%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM533+2 : TPTP v9.3.1. Released v4.0.0.
% 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 : n011.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 10:34:20 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 142 ( 88 unt; 0 typ; 0 def)
% Number of atoms : 791 ( 226 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 913 ( 187 ~; 170 |; 29 &; 481 @)
% ( 0 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 144 ( 0 ^; 144 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_aSubsetOf0,type,
aSubsetOf0: $i > $i > $o ).
thf(tp_isCountable0,type,
isCountable0: $i > $o ).
thf(tp_isFinite0,type,
isFinite0: $i > $o ).
thf(tp_sK1_W0,type,
sK1_W0: $i ).
thf(tp_slcrc0,type,
slcrc0: $i ).
thf(tp_xA,type,
xA: $i ).
thf(tp_xB,type,
xB: $i ).
thf(tp_xC,type,
xC: $i ).
thf(1,axiom,
! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
thf(2,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
thf(3,axiom,
! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isFinite0 @ W0 ) )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ( isFinite0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
thf(4,axiom,
! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ( W0 != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(5,axiom,
! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ~ ( isFinite0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
thf(6,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isCountable0 @ W0 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCntRel) ).
thf(7,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
thf(8,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isFinite0 @ W0 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFinRel) ).
thf(9,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(10,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(11,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(12,axiom,
( ( aSet0 @ xA )
& ( aSet0 @ xB )
& ( aSet0 @ xC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__522) ).
thf(13,conjecture,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xB ) )
& ( aSubsetOf0 @ xA @ xB )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xB )
=> ( aElementOf0 @ W0 @ xC ) )
& ( aSubsetOf0 @ xB @ xC ) )
=> ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(14,negated_conjecture,
( ( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xB ) )
& ( aSubsetOf0 @ xA @ xB )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xB )
=> ( aElementOf0 @ W0 @ xC ) )
& ( aSubsetOf0 @ xB @ xC ) )
=> ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xB ) )
& ( aSubsetOf0 @ xA @ xB )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xB )
=> ( aElementOf0 @ W0 @ xC ) )
& ( aSubsetOf0 @ xB @ xC ) )
=> ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isFinite0 @ W0 ) )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ( isFinite0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ( W0 != slcrc0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isCountable0 @ W0 ) )
=> ~ ( isFinite0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isCountable0 @ W0 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( isFinite0 @ slcrc0 )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( ( isFinite0 @ W0 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ( aSet0 @ xA )
& ( aSet0 @ xB )
& ( aSet0 @ xC ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xB ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(29,plain,
( ( aSubsetOf0 @ xA @ xB )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(30,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xB )
=> ( aElementOf0 @ W0 @ xC ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(31,plain,
( ( aSubsetOf0 @ xB @ xC )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(32,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) )
= $false ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(33,plain,
( ( ~ ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xA )
=> ( aElementOf0 @ W0 @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(34,plain,
( ( ( aElementOf0 @ sK1_W0 @ xA )
& ~ ( aElementOf0 @ sK1_W0 @ xC )
& ~ ( aSubsetOf0 @ xA @ xC ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(35,plain,
( ( ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xA )
| ( aElementOf0 @ W0 @ xB ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(36,plain,
( ( ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xB )
| ( aElementOf0 @ W0 @ xC ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(37,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( aSet0 @ W1 )
| ~ ( aSubsetOf0 @ W0 @ W1 )
| ~ ( aSubsetOf0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(38,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ( aSubsetOf0 @ W0 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(39,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isFinite0 @ W0 )
| ! [W1: $i] :
( ~ ( aSubsetOf0 @ W1 @ W0 )
| ( isFinite0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(40,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isCountable0 @ W0 )
| ( W0 != slcrc0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(41,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isCountable0 @ W0 )
| ~ ( isFinite0 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(42,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(43,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(44,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(45,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(46,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(47,plain,
( ( ( aSet0 @ xA )
& ( aSet0 @ xB )
& ( aSet0 @ xC ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(48,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(49,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(50,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ! [W1: $i] :
( ~ ( aElementOf0 @ W1 @ W0 )
| ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(51,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(52,plain,
( ( isFinite0 @ slcrc0 )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(53,plain,
( ( ! [W0: $i] :
~ ( aSet0 @ W0 )
| $true )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(54,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isCountable0 @ W0 )
| ~ ( isFinite0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(55,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isCountable0 @ W0 )
| ( W0 != slcrc0 ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(56,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( isFinite0 @ W0 )
| ! [W1: $i] :
( ~ ( aSubsetOf0 @ W1 @ W0 )
| ( isFinite0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(57,plain,
( ( ! [W0: $i] :
( ~ ( aSet0 @ W0 )
| ( aSubsetOf0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(58,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aSet0 @ W0 )
| ~ ( aSet0 @ W1 )
| ~ ( aSubsetOf0 @ W0 @ W1 )
| ~ ( aSubsetOf0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(59,plain,
( ( aSubsetOf0 @ xB @ xC )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(60,plain,
( ( ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xB )
| ( aElementOf0 @ W0 @ xC ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(61,plain,
( ( aSubsetOf0 @ xA @ xB )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(62,plain,
( ( ! [W0: $i] :
( ~ ( aElementOf0 @ W0 @ xA )
| ( aElementOf0 @ W0 @ xB ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(63,plain,
( ( ( aElementOf0 @ sK1_W0 @ xA )
& ~ ( aElementOf0 @ sK1_W0 @ xC )
& ~ ( aSubsetOf0 @ xA @ xC ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(64,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ sK1_W0 @ xA )
| ~ ~ ( aElementOf0 @ sK1_W0 @ xC ) )
| ~ ~ ( aSubsetOf0 @ xA @ xC ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(65,plain,
( ( ~ ( ~ ~ ( ~ ( aSet0 @ xA )
| ~ ( aSet0 @ xB ) )
| ~ ( aSet0 @ xC ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(66,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(67,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(68,plain,
! [SV3: $i] :
( ( ~ ( aSet0 @ SV3 )
| ! [SY16: $i] :
( ~ ( aElementOf0 @ SY16 @ SV3 )
| ( aElement0 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(69,plain,
( ( ( ! [W0: $i] :
~ ( aSet0 @ W0 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(70,plain,
( ( ( ! [W0: $i] :
~ ( aSet0 @ W0 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(71,plain,
! [SV4: $i] :
( ( ~ ( aSet0 @ SV4 )
| ~ ( isCountable0 @ SV4 )
| ~ ( isFinite0 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV5: $i] :
( ( ~ ( aSet0 @ SV5 )
| ~ ( isCountable0 @ SV5 )
| ( SV5 != slcrc0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(73,plain,
! [SV6: $i] :
( ( ~ ( aSet0 @ SV6 )
| ~ ( isFinite0 @ SV6 )
| ! [SY17: $i] :
( ~ ( aSubsetOf0 @ SY17 @ SV6 )
| ( isFinite0 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(74,plain,
! [SV7: $i] :
( ( ~ ( aSet0 @ SV7 )
| ( aSubsetOf0 @ SV7 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(75,plain,
! [SV8: $i] :
( ( ! [SY18: $i] :
( ~ ( aSet0 @ SV8 )
| ~ ( aSet0 @ SY18 )
| ~ ( aSubsetOf0 @ SV8 @ SY18 )
| ~ ( aSubsetOf0 @ SY18 @ SV8 )
| ( SV8 = SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(76,plain,
! [SV9: $i] :
( ( ~ ( aElementOf0 @ SV9 @ xB )
| ( aElementOf0 @ SV9 @ xC ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV10: $i] :
( ( ~ ( aElementOf0 @ SV10 @ xA )
| ( aElementOf0 @ SV10 @ xB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(78,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK1_W0 @ xA )
| ~ ~ ( aElementOf0 @ sK1_W0 @ xC ) )
| ~ ~ ( aSubsetOf0 @ xA @ xC ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(79,plain,
( ( ~ ~ ( ~ ( aSet0 @ xA )
| ~ ( aSet0 @ xB ) )
| ~ ( aSet0 @ xC ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(80,plain,
! [SV3: $i] :
( ( ( ~ ( aSet0 @ SV3 ) )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( aElementOf0 @ SY16 @ SV3 )
| ( aElement0 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV11: $i] :
( ( ( ~ ( aSet0 @ SV11 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV12: $i] :
( ( ( ~ ( aSet0 @ SV12 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV4: $i] :
( ( ( ~ ( aSet0 @ SV4 )
| ~ ( isCountable0 @ SV4 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV5: $i] :
( ( ( ~ ( aSet0 @ SV5 )
| ~ ( isCountable0 @ SV5 ) )
= $true )
| ( ( SV5 != slcrc0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV6: $i] :
( ( ( ~ ( aSet0 @ SV6 )
| ~ ( isFinite0 @ SV6 ) )
= $true )
| ( ( ! [SY17: $i] :
( ~ ( aSubsetOf0 @ SY17 @ SV6 )
| ( isFinite0 @ SY17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV7: $i] :
( ( ( ~ ( aSet0 @ SV7 ) )
= $true )
| ( ( aSubsetOf0 @ SV7 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( aSet0 @ SV8 )
| ~ ( aSet0 @ SV13 )
| ~ ( aSubsetOf0 @ SV8 @ SV13 )
| ~ ( aSubsetOf0 @ SV13 @ SV8 )
| ( SV8 = SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV9: $i] :
( ( ( ~ ( aElementOf0 @ SV9 @ xB ) )
= $true )
| ( ( aElementOf0 @ SV9 @ xC )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV10: $i] :
( ( ( ~ ( aElementOf0 @ SV10 @ xA ) )
= $true )
| ( ( aElementOf0 @ SV10 @ xB )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(90,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK1_W0 @ xA )
| ~ ~ ( aElementOf0 @ sK1_W0 @ xC ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(91,plain,
( ( ~ ~ ( aSubsetOf0 @ xA @ xC ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(92,plain,
( ( ~ ~ ( ~ ( aSet0 @ xA )
| ~ ( aSet0 @ xB ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(93,plain,
( ( ~ ( aSet0 @ xC ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(94,plain,
! [SV3: $i] :
( ( ( aSet0 @ SV3 )
= $false )
| ( ( ! [SY16: $i] :
( ~ ( aElementOf0 @ SY16 @ SV3 )
| ( aElement0 @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV11: $i] :
( ( ( aSet0 @ SV11 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(96,plain,
! [SV12: $i] :
( ( ( aSet0 @ SV12 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(97,plain,
! [SV4: $i] :
( ( ( ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ( isCountable0 @ SV4 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(98,plain,
! [SV5: $i] :
( ( ( ~ ( aSet0 @ SV5 ) )
= $true )
| ( ( ~ ( isCountable0 @ SV5 ) )
= $true )
| ( ( SV5 != slcrc0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(99,plain,
! [SV6: $i] :
( ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV6 ) )
= $true )
| ( ( ! [SY17: $i] :
( ~ ( aSubsetOf0 @ SY17 @ SV6 )
| ( isFinite0 @ SY17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(100,plain,
! [SV7: $i] :
( ( ( aSet0 @ SV7 )
= $false )
| ( ( aSubsetOf0 @ SV7 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( aSet0 @ SV8 )
| ~ ( aSet0 @ SV13 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV8 @ SV13 )
| ~ ( aSubsetOf0 @ SV13 @ SV8 )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV9: $i] :
( ( ( aElementOf0 @ SV9 @ xB )
= $false )
| ( ( aElementOf0 @ SV9 @ xC )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV10: $i] :
( ( ( aElementOf0 @ SV10 @ xA )
= $false )
| ( ( aElementOf0 @ SV10 @ xB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(104,plain,
( ( ~ ( ~ ( aElementOf0 @ sK1_W0 @ xA )
| ~ ~ ( aElementOf0 @ sK1_W0 @ xC ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(105,plain,
( ( ~ ( aSubsetOf0 @ xA @ xC ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(106,plain,
( ( ~ ( ~ ( aSet0 @ xA )
| ~ ( aSet0 @ xB ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(107,plain,
( ( aSet0 @ xC )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(108,plain,
! [SV3: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ SV3 )
| ( aElement0 @ SV14 ) )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV4: $i] :
( ( ( aSet0 @ SV4 )
= $false )
| ( ( ~ ( isCountable0 @ SV4 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV5: $i] :
( ( ( aSet0 @ SV5 )
= $false )
| ( ( ~ ( isCountable0 @ SV5 ) )
= $true )
| ( ( SV5 != slcrc0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV6: $i] :
( ( ( aSet0 @ SV6 )
= $false )
| ( ( ~ ( isFinite0 @ SV6 ) )
= $true )
| ( ( ! [SY17: $i] :
( ~ ( aSubsetOf0 @ SY17 @ SV6 )
| ( isFinite0 @ SY17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( aSet0 @ SV8 ) )
= $true )
| ( ( ~ ( aSet0 @ SV13 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV8 @ SV13 )
| ~ ( aSubsetOf0 @ SV13 @ SV8 )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(113,plain,
( ( ~ ( aElementOf0 @ sK1_W0 @ xA )
| ~ ~ ( aElementOf0 @ sK1_W0 @ xC ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(114,plain,
( ( aSubsetOf0 @ xA @ xC )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
( ( ~ ( aSet0 @ xA )
| ~ ( aSet0 @ xB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV3: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ SV3 ) )
= $true )
| ( ( aElement0 @ SV14 )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(117,plain,
! [SV4: $i] :
( ( ( isCountable0 @ SV4 )
= $false )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( ~ ( isFinite0 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV5: $i] :
( ( ( isCountable0 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( SV5 != slcrc0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV6: $i] :
( ( ( isFinite0 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false )
| ( ( ! [SY17: $i] :
( ~ ( aSubsetOf0 @ SY17 @ SV6 )
| ( isFinite0 @ SY17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV13: $i,SV8: $i] :
( ( ( aSet0 @ SV8 )
= $false )
| ( ( ~ ( aSet0 @ SV13 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV8 @ SV13 )
| ~ ( aSubsetOf0 @ SV13 @ SV8 )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(121,plain,
( ( ~ ( aElementOf0 @ sK1_W0 @ xA ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(122,plain,
( ( ~ ~ ( aElementOf0 @ sK1_W0 @ xC ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(123,plain,
( ( ~ ( aSet0 @ xA ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(124,plain,
( ( ~ ( aSet0 @ xB ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(125,plain,
! [SV3: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ SV3 )
= $false )
| ( ( aElement0 @ SV14 )
= $true )
| ( ( aSet0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV4: $i] :
( ( ( isFinite0 @ SV4 )
= $false )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( isCountable0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(127,plain,
! [SV5: $i] :
( ( ( SV5 = slcrc0 )
= $false )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( isCountable0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(128,plain,
! [SV6: $i,SV15: $i] :
( ( ( ~ ( aSubsetOf0 @ SV15 @ SV6 )
| ( isFinite0 @ SV15 ) )
= $true )
| ( ( aSet0 @ SV6 )
= $false )
| ( ( isFinite0 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV8: $i,SV13: $i] :
( ( ( aSet0 @ SV13 )
= $false )
| ( ( aSet0 @ SV8 )
= $false )
| ( ( ~ ( aSubsetOf0 @ SV8 @ SV13 )
| ~ ( aSubsetOf0 @ SV13 @ SV8 )
| ( SV8 = SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(130,plain,
( ( aElementOf0 @ sK1_W0 @ xA )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(131,plain,
( ( ~ ( aElementOf0 @ sK1_W0 @ xC ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(132,plain,
( ( aSet0 @ xA )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(133,plain,
( ( aSet0 @ xB )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(134,plain,
! [SV6: $i,SV15: $i] :
( ( ( ~ ( aSubsetOf0 @ SV15 @ SV6 ) )
= $true )
| ( ( isFinite0 @ SV15 )
= $true )
| ( ( aSet0 @ SV6 )
= $false )
| ( ( isFinite0 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( aSubsetOf0 @ SV8 @ SV13 )
| ~ ( aSubsetOf0 @ SV13 @ SV8 ) )
= $true )
| ( ( SV8 = SV13 )
= $true )
| ( ( aSet0 @ SV8 )
= $false )
| ( ( aSet0 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(136,plain,
( ( aElementOf0 @ sK1_W0 @ xC )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(137,plain,
! [SV6: $i,SV15: $i] :
( ( ( aSubsetOf0 @ SV15 @ SV6 )
= $false )
| ( ( isFinite0 @ SV15 )
= $true )
| ( ( aSet0 @ SV6 )
= $false )
| ( ( isFinite0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( aSubsetOf0 @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV13 @ SV8 ) )
= $true )
| ( ( SV8 = SV13 )
= $true )
| ( ( aSet0 @ SV8 )
= $false )
| ( ( aSet0 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV13: $i,SV8: $i] :
( ( ( aSubsetOf0 @ SV8 @ SV13 )
= $false )
| ( ( ~ ( aSubsetOf0 @ SV13 @ SV8 ) )
= $true )
| ( ( SV8 = SV13 )
= $true )
| ( ( aSet0 @ SV8 )
= $false )
| ( ( aSet0 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(140,plain,
! [SV8: $i,SV13: $i] :
( ( ( aSubsetOf0 @ SV13 @ SV8 )
= $false )
| ( ( aSubsetOf0 @ SV8 @ SV13 )
= $false )
| ( ( SV8 = SV13 )
= $true )
| ( ( aSet0 @ SV8 )
= $false )
| ( ( aSet0 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(141,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,140,137,136,133,132,130,127,126,125,114,107,103,102,100,96,95,67,66,61,59]) ).
thf(142,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM533+2 : TPTP v9.3.1. Released v4.0.0.
% 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 : n011.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 13:24:21 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: 12
% 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:0,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:141,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 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: 142 ****
% 0.07/0.24 %**** clause counter: 141 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:141,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------