%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM557+3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 10:34:26 AM UTC 2026
% Result : Theorem 0.71s 0.31s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 94 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 723 ( 224 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1109 ( 271 ~; 222 |; 26 &; 567 @)
% ( 0 <=>; 23 =>; 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 : 30 ( 27 usr; 13 con; 0-2 aty)
% Number of variables : 137 ( 0 ^; 137 !; 0 ?; 137 :)
% 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_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_isCountable0,type,
isCountable0: $i > $o ).
thf(tp_isFinite0,type,
isFinite0: $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sbrdtbr0,type,
sbrdtbr0: $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtmndt0,type,
sdtmndt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_slbdtrb0,type,
slbdtrb0: $i > $i ).
thf(tp_slbdtsldtrb0,type,
slbdtsldtrb0: $i > $i > $i ).
thf(tp_slcrc0,type,
slcrc0: $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_szNzAzT0,type,
szNzAzT0: $i ).
thf(tp_szmzazxdt0,type,
szmzazxdt0: $i > $i ).
thf(tp_szmzizndt0,type,
szmzizndt0: $i > $i ).
thf(tp_szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
thf(tp_xP,type,
xP: $i ).
thf(tp_xQ,type,
xQ: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xT,type,
xT: $i ).
thf(tp_xk,type,
xk: $i ).
thf(tp_xx,type,
xx: $i ).
thf(tp_xy,type,
xy: $i ).
thf(41,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 )
& ( aSet0 @ W2 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W2 ) )
=> ( aSubsetOf0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
thf(42,axiom,
! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).
thf(43,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
thf(53,axiom,
( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xP @ xS )
& ( ( sbrdtbr0 @ xP )
= xk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2431) ).
thf(61,axiom,
aElementOf0 @ xx @ xS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
thf(64,axiom,
aElementOf0 @ xk @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
thf(65,conjecture,
( ( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(66,negated_conjecture,
( ( ( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[65]) ).
thf(67,plain,
( ( ( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) )
= $false ),
inference(unfold_def,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 )
& ( aSet0 @ W2 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W2 ) )
=> ( aSubsetOf0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(69,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(70,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(71,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xP @ xS )
& ( ( sbrdtbr0 @ xP )
= xk ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(72,plain,
( ( aElementOf0 @ xx @ xS )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(73,plain,
( ( aElementOf0 @ xk @ szNzAzT0 )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(74,plain,
( ( ~ ( ( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[67]) ).
thf(75,plain,
( ( aElementOf0 @ xk @ szNzAzT0 )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(76,plain,
( ( aElementOf0 @ xx @ xS )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(77,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xP @ xS )
& ( ( sbrdtbr0 @ xP )
= xk ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(78,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(79,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(80,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 )
& ( aSet0 @ W2 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W2 ) )
=> ( aSubsetOf0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(81,plain,
( ( ~ ( ( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(82,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ~ ( aSubsetOf0 @ xP @ xS ) )
| ( ( sbrdtbr0 @ xP )
!= xk ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(83,plain,
( ( ~ ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
| ( ( sbrdtbr0 @ xP )
!= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ( aSubsetOf0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SX0 @ SX1 )
| ~ ( aSubsetOf0 @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 ) )
| ~ ( aSet0 @ SX2 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SX0 @ SX1 )
| ~ ( aSubsetOf0 @ SX1 @ SX2 ) )
| ( aSubsetOf0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(87,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ~ ( aSubsetOf0 @ xP @ xS ) )
| ( ( sbrdtbr0 @ xP )
!= xk ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(88,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
| ( ( sbrdtbr0 @ xP )
!= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV1: $i] :
( ( ~ ( aSet0 @ SV1 )
| ( aSubsetOf0 @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV2: $i] :
( ( ! [SY8: $i] :
( ~ ~ ( ~ ( aSet0 @ SV2 )
| ~ ( aSet0 @ SY8 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SY8 )
| ~ ( aSubsetOf0 @ SY8 @ SV2 ) )
| ( SV2 = SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV3: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SY9 ) )
| ~ ( aSet0 @ SY10 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SY9 )
| ~ ( aSubsetOf0 @ SY9 @ SY10 ) )
| ( aSubsetOf0 @ SV3 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(92,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ~ ( aSubsetOf0 @ xP @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(93,plain,
( ( ( sbrdtbr0 @ xP )
!= xk )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(94,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
| ( ( sbrdtbr0 @ xP )
!= xk ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(95,plain,
( ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(96,plain,
! [SV1: $i] :
( ( ( ~ ( aSet0 @ SV1 ) )
= $true )
| ( ( aSubsetOf0 @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ~ ( ~ ( aSet0 @ SV2 )
| ~ ( aSet0 @ SV4 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
| ( SV2 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY11: $i] :
( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) )
| ~ ( aSet0 @ SY11 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SY11 ) )
| ( aSubsetOf0 @ SV3 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(99,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ~ ( aSubsetOf0 @ xP @ xS ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(100,plain,
( ( ( sbrdtbr0 @ xP )
= xk )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(101,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
| ( ( sbrdtbr0 @ xP )
!= xk ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(102,plain,
! [SV1: $i] :
( ( ( aSet0 @ SV1 )
= $false )
| ( ( aSubsetOf0 @ SV1 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV2 )
| ~ ( aSet0 @ SV4 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
| ( SV2 = SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) )
| ~ ( aSet0 @ SV6 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(105,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ~ ( aSubsetOf0 @ xP @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(106,plain,
( ( ( ~ ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) ) )
= $true )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV2 )
| ~ ( aSet0 @ SV4 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
| ( SV2 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) )
| ~ ( aSet0 @ SV6 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(109,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(110,plain,
( ( ~ ( aSubsetOf0 @ xP @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(111,plain,
( ( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
= $false )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( aSet0 @ SV2 )
| ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
| ( SV2 = SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(113,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) )
| ~ ( aSet0 @ SV6 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(115,plain,
( ( aSubsetOf0 @ xP @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(116,plain,
( ( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(117,plain,
( ( ( aSubsetOf0 @ xP @ xS )
= $false )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(118,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( aSet0 @ SV2 ) )
= $true )
| ( ( ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
| ( SV2 = SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(119,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) )
| ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(120,plain,
! [SV7: $i] :
( ( ~ ( aElementOf0 @ SV7 @ xP )
| ( aElementOf0 @ SV7 @ xS ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(121,plain,
( ( ( ~ ( aElementOf0 @ sK1_SX0 @ xP )
| ( aElementOf0 @ sK1_SX0 @ xS ) )
= $false )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(122,plain,
( ( ( ( sbrdtbr0 @ xP )
= xk )
= $false )
| ( ( aSubsetOf0 @ xP @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV4: $i,SV2: $i] :
( ( ( aSet0 @ SV2 )
= $false )
| ( ( ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
| ( SV2 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) ) )
= $true )
| ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ xP ) )
= $true )
| ( ( aElementOf0 @ SV7 @ xS )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(126,plain,
( ( ( ~ ( aElementOf0 @ sK1_SX0 @ xP ) )
= $false )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(127,plain,
( ( ( aElementOf0 @ sK1_SX0 @ xS )
= $false )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV2: $i,SV4: $i] :
( ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV2 )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
| ( SV2 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(129,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) ) )
= $false )
| ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV7: $i] :
( ( ( aElementOf0 @ SV7 @ xP )
= $false )
| ( ( aElementOf0 @ SV7 @ xS )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(131,plain,
( ( ( aElementOf0 @ sK1_SX0 @ xP )
= $true )
| ( ( ( sbrdtbr0 @ xP )
!= xk )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(132,plain,
( ( ( ( sbrdtbr0 @ xP )
= xk )
= $false )
| ( ( aElementOf0 @ sK1_SX0 @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) ) )
= $true )
| ( ( SV2 = SV4 )
= $true )
| ( ( aSet0 @ SV2 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV5 ) )
= $true )
| ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(135,plain,
( ( ( ( sbrdtbr0 @ xP )
= xk )
= $false )
| ( ( aElementOf0 @ sK1_SX0 @ xP )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) ) )
= $false )
| ( ( SV2 = SV4 )
= $true )
| ( ( aSet0 @ SV2 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(137,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( aSet0 @ SV3 ) )
= $true )
| ( ( ~ ( aSet0 @ SV5 ) )
= $true )
| ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( aSubsetOf0 @ SV2 @ SV4 )
| ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
= $true )
| ( ( SV2 = SV4 )
= $true )
| ( ( aSet0 @ SV2 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(139,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( aSet0 @ SV3 )
= $false )
| ( ( ~ ( aSet0 @ SV5 ) )
= $true )
| ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(140,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( aSubsetOf0 @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
= $true )
| ( ( SV2 = SV4 )
= $true )
| ( ( aSet0 @ SV2 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(141,plain,
! [SV6: $i,SV3: $i,SV5: $i] :
( ( ( aSet0 @ SV5 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(142,plain,
! [SV4: $i,SV2: $i] :
( ( ( aSubsetOf0 @ SV2 @ SV4 )
= $false )
| ( ( ~ ( aSubsetOf0 @ SV4 @ SV2 ) )
= $true )
| ( ( SV2 = SV4 )
= $true )
| ( ( aSet0 @ SV2 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(143,plain,
! [SV5: $i,SV3: $i,SV6: $i] :
( ( ( aSet0 @ SV6 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
| ( aSubsetOf0 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(144,plain,
! [SV2: $i,SV4: $i] :
( ( ( aSubsetOf0 @ SV4 @ SV2 )
= $false )
| ( ( aSubsetOf0 @ SV2 @ SV4 )
= $false )
| ( ( SV2 = SV4 )
= $true )
| ( ( aSet0 @ SV2 )
= $false )
| ( ( aSet0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(145,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV6 )
= $true )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(146,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) ) )
= $false )
| ( ( aSubsetOf0 @ SV3 @ SV6 )
= $true )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(147,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( aSubsetOf0 @ SV3 @ SV5 )
| ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV6 )
= $true )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(148,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( aSubsetOf0 @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV6 )
= $true )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(149,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( aSubsetOf0 @ SV3 @ SV5 )
= $false )
| ( ( ~ ( aSubsetOf0 @ SV5 @ SV6 ) )
= $true )
| ( ( aSubsetOf0 @ SV3 @ SV6 )
= $true )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(150,plain,
! [SV3: $i,SV6: $i,SV5: $i] :
( ( ( aSubsetOf0 @ SV5 @ SV6 )
= $false )
| ( ( aSubsetOf0 @ SV3 @ SV5 )
= $false )
| ( ( aSubsetOf0 @ SV3 @ SV6 )
= $true )
| ( ( aSet0 @ SV5 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(151,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,150,144,135,132,130,122,115,102,100,95,76]) ).
thf(152,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM557+3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 13:25:16 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.71/0.31
% 0.71/0.31 No.of.Axioms: 6
% 0.71/0.31
% 0.71/0.31 Length.of.Defs: 0
% 0.71/0.31
% 0.71/0.31 Contains.Choice.Funs: false
% 0.71/0.31 ...
% 0.71/0.31
% 0.71/0.31 ********************************
% 0.71/0.31 * All subproblems solved! *
% 0.71/0.31 ********************************
% 0.71/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,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:151,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.71/0.31
% 0.71/0.31 %**** Beginning of derivation protocol ****
% 0.71/0.31 % SZS output start CNFRefutation
% See solution above
% 0.71/0.31
% 0.71/0.31 %**** End of derivation protocol ****
% 0.71/0.31 %**** no. of clauses in derivation: 94 ****
% 0.71/0.31 %**** clause counter: 151 ****
% 0.71/0.31
% 0.71/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,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:151,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------