%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n018.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 10:42:54 AM UTC 2026
% Result : Theorem 0.58s 0.29s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 145 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 1291 ( 401 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 2321 ( 545 ~; 451 |; 6 &;1290 @)
% ( 12 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 5 con; 0-2 aty)
% Number of variables : 343 ( 0 ^; 343 !; 0 ?; 343 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cap_closed,type,
cap_closed: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_finite_subsets,type,
finite_subsets: $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i ).
thf(tp_sK3_SY34,type,
sK3_SY34: $i > $i > $i ).
thf(tp_sK4_SY31,type,
sK4_SY31: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(25,axiom,
! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( preboolean @ B )
=> ( ( B
= ( finite_subsets @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( ( subset @ C @ A )
& ( finite @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(34,conjecture,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(35,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( finite_subsets @ A ) @ ( finite_subsets @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(40,plain,
( ( ! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( preboolean @ B )
=> ( ( B
= ( finite_subsets @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( ( subset @ C @ A )
& ( finite @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(44,plain,
( ( ! [SY18: $i] :
( ( subset @ sK1_A @ SY18 )
=> ( subset @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(45,plain,
( ( ( subset @ sK1_A @ sK2_SY18 )
=> ( subset @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY18 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(46,plain,
( ( subset @ sK1_A @ sK2_SY18 )
= $true ),
inference(standard_cnf,[status(thm)],[45]) ).
thf(47,plain,
( ( subset @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY18 ) )
= $false ),
inference(standard_cnf,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ( subset @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY18 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( preboolean @ B )
=> ( ( B
= ( finite_subsets @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( ( subset @ C @ A )
& ( finite @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(56,plain,
( ( subset @ sK1_A @ sK2_SY18 )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(57,plain,
( ( ~ ( subset @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY18 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( preboolean @ SX1 )
| ~ ( ~ ( ( SX1
!= ( finite_subsets @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ~ ( finite @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX0 )
| ~ ( finite @ SX2 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ~ ( finite @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX0 )
| ~ ( finite @ SX2 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( finite_subsets @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( finite_subsets @ SX0 ) )
| ( finite @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(63,plain,
! [SV1: $i] :
( ( preboolean @ ( finite_subsets @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV2: $i] :
( ( ! [SY19: $i] : ( subset @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(65,plain,
( ( subset @ ( finite_subsets @ sK1_A ) @ ( finite_subsets @ sK2_SY18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
( ~ ( preboolean @ SY20 )
| ~ ( ~ ( ( SY20
!= ( finite_subsets @ SV3 ) )
| ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SY20 )
| ~ ( ~ ( subset @ SY21 @ SV3 )
| ~ ( finite @ SY21 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY21 @ SV3 )
| ~ ( finite @ SY21 ) )
| ( in @ SY21 @ SY20 ) ) ) )
| ~ ( ~ ! [SY22: $i] :
~ ( ~ ( ~ ( in @ SY22 @ SY20 )
| ~ ( ~ ( subset @ SY22 @ SV3 )
| ~ ( finite @ SY22 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY22 @ SV3 )
| ~ ( finite @ SY22 ) )
| ( in @ SY22 @ SY20 ) ) )
| ( SY20
= ( finite_subsets @ SV3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV4: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ~ ( ~ ( subset @ SV4 @ SY23 )
| ~ ( subset @ SY23 @ SY24 ) )
| ( subset @ SV4 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV5: $i] :
( ( ! [SY25: $i] :
~ ( ~ ( ~ ( element @ SV5 @ ( powerset @ SY25 ) )
| ( subset @ SV5 @ SY25 ) )
| ~ ( ~ ( subset @ SV5 @ SY25 )
| ( element @ SV5 @ ( powerset @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV6: $i] :
( ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( finite_subsets @ SV6 ) )
| ( finite @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV7: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ~ ( subset @ SV7 @ SY27 )
| ! [SY28: $i] :
( ~ ( in @ SY28 @ SV7 )
| ( in @ SY28 @ SY27 ) ) )
| ~ ( ~ ! [SY29: $i] :
( ~ ( in @ SY29 @ SV7 )
| ( in @ SY29 @ SY27 ) )
| ( subset @ SV7 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(72,plain,
! [SV3: $i,SV9: $i] :
( ( ~ ( preboolean @ SV9 )
| ~ ( ~ ( ( SV9
!= ( finite_subsets @ SV3 ) )
| ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) )
| ~ ( ~ ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) )
| ( SV9
= ( finite_subsets @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY32: $i] :
( ~ ~ ( ~ ( subset @ SV4 @ SV10 )
| ~ ( subset @ SV10 @ SY32 ) )
| ( subset @ SV4 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( element @ SV5 @ ( powerset @ SV11 ) )
| ( subset @ SV5 @ SV11 ) )
| ~ ( ~ ( subset @ SV5 @ SV11 )
| ( element @ SV5 @ ( powerset @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV6: $i,SV12: $i] :
( ( ~ ( element @ SV12 @ ( finite_subsets @ SV6 ) )
| ( finite @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV7 @ SV13 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV7 )
| ( in @ SY33 @ SV13 ) ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV7 )
| ( in @ SY34 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( preboolean @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( ( SV9
!= ( finite_subsets @ SV3 ) )
| ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) )
| ~ ( ~ ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) )
| ( SV9
= ( finite_subsets @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ~ ~ ( ~ ( subset @ SV4 @ SV10 )
| ~ ( subset @ SV10 @ SV14 ) )
| ( subset @ SV4 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( element @ SV5 @ ( powerset @ SV11 ) )
| ( subset @ SV5 @ SV11 ) )
| ~ ( ~ ( subset @ SV5 @ SV11 )
| ( element @ SV5 @ ( powerset @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( finite_subsets @ SV6 ) ) )
= $true )
| ( ( finite @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV13 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV7 )
| ( in @ SY33 @ SV13 ) ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV7 )
| ( in @ SY34 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV3: $i,SV9: $i] :
( ( ( preboolean @ SV9 )
= $false )
| ( ( ~ ( ~ ( ( SV9
!= ( finite_subsets @ SV3 ) )
| ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) )
| ~ ( ~ ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) )
| ( SV9
= ( finite_subsets @ SV3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV4 @ SV10 )
| ~ ( subset @ SV10 @ SV14 ) ) )
= $true )
| ( ( subset @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( element @ SV5 @ ( powerset @ SV11 ) )
| ( subset @ SV5 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ SV11 )
| ( element @ SV5 @ ( powerset @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV6: $i,SV12: $i] :
( ( ( element @ SV12 @ ( finite_subsets @ SV6 ) )
= $false )
| ( ( finite @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV13 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV7 )
| ( in @ SY33 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV7 )
| ( in @ SY34 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( ( SV9
!= ( finite_subsets @ SV3 ) )
| ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) )
| ~ ( ~ ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) )
| ( SV9
= ( finite_subsets @ SV3 ) ) ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( subset @ SV4 @ SV10 )
| ~ ( subset @ SV10 @ SV14 ) ) )
= $false )
| ( ( subset @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( element @ SV5 @ ( powerset @ SV11 ) )
| ( subset @ SV5 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(92,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV11 )
| ( element @ SV5 @ ( powerset @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(93,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV13 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV7 )
| ( in @ SY33 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV7 )
| ( in @ SY34 @ SV13 ) )
| ( subset @ SV7 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(95,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( ( SV9
!= ( finite_subsets @ SV3 ) )
| ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(96,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( ~ ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) )
| ( SV9
= ( finite_subsets @ SV3 ) ) ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(97,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV10 )
| ~ ( subset @ SV10 @ SV14 ) )
= $true )
| ( ( subset @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(98,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( element @ SV5 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( subset @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV11 ) )
= $true )
| ( ( element @ SV5 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV13 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV7 )
| ( in @ SY33 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV7 )
| ( in @ SY34 @ SV13 ) ) )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV3: $i,SV9: $i] :
( ( ( ( SV9
!= ( finite_subsets @ SV3 ) )
| ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(103,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) )
| ( SV9
= ( finite_subsets @ SV3 ) ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(104,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV10 ) )
= $true )
| ( ( ~ ( subset @ SV10 @ SV14 ) )
= $true )
| ( ( subset @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV11: $i,SV5: $i] :
( ( ( element @ SV5 @ ( powerset @ SV11 ) )
= $false )
| ( ( subset @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV11: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV11 )
= $false )
| ( ( element @ SV5 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV13: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV13 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV7 )
| ( in @ SY33 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV13: $i,SV7: $i] :
( ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ SV7 )
| ( in @ SY34 @ SV13 ) ) )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV3: $i,SV9: $i] :
( ( ( SV9
!= ( finite_subsets @ SV3 ) )
= $true )
| ( ( ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV10 )
= $false )
| ( ( ~ ( subset @ SV10 @ SV14 ) )
= $true )
| ( ( subset @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV13: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV7 )
| ( in @ SV15 @ SV13 ) )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK3_SY34 @ SV13 @ SV7 ) @ SV7 )
| ( in @ ( sK3_SY34 @ SV13 @ SV7 ) @ SV13 ) )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(114,plain,
! [SV3: $i,SV9: $i] :
( ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY30 @ SV3 )
| ~ ( finite @ SY30 ) )
| ( in @ SY30 @ SV9 ) ) ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV3: $i,SV9: $i] :
( ( ( ! [SY31: $i] :
~ ( ~ ( ~ ( in @ SY31 @ SV9 )
| ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY31 @ SV3 )
| ~ ( finite @ SY31 ) )
| ( in @ SY31 @ SV9 ) ) ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV4: $i,SV14: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV14 )
= $false )
| ( ( subset @ SV4 @ SV10 )
= $false )
| ( ( subset @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV13: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV7 ) )
= $true )
| ( ( in @ SV15 @ SV13 )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK3_SY34 @ SV13 @ SV7 ) @ SV7 ) )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(119,plain,
! [SV7: $i,SV13: $i] :
( ( ( in @ ( sK3_SY34 @ SV13 @ SV7 ) @ SV13 )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(120,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV16 @ SV9 )
| ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) )
| ( in @ SV16 @ SV9 ) ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
| ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(122,plain,
! [SV13: $i,SV7: $i,SV15: $i] :
( ( ( in @ SV15 @ SV7 )
= $false )
| ( ( in @ SV15 @ SV13 )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV7: $i,SV13: $i] :
( ( ( in @ ( sK3_SY34 @ SV13 @ SV7 ) @ SV7 )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(124,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV9 )
| ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) )
| ( in @ SV16 @ SV9 ) ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
| ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(126,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV9 )
| ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(127,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) )
| ( in @ SV16 @ SV9 ) ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(128,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
| ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV9 )
| ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(130,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) )
| ( in @ SV16 @ SV9 ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(131,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
| ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(133,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) )
= $true )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(134,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(135,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(136,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( in @ SV16 @ SV9 )
= $false )
| ( ( ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) ) )
= $false )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV9: $i,SV3: $i] :
( ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(139,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(140,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) )
= $false )
| ( ( in @ SV16 @ SV9 )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV3 )
| ~ ( finite @ SV16 ) )
= $true )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(142,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) )
= $false )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 ) )
= $true )
| ( ( ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV3 ) )
= $false )
| ( ( in @ SV16 @ SV9 )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(145,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( finite @ SV16 ) )
= $false )
| ( ( in @ SV16 @ SV9 )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(146,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( finite @ SV16 ) )
= $true )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(147,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
= $false )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(148,plain,
! [SV9: $i,SV3: $i] :
( ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $false )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(149,plain,
! [SV9: $i,SV3: $i] :
( ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV3 )
= $true )
| ( ( in @ SV16 @ SV9 )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(151,plain,
! [SV3: $i,SV9: $i,SV16: $i] :
( ( ( finite @ SV16 )
= $true )
| ( ( in @ SV16 @ SV9 )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(152,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV3 )
= $false )
| ( ( ~ ( finite @ SV16 ) )
= $true )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
= $true )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(154,plain,
! [SV9: $i,SV3: $i] :
( ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(155,plain,
! [SV9: $i,SV3: $i,SV16: $i] :
( ( ( finite @ SV16 )
= $false )
| ( ( subset @ SV16 @ SV3 )
= $false )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $false )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(156,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
= $false )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(157,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
| ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 ) )
= $false )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(159,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
= $false )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(160,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
= $false )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(161,plain,
! [SV9: $i,SV3: $i] :
( ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $false )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(162,plain,
! [SV9: $i,SV3: $i] :
( ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $true )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV9: $i,SV3: $i] :
( ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $true )
| ( ( in @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) ) )
= $true )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(165,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
| ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
= $false )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(166,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 ) )
= $false )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(167,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) ) )
= $false )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(168,plain,
! [SV9: $i,SV3: $i] :
( ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $true )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(169,plain,
! [SV9: $i,SV3: $i] :
( ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $true )
| ( ( subset @ ( sK4_SY31 @ SV3 @ SV9 ) @ SV3 )
= $false )
| ( ( finite @ ( sK4_SY31 @ SV3 @ SV9 ) )
= $false )
| ( ( SV9
= ( finite_subsets @ SV3 ) )
= $true )
| ( ( preboolean @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(170,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,169,168,163,162,161,155,151,150,148,123,122,119,116,106,105,86,71,65,63]) ).
thf(171,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.09/0.17 % Computer : n018.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:02:52 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.58/0.29
% 0.58/0.29 No.of.Axioms: 7
% 0.58/0.29
% 0.58/0.29 Length.of.Defs: 0
% 0.58/0.29
% 0.58/0.29 Contains.Choice.Funs: false
% 0.58/0.29 ....
% 0.58/0.29
% 0.58/0.29 ********************************
% 0.58/0.29 * All subproblems solved! *
% 0.58/0.29 ********************************
% 0.58/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:170,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.58/0.29
% 0.58/0.29 %**** Beginning of derivation protocol ****
% 0.58/0.29 % SZS output start CNFRefutation
% See solution above
% 0.58/0.29
% 0.58/0.29 %**** End of derivation protocol ****
% 0.58/0.29 %**** no. of clauses in derivation: 145 ****
% 0.58/0.29 %**** clause counter: 170 ****
% 0.58/0.29
% 0.58/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:170,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------