%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM692^4 : 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 : 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 08:16:51 AM UTC 2026
% Result : Theorem 0.81s 0.49s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 293 ( 50 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 693 ( 69 ~; 54 |; 10 &; 509 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 121 ( 80 ^; 41 !; 0 ?; 121 :)
% 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_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.zX37i1gizr/E---3.1_3087740.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.p',def_imp) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.p',def_iii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.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.zX37i1gizr/E---3.1_3087740.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.zX37i1gizr/E---3.1_3087740.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.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/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.p',def_lessis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.p',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.p',def_n_is) ).
thf(satz23a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X321: $i] : ( in @ X321 @ nat )
@ ^ [X322: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( lessis @ X1 @ X322 )
=> ( ( lessis @ X4 @ X13 )
=> ( lessis @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X322 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.p',satz23a) ).
thf(satz22d,axiom,
( 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/sandbox2/tmp/tmp.zX37i1gizr/E---3.1_3087740.p',satz22d) ).
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.zX37i1gizr/E---3.1_3087740.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.zX37i1gizr/E---3.1_3087740.p',satz19f) ).
thf(c_0_14,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_15,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_16,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_17,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_18,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_20,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_21,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_22,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_23,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,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_17,c_0_15]),c_0_18]) ).
thf(c_0_25,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_19]) ).
thf(c_0_26,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X321: $i] : ( in @ X321 @ nat )
@ ^ [X322: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( lessis @ X1 @ X322 )
=> ( ( lessis @ X4 @ X13 )
=> ( lessis @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X322 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz23a]) ).
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_20,c_0_21]) ).
thf(c_0_28,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_22,c_0_23]),c_0_24]),c_0_25]) ).
thf(c_0_29,negated_conjecture,
~ ! [X393: $i] :
( ( in @ X393 @ nat )
=> ! [X392: $i] :
( ( in @ X392 @ nat )
=> ! [X391: $i] :
( ( in @ X391 @ nat )
=> ! [X390: $i] :
( ( in @ X390 @ nat )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X392 @ X393 ) )
=> ~ $true )
=> ( X393 = X392 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X390 @ X391 ) )
=> ~ $true )
=> ( X391 = X390 ) )
=> ( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X392 @ X390 ) @ ( n_pl @ X393 @ X391 ) ) )
=> ~ $true )
=> ( ( n_pl @ X393 @ X391 )
= ( n_pl @ X392 @ X390 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_26]),c_0_27]),c_0_28]) ).
thf(c_0_30,plain,
! [X488: $i] :
( ( in @ X488 @ nat )
=> ! [X487: $i] :
( ( in @ X487 @ nat )
=> ! [X486: $i] :
( ( in @ X486 @ nat )
=> ! [X485: $i] :
( ( in @ X485 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X487 @ X488 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X485 @ X486 ) )
=> ~ $true )
=> ( X486 = X485 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X487 @ X485 ) @ ( n_pl @ X488 @ X486 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz22d]),c_0_27]),c_0_23]),c_0_28]) ).
thf(c_0_31,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 ) )
| ( esk1_0 = esk2_0 ) )
& ( $true
| ( esk1_0 = esk2_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 ) ) )
| ~ $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_29])])])])]) ).
thf(c_0_32,plain,
! [X692: $i,X693: $i,X694: $i,X695: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ X695 @ X694 ) )
| ~ $true
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X693 @ X695 ) @ ( n_pl @ X692 @ X694 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X693 @ X692 ) )
| ~ ( in @ X695 @ nat )
| ~ ( in @ X694 @ nat )
| ~ ( in @ X693 @ nat )
| ~ ( in @ X692 @ nat ) )
& ( ( X694 != X695 )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X693 @ X695 ) @ ( n_pl @ X692 @ X694 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X693 @ X692 ) )
| ~ ( in @ X695 @ nat )
| ~ ( in @ X694 @ nat )
| ~ ( in @ X693 @ nat )
| ~ ( in @ X692 @ 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_30])])])])]) ).
thf(c_0_33,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_34,plain,
! [X1: $i,X4: $i,X5: $i,X6: $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 @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X6 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_35,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(cn,[status(thm)],[c_0_33]) ).
thf(c_0_36,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_34]) ).
thf(c_0_37,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_38,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_39,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_41,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ~ ( 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(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40])]) ).
thf(c_0_42,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
| ( esk3_0 = esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_43,negated_conjecture,
( ( esk4_0 = esk3_0 )
| ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_44,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ( esk1_0 = esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_45,plain,
! [X423: $i] :
( ( in @ X423 @ nat )
=> ! [X422: $i] :
( ( in @ X422 @ nat )
=> ! [X421: $i] :
( ( in @ X421 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X422 @ X423 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X422 @ X421 ) @ ( n_pl @ X423 @ X421 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19c]),c_0_27]),c_0_23]) ).
thf(c_0_46,negated_conjecture,
( ( esk2_0 = esk1_0 )
| ( esk4_0 = esk3_0 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_47,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_45])])])]) ).
thf(c_0_48,negated_conjecture,
( ( esk2_0 = esk1_0 )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk3_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
thf(c_0_49,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_47]) ).
thf(c_0_50,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 @ X427 @ X428 ) @ ( n_pl @ X427 @ X429 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19f]),c_0_27]),c_0_23]) ).
thf(c_0_51,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_48,c_0_49]),c_0_39]),c_0_38]),c_0_37])]),c_0_44]) ).
thf(c_0_52,plain,
! [X634: $i,X635: $i,X636: $i] :
( ~ ( in @ X634 @ nat )
| ~ ( in @ X635 @ nat )
| ~ ( in @ X636 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X635 @ X634 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X636 @ X635 ) @ ( n_pl @ X636 @ X634 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])]) ).
thf(c_0_53,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
thf(c_0_54,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_52]) ).
thf(c_0_55,negated_conjecture,
( ( n_pl @ esk1_0 @ esk3_0 )
!= ( n_pl @ esk2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_56,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(spm,[status(thm)],[c_0_53,c_0_54]),c_0_37]),c_0_40]),c_0_39])]) ).
thf(c_0_57,negated_conjecture,
( ( n_pl @ esk1_0 @ esk4_0 )
!= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_55,c_0_51]) ).
thf(c_0_58,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[c_0_42,c_0_56]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM692^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n008.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 12:40:24 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.26 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.zX37i1gizr/E---3.1_3087740.p
% 0.81/0.49 % Version: 3.5.1-ho
% 0.81/0.49 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.81/0.49 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.49 % Starting lpo1_fix with 900s (3) cores
% 0.81/0.49 % Starting full_lambda_9 with 300s (1) cores
% 0.81/0.49 % Starting almost_fo_4 with 300s (1) cores
% 0.81/0.49 % Starting new_ho_9 with 300s (1) cores
% 0.81/0.49 % Starting pre_casc_4 with 300s (1) cores
% 0.81/0.49 % Starting ho_unfolding_6 with 300s (1) cores
% 0.81/0.49 % full_lambda_9 with pid 3087782 completed with status 0
% 0.81/0.49 % Result found by full_lambda_9
% 0.81/0.49 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.81/0.49 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.49 % Starting lpo1_fix with 900s (3) cores
% 0.81/0.49 % Starting full_lambda_9 with 300s (1) cores
% 0.81/0.49 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.81/0.49 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.81/0.49 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.81/0.49 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.81/0.49 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.81/0.49 % Starting SubtermCWHack with 28s (1) cores
% 0.81/0.49 % SubtermCWHack with pid 3087801 completed with status 0
% 0.81/0.49 % Result found by SubtermCWHack
% 0.81/0.49 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.81/0.49 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.49 % Starting lpo1_fix with 900s (3) cores
% 0.81/0.49 % Starting full_lambda_9 with 300s (1) cores
% 0.81/0.49 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.81/0.49 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.81/0.49 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.81/0.49 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.81/0.49 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.81/0.49 % Starting SubtermCWHack with 28s (1) cores
% 0.81/0.49 % Preprocessing time : 0.006 s
% 0.81/0.49
% 0.81/0.49 % Proof found!
% 0.81/0.49 % SZS status Theorem
% 0.81/0.49 % SZS output start CNFRefutation
% See solution above
% 0.81/0.49 % Parsed axioms : 396
% 0.81/0.49 % Removed by relevancy pruning/SinE : 263
% 0.81/0.49 % Initial clauses : 358
% 0.81/0.49 % Removed in clause preprocessing : 181
% 0.81/0.49 % Initial clauses in saturation : 177
% 0.81/0.49 % Processed clauses : 1168
% 0.81/0.49 % ...of these trivial : 15
% 0.81/0.49 % ...subsumed : 508
% 0.81/0.49 % ...remaining for further processing : 645
% 0.81/0.49 % Other redundant clauses eliminated : 36
% 0.81/0.49 % Clauses deleted for lack of memory : 0
% 0.81/0.49 % Backward-subsumed : 2
% 0.81/0.49 % Backward-rewritten : 12
% 0.81/0.49 % Generated clauses : 3680
% 0.81/0.49 % ...of the previous two non-redundant : 3423
% 0.81/0.49 % ...aggressively subsumed : 0
% 0.81/0.49 % Contextual simplify-reflections : 1
% 0.81/0.49 % Paramodulations : 3633
% 0.81/0.49 % Factorizations : 2
% 0.81/0.49 % NegExts : 0
% 0.81/0.49 % Equation resolutions : 41
% 0.81/0.49 % Disequality decompositions : 0
% 0.81/0.49 % Total rewrite steps : 1264
% 0.81/0.49 % ...of those cached : 1222
% 0.81/0.49 % Propositional unsat checks : 0
% 0.81/0.49 % Propositional check models : 0
% 0.81/0.49 % Propositional check unsatisfiable : 0
% 0.81/0.49 % Propositional clauses : 0
% 0.81/0.49 % Propositional clauses after purity: 0
% 0.81/0.49 % Propositional unsat core size : 0
% 0.81/0.49 % Propositional preprocessing time : 0.000
% 0.81/0.49 % Propositional encoding time : 0.000
% 0.81/0.49 % Propositional solver time : 0.000
% 0.81/0.49 % Success case prop preproc time : 0.000
% 0.81/0.49 % Success case prop encoding time : 0.000
% 0.81/0.49 % Success case prop solver time : 0.000
% 0.81/0.49 % Current number of processed clauses : 613
% 0.81/0.49 % Positive orientable unit clauses : 31
% 0.81/0.49 % Positive unorientable unit clauses: 0
% 0.81/0.49 % Negative unit clauses : 382
% 0.81/0.49 % Non-unit-clauses : 200
% 0.81/0.49 % Current number of unprocessed clauses: 2432
% 0.81/0.49 % ...number of literals in the above : 6400
% 0.81/0.49 % Current number of archived formulas : 0
% 0.81/0.49 % Current number of archived clauses : 15
% 0.81/0.49 % Clause-clause subsumption calls (NU) : 10669
% 0.81/0.49 % Rec. Clause-clause subsumption calls : 5845
% 0.81/0.49 % Non-unit clause-clause subsumptions : 392
% 0.81/0.49 % Unit Clause-clause subsumption calls : 41288
% 0.81/0.49 % Rewrite failures with RHS unbound : 0
% 0.81/0.49 % BW rewrite match attempts : 9
% 0.81/0.49 % BW rewrite match successes : 2
% 0.81/0.49 % Condensation attempts : 0
% 0.81/0.49 % Condensation successes : 0
% 0.81/0.49 % Termbank termtop insertions : 106645
% 0.81/0.49 % Search garbage collected termcells : 18325
% 0.81/0.49
% 0.81/0.49 % -------------------------------------------------
% 0.81/0.49 % User time : 0.162 s
% 0.81/0.49 % System time : 0.025 s
% 0.81/0.49 % Total time : 0.186 s
% 0.81/0.49 % Maximum resident set size: 6860 pages
% 0.81/0.49
% 0.81/0.49 % -------------------------------------------------
% 0.81/0.49 % User time : 0.172 s
% 0.81/0.49 % System time : 0.032 s
% 0.81/0.49 % Total time : 0.204 s
% 0.81/0.49 % Maximum resident set size: 5376 pages
% 0.81/0.49 % E exiting
%------------------------------------------------------------------------------