.61 % Propositional clauses : 0
% 2.17/0.61 % Propositional clauses after purity: 0
% 2.17/0.61 % Propositional unsat core size : 0
% 2.17/0.61 % Propositional preprocessing time : 0.000
% 2.17/0.61 % Propositional encoding time : 0.000
% 2.17/0.61 % Propositional solver time : 0.000
% 2.17/0.61 % Success case prop preproc time : 0.000
% 2.17/0.61 % Success case prop encoding time : 0.000
% 2.17/0.61 % Success case prop solver time : 0.000
% 2.17/0.61 % Current number of processed clauses : 339
% 2.17/0.61 % Positive orientable unit clauses : 97
% 2.17/0.61 % Positive unorientable unit clauses: 4
% 2.17/0.61 % Negative unit clauses : 35
% 2.17/0.61 % Non-unit-clauses : 203
% 2.17/0.61 % Current number of unprocessed clauses: 2934
% 2.17/0.61 % ...number of literals in the above : 9827
% 2.17/0.61 % Current number of archived formulas : 0
% 2.17/0.61 % Current number of archived clauses : 418
% 2.17/0.61 % Clause-clause subsumption calls (NU) : 133668
% 2.17/0.61 % Rec. Clause-clause subsumption calls : 12939
% 2.17/0.61 % Non-unit clause-clause subsumptions : 73
% 2.17/0.61 % Unit Clause-clause subsumption calls : 3761
% 2.17/0.61 % Rewrite failures with RHS unbound : 0
% 2.17/0.61 % BW rewrite match attempts : 88
% 2.17/0.61 % BW rewrite match successes : 18
% 2.17/0.61 % Condensation attempts : 0
% 2.17/0.61 % Condensation successes : 0
% 2.17/0.61 % Termbank termtop insertions : 206503
% 2.17/0.61 % Search garbage collected termcells : 46814
% 2.17/0.61
% 2.17/0.61 % -------------------------------------------------
% 2.17/0.61 % User time : 0.214 s
% 2.17/0.61 % System time : 0.029 s
% 2.17/0.61 % Total time : 0.244 s
% 2.17/0.61 % Maximum resident set size: 10188 pages
% 2.17/0.61
% 2.17/0.61 % -------------------------------------------------
% 2.17/0.61 % User time : 0.531 s
% 2.17/0.61 % System time : 0.062 s
% 2.17/0.61 % Total time : 0.592 s
% 2.17/0.61 % Maximum resident set size: 5376 pages
% 2.17/0.61 % E exiting
%------------------------------------------------------------------------------