%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:28 AM UTC 2026
% Result : Theorem 0.09s 0.32s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 113 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 783 ( 341 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1116 ( 268 ~; 235 |; 12 &; 578 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 210 ( 0 ^; 210 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
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_function,type,
function: $i > $o ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY24,type,
sK3_SY24: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(4,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(6,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(8,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(28,conjecture,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(29,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[28]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[29]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(35,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(36,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(37,plain,
$true = $true,
inference(unfold_def,[status(thm)],[8]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(41,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(42,plain,
( ( ! [SY15: $i] :
( ( in @ SY15 @ sK1_A )
=> ( ( apply @ ( identity_relation @ sK1_A ) @ SY15 )
= SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(43,plain,
( ( ( in @ sK2_SY15 @ sK1_A )
=> ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY15 )
= sK2_SY15 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(44,plain,
( ( in @ sK2_SY15 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(45,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY15 )
= sK2_SY15 )
= $false ),
inference(standard_cnf,[status(thm)],[43]) ).
thf(46,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY15 )
!= sK2_SY15 )
= $true ),
inference(polarity_switch,[status(thm)],[45]) ).
thf(47,plain,
$true = $true,
inference(copy,[status(thm)],[41]) ).
thf(48,plain,
$true = $true,
inference(copy,[status(thm)],[40]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(51,plain,
$true = $true,
inference(copy,[status(thm)],[37]) ).
thf(52,plain,
$true = $true,
inference(copy,[status(thm)],[36]) ).
thf(53,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(58,plain,
( ( in @ sK2_SY15 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(59,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY15 )
!= sK2_SY15 )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ~ ( ~ ( ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ( ( relation_dom @ SX1 )
!= SX0 )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SX1 )
!= SX0 )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(61,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( identity_relation @ SX0 ) )
| ~ ( function @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(63,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(66,plain,
! [SV1: $i] :
( ( relation @ ( identity_relation @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(67,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY15 )
= sK2_SY15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
( ~ ~ ( ~ ( relation @ SY16 )
| ~ ( function @ SY16 ) )
| ~ ( ~ ( ( SY16
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SY16 )
!= SV2 )
| ~ ! [SY17: $i] :
( ~ ( in @ SY17 @ SV2 )
| ( ( apply @ SY16 @ SY17 )
= SY17 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SY16 )
!= SV2 )
| ~ ! [SY18: $i] :
( ~ ( in @ SY18 @ SV2 )
| ( ( apply @ SY16 @ SY18 )
= SY18 ) ) )
| ( SY16
= ( identity_relation @ SV2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV3: $i] :
( ( ~ ( ~ ( relation @ ( identity_relation @ SV3 ) )
| ~ ( function @ ( identity_relation @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
~ ~ ( ~ ( in @ SV4 @ SY19 )
| ~ ( empty @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV5: $i] :
( ( ! [SY20: $i] :
( ~ ( in @ SV5 @ SY20 )
| ( element @ SV5 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV6: $i] :
( ( ! [SY21: $i] :
( ~ ( element @ SV6 @ SY21 )
| ( empty @ SY21 )
| ( in @ SV6 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV7: $i] :
( ( ! [SY22: $i] :
( ~ ( in @ SV7 @ SY22 )
| ~ ( in @ SY22 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV2: $i,SV8: $i] :
( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV3: $i] :
( ( ~ ( relation @ ( identity_relation @ SV3 ) )
| ~ ( function @ ( identity_relation @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ~ ( ~ ( in @ SV4 @ SV9 )
| ~ ( empty @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV10 )
| ( element @ SV5 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( element @ SV6 @ SV11 )
| ( empty @ SV11 )
| ( in @ SV6 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV12 )
| ~ ( in @ SV12 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV3: $i] :
( ( ~ ( relation @ ( identity_relation @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV3: $i] :
( ( ~ ( function @ ( identity_relation @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(83,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( in @ SV4 @ SV9 )
| ~ ( empty @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV10 ) )
= $true )
| ( ( element @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ SV11 ) )
= $true )
| ( ( ( empty @ SV11 )
| ( in @ SV6 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV3: $i] :
( ( relation @ ( identity_relation @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV3: $i] :
( ( function @ ( identity_relation @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV9 )
| ~ ( empty @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(91,plain,
! [SV10: $i,SV5: $i] :
( ( ( in @ SV5 @ SV10 )
= $false )
| ( ( element @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV11: $i,SV6: $i] :
( ( ( element @ SV6 @ SV11 )
= $false )
| ( ( ( empty @ SV11 )
| ( in @ SV6 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV12: $i,SV7: $i] :
( ( ( in @ SV7 @ SV12 )
= $false )
| ( ( ~ ( in @ SV12 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(95,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV9 ) )
= $true )
| ( ( ~ ( empty @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV6: $i,SV11: $i] :
( ( ( empty @ SV11 )
= $true )
| ( ( in @ SV6 @ SV11 )
= $true )
| ( ( element @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV7: $i,SV12: $i] :
( ( ( in @ SV12 @ SV7 )
= $false )
| ( ( in @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV9: $i,SV4: $i] :
( ( ( in @ SV4 @ SV9 )
= $false )
| ( ( ~ ( empty @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV2: $i,SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(101,plain,
! [SV4: $i,SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( in @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(102,plain,
! [SV2: $i,SV8: $i] :
( ( ( function @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( ~ ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(104,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(105,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(106,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( SV8
!= ( identity_relation @ SV2 ) )
| ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(107,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
| ( SV8
= ( identity_relation @ SV2 ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(108,plain,
! [SV2: $i,SV8: $i] :
( ( ( SV8
!= ( identity_relation @ SV2 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(109,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) ) )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(110,plain,
! [SV2: $i,SV8: $i] :
( ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(111,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) ) )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(112,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(113,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( ( relation_dom @ SV8 )
!= SV2 )
| ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(114,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( relation_dom @ SV8 )
!= SV2 )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(115,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(116,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( relation_dom @ SV8 )
!= SV2 )
= $true )
| ( ( ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( relation_dom @ SV8 )
= SV2 )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(118,plain,
! [SV8: $i,SV2: $i] :
( ( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ SV2 )
| ( ( apply @ SV8 @ SY23 )
= SY23 ) ) )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(119,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( relation_dom @ SV8 )
= SV2 )
= $false )
| ( ( ~ ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(120,plain,
! [SV8: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV2 )
| ( ( apply @ SV8 @ SV13 )
= SV13 ) )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(121,plain,
! [SV8: $i,SV2: $i] :
( ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV2 )
| ( ( apply @ SV8 @ SY24 )
= SY24 ) ) )
= $false )
| ( ( ( relation_dom @ SV8 )
= SV2 )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(122,plain,
! [SV8: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV2 ) )
= $true )
| ( ( ( apply @ SV8 @ SV13 )
= SV13 )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(123,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK3_SY24 @ SV8 @ SV2 ) @ SV2 )
| ( ( apply @ SV8 @ ( sK3_SY24 @ SV8 @ SV2 ) )
= ( sK3_SY24 @ SV8 @ SV2 ) ) )
= $false )
| ( ( ( relation_dom @ SV8 )
= SV2 )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(124,plain,
! [SV8: $i,SV2: $i,SV13: $i] :
( ( ( in @ SV13 @ SV2 )
= $false )
| ( ( ( apply @ SV8 @ SV13 )
= SV13 )
= $true )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(125,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK3_SY24 @ SV8 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ( relation_dom @ SV8 )
= SV2 )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(126,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( apply @ SV8 @ ( sK3_SY24 @ SV8 @ SV2 ) )
= ( sK3_SY24 @ SV8 @ SV2 ) )
= $false )
| ( ( ( relation_dom @ SV8 )
= SV2 )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(127,plain,
! [SV2: $i,SV8: $i] :
( ( ( in @ ( sK3_SY24 @ SV8 @ SV2 ) @ SV2 )
= $true )
| ( ( ( relation_dom @ SV8 )
= SV2 )
= $false )
| ( ( SV8
= ( identity_relation @ SV2 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(128,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,127,126,124,117,101,97,96,91,89,88,67,66,58,52,51,48]) ).
thf(129,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Oct 6 15:07:57 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.32
% 0.09/0.32 No.of.Axioms: 11
% 0.09/0.32
% 0.09/0.32 Length.of.Defs: 0
% 0.09/0.32
% 0.09/0.32 Contains.Choice.Funs: false
% 0.09/0.32 ...
% 0.09/0.32
% 0.09/0.32 ********************************
% 0.09/0.32 * All subproblems solved! *
% 0.09/0.32 ********************************
% 0.09/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:12,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:128,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.32
% 0.09/0.32 %**** Beginning of derivation protocol ****
% 0.09/0.32 % SZS output start CNFRefutation
% See solution above
% 0.09/0.32
% 0.09/0.32 %**** End of derivation protocol ****
% 0.09/0.32 %**** no. of clauses in derivation: 113 ****
% 0.09/0.32 %**** clause counter: 128 ****
% 0.09/0.32
% 0.09/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:12,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:128,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------