%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET596+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 : n016.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 10:40:28 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 117 ( 70 unt; 0 typ; 0 def)
% Number of atoms : 627 ( 214 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1110 ( 240 ~; 162 |; 12 &; 672 @)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 254 ( 0 ^; 254 !; 0 ?; 254 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SY21,type,
sK3_SY21: $i ).
thf(tp_sK4_SY32,type,
sK4_SY32: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(3,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(6,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(7,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
thf(8,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(9,axiom,
! [B: $i,C: $i,D: $i] :
( ( subset @ B @ C )
=> ( subset @ ( intersection @ B @ D ) @ ( intersection @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subset) ).
thf(10,axiom,
! [B: $i] :
( ( subset @ B @ empty_set )
=> ( B = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).
thf(11,conjecture,
! [B: $i,C: $i,D: $i] :
( ( ( subset @ B @ C )
& ( ( intersection @ C @ D )
= empty_set ) )
=> ( ( intersection @ B @ D )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th55) ).
thf(12,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( subset @ B @ C )
& ( ( intersection @ C @ D )
= empty_set ) )
=> ( ( intersection @ B @ D )
= empty_set ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( ( subset @ B @ C )
& ( ( intersection @ C @ D )
= empty_set ) )
=> ( ( intersection @ B @ D )
= empty_set ) ) )
= $false ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( subset @ B @ C )
=> ( subset @ ( intersection @ B @ D ) @ ( intersection @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(21,plain,
( ( ! [B: $i] :
( ( subset @ B @ empty_set )
=> ( B = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(22,plain,
( ( ! [SY19: $i,SY20: $i] :
( ( ( subset @ sK1_B @ SY19 )
& ( ( intersection @ SY19 @ SY20 )
= empty_set ) )
=> ( ( intersection @ sK1_B @ SY20 )
= empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(23,plain,
( ( ! [SY21: $i] :
( ( ( subset @ sK1_B @ sK2_SY19 )
& ( ( intersection @ sK2_SY19 @ SY21 )
= empty_set ) )
=> ( ( intersection @ sK1_B @ SY21 )
= empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ( ( subset @ sK1_B @ sK2_SY19 )
& ( ( intersection @ sK2_SY19 @ sK3_SY21 )
= empty_set ) )
=> ( ( intersection @ sK1_B @ sK3_SY21 )
= empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(25,plain,
( ( subset @ sK1_B @ sK2_SY19 )
= $true ),
inference(standard_cnf,[status(thm)],[24]) ).
thf(26,plain,
( ( ( intersection @ sK2_SY19 @ sK3_SY21 )
= empty_set )
= $true ),
inference(standard_cnf,[status(thm)],[24]) ).
thf(27,plain,
( ( ( intersection @ sK1_B @ sK3_SY21 )
= empty_set )
= $false ),
inference(standard_cnf,[status(thm)],[24]) ).
thf(28,plain,
( ( ( intersection @ sK1_B @ sK3_SY21 )
!= empty_set )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(29,plain,
( ( ! [B: $i] :
( ( subset @ B @ empty_set )
=> ( B = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(30,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( subset @ B @ C )
=> ( subset @ ( intersection @ B @ D ) @ ( intersection @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(32,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(33,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(34,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(35,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(36,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(37,plain,
( ( ( intersection @ sK2_SY19 @ sK3_SY21 )
= empty_set )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(38,plain,
( ( subset @ sK1_B @ sK2_SY19 )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(39,plain,
( ( ( intersection @ sK1_B @ sK3_SY21 )
!= empty_set )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(40,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(41,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)],[33]) ).
thf(42,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(43,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( intersection @ SX0 @ SX2 ) @ ( intersection @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 ) )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(45,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY22: $i] :
( ( intersection @ SV2 @ SY22 )
= ( intersection @ SY22 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV3: $i] :
( ( subset @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
( ( ( intersection @ sK1_B @ sK3_SY21 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV4: $i] :
( ( ~ ( subset @ SV4 @ empty_set )
| ( SV4 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV5: $i] :
( ( ! [SY23: $i] :
~ ( ~ ( ~ ( subset @ SV5 @ SY23 )
| ! [SY24: $i] :
( ~ ( member @ SY24 @ SV5 )
| ( member @ SY24 @ SY23 ) ) )
| ~ ( ~ ! [SY25: $i] :
( ~ ( member @ SY25 @ SV5 )
| ( member @ SY25 @ SY23 ) )
| ( subset @ SV5 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV6: $i] :
( ( ! [SY26: $i] :
~ ( ~ ( ( SV6 != SY26 )
| ~ ( ~ ( subset @ SV6 @ SY26 )
| ~ ( subset @ SY26 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SY26 )
| ~ ( subset @ SY26 @ SV6 ) )
| ( SV6 = SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV7: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( subset @ SV7 @ SY27 )
| ( subset @ ( intersection @ SV7 @ SY28 ) @ ( intersection @ SY27 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV8: $i] :
( ( ! [SY29: $i,SY30: $i] :
~ ( ~ ( ~ ( member @ SY30 @ ( intersection @ SV8 @ SY29 ) )
| ~ ( ~ ( member @ SY30 @ SV8 )
| ~ ( member @ SY30 @ SY29 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY30 @ SV8 )
| ~ ( member @ SY30 @ SY29 ) )
| ( member @ SY30 @ ( intersection @ SV8 @ SY29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV9: $i,SV2: $i] :
( ( ( intersection @ SV2 @ SV9 )
= ( intersection @ SV9 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV4: $i] :
( ( ( ~ ( subset @ SV4 @ empty_set ) )
= $true )
| ( ( SV4 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV5 @ SV10 )
| ! [SY31: $i] :
( ~ ( member @ SY31 @ SV5 )
| ( member @ SY31 @ SV10 ) ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SV10 ) )
| ( subset @ SV5 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ~ ( ( SV6 != SV11 )
| ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) )
| ( SV6 = SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV12: $i,SV7: $i] :
( ( ! [SY33: $i] :
( ~ ( subset @ SV7 @ SV12 )
| ( subset @ ( intersection @ SV7 @ SY33 ) @ ( intersection @ SV12 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV13: $i,SV8: $i] :
( ( ! [SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ ( intersection @ SV8 @ SV13 ) )
| ~ ( ~ ( member @ SY34 @ SV8 )
| ~ ( member @ SY34 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY34 @ SV8 )
| ~ ( member @ SY34 @ SV13 ) )
| ( member @ SY34 @ ( intersection @ SV8 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(61,plain,
! [SV4: $i] :
( ( ( subset @ SV4 @ empty_set )
= $false )
| ( ( SV4 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ SV10 )
| ! [SY31: $i] :
( ~ ( member @ SY31 @ SV5 )
| ( member @ SY31 @ SV10 ) ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SV10 ) )
| ( subset @ SV5 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ( SV6 != SV11 )
| ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) )
| ( SV6 = SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV14: $i,SV12: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV12 )
| ( subset @ ( intersection @ SV7 @ SV14 ) @ ( intersection @ SV12 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
| ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) )
| ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ SV10 )
| ! [SY31: $i] :
( ~ ( member @ SY31 @ SV5 )
| ( member @ SY31 @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ! [SY32: $i] :
( ~ ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SV10 ) )
| ( subset @ SV5 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ( SV6 != SV11 )
| ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) )
| ( SV6 = SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV14: $i,SV12: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV12 ) )
= $true )
| ( ( subset @ ( intersection @ SV7 @ SV14 ) @ ( intersection @ SV12 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
| ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) )
| ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV10 )
| ! [SY31: $i] :
( ~ ( member @ SY31 @ SV5 )
| ( member @ SY31 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ! [SY32: $i] :
( ~ ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SV10 ) )
| ( subset @ SV5 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(74,plain,
! [SV11: $i,SV6: $i] :
( ( ( SV6 != SV11 )
| ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(75,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) )
| ( SV6 = SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(76,plain,
! [SV14: $i,SV12: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV12 )
= $false )
| ( ( subset @ ( intersection @ SV7 @ SV14 ) @ ( intersection @ SV12 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
| ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(78,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) )
| ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(79,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV10 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( member @ SY31 @ SV5 )
| ( member @ SY31 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ! [SY32: $i] :
( ~ ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SV10 ) ) )
= $true )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV11: $i,SV6: $i] :
( ( ( SV6 != SV11 )
= $true )
| ( ( ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
| ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(84,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ~ ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) )
| ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(85,plain,
! [SV10: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV10 )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( member @ SY31 @ SV5 )
| ( member @ SY31 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV10: $i,SV5: $i] :
( ( ( ! [SY32: $i] :
( ~ ( member @ SY32 @ SV5 )
| ( member @ SY32 @ SV10 ) ) )
= $false )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV11: $i,SV6: $i] :
( ( ( SV6 = SV11 )
= $false )
| ( ( ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) ) )
= $false )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV10: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV5 )
| ( member @ SV16 @ SV10 ) )
= $true )
| ( ( subset @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK4_SY32 @ SV10 @ SV5 ) @ SV5 )
| ( member @ ( sK4_SY32 @ SV10 @ SV5 ) @ SV10 ) )
= $false )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(93,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) )
= $false )
| ( ( SV6 = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV11 )
| ~ ( subset @ SV11 @ SV6 ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(95,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV10: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV5 ) )
= $true )
| ( ( member @ SV16 @ SV10 )
= $true )
| ( ( subset @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK4_SY32 @ SV10 @ SV5 ) @ SV5 ) )
= $false )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV5: $i,SV10: $i] :
( ( ( member @ ( sK4_SY32 @ SV10 @ SV5 ) @ SV10 )
= $false )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(100,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV11 ) )
= $false )
| ( ( SV6 = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(101,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV6 ) )
= $false )
| ( ( SV6 = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(102,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ SV6 ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV8 )
| ~ ( member @ SV15 @ SV13 ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV10: $i,SV5: $i,SV16: $i] :
( ( ( member @ SV16 @ SV5 )
= $false )
| ( ( member @ SV16 @ SV10 )
= $true )
| ( ( subset @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV5: $i,SV10: $i] :
( ( ( member @ ( sK4_SY32 @ SV10 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(107,plain,
! [SV11: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV11 )
= $true )
| ( ( SV6 = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV6: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV6 )
= $true )
| ( ( SV6 = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(109,plain,
! [SV11: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( ~ ( subset @ SV11 @ SV6 ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV8 ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(111,plain,
! [SV8: $i,SV13: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV13 ) )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(112,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV8 ) )
= $true )
| ( ( ~ ( member @ SV15 @ SV13 ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV6: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV6 )
= $false )
| ( ( subset @ SV6 @ SV11 )
= $false )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( member @ SV15 @ SV8 )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(115,plain,
! [SV8: $i,SV13: $i,SV15: $i] :
( ( ( member @ SV15 @ SV13 )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(116,plain,
! [SV13: $i,SV8: $i,SV15: $i] :
( ( ( member @ SV15 @ SV8 )
= $false )
| ( ( ~ ( member @ SV15 @ SV13 ) )
= $true )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV8: $i,SV13: $i,SV15: $i] :
( ( ( member @ SV15 @ SV13 )
= $false )
| ( ( member @ SV15 @ SV8 )
= $false )
| ( ( member @ SV15 @ ( intersection @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(118,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,117,115,114,113,108,107,106,105,99,76,61,55,54,48,47,38]) ).
thf(119,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET596+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
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 14:51:59 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 8
% 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:10,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:118,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
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 117 ****
% 0.07/0.25 %**** clause counter: 118 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------