%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET974+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:42:40 AM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 78 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 418 ( 127 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1363 ( 296 ~; 104 |; 18 &; 935 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 6 con; 0-5 aty)
% Number of variables : 284 ( 0 ^; 281 !; 3 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
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_SY17,type,
sK2_SY17: $i ).
thf(tp_sK3_SY20,type,
sK3_SY20: $i ).
thf(tp_sK4_SY22,type,
sK4_SY22: $i ).
thf(tp_sK5_SY47,type,
sK5_SY47: $i > $i > $i > $i > $i > $i ).
thf(tp_sK6_SY49,type,
sK6_SY49: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_SY38,type,
sK7_SY38: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $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] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( ordered_pair @ F @ G ) )
& ( in @ F @ ( set_intersection2 @ B @ D ) )
& ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(12,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( ordered_pair @ F @ G ) )
& ( in @ F @ ( set_intersection2 @ B @ D ) )
& ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [SY17: $i,SY18: $i,SY19: $i] :
( ( ( disjoint @ sK1_A @ SY17 )
| ( disjoint @ SY18 @ SY19 ) )
=> ( disjoint @ ( cartesian_product2 @ sK1_A @ SY18 ) @ ( cartesian_product2 @ SY17 @ SY19 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(19,plain,
( ( ! [SY20: $i,SY21: $i] :
( ( ( disjoint @ sK1_A @ sK2_SY17 )
| ( disjoint @ SY20 @ SY21 ) )
=> ( disjoint @ ( cartesian_product2 @ sK1_A @ SY20 ) @ ( cartesian_product2 @ sK2_SY17 @ SY21 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ! [SY22: $i] :
( ( ( disjoint @ sK1_A @ sK2_SY17 )
| ( disjoint @ sK3_SY20 @ SY22 ) )
=> ( disjoint @ ( cartesian_product2 @ sK1_A @ sK3_SY20 ) @ ( cartesian_product2 @ sK2_SY17 @ SY22 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
( ( ( ( disjoint @ sK1_A @ sK2_SY17 )
| ( disjoint @ sK3_SY20 @ sK4_SY22 ) )
=> ( disjoint @ ( cartesian_product2 @ sK1_A @ sK3_SY20 ) @ ( cartesian_product2 @ sK2_SY17 @ sK4_SY22 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ( disjoint @ sK1_A @ sK2_SY17 )
| ( disjoint @ sK3_SY20 @ sK4_SY22 ) )
= $true ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(23,plain,
( ( disjoint @ ( cartesian_product2 @ sK1_A @ sK3_SY20 ) @ ( cartesian_product2 @ sK2_SY17 @ sK4_SY22 ) )
= $false ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( disjoint @ ( cartesian_product2 @ sK1_A @ sK3_SY20 ) @ ( cartesian_product2 @ sK2_SY17 @ sK4_SY22 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( ordered_pair @ F @ G ) )
& ( in @ F @ ( set_intersection2 @ B @ D ) )
& ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(28,plain,
( ( ( disjoint @ sK1_A @ sK2_SY17 )
| ( disjoint @ sK3_SY20 @ sK4_SY22 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(29,plain,
( ( ~ ( disjoint @ ( cartesian_product2 @ sK1_A @ sK3_SY20 ) @ ( cartesian_product2 @ sK2_SY17 @ sK4_SY22 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ~ ( ~ ( in @ SX0 @ ( set_intersection2 @ ( cartesian_product2 @ SX1 @ SX2 ) @ ( cartesian_product2 @ SX3 @ SX4 ) ) )
| ~ ! [SX5: $i,SX6: $i] :
~ ~ ( ~ ~ ( ( SX0
!= ( ordered_pair @ SX5 @ SX6 ) )
| ~ ( in @ SX5 @ ( set_intersection2 @ SX1 @ SX3 ) ) )
| ~ ( in @ SX6 @ ( set_intersection2 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( disjoint @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(33,plain,
( ( ( disjoint @ sK1_A @ sK2_SY17 )
= $true )
| ( ( disjoint @ sK3_SY20 @ sK4_SY22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( disjoint @ ( cartesian_product2 @ sK1_A @ sK3_SY20 ) @ ( cartesian_product2 @ sK2_SY17 @ sK4_SY22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV1: $i] :
( ( ! [SY23: $i,SY24: $i,SY25: $i,SY26: $i] :
~ ~ ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SY23 @ SY24 ) @ ( cartesian_product2 @ SY25 @ SY26 ) ) )
| ~ ! [SY27: $i,SY28: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY27 @ SY28 ) )
| ~ ( in @ SY27 @ ( set_intersection2 @ SY23 @ SY25 ) ) )
| ~ ( in @ SY28 @ ( set_intersection2 @ SY24 @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV2: $i] :
( ( ! [SY29: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV2 @ SY29 )
| ~ ! [SY30: $i] :
~ ( in @ SY30 @ ( set_intersection2 @ SV2 @ SY29 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ SY31 @ ( set_intersection2 @ SV2 @ SY29 ) )
| ~ ( disjoint @ SV2 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV3: $i] :
( ( ! [SY32: $i] :
( ~ ( disjoint @ SV3 @ SY32 )
| ( disjoint @ SY32 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY33: $i,SY34: $i,SY35: $i] :
~ ~ ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SY33 ) @ ( cartesian_product2 @ SY34 @ SY35 ) ) )
| ~ ! [SY36: $i,SY37: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY36 @ SY37 ) )
| ~ ( in @ SY36 @ ( set_intersection2 @ SV4 @ SY34 ) ) )
| ~ ( in @ SY37 @ ( set_intersection2 @ SY33 @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV2 @ SV5 )
| ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) )
| ~ ( disjoint @ SV2 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( disjoint @ SV3 @ SV6 )
| ( disjoint @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ! [SY40: $i,SY41: $i] :
~ ~ ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SY40 @ SY41 ) ) )
| ~ ! [SY42: $i,SY43: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY42 @ SY43 ) )
| ~ ( in @ SY42 @ ( set_intersection2 @ SV4 @ SY40 ) ) )
| ~ ( in @ SY43 @ ( set_intersection2 @ SV7 @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV2 @ SV5 )
| ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) )
| ~ ( disjoint @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( disjoint @ SV3 @ SV6 ) )
= $true )
| ( ( disjoint @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ! [SY44: $i] :
~ ~ ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SY44 ) ) )
| ~ ! [SY45: $i,SY46: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY45 @ SY46 ) )
| ~ ( in @ SY45 @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY46 @ ( set_intersection2 @ SV7 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV2 @ SV5 )
| ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) )
| ~ ( disjoint @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV6: $i,SV3: $i] :
( ( ( disjoint @ SV3 @ SV6 )
= $false )
| ( ( disjoint @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ~ ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
| ~ ! [SY47: $i,SY48: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY47 @ SY48 ) )
| ~ ( in @ SY47 @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY48 @ ( set_intersection2 @ SV7 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV2 @ SV5 )
| ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) )
| ~ ( disjoint @ SV2 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
| ~ ! [SY47: $i,SY48: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY47 @ SY48 ) )
| ~ ( in @ SY47 @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY48 @ ( set_intersection2 @ SV7 @ SV9 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV2 @ SV5 )
| ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) )
| ~ ( disjoint @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
| ~ ! [SY47: $i,SY48: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY47 @ SY48 ) )
| ~ ( in @ SY47 @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY48 @ ( set_intersection2 @ SV7 @ SV9 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( disjoint @ SV2 @ SV5 )
| ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) )
| ~ ( disjoint @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY47 @ SY48 ) )
| ~ ( in @ SY47 @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY48 @ ( set_intersection2 @ SV7 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ~ ( disjoint @ SV2 @ SV5 ) )
= $true )
| ( ( ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false )
| ( ( ~ ! [SY47: $i,SY48: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY47 @ SY48 ) )
| ~ ( in @ SY47 @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY48 @ ( set_intersection2 @ SV7 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( disjoint @ SV2 @ SV5 ) )
= $false )
| ( ( ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV9: $i,SV7: $i,SV8: $i,SV4: $i,SV1: $i] :
( ( ( ! [SY47: $i,SY48: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ SY47 @ SY48 ) )
| ~ ( in @ SY47 @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY48 @ ( set_intersection2 @ SV7 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV5: $i,SV2: $i] :
( ( ( disjoint @ SV2 @ SV5 )
= $true )
| ( ( ~ ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(65,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY39: $i] :
~ ( in @ SY39 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(66,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( ! [SY49: $i] :
~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ SY49 ) )
| ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ SY49 @ ( set_intersection2 @ SV7 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(67,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY38: $i] :
~ ( in @ SY38 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $false )
| ( ( disjoint @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV5: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
| ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) @ ( set_intersection2 @ SV7 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(70,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK7_SY38 @ SV5 @ SV2 ) @ ( set_intersection2 @ SV2 @ SV5 ) ) )
= $false )
| ( ( disjoint @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(71,plain,
! [SV5: $i,SV2: $i,SV10: $i] :
( ( ( in @ SV10 @ ( set_intersection2 @ SV2 @ SV5 ) )
= $false )
| ( ( ~ ( disjoint @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
| ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) @ ( set_intersection2 @ SV7 @ SV9 ) ) ) )
= $true )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ ( sK7_SY38 @ SV5 @ SV2 ) @ ( set_intersection2 @ SV2 @ SV5 ) )
= $true )
| ( ( disjoint @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV10: $i,SV5: $i,SV2: $i] :
( ( ( disjoint @ SV2 @ SV5 )
= $false )
| ( ( in @ SV10 @ ( set_intersection2 @ SV2 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( ~ ~ ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
| ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) )
| ~ ( in @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) @ ( set_intersection2 @ SV7 @ SV9 ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( ~ ~ ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
| ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(77,plain,
! [SV1: $i,SV9: $i,SV7: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) @ ( set_intersection2 @ SV7 @ SV9 ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(78,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
| ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) ) )
= $true )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(79,plain,
! [SV1: $i,SV9: $i,SV7: $i,SV8: $i,SV4: $i] :
( ( ( in @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) @ ( set_intersection2 @ SV7 @ SV9 ) )
= $true )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(80,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
| ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(81,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( SV1
!= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(82,plain,
! [SV1: $i,SV4: $i,SV8: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) ) )
= $false )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(83,plain,
! [SV4: $i,SV8: $i,SV7: $i,SV9: $i,SV1: $i] :
( ( ( SV1
= ( ordered_pair @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( sK6_SY49 @ SV4 @ SV8 @ SV7 @ SV9 @ SV1 ) ) )
= $true )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(84,plain,
! [SV1: $i,SV4: $i,SV8: $i,SV7: $i,SV9: $i] :
( ( ( in @ ( sK5_SY47 @ SV9 @ SV7 @ SV8 @ SV4 @ SV1 ) @ ( set_intersection2 @ SV4 @ SV8 ) )
= $true )
| ( ( in @ SV1 @ ( set_intersection2 @ ( cartesian_product2 @ SV4 @ SV7 ) @ ( cartesian_product2 @ SV8 @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(85,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,84,83,79,74,73,47,34]) ).
thf(86,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.17 % Computer : n015.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Oct 6 15:01:13 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.24
% 0.12/0.24 No.of.Axioms: 3
% 0.12/0.24
% 0.12/0.24 Length.of.Defs: 0
% 0.12/0.24
% 0.12/0.24 Contains.Choice.Funs: false
% 0.12/0.24 ..
% 0.12/0.24
% 0.12/0.24 ********************************
% 0.12/0.24 * All subproblems solved! *
% 0.12/0.24 ********************************
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:85,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.24
% 0.12/0.24 %**** Beginning of derivation protocol ****
% 0.12/0.24 % SZS output start CNFRefutation
% See solution above
% 0.12/0.24
% 0.12/0.24 %**** End of derivation protocol ****
% 0.12/0.24 %**** no. of clauses in derivation: 78 ****
% 0.12/0.24 %**** clause counter: 85 ****
% 0.12/0.24
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:85,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------