%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU591^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n020.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 10:45:23 AM UTC 2026
% Result : Theorem 0.63s 0.28s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 27 unt; 0 typ; 2 def)
% Number of atoms : 289 ( 76 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 677 ( 20 ~; 31 |; 2 &; 613 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 192 ( 121 ^; 71 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $o ) > $i ).
thf(binintersect,definition,
( binintersect
= ( ^ [A: $i,B: $i] :
( dsetconstr @ A
@ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersect) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(1,conjecture,
( dsetconstrEL
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(2,negated_conjecture,
( ( dsetconstrEL
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ SY0
@ ^ [SY5: $i] : ( in @ SY5 @ SY1 ) ) )
=> ( in @ SY2 @ SY0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersect,dsetconstrEL]) ).
thf(4,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ SY0
@ ^ [SY5: $i] : ( in @ SY5 @ SY1 ) ) )
=> ( in @ SY2 @ SY0 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ SY0
@ ^ [SY5: $i] : ( in @ SY5 @ SY1 ) ) )
=> ( in @ SY2 @ SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SY18: $i] : ( in @ SY18 @ sK2_SY14 ) ) )
& ~ ( in @ sK3_SY17 @ sK1_SY0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SY18: $i] : ( in @ SY18 @ sK2_SY14 ) ) )
& ~ ( in @ sK3_SY17 @ sK1_SY0 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
| ~ ~ ( in @ sK3_SY17 @ sK1_SY0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,binintersect,dsetconstrEL]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY20: $i > $o,SY21: $i] :
( ~ ( in @ SY21
@ ( dsetconstr @ SV1
@ ^ [Xy: $i] : ( SY20 @ Xy ) ) )
| ( in @ SY21 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
| ~ ~ ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SY23
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) )
| ( in @ SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) )
| ( in @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) ) )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( in @ sK3_SY17 @ sK1_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) )
= $false )
| ( ( in @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) ) )
= $false ),
inference(res,[status(thm)],[21,18]) ).
thf(24,plain,
( ( sK1_SY0
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
= $false ),
inference(extuni,[status(esa)],[23]) ).
thf(26,plain,
! [SV4: $i > $o,SV5: $i,SV6: $i] :
( ( ( in @ SV6
@ ( dsetconstr @ SV5
@ ^ [SX0: $i] : ( SV4 @ SX0 ) ) )
= $false )
| ( ( in @ SV6 @ SV5 )
= $true ) ),
inference(rename,[status(thm)],[22]) ).
thf(30,plain,
! [SV4: $i > $o,SV5: $i,SV6: $i] :
( ( ( ( in @ SV6 @ SV5 )
= ( in @ sK3_SY17 @ sK1_SY0 ) )
= $false )
| ( ( in @ SV6
@ ( dsetconstr @ SV5
@ ^ [SX0: $i] : ( SV4 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[26,21]) ).
thf(31,plain,
! [SV4: $i > $o,SV5: $i,SV6: $i] :
( ( ( ( in @ SV6
@ ( dsetconstr @ SV5
@ ^ [SX0: $i] : ( SV4 @ SX0 ) ) )
= ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) ) )
= $false )
| ( ( in @ SV6 @ SV5 )
= $true ) ),
inference(res,[status(thm)],[26,18]) ).
thf(32,plain,
! [SV21: $i > $i > $i,SV20: $i > $i > $i] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ SX0 ) )
= sK2_SY14 )
= $false )
| ( ( in
@ ( SV20
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ SX0 ) )
@ ( sK5_E
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) )
@ ( SV21
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ SX0 ) )
@ ( sK5_E
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( in
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( SV20
@ ( sK5_E
@ ^ [SX1: $i] : SX1
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV21
@ ( sK5_E
@ ^ [SX1: $i] : SX1
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 ) ) )
@ ( sK5_E
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( sK4_E @ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) @ SX0 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(33,plain,
! [SV21: $i > $i > $i,SV20: $i > $i > $i] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( in
@ ( SV20
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ sK2_SY14 ) )
@ ( sK5_E
@ ^ [SX0: $i] : sK2_SY14
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) )
@ ( SV21
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ sK2_SY14 ) )
@ ( sK5_E
@ ^ [SX0: $i] : sK2_SY14
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) ) )
= $true )
| ( ( in
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( SV20
@ ( sK5_E
@ ^ [SX1: $i] : sK2_SY14
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV21
@ ( sK5_E
@ ^ [SX1: $i] : sK2_SY14
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 ) ) )
@ sK2_SY14 )
= $true ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( sK4_E @ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) @ sK2_SY14 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(34,plain,
! [SV21: $i > $i > $i,SV20: $i > $i > $i] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ SX0 ) )
= sK2_SY14 )
= $false )
| ( ( in
@ ( SV20
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ SX0 ) )
@ ( sK5_E
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) )
@ ( SV21
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ SX0 ) )
@ ( sK5_E
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( in
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( SV20
@ ( sK5_E
@ ^ [SX1: $i] : SX1
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV21
@ ( sK5_E
@ ^ [SX1: $i] : SX1
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 ) ) )
@ ( sK5_E
@ ^ [SX0: $i] : SX0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( sK4_E @ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) @ SX0 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(35,plain,
! [SV21: $i > $i > $i,SV20: $i > $i > $i] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( in
@ ( SV20
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ sK2_SY14 ) )
@ ( sK5_E
@ ^ [SX0: $i] : sK2_SY14
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) )
@ ( SV21
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( sK4_E
@ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) )
@ sK2_SY14 ) )
@ ( sK5_E
@ ^ [SX0: $i] : sK2_SY14
@ ^ [SX0: $i,SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) ) )
= $false )
| ( ( in
@ ( sK4_E
@ ^ [SX0: $i] :
( in
@ ( SV20
@ ( sK5_E
@ ^ [SX1: $i] : sK2_SY14
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 )
@ ( SV21
@ ( sK5_E
@ ^ [SX1: $i] : sK2_SY14
@ ^ [SX1: $i,SX2: $i] : ( in @ ( SV20 @ SX1 @ SX2 ) @ ( SV21 @ SX1 @ SX2 ) ) )
@ SX0 ) ) )
@ sK2_SY14 )
= $false ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( sK4_E @ ^ [SX1: $i] : ( in @ ( SV20 @ SX0 @ SX1 ) @ ( SV21 @ SX0 @ SX1 ) ) ) @ sK2_SY14 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(36,plain,
! [SV13: $i > $i > $o] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( in @ ( sK4_E @ ( SV13 @ SX0 ) ) @ SX0 ) )
= sK2_SY14 )
= $false )
| ( ( ( sK4_E
@ ( SV13
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( sK4_E @ ( SV13 @ SX0 ) ) @ SX0 ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( in @ ( sK4_E @ ( SV13 @ SX0 ) ) @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( sK4_E @ ( SV13 @ SX0 ) ) @ SX0 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(37,plain,
! [SV13: $i > $i > $o] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( ( sK4_E
@ ( SV13
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( sK4_E @ ( SV13 @ SX0 ) ) @ sK2_SY14 ) ) ) )
= ( sK4_E
@ ^ [SX0: $i] : ( in @ ( sK4_E @ ( SV13 @ SX0 ) ) @ sK2_SY14 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( sK4_E @ ( SV13 @ SX0 ) ) @ sK2_SY14 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(38,plain,
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( ( sK4_E
@ ^ [SX0: $i] : ( in @ SX0 @ SX0 ) )
= sK2_SY14 )
= $false ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ SX0 @ SX0 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(39,plain,
( ( in @ sK3_SY17 @ sK1_SY0 )
= $true ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(40,plain,
! [SV10: $i > $i,SV9: $i > $i] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( in
@ ( SV9
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ) )
@ ( SV10
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ) ) )
= $true )
| ( ( in
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) )
@ sK2_SY14 )
= $true ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(41,plain,
! [SV10: $i > $i,SV9: $i > $i] :
( ( ( in @ sK3_SY17 @ sK1_SY0 )
= $true )
| ( ( in
@ ( SV9
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ) )
@ ( SV10
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) ) ) )
= $false )
| ( ( in
@ ( sK4_E
@ ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) )
@ sK2_SY14 )
= $false ) ),
inference(extuni,[status(esa)],[31:[bind(SV4,$thf( ^ [SX0: $i] : ( in @ ( SV9 @ SX0 ) @ ( SV10 @ SX0 ) ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(42,plain,
! [SV4: $i > $o,SV5: $i] :
( ( ( in @ sK3_SY17 @ SV5 )
= $true )
| ( ( ( dsetconstr @ SV5
@ ^ [SX0: $i] : ( SV4 @ SX0 ) )
= ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[31:[bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(43,plain,
! [SV4: $i > $o] :
( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( SV4 @ SX0 ) ) )
= $false ),
inference(extuni,[status(esa)],[30:[bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK3_SY17 ))]]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,43,42,41,40,39,38,37,36,35,34,33,32,26,24,21]) ).
thf(45,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU591^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.17 % Computer : n020.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:29:21 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.28
% 0.63/0.28 No.of.Axioms: 0
% 0.63/0.28
% 0.63/0.28 Length.of.Defs: 391
% 0.63/0.28
% 0.63/0.28 Contains.Choice.Funs: false
% 0.63/0.28 .
% 0.63/0.28
% 0.63/0.28 ********************************
% 0.63/0.28 * All subproblems solved! *
% 0.63/0.28 ********************************
% 0.63/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:5,foatp_calls:2,translation:fof_experiment)
% 0.63/0.28
% 0.63/0.28 %**** Beginning of derivation protocol ****
% 0.63/0.28 % SZS output start CNFRefutation
% See solution above
% 0.63/0.28
% 0.63/0.28 %**** End of derivation protocol ****
% 0.63/0.28 %**** no. of clauses in derivation: 41 ****
% 0.63/0.28 %**** clause counter: 44 ****
% 0.63/0.28
% 0.63/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:5,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------