%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU200+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/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 10:43:23 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 123 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 599 ( 161 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 817 ( 173 ~; 110 |; 15 &; 490 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 124 ( 0 ^; 118 !; 6 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
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_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(8,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(14,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(17,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(18,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(20,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(31,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(34,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(35,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(41,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(44,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(46,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[31]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(51,plain,
( ( ! [SY15: $i] :
( ( relation @ SY15 )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ SY15 ) ) @ ( relation_rng @ SY15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(52,plain,
( ( ( relation @ sK2_SY15 )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY15 ) ) @ ( relation_rng @ sK2_SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(53,plain,
( ( relation @ sK2_SY15 )
= $true ),
inference(standard_cnf,[status(thm)],[52]) ).
thf(54,plain,
( ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY15 ) ) @ ( relation_rng @ sK2_SY15 ) )
= $false ),
inference(standard_cnf,[status(thm)],[52]) ).
thf(55,plain,
( ( ~ ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY15 ) ) @ ( relation_rng @ sK2_SY15 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(57,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(58,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(59,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(60,plain,
$true = $true,
inference(copy,[status(thm)],[46]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(62,plain,
$true = $true,
inference(copy,[status(thm)],[44]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(65,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(66,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(70,plain,
( ( relation @ sK2_SY15 )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(71,plain,
( ( ~ ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY15 ) ) @ ( relation_rng @ sK2_SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(72,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(73,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(74,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng_restriction @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(80,plain,
! [SV1: $i] :
( ( ! [SY16: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(81,plain,
( ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY15 ) ) @ ( relation_rng @ sK2_SY15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(82,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ~ ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(84,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY17: $i] :
( ~ ( relation @ SY17 )
| ( relation @ ( relation_rng_restriction @ SV3 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) )
| ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV5: $i] :
( ( ! [SY18: $i] :
( ~ ( relation @ SY18 )
| ( subset @ ( relation_rng_restriction @ SV5 @ SY18 ) @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ! [SY19: $i] :
( ~ ( relation @ SY19 )
| ~ ( subset @ SV6 @ SY19 )
| ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SY19 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( relation @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(91,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(92,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(93,plain,
( ( ~ ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(94,plain,
! [SV3: $i,SV9: $i] :
( ( ~ ( relation @ SV9 )
| ( relation @ ( relation_rng_restriction @ SV3 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV5: $i,SV10: $i] :
( ( ~ ( relation @ SV10 )
| ( subset @ ( relation_rng_restriction @ SV5 @ SV10 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ! [SY19: $i] :
( ~ ( relation @ SY19 )
| ~ ( subset @ SV6 @ SY19 )
| ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SY19 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SY19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( relation @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(99,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(100,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
( ( ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(102,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV5 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ! [SY19: $i] :
( ~ ( relation @ SY19 )
| ~ ( subset @ SV6 @ SY19 )
| ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SY19 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SY19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( relation @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(107,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(108,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV2 ) )
| ~ ( relation @ ( relation_rng @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(109,plain,
( ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV3: $i,SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV3 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(112,plain,
! [SV5: $i,SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV5 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 )
| ~ ( subset @ SV6 @ SV11 )
| ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(114,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(115,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(116,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(117,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(118,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(119,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(120,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ SV4 ) )
= $true )
| ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV6 @ SV11 )
| ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(122,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(123,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(124,plain,
! [SV2: $i] :
( ( ( empty @ ( relation_rng @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(125,plain,
! [SV2: $i] :
( ( ( relation @ ( relation_rng @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(126,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(127,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(128,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $false )
| ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV6: $i,SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( subset @ SV6 @ SV11 )
| ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(130,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(132,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) ) ) )
= $true )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(133,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( empty @ SV4 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(134,plain,
! [SV11: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) ) ) )
= $true )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(135,plain,
! [SV4: $i] :
( ( ( empty @ ( relation_rng @ SV4 ) )
= $false )
| ( ( empty @ SV4 )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(136,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) )
| ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) ) )
= $false )
| ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(137,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) ) )
= $false )
| ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(138,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) ) )
= $false )
| ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(139,plain,
! [SV11: $i,SV6: $i] :
( ( ( subset @ ( relation_dom @ SV6 ) @ ( relation_dom @ SV11 ) )
= $true )
| ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(140,plain,
! [SV11: $i,SV6: $i] :
( ( ( subset @ ( relation_rng @ SV6 ) @ ( relation_rng @ SV11 ) )
= $true )
| ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(141,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[57,140,139,135,130,127,126,125,124,123,112,110,106,90,81,70,62,60,59,58]) ).
thf(142,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU200+1 : TPTP v9.3.1. Released v3.3.0.
% 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 15:04:46 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
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 14
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 0
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24 ..
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:141,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24
% 0.08/0.24 %**** End of derivation protocol ****
% 0.08/0.24 %**** no. of clauses in derivation: 123 ****
% 0.08/0.24 %**** clause counter: 141 ****
% 0.08/0.24
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:141,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------