%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM667^4 : 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 : n012.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 08:16:46 AM UTC 2026
% Result : Theorem 200.44s 29.19s
% Output : CNFRefutation 200.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 252 ( 114 equ; 0 cnn)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 444 ( 52 ~; 49 |; 9 &; 293 @)
% ( 0 <=>; 39 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 124 ( 105 ^; 19 !; 0 ?; 124 :)
% 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_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_150,type,
iii: $i > $i > $o ).
thf(decl_153,type,
lessis: $i > $i > $o ).
thf(decl_155,type,
esk1_0: $i ).
thf(decl_156,type,
esk2_0: $i ).
thf(decl_157,type,
esk3_0: $i ).
thf(decl_172,type,
esk6_0: $i ).
thf(decl_173,type,
esk7_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.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/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_n_is) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_imp) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_iii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_l_or) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_lessis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_n_some) ).
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.2sgshKTVJ4/E---3.1_36331.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',def_is_of) ).
thf(satz17,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X261: $i] : ( in @ X261 @ nat )
@ ^ [X262: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( lessis @ X1 @ X262 )
=> ( ( lessis @ X262 @ X4 )
=> ( lessis @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',satz17) ).
thf(satz16a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X253: $i] : ( in @ X253 @ nat )
@ ^ [X254: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( lessis @ X1 @ X254 )
=> ( ( iii @ X254 @ X4 )
=> ( iii @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sgshKTVJ4/E---3.1_36331.p',satz16a) ).
thf(c_0_13,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_14,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_15,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_13]) ).
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,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_19,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_21,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_22,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_23,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),def_n_some]) ).
thf(c_0_24,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_17]),c_0_21]) ).
thf(c_0_25,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_26,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_27,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X261: $i] : ( in @ X261 @ nat )
@ ^ [X262: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( lessis @ X1 @ X262 )
=> ( ( lessis @ X262 @ X4 )
=> ( lessis @ X1 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz17]) ).
thf(c_0_28,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22,c_0_23]),c_0_15]),c_0_24]) ).
thf(c_0_29,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,negated_conjecture,
~ ! [X320: $i] :
( ( in @ X320 @ nat )
=> ! [X319: $i] :
( ( in @ X319 @ nat )
=> ! [X318: $i] :
( ( in @ X318 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Z0: $i] :
( X319
= ( n_pl @ X320 @ Z0 ) ) )
=> ~ $true )
=> ( X320 = X319 ) )
=> ( ( ( ( l_some @ nat
@ ^ [Z0: $i] :
( X318
= ( n_pl @ X319 @ Z0 ) ) )
=> ~ $true )
=> ( X319 = X318 ) )
=> ( ( ( l_some @ nat
@ ^ [Z0: $i] :
( X318
= ( n_pl @ X320 @ Z0 ) ) )
=> ~ $true )
=> ( X320 = X318 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_27]),c_0_28]),c_0_29]) ).
thf(c_0_31,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( ( l_some @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) ) )
| ( esk1_0 = esk2_0 ) )
& ( $true
| ( esk1_0 = esk2_0 ) )
& ( ( l_some @ nat
@ ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk2_0 @ Z0 ) ) )
| ( esk2_0 = esk3_0 ) )
& ( $true
| ( esk2_0 = esk3_0 ) )
& ( ~ ( l_some @ nat
@ ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk1_0 @ Z0 ) ) )
| ~ $true )
& ( esk1_0 != esk3_0 ) ),
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_30])])])])]) ).
thf(c_0_32,negated_conjecture,
( ~ ( l_some @ nat
@ ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk1_0 @ Z0 ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_33,plain,
! [X331: $i] :
( ( in @ X331 @ nat )
=> ! [X330: $i] :
( ( in @ X330 @ nat )
=> ! [X329: $i] :
( ( in @ X329 @ nat )
=> ( ( ( ( l_some @ nat
@ ^ [Z0: $i] :
( X330
= ( n_pl @ X331 @ Z0 ) ) )
=> ~ $true )
=> ( X331 = X330 ) )
=> ( ( l_some @ nat
@ ^ [Z0: $i] :
( X329
= ( n_pl @ X330 @ Z0 ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] :
( X329
= ( n_pl @ X331 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz16a]),c_0_23]),c_0_28]),c_0_29]) ).
thf(c_0_34,negated_conjecture,
~ ( l_some @ nat
@ ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk1_0 @ Z0 ) ) ),
inference(cn,[status(thm)],[c_0_32]) ).
thf(c_0_35,negated_conjecture,
( ( l_some @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) ) )
| ( esk1_0 = esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_36,plain,
! [X412: $i,X413: $i,X414: $i] :
( ( ~ ( l_some @ nat
@ ^ [Z0: $i] :
( X413
= ( n_pl @ X412 @ Z0 ) ) )
| ~ $true
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( X414
= ( n_pl @ X413 @ Z0 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] :
( X414
= ( n_pl @ X412 @ Z0 ) ) )
| ~ ( in @ X414 @ nat )
| ~ ( in @ X413 @ nat )
| ~ ( in @ X412 @ nat ) )
& ( ( X412 != X413 )
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( X414
= ( n_pl @ X413 @ Z0 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] :
( X414
= ( n_pl @ X412 @ Z0 ) ) )
| ~ ( in @ X414 @ nat )
| ~ ( in @ X413 @ nat )
| ~ ( in @ X412 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])])]) ).
thf(c_0_37,plain,
( ( esk2_0 = esk1_0 )
| ( ( ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk1_0 @ Z0 ) ) )
!= ( ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) ) ) ) ),
inference(ext_sup,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_38,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] :
( X5
= ( n_pl @ X4 @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) ) )
| ~ $true
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( X5
= ( n_pl @ X1 @ Z0 ) ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_39,plain,
( ( esk2_0 = esk1_0 )
| ( ( esk3_0
= ( n_pl @ esk1_0 @ esk6_0 ) )
<~> ( esk2_0
= ( n_pl @ esk1_0 @ esk6_0 ) ) ) ),
inference(neg_ext,[status(thm)],[c_0_37]) ).
thf(c_0_40,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] :
( X5
= ( n_pl @ X4 @ Z0 ) ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( X5
= ( n_pl @ X1 @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) ) ) ),
inference(cn,[status(thm)],[c_0_38]) ).
thf(c_0_41,negated_conjecture,
( ( l_some @ nat
@ ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk2_0 @ Z0 ) ) )
| ( esk2_0 = esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_42,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_43,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_44,plain,
( ( ( n_pl @ esk1_0 @ esk6_0 )
= esk2_0 )
| ( ( n_pl @ esk1_0 @ esk6_0 )
= esk3_0 )
| ( esk2_0 = esk1_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_39]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i] :
( ( esk3_0 = esk2_0 )
| ( l_some @ nat
@ ^ [Z0: $i] :
( esk3_0
= ( n_pl @ X1 @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ X1 @ Z0 ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
thf(c_0_46,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_47,plain,
( ( esk3_0 = esk2_0 )
| ( ( ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk2_0 @ Z0 ) ) )
!= ( ^ [Z0: $i] :
( esk3_0
= ( n_pl @ esk1_0 @ Z0 ) ) ) ) ),
inference(ext_sup,[status(thm)],[c_0_34,c_0_41]) ).
thf(c_0_48,plain,
( ( ( n_pl @ esk1_0 @ esk6_0 )
= esk2_0 )
| ( esk2_0 = esk1_0 )
| ( esk3_0 != esk2_0 ) ),
inference(ef,[status(thm)],[c_0_44]) ).
thf(c_0_49,negated_conjecture,
( ( esk2_0 = esk1_0 )
| ( esk3_0 = esk2_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_46])]),c_0_34]) ).
thf(c_0_50,plain,
( ( esk3_0 = esk2_0 )
| ( ( esk3_0
= ( n_pl @ esk2_0 @ esk7_0 ) )
<~> ( esk3_0
= ( n_pl @ esk1_0 @ esk7_0 ) ) ) ),
inference(neg_ext,[status(thm)],[c_0_47]) ).
thf(c_0_51,plain,
( ( esk2_0 = esk1_0 )
| ( ( n_pl @ esk1_0 @ esk6_0 )
!= esk3_0 )
| ( ( n_pl @ esk1_0 @ esk6_0 )
!= esk2_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_39]) ).
thf(c_0_52,plain,
( ( ( n_pl @ esk1_0 @ esk6_0 )
= esk2_0 )
| ( esk2_0 = esk1_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_53,plain,
( ( esk3_0 = esk2_0 )
| ( ( n_pl @ esk2_0 @ esk7_0 )
!= esk3_0 )
| ( ( n_pl @ esk1_0 @ esk7_0 )
!= esk3_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_50]) ).
thf(c_0_54,plain,
esk2_0 = esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_49]) ).
thf(c_0_55,negated_conjecture,
esk1_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_56,plain,
( ( ( n_pl @ esk1_0 @ esk7_0 )
= esk3_0 )
| ( ( n_pl @ esk2_0 @ esk7_0 )
= esk3_0 )
| ( esk3_0 = esk2_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_50]) ).
thf(c_0_57,plain,
( ( n_pl @ esk1_0 @ esk7_0 )
!= esk3_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_54])]),c_0_55]) ).
thf(c_0_58,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_54]),c_0_54])]),c_0_55]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM667^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.03 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.14 % Computer : n012.cluster.edu
% 0.05/0.14 % Model : x86_64 x86_64
% 0.05/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.14 % Memory : 8046.5625MB
% 0.05/0.14 % OS : Linux 6.8.0-71-generic
% 0.05/0.14 % CPULimit : 300
% 0.05/0.14 % WCLimit : 300
% 0.05/0.14 % DateTime : Tue Sep 29 12:33:03 UTC 2026
% 0.05/0.14 % CPUTime :
% 0.05/0.14 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.17 Running higher-order theorem proving
% 0.05/0.19 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.2sgshKTVJ4/E---3.1_36331.p
% 200.44/29.19 % Version: 3.5.1-ho
% 200.44/29.19 % Preprocessing class: HSLMSMSSLLLCHSA.
% 200.44/29.19 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 200.44/29.19 % Starting lpo1_fix with 900s (3) cores
% 200.44/29.19 % Starting full_lambda_9 with 300s (1) cores
% 200.44/29.19 % Starting almost_fo_4 with 300s (1) cores
% 200.44/29.19 % Starting new_ho_9 with 300s (1) cores
% 200.44/29.19 % Starting pre_casc_4 with 300s (1) cores
% 200.44/29.19 % Starting ho_unfolding_6 with 300s (1) cores
% 200.44/29.19 % pre_casc_4 with pid 36352 completed with status 0
% 200.44/29.19 % Result found by pre_casc_4
% 200.44/29.19 % Preprocessing class: HSLMSMSSLLLCHSA.
% 200.44/29.19 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 200.44/29.19 % Starting lpo1_fix with 900s (3) cores
% 200.44/29.19 % Starting full_lambda_9 with 300s (1) cores
% 200.44/29.19 % Starting almost_fo_4 with 300s (1) cores
% 200.44/29.19 % Starting new_ho_9 with 300s (1) cores
% 200.44/29.19 % Starting pre_casc_4 with 300s (1) cores
% 200.44/29.19 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 200.44/29.19 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 200.44/29.19 % Search class: HGHSM-FFMM31-DHSMMSBN
% 200.44/29.19 % partial match(2): HGHSM-FFMM31-SHSSMSBN
% 200.44/29.19 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 200.44/29.19 % Starting SubtermCWHack with 28s (1) cores
% 200.44/29.19 % SubtermCWHack with pid 36354 completed with status 8
% 200.44/29.19 % Starting pre_casc_4 with 31s (1) cores
% 200.44/29.19 % pre_casc_4 with pid 36424 completed with status 0
% 200.44/29.19 % Result found by pre_casc_4
% 200.44/29.19 % Preprocessing class: HSLMSMSSLLLCHSA.
% 200.44/29.19 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 200.44/29.19 % Starting lpo1_fix with 900s (3) cores
% 200.44/29.19 % Starting full_lambda_9 with 300s (1) cores
% 200.44/29.19 % Starting almost_fo_4 with 300s (1) cores
% 200.44/29.19 % Starting new_ho_9 with 300s (1) cores
% 200.44/29.19 % Starting pre_casc_4 with 300s (1) cores
% 200.44/29.19 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 200.44/29.19 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 200.44/29.19 % Search class: HGHSM-FFMM31-DHSMMSBN
% 200.44/29.19 % partial match(2): HGHSM-FFMM31-SHSSMSBN
% 200.44/29.19 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 200.44/29.19 % Starting SubtermCWHack with 28s (1) cores
% 200.44/29.19 % SubtermCWHack with pid 36354 completed with status 8
% 200.44/29.19 % Starting pre_casc_4 with 31s (1) cores
% 200.44/29.19 % Preprocessing time : 0.003 s
% 200.44/29.19 % Presaturation interreduction done
% 200.44/29.19
% 200.44/29.19 % Proof found!
% 200.44/29.19 % SZS status Theorem
% 200.44/29.19 % SZS output start CNFRefutation
% See solution above
% 200.44/29.19 % Parsed axioms : 364
% 200.44/29.19 % Removed by relevancy pruning/SinE : 290
% 200.44/29.19 % Initial clauses : 137
% 200.44/29.19 % Removed in clause preprocessing : 31
% 200.44/29.19 % Initial clauses in saturation : 106
% 200.44/29.19 % Processed clauses : 2328
% 200.44/29.19 % ...of these trivial : 63
% 200.44/29.19 % ...subsumed : 1003
% 200.44/29.19 % ...remaining for further processing : 1261
% 200.44/29.19 % Other redundant clauses eliminated : 11
% 200.44/29.19 % Clauses deleted for lack of memory : 0
% 200.44/29.19 % Backward-subsumed : 39
% 200.44/29.19 % Backward-rewritten : 267
% 200.44/29.19 % Generated clauses : 21302
% 200.44/29.19 % ...of the previous two non-redundant : 9837
% 200.44/29.19 % ...aggressively subsumed : 0
% 200.44/29.19 % Contextual simplify-reflections : 18
% 200.44/29.19 % Paramodulations : 9906
% 200.44/29.19 % Factorizations : 8
% 200.44/29.19 % NegExts : 70
% 200.44/29.19 % Equation resolutions : 17
% 200.44/29.19 % Disequality decompositions : 0
% 200.44/29.19 % Total rewrite steps : 4670
% 200.44/29.19 % ...of those cached : 4432
% 200.44/29.19 % Propositional unsat checks : 0
% 200.44/29.19 % Propositional check models : 0
% 200.44/29.19 % Propositional check unsatisfiable : 0
% 200.44/29.19 % Propositional clauses : 0
% 200.44/29.19 % Propositional clauses after purity: 0
% 200.44/29.19 % Propositional unsat core size : 0
% 200.44/29.19 % Propositional preprocessing time : 0.000
% 200.44/29.19 % Propositional encoding time : 0.000
% 200.44/29.19 % Propositional solver time : 0.000
% 200.44/29.19 % Success case prop preproc time : 0.000
% 200.44/29.19 % Success case prop encoding time : 0.000
% 200.44/29.19 % Success case prop solver time : 0.000
% 200.44/29.19 % Current number of processed clauses : 850
% 200.44/29.19 % Positive orientable unit clauses : 163
% 200.44/29.19 % Positive unorientable unit clauses: 0
% 200.44/29.19 % Negative unit clauses : 249
% 200.44/29.19 % Non-unit-clauses : 438
% 200.44/29.19 % Current number of unprocessed clauses: 7540
% 200.44/29.19 % ...number of literals in the above : 17291
% 200.44/29.19 % Current number of archived formulas : 0
% 200.44/29.19 % Current number of archived clauses : 404
% 200.44/29.19 % Clause-clause subsumption calls (NU) : 57594
% 200.44/29.19 % Rec. Clause-clause subsumption calls : 17623
% 200.44/29.19 % Non-unit clause-clause subsumptions : 410
% 200.44/29.19 % Unit Clause-clause subsumption calls : 11093
% 200.44/29.19 % Rewrite failures with RHS unbound : 0
% 200.44/29.19 % BW rewrite match attempts : 8968
% 200.44/29.19 % BW rewrite match successes : 44
% 200.44/29.19 % Condensation attempts : 0
% 200.44/29.19 % Condensation successes : 0
% 200.44/29.19 % Termbank termtop insertions : 1113339
% 200.44/29.19 % Search garbage collected termcells : 8111
% 200.44/29.19
% 200.44/29.19 % -------------------------------------------------
% 200.44/29.19 % User time : 27.897 s
% 200.44/29.19 % System time : 0.701 s
% 200.44/29.19 % Total time : 28.598 s
% 200.44/29.19 % Maximum resident set size: 5216 pages
% 200.44/29.19
% 200.44/29.19 % -------------------------------------------------
% 200.44/29.19 % User time : 27.904 s
% 200.44/29.19 % System time : 0.704 s
% 200.44/29.19 % Total time : 28.608 s
% 200.44/29.19 % Maximum resident set size: 5120 pages
% 200.44/29.19 % E exiting
%------------------------------------------------------------------------------