%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU165+3 : 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 : n009.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 10:43:12 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 111 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 591 ( 147 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1396 ( 284 ~; 148 |; 17 &; 926 @)
% ( 11 <=>; 10 =>; 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 : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 270 ( 0 ^; 270 !; 0 ?; 270 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SY15,type,
sK3_SY15: $i ).
thf(tp_sK4_SY17,type,
sK4_SY17: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(8,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [SY12: $i,SY13: $i,SY14: $i] :
( ( in @ ( ordered_pair @ sK1_A @ SY12 ) @ ( cartesian_product2 @ SY13 @ SY14 ) )
<=> ( ( in @ sK1_A @ SY13 )
& ( in @ SY12 @ SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(15,plain,
( ( ! [SY15: $i,SY16: $i] :
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ SY15 @ SY16 ) )
<=> ( ( in @ sK1_A @ SY15 )
& ( in @ sK2_SY12 @ SY16 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [SY17: $i] :
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ SY17 ) )
<=> ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
<=> ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ sK4_SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
=> ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ sK4_SY17 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[17]) ).
thf(19,plain,
( ( ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ sK4_SY17 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[17]) ).
thf(20,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
=> ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ sK4_SY17 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ sK4_SY17 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(24,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(25,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
=> ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ sK4_SY17 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
| ~ ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(29,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV2: $i] :
( ( ! [SY19: $i,SY20: $i,SY21: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV2 @ SY19 ) @ ( cartesian_product2 @ SY20 @ SY21 ) )
| ~ ( ~ ( in @ SV2 @ SY20 )
| ~ ( in @ SY19 @ SY21 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV2 @ SY20 )
| ~ ( in @ SY19 @ SY21 ) )
| ( in @ ( ordered_pair @ SV2 @ SY19 ) @ ( cartesian_product2 @ SY20 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
| ~ ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ~ ( in @ SV3 @ SY22 )
| ~ ( in @ SY22 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY23: $i,SY24: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SY23 @ SY24 ) )
| ~ ( ~ ( in @ SV2 @ SY23 )
| ~ ( in @ SV5 @ SY24 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV2 @ SY23 )
| ~ ( in @ SV5 @ SY24 ) )
| ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SY23 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV4: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY25: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SY25 ) )
| ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SY25 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SY25 ) )
| ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
| ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) )
| ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ( ~ ( in @ sK1_A @ sK3_SY15 ) )
= $true )
| ( ( ~ ( in @ sK2_SY12 @ sK4_SY17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ SV3 @ SV6 )
= $false )
| ( ( ~ ( in @ SV6 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
| ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) )
| ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
( ( ( in @ sK1_A @ sK3_SY15 )
= $false )
| ( ( ~ ( in @ sK2_SY12 @ sK4_SY17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ SV3 )
= $false )
| ( ( in @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
| ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) )
| ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
( ( ( in @ sK2_SY12 @ sK4_SY17 )
= $false )
| ( ( in @ sK1_A @ sK3_SY15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
| ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) )
| ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV7 )
| ~ ( in @ SV5 @ SV8 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(60,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV7 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(61,plain,
! [SV7: $i,SV2: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV5 @ SV8 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( in @ SV2 @ SV7 )
= $true )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV7: $i,SV2: $i,SV8: $i,SV5: $i] :
( ( ( in @ SV5 @ SV8 )
= $true )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(65,plain,
! [SV8: $i,SV5: $i,SV7: $i,SV2: $i] :
( ( ( in @ SV2 @ SV7 )
= $false )
| ( ( ~ ( in @ SV5 @ SV8 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV7: $i,SV2: $i,SV8: $i,SV5: $i] :
( ( ( in @ SV5 @ SV8 )
= $false )
| ( ( in @ SV2 @ SV7 )
= $false )
| ( ( in @ ( ordered_pair @ SV2 @ SV5 ) @ ( cartesian_product2 @ SV7 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(67,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,66,64,63,51,48,40]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(71,plain,
( ( ~ ( ( ( in @ sK1_A @ sK3_SY15 )
& ( in @ sK2_SY12 @ sK4_SY17 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(72,plain,
( ( ~ ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(75,plain,
! [SV9: $i] :
( ( ! [SY26: $i] :
~ ( empty @ ( ordered_pair @ SV9 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(76,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV10: $i] :
( ( ! [SY27: $i] :
( ~ ( in @ SV10 @ SY27 )
| ~ ( in @ SY27 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV11: $i] :
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SY28 ) @ ( cartesian_product2 @ SY29 @ SY30 ) )
| ~ ( ~ ( in @ SV11 @ SY29 )
| ~ ( in @ SY28 @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV11 @ SY29 )
| ~ ( in @ SY28 @ SY30 ) )
| ( in @ ( ordered_pair @ SV11 @ SY28 ) @ ( cartesian_product2 @ SY29 @ SY30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV12: $i,SV9: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV9 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(80,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY12 ) @ ( cartesian_product2 @ sK3_SY15 @ sK4_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(82,plain,
! [SV13: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV13 )
| ~ ( in @ SV13 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV14: $i,SV11: $i] :
( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SY31 @ SY32 ) )
| ~ ( ~ ( in @ SV11 @ SY31 )
| ~ ( in @ SV14 @ SY32 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV11 @ SY31 )
| ~ ( in @ SV14 @ SY32 ) )
| ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SY31 @ SY32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV12: $i,SV9: $i] :
( ( empty @ ( ordered_pair @ SV9 @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(86,plain,
! [SV13: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV15: $i,SV14: $i,SV11: $i] :
( ( ! [SY33: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SY33 ) )
| ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SY33 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SY33 ) )
| ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
( ( ~ ( in @ sK1_A @ sK3_SY15 )
| ~ ( in @ sK2_SY12 @ sK4_SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV13: $i,SV10: $i] :
( ( ( in @ SV10 @ SV13 )
= $false )
| ( ( ~ ( in @ SV13 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV16: $i,SV15: $i,SV14: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
| ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) )
| ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(91,plain,
( ( ~ ( in @ sK1_A @ sK3_SY15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(92,plain,
( ( ~ ( in @ sK2_SY12 @ sK4_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(93,plain,
! [SV10: $i,SV13: $i] :
( ( ( in @ SV13 @ SV10 )
= $false )
| ( ( in @ SV10 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV16: $i,SV15: $i,SV14: $i,SV11: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
| ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) )
| ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(95,plain,
( ( in @ sK1_A @ sK3_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(96,plain,
( ( in @ sK2_SY12 @ sK4_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV16: $i,SV15: $i,SV14: $i,SV11: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
| ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(98,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) )
| ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(99,plain,
! [SV16: $i,SV15: $i,SV14: $i,SV11: $i] :
( ( ~ ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
| ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(100,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ~ ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) )
| ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(101,plain,
! [SV16: $i,SV15: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(102,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV16: $i,SV15: $i,SV14: $i,SV11: $i] :
( ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(104,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(105,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(106,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV15 )
| ~ ( in @ SV14 @ SV16 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(107,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV15 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(108,plain,
! [SV15: $i,SV11: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(109,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV16 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(110,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( in @ SV11 @ SV15 )
= $true )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(111,plain,
! [SV15: $i,SV11: $i,SV16: $i,SV14: $i] :
( ( ( in @ SV14 @ SV16 )
= $true )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(112,plain,
! [SV16: $i,SV14: $i,SV15: $i,SV11: $i] :
( ( ( in @ SV11 @ SV15 )
= $false )
| ( ( ~ ( in @ SV14 @ SV16 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV15: $i,SV11: $i,SV16: $i,SV14: $i] :
( ( ( in @ SV14 @ SV16 )
= $false )
| ( ( in @ SV11 @ SV15 )
= $false )
| ( ( in @ ( ordered_pair @ SV11 @ SV14 ) @ ( cartesian_product2 @ SV15 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(114,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[81,113,111,110,96,95,93,84]) ).
thf(115,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[114,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+3 : 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
% 0.09/0.17 % Computer : n009.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 15:02:32 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.24
% 0.09/0.24 No.of.Axioms: 3
% 0.09/0.24
% 0.09/0.24 Length.of.Defs: 0
% 0.09/0.24
% 0.09/0.24 Contains.Choice.Funs: false
% 0.09/0.24 ...
% 0.09/0.24
% 0.09/0.24 ********************************
% 0.09/0.24 * All subproblems solved! *
% 0.09/0.24 ********************************
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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)
% 0.09/0.24
% 0.09/0.24 %**** Beginning of derivation protocol ****
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24
% 0.09/0.24 %**** End of derivation protocol ****
% 0.09/0.24 %**** no. of clauses in derivation: 111 ****
% 0.09/0.24 %**** clause counter: 114 ****
% 0.09/0.24
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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)
%------------------------------------------------------------------------------