%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET625+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:40:38 AM UTC 2026
% Result : Theorem 0.11s 0.20s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 80 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 443 ( 111 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 800 ( 191 ~; 114 |; 9 &; 468 @)
% ( 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 : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 185 ( 0 ^; 182 !; 3 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_intersect,type,
intersect: $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_sK4_SY23,type,
sK4_SY23: $i > $i > $i ).
thf(tp_sK5_SY24,type,
sK5_SY24: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(2,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(5,conjecture,
! [B: $i,C: $i,D: $i] :
( ( ( intersect @ B @ C )
& ( subset @ C @ D ) )
=> ( intersect @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th101) ).
thf(6,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( intersect @ B @ C )
& ( subset @ C @ D ) )
=> ( intersect @ B @ D ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( intersect @ B @ C )
& ( subset @ C @ D ) )
=> ( intersect @ B @ D ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [SY12: $i,SY13: $i] :
( ( ( intersect @ sK1_B @ SY12 )
& ( subset @ SY12 @ SY13 ) )
=> ( intersect @ sK1_B @ SY13 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ! [SY14: $i] :
( ( ( intersect @ sK1_B @ sK2_SY12 )
& ( subset @ sK2_SY12 @ SY14 ) )
=> ( intersect @ sK1_B @ SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ( ( intersect @ sK1_B @ sK2_SY12 )
& ( subset @ sK2_SY12 @ sK3_SY14 ) )
=> ( intersect @ sK1_B @ sK3_SY14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( intersect @ sK1_B @ sK2_SY12 )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(16,plain,
( ( subset @ sK2_SY12 @ sK3_SY14 )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(17,plain,
( ( intersect @ sK1_B @ sK3_SY14 )
= $false ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( intersect @ sK1_B @ sK3_SY14 ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(20,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(21,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(23,plain,
( ( subset @ sK2_SY12 @ sK3_SY14 )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( intersect @ sK1_B @ sK2_SY12 )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( ~ ( intersect @ sK1_B @ sK3_SY14 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ( intersect @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( intersect @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( intersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(29,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
( ( intersect @ sK1_B @ sK3_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
~ ( ~ ( ~ ( subset @ SV2 @ SY15 )
| ! [SY16: $i] :
( ~ ( member @ SY16 @ SV2 )
| ( member @ SY16 @ SY15 ) ) )
| ~ ( ~ ! [SY17: $i] :
( ~ ( member @ SY17 @ SV2 )
| ( member @ SY17 @ SY15 ) )
| ( subset @ SV2 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: $i] :
( ( ! [SY18: $i] :
( ~ ( intersect @ SV3 @ SY18 )
| ( intersect @ SY18 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
~ ( ~ ( ~ ( intersect @ SV4 @ SY19 )
| ~ ! [SY20: $i] :
~ ~ ( ~ ( member @ SY20 @ SV4 )
| ~ ( member @ SY20 @ SY19 ) ) )
| ~ ( ~ ~ ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV4 )
| ~ ( member @ SY21 @ SY19 ) )
| ( intersect @ SV4 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV2 @ SV5 )
| ! [SY22: $i] :
( ~ ( member @ SY22 @ SV2 )
| ( member @ SY22 @ SV5 ) ) )
| ~ ( ~ ! [SY23: $i] :
( ~ ( member @ SY23 @ SV2 )
| ( member @ SY23 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( intersect @ SV3 @ SV6 )
| ( intersect @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( intersect @ SV4 @ SV7 )
| ~ ! [SY24: $i] :
~ ~ ( ~ ( member @ SY24 @ SV4 )
| ~ ( member @ SY24 @ SV7 ) ) )
| ~ ( ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( member @ SY25 @ SV4 )
| ~ ( member @ SY25 @ SV7 ) )
| ( intersect @ SV4 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV5 )
| ! [SY22: $i] :
( ~ ( member @ SY22 @ SV2 )
| ( member @ SY22 @ SV5 ) ) )
| ~ ( ~ ! [SY23: $i] :
( ~ ( member @ SY23 @ SV2 )
| ( member @ SY23 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( intersect @ SV3 @ SV6 ) )
= $true )
| ( ( intersect @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ( ~ ( intersect @ SV4 @ SV7 )
| ~ ! [SY24: $i] :
~ ~ ( ~ ( member @ SY24 @ SV4 )
| ~ ( member @ SY24 @ SV7 ) ) )
| ~ ( ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( member @ SY25 @ SV4 )
| ~ ( member @ SY25 @ SV7 ) )
| ( intersect @ SV4 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV5 )
| ! [SY22: $i] :
( ~ ( member @ SY22 @ SV2 )
| ( member @ SY22 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ! [SY23: $i] :
( ~ ( member @ SY23 @ SV2 )
| ( member @ SY23 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV6: $i,SV3: $i] :
( ( ( intersect @ SV3 @ SV6 )
= $false )
| ( ( intersect @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ( ~ ( intersect @ SV4 @ SV7 )
| ~ ! [SY24: $i] :
~ ~ ( ~ ( member @ SY24 @ SV4 )
| ~ ( member @ SY24 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ( ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( member @ SY25 @ SV4 )
| ~ ( member @ SY25 @ SV7 ) )
| ( intersect @ SV4 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV5 )
| ! [SY22: $i] :
( ~ ( member @ SY22 @ SV2 )
| ( member @ SY22 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY23: $i] :
( ~ ( member @ SY23 @ SV2 )
| ( member @ SY23 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ( intersect @ SV4 @ SV7 )
| ~ ! [SY24: $i] :
~ ~ ( ~ ( member @ SY24 @ SV4 )
| ~ ( member @ SY24 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( member @ SY25 @ SV4 )
| ~ ( member @ SY25 @ SV7 ) )
| ( intersect @ SV4 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV5 ) )
= $true )
| ( ( ! [SY22: $i] :
( ~ ( member @ SY22 @ SV2 )
| ( member @ SY22 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( member @ SY23 @ SV2 )
| ( member @ SY23 @ SV5 ) ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( intersect @ SV4 @ SV7 ) )
= $true )
| ( ( ~ ! [SY24: $i] :
~ ~ ( ~ ( member @ SY24 @ SV4 )
| ~ ( member @ SY24 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ~ ! [SY25: $i] :
~ ~ ( ~ ( member @ SY25 @ SV4 )
| ~ ( member @ SY25 @ SV7 ) ) )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV5: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV5 )
= $false )
| ( ( ! [SY22: $i] :
( ~ ( member @ SY22 @ SV2 )
| ( member @ SY22 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY23: $i] :
( ~ ( member @ SY23 @ SV2 )
| ( member @ SY23 @ SV5 ) ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV7: $i,SV4: $i] :
( ( ( intersect @ SV4 @ SV7 )
= $false )
| ( ( ~ ! [SY24: $i] :
~ ~ ( ~ ( member @ SY24 @ SV4 )
| ~ ( member @ SY24 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( member @ SY25 @ SV4 )
| ~ ( member @ SY25 @ SV7 ) ) )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV2 )
| ( member @ SV8 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK4_SY23 @ SV5 @ SV2 ) @ SV2 )
| ( member @ ( sK4_SY23 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(59,plain,
! [SV7: $i,SV4: $i] :
( ( ( ! [SY24: $i] :
~ ~ ( ~ ( member @ SY24 @ SV4 )
| ~ ( member @ SY24 @ SV7 ) ) )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV7: $i,SV4: $i] :
( ( ( ! [SY25: $i] :
~ ~ ( ~ ( member @ SY25 @ SV4 )
| ~ ( member @ SY25 @ SV7 ) ) )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV2 ) )
= $true )
| ( ( member @ SV8 @ SV5 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK4_SY23 @ SV5 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV2: $i,SV5: $i] :
( ( ( member @ ( sK4_SY23 @ SV5 @ SV2 ) @ SV5 )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV7 ) ) )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(65,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ SV9 @ SV4 )
| ~ ( member @ SV9 @ SV7 ) ) )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( member @ SV8 @ SV2 )
= $false )
| ( ( member @ SV8 @ SV5 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV2: $i,SV5: $i] :
( ( ( member @ ( sK4_SY23 @ SV5 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV7 ) ) )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ~ ( member @ SV9 @ SV4 )
| ~ ( member @ SV9 @ SV7 ) ) )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV7 ) )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV4 )
| ~ ( member @ SV9 @ SV7 ) )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(72,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV4 ) )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(73,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV7 ) )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV4 ) )
= $true )
| ( ( ~ ( member @ SV9 @ SV7 ) )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV4: $i,SV7: $i] :
( ( ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV4: $i,SV7: $i] :
( ( ( member @ ( sK5_SY24 @ SV7 @ SV4 ) @ SV7 )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( member @ SV9 @ SV4 )
= $false )
| ( ( ~ ( member @ SV9 @ SV7 ) )
= $true )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( member @ SV9 @ SV7 )
= $false )
| ( ( member @ SV9 @ SV4 )
= $false )
| ( ( intersect @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(79,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,78,76,75,67,66,63,42,30,29,24]) ).
thf(80,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET625+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.11/0.15 % Computer : n008.cluster.edu
% 0.11/0.15 % Model : x86_64 x86_64
% 0.11/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.15 % Memory : 8046.5625MB
% 0.11/0.15 % OS : Linux 6.8.0-71-generic
% 0.11/0.15 % CPULimit : 300
% 0.11/0.15 % WCLimit : 300
% 0.11/0.15 % DateTime : Tue Oct 6 14:48:09 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.20
% 0.11/0.20 No.of.Axioms: 4
% 0.11/0.20
% 0.11/0.20 Length.of.Defs: 0
% 0.11/0.20
% 0.11/0.20 Contains.Choice.Funs: false
% 0.11/0.20 ..
% 0.11/0.20
% 0.11/0.20 ********************************
% 0.11/0.20 * All subproblems solved! *
% 0.11/0.20 ********************************
% 0.11/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,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:79,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.20
% 0.11/0.20 %**** Beginning of derivation protocol ****
% 0.11/0.20 % SZS output start CNFRefutation
% See solution above
% 0.11/0.20
% 0.11/0.20 %**** End of derivation protocol ****
% 0.11/0.20 %**** no. of clauses in derivation: 80 ****
% 0.11/0.20 %**** clause counter: 79 ****
% 0.11/0.20
% 0.11/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,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:79,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------