%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP049^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 Oct 7 10:23:49 AM UTC 2026
% Result : Theorem 1.92s 0.54s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 203 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 1239 ( 403 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2527 ( 616 ~; 407 |; 18 &;1441 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 297 ( 297 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 4 con; 0-4 aty)
% Number of variables : 613 ( 154 ^; 441 !; 18 ?; 613 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_list_P559422087at_nat,type,
list_P559422087at_nat: $tType ).
thf(tp_list_nat,type,
list_nat: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_produc1271302400at_nat,type,
produc1271302400at_nat: $tType ).
thf(tp_produc1695820582at_nat,type,
produc1695820582at_nat: $tType ).
thf(tp_produc842455143at_nat,type,
produc842455143at_nat: $tType ).
thf(tp_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(tp_set_Pr1287749686at_nat,type,
set_Pr1287749686at_nat: $tType ).
thf(tp_set_Pr1490359111at_nat,type,
set_Pr1490359111at_nat: $tType ).
thf(tp_set_Pr1746169692at_nat,type,
set_Pr1746169692at_nat: $tType ).
thf(tp_set_Pr1986765409at_nat,type,
set_Pr1986765409at_nat: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_se1612935105at_nat,type,
set_se1612935105at_nat: $tType ).
thf(tp_set_set_nat,type,
set_set_nat: $tType ).
thf(tp_adjacent_nodes_a,type,
adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(tp_c,type,
c: product_prod_nat_nat > a ).
thf(tp_collec1606769740at_nat,type,
collec1606769740at_nat: ( set_Pr1986765409at_nat > $o ) > set_se1612935105at_nat ).
thf(tp_collec7649004at_nat,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_collect_set_nat,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(tp_connected_a,type,
connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).
thf(tp_domain37934156at_nat,type,
domain37934156at_nat: set_Pr1490359111at_nat > set_Pr1986765409at_nat ).
thf(tp_domain_nat_nat,type,
domain_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(tp_e_a,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(tp_edmond1517640972ysis_a,type,
edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
thf(tp_edmond475474835dges_a,type,
edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
thf(tp_finite1457549322at_nat,type,
finite1457549322at_nat: set_se1612935105at_nat > $o ).
thf(tp_finite2000257047at_nat,type,
finite2000257047at_nat: set_Pr1287749686at_nat > $o ).
thf(tp_finite2012248349et_nat,type,
finite2012248349et_nat: set_set_nat > $o ).
thf(tp_finite277291581at_nat,type,
finite277291581at_nat: set_Pr1746169692at_nat > $o ).
thf(tp_finite48957584at_nat,type,
finite48957584at_nat: set_Pr1490359111at_nat > $o ).
thf(tp_finite772653738at_nat,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(tp_finite_Graph_a,type,
finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(tp_image_1655366419at_nat,type,
image_1655366419at_nat: set_Pr1490359111at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(tp_image_2142699582at_nat,type,
image_2142699582at_nat: set_Pr1287749686at_nat > set_Pr1986765409at_nat > set_nat ).
thf(tp_image_981520924at_nat,type,
image_981520924at_nat: set_Pr1746169692at_nat > set_nat > set_Pr1986765409at_nat ).
thf(tp_image_nat_nat,type,
image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).
thf(tp_incoming_a,type,
incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(tp_incoming_a2,type,
incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(tp_isPath_a,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isShortestPath_a,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isSimplePath_a,type,
isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_member1293241661at_nat,type,
member1293241661at_nat: produc1695820582at_nat > set_Pr1746169692at_nat > $o ).
thf(tp_member2027625872at_nat,type,
member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
thf(tp_member298845450at_nat,type,
member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
thf(tp_member701585322at_nat,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(tp_member868723479at_nat,type,
member868723479at_nat: produc1271302400at_nat > set_Pr1287749686at_nat > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_set_nat,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(tp_ord_le1039616028_nat_o,type,
ord_le1039616028_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(tp_ord_le148299708at_nat,type,
ord_le148299708at_nat: set_Pr1746169692at_nat > set_Pr1746169692at_nat > $o ).
thf(tp_ord_le1578155910_nat_o,type,
ord_le1578155910_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(tp_ord_le1837363350at_nat,type,
ord_le1837363350at_nat: set_Pr1287749686at_nat > set_Pr1287749686at_nat > $o ).
thf(tp_ord_le465611495at_nat,type,
ord_le465611495at_nat: set_Pr1490359111at_nat > set_Pr1490359111at_nat > $o ).
thf(tp_ord_le841296385at_nat,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_nat_o,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_outgoing_a,type,
outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(tp_outgoing_a2,type,
outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(tp_produc1168807639at_nat,type,
produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat ).
thf(tp_produc1933845336at_nat,type,
produc1933845336at_nat: nat > product_prod_nat_nat > produc1695820582at_nat ).
thf(tp_produc2055342601at_nat,type,
produc2055342601at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > set_nat ) > set_Pr1287749686at_nat ).
thf(tp_produc2056081288at_nat,type,
produc2056081288at_nat: set_Pr1986765409at_nat > ( product_prod_nat_nat > set_Pr1986765409at_nat ) > set_Pr1490359111at_nat ).
thf(tp_produc45129834at_nat,type,
produc45129834at_nat: set_nat > ( nat > set_nat ) > set_Pr1986765409at_nat ).
thf(tp_produc894163943at_nat,type,
produc894163943at_nat: set_nat > ( nat > set_Pr1986765409at_nat ) > set_Pr1746169692at_nat ).
thf(tp_produc947540346at_nat,type,
produc947540346at_nat: product_prod_nat_nat > nat > produc1271302400at_nat ).
thf(tp_product_Pair_nat_nat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(tp_product_swap_nat_nat,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(tp_range_nat_nat,type,
range_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(tp_reachableNodes_a,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(tp_s,type,
s: nat ).
thf(tp_sK1_SY47,type,
sK1_SY47: set_Pr1986765409at_nat > list_P559422087at_nat ).
thf(tp_sK2_SY45,type,
sK2_SY45: ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(tp_sK3_SY60,type,
sK3_SY60: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(tp_set_Pr2131844118at_nat,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(tp_set_nat2,type,
set_nat2: list_nat > set_nat ).
thf(tp_t,type,
t: nat ).
thf(tp_transi1484096900at_nat,type,
transi1484096900at_nat: set_Pr1490359111at_nat > set_Pr1490359111at_nat ).
thf(tp_transi1645084429cl_nat,type,
transi1645084429cl_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(tp_v_a,type,
v_a: ( product_prod_nat_nat > a ) > set_nat ).
thf(218,axiom,
! [A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ? [Xs2: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Xs2 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_finite__list) ).
thf(288,axiom,
! [Xs: list_P559422087at_nat] : ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_List_Ofinite__set) ).
thf(294,axiom,
! [A: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B2 )
=> ( ( finite772653738at_nat @ B2 )
=> ( finite772653738at_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_finite__subset) ).
thf(296,axiom,
! [S3: set_Pr1986765409at_nat,T2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ S3 @ T2 )
=> ( ~ ( finite772653738at_nat @ S3 )
=> ~ ( finite772653738at_nat @ T2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_infinite__super) ).
thf(298,axiom,
! [B2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A @ B2 )
=> ( finite772653738at_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rev__finite__subset) ).
thf(314,axiom,
! [P3: product_prod_nat_nat > $o] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ? [X_1: product_prod_nat_nat] : ( P3 @ X_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_not__finite__existsD) ).
thf(322,axiom,
! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Uu: product_prod_nat_nat] :
? [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
( ( Uu
= ( F @ X @ Y ) )
& ( P3 @ X )
& ( Q @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__image__set2) ).
thf(326,axiom,
! [P3: product_prod_nat_nat > $o,F: product_prod_nat_nat > product_prod_nat_nat] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Uu: product_prod_nat_nat] :
? [X: product_prod_nat_nat] :
( ( Uu
= ( F @ X ) )
& ( P3 @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite__image__set) ).
thf(336,axiom,
! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > product_prod_nat_nat > $o] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
? [Y: product_prod_nat_nat] :
( ( P3 @ Y )
& ( Q @ X @ Y ) ) ) )
= ( ! [Y: product_prod_nat_nat] :
( ( P3 @ Y )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] : ( Q @ X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__Collect__bounded__ex) ).
thf(338,axiom,
! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
( ( P3 @ X )
| ( Q @ X ) ) ) )
= ( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
& ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__Collect__disjI) ).
thf(340,axiom,
! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
( ( P3 @ X )
& ( Q @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__Collect__conjI) ).
thf(347,axiom,
! [V: nat] : ( connected_a @ c @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_connected__refl) ).
thf(349,axiom,
finite_Graph_a @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Finite__Graph__axioms) ).
thf(351,axiom,
finite772653738at_nat @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__E) ).
thf(352,axiom,
edmond475474835dges_a = edmond475474835dges_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ek__analysis__defs_OspEdges_Ocong) ).
thf(353,axiom,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062) ).
thf(354,axiom,
edmond1517640972ysis_a @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ek__analysis__axioms) ).
thf(355,conjecture,
finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(356,negated_conjecture,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $false ),
inference(negate_conjecture,[status(cth)],[355]) ).
thf(357,plain,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $false ),
inference(unfold_def,[status(thm)],[356]) ).
thf(358,plain,
( ( ! [A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ? [Xs2: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Xs2 )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(359,plain,
( ( ! [Xs: list_P559422087at_nat] : ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(360,plain,
( ( ! [A: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B2 )
=> ( ( finite772653738at_nat @ B2 )
=> ( finite772653738at_nat @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(361,plain,
( ( ! [S3: set_Pr1986765409at_nat,T2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ S3 @ T2 )
=> ( ~ ( finite772653738at_nat @ S3 )
=> ~ ( finite772653738at_nat @ T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(362,plain,
( ( ! [B2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A @ B2 )
=> ( finite772653738at_nat @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(363,plain,
( ( ! [P3: product_prod_nat_nat > $o] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ? [X_1: product_prod_nat_nat] : ( P3 @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(364,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Uu: product_prod_nat_nat] :
? [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
( ( Uu
= ( F @ X @ Y ) )
& ( P3 @ X )
& ( Q @ Y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(365,plain,
( ( ! [P3: product_prod_nat_nat > $o,F: product_prod_nat_nat > product_prod_nat_nat] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Uu: product_prod_nat_nat] :
? [X: product_prod_nat_nat] :
( ( Uu
= ( F @ X ) )
& ( P3 @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(366,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > product_prod_nat_nat > $o] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
? [Y: product_prod_nat_nat] :
( ( P3 @ Y )
& ( Q @ X @ Y ) ) ) )
= ( ! [Y: product_prod_nat_nat] :
( ( P3 @ Y )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] : ( Q @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(367,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
( ( P3 @ X )
| ( Q @ X ) ) ) )
= ( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
& ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(368,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
( ( P3 @ X )
& ( Q @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(369,plain,
( ( ! [V: nat] : ( connected_a @ c @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(370,plain,
( ( finite_Graph_a @ c )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(371,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(372,plain,
( ( edmond475474835dges_a = edmond475474835dges_a )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(373,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(374,plain,
( ( edmond1517640972ysis_a @ c )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(375,plain,
( ( ~ ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[357]) ).
thf(376,plain,
( ( edmond1517640972ysis_a @ c )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(377,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(378,plain,
( ( edmond475474835dges_a = edmond475474835dges_a )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(379,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(380,plain,
( ( finite_Graph_a @ c )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(381,plain,
( ( ! [V: nat] : ( connected_a @ c @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(382,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
( ( P3 @ X )
& ( Q @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(383,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
( ( P3 @ X )
| ( Q @ X ) ) ) )
= ( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
& ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(384,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > product_prod_nat_nat > $o] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] :
? [Y: product_prod_nat_nat] :
( ( P3 @ Y )
& ( Q @ X @ Y ) ) ) )
= ( ! [Y: product_prod_nat_nat] :
( ( P3 @ Y )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] : ( Q @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(385,plain,
( ( ! [P3: product_prod_nat_nat > $o,F: product_prod_nat_nat > product_prod_nat_nat] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Uu: product_prod_nat_nat] :
? [X: product_prod_nat_nat] :
( ( Uu
= ( F @ X ) )
& ( P3 @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(386,plain,
( ( ! [P3: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o,F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
( ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ( ( finite772653738at_nat @ ( collec7649004at_nat @ Q ) )
=> ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [Uu: product_prod_nat_nat] :
? [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
( ( Uu
= ( F @ X @ Y ) )
& ( P3 @ X )
& ( Q @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(387,plain,
( ( ! [P3: product_prod_nat_nat > $o] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ P3 ) )
=> ? [X_1: product_prod_nat_nat] : ( P3 @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(388,plain,
( ( ! [B2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A @ B2 )
=> ( finite772653738at_nat @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(389,plain,
( ( ! [S3: set_Pr1986765409at_nat,T2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ S3 @ T2 )
=> ( ~ ( finite772653738at_nat @ S3 )
=> ~ ( finite772653738at_nat @ T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(390,plain,
( ( ! [A: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B2 )
=> ( ( finite772653738at_nat @ B2 )
=> ( finite772653738at_nat @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(391,plain,
( ( ! [Xs: list_P559422087at_nat] : ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(392,plain,
( ( ! [A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ? [Xs2: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Xs2 )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(393,plain,
( ( ~ ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(394,plain,
( ( ! [SX0: product_prod_nat_nat > $o,SX1: product_prod_nat_nat > $o] :
( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SX2: product_prod_nat_nat] :
( ( SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= ( ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SX0 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(395,plain,
( ( ! [SX0: product_prod_nat_nat > $o,SX1: product_prod_nat_nat > $o] :
( ~ ( ( finite772653738at_nat @ ( collec7649004at_nat @ SX0 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ SX1 ) ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SX2: product_prod_nat_nat] :
~ ( ~ ( SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(396,plain,
( ( ! [SX0: product_prod_nat_nat > $o,SX1: product_prod_nat_nat > product_prod_nat_nat > $o] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SX0 ) )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SX2: product_prod_nat_nat] :
~ ! [SX3: product_prod_nat_nat] :
~ ~ ( ~ ( SX0 @ SX3 )
| ~ ( SX1 @ SX2 @ SX3 ) ) ) )
= ( ! [SX2: product_prod_nat_nat] :
( ~ ( SX0 @ SX2 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SX3: product_prod_nat_nat] : ( SX1 @ SX3 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(397,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 )
| ( finite772653738at_nat @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(398,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ( finite772653738at_nat @ SX1 )
| ( finite772653738at_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(399,plain,
( ( ! [SX0: product_prod_nat_nat > $o] :
( ~ ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SX0 ) )
| ~ ! [SX1: product_prod_nat_nat] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(400,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ~ ( finite772653738at_nat @ SX0 )
| ~ ( finite772653738at_nat @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(401,plain,
( ( ! [SX0: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ! [SX1: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ SX1 )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(402,plain,
( ( ~ ( finite772653738at_nat @ ( e_a @ c ) )
| ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(403,plain,
( ( ! [SX0: product_prod_nat_nat > $o,SX1: product_prod_nat_nat > product_prod_nat_nat] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SX0 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SX2: product_prod_nat_nat] :
~ ! [SX3: product_prod_nat_nat] :
~ ~ ( ( SX2
!= ( SX1 @ SX3 ) )
| ~ ( SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(404,plain,
( ( ! [SX0: product_prod_nat_nat > $o,SX1: product_prod_nat_nat > $o,SX2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SX0 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SX1 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SX3: product_prod_nat_nat] :
~ ! [SX4: product_prod_nat_nat] :
~ ~ ! [SX5: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SX3
!= ( SX2 @ SX4 @ SX5 ) )
| ~ ( SX0 @ SX4 ) )
| ~ ( SX1 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(405,plain,
( ( ! [SV1: product_prod_nat_nat > a] :
( ( edmond475474835dges_a @ SV1 )
= ( edmond475474835dges_a @ SV1 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[378]) ).
thf(406,plain,
( ( edmond475474835dges_a = edmond475474835dges_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[378]) ).
thf(407,plain,
! [SV2: nat] :
( ( connected_a @ c @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(408,plain,
! [SV3: list_P559422087at_nat] :
( ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(409,plain,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(410,plain,
! [SV4: product_prod_nat_nat > $o] :
( ( ! [SY34: product_prod_nat_nat > $o] :
( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY35: product_prod_nat_nat] :
( ( SV4 @ SY35 )
| ( SY34 @ SY35 ) ) ) )
= ( ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SY34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(411,plain,
! [SV5: product_prod_nat_nat > $o] :
( ( ! [SY36: product_prod_nat_nat > $o] :
( ~ ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV5 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ SY36 ) ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY37: product_prod_nat_nat] :
~ ( ~ ( SV5 @ SY37 )
| ~ ( SY36 @ SY37 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(412,plain,
! [SV6: product_prod_nat_nat > $o] :
( ( ! [SY38: product_prod_nat_nat > product_prod_nat_nat > $o] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY39: product_prod_nat_nat] :
~ ! [SY40: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY40 )
| ~ ( SY38 @ SY39 @ SY40 ) ) ) )
= ( ! [SY41: product_prod_nat_nat] :
( ~ ( SV6 @ SY41 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SX3: product_prod_nat_nat] : ( SY38 @ SX3 @ SY41 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(413,plain,
! [SV7: set_Pr1986765409at_nat] :
( ( ! [SY43: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SV7 )
| ~ ( ord_le841296385at_nat @ SY43 @ SV7 )
| ( finite772653738at_nat @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(414,plain,
! [SV8: set_Pr1986765409at_nat] :
( ( ! [SY44: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV8 @ SY44 )
| ~ ( finite772653738at_nat @ SY44 )
| ( finite772653738at_nat @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(415,plain,
! [SV9: product_prod_nat_nat > $o] :
( ( ~ ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV9 ) )
| ~ ! [SY45: product_prod_nat_nat] :
~ ( SV9 @ SY45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(416,plain,
! [SV10: set_Pr1986765409at_nat] :
( ( ! [SY46: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV10 @ SY46 )
| ~ ~ ( finite772653738at_nat @ SV10 )
| ~ ( finite772653738at_nat @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(417,plain,
! [SV11: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV11 )
| ~ ! [SY47: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ SY47 )
!= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(418,plain,
( ( ( ~ ( finite772653738at_nat @ ( e_a @ c ) ) )
= $true )
| ( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(419,plain,
! [SV12: product_prod_nat_nat > $o] :
( ( ! [SY48: product_prod_nat_nat > product_prod_nat_nat] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV12 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY49: product_prod_nat_nat] :
~ ! [SY50: product_prod_nat_nat] :
~ ~ ( ( SY49
!= ( SY48 @ SY50 ) )
| ~ ( SV12 @ SY50 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(420,plain,
! [SV13: product_prod_nat_nat > $o] :
( ( ! [SY51: product_prod_nat_nat > $o,SY52: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV13 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SY51 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY53: product_prod_nat_nat] :
~ ! [SY54: product_prod_nat_nat] :
~ ~ ! [SY55: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SY53
!= ( SY52 @ SY54 @ SY55 ) )
| ~ ( SV13 @ SY54 ) )
| ~ ( SY51 @ SY55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(421,plain,
! [SV14: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV14 )
= ( edmond475474835dges_a @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(422,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= ( ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(423,plain,
! [SV16: product_prod_nat_nat > $o,SV5: product_prod_nat_nat > $o] :
( ( ~ ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV5 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ SV16 ) ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY57: product_prod_nat_nat] :
~ ( ~ ( SV5 @ SY57 )
| ~ ( SV16 @ SY57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(424,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(425,plain,
! [SV18: set_Pr1986765409at_nat,SV7: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV7 )
| ~ ( ord_le841296385at_nat @ SV18 @ SV7 )
| ( finite772653738at_nat @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(426,plain,
! [SV19: set_Pr1986765409at_nat,SV8: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ SV8 @ SV19 )
| ~ ( finite772653738at_nat @ SV19 )
| ( finite772653738at_nat @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(427,plain,
! [SV9: product_prod_nat_nat > $o] :
( ( ( ~ ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV9 ) ) )
= $true )
| ( ( ~ ! [SY45: product_prod_nat_nat] :
~ ( SV9 @ SY45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(428,plain,
! [SV20: set_Pr1986765409at_nat,SV10: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ SV10 @ SV20 )
| ~ ~ ( finite772653738at_nat @ SV10 )
| ~ ( finite772653738at_nat @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(429,plain,
! [SV11: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV11 ) )
= $true )
| ( ( ~ ! [SY47: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ SY47 )
!= SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(430,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
= $false )
| ( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(431,plain,
! [SV21: product_prod_nat_nat > product_prod_nat_nat,SV12: product_prod_nat_nat > $o] :
( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV12 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY62: product_prod_nat_nat] :
~ ! [SY63: product_prod_nat_nat] :
~ ~ ( ( SY62
!= ( SV21 @ SY63 ) )
| ~ ( SV12 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(432,plain,
! [SV22: product_prod_nat_nat > $o,SV13: product_prod_nat_nat > $o] :
( ( ! [SY64: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV13 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV22 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY65: product_prod_nat_nat] :
~ ! [SY66: product_prod_nat_nat] :
~ ~ ! [SY67: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SY65
!= ( SY64 @ SY66 @ SY67 ) )
| ~ ( SV13 @ SY66 ) )
| ~ ( SV22 @ SY67 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(433,plain,
! [SV14: product_prod_nat_nat > a] :
( ( ! [SV23: nat] :
( ( edmond475474835dges_a @ SV14 @ SV23 )
= ( edmond475474835dges_a @ SV14 @ SV23 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[421]) ).
thf(434,plain,
! [SV14: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV14 )
= ( edmond475474835dges_a @ SV14 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[421]) ).
thf(435,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ~ ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
| ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[422]) ).
thf(436,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= ( ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[422]) ).
thf(437,plain,
! [SV16: product_prod_nat_nat > $o,SV5: product_prod_nat_nat > $o] :
( ( ( ~ ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV5 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ SV16 ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY57: product_prod_nat_nat] :
~ ( ~ ( SV5 @ SY57 )
| ~ ( SV16 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(438,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) ) )
= $true )
| ( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(439,plain,
! [SV18: set_Pr1986765409at_nat,SV7: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV7 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV18 @ SV7 )
| ( finite772653738at_nat @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(440,plain,
! [SV19: set_Pr1986765409at_nat,SV8: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV8 @ SV19 ) )
= $true )
| ( ( ~ ( finite772653738at_nat @ SV19 )
| ( finite772653738at_nat @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(441,plain,
! [SV9: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV9 ) ) )
= $false )
| ( ( ~ ! [SY45: product_prod_nat_nat] :
~ ( SV9 @ SY45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(442,plain,
! [SV20: set_Pr1986765409at_nat,SV10: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV10 @ SV20 ) )
= $true )
| ( ( ~ ~ ( finite772653738at_nat @ SV10 )
| ~ ( finite772653738at_nat @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(443,plain,
! [SV11: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV11 )
= $false )
| ( ( ~ ! [SY47: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ SY47 )
!= SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(444,plain,
! [SV21: product_prod_nat_nat > product_prod_nat_nat,SV12: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV12 ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY62: product_prod_nat_nat] :
~ ! [SY63: product_prod_nat_nat] :
~ ~ ( ( SY62
!= ( SV21 @ SY63 ) )
| ~ ( SV12 @ SY63 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(445,plain,
! [SV24: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,SV22: product_prod_nat_nat > $o,SV13: product_prod_nat_nat > $o] :
( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV13 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV22 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY68: product_prod_nat_nat] :
~ ! [SY69: product_prod_nat_nat] :
~ ~ ! [SY70: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SY68
!= ( SV24 @ SY69 @ SY70 ) )
| ~ ( SV13 @ SY69 ) )
| ~ ( SV22 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(446,plain,
! [SV25: nat,SV14: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV14 @ SV25 )
= ( edmond475474835dges_a @ SV14 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(447,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(448,plain,
! [SV16: product_prod_nat_nat > $o,SV5: product_prod_nat_nat > $o] :
( ( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV5 ) )
| ( finite772653738at_nat @ ( collec7649004at_nat @ SV16 ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY57: product_prod_nat_nat] :
~ ( ~ ( SV5 @ SY57 )
| ~ ( SV16 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(449,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false )
| ( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(450,plain,
! [SV18: set_Pr1986765409at_nat,SV7: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV7 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV18 @ SV7 )
| ( finite772653738at_nat @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(451,plain,
! [SV19: set_Pr1986765409at_nat,SV8: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV8 @ SV19 )
= $false )
| ( ( ~ ( finite772653738at_nat @ SV19 )
| ( finite772653738at_nat @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(452,plain,
! [SV9: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV9 ) )
= $true )
| ( ( ~ ! [SY45: product_prod_nat_nat] :
~ ( SV9 @ SY45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(453,plain,
! [SV20: set_Pr1986765409at_nat,SV10: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV10 @ SV20 )
= $false )
| ( ( ~ ~ ( finite772653738at_nat @ SV10 )
| ~ ( finite772653738at_nat @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(454,plain,
! [SV11: set_Pr1986765409at_nat] :
( ( ( ! [SY47: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ SY47 )
!= SV11 ) )
= $false )
| ( ( finite772653738at_nat @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(455,plain,
! [SV21: product_prod_nat_nat > product_prod_nat_nat,SV12: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV12 ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY62: product_prod_nat_nat] :
~ ! [SY63: product_prod_nat_nat] :
~ ~ ( ( SY62
!= ( SV21 @ SY63 ) )
| ~ ( SV12 @ SY63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(456,plain,
! [SV24: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,SV22: product_prod_nat_nat > $o,SV13: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV13 ) ) )
= $true )
| ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV22 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY68: product_prod_nat_nat] :
~ ! [SY69: product_prod_nat_nat] :
~ ~ ! [SY70: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SY68
!= ( SV24 @ SY69 @ SY70 ) )
| ~ ( SV13 @ SY69 ) )
| ~ ( SV22 @ SY70 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(457,plain,
! [SV25: nat,SV14: product_prod_nat_nat > a] :
( ( ! [SV26: nat] :
( ( edmond475474835dges_a @ SV14 @ SV25 @ SV26 )
= ( edmond475474835dges_a @ SV14 @ SV25 @ SV26 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[446]) ).
thf(458,plain,
! [SV25: nat,SV14: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV14 @ SV25 )
= ( edmond475474835dges_a @ SV14 @ SV25 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[446]) ).
thf(459,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(460,plain,
! [SV16: product_prod_nat_nat > $o,SV5: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV5 ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY57: product_prod_nat_nat] :
~ ( ~ ( SV5 @ SY57 )
| ~ ( SV16 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(461,plain,
! [SV5: product_prod_nat_nat > $o,SV16: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV16 ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY57: product_prod_nat_nat] :
~ ( ~ ( SV5 @ SY57 )
| ~ ( SV16 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(462,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
| ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[449]) ).
thf(463,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[449]) ).
thf(464,plain,
! [SV7: set_Pr1986765409at_nat,SV18: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV18 @ SV7 ) )
= $true )
| ( ( finite772653738at_nat @ SV18 )
= $true )
| ( ( finite772653738at_nat @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(465,plain,
! [SV8: set_Pr1986765409at_nat,SV19: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV19 ) )
= $true )
| ( ( finite772653738at_nat @ SV8 )
= $true )
| ( ( ord_le841296385at_nat @ SV8 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(466,plain,
! [SV9: product_prod_nat_nat > $o] :
( ( ( ! [SY45: product_prod_nat_nat] :
~ ( SV9 @ SY45 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(467,plain,
! [SV20: set_Pr1986765409at_nat,SV10: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( finite772653738at_nat @ SV10 ) )
= $true )
| ( ( ~ ( finite772653738at_nat @ SV20 ) )
= $true )
| ( ( ord_le841296385at_nat @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(468,plain,
! [SV11: set_Pr1986765409at_nat] :
( ( ( ( set_Pr2131844118at_nat @ ( sK1_SY47 @ SV11 ) )
!= SV11 )
= $false )
| ( ( finite772653738at_nat @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[454]) ).
thf(469,plain,
! [SV24: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,SV22: product_prod_nat_nat > $o,SV13: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV13 ) )
= $false )
| ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV22 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY68: product_prod_nat_nat] :
~ ! [SY69: product_prod_nat_nat] :
~ ~ ! [SY70: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SY68
!= ( SV24 @ SY69 @ SY70 ) )
| ~ ( SV13 @ SY69 ) )
| ~ ( SV22 @ SY70 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(470,plain,
! [SV27: nat,SV25: nat,SV14: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV14 @ SV25 @ SV27 )
= ( edmond475474835dges_a @ SV14 @ SV25 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(471,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(472,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(473,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(474,plain,
! [SV7: set_Pr1986765409at_nat,SV18: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV18 @ SV7 )
= $false )
| ( ( finite772653738at_nat @ SV18 )
= $true )
| ( ( finite772653738at_nat @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(475,plain,
! [SV8: set_Pr1986765409at_nat,SV19: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV19 )
= $false )
| ( ( finite772653738at_nat @ SV8 )
= $true )
| ( ( ord_le841296385at_nat @ SV8 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(476,plain,
! [SV9: product_prod_nat_nat > $o] :
( ( ( ~ ( SV9 @ ( sK2_SY45 @ SV9 ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[466]) ).
thf(477,plain,
! [SV20: set_Pr1986765409at_nat,SV10: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV10 ) )
= $false )
| ( ( ~ ( finite772653738at_nat @ SV20 ) )
= $true )
| ( ( ord_le841296385at_nat @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(478,plain,
! [SV11: set_Pr1986765409at_nat] :
( ( ( ( set_Pr2131844118at_nat @ ( sK1_SY47 @ SV11 ) )
= SV11 )
= $true )
| ( ( finite772653738at_nat @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(479,plain,
! [SV13: product_prod_nat_nat > $o,SV24: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,SV22: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV22 ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY68: product_prod_nat_nat] :
~ ! [SY69: product_prod_nat_nat] :
~ ~ ! [SY70: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SY68
!= ( SV24 @ SY69 @ SY70 ) )
| ~ ( SV13 @ SY69 ) )
| ~ ( SV22 @ SY70 ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(480,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(481,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(482,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(483,plain,
! [SV9: product_prod_nat_nat > $o] :
( ( ( SV9 @ ( sK2_SY45 @ SV9 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(484,plain,
! [SV20: set_Pr1986765409at_nat,SV10: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV10 )
= $true )
| ( ( ~ ( finite772653738at_nat @ SV20 ) )
= $true )
| ( ( ord_le841296385at_nat @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(485,plain,
! [SV13: product_prod_nat_nat > $o,SV24: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,SV22: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV22 ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY68: product_prod_nat_nat] :
~ ! [SY69: product_prod_nat_nat] :
~ ~ ! [SY70: product_prod_nat_nat] :
~ ~ ( ~ ~ ( ( SY68
!= ( SV24 @ SY69 @ SY70 ) )
| ~ ( SV13 @ SY69 ) )
| ~ ( SV22 @ SY70 ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(486,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(487,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(488,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) ) )
= $true )
| ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(489,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(490,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(491,plain,
! [SV10: set_Pr1986765409at_nat,SV20: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV20 )
= $false )
| ( ( finite772653738at_nat @ SV10 )
= $true )
| ( ( ord_le841296385at_nat @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(492,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(493,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(494,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(495,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(496,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[490]) ).
thf(497,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(498,plain,
! [SV4: product_prod_nat_nat > $o,SV15: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(499,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(500,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(501,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(502,plain,
! [SV6: product_prod_nat_nat > $o,SV17: product_prod_nat_nat > product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(503,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(504,plain,
! [SV4: product_prod_nat_nat > $o,SV15: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(505,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
| ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(506,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(507,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(508,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(509,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(510,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(511,plain,
! [SV4: product_prod_nat_nat > $o,SV15: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(512,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(513,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(514,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV28: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ SV28 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY72: product_prod_nat_nat] : ( SV17 @ SY72 @ SV28 ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(515,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
| ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(516,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(517,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(518,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY56: product_prod_nat_nat] :
( ( SV4 @ SY56 )
| ( SV15 @ SY56 ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(519,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(520,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV28: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ SV28 ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY72: product_prod_nat_nat] : ( SV17 @ SY72 @ SV28 ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(521,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) ) )
= $false )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(522,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $false )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(523,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(524,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(525,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
| ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(526,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV28: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( SV6 @ SV28 )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY72: product_prod_nat_nat] : ( SV17 @ SY72 @ SV28 ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(527,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY58: product_prod_nat_nat] :
~ ! [SY59: product_prod_nat_nat] :
~ ~ ( ~ ( SV6 @ SY59 )
| ~ ( SV17 @ SY58 @ SY59 ) ) ) )
= $true )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(528,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV6: product_prod_nat_nat > $o] :
( ( ( ! [SY60: product_prod_nat_nat] :
( ~ ( SV6 @ SY60 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY61: product_prod_nat_nat] : ( SV17 @ SY61 @ SY60 ) ) ) ) )
= $true )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(529,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV29: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ SV29 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY73: product_prod_nat_nat] : ( SV17 @ SY73 @ SV29 ) ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(530,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(531,plain,
! [SV4: product_prod_nat_nat > $o,SV15: product_prod_nat_nat > $o] :
( ( ( ~ ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(532,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV30: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ SV30 )
| ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY74: product_prod_nat_nat] : ( SV17 @ SY74 @ SV30 ) ) ) )
= $true )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(533,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV29: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ SV29 ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY73: product_prod_nat_nat] : ( SV17 @ SY73 @ SV29 ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(534,plain,
! [SV15: product_prod_nat_nat > $o,SV4: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(535,plain,
! [SV4: product_prod_nat_nat > $o,SV15: product_prod_nat_nat > $o] :
( ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV4 ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(536,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV30: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( ~ ( SV6 @ SV30 ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY74: product_prod_nat_nat] : ( SV17 @ SY74 @ SV30 ) ) )
= $true )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(537,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV29: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( SV6 @ SV29 )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY73: product_prod_nat_nat] : ( SV17 @ SY73 @ SV29 ) ) )
= $true )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY71: product_prod_nat_nat] : ( SV17 @ SY71 @ ( sK3_SY60 @ SV17 @ SV6 ) ) ) )
= $false )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(538,plain,
! [SV17: product_prod_nat_nat > product_prod_nat_nat > $o,SV30: product_prod_nat_nat,SV6: product_prod_nat_nat > $o] :
( ( ( SV6 @ SV30 )
= $false )
| ( ( finite772653738at_nat
@ ( collec7649004at_nat
@ ^ [SY74: product_prod_nat_nat] : ( SV17 @ SY74 @ SV30 ) ) )
= $true )
| ( ( SV6 @ ( sK3_SY60 @ SV17 @ SV6 ) )
= $true )
| ( ( finite772653738at_nat @ ( collec7649004at_nat @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(539,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[376,538,537,535,534,527,526,523,518,511,510,506,492,491,485,483,478,475,474,470,463,461,460,458,455,436,434,430,409,408,407,406,380,379]) ).
thf(540,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[539]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP049^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 11:15:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.92/0.54 ..
% 1.92/0.54
% 1.92/0.54 No.of.Axioms: 17
% 1.92/0.54
% 1.92/0.54 Length.of.Defs: 0
% 1.92/0.54
% 1.92/0.54 Contains.Choice.Funs: false
% 1.92/0.54 ........
% 1.92/0.54
% 1.92/0.54 ********************************
% 1.92/0.54 * All subproblems solved! *
% 1.92/0.54 ********************************
% 1.92/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:539,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.92/0.54
% 1.92/0.54 %**** Beginning of derivation protocol ****
% 1.92/0.54 % SZS output start CNFRefutation
% See solution above
% 1.92/0.54
% 1.92/0.54 %**** End of derivation protocol ****
% 1.92/0.54 %**** no. of clauses in derivation: 203 ****
% 1.92/0.54 %**** clause counter: 539 ****
% 1.92/0.54
% 1.92/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:539,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------