%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM690^4 : 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 : n008.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 08:16:50 AM UTC 2026
% Result : Theorem 0.68s 0.50s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 60 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 283 ( 48 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 624 ( 57 ~; 41 |; 8 &; 470 @)
% ( 0 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 128 ( 90 ^; 38 !; 0 ?; 128 :)
% 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_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_152,type,
moreis: $i > $i > $o ).
thf(decl_153,type,
lessis: $i > $i > $o ).
thf(decl_156,type,
esk1_0: $i ).
thf(decl_157,type,
esk2_0: $i ).
thf(decl_158,type,
esk3_0: $i ).
thf(decl_159,type,
esk4_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_imp) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_iii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_l_or) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_e_is) ).
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.680r0v9bat/E---3.1_3086805.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_is_of) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_lessis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_n_is) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',def_d_29_ii) ).
thf(satz22d,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X317: $i] : ( in @ X317 @ nat )
@ ^ [X318: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( iii @ X1 @ X318 )
=> ( ( lessis @ X4 @ X13 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X318 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',satz22d) ).
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.680r0v9bat/E---3.1_3086805.p',def_moreis) ).
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.680r0v9bat/E---3.1_3086805.p',satz6) ).
thf(satz22b,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X313: $i] : ( in @ X313 @ nat )
@ ^ [X314: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( d_29_ii @ X1 @ X314 )
=> ( ( moreis @ X4 @ X13 )
=> ( d_29_ii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X314 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',satz22b) ).
thf(satz19c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X271: $i] : ( in @ X271 @ nat )
@ ^ [X272: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ X1 @ X272 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X272 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.680r0v9bat/E---3.1_3086805.p',satz19c) ).
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 @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_19,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_20,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
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,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_25,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_18,def_n_some]) ).
thf(c_0_26,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_17]),c_0_20]) ).
thf(c_0_27,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_21]) ).
thf(c_0_28,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_29,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X317: $i] : ( in @ X317 @ nat )
@ ^ [X318: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( iii @ X1 @ X318 )
=> ( ( lessis @ X4 @ X13 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X318 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz22d]) ).
thf(c_0_30,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_31,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]) ).
thf(c_0_32,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_33,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_28,def_n_some]) ).
thf(c_0_34,negated_conjecture,
~ ! [X389: $i] :
( ( in @ X389 @ nat )
=> ! [X388: $i] :
( ( in @ X388 @ nat )
=> ! [X387: $i] :
( ( in @ X387 @ nat )
=> ! [X386: $i] :
( ( in @ X386 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X388 @ X389 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X386 @ X387 ) )
=> ~ $true )
=> ( X387 = X386 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X388 @ X386 ) @ ( n_pl @ X389 @ X387 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_29]),c_0_25]),c_0_30]),c_0_31]) ).
thf(c_0_35,plain,
! [X404: $i] :
( ( in @ X404 @ nat )
=> ! [X403: $i] :
( ( in @ X403 @ nat )
=> ( ( n_pl @ X404 @ X403 )
= ( n_pl @ X403 @ X404 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_30]),c_0_27]) ).
thf(c_0_36,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_32,c_0_33]),c_0_26]),c_0_27]) ).
thf(c_0_37,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( in @ esk4_0 @ nat )
& ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
& ( ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
| ( esk3_0 = esk4_0 ) )
& ( $true
| ( esk3_0 = esk4_0 ) )
& ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ 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_34])])])])]) ).
thf(c_0_38,plain,
! [X602: $i,X603: $i] :
( ~ ( in @ X602 @ nat )
| ~ ( in @ X603 @ nat )
| ( ( n_pl @ X602 @ X603 )
= ( n_pl @ X603 @ X602 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
thf(c_0_39,plain,
! [X522: $i] :
( ( in @ X522 @ nat )
=> ! [X521: $i] :
( ( in @ X521 @ nat )
=> ! [X520: $i] :
( ( in @ X520 @ nat )
=> ! [X519: $i] :
( ( in @ X519 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X522 @ X521 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X520 @ X519 ) )
=> ~ $true )
=> ( X520 = X519 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X522 @ X520 ) @ ( n_pl @ X521 @ X519 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz22b]),c_0_33]),c_0_30]),c_0_36]) ).
thf(c_0_40,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_41,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_38]) ).
thf(c_0_42,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_43,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_44,plain,
! [X714: $i,X715: $i,X716: $i,X717: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ X716 @ X717 ) )
| ~ $true
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X714 @ X716 ) @ ( n_pl @ X715 @ X717 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X714 @ X715 ) )
| ~ ( in @ X717 @ nat )
| ~ ( in @ X716 @ nat )
| ~ ( in @ X715 @ nat )
| ~ ( in @ X714 @ nat ) )
& ( ( X716 != X717 )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X714 @ X716 ) @ ( n_pl @ X715 @ X717 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X714 @ X715 ) )
| ~ ( in @ X717 @ nat )
| ~ ( in @ X716 @ nat )
| ~ ( in @ X715 @ nat )
| ~ ( in @ X714 @ 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_39])])])])]) ).
thf(c_0_45,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk4_0 @ esk2_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
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 @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_47,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_48,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_49,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk4_0 @ esk2_0 ) @ ( n_pl @ esk3_0 @ esk1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_41]),c_0_46]),c_0_47])]) ).
thf(c_0_50,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_51,negated_conjecture,
l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_52,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
| ( esk3_0 = esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_53,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_46]),c_0_43]),c_0_47]),c_0_42])]) ).
thf(c_0_54,plain,
! [X429: $i] :
( ( in @ X429 @ nat )
=> ! [X428: $i] :
( ( in @ X428 @ nat )
=> ! [X427: $i] :
( ( in @ X427 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X428 @ X429 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X428 @ X427 ) @ ( n_pl @ X429 @ X427 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19c]),c_0_25]),c_0_30]) ).
thf(c_0_55,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_56,plain,
! [X622: $i,X623: $i,X624: $i] :
( ~ ( in @ X622 @ nat )
| ~ ( in @ X623 @ nat )
| ~ ( in @ X624 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X623 @ X622 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X623 @ X624 ) @ ( n_pl @ X622 @ X624 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
thf(c_0_57,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk3_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_40,c_0_55]) ).
thf(c_0_58,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X4 @ X5 ) @ ( n_pl @ X1 @ X5 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[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_51]),c_0_46]),c_0_42]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM690^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:40:09 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.680r0v9bat/E---3.1_3086805.p
% 0.68/0.50 % Version: 3.5.1-ho
% 0.68/0.50 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.68/0.50 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.50 % Starting lpo1_fix with 900s (3) cores
% 0.68/0.50 % Starting full_lambda_9 with 300s (1) cores
% 0.68/0.50 % Starting almost_fo_4 with 300s (1) cores
% 0.68/0.50 % Starting new_ho_9 with 300s (1) cores
% 0.68/0.50 % Starting pre_casc_4 with 300s (1) cores
% 0.68/0.50 % Starting ho_unfolding_6 with 300s (1) cores
% 0.68/0.50 % full_lambda_9 with pid 3086828 completed with status 0
% 0.68/0.50 % Result found by full_lambda_9
% 0.68/0.50 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.68/0.50 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.50 % Starting lpo1_fix with 900s (3) cores
% 0.68/0.50 % Starting full_lambda_9 with 300s (1) cores
% 0.68/0.50 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.68/0.50 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.68/0.50 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.68/0.50 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.68/0.50 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.68/0.50 % Starting SubtermCWHack with 28s (1) cores
% 0.68/0.50 % SubtermCWHack with pid 3086839 completed with status 0
% 0.68/0.50 % Result found by SubtermCWHack
% 0.68/0.50 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.68/0.50 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.50 % Starting lpo1_fix with 900s (3) cores
% 0.68/0.50 % Starting full_lambda_9 with 300s (1) cores
% 0.68/0.50 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.68/0.50 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.68/0.50 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.68/0.50 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.68/0.50 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.68/0.50 % Starting SubtermCWHack with 28s (1) cores
% 0.68/0.50 % Preprocessing time : 0.006 s
% 0.68/0.50
% 0.68/0.50 % Proof found!
% 0.68/0.50 % SZS status Theorem
% 0.68/0.50 % SZS output start CNFRefutation
% See solution above
% 0.68/0.50 % Parsed axioms : 394
% 0.68/0.50 % Removed by relevancy pruning/SinE : 263
% 0.68/0.50 % Initial clauses : 346
% 0.68/0.50 % Removed in clause preprocessing : 175
% 0.68/0.50 % Initial clauses in saturation : 171
% 0.68/0.50 % Processed clauses : 1140
% 0.68/0.50 % ...of these trivial : 11
% 0.68/0.50 % ...subsumed : 495
% 0.68/0.50 % ...remaining for further processing : 634
% 0.68/0.50 % Other redundant clauses eliminated : 33
% 0.68/0.50 % Clauses deleted for lack of memory : 0
% 0.68/0.50 % Backward-subsumed : 1
% 0.68/0.50 % Backward-rewritten : 2
% 0.68/0.50 % Generated clauses : 3477
% 0.68/0.50 % ...of the previous two non-redundant : 3233
% 0.68/0.50 % ...aggressively subsumed : 0
% 0.68/0.50 % Contextual simplify-reflections : 0
% 0.68/0.50 % Paramodulations : 3433
% 0.68/0.50 % Factorizations : 2
% 0.68/0.50 % NegExts : 0
% 0.68/0.50 % Equation resolutions : 38
% 0.68/0.50 % Disequality decompositions : 0
% 0.68/0.50 % Total rewrite steps : 1218
% 0.68/0.50 % ...of those cached : 1177
% 0.68/0.50 % Propositional unsat checks : 0
% 0.68/0.50 % Propositional check models : 0
% 0.68/0.50 % Propositional check unsatisfiable : 0
% 0.68/0.50 % Propositional clauses : 0
% 0.68/0.50 % Propositional clauses after purity: 0
% 0.68/0.50 % Propositional unsat core size : 0
% 0.68/0.50 % Propositional preprocessing time : 0.000
% 0.68/0.50 % Propositional encoding time : 0.000
% 0.68/0.50 % Propositional solver time : 0.000
% 0.68/0.50 % Success case prop preproc time : 0.000
% 0.68/0.50 % Success case prop encoding time : 0.000
% 0.68/0.50 % Success case prop solver time : 0.000
% 0.68/0.50 % Current number of processed clauses : 616
% 0.68/0.50 % Positive orientable unit clauses : 32
% 0.68/0.50 % Positive unorientable unit clauses: 0
% 0.68/0.50 % Negative unit clauses : 389
% 0.68/0.50 % Non-unit-clauses : 195
% 0.68/0.50 % Current number of unprocessed clauses: 2260
% 0.68/0.50 % ...number of literals in the above : 5832
% 0.68/0.50 % Current number of archived formulas : 0
% 0.68/0.50 % Current number of archived clauses : 4
% 0.68/0.50 % Clause-clause subsumption calls (NU) : 9561
% 0.68/0.50 % Rec. Clause-clause subsumption calls : 5497
% 0.68/0.50 % Non-unit clause-clause subsumptions : 374
% 0.68/0.50 % Unit Clause-clause subsumption calls : 41184
% 0.68/0.50 % Rewrite failures with RHS unbound : 0
% 0.68/0.50 % BW rewrite match attempts : 11
% 0.68/0.50 % BW rewrite match successes : 1
% 0.68/0.50 % Condensation attempts : 0
% 0.68/0.50 % Condensation successes : 0
% 0.68/0.50 % Termbank termtop insertions : 101057
% 0.68/0.50 % Search garbage collected termcells : 17388
% 0.68/0.50
% 0.68/0.50 % -------------------------------------------------
% 0.68/0.50 % User time : 0.142 s
% 0.68/0.50 % System time : 0.011 s
% 0.68/0.50 % Total time : 0.153 s
% 0.68/0.50 % Maximum resident set size: 6596 pages
% 0.68/0.50
% 0.68/0.50 % -------------------------------------------------
% 0.68/0.50 % User time : 0.154 s
% 0.68/0.50 % System time : 0.017 s
% 0.68/0.50 % Total time : 0.170 s
% 0.68/0.50 % Maximum resident set size: 5376 pages
% 0.68/0.50 % E exiting
%------------------------------------------------------------------------------