%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM691^4 : 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 : n026.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 1.49s 0.46s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 305 ( 53 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 704 ( 69 ~; 54 |; 10 &; 520 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 127 ( 86 ^; 41 !; 0 ?; 127 :)
% 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_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/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_imp) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_d_29_ii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_l_or) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.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/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_is_of) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_moreis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_n_is) ).
thf(satz23,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X319: $i] : ( in @ X319 @ nat )
@ ^ [X320: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( moreis @ X1 @ X320 )
=> ( ( moreis @ X4 @ X13 )
=> ( moreis @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X320 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',satz23) ).
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/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',satz22b) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',def_iii) ).
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/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',satz19c) ).
thf(satz19f,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X277: $i] : ( in @ X277 @ nat )
@ ^ [X278: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ X1 @ X278 )
=> ( iii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X278 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4dPvN6c6uR/E---3.1_537990.p',satz19f) ).
thf(c_0_15,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_16,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_17,plain,
( 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_18,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_19,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
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,
( 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_22,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_23,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_24,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,def_n_some]) ).
thf(c_0_25,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_16]),c_0_19]) ).
thf(c_0_26,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_20]) ).
thf(c_0_27,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X319: $i] : ( in @ X319 @ nat )
@ ^ [X320: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( moreis @ X1 @ X320 )
=> ( ( moreis @ X4 @ X13 )
=> ( moreis @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X320 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz23]) ).
thf(c_0_28,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_29,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_23,c_0_24]),c_0_25]),c_0_26]) ).
thf(c_0_30,negated_conjecture,
~ ! [X391: $i] :
( ( in @ X391 @ nat )
=> ! [X390: $i] :
( ( in @ X390 @ nat )
=> ! [X389: $i] :
( ( in @ X389 @ nat )
=> ! [X388: $i] :
( ( in @ X388 @ nat )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X391 @ X390 ) )
=> ~ $true )
=> ( X391 = X390 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X389 @ X388 ) )
=> ~ $true )
=> ( X389 = X388 ) )
=> ( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X391 @ X389 ) @ ( n_pl @ X390 @ X388 ) ) )
=> ~ $true )
=> ( ( n_pl @ X391 @ X389 )
= ( n_pl @ X390 @ X388 ) ) ) ) ) ) ) ) ),
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,plain,
! [X514: $i] :
( ( in @ X514 @ nat )
=> ! [X513: $i] :
( ( in @ X513 @ nat )
=> ! [X512: $i] :
( ( in @ X512 @ nat )
=> ! [X511: $i] :
( ( in @ X511 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X514 @ X513 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X512 @ X511 ) )
=> ~ $true )
=> ( X512 = X511 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X514 @ X512 ) @ ( n_pl @ X513 @ X511 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz22b]),c_0_24]),c_0_28]),c_0_29]) ).
thf(c_0_32,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( in @ esk4_0 @ nat )
& ( ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ( esk1_0 = esk2_0 ) )
& ( $true
| ( esk1_0 = esk2_0 ) )
& ( ( l_some @ nat @ ( diffprop @ esk3_0 @ esk4_0 ) )
| ( esk3_0 = esk4_0 ) )
& ( $true
| ( esk3_0 = esk4_0 ) )
& ( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk4_0 ) ) )
| ~ $true )
& ( ( n_pl @ esk1_0 @ esk3_0 )
!= ( n_pl @ esk2_0 @ esk4_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_33,plain,
! [X710: $i,X711: $i,X712: $i,X713: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ X712 @ X713 ) )
| ~ $true
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X710 @ X712 ) @ ( n_pl @ X711 @ X713 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X710 @ X711 ) )
| ~ ( in @ X713 @ nat )
| ~ ( in @ X712 @ nat )
| ~ ( in @ X711 @ nat )
| ~ ( in @ X710 @ nat ) )
& ( ( X712 != X713 )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X710 @ X712 ) @ ( n_pl @ X711 @ X713 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X710 @ X711 ) )
| ~ ( in @ X713 @ nat )
| ~ ( in @ X712 @ nat )
| ~ ( in @ X711 @ nat )
| ~ ( in @ X710 @ 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_31])])])])]) ).
thf(c_0_34,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk4_0 ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_35,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_33]) ).
thf(c_0_36,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk4_0 ) ) ),
inference(cn,[status(thm)],[c_0_34]) ).
thf(c_0_37,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_35]) ).
thf(c_0_38,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_39,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_40,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_41,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_43,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ~ ( l_some @ nat @ ( diffprop @ esk3_0 @ esk4_0 ) ) ),
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_36,c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]) ).
thf(c_0_44,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk3_0 @ esk4_0 ) )
| ( esk3_0 = esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_45,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_42,def_n_some]) ).
thf(c_0_46,negated_conjecture,
( ( esk4_0 = esk3_0 )
| ~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_47,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ( esk1_0 = esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_48,plain,
! [X431: $i] :
( ( in @ X431 @ nat )
=> ! [X430: $i] :
( ( in @ X430 @ nat )
=> ! [X429: $i] :
( ( in @ X429 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X430 @ X431 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X430 @ X429 ) @ ( n_pl @ X431 @ X429 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19c]),c_0_45]),c_0_28]) ).
thf(c_0_49,negated_conjecture,
( ( esk2_0 = esk1_0 )
| ( esk4_0 = esk3_0 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_50,plain,
! [X628: $i,X629: $i,X630: $i] :
( ~ ( in @ X628 @ nat )
| ~ ( in @ X629 @ nat )
| ~ ( in @ X630 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X629 @ X628 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X629 @ X630 ) @ ( n_pl @ X628 @ X630 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
thf(c_0_51,negated_conjecture,
( ( esk2_0 = esk1_0 )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk3_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_49]) ).
thf(c_0_52,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_50]) ).
thf(c_0_53,plain,
! [X440: $i] :
( ( in @ X440 @ nat )
=> ! [X439: $i] :
( ( in @ X439 @ nat )
=> ! [X438: $i] :
( ( in @ X438 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X439 @ X440 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X438 @ X439 ) @ ( n_pl @ X438 @ X440 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19f]),c_0_45]),c_0_28]) ).
thf(c_0_54,negated_conjecture,
esk2_0 = esk1_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_41]),c_0_39]),c_0_38])]),c_0_47]) ).
thf(c_0_55,plain,
! [X637: $i,X638: $i,X639: $i] :
( ~ ( in @ X637 @ nat )
| ~ ( in @ X638 @ nat )
| ~ ( in @ X639 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X638 @ X637 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X639 @ X638 ) @ ( n_pl @ X639 @ X637 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
thf(c_0_56,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk1_0 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_54]) ).
thf(c_0_57,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X4 ) @ ( n_pl @ X5 @ X1 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_58,negated_conjecture,
( ( n_pl @ esk1_0 @ esk3_0 )
!= ( n_pl @ esk2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_59,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk3_0 @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_39]),c_0_41]),c_0_40])]) ).
thf(c_0_60,negated_conjecture,
( ( n_pl @ esk1_0 @ esk4_0 )
!= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_58,c_0_54]) ).
thf(c_0_61,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[c_0_44,c_0_59]) ).
thf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM691^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n026.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 12:42:27 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.25 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.4dPvN6c6uR/E---3.1_537990.p
% 1.49/0.46 % Version: 3.5.1-ho
% 1.49/0.46 % Preprocessing class: HSLMSMSSLLLCHSA.
% 1.49/0.46 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.46 % Starting lpo1_fix with 900s (3) cores
% 1.49/0.46 % Starting full_lambda_9 with 300s (1) cores
% 1.49/0.46 % Starting almost_fo_4 with 300s (1) cores
% 1.49/0.46 % Starting new_ho_9 with 300s (1) cores
% 1.49/0.46 % Starting pre_casc_4 with 300s (1) cores
% 1.49/0.46 % Starting ho_unfolding_6 with 300s (1) cores
% 1.49/0.46 % full_lambda_9 with pid 538004 completed with status 0
% 1.49/0.46 % Result found by full_lambda_9
% 1.49/0.46 % Preprocessing class: HSLMSMSSLLLCHSA.
% 1.49/0.46 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.46 % Starting lpo1_fix with 900s (3) cores
% 1.49/0.46 % Starting full_lambda_9 with 300s (1) cores
% 1.49/0.46 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 1.49/0.46 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 1.49/0.46 % Search class: HGHSM-FSLM32-DHSMMSBN
% 1.49/0.46 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 1.49/0.46 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 1.49/0.46 % Starting SubtermCWHack with 28s (1) cores
% 1.49/0.46 % SubtermCWHack with pid 538010 completed with status 0
% 1.49/0.46 % Result found by SubtermCWHack
% 1.49/0.46 % Preprocessing class: HSLMSMSSLLLCHSA.
% 1.49/0.46 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.46 % Starting lpo1_fix with 900s (3) cores
% 1.49/0.46 % Starting full_lambda_9 with 300s (1) cores
% 1.49/0.46 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 1.49/0.46 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 1.49/0.46 % Search class: HGHSM-FSLM32-DHSMMSBN
% 1.49/0.46 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 1.49/0.46 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 1.49/0.46 % Starting SubtermCWHack with 28s (1) cores
% 1.49/0.46 % Preprocessing time : 0.006 s
% 1.49/0.46
% 1.49/0.46 % Proof found!
% 1.49/0.46 % SZS status Theorem
% 1.49/0.46 % SZS output start CNFRefutation
% See solution above
% 1.49/0.46 % Parsed axioms : 395
% 1.49/0.46 % Removed by relevancy pruning/SinE : 263
% 1.49/0.46 % Initial clauses : 350
% 1.49/0.46 % Removed in clause preprocessing : 176
% 1.49/0.46 % Initial clauses in saturation : 174
% 1.49/0.46 % Processed clauses : 1146
% 1.49/0.46 % ...of these trivial : 13
% 1.49/0.46 % ...subsumed : 495
% 1.49/0.46 % ...remaining for further processing : 638
% 1.49/0.46 % Other redundant clauses eliminated : 34
% 1.49/0.46 % Clauses deleted for lack of memory : 0
% 1.49/0.46 % Backward-subsumed : 2
% 1.49/0.46 % Backward-rewritten : 12
% 1.49/0.46 % Generated clauses : 3465
% 1.49/0.46 % ...of the previous two non-redundant : 3220
% 1.49/0.46 % ...aggressively subsumed : 0
% 1.49/0.46 % Contextual simplify-reflections : 1
% 1.49/0.46 % Paramodulations : 3420
% 1.49/0.46 % Factorizations : 2
% 1.49/0.46 % NegExts : 0
% 1.49/0.46 % Equation resolutions : 39
% 1.49/0.46 % Disequality decompositions : 0
% 1.49/0.46 % Total rewrite steps : 1186
% 1.49/0.46 % ...of those cached : 1145
% 1.49/0.46 % Propositional unsat checks : 0
% 1.49/0.46 % Propositional check models : 0
% 1.49/0.46 % Propositional check unsatisfiable : 0
% 1.49/0.46 % Propositional clauses : 0
% 1.49/0.46 % Propositional clauses after purity: 0
% 1.49/0.46 % Propositional unsat core size : 0
% 1.49/0.46 % Propositional preprocessing time : 0.000
% 1.49/0.46 % Propositional encoding time : 0.000
% 1.49/0.46 % Propositional solver time : 0.000
% 1.49/0.46 % Success case prop preproc time : 0.000
% 1.49/0.46 % Success case prop encoding time : 0.000
% 1.49/0.46 % Success case prop solver time : 0.000
% 1.49/0.46 % Current number of processed clauses : 608
% 1.49/0.46 % Positive orientable unit clauses : 31
% 1.49/0.46 % Positive unorientable unit clauses: 0
% 1.49/0.46 % Negative unit clauses : 382
% 1.49/0.46 % Non-unit-clauses : 195
% 1.49/0.46 % Current number of unprocessed clauses: 2248
% 1.49/0.46 % ...number of literals in the above : 5817
% 1.49/0.46 % Current number of archived formulas : 0
% 1.49/0.46 % Current number of archived clauses : 15
% 1.49/0.46 % Clause-clause subsumption calls (NU) : 9975
% 1.49/0.46 % Rec. Clause-clause subsumption calls : 5643
% 1.49/0.46 % Non-unit clause-clause subsumptions : 380
% 1.49/0.46 % Unit Clause-clause subsumption calls : 41275
% 1.49/0.46 % Rewrite failures with RHS unbound : 0
% 1.49/0.46 % BW rewrite match attempts : 9
% 1.49/0.46 % BW rewrite match successes : 2
% 1.49/0.46 % Condensation attempts : 0
% 1.49/0.46 % Condensation successes : 0
% 1.49/0.46 % Termbank termtop insertions : 101972
% 1.49/0.46 % Search garbage collected termcells : 17826
% 1.49/0.46
% 1.49/0.46 % -------------------------------------------------
% 1.49/0.46 % User time : 0.156 s
% 1.49/0.46 % System time : 0.018 s
% 1.49/0.46 % Total time : 0.174 s
% 1.49/0.46 % Maximum resident set size: 6856 pages
% 1.49/0.46
% 1.49/0.46 % -------------------------------------------------
% 1.49/0.46 % User time : 0.167 s
% 1.49/0.46 % System time : 0.024 s
% 1.49/0.46 % Total time : 0.191 s
% 1.49/0.46 % Maximum resident set size: 5632 pages
% 1.49/0.46 % E exiting
%------------------------------------------------------------------------------