%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM405+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 : n026.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 10:33:36 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 88 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 477 ( 120 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 819 ( 216 ~; 125 |; 6 &; 454 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 156 ( 0 ^; 153 !; 3 ?; 156 :)
% 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_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_non_empty,type,
relation_non_empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i > $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( in @ B @ A )
<=> ( ordinal @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(33,conjecture,
! [A: $i] :
~ ! [B: $i] :
( ( ordinal @ B )
=> ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_ordinal1) ).
thf(34,negated_conjecture,
( ( ! [A: $i] :
~ ! [B: $i] :
( ( ordinal @ B )
=> ( in @ B @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,plain,
( ( ! [A: $i] :
~ ! [B: $i] :
( ( ordinal @ B )
=> ( in @ B @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(37,plain,
( ( ! [A: $i] :
~ ! [B: $i] :
( ( in @ B @ A )
<=> ( ordinal @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(39,plain,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(41,plain,
( ( ~ ! [SY13: $i] :
( ( ordinal @ SY13 )
=> ( in @ SY13 @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(42,plain,
( ( ! [SY13: $i] :
( ( ordinal @ SY13 )
=> ( in @ SY13 @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(44,plain,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(46,plain,
( ( ! [A: $i] :
~ ! [B: $i] :
( ( in @ B @ A )
<=> ( ordinal @ B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(48,plain,
( ( ! [SY13: $i] :
( ( ordinal @ SY13 )
=> ( in @ SY13 @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ( ordinal @ SX1 ) )
| ~ ( ~ ( ordinal @ SX1 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(51,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( ordinal @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( ordinal @ SX2 ) )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(52,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(54,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( in @ SX0 @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(55,plain,
! [SV1: $i] :
( ( ! [SY14: $i] :
( ~ ( in @ SV1 @ SY14 )
| ~ ( in @ SY14 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV2: $i] :
( ( ~ ! [SY15: $i] :
~ ( ~ ( ~ ( in @ SY15 @ SV2 )
| ( ordinal @ SY15 ) )
| ~ ( ~ ( ordinal @ SY15 )
| ( in @ SY15 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV3: $i] :
( ( ~ ! [SY16: $i] :
~ ! [SY17: $i] :
~ ( ~ ( ~ ( in @ SY17 @ SY16 )
| ~ ( ~ ( in @ SY17 @ SV3 )
| ~ ( ordinal @ SY17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY17 @ SV3 )
| ~ ( ordinal @ SY17 ) )
| ( in @ SY17 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV4: $i] :
( ( ! [SY18: $i] :
~ ~ ( ~ ( in @ SV4 @ SY18 )
| ~ ( empty @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV5: $i] :
( ( ! [SY19: $i] :
( ~ ( in @ SV5 @ SY19 )
| ( element @ SV5 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV6: $i] :
( ( ~ ( ordinal @ SV6 )
| ( in @ SV6 @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV7 )
| ~ ( in @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
~ ( ~ ( ~ ( in @ SY15 @ SV2 )
| ( ordinal @ SY15 ) )
| ~ ( ~ ( ordinal @ SY15 )
| ( in @ SY15 @ SV2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV3: $i] :
( ( ! [SY16: $i] :
~ ! [SY17: $i] :
~ ( ~ ( ~ ( in @ SY17 @ SY16 )
| ~ ( ~ ( in @ SY17 @ SV3 )
| ~ ( ordinal @ SY17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY17 @ SV3 )
| ~ ( ordinal @ SY17 ) )
| ( in @ SY17 @ SY16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ~ ( ~ ( in @ SV4 @ SV8 )
| ~ ( empty @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV9: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV9 )
| ( element @ SV5 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV6: $i] :
( ( ( ~ ( ordinal @ SV6 ) )
= $true )
| ( ( in @ SV6 @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV2: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
| ( ordinal @ ( sK2_SY15 @ SV2 ) ) )
| ~ ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(69,plain,
! [SV3: $i] :
( ( ~ ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ ( sK3_SY16 @ SV3 ) )
| ~ ( ~ ( in @ SY20 @ SV3 )
| ~ ( ordinal @ SY20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY20 @ SV3 )
| ~ ( ordinal @ SY20 ) )
| ( in @ SY20 @ ( sK3_SY16 @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(70,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( ~ ( in @ SV4 @ SV8 )
| ~ ( empty @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV9 ) )
= $true )
| ( ( element @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV6: $i] :
( ( ( ordinal @ SV6 )
= $false )
| ( ( in @ SV6 @ sK1_A )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV2: $i] :
( ( ~ ( ~ ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
| ( ordinal @ ( sK2_SY15 @ SV2 ) ) )
| ~ ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(75,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ ( sK3_SY16 @ SV3 ) )
| ~ ( ~ ( in @ SY20 @ SV3 )
| ~ ( ordinal @ SY20 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY20 @ SV3 )
| ~ ( ordinal @ SY20 ) )
| ( in @ SY20 @ ( sK3_SY16 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(76,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV8 )
| ~ ( empty @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(77,plain,
! [SV9: $i,SV5: $i] :
( ( ( in @ SV5 @ SV9 )
= $false )
| ( ( element @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
| ( ordinal @ ( sK2_SY15 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
| ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) )
| ( in @ SV10 @ ( sK3_SY16 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV8 ) )
= $true )
| ( ( ~ ( empty @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV2: $i] :
( ( ( ~ ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
| ( ordinal @ ( sK2_SY15 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ( ~ ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
| ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) )
| ( in @ SV10 @ ( sK3_SY16 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV8: $i,SV4: $i] :
( ( ( in @ SV4 @ SV8 )
= $false )
| ( ( ~ ( empty @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV2: $i] :
( ( ( ~ ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(86,plain,
! [SV2: $i] :
( ( ( ordinal @ ( sK2_SY15 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ( ~ ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
| ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) )
| ( in @ SV10 @ ( sK3_SY16 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV4: $i,SV8: $i] :
( ( ( empty @ SV8 )
= $false )
| ( ( in @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV2: $i] :
( ( ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
= $true )
| ( ( ~ ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(91,plain,
! [SV2: $i] :
( ( ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ordinal @ ( sK2_SY15 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
| ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) )
| ( in @ SV10 @ ( sK3_SY16 @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV2: $i] :
( ( ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) )
| ( in @ ( sK2_SY15 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(95,plain,
! [SV2: $i] :
( ( ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) ) )
= $false )
| ( ( ordinal @ ( sK2_SY15 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV2: $i] :
( ( ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
= $false )
| ( ( ordinal @ ( sK2_SY15 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(97,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( sK3_SY16 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) )
= $true )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV2: $i] :
( ( ( ~ ( ordinal @ ( sK2_SY15 @ SV2 ) ) )
= $false )
| ( ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV2: $i] :
( ( ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
= $false )
| ( ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV2: $i] :
( ( ( ordinal @ ( sK2_SY15 @ SV2 ) )
= $true )
| ( ( ordinal @ ( sK2_SY15 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV3: $i,SV10: $i] :
( ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) ) )
= $false )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV2: $i] :
( ( ( ordinal @ ( sK2_SY15 @ SV2 ) )
= $true )
| ( ( in @ ( sK2_SY15 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(105,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) )
= $false )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(106,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 )
| ~ ( ordinal @ SV10 ) )
= $true )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(107,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 ) )
= $false )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(108,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( ordinal @ SV10 ) )
= $false )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(109,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 ) )
= $true )
| ( ( ~ ( ordinal @ SV10 ) )
= $true )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(110,plain,
! [SV3: $i,SV10: $i] :
( ( ( in @ SV10 @ SV3 )
= $true )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(111,plain,
! [SV3: $i,SV10: $i] :
( ( ( ordinal @ SV10 )
= $true )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(112,plain,
! [SV3: $i,SV10: $i] :
( ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ~ ( ordinal @ SV10 ) )
= $true )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV3: $i,SV10: $i] :
( ( ( ordinal @ SV10 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( in @ SV10 @ ( sK3_SY16 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(114,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,113,111,110,104,101,100,96,89,78,77]) ).
thf(115,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 13:14:31 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.28
% 0.08/0.28 No.of.Axioms: 5
% 0.08/0.28
% 0.08/0.28 Length.of.Defs: 0
% 0.08/0.28
% 0.08/0.28 Contains.Choice.Funs: false
% 0.08/0.28 ..
% 0.08/0.28
% 0.08/0.28 ********************************
% 0.08/0.28 * All subproblems solved! *
% 0.08/0.28 ********************************
% 0.08/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:114,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.28
% 0.08/0.28 %**** Beginning of derivation protocol ****
% 0.08/0.28 % SZS output start CNFRefutation
% See solution above
% 0.08/0.28
% 0.08/0.28 %**** End of derivation protocol ****
% 0.08/0.28 %**** no. of clauses in derivation: 88 ****
% 0.08/0.28 %**** clause counter: 114 ****
% 0.08/0.28
% 0.08/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:114,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------