%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET631+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 : 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 10:40:40 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 79 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 459 ( 117 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 959 ( 267 ~; 125 |; 6 &; 546 @)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 196 ( 0 ^; 193 !; 3 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
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_SY11,type,
sK2_SY11: $i ).
thf(tp_sK3_SY13,type,
sK3_SY13: $i ).
thf(tp_sK4_SY21,type,
sK4_SY21: $i > $i > $i ).
thf(1,axiom,
! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(2,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(3,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(4,conjecture,
! [B: $i,C: $i,D: $i] :
( ( intersect @ B @ ( difference @ C @ D ) )
=> ( intersect @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th113) ).
thf(5,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersect @ B @ ( difference @ C @ D ) )
=> ( intersect @ B @ C ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersect @ B @ ( difference @ C @ D ) )
=> ( intersect @ B @ C ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [SY11: $i,SY12: $i] :
( ( intersect @ sK1_B @ ( difference @ SY11 @ SY12 ) )
=> ( intersect @ sK1_B @ SY11 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [SY13: $i] :
( ( intersect @ sK1_B @ ( difference @ sK2_SY11 @ SY13 ) )
=> ( intersect @ sK1_B @ sK2_SY11 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ( intersect @ sK1_B @ ( difference @ sK2_SY11 @ sK3_SY13 ) )
=> ( intersect @ sK1_B @ sK2_SY11 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
( ( intersect @ sK1_B @ ( difference @ sK2_SY11 @ sK3_SY13 ) )
= $true ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(14,plain,
( ( intersect @ sK1_B @ sK2_SY11 )
= $false ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( intersect @ sK1_B @ sK2_SY11 ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(18,plain,
( ( ! [B: $i,C: $i] :
( ( intersect @ B @ C )
=> ( intersect @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(19,plain,
( ( intersect @ sK1_B @ ( difference @ sK2_SY11 @ sK3_SY13 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ~ ( intersect @ sK1_B @ sK2_SY11 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(22,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)],[17]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( intersect @ SX0 @ SX1 )
| ( intersect @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(24,plain,
( ( intersect @ sK1_B @ sK2_SY11 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i] :
~ ( ~ ( ~ ( member @ SY15 @ ( difference @ SV1 @ SY14 ) )
| ~ ( ~ ( member @ SY15 @ SV1 )
| ~ ~ ( member @ SY15 @ SY14 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY15 @ SV1 )
| ~ ~ ( member @ SY15 @ SY14 ) )
| ( member @ SY15 @ ( difference @ SV1 @ SY14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
~ ( ~ ( ~ ( intersect @ SV2 @ SY16 )
| ~ ! [SY17: $i] :
~ ~ ( ~ ( member @ SY17 @ SV2 )
| ~ ( member @ SY17 @ SY16 ) ) )
| ~ ( ~ ~ ! [SY18: $i] :
~ ~ ( ~ ( member @ SY18 @ SV2 )
| ~ ( member @ SY18 @ SY16 ) )
| ( intersect @ SV2 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ~ ( intersect @ SV3 @ SY19 )
| ( intersect @ SY19 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY20: $i] :
~ ( ~ ( ~ ( member @ SY20 @ ( difference @ SV1 @ SV4 ) )
| ~ ( ~ ( member @ SY20 @ SV1 )
| ~ ~ ( member @ SY20 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY20 @ SV1 )
| ~ ~ ( member @ SY20 @ SV4 ) )
| ( member @ SY20 @ ( difference @ SV1 @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( intersect @ SV2 @ SV5 )
| ~ ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV2 )
| ~ ( member @ SY21 @ SV5 ) ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SV2 )
| ~ ( member @ SY22 @ SV5 ) )
| ( intersect @ SV2 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( intersect @ SV3 @ SV6 )
| ( intersect @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
| ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) )
| ( member @ SV7 @ ( difference @ SV1 @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( intersect @ SV2 @ SV5 )
| ~ ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV2 )
| ~ ( member @ SY21 @ SV5 ) ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SV2 )
| ~ ( member @ SY22 @ SV5 ) )
| ( intersect @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( intersect @ SV3 @ SV6 ) )
= $true )
| ( ( intersect @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( ~ ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
| ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) )
| ( member @ SV7 @ ( difference @ SV1 @ SV4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( intersect @ SV2 @ SV5 )
| ~ ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV2 )
| ~ ( member @ SY21 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ~ ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SV2 )
| ~ ( member @ SY22 @ SV5 ) )
| ( intersect @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ( intersect @ SV3 @ SV6 )
= $false )
| ( ( intersect @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( ~ ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
| ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) )
| ( member @ SV7 @ ( difference @ SV1 @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( intersect @ SV2 @ SV5 )
| ~ ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV2 )
| ~ ( member @ SY21 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SV2 )
| ~ ( member @ SY22 @ SV5 ) )
| ( intersect @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
| ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) )
| ( member @ SV7 @ ( difference @ SV1 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( intersect @ SV2 @ SV5 ) )
= $true )
| ( ( ~ ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV2 )
| ~ ( member @ SY21 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ~ ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SV2 )
| ~ ( member @ SY22 @ SV5 ) ) )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ ( difference @ SV1 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) )
= $true )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: $i,SV2: $i] :
( ( ( intersect @ SV2 @ SV5 )
= $false )
| ( ( ~ ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV2 )
| ~ ( member @ SY21 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SV2 )
| ~ ( member @ SY22 @ SV5 ) ) )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) ) )
= $false )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY21: $i] :
~ ~ ( ~ ( member @ SY21 @ SV2 )
| ~ ( member @ SY21 @ SV5 ) ) )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SV2 )
| ~ ( member @ SY22 @ SV5 ) ) )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) )
= $false )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV1 )
| ~ ~ ( member @ SV7 @ SV4 ) )
= $true )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV2 )
| ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV5 ) ) )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(57,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( member @ SV8 @ SV2 )
| ~ ( member @ SV8 @ SV5 ) ) )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV1 ) )
= $false )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ~ ( member @ SV7 @ SV4 ) )
= $false )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(60,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV1 ) )
= $true )
| ( ( ~ ~ ( member @ SV7 @ SV4 ) )
= $true )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV2 )
| ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV5 ) ) )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(62,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( ~ ( member @ SV8 @ SV2 )
| ~ ( member @ SV8 @ SV5 ) ) )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( member @ SV7 @ SV1 )
= $true )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV4 ) )
= $true )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(65,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( member @ SV7 @ SV1 )
= $false )
| ( ( ~ ~ ( member @ SV7 @ SV4 ) )
= $true )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV2 )
| ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV2 )
| ~ ( member @ SV8 @ SV5 ) )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( member @ SV7 @ SV4 )
= $false )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV4 ) )
= $false )
| ( ( member @ SV7 @ SV1 )
= $false )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV2 ) )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ( member @ SV8 @ SV5 ) )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( member @ SV7 @ SV4 )
= $true )
| ( ( member @ SV7 @ SV1 )
= $false )
| ( ( member @ SV7 @ ( difference @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV2: $i,SV5: $i] :
( ( ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV2 )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV2: $i,SV5: $i] :
( ( ( member @ ( sK4_SY21 @ SV5 @ SV2 ) @ SV5 )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( member @ SV8 @ SV2 )
= $false )
| ( ( ~ ( member @ SV8 @ SV5 ) )
= $true )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( member @ SV8 @ SV5 )
= $false )
| ( ( member @ SV8 @ SV2 )
= $false )
| ( ( intersect @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(78,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,77,75,74,73,68,63,37,24]) ).
thf(79,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET631+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
% 0.07/0.19 % Computer : n009.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:47:47 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 3
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 0
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24 ..
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/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:78,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 79 ****
% 0.07/0.24 %**** clause counter: 78 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/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:78,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------